Diss. ETH No. 20155
Poly (Lactic Acid)
Polycondensation, Degradation
and Nanoparticles synthesis
A dissertation submitted to
ETH ZURICH
for the degree of
Doctor of Sciences
presented by
Fabio Codari
Master of Science in Chemical Engineering
Politecnico di Milano
born on July 27, 1983
citizen of Italy
accepted on the recommendation of
Prof. Dr. M. Morbidelli (ETH Zürich), examiner
Prof. Dr. W. J. Stark (ETH Zürich), co-examiner
Zürich 2011
Acknowledgment
There are really many persons which I want to remember in my acknowledgment, the
ones who gave me the opportunity to do my PhD, the ones who helped and supported
me during this time and those who made the last years for sure a unique time of my life.
I thank Prof. Morbidelli, for the opportunity to carry out my PhD in his group and for
his advices and help on the choice of the next step in my career. Thanks to Dr. Storti for
his guidance, encouragement and support from the beginning to the end of my PhD.
Thanks to Miro, Marco and Davide not only for their supervision but also for all the
times I got from them suggestions and comforts.
Thanks to all present and former members of the Morbidelli’s group not only for the
support at work but especially for the nice time I had in the last years. Only when
working in such an multicultural group one can face with so many cultures and points
of views. Being open minded is the only way to go further the first impression you have
and understand and respect the others. I really found good friends ready to celebrate
any good news and very close during the hard times. Thanks guys I will miss you.
Distance is often the first reason why good friends get lost… I will be in Winterthur so
let’s make it weak! A special thank goes to Paolo, Ivano (the …ons), Stefano (always
present in the last unsleepy nights!!!), Matteo (Brac), Alessio, Jogesh (taclù amini
dada), Rosario, Davide, Yingcui (the p…er), Ben, Marija, Ben, Tomek and Bertry
(FFF) for all the time we spent together and more….
Paolo, you and me have shared this experience since the beginning, not only the PhD
but also leaving our families, thanks for everything. Arrived at the turning point I wish
you all the best for your new life in Zurich.
I
Thanks to all the master students I had the pleasure to work with, to the friend from
Werkstatt, Schalter and Mensa (even if I did not manage to cancel the pizza away from
the menu).
Thanks to Uhde Inventa Fisher and in particular to Dr. Muelbauer, Dr. Schaller and Dr.
Hagen for their contribution in the industrial collaboration I worked on in these years.
(A special though is for Udo: thanks to you I have to proof that not only Italians are
crazy about football!)
Un ringraziamento particolare va a tutta la mia famiglia. In questi anni in cui sono stato
lontano la cosa che sicuramente mi è più mancata è la quotidianità del vivere insieme
ma forse questo è anche un punto di forza perché purtroppo quando le cose le si ha a
portata di mano si tende a darle per scontate mentre ora per me non è più così. Grazie
per il vostro supporto, un abbraccio!
Grazie ad Elena per essermi sempre stata vicina e per aver appoggiato tutte le mie
scelte.
Per ultimi, ma non perché meno importanti, voglio ricordare tutti gli amici che 4 anni fa
hanno festeggiato con me la mia partenza… vi ho sempre sentito vicino ed i pochi
momenti che siamo riusciti a condividere in questi anni quando rientravo per il
weekend sono sempre stati piacevoli. Grazie per questo e per essermi stati sempre e
comunque vicini soprattutto nei momenti di difficoltà.
Once more, thanks to all of you
II
“Another turning point a fork stuck in the road
Time grabs you by the wrist directs you where to go
So make the best of this test and don't ask why
It's not a question but a lesson learned in time
It's something unpredictable but in the end
It's right I hope you've had the time of your life
So take the photographs and still frames in your mind
Hang it on a shelf in good health and good time
Tattoos and memories and dead skin on trial
For what it's worth it was worth all the while”
G.D. Time of your life
III
IV
Abstract
Polycondensation of lactic acid has been studied through experiments and
modeling in an attempt to investigate chemical equilibrium, reaction kinetics and
transport phenomena. Of remarkable importance is the full characterization of the
system composition achieved by HPLC which allowed a detailed study of the system.
Experiments were run in a wide range of operating conditions, i.e. batch and semi-batch
mode, at different temperatures, pressures and reactor stirring rates. A comprehensive
model of the reacting system, accounting for a kinetic scheme involving all
polycondensation reactions as well as lactide forming reactions has been developed. All
model parameters have been evaluated from independent sources or by direct fitting of
the model prediction to the experimental data. A remarkably good agreement has been
obtained between the model predictions and experiments.
The reversible reaction of hydrolysis has been investigated focusing on the
effect of temperature, chain length and chirality on the reaction kinetics. A detailed
model based on the preferential chain end scission mechanism proposed in the literature
has been adopted and used to evaluate the kinetic parameters involved. Good
agreement between model predictions and experimental data has been obtained. This
model can be applied to predict the hydrolysis of polymer chains of any length.
In addition, this thesis presents a comprehensive study on nanoparticles
preparation through flash-nanoprecipitation. The experiments have been run in a multi
inlet vortex mixer and the effect of mixing performances, polymer concentration,
molecular weight and feeding strategy of the polymer solution have been investigated.
Through such a technique, narrow dispersed nanoparticles with size in the range 25 to
V
300 nm can be produced. The process is suitable for the production of multifunctional
nanoparticles by blending of different polymers. Furthermore, an alternative strategy
for the production of multifunctional nanoclusters, based on a new technology
involving aggregation of primary nanoparticles and controlled breakage of the
aggregates in the presence of stabilizing agents, has been investigated. As proof of the
concept the technology has been tested as a function of primary nanoparticles size,
surfactant concentration and applied shear forces. When nanoparticles with different
functionalities are used, the proposed methodology leads to the production of heteronanocluster compact in structure which can be used as multifunctional drug delivery
devices.
VI
Sommario
In questa tesi è stata studiata la reazione di policondensazione di acido lattico
sia a livello sperimentale che modellistico. In particolare, sono stati considerati i diversi
equilibri chimici coinvolti, la cinetica di reazione e i fenomeni di trasporto. Di
particolare importanza è la completa caratterizzazione della composizione del sistema
di reazione ottenuta attraverso HPLC. Gli esperimenti sono stati condotti in un vasto
campo di condizioni operative. In particolare, l’equilibrio chimico è stato studiato
attraverso prove batch a diverse temperature mentre la cinetica di reazione e i fenomeni
di trasporto sono stati analizzati in un reattore semibatch variando la velocità di
agitazione del sistema, la temperatura e la pressione di reazione.
Un modello matematico è stato sviluppato adottando uno schema cinetico che
comprende tutte le reazioni di policondensazione e le reazioni di formazione del lattide.
I parametri del modello sono stati valutati dalla letteratura, da prove indipendenti o
direttamente fittati dai dati sperimentali. Un buon accordo tra le predizioni del modello
e i dati sperimentali è stato ottenuto per tutte le condizioni operative studiate.
Nella seconda parte della tesi, la reazione di idrolisi di oligomeri di acido lattico
è stata studiata valutando l’effetto della temperatura, della composizione chirale e della
lunghezza di catena sulla cinetica di reazione. Un modello dettagliato, basato sul
meccanismo proposto in letteratura di rottura preferenziale degli esteri vicini ai gruppi
terminali di catena, è stato adottato per valutare i parametri cinetici. Si è trovato un
buon accordo tra i dati sperimentali e le predizioni del modello. Questo modello può
essere esteso alla valutazione della cinetica di idrolisi per tutte le lunghezze di catena.
VII
Nell’ultima parte di questa tesi, è stato condotto uno studio di precipitazione di
nanoparticelle di acido polilattico. Gli esperimenti sono stati condotti in un mixer
statico in cui una fase organica con disciolto il polimero, viene miscelata
tangenzialmente con un non solvente. In particolare sono stati valutati gli effetti del
miscelamento, della concentrazione e peso molecolare del polimero e della strategia di
alimentazione della fase polimerica sulla dimensione delle particelle prodotte. Sono
state ottenute nanoparticelle di dimensioni tra 25 e 300 nm. Si è inoltre trovato che,
premiscelando diversi tipi di polimeri in fase organica, si possono produrre nano
particelle con diverse funzionalità superficiali. In fine, questa tesi presenta una strategia
alternativa per la produzione di nano aggregati di particelle, al fine di produrre
aggregati compatti e con diverse funzionalità. In particolare, nanoparticelle primarie
sono inizialmente aggregate in aggregati di grandi dimensioni che in seguito, per effetto
di forze tangenziali generate attraverso un orefizio, vengono ridotti a nanoaggregati. Il
processo è stato analizzato variando la dimensione delle particelle primarie, la
concentrazione di stabilizzante utilizzato durante il processo di rottura degli aggregati e
l’entità delle forze tangenziali. Utilizzando nanoparticelle di diversa natura e con
diverse proprietà superficiali, la strategia proposta può essere adottata per la produzione
di aggregati multifunzionali per la somministrazione di farmaci.
VIII
Contents
Acknowledgements
I
Abstract
V
Sommario
VII
Contents
IX
1. Introduction
1
1.1 Lactic acid polycondensation
1
1.2. Poly(lactic acid) degradation
3
1.3 Nanoparticles and Nanoclusters production
4
1.4 Thesis outlook
5
2. Characterization of low molecular weight PLA by HPLC
9
2.1 Introduction
9
2.2 Experimental Part
12
2.2.1 Reaction set up
12
2.2.2 Reaction procedure
13
2.2.3 High Performance Liquid Chromatography (HPLC)
13
2.2.4 Non Aqueous Solution Titration (NAST)
14
2.2.5 Proton Nuclear Magnetic Resonance (H NMR)
14
2.2.6 Karl Fischer
15
2.3 Results and Discussion
15
2.3.1 Assessment of the analytical conditions
15
2.3.2 Calibration procedure
17
2.4 Application: characterization of LA polycondensation
23
2.5 Conclusions
29
IX
3. Chemical Equilibria in Bulk Melt Polycondensation of Lactic Acid
31
3.1 Introduction
31
3.2 Materials and Methods
35
3.2.1 Material
35
3.2.2 Chemical equilibrium experiments
36
3.2.3 HPLC analysis
36
3.2.4 Karl Fisher (KF) measurements
37
3.3 Results and discussions
37
3.3.1 Equilibrium Constant Evaluation
45
3.3.2 Implication on the behavior of a polycondensation reactor
50
3.4 Conclusions
52
4. Kinetics of Bulk Melt Polycondensation of Lactic Acid
53
4.1 Introduction
53
4.2 Experimental part
57
4.2.1 Material
57
4.2.2 Reactor setup
57
4.2.3 Polycondensation reactions
59
4.2.4 HPLC reversed phase
61
4.2.5 Chiral HPLC
61
4.2.6 Karl-Fischer Titration
62
4.2.7 Gas Chromatography
62
4.2.8 Rheological measurements
62
4.3 Model Development
63
4.3.1 Model assumptions
63
4.3.2 Model constitutive equations
65
4.4 Parameter Evaluation
70
4.5 Comparison between experimental data and model predictions
77
4.6 The impact of mass transport limitations on reaction kinetic
83
4.7 Conclusions
86
5. Kinetics of the Hydrolitic degradation of Poly(Lactic Acid)
89
5.1 Introduction
89
5.2 Experimental part
91
5.2.1 Materials
91
5.2.2 PLA oligomer synthesis, separation and degradation
92
5.2.3 Reverse Phase HPLC analysis
93
X
5.2.4 Chiral HPLC analysis
5.3 Results and Discussion
94
94
5.3.1 The Random Chain Scission mechanism (RCS)
96
5.3.2 The Preferential Chain End Scission mechanism (PCES)
100
5.3.3 Effect of chiral composition
104
5.4 Conclusions
107
6. A comprehensive study on PLA nanoparticles production by flash -
109
nanoprecipitation
6.1 Introduction
109
6.2 Materials and methods
112
6.2.1 Materials
112
6.2.2 Polymer synthesis and characterization
112
6.2.3 NPs flash nanoprecipitation
114
6.2.4 Nonoparticles suspension characterization
116
6.3 Results and discussions
117
6.3.1 The role of mixing
117
6.3.2 The effect of polymer concentration in the organic phase
124
6.3.3 The effect of polymer molecular weight
130
6.3.4 Alternative feeding strategies
132
6.4 Conclusion
137
7. Magnetic Hetero-Nanoclusters Preparation through Aggregation and
139
Controlled Breakage
7.1 Introduction
139
7.2 Materials and Methods
141
7.2.1 Primary nanoparticles synthesis
141
7.2.2 Nanoclusters preparation
143
7.2.3 NPs and NCs characterization
145
7.3 Results and discussions
148
7.4 Conclusion
163
8. Conclusions and Outlook
165
8.1 Lactic acid polycondensation
165
8.2 Poly(lactic acid) degradation
167
8.3 Nanoparticles and Nanoclusters production
167
XI
Appendix A
169
Appendix B
173
Bibliography
183
Curriculum Vitae
195
Pubblications
196
Conferences
196
XII
Chapter 1. Introduction
1.1
Lactic acid polycondensation
Poly-lactic acid (PLA) is a biodegradable aliphatic polyester industrially obtained
from renewable resources, such as corn or sugar beets. The monomer, lactic acid (LA),
is mainly produced by a bacterial fermentation batch process[1] and, having a chiral
carbon, exhibits two isomeric forms, L and D.
In the last decades, increasing efforts have been registered both from academia and
industry towards understanding and deepening the large-scale production processes of
poly(lactic acid) (PLA). Accordingly, a large fraction of the degradable polymer market
from renewable resources is nowadays covered by this type of material.[1] Major
attention has been devoted to reaction strategies aimed to improve the mechanical,
optical and rheological properties of the polymer, which are crucial for commodities
applications such as film packaging, cups, bottles, and fibers.[2-4] Moreover, due to its
biodegradability and biocompatibility, PLA has been approved by the regulatory
agencies of many countries for medical applications such as suture threads, implantable
scaffolds, bone fixation devices, and micro- and nano-capsules.[5] In all cases, polymer
molecular weight, polymer purity in terms of side products and residual monomers,
chain microstructure (chiral and chemical composition) are aspects to be carefully
considered and can be tuned by thoroughly designing the polymerization process
conditions.[6]
Two main routes have been largely studied in the literature for PLA production: the
bulk Melt Polycondensation (MP) of lactic acid (LA), and the Ring-Opening
1
Polymerization (ROP) of lactide, the cyclic dimer of LA. The most popular industrial
production strategy is actually a combination of the two routes into a multistep process.
LA is first polymerized to a low molecular weight polymer (so called prepolymer) by
polycondensation (< 10,000 Da) and then depolymerized and converted to the cyclic
dimer in a catalytic step usually carried out at high temperature and low pressure.
Finally lactide undergoes ROP after suitable purification, leading to high molecular
weight polymer (> 100,000 Da).[2, 7]
Being polycondensation the first step of the entire process, the reaction path has
to be carefully designed in order to optimize the extent of polymerization and minimize
the side reactions which affect the purity of the final cyclic dimer produced from the
pre-polymer itself. In general, in lactic acid polycondensation polymer chains bearing
two functional groups (alcoholic and carboxylic) undergo self-esterification leading to
longer chains while producing water. Such water has to be removed from the reacting
mixture in order to shift the chemical equilibrium towards the polymer product:
because of the unfavorable chemical equilibrium[8] and the operative transport
limitations (the system becomes increasingly viscous at increasing extent of reaction),
polycondensation is not suitable to produce high molecular weight PLA. The reaction
scheme is complicated by the occurrence of multiple side reactions like discoloration,
cyclization, transesterification and racemization.[9-11]. Among them, the most
interesting is indeed the formation of lactide through ring closure reactions, i.e. backbiting and end-biting reactions. In particular, back-biting reaction refers to the
formation of cyclic compounds through intramolecular reactions between the
hydroxylic end group of the polymer chain and an ester bond in the chain backbone.
2
1.2
Poly(lactic acid) degradation
Poly-lactic acid has significant interest as hydrolytically degradable, non-toxic
material for carriers and devices used for drug delivery medical applications.
Degradation studies have been performed in different systems of interest, such as nano
and microparticles,[12] as well as tablets and suture threads.[13, 14] When dealing with
degradation of polymeric devices, the overall degradation process is the result of the
interplay between degradation kinetics and diffusive phenomena of water and of the
short degradation products through the device. The degradation rate controls the device
erosion mechanism depending on the relevance of these phenomena. In particular, two
erosion paths are described in the literature: i) bulk erosion, which occurs when water
diffusion is faster than polymer degradation thus leading to a homogeneous degradation
of the device; ii) surface erosion, when the device is eroded starting from the external
surface and moving towards the interior, as a consequence of the faster polymer
degradation with respect to water diffusion.[15, 16] A particular case of bulk
degradation occurs for large size devices when the degradation products (oligomers) do
not diffuse fast enough so that they accumulate in the interior of the object thus creating
a pH gradient from the center to the surface which implies a profile of degradation
rates.[17, 18] For small size devices, such as nano and microparticles, the characteristic
dimension of the device is larger than the outer diffusion layer and, since the diffusion
of degradation products is not limited, degradation proceeds through the bulk erosion
path.[19], [20, 21] The knowledge of the degradation kinetics of PLA is a key
parameter when designing such drug releasing devices as it is a tunable parameter to
modulate the drug release profiles.[22]
3
Since the hydrolysis kinetics is influenced by a large variety of factors, a deep
understanding of the degradation path is required in order to develop a material suitable
for the delivery of pharmaceuticals. pH has a strong impact on the polymer degradation
since it acts both on the reaction mechanism as well as on its kinetics. Two different
mechanisms were reported depending upon the nature of the medium.[23] While in
acidic media the hydrolysis reaction of the ester bonds catalyzed by protons is
dominating, at higher pH values a preferential backbiting mechanism leading to the
formation of lactide is observed.[23, 24]
1.3
Nanoparticles and Nanoclusters production
In the last decades, degradable polymeric nanoparticles (NPs) have found large
attention in the literature with respect to their production, functionalization, stability
and degradation path.[15, 25-28] In particular, due to their high versatility,
biocompatibility and bioavailability, they have been widely considered in
pharmaceutical applications as drug delivery system for the administration of
hydrophilic as well as hydrophobic active compounds and as targeting and imaging
agent nanocarriers.[29-33] A major challenge in nanotechnology is to incorporate
different functionalities into small size devices to improve their properties and obtain
multifunctional particles characterized by high versatility and applicability. The
improvement of material properties and performance is an interdisciplinary topic
involving the synthesis of functional compounds and the engineering of their structure.
Due to their physical properties, chemical versatility and surface functionality, NPs
provide a unique solution for a wide range of applications. Different kinds of materials
have been used, including inorganic (e.g. silica, iron oxide and gold), and organic. In
4
general, polymers used for this application are biodegradable polyesters, such as
polylactic acid, polyglycolic acid (PGA), polycaprolactone (PCL) and their
copolymers, as well as other polyesters based materials such as polyethylene glycol
(PEG) block copolymers and therapeutics conjugates. [34-39]
An alternative strategy for the preparation of multifunctional devices is the
production of nanoclusters (NCs) composed of primary particles with different surface
functionalizations.[40] The use of NCs found large attention in the production of
sensors and microelectronics as well as in cellular imaging and therapy due to particles
segregation and enhancement of functionality, such as the enhanced absorbance used in
biomedical imaging and therapy.[41, 42]
1.4 Thesis outlook
In the first part of this Thesis (Chapter 2 to Chapter 5), a detailed analysis of LA
polycondensation reaction is presented. In Chapter 2, liquid chromatography (HPLC) is
applied to separate all the different components in the reacting mixture based on their
chain length. In particular, the oligomers separation is achieved by reverse phase
chromatography working in gradient from adsorption to elution conditions. The
reported characterization is an effective tool to investigate both the production of PLA
by polycondensation and the polymer degradation. A novel calibration procedure,
which allows the full characterization of PLA samples of low molecular weight by
determining the concentration of each individual oligomer, is developed. The proposed
analytical technique is applied to monitor the development of a polycondensation
reaction performed at 150°C and 133.3 mbar for 12 hours.
5
Taking advantage of this detailed characterization, the chemical equilibria of the
bulk melt polycondensation of lactic acid (LA) are investigated in Chapter 3. Batch
equilibrium experiments have been carried out in a broad temperature range (110-165
°C) and for low molecular weight pre-polymers at different initial compositions giving
new insights in the thermodynamic behavior of the system. A comprehensive kinetic
scheme accounting for lactide formation and chain length dependent rate constants for
the polycondensation reactions is proposed and validated by comparison with
experimental data.
As a natural evolution of the equilibrium study, reaction kinetics and transport
phenomena are analyzed in Chapter 4. Lactic acid polycondensation reactions have
been performed in a large range of different operating parameters, i.e. pressure,
temperature and stirring rate conditions. A comprehensive model accounting for
reaction kinetics, equilibrium and mass transport has been developed based on a
detailed kinetic scheme involving chain length dependent reactivity of the
polycondensation reactions and lactide formation by end- and back-biting reactions.
The mass transport coefficient has been expressed as a function of product properties (
polymer molecular weight) and operating conditions (temperature and stirring rate).
Model parameter values have been estimated from independent literature sources or by
direct fitting of the model predictions to the experimental results. The model developed
is proved to be a reliable design tool for wide range of operating conditions.
In Chapter 5, a kinetic study of the reversed reaction, polymer hydrolysis, is
presented for low molecular weight species as a function of oligomer chain lengths and
chirality at acidic pH and temperatures in the range from 40 to 120 °C. This specific
range was explored in order to cover conditions of interest for both medical and
industrial applications. In agreement with the preferential chain end scission
6
mechanism suggested in the literature, the ester groups were classified as α and β
according to their position inside the chain. Based on this kinetic scheme, the
experimental data were interpreted through a suitable kinetic model and the kinetic
parameters of the different ester hydrolysis were estimated.
In the last part of the Thesis (Chapters 6 and 7), the preparation of nanoparticles
and nanoclusters is discussed. In Chapter 6, Poly DL-lactic acid nanoparticles are
produced by flash-nanoprecipitation. PLA samples synthesized in bulk by ring opening
polymerization of DL-lactide were dissolved in a suitable solvent. Then, nanoparticles
precipitation is carried out by mixing the polymer solution with a non-solvent in a
multi-inlet vortex mixer. The process performances are investigated as a function of
mixer geometry, solvent and non-solvent ratio, polymer concentration and molecular
weight and polymer solution feeding strategy.
As an alternative route, the production of homo- and hetero-Nano-Clusters (NCs)
composed of different primary nanoparticles using a combination of irreversible
aggregation and controlled breakup is discussed in Chapter 7. Primary nanoparticles of
different types are first aggregated under shear in diffusion limited (DLCA) regime by
salt addition, leading to large size clusters with compact structure. Cluster size
reduction is then achieved by controlled breakage in contracting nozzle in the presence
of surfactant. A systematic study on the role of selected key parameters, i.e. primary
nanoparticles size, surfactant concentration and shear rate, was carried out to optimize
the cluster morphology.
Finally, the major achievements of the present work are summarized in Chapter 8
and a short outlook is provided.
7
8
Chapter 2. Characterization of low molecular weight
PLA by HPLC
2.1 Introduction
Poly-lactic acid (PLA) is a biodegradable aliphatic polyester produced industrially
both on large and small scale. It is used for a wide variety of applications, ranging from
biomedical applications to raw material for food packaging, bottles and consumables in
general. Due to its excellent mechanical properties, permeability, transparency and
environmental compatibility, PLA is in fact one of the most interesting polymeric
candidates to replace on the market non-biodegradable petroleum based synthetic
polymers.[1] Recently, polymers based on lactic acid received special attention in the
field of medical applications because these polyesters degrade in the human body by
hydrolysis of the ester backbone to non-harmful and non-toxic compounds. In
particular, PLA-based suture materials are used since many years because of their
excellent safety and biocompatibility.[14, 43-45] These compounds are also used in the
production of implantable medical devices, in dental applications and, more recently, as
scaffolds for autografted new skin, wound covers, anastomose systems and stents.[46,
47] All of these devices can be loaded with a large number of different compounds
such as drugs, pharmacological active principles, release modifiers and molecules
suitable for Magnetic Resonance Imaging (MRI). Being the release of such compounds
operative before or during degradation, a comprehensive study of the whole process has
to take into account the formation of PLA oligomers.
9
Low Molecular Weight (LMW; order of 10 kDa) polymers are typically produced
by direct polycondensation. [48, 49] Even though it is the raw material of the industrial
production of high molecular weight PLA by ring opening polymerization, LMW PLA
finds application as it is, for example in the biomedical field.
Among the various characterization techniques for molecular weight of polymers,
gel permeation chromatography (GPC) is probably the most popular since the complete
molecular weight distribution is provided. However, calibration is required: expensive
PLA standards are available on the market or the “universal calibration” can be applied.
In the latter case, the selection of reliable values of the Mark-Houwink constants is an
issue, due to the largely different values reported in the literature.[1] However, GPC is
mainly applied to HMW polymers, since super positions with peaks originated by
LMW impurities complicate the interpretation of the elution profiles. Therefore, GPC is
not further discussed in the present work. As an alternative, NMR spectroscopy and
aqueous titration of the carboxylic acid end groups are good choices to characterize
LMW PLA even if they provide the number average molecular weight only. 1H NMR
is used to detect characteristic groups inside the macromolecules. In the case of PLA,
the relevant peaks in 1H NMR spectra are characteristic of the chemical shifts of
hydrogen atoms present in methyl groups (δ=1.55), methine groups (δ=5.15) and
methine groups next to the terminal hydroxyl group (δ=4.4), so called α-methine [50,
51]. However, owing to spectra sensitivity, it is rare that molecular weights larger than
10 kDa can be accurately determined by this technique. Aqueous titration of the
carboxylic acid end groups can be also applied to determine the number average
molecular weight (Mn) of PLA samples. Usually the titration is performed by sodium
hydroxide in water solution using phenolphthalein as indicator. Limitations of this
approach are both the possible hydrolysis of ester bonds and the low solubility of PLA
10
in water. In order to overcome these difficulties, Non Aqueous Solution Titration
(NAST) is sometimes carried out, as reported by Kassab et al..[52] This approach
completely removes the solubility problem and, moreover, minimizes the possibility of
hydrolysis. However, a significant disadvantage of this technique is the detection limit:
for Mn higher than 5 kDa, the concentration of carboxylic acid end groups becomes too
small and the results are usually inaccurate.
High Performance Liquid Chromatography (HPLC) represents an alternative
analytical technique for investigating the entire chain length distribution of LMW PLA.
The first significant contribution focused on the characterization of aqueous solutions
of organic acids by liquid chromatography was published by Marvel and Rands[53],
who investigated the separation of water soluble organic acids by changing the polarity
of the mobile phase. This provided the basis for the development of a new separation
method which was more accurate, easy and efficient than those used so far such as
fractional distillation, fractional crystallization and fractional extraction. The
application of this procedure to LA aqueous systems was first proposed by
Montgomery in 1952.[54] He was able to separate monomer, linear dimer and trimer,
while higher oligomers were considered as a single component.
More recently a major contribution was reported by Vu et al.[55] who used HPLC to
separate oligomer species in concentrated lactic acid solutions. The nature of the peaks
in the chromatogram was determined by GC/MS. In this work not only very short PLA
chains were separated, but an effective approach to HPLC calibration was developed.
Such a calibration procedure is complicated by the fact that polymer standards at
different chain lengths are usually not available and have to be synthesized ad-hoc. In
the above mentioned work, LA oligomers of different chain lengths were prepared by
diluting analytical grade aqueous solutions of LA at different ratios and characterized
11
by titration. Accordingly, in order to calibrate the linear dimer, a solution of monomer
and dimer was first analyzed by HPLC. Then, given the calibration factor of the
monomer and the total free acidity of the system, the peak area of the linear dimer in
the chromatogram was correlated to the corresponding concentration estimated from
the total number of carboxylic end groups not due to the monomer. The limitation of
this approach is that any inaccuracy in the monomer calibration affects the calibration
of the dimer. This effect can be particularly severe because the peak of the dimer must
be kept much smaller than that of the monomer to prevent the formation of higher
oligomers. Such limitations are expected to reduce the reliability of the final result. In
this particular case[55], the ratio between the calibration factors of dimer and monomer
was estimated as 1.43, and the same value was used for all higher oligomers.
The aim of the present work is to reexamine the application of HPLC, and in
particular reverse phase chromatography (RP-HPLC), to characterize the PLA chain
length distribution. A new and reliable calibration strategy which does not involve
other analytical techniques is developed. The newly developed HPLC-based technique
is validated by comparison to titration in non aqueous solvent and 1H NMR. Finally, in
order to assess the proposed technique, the evolution in time of the mole fractions of
different PLA oligomers during the polycondensation reaction is measured.
2.2 Experimental Part
2.2.1
Reaction set up
A 250 ml glass reactor (Büchi, Switzerland) equipped with pressure sensor, head
and bottom temperature indicator, sampling port and metal heating jacket was used.
The temperature was controlled by an external oil bath (Polystat CC3, Huber,
12
Germany). The reactor was connected to a pump capable of 6 mbar as maximum
vacuum through a digital vacuum controller (DVR-300-MR; K-JEM Scientific Inc.,
USA) regulating the pressure with accuracy ± 0.5 mbar over a range of 0-1013 mbar.
Between the reactor and the pressure controller the vacuum line was intercepted by a
one-neck glass flask cooled at – 40 °C by a mixture dry ice/isopropanol in order to
condense water and oligomers leaving the reactor in the vapour phase. The nitrogen
line was connected to the reactor through a valve in order to quickly switch from
vacuum to atmospheric pressure so for sampling of both the reaction mixture and the
condensed vapours. Since the nitrogen purge could contain water, the nitrogen line was
filled with desiccant silica gel to fully dehydrate the gas flow.
2.2.2
Reaction procedure
L-Lactic acid reagent grade (90% w/w of purity; Acros Organics, Belgium) was
used without any further treatment with an initial load of 130 g. The polycondensation
reactions were carried out in two steps, dehydration (or pre-treatment) and
polycondensation. The pre-treatment was used to remove most of the initial water and
to favour pre-polymer formation. For all reactions, this step was carried out for 2 hours
at 90 °C. At the same time, the pressure was reduced in steps of 33 mbar every 30
minutes from 266.6 mbar to 133.3 mbar. After the pre-treatment, the temperature was
increased up to 150 °C while the pressure was maintained at 133.3 mbar until the end
of the reaction.
2.2.3
High Performance Liquid Chromatography (HPLC)
The oligomer analyses were carried out by reverse phase chromatography on a
Agilent Eclipse XDB C18 column (3.9 mm × 150 mm particle size 3.5 μm) using an
13
Agilent 1200 series apparatus (Agilent, USA) equipped with UV detector set at 210
nm. The mobile phase was a water-acetonitrile (Acros Organics) mixture in gradient
concentration, acidified with phosphoric acid 0.1% v/v (Merk). This acid pH was
chosen in order to preserve the efficiency of the column. The column oven temperature
was maintained at 40 °C and the mobile phase flowrate 1 ml·min-1. The following
gradient profile was selected: starting with a mobile phase of 98% v/v water, after 2
min the acetonitrile concentration was ramped linearly to 100% v/v in 25 min,
maintained constant at 100% v/v for 30 min and finally returned back to 98% v/v water.
2.2.4
Non Aqueous Solution Titration (NAST)
The titrations were carried out using a sodium ethoxide (Acros Organics) solution
with bromothymol blue as indicator (Acros Organics). The polymer was dissolved
initially in 20 ml of a CH2Cl2/CH3CH2OH (1/1 v/v) mixture (both purchased by Acros
Organics). The base solution was prepared dissolving the salt, CH3CH2ONa, in ethanol.
Then, it was standardized by means of a primary standard solution of monobasic
potassium phthalate (Fluka) . Solvent acidity was considered in the data treatment.
2.2.5
Proton Nuclear Magnetic Resonance (1H NMR)
NMR spectra were recorded by a 500 Ultrashield NMR spectrometer (Bruker,
Switzerland) at room temperature with CDCl3 as solvent. Mn was evaluated from the
spectrum by the relation:
M n  90  72
methine proton signal
 -methine proton signal
(2.1)
where 90 and 72 represent the molecular weights of monomer and repeating unit
respectively, and -methine the methine groups next to the terminal hydroxyl group.
14
2.2.6 Karl Fischer
Water content in the polymer was analyzed by 831 KF Coulometer (Metrohm,
Switzerland). PLA samples were dissolved in extra dry acetonitrile (water content < 10
ppm; Acros Organics) and analyzed in the liquid phase. The initial water content of
acetonitrile was accounted for when treating the data.
2.3 Results and Discussion
2.3.1 Assessment of the analytical conditions
PLA samples were produced by polycondensation following the procedure reported
in Section 2.2 and analyzed by HPLC. In Figure 2.1, a typical chromatogram obtained
for a LMW PLA produced at 150 °C in 1.75 hours is reported. Since species at
different hydrophobicity can be separated under gradient conditions from hydrophilic to
hydrophobic, it can be safely assumed that each peak in the chromatogram corresponds
to a polymer chain of specific length. It is worth to mention that multiple peaks which
sometimes appear in the chromatogram as shoulders of the main peaks (for example the
peak eluted at 7 minutes in Figure 2.1)
Figure 2.1. Chromatogram of LMW PLA produced at 150°C in 1.75 hours.
15
Figure 2.2. Chromatogram of LMW PLA produced at 150°C in 12 hours.
Figure 2.3. Chromatogram of LMW PLA produced at 150°C in 12 hours (gradient from 2 to
100% v/v of acetonitrile in 120 min; two columns in series).
are most probably due to different chiral structures of polymer chains with the same
length and thus in the calibration procedure such peaks are lumped together. The
elution time of different oligomers increases with their hydrophobicity and thus with
their chain length. It is worth noticing that the cyclic compounds can be assumed to be
absent under these conditions with the exception of lactide, the cyclic dimer of lactic
acid.[56] Thus, the first three peaks (elution times from about 2 to 10 min) correspond
to monomer, dimer and lactide, respectively. All the following peaks correspond to
longer linear oligomers, starting from the trimer.
16
To obtain quantitative information on the molar concentration of each oligomer in
the polymer sample, a suitable calibration is needed for each species. The area Ai of
each peak can be related to the number of moles of a single component, ni, through a
calibration factor, ki, that is:
ni  ki Ai
(2.2)
As an example, the chromatogram of a PLA sample with average molecular weight
larger than that in Figure 2.1 (reaction temperature 150 °C, reaction time of 12 hours) is
shown in Figure 2.2. In this case, the peak resolution in the high molecular weight
region is not satisfactory. Such fractionation can be improved using longer columns
along with “slower” gradients, as shown in Figure 2.3, where two columns in series and
a gradient from 2 to 100% v/v of acetonitrile in 150 min have been adopted. By further
comparing the two previous figures it can be concluded that the areas are fully
independent upon the operating gradient. This shows the independence between the
gradient profile and the calibration curve, which therefore implies that the elution
conditions can be tuned to achieve the best resolution without affecting the calibration
factors.
2.3.2 Calibration procedure
The calibration procedure is based on two consecutive steps and is described below
(LAn indicates the linear chain oligomers made of n repeating units and LAc2 the
lactide, i.e the cyclic dimer).

First step: LA1, LA2 and LAc2 calibration
The cyclic dimer of lactic acid, LAc2, is used as a standard. Any error at this stage
propagates to all the rest of the calibration procedure and thus this initial step has to be
done carefully. The LAc2 response factor is obtained by analyzing solutions of lactide
17
in acetonitrile at different concentrations; the resulting value is kc2=1.03·10-10
mol·mAU-1·min-1. The calibration factors for the monomer, LA1, and the linear dimer,
LA2, were determined by monitoring the concentrations of the different species during
the hydrolysis reactions of lactide. Namely, after dissolving lactide in water, the
following reactions take place:
LAC 2  W  LA2
(2.3)
LA2  W  2LA1
(2.4)
At low temperature (T ≤ 70 oC), these reactions are slow enough to exhibit a significant
initial interval of time where only the first reaction occurs. This is evident from the
chromatograms measured at different times shown in Figure 2.4. Initially only the
peaks of lactide and linear dimer are present. After 30 minutes, the initial peak of
lactide is “consumed” to produce some linear dimer without the formation of the
monomer. On the other hand, the peak of monomer appears and becomes dominant at
longer reaction times (90 minutes).
Figure 2.4. Hydrolysis reactions of lactide: _____ initial condition, ---- after 30 min; -.-. after 90
min).
18
From these data, the calibration factors of linear dimer and monomer are estimated
as k2 = 9.54·10-11 mol·mAU-1·min-1 and k1 = 2.53·10-10 mol·mAU-1·min-1, respectively.

Second step: LAn (n>2) calibration
In order to get the calibration for chains longer than 2, a semi-preparative HPLC
analysis of a LMW PLA sample was carried out. The adopted conditions were the same
as the analytical ones described in the experimental section except for the loaded
amount of sample which was equal to 100 mg. The different fractions, each one
corresponding to a specific peak and therefore to a specific chain length, were collected
in closed vials. Each of them was then partially hydrolyzed at 70 °C and the
corresponding evolution was monitored by HPLC. For example, analyzing the trimer
(LA3) fraction, the LA3 peak only was initially detected in the chromatogram.
However, later on during the hydrolysis reaction, some LA2 and LA1 were formed, as
clearly indicated by the decreasing area of the LA3 peak and increasing areas of the
LA2 and LA1 peaks. Assuming the calibration factors k1 and k2 as obtained in the first
calibration step, the numbers of moles of both species were evaluated. Since those
moles were produced by hydrolysis of LA3, it was possible to estimate the moles of
LA3 consumed. By means of peak area change given and consumed number of moles,
the corresponding calibration factor, k3, was finally evaluated. The equation relating the
number of moles of the species to be calibrated consumed by hydrolysis, Δni, to the
number of moles of all formed species, nj (j ≤ i) is generally expressed as:
i 1
 jn
j 1
i
j
 ni
(2.5)
19
This same procedure was sequentially applied to longer chain species, up to nine
monomer units: the estimated calibration factors, average values of repeated
experiments, are summarized in Table 2.1.
According to the Beer-Lambert law, the measured absorbance is directly
proportional to the molar absorption coefficient, , which is an intrinsic property of
each molecule. In particular, when more than one absorbing group (so-called
chromophore) is present in a molecule, the overall absorbance is the sum of the
absorbancies of each individual chromophore. The absorbing groups in PLA are the
carboxylic and the ester groups and both of them absorb at wavelengths around 210
nm. Accordingly, should increase linearly with the chain length (each repeating unit
introduces one more ester group in the chain) and the peak area at constant number of
moles is decreasing at increasing chain length. On the other hand, according to
Equation 2.2, the peak area is also inversely proportional to the calibration factor:
therefore, an inverse proportionality between absorption coefficient and calibration
factor is expected, i.e.:
i 
1
ki
(2.6)
The reciprocal of the calibration factor is plotted vs. the chain length in Figure 2.5.
As a confirmation of the previous arguments, the behavior is quite linear and well
approximated by the equation ki  2.31 1010 i . The applicability of such equation has
been extended to all chain lengths, i.e. i>9.
20
Figure 2.5. Reciprocal of the calibration factor vs. chain length.
Table 2.1. HPLC calibration factors.
Species
LA1
LA2
LAC2
LA3
LA4
LA5
LA6
LA7
LA8
LA9
kn · 1011
mol·mAU-1·min-1
25.30
9.54
10.30
8.00
5.69
4.53
3.84
3.12
2.82
2.77
21
Validation of the calibration procedure
In order to validate the proposed calibration method, LMW PLA samples were
characterized using different analytical techniques. The values of the number average
molecular weights of selected PLA samples (produced at 150 °C and different reaction
times, following the recipe reported in Section 3) measured by NAST, HPLC and 1H
NMR are compared in Table 2.2.
The discrepancies between Mn values from HPLC and the average values from
1
HNMR and NAST are always below 10% ranging from 9 to 0.5 %. The average error
is below 5%, which is believed more than acceptable. It is worth noticing that two
different characteristic groups are detected by NAST and 1H NMR, carboxylic end
groups and tertiary hydrogens, respectively: this makes the two techniques fully
independent and supports the HPLC validation.
Table 2.2. Comparative evaluation of the different techniques applied to measure the
number average molecular weight.
sample
22
Mn (Da)
1
H NMR
288
NAST
290
402
392
408
C
468
475
503
D
595
580
620
E
657
711
710
F
817
700
852
A
HPLC
315
B
2.4. Application: characterization of LA polycondensation
In this section, the developed HPLC characterization technique is applied to monitor
the melt polycondensation of LA in a range of molecular weights of industrial
relevance. As anticipated, the reaction was carried out in the setup described in section
2.3, at 150 °C and 133.32 mbar for 12 hours. During the reaction, samples of both
liquid and gas phases were collected. Through HPLC analysis, the mole fraction
profiles of many different oligomers were monitored during the reaction as well as the
profiles of polymer average properties such as number average molecular weight (Mn),
weight average molecular weight (Mw) and polydispersity index (PDI).
As it is well known [56], polycondensation of lactic acid is a step-growth reaction. It
involves a carboxylic acid end-group and an alcoholic end-group of two generic chains,
which react together to produce a longer chain through the release of a water molecule.
Under the assumptions of equal reactivity of the functional groups and reactivity
independent upon chain length, the final distribution of chain length is well
approximated by a Gaussian distribution.
Species with chain length up to 45 units were detected by HPLC: the corresponding
molar fraction values are shown as a function of time in Figure 6 (a-f) for oligomers
made of up to 21 monomer units.
By visual inspection of the mole fraction profiles, it appears that shorter chains are
quickly consumed to form longer ones. The general trend for each oligomer is first
increasing and then decreasing, as expected for a set of consecutive reactions. The time
at which a given oligomer appears is longer, the higher its molecular weight.
23
a
b
c
d
e
f
Figure 2.6. Mole fraction as a function of time for different oligomers. (a) o LA1, * LA2; (b) o
LA3, * LA4 , x LA5; (c) o LA6, * LA7 , x LA8, + LA9; (d) o LA10, * LA11 , x LA12, + LA13; (e) o
LA14, * LA15 , x LA16, + LA17; (f) o LA18, * LA19 , x LA20, + LA21.
24
Using the detailed values in Figure 2.6, the complete molecular weight number
distributions and the corresponding average properties are readily evaluated at any
time, as shown in Figures 2.7 and 2.8.
It is worth noticing that the time evolutions of all polymer properties reported above
are in agreement with the stepwise reaction mechanism characteristic of PLA
polycondensation. The number average molecular weight increases to about 400 Da in
12 hours. The behaviour is not linear and this is due to water diffusion limitations:
since the pressure in the system is not low enough to ensure complete water removal,
the reaction rate slows down while approaching equilibrium conditions. The major
change in PDI is taking place during the first 6 hours, while an asymptotic value around
1.7 is finally reached.
Liquid chromatography has been also used to characterize the gas phase
composition. Condensed samples were collected at different reaction times and then
analyzed by HPLC. It is worth noticing that, differently from the case of the polymer
samples, the measured gas phase compositions are actually cumulative values between
two sampling times. However, being the sample intervals quite short with respect to the
reaction time, this effect is not expected to be significant.
The cumulative amount of condensate is reported in Figure 2.9a as a function of
time. As expected for step growth polymerization, the amount of volatile components
leaving the reaction mixture in vapour phase decreases during the reaction. Five
different major species have been detected: water, monomer, lactide, dimer and trimer.
The mole fractions of all these species are shown in Figure 2.9b as a function of time.
Water is the dominant component, followed by the monomer whose concentration
decreases in time. Dimer, lactide and trimer are present only as traces. Such profiles
25
reflect the interplay between the vapour-liquid equilibrium and the transport rate at the
considered operating conditions.
Figure 2.7. PLA number distribution of molecular weights at various reaction times (o 1.75 h, *
4.6 h, x 12 h).
a
b
Figure 2.8. Average molecular weights as a function of time: a) Mn (●) and Mw (○); b) PDI.
26
Consistency and data reproducibility
In Figure 2.10 it is shown a comparison between two polycondensation
reactions run in the same conditions as described in section 2.2. Good data
reproducibility is achieved which once more supports the HPLC characterization
technique developed here.
Further validation can be done comparing the amount of vaporized water
measured experimentally by condensing the gas phase, and that evaluated from the
water mass balance as reported in the following. At each reaction time the water
content in the polymer melt is given by:
W (t )  W0  Wr  Wvap
(2.7)
where W(t) indicates the water content of the reacting mixture at time t, W0 the initial
water content, Wr the water produced by the reaction and Wvap the water vaporized. W,
W0 and Wevap are experimental data and the water produced by the reaction is easily
estimated by:
Wr  1  0
(2.8)
where λ1 and λ0 indicate the zero and the first order moments of the molecular weight

distribution (  j   n j LAn ), experimentally determined as:
n 1
 j   j   j ,0
j=0,1
(2.9)
where the subscript 0 refers to the initial condition.
27
a
b
Figure 2.9. a) Total amount of condensate, b) volatile components mass fractions ( o water, □
monomer, x dimer, * lactide, + trimer).
a
b
Figure 2.10. Reproducibility of experimental data. (a) o LA1, □ LA2; (b) o LA3, □ LA4 , ◊ LA5.
(empty and full markers correspond to two different reactions run in the same experimental
condition).
28
The comparison between the amount of water collected into the condenser and that
estimated through the material balance is shown in Figure 2.11. A satisfactory
agreement is verified, thus supporting the whole characterization approach.
Figure 2.11. Comparison on vaporized water. o: from condensed data; ●: from HPLC data.
2.5. Conclusions
A comprehensive monitoring of the evolution of the mole fraction of PLA oligomers
as a function of time has been developed based on HPLC. An effective and reliable
calibration technique has been assessed and validated. The calibration factors for the
first ten oligomers have been determined and a linear relation between the reciprocal of
such factor and chain length has been found. The reliability of the proposed
characterization has been checked by comparison with average values of the chain
length distributions obtained for PLA samples by 1H NMR and NAST. Finally, the
detailed monitoring of a PLA polycondensation reaction has been performed at 150 °C
and 133.32 mbar for 12 hours. The reliability of such technique is clearly established,
in terms of compositions of liquid and gas phases and molecular weight properties.
29
30
Chapter 3. Chemical Equilibria in Bulk Melt
Polycondensation of Lactic Acid
3.1 Introduction
In the last decades, Poly(lactic acid) (PLA) based materials, such as homopolymers, copolymers, blends and stereocomplexes, have attracted large interest in the
literature due to their biodegradability, biocompatibility and mechanical properties
which make them suitable for a wide range of applications.[57] Two main routes can be
followed to produce PLA: bulk melt polycondensation of lactic acid[48], and ring
opening polymerization (ROP) of lactide,[58] the cyclic dimer of the acid. While the
monomer purity is crucial with respect to the end-use properties of the polymer in the
latter case, the quality of the polymer produced by polycondensation is much less
affected by impurities.[6] On the other hand, ROP typically leads to high molecular
weight PLA, while low molecular weight polymer (1-5 kDa) is produced by
polycondensation. Therefore, the industrial production strategy is actually a combined
process based on ROP of lactide obtained by catalytic degradation of a low molecular
weight pre-polymer produced by polycondensation.[57] Being polycondensation the
first step of the entire process, the reaction path has to be carefully designed in order to
optimize the extent of polymerization and minimize the side reactions which affect the
purity of the final cyclic dimer produced from the pre-polymer itself.
PLA polycondensation involves reversible reactions in which different
functional groups (carboxylic and hydroxyl) of different species (monomer and/or
31
polymer chains) react together producing a longer chain through the formation of an
ester bond (E) and releasing water (W) as side product. Due to the reversible nature of
the reaction, chemical equilibrium often represents the major restriction to high
conversion. In order to push the reaction as most as possible towards the products, thus
promoting the formation of longer and longer chains, water removal has to be
maximized. Due to the increase of polymer viscosity during the reaction, water removal
becomes an issue and conditions of strong diffusion limitations are easily established
when high molecular weights are targeted.[59]
The general reaction scheme in terms of functional groups is[8]:
p
k


COOH  OH 
 E W
kd
(3.1)
where k p and k d indicate the propagation and depropagation rate constants,
respectively. It is well known that cyclic species are formed during polycondensation
by chain-folding reactions. In particular, relevant amounts of lactide can be produced
by end- and back-biting. [57, 60, 61] Since these side reactions produce shorter chains,
thus degrading the resulting polymer, reflux condensers are used to recycle back to the
reactor the lactide in order to limit its production by establishing equilibrium
conditions.[62]
The equilibrium composition can be evaluated given the equilibrium constant in
terms of reactant and product activities, ai , as follows:
K eq (T ) 
k p (T )
  aivi (T , x)
d
k (T )
i
(3.2)
Expressing the activity as the component mole fraction, xi , times the corresponding
activity coefficient,  i , the equilibrium constant is conveniently rewritten as the
product of two coefficients, the first involving the mixture composition, usually
32
indicated as apparent equilibrium constant Kx, and the second accounting for the
mixture non-ideal behavior, Kγ:
K eq (T )    xi i  i  K x (T , x) K  (T , x)
v
(3.3)
i
In ideal systems, all activity coefficients have unitary value and the composition
equilibrium constant is equal to the true thermodynamic constant, thus being function
of temperature only. Therefore, by measuring the system composition at equilibrium,
non-constant values of the composition equilibrium constant at constant temperature
are a clear proof of non-ideal behaviour. This is the case for various polymers produced
by polycondensation, such as PET and Nylon.[63-66]
Focusing on PLA produced by polycondensation, the apparent equilibrium
constant is often defined in the literature in terms of functional groups, in agreement
with the reaction scheme in Equation 3.1:
Kx 
xCOO xw
xCOOH xOH
(3.4)
where xw , xCOO , xCOOH and xOH represent the mole fractions of water, ester, carboxylic
and hydroxyl groups, respectively.
Thurmond and Edgar[67] studied the chemical equilibrium established in different
mixtures of lactide, lactic acid and water at 100 and 155°C for different equilibration
times ranging from 9 hours to 2 weeks. Due to analytical difficulties, it was concluded
that the concentration of the condensation products was not measured with enough
accuracy: therefore, even though values of all apparent equilibrium constants were
provided, the only one reliable is that of the reaction forming lactide and water from
lactic acid. Values in the range 0.051-0.066 are given for water contents ranging from
76 to 11 % w/w; such values are reported as practically independent of temperature.
33
Eder and Kutter[68] presented similar results, once more indicating equilibrium
composition not substantially affected by temperature. The equilibrium conditions were
established in 100 hours at ambient temperature and in 12 hours at 100°C. Moreover,
the same equilibrium composition was measured after equilibrating mixtures with the
same initial amounts of lactoyl repeating units and water but different initial values of
the average degree of polymerization.
In 1936, Bezzi et al.[69] carried out a comprehensive kinetic and equilibrium analysis
of lactic acid polycondensation. The equilibration of mixtures with different initial
contents of water and lactic acid were studied at 145°C after 60-80 hours of reaction.
Total free acidity, total number of ester groups and average degree of polymerization at
equilibrium were measured by titration. Assuming different reactivity of the ester
groups inside the polymer backbone or close to chain ends, two different equilibrium
constants have been defined, consistently with the following kinetic scheme:
K1
x


COOH 1  OH 
 E  W
Kp
x


COOH n  OH 
 E  W
(3.5)
n>1
(3.6)
where COOH n indicates the carboxylic end group in a polymer chain with length n,
E and E the ester bonds adjacent and non-adjacent to the chain end groups,
respectively, and K 1x and K xp the apparent equilibrium constants defined in terms of
mole fractions. The values K 1x = 0.21 and K xp = 0.41 were reported as estimated from
experimental data.
More recently, Vu et al.[55] carried out an equilibrium study in concentrated lactic acid
solutions at two different temperatures, 80 and 100oC. A constant value of the apparent
34
equilibrium constant equal to 0.2 was estimated by least squares regression on the
measured equilibrium concentrations. No formation of lactide was observed.
All previous papers were dealing with reaction equilibria, but physical (vapour-liquid)
equilibrium has been also studied. Sanz et al.[70] reported a VLE study for the ternary
mixture water, lactic acid and linear dimer. Notably, some non-ideal behaviour of the
liquid mixture was identified and accounted for through activity coefficient values in
the ranges 0.72-1.1 and 0.11-0.2 for water and monomer, respectively.
The aim of the present work is to analyse experimentally chemical equilibria in
bulk melt polycondensation of lactic acid. The dependence of the apparent equilibrium
constant upon the system composition is investigated running equilibrium batch
experiments at different temperatures, from 110 up to 165 °C. Taking advantage of the
detailed characterization of composition based on liquid chromatography described in a
previous work,[71] several insights into the equilibrium behaviour of the system are
provided. In particular, reactivity dependences upon chain length and non-ideal
behaviour of the equilibrium reactions of lactide formation, probably the most
interesting step from the industrial viewpoint, are discussed.
3.2 Materials and Methods
3.2.1 Material
L-Lactic acid reagent grade with a 90% w/w of purity, acetonitrile extra dry
(water content < 10 ppm) and sulfuric acid 95-97% were supplied by Acros Organics.
Acetonitrile E Chromasolv for HPLC was purchased from Sigma-Aldrich. All the
reagents were used as received without further purification.
35
3.2.2 Chemical equilibrium experiments
PLA samples with different composition were prepared in a pre-polymerization
reaction step. 100 g of lactic acid were charged in a 200 ml round bottom flask
equipped with magnetic stirring and temperature sensor. The temperature was set to
150°C and the reaction was run for 15 hours. This relatively low temperature was
chosen in order to minimize side reactions such as cyclization[10] and thermal
decomposition.[72] Nitrogen flow was applied during the reaction to enhance water
removal. At different reaction times, polymer samples were withdrawn from the reactor
and sealed in glass vials. Each mixture inside the vials was then left for very long time
(up to 30 hours) at different, constant temperatures (110-165°C) in order to establish
equilibrium conditions in batch reactor. The actual achievement of reaction equilibrium
was verified by analyzing a specific sample at different times. Mass balance was
verified for each vial by weighting the samples before and after equilibration: the
internal mass was constant with an experimental error of 0.5%. In these experiments, it
was found important to minimize the gas to liquid volume ratio inside the vials in order
to minimize the amount of volatiles (mainly water) leaving the reaction locus by
vaporization. After equilibration, the samples were characterized by KF to measure the
water content and by HPLC to evaluate the complete oligomer composition
distribution.
3.2.3 HPLC analysis
The oligomer analysis was carried out by reverse phase chromatography on two
Agilent Eclipse XDB C18 columns (3.9mm×150 mm particle size 3.5 μm) using an
Agilent 1200 series apparatus (Agilent) equipped with UV detector set at wavelength
equal to 210 nm, autosampler and column oven (temperature set at 40 °C). The mobile
36
phase was a mixture of water and acetonitrile in gradient concentration, acidified with
phosphoric acid (0.1% v/v). The flow rate was 1 ml/min. Further information about this
characterization and the calibration procedure are reported in a previous work.[71] The
gradient profile in the eluent was selected in order to separate the different oligomers
based on their hydrophobicity. Starting with a mobile phase of 98% v/v water, after 2
min the acetonitrile concentration was ramped linearly to 100% v/v in 120 min,
maintained constant at 100% v/v for 20 min and finally returned back to 98% v/v water.
3.2.4 Karl Fisher (KF) measurements
Water content in the polymer was analyzed by 831 KF Coulometer (Metrohm,
Switzerland). PLA samples were dissolved in extra dry acetonitrile (water content < 10
ppm; Acros Organics, Belgium) and analyzed in the liquid phase. Initial acetonitrile
water content was accounted for when treating the data.
3.3
Results and discussions
As already mentioned, the equilibrium of lactic acid polycondensation in bulk
melt was investigated by measuring the equilibrium composition of samples produced
in a pre-polymerization step under nitrogen flow in semibatch mode and equilibrated in
batch conditions at constant temperature. As shown in Figure 3.1a, the complete
composition distribution of the different oligomers is accessible by HPLC11, as well as
the amounts of monomer (P1) and lactide (LT).
This detailed picture is completed by measuring the water amount by KF
titration. In order to determine the characteristic time required for sample equilibration,
a preliminary reaction on two different samples with different initial molecular weights
37
was carried out at 150 °C for 30 hours. As shown in Figure 3.1b, chemical equilibrium
is fully established within 20 hours for both samples. Accordingly, an equilibration
time equal to 25 hours was adopted in all subsequent experiments.
a
…...
b
Figure 3.1. a: HPLC chromatogram of a generic sample after equilibration at 150 °C. b: Mn (○)
and xw (◊) as a function of time for low (empty symbols) and high (full symbols) molecular
weight samples.
The equilibrium experiments were carried out at various temperatures (110-165
°C) and initial compositions. The obtained results are interpreted based on a detailed
kinetic scheme accounting for the reactions forming lactide as well as for the
38
dependence of reactivity (and therefore of the apparent equilibrium constants) upon the
chain lengths. The following kinetic scheme is considered:
kp
n ,m

Pn  Pm 
Pn  m  W
kd
(3.7)
n m
kp
bb ,n


Pn 
 Pn  2  LT
kd
(3.8)
bb ,n2
p
keb


P2 
 LT  W
kd
(3.9)
eb
where knp, m and kndm represent propagation and depropagation rate constants of the
polycondensation reaction between two chains of generic length n and m to form an
oligomer with chain length n+m and water. Equations 3.8 and 3.9 are instead those
responsible for lactide formation: kbbp ,n and kbbd ,n2 indicate propagation and
depropagation rate constants of the back biting reactions (bb) of the generic n-mer
oligomer, while kebp and kebd are propagation and depropagation rate constants of the
end-biting reactions (eb) of the linear dimer. The expressions of the corresponding
apparent equilibrium constants are defined in terms of mole fractions as follows:
K nx,m 
xn  m xW
xn xm
(3.10)
K bbx , n 
xn  2 xLT
xn
(3.11)
K ebx 
xW x LT
x2
(3.12)
A large number of reactions, N R , is involved:
N2 M
NR 
4
(3.13)
39
where N represents the maximum considered oligomer chain length and M is equal to 0
for even N values and equal to 1 for odd values. As it is well known, not all such
reactions are needed to characterize the chemical equilibrium of the system. The
number of thermodynamically independent reactions is in fact equal to the difference
between the number of all molecular species (N+2) and that of the corresponding
atomic species (two only, since the ratio between hydrogen and oxygen is constant for
all molecular species and equal to 2). Accordingly, the number of thermodynamically
independent reactions, NIR, is:
N IR   N  2   2  N
(3.14)
and any set of N reactions out of the general kinetic scheme presented above is enough
to evaluate the full equilibrium composition of the system. A convenient choice could
be all (N-1) polycondensation reactions involving the monomer and one single lactideforming reaction, for example by end-biting. Accordingly, the following simplified
reaction scheme is considered for investigating equilibrium condition:
kp
1, n


P1  Pn 
 Pn 1  W
kd
n 1
(3.15)
1, n
p
keb


P2 
 LT  W
kd
(3.16)
eb
Note that the system exhibits one single compositional degree of freedom at
equilibrium. In fact, (N+2) species are involved and (N+1) relationships among them (N
independent reactions identified above along with the stoichiometric constraint) apply:
if water is selected as reference species, any system property at equilibrium can be
represented as a function of the water content only.
Since the full composition has been measured for all experiments, the values of
the apparent equilibrium constants of the reactions involving the monomer, K1,xn , can
40
be calculated from Equation 3.10. These values are shown in Figure 3.2 for samples at
different equilibrium composition and temperature.
It is seen that the K1,xn values for n = 1 are always larger than those of the
reactions involving longer oligomers; in addition, the latter reactions exhibit the same
value of equilibrium constant, practically independent of the oligomer chain length. In
mathematical terms, the following constraints are then fulfilled:
x
x
K1,1x  K1,2
 K1,3
 K1,xn
n 1
(3.17)
Such behavior can be explained based on the different nature of the ester bonds. As
already mentioned, the reactivity of the ester groups adjacent to the polar chain end
groups is expectedly different from that of the ester groups inside the chain backbone.
Therefore, all reactions in Eq. 15 involve the same type of ester groups with the
exception of the one involving the linear dimer, the only species whose reactivity is
influenced by both polymer chain end groups at the same time. Note that the different
reactivity of the terminal esters was also reported in hydrolysis studies and it is the
basis of the “preferential chain end scission” mechanism occurring in acidic
condition.[23]
Moreover, very similar values of the apparent equilibrium constant are found for
samples at different equilibrium compositions and temperatures. This finding supports
two important conclusions: (i) the mixture behavior is very close to ideality for the
polycondensation reactions; (ii) polycondensation equilibria are not affected by
temperature to a significant extent. Of course, both the previous conclusions are valid
inside the range of experimental conditions investigated in this work.
41
a
b
x
Figure 3.2. Experimental values of K1,n as a function of reactant chain length. a: 130 °C, b:
150 °C. Different symbols correspond to different equilibrium compositions: (a) ○
(xw=0.139), □ (xw=0.086), ◊ (xw=0.079) and * (xw=0.057); (b) ○ (xw=0.173), □ (xw=0.116), ◊
(xw=0.112) and * (xw=0.085).
42
x
Figure 3.3. Experimental values of K eb as a function of water mole fraction. Symbols identify
different temperature (○: 110 °C, x: 130 °C, ◊: 150 °C, □: 165 °C). Calculated curves: dashdotted = CS, continuous = CSi.
Let us now consider the equilibrium behavior of the end-biting reaction
(Equation 3.16). Since no chain length dependence is possible in this case, we can
focus directly on composition and temperature. Taking advantage of the single degree
of freedom in terms of composition, all K ebx values are shown in Figure 3.3 as a
function of water at different temperatures. At water mole fractions smaller than 0.2, a
strong effect of the system composition on K ebx is observed. In particular, the smaller
the water mole fraction is, the larger is K ebx . This trend suggests that the end biting
reaction has non-ideal thermodynamic behavior within the composition range
considered. On the contrary, at water mole fractions larger than 0.2, such composition
dependence becomes negligible. Once more, no significant dependence upon
temperature is noticed in the entire range of water contents under examination;
43
therefore, as already done for the polycondensation reactions, any thermal effect on this
reaction equilibrium can be neglected.
Thus from the above result we can conclude that the characterization of the
reaction equilibrium of the entire system can be achieved using the simplified set of
reactions (3.15)-(3.16) but involving three equilibrium constants only:
x

K1x  K1,1
x2 xW
x1 x1
K px  K1,xn 
xn 1 xW
xn x1
K ebx 
(3.18)
n 1
(3.19)
xW xLT
x2
(3.20)
It is worth noting that this conclusion has a significant impact on the description of the
equilibrium behavior of this system. Working out Equations (3.18)-(3.20), the
following relationships are in fact readily obtained:
n 2
 x 
xn
  K px  K1x  1 
xW
 xW 
xLT
 x 
K K  1 
 xW 
x
1
n
n 1
(3.21)
2
x
eb
(3.22)
which can be used to express the equilibrium constants of the reactions we excluded
from our equilibrium analysis (i.e., all polycondensation reactions involving oligomers
(Equation 3.7 with n, m > 1) and the back-biting reactions (Equation 3.8)) as follows:
K
x
n ,m
K 

K bbx ,n 
44
x 2
p
K
x
1
K ebx K1x
K 
x 2
p
x
 K pp
 K bbx
n, m  1
(3.23)
(3.24)
3.3.1
Equilibrium Constant Evaluation
Let us now proceed to the evaluation of the three equilibrium constants
K1x , K px and Kebx as a function of water mole fraction. This is straightforward for the
reaction of the monomer with itself, K1x , and for the end-biting reaction, K ebx . For the
reactions of the monomer with longer oligomers, K px , the following expression is
obtained by summing up equation (3.21) for n from 2 up to N:
K px 
xW 1  x1  x2  xW  xLT
x1
1  x1  xW  xLT
(3.25)
This specific form is quite convenient because the mole fractions of a few, low
molecular weight species are involved, which is expected to increase the accuracy of
the experimental evaluation of the constant.
All estimated values of the apparent equilibrium constants are shown as a
function of xW in Figure 3.4 for the polycondensation reactions and in Figure 3.3 for
the end-biting reaction. As already noticed, all data measured at different temperatures
are merged into a single data set. By fitting the data in Figure 3.4, the two apparent
equilibrium constants, K1x =0.330 and K px  0.275 , are estimated.
The picture is more complicated in the end-biting case (Figure 3.3), where a clear
dependence upon composition is found. As a first approximation, a constant value of
K ebx equal to 0.01 can be estimated by simply averaging all available data. This value
would be consistent with the assumption of ideal thermodynamic and we refer to this
case in the following as “ideal” (Figure 3.3 solid line). On the other hand, the non-ideal
behavior of the mixture can be accounted for in an effective way by fitting the K ebx
dependence upon composition in an empirical way. The data points were fitted through
45
a cubic smoothing spline interpolation (CSAPS in MATLAB package): the resulting
interpolating curve is shown in Figure 3.3 (dash-dotted line) and we will identify the
model accounting for such composition dependence as “non-ideal”. Note that a similar
approach was previously applied by Doherty et al.[73] to Nylon polycondensation in
order to account for the system non-ideality.
Figure 3.4. Apparent equilibrium constant of the polycondensation reactions as a
function of water mole fraction: K1x (open symbols), K px (solid symbols).
Given the values of the equilibrium constants of all the independent reactions,
the full equilibrium compositions can be predicted combining equations (3.21) and
(3.22) with the following stoichiometric relationship:
N
xn
n 2
W
x

x1 xLT
1

1 
xW xW
xW
(3.26)
This way, a system of N  1 non-linear equations with N  2 unknowns is obtained; as
expected, the mole fraction of one reference species (water) is needed to calculate the
46
equilibrium composition of the whole system. A convenient numerical strategy is based
on solving first the following cubic equation with respect to the monomer mole
fraction:
K
x
eb
K px K1x  x13   xw 2 K1x  K ebx K1x xw  K px xw 2  x12 
  xw 3  K px xw 2  K px xw 3  x1  xw 3 1  xw   0
(3.27)
and then equations (3.21) and (3.22) for xn (with n > 1) and xLT .
A detailed comparison between model predictions and experimental data for each
individual chemical species in the system is shown in Figure 3.5 as a function of the
water mole fraction for both ideal and non-ideal models. Minor differences between the
two are found for monomer and oligomers: the equilibrium compositions are predicted
with good accuracy for all species, with an average error around 4%. Model
discrimination becomes possible in the case of lactide: even though the lactide
concentration is much better predicted when the dependence of the corresponding
equilibrium constant upon composition is accounted for (non-ideal model), the
increasing behavior of lactide mole fraction at decreasing water content is qualitatively
reproduced also with constant value of K ebx (ideal model).
Let us now focus on the polymer quality, i.e. its average chain length. Taking
advantage of the recursive relationship (3.21), the following equation for the number
average degree of polymerization, DPn , is obtained:
DPn 

 
 x K


K1x x1 2 xw  K px x1  xw  K px x1
x
w

 K px x1  xw
1
x
1
 K px
2
(3.28)
47
Assuming chain length independent reactivity (i.e., K1x  K px  K x ), equation (3.28)
reduces to the classical relation between degree of polymerization and water mole
fraction:
DPn  K x
(1  xW )
1
xW
(3.29)
Equation (3.29) can be directly obtained re-writing Equation 3.4 in terms of moments
of the polymer properties as:
Kx 
 1  0  W
02
(3.30)
where 0 and 1 are the moments of the molecular weight distribution of the first two
orders, zero and one. It is consistent with the simplest scheme of polycondensation
which neglects all chain length dependences and lactide formation. As shown in the
inset of Figure 3.6, a good linearity is found with a value of the apparent equilibrium
constant K x  0.255 .
In the same figure, the predictions of DPn accounting and neglecting all dependences
upon chain length (equations 3.28 and 3.29) are also shown: the results are practically
superimposed, thus indicating that no model discrimination is possible when the
polymer molecular weight only is examined. This finding explains why chain length
dependent reactivity is neglected in most previous works: detailed composition data
such as those shown in Figure 3.5 are needed to identify such effect.
48
Figure 3.5. Oligomer mole fractions as a function of water mole fraction. Symbols:
experimental data. Calculated curves: continuous= ideal, dash-dotted = non-ideal, dashed =
reactivity independent on chain length.
49
Figure 3.6. DPn as a function of xW (in the snapshot: the ratio between non-water and water,
(1  xW ) / xW ). Data obtained at (o)110oC, (□) 130oC, (◊) 150oC and (*)165 oC. (--) reactivity
independent on chain length, Equation 3.29; (-) ideal, Equation 3.28.
3.3.2
Implication on the behavior of a polycondensation reactor
Finally, a few additional remarks about the behavior of a polycondensation
reactor can be made by looking at a “reduced” pseudo-ternary system involving only
water, monomer and linear oligomers. Lactide is neglected since it is invariably a minor
species at all examined conditions. In Figure 3.7 it is shown the line describing the
composition of such a reduced system at equilibrium conditions, with the circles
representing the measured experimental data.
50
Figure 3.7. Ternary diagram water (W) / monomer (M) / polymer (P). Symbols: experimental
data. The curve is calculated with the ideal model. Path 1 = ABD; Path 2 = ACD.
It is seen that the equilibrium line represents a definite constraint with respect to
the composition regions which can be accessed in a semibatch reactor where water can
be removed by evaporation. Starting in fact from a generic mixture monomer-water
(MW side of the triangle), two limiting reaction paths are readily identified, depending
upon the selected operating conditions for the polymerization reactor:
(i)
if water removal is much faster than the reaction progress (chemical regime),
the reaction path will evolve close to the triangle sides MW and MP, corresponding to a
reaction carried out under conditions of almost complete water removal (path A in
Figure 3.7);
(ii)
if instead water removal is much slower than the reaction progress, the reaction
path approaches the equilibrium curve as quickly as possible and then proceeds as a
51
series of equilibrium conditions, thus following the equilibrium curve (path B in Figure
3.7).
We can then conclude that the location of the actual reaction path in this diagram
provides a clear indication about the operating regime in a generic polycondensation
reactor depending upon its closeness to one or the other of the two limiting behaviors
discussed above.
3.4
Conclusions
Reaction equilibrium of lactic acid polycondensation in bulk melt was
investigated over a wide range of temperatures (110-165 °C) and compositions. A
detailed characterization of the system, in terms of water, lactide, lactic acid and lactic
acid oligomers, was obtained combining HPLC and KF titration. As previously
suggested in the literature, a negligible temperature effect on the reaction equilibrium
was found within the investigated temperature range. Taking advantage of the detailed
characterization, a complete kinetic scheme accounting for chain length dependent
reactivity, lactide formation through end- biting and back-biting reactions and non-ideal
thermodynamic behavior has been proposed. Three equilibrium constants are found to
be sufficient to predict the equilibrium composition of the system: K1x , K px and K ebx ,
where only the last constant exhibits a relevant dependence upon the system
composition. Finally, the equilibrium constants of all the involved reactions have been
quantitatively expressed as a function of these three constants, thus making complete
the modeling of the reacting system.
52
Chapter 4. Kinetics of Bulk Melt Polycondensation of
Lactic Acid
4.1 Introduction
Increasing efforts have been registered in the last decades both from academia and
industry towards understanding and deepening the large-scale production processes of
poly(lactic acid) (PLA). Accordingly, a large fraction of the market of degradable
polymers from renewable resources is nowadays covered by this type of material.[1]
Major attention has been devoted to reaction strategies aimed to improve mechanical,
optical and rheological polymer properties, which are crucial for commodity
applications such as film packaging, cups, bottles, and fibers.[2-4] Moreover, due to its
biodegradability and biocompatibility, PLA has been approved by the regulatory
agencies of many countries for medical applications such as suture threads, implantable
scaffolds, bone fixation devices, and micro- and nano-capsules.[5] In all cases, polymer
molecular weight, polymer purity in terms of side products and residual monomers,
chain microstructure (chiral and chemical composition) are aspects to be carefully
considered when designing the operating conditions of the polymerization process.[6]
Two main routes have been largely studied in the literature for PLA production:
the bulk Melt Polycondensation (MP) of lactic acid (LA), and the Ring-Opening
Polymerization (ROP) of lactide, the cyclic dimer of LA. The most popular industrial
production strategy is actually a combination of the two routes into a multistep process.
LA is first polymerized to a low molecular weight polymer (so called prepolymer) by
53
polycondensation (< 10,000 Da) and then depolymerized and converted to the cyclic
dimer in a catalytic step usually carried out at high temperature and low pressure.
Finally lactide undergoes ROP after suitable purification, leading to high molecular
weight polymer (> 100,000 Da).[2, 7]
The first process step is the classical polycondensation reaction in which
polymer chains bearing two functional groups (alcoholic and carboxylic) undergoes
esterification leading to longer chains while producing water. Such water has to be
removed from the reacting mixture in order to shift the chemical equilibrium towards
the polymer product: because of the unfavorable chemical equilibrium[8] and the
operative transport limitations (the system becomes increasingly viscous at increasing
extent of reaction), polycondensation is not suitable to produce high molecular weight
PLA.
The reaction scheme is complicated by the occurrence of multiple side reactions
like discoloration, cyclization, transesterification and racemization.[9-11]. Among
them, the most interesting is indeed the formation of lactide through ring closure
reactions, i.e. back-biting and end-biting reactions. In particular, back-biting reaction
refers to the formation of cyclic compounds through intramolecular reactions between
the hydroxylic end group of the polymer chain and an ester bond in the chain backbone.
While linear oligomers are formed by back-biting, end-biting reactions produce water.
Since the production of lactide is the aim of the next process step, a large number of
literature works appeared focused on lactide formation. The effect of different metal
catalysts (Sn, Al, Ti, Zn, Zr) on lactide production from PLA oligomers was studied by
Yoo et al.[74] and Noda and Okuyama.[75] On the other hand, Sinclair et al.[76]
patented an innovative method to produce lactide from PLA oligomers. Overall, the
54
contribution of reactions forming lactide should be definitely considered when
analyzing the polycondensation of lactic acid.
A large number of experimental works have been published. About the
identification of effective catalysts, a wide variety of metal-based catalysts such as Sn
and Zn were reported to be effective.[61] On the other hand, the same catalysts
introduce undesired effects: as an example, polymer discoloration is usually enhanced,
most probably due to side reactions occurring at high reaction temperatures and
residence times. To prevent such discoloration, the addition of p-toluenesulfonic acid
(TSA) as co-catalyst has been suggested.[9, 11] Moreover, polymer racemization
caused by interchange reactions occurring by cleavage of an alkyl-oxygen bond of an
ester group is effectively enhanced by Lewis acid catalysts, especially at high
temperatures.[61] Finally, the use of a specific catalyst during the prepolymerization
step could have detrimental effects in the next process step aimed to produce lactide. At
the same time, different reaction policies have been investigated to improve the
reaction performances in terms of maximum chain length: unconventional pressure
profiles,[77] the use of microwave reactors,[78] the use of supercritical fluids[79] or
azeotropic solvent mixtures as reaction media[80] and solid state polymerization.[81,
82] In summary, the literature experimental results are often contradictory and it is
difficult to organize them in a consistent, unifying picture.
In contrast to such a large body of experimental studies, a few modeling works
only appeared in the literature for this specific polymer. In fact, even though the role of
transport resistances was deeply investigated for other polycondensation systems, such
as Poly(ethylene terephthalate), PET, and polyamides (e.g. Nylon-6), practically no
information is available for PLA.[83, 84] Notably, in the previous modeling literature
on different polycondensation reactions, the rate of mass transport was shown to be
55
strongly affected by polymer molecular weight and rate of stirring.[84, 85] Such
transport limitations have been investigated on different reactor configurations, i.e.
rotating disk reactors, screw type reactors, wiped films, reactive distillation columns
and stirred tanks.[83, 86] In particular, Jacobsen and Ray[59] introduced the “mass
transfer potential” (MTP), a parameter quantifying the relevance of the mass transport
limitations as a function of the equilibrium constant of the reaction. Accordingly, being
the equilibrium constant of PLA polycondensation smaller than 1, the system is
expected to be strongly limited by transport resistances. As an exception, Harshe et
al.[48, 87] proposed a model for PLA polycondensation: it involves the most
conventional kinetic scheme assuming reactivity independent upon chain length and
irreversible transport rate. The impact of transport phenomena was evaluated through a
set of parametric simulations accounting for the mass transport coefficient function of
polymer molecular weight. By fitting the model predictions to experimental data
obtained under Nitrogen flow (i.e., conditions expected to minimize transport
resistances), it was concluded that the reaction proceeds quite close to the chemical
regime, with easy water removal. Under this assumption, the evaluation of the
propagation rate coefficient was carried out assuming instantaneous water removal.
Following our previous study of chemical equilibria in bulk melt
polycondensation of LA,[88] a kinetic analysis of the same system is reported in this
work. Polycondensation reactions have been carried out in semibatch reactor at
different temperatures, pressures and stirring rates aimed to elucidate the interplay
between reaction kinetics and transport phenomena on the system evolution. Different
analytical techniques have been used to achieve full chemical characterization of both
the phases in the reactor, polymer melt and gas. Taking advantage of such set of
experimental data, with details not previously accessible in the literature, a
56
comprehensive description of the system evolution has been obtained. Then, a
corresponding mathematical model, involving chemical equilibrium, kinetics and
transport phenomena, has been developed. Lactide formation was accounted for in the
model. All model parameters have been evaluated from independent literature sources
or by direct fitting of the model predictions to the experimental data. The main
achievement of this work is the identification of the operating regime, which is limited
by transport resistances when stirred tank reactor is used removing volatile byproducts
both by Nitrogen flow or vacuum. The complete understanding of the impact of
transport limitations is essential to the reliable evaluation of the rate constants of the
different reactions: such values make the final model a reliable design tool for a wide
range of operating conditions.
4.2 Experimental Part
4.2.1
Materials
L-Lactic acid reagent grade (90% w/w of purity; Acros Organics, Belgium), HPLC
grade acetonitrile (Fluka, ) orthophosphoric acid (Fluka, ), copper II sulphate
(anhydrous 98%; Acros Organics, Belgium) and Hydranal® - Coulomat (Fluka, ) were
used.
4.2.2 Reactor setup
All runs were carried out in the apparatus sketched in Figure 4.1. The experimental
setup consists of a 250 ml glass reactor (Büchi, Switzerland) equipped with a
mechanical stirrer magnetically coupled to an electrical motor (RZR 2052 Control;
Heidolph, Germany).
57
Figure 4.1. Schematic representation of the reactor setup. a) reactor, b) mass flow meter, c)
stirrer motor, d) sampling port, e) ice trap, f) vertical condenser, g) septum, h) pressure
controller, i) vacuum pump.
The reactor internal diameter is 5.2 cm and the stirrer is a propeller type with diameter
equal to 3.5 cm. The reactor temperature was controlled by an external heating bath
(Polystat CC3; Huber, Germany) through a metal heating jacket equipped with glass
window. The reactor pressure was set through a digital vacuum controller (DVR-300MR; K-JEM Scientific Inc., USA) regulating the pressure with accuracy ± 0.5 mbar
over a range of 0-1013 mbar, connected to a vacuum pump capable of 1 mbar as
minimum pressure. The reactor head is equipped with six necks out of which three are
connected with head and bottom temperature indicators (± 0.5°C) and pressure sensor
(Digital manometer dV-2; Keller, Switzerland; ± 1 mbar) and one is used as sampling
port to collect samples of molten polymer. One neck is connected to the Nitrogen line
pre-heated by an electrical heating tape and with flow rate controlled through a mass
flow meter (Brooks 5850E; USA). The Nitrogen line is intercepted with desiccant trap
58
(silica gel) to fully dehydrate the gas flow. Finally, the last head-neck is used to connect
the reactor to an ice cooled condenser at the top of which a vertical condenser was
installed working at temperature low enough to avoid loss of volatile materials. The
temperature in the vertical condenser was regulated by means of an aqueous solution of
ethylenglycol (0.3 % w/w) circulating through a cryostatic system (RK20; Lauda,
Germany). Due to the possible accumulation of condensed volatile compounds on the
cold inner wall of the vertical condenser, a septum was placed at the top of the
condenser itself to allow the injection of a liquid solvent (acetonitrile) to fully recover
all condensed products.
Table 4.1. Operating conditions of all experimental runs.
4.2.3
run
T (°C)
P (mbar)
N (rpm)
1
150
150
400
2
150
200
400
3
150
300
400
4
150
150
100
5
150
150
200
6
130
N2
400
7
150
N2
400
8
170
N2
400
9
190
N2
400
Polycondensation reactions
The polycondensation reactions were carried out in two consecutive steps, monomer
dehydration and polycondensation. The dehydration step was carried out for 2 hours at
90 °C and the pressure was reduced in steps of 33 mbar every 30 minutes from 266.6
mbar to 133.3 mbar. This pre-treatment is aimed to remove most of the water initially
59
present in the monomer mixture (around 10 % w/w) at low enough temperature to
prevent/minimize the extent of the polycondensation reaction. After monomer
dehydration, temperature and pressure were set to reaction condition, which were
established in less than 20 minutes: the time at which the set point values of
temperature and pressure were established was considered the initial time of the
reaction.
The operating conditions of all performed experiments are summarized in Table 4.1.
Two different types of reactions were carried out, (i) under Nitrogen flow and (ii) under
vacuum; in both cases, temperature (reactor and heating tape) and pressure were kept
constant all along the reaction. In the first case, the vertical condenser was disconnected
from the vacuum controller and a constant Nitrogen flow rate of 200 ml/min was used.
Samples of reacting melt were collected at different time intervals from the sampling
port by means of a thin glass tube. At the same time, samples of the gas phase leaving
the reactor were collected after condensation: first, the vertical condenser was washed
with acetonitrile to recover all volatiles on the condensed wall and then the ice-cooled
condenser was replaced by a new one. When operating under vacuum, the system was
connected to the vacuum pump and the same sampling procedure was used after
reestablishing atmospheric pressure conditions by Nitrogen flow. During sampling,
such flow was kept constant to prevent contamination through the sampling port. While
the composition of both phases, molten and gaseous, was reliably characterized by
HPLC, GC and KF titration as detailed in the next, large errors were found in the
evaluation of the total condensed mass. This is most probably due to inaccurate
recovery of the condensate itself, in particular when large amount of acetonitrile was
used to wash the vertical condenser. On the other hand, this same quantity could be
much better estimated in a different way. As already mentioned, the reactor was
60
equipped with a glass window and the volume change of the melt phase during the
reaction could be visually measured by a camera. Thus, the total mass evaporated was
directly estimated from such volume change using equations and parameters given in
the next section.
4.2.4
HPLC reversed phase
Polymer and condensed gas samples were characterized in terms of oligomers
composition using a previously published reversed phase chromatographic method.[71]
Briefly, the analyses were carried out on two Agilent Eclipse XDB C18 columns in
series (3.9mm×150 mm particle size 3.5 μm) in an HPLC apparatus (Agilent 1200
series; USA) equipped with UV detector set at 210 nm, autosampler and column oven
(set at 40 °C). The mobile phase was a mixture of water and acetonitrile both acidified
with phosphoric acid (0.1% v/v). The separation was run at total flow rate of 1 ml/min
using the following solvent gradient profile: starting with mobile phase of 98% v/v
water, after 2 min the acetonitrile concentration was ramped linearly to 100% v/v in
120 min, maintained constant at 100% v/v for 20 min and finally returned back to 98%
v/v water. Additional information about the measurement protocol and the calibration
procedure are reported elsewhere.[71]
4.2.5
Chiral HPLC
The separation of the mixtures of isomers of L and D lactic acids has been carried out
using a Chirex 3126 (D)-penicillamin (Phenomenex, USA) column (length 150 mm,
internal diameter 4.6 mm, particle diameter 5 μm) and the same HPLC apparatus
described above. An aqueous solution of Copper(II) sulfate 3 mM was used as eluent at
61
flow rate of 1 ml/min. The polymer samples were hydrolyzed in 1M sodium hydroxide
solution over night at 80°C and then filtered before injection.
4.2.6
Karl-Fischer Titration
Water contents were determined by 831 KF Coulometer (Metrohm, Switzerland). PLA
samples were first dissolved in extra dry acetonitrile (water content < 10 ppm; Acros
Organics, Belgium) and then injected in liquid phase into the instrument. Water content
of the solvent used to dissolve the polymer was accounted for when treating the data.
4.2.7
Gas Chromatography
All analyses were carried out using a Hewlett Packard gas chromatography HP6890
apparatus, equipped with a crosslinked 5% PH ME Siloxane HP column (length 30 m,
internal diameter 0.3 mm, particle diameter 0.25 µm) (USA) and TCD detector. Helium
was used as carrier gas at flow rate of 1 ml/min. Injector and detector were set at 250
°C and the column temperature was maintained at 60 °C for 10 minutes and then raised
to 250 °C in 20 minutes. Calibration was carried out by injecting acetonitrile water
mixtures with known amount of water.
4.2.8
Rheological measurements
Polymer melt viscosity was measured as a function of temperature (from 110 °C to 170
°C) and molecular weight by means of a Physica MCR300 rheometer (Anton Paar,
USA) using a cone-plate geometry with cone diameter of 30 mm and cone angle 2°. All
the measurements were carried out with frequencies ranging from 1 to 103 1/s. The
distance between plate and cone was maintained at about 0.05 mm at the center to
ensure a reasonable aspect ratio and minimize edge effects during testing.
62
4.3 Model Development
4.3.1 Model assumptions
The model is developed based on the following assumptions:

Monomer has different reactivity than longer oligomers
From chemical equilibrium studies,[88] lactic acid was found to exhibit different
reactivity compared to larger oligomers. This finding is in agreement with literature
data specific for PLA but also for other polycondensation systems. [8, 89-93]

Racemization is negligible
The extent of racemization (D content) was measured as a function of time for runs 6 to
8. As shown in Figure 4.2, 2 % mol D content was measured after pretreatment and this
value did not change significantly during the reaction.
Figure 4.2. D content (%) during polycondensation reactions carried out under Nitrogen flow at
different temperatures: ○ 130 °C, ♦ 150 °C, □ 170 °C.
63

Negligible formation of cyclic compounds by intramolecular reactions
According to the literature, the formation of cyclic species is a function of the reaction
temperature and the size of the formed rings. [94] For PLA, Kèki et al. [10]
investigated the formation of cycles in PLA polycondensation through MALDI-TOF
analysis and they found that cycles are formed in large extent only for reaction
temperature larger than 180°C. Since most of our experiments were carried out at lower
temperature (with the exception of one single reaction, run 9 in Table 4.1), cyclization
reactions have not been included in the model kinetic scheme.

Interchange reactions are negligible
Three main mechanisms have been proposed as responsible of chain reshuffling or
interchange reactions: intermolecular alcoholysis, intermolecular acidolysis and
transesterification[95]. Alcoholysis is generally considered the most favored in
polycondensation; accordingly, a generic chain attacks via its hydroxyl end group an
ester group of a different polymer chain with formation of shorter attacked chain and
longer attacking chain. However, literature works reporting conclusive evidences about
the impact of exchange reactions are lacking: therefore, such reactions have not been
included in the final kinetic scheme.

Water and LA only are considered volatile
This assumption is supported by the gas phase experimental data, where these two
species were indeed the major components and all the others were found as traces (e.g,
see Figure 4.10). Moreover, Achmad et al. [96] reported that water, LA and lactide
were detected in gas phase under vacuum (10 mmHg) higher than that considered here:
64
this is consistent with the volatility ranking of the species and further supports our
assumption.

Completely mixed system
The absence of temperature and composition gradients is reasonably expected due to
the intense mechanical stirring and the limited system viscosity (relatively low final
value of polymer molecular weight).
4.3.2 Model constitutive equations
As anticipated, the reactions are run in semibatch mode to remove volatiles and
increase the polymer molecular weight. Being the system affected by reaction kinetics,
transport phenomena and volume change of the reacting mixture, the material balances
for liquid and gas phase are:
dCi
C dVl
 ri  i  i
dt
Vl dt
(4.1)
N
dGi
G dVg

  g yi  i Vl  i
dt
Vg
Vg
Vg dt
(4.2)
where Ci and Gi represent the molar concentration of i-th species in liquid and gas
phase, N g the total molar flow rate of the gaseous stream removed by the vacuum
pump, yi the gas phase mole fraction, Vl and Vg the volumes of liquid and gas phase
inside the reactor, i the mass transport term and ri the reaction term. The detailed
expressions of the different terms are provided in the following.
65

Kinetics
The standard reaction scheme of polycondensation is:
k
p


Pn  Pm 

 Pnm W
k
(4.3)
d
where k p and kd represent the polymerization and de-polymerization rate constants,
respectively, considered independent of chain length. In this work, based on previous
results on chemical equilibria in lactic acid polycondensation [88], the different
reactivity of the monomer compared to that of longer oligomers was accounted for.
Accordingly, the more detailed kinetic scheme shown in Figure 4.3 was considered.
a.
k1p


P1  P1 

 P2 W
k1
d
k pp
b.

 Pn 1  W
P1  Pn 
p 
c.
p

 P W
Pm  Pn 
pp  n  m
d.


P2 
 LT  W
k eb
e.
p


Pn 
 LT  Pn  2
k bb
kd
k pp
kd
k eb
p
d
k bb
d
Figure 4.3. Kinetic scheme.
In particular, the reaction between two monomers (a), monomer and any longer
oligomer (b) and the oligomers with chain length from linear dimer on (c) are included.
Moreover, the lactide forming reactions, end- and back-biting, are considered (d, e).
Such two reactions, usually neglected in previous modeling contributions[87] have
been included because of their relevance for the industrial multistep process discussed
in the Introduction. For the r-th reaction, k pr and k dr represent the forward and
66
backward rate constants, respectively. With reference to the kinetic scheme and the
previously discussed model assumptions, the corresponding expressions of the reaction
terms in Equations 4.1 are:
k 1p
r1  2k C  2
1
p
2
1
r2  k 1pC12 
2
k ppp
x
K pp
x
1
K
C2CW  2k C1 (0  C1 )  2
p
p
k 1p
k pp
K1
x
p
C2CW  2k ppC2C1  2
x

CW  Cm  k C2 
eb
p
m4
rn  2k ppC1  Cn 1  Cn   2

K
k peb
K ebx Ctot
k pp
K
x
p
k pbb

CW  Cm 
m 3
x
bb
K Ctot
C1CLT  k pbbC3 (4.4)
CW C3  2k pppC2  0  C1  
C LT CW  k C4 
bb
p
(4.5)
k pbb
K bbx Ctot
C LT C2
k pp
n 2

pp 
C
C
C
k


W  n 1
n
p   C m C n  m  2C n  0  C1   
x
Kp
 m2

k ppp
bb
kp
 

C
C LT  Cn 2  Cn   k pbb  Cn  2  Cn 
W   C m  ( n  3)C n  
x
x
K pp
K
C
 mn 2

bb tot
n3
rW  k C 
1
p
2
1
k 1p

k pp

m2
Kp
m 3
C2CW  2k C1  Cm  2
x
p
p
K1
+ k ppp  0  C1  
2

k pbb
n 3
K bbx Ctot
rLT  k pbb  Cn 
k
pp
p
x
pp
K
CW  Cm +
x

k peb
m4
K ebx Ctot
CW  ( m - 3)Cm  k pebC2 

k peb
n 1
K ebx Ctot
CLT  Cn  k pebC2 
(4.6)
CLT CW
(4.7)
C LT CW
(4.8)
where Cn , CW and CLT indicate the molar concentrations of monomer and oligomers,
water and lactide, respectively, Ctot is defined as CLT  Cw  0 and K rx is the
equilibrium constant of r-th reaction.

Mass transport
In the frame of the two film theory, all transfer resistances are concentrated in the
boundary layers at the liquid-gas interface.[97] Assuming equilibrium conditions and
67
no accumulation at the interface, the following classical expression of the rates of mass
transport in each phase applies:
i  k x ,i aCtot  xi  xi*   k y ,i aCtot  yi*  yi

(4.9)
where k x ,i and k y ,i indicate the mass transport coefficients in liquid and gas phase,
respectively, a the specific interphase area, xi and yi the mole fractions of the i-th
component in melt and gas bulk phases and xi* and yi* the same mole fractions at the
interphase, assumed in equilibrium. Due to the large diffusion coefficients in gas phase,
the vapor phase composition can be assumed homogeneous and equal to the interface
value. Under these conditions, the mass transfer rate is fully determined by the
resistance in the liquid phase and the mass flow rate is given by the first of the two
equalities in Equation (4.9). Moreover, xi* is evaluated through the ideal Dalton-Raoult
law:
xi* 
Pyi
Pi o
(4.10)
where P is the total pressure and Pi o the vapor pressure of i-th component.

Phase volumes and pump molar flow rate
Liquid and gaseous volumes and molar flow rate removed by the vacuum pump ( N g )
are evaluated assuming volume additivity in liquid mixture and constant pressure inside
the reactor, as established by the pressure controller. In particular, consistently with the
first assumption, the following relationship is obtained:
MW CW
W
68


n 1
M nCn
n

M LT CLT
 LT
1
(4.11)
where Ci is the molar concentration of component i in the reacting mixture, M i its
molecular weight and  i its pure component mass density.
Differentiating Equation (4.11) in time, the following equation is obtained:
MW dCW  M n dCn M LT dCLT


0
W dt n1 n dt
 LT dt
(4.12)
which, after combination with the material balances of the different species, Equations
(4.1), provides the following explicit equation for the liquid volume:
dVl
M
 Vl  i  ri  i 
dt
i i
(4.13)
As expected, the volume change in the liquid phase is due to chemical reaction and
mass removal by vaporization. Given the volume of the liquid phase by integration of
the last previous equation, the volume of the gas phase is readily evaluated as:
Vg  VR  Vl
(4.14)
where VR is the constant reactor volume.
Finally, the gas flow rate removed by the vacuum pump can be evaluated from the
condition of constant pressure. Namely, by time differentiation of the total number of
moles in the gas phase, ng  Vg  Gi (where the summation includes all volatile
i
species), the following relationship is obtained:
dng
dt
 iVl  N g
(4.15)
i
Assuming ideal gas, the following relationship provides N g as a function of time:
N g   iVl   Gi
i
i
dVl
dt
(4.16)
69
4.4 Parameter Evaluation
The model presented above involves a large number of parameters, from kinetic and
equilibrium reaction constants, to vapor-liquid equilibrium properties such as vapor
pressures, to transport properties such as transport coefficients and melt phase
viscosity. Their evaluation is indeed non trivial and it is discussed in this section: as
usual, as many as possible parameter values are first obtained from independent sources
(literature, non-reactive experiments) and the remaining ones are estimated by direct
fitting of the model predictions to our own experiments.
As detailed in Equations 4.4-4.8, 5 kinetic constants and 5 equilibrium constants
are involved in the considered set of reactions. The values of the equilibrium constants
are available because they were reported in a previous work. The remaining 5 rate
coefficients were considered fitting parameters.
Since reliable values of polymer density are available only for high molecular
weight polymers, the densities of monomer and oligomers is assumed independent
upon molecular weight and temperature:
1   2  ...   n   P
(4.17)
Moreover, in agreement with the literature [98], the value of monomer and oligomer
density was assumed equal to that of lactide, i.e.  P   LT .
For the evaluation of the transport rates through Equations (4.9) and (4.10),
vapor pressure, activity and transport coefficient of each component are needed.
Vapor pressures have been calculated through the classical Antoine equation using the
parameter values reported by Sanz et al. [41].
About the transport coefficients, k x ,i , the following conventional expression in terms of
dimensionless groups and valid for stirred tanks has been considered:
70
c1
N Sh   N Re
N Scc2
(4.18)
where  , c1 and c2 are constants characteristic of a specific reactor and stirrer geometry
and N Sh , N Re and N Sc are Sherwood, Reynolds and Schmidt numbers, respectively.
They are defined as follows:
N Sh 
N Re 
N Sc 
ki , x L
Di
(4.19)
Nd 2 mix

(4.20)

Di  mix
(4.21)
thus involving characteristic lengths ( L and d are reactor and stirrer diameters),
physical properties ( and  mix are viscosity and density of the liquid mixture, Di is
the coefficient of molecular diffusion of i-th component) and operating conditions ( N
is the stirring rate). The values of constants c1 and c2 have been assumed equal to those
typical of stirred tanks in laminar regime,[97] i.e. 0.5 and 0.333, respectively. To work
out a convenient relationship for the mass transport coefficient, k x ,i , some of these
quantities are expressed as a function of the reaction extent.
Consistently with the assumption of volume additivity and taking advantage of
Equation (4.17), the density of the liquid mixture was evaluated as ratio of the
corresponding total mass and volume,  mix  M l / Vl . While the volume was evaluated
by integration of Equation (4.13), the total mass was readily calculated from the

concentrations of the different species as M l  CW MW  CLT M LT   Cn M n .
n 1
71
The diffusion coefficients of the different species in the molten polymer mixture were
estimated through the classical equation by Wilke-Chang[99]:
Di 
7.4  10 8  M n T
0.6
V i
(4.22)
where  represents the association factor (equal to 2.6 for associated species)[99], V i
the molar volume of the i-th species at normal boiling point, T the temperature and M n
the number average molecular weight of the reacting mixture excluding water and
lactide (minor species).
Figure 4.4. Effect of shear rate on polymer melt viscosity as a function of molecular weight for
the experiments at 150 °C. Symbols: (●) 90 Da; (○) 200 Da; (■) 400 Da; (□) 600 Da.
72
The last property to be evaluated as a function of time is the viscosity of the liquid
mixture,  . Once more, literature values of PLA viscosity were reported for high
molecular weight polymers only, along with the indication of strong effects of the
polymer molecular weight and optical purity. However, at low molecular weights like
in the pre-polymerization reactor under examination, the rheological behavior is very
different and constant viscosity is expected at low shear rate.[6, 98, 100, 101] Because
of the lack of literature data at these conditions, the dependence of the polymer
viscosity on polymer molecular weight, M n , and temperature was investigated
experimentally in the ranges 90-600 Da and 110-170 oC. The measurements were run at
variable shear rates,  , ranging from 60 to 1000 s-1. As shown in Figure 4.4 for the
experiments at 150 oC, the molten polymer viscosity resulted practically independent
on shear rate; this same behavior was found at all examined temperatures and it
confirms Newtonian behavior of the liquid melt under examination.[102] Thus, the
following relation between the number average molecular weight and zero shear
viscosity, 0 , can be applied:
c4
  0  c3 M n
(4.23)
where c3 and c4 are two additional constants which values are determined by direct
fitting to the results of the rheological measurements. Such results are shown in Figure
4.5 as a function of temperature.[103]
73
Figure 4.5. Effect of molecular weight on melt polymer viscosity as a function of temperature:
(■) 110 °C; (○) 130 °C; (♦) 150 °C; (◊) 170 °C.
While the estimated values of c3 have been correlated through an Arrhenius type
equation, a linear relation in temperature was used for c4 :
 8262.7

c3  exp  
 6.4361
T


(4.24)
c4  -1.4 10 2 T  7.45
(4.25)
Notably, the estimated values of c4 are inside the typical range of values reported in the
literature for mixtures of polymers well below the critical molecular weight of
entanglement.[100, 104, 105] The measured values indicate that the viscosity of the
liquid mixture varies from 1.5 to 210 mPa s at the different operating conditions;
74
accordingly, the maximum value of NRe is close to 6,000. Being the reactor operated in
laminar regime, the shear rate is simply proportional to the stirring rate:
  f N
(4.26)
where the value of the constant f is determined by the selected type of stirrer. For
propeller-type stirrer, f is equal to 10 [106] and, therefore, the largest  achieved in our
experiments is 66 s-1, a value indeed included in the range of values explored by the
rheological measurements.
Plugging Equations 4.22 and 4.23 into Equation 4.18, the following relationship
between the mass transport coefficient and the selected product and process parameters
(polymer molecular weight, stirring rate, and system density) is readily obtained:
k x ,i  i M n0.3330.833c4 N 0.5  0.167
(4.27)
where all constants and temperature dependences have been lumped into the new
quantity  i . The latter quantity was considered an additional adjustable parameter,
which value is different at different temperature. Accordingly, since the values of c3
and c4 are given,  i of the two volatiles are the fitting parameters required to estimate
the corresponding transport coefficients.
To conclude, all model parameters have been evaluated a priori but the series of
the “direct” rate constants, k px , and the parameters in Equation (4.27), i . Such large
number of adjustable parameters (seven) has been evaluated by direct fitting of the
model predictions to the experimental data following the strategy detailed below. The
objective function to be minimized was defined as the summation of the average
relative errors for concentrations in melt phase, average molecular weights, and overall
75
amounts collected in condensed phase. To handle the minimization problem in a
reliable way, the optimization was carried out in two steps:
Step 1: parameter evaluation was carried out for runs 1-5 and 7 in Table 4.1, all at the
same temperature, under the assumption of negligible lactide production:
k peb  k pbb  0
(4.28)
This way, the estimated values of k 1p and k pp resulted very similar: therefore, they were
assumed equal, thus reducing the number of fitting parameters by one.
Step 2: lactide formation reactions were accounted for and, using all parameter values
as estimated in Step 1, k peb and k bb
p were evaluated using the same set of experimental
data. Since the model predictions were practically the same (with the exception of the
profile of lactide concentration), the reliability of this approach was confirmed.
The application of this strategy to all experiments resulted in relatively large average
errors, close to 18%. To improve the agreement between model and experiments, the
separate fitting of the two sets of reactions, under Nitrogen flow and under vacuum,
was carried out. This way, the final error was significantly reduced and always about
10%. On the other hand, the values of all kinetic constants remained practically
constant while the values of i only were different in the two cases (the value
estimated under Nitrogen flow was about four times the one under vacuum). This
discrepancy could be imputed to the simplistic description of the vapor-liquid
equilibrium implied by Equation (4.10): the different values of the transport parameter
are most probably accounting for non-ideal behavior in the liquid mixture which
relevance is different at the two operating conditions, vacuum or Nitrogen flow.
76
Table 4.2. Model parameter values.
Parameter
Value or relationship
Unit
Source
k 1p  k pp
exp(-14552/T+33.22)
l/mol/h
this work
k ppp
exp(-15115/T+33.36)
l/mol/h
this work
k
eb
p
exp(-11,599/T+17)
l/mol/h
this work
k
bb
p
exp(-20,754/T+36)
l/mol/h
this work
0.33
-
[88]
0.275
-
[88]
-
[88]
-
[88]
-
[88]
K 1x
K
p
x
K 
p 2
x
K xpp
K xeb
K 1x
0.015
K xeb K 1x
K xbb
K 
p 2
x
w
exp(4864/T-10.48) (12.15 vacuum 150 °C)
-
this work
m
exp(5276/T-15.72) (0.013 vacuum 150 °C)
-
this work
p
1.285
g/l
[98]
V W
V m
19.76
cm3/mol
[107]
98
cm3/mol
[107]
4.5 Comparison between experimental data and model predictions
The values of all model parameters are summarized in Table 4.2. As shown in
Figure 4.6 for the reactions under Nitrogen flow at different temperatures, good
agreements between model and experiments were found for the composition in melt
phase. The different behaviour at the different temperatures is well reproduced,
especially for the longer oligomers.
Given the entire composition of the melt phase in terms of oligomer
concentrations, the average polymer properties can be readily evaluated from the
experimental data as:
77
M n  M eg  M ru
1
0
(4.29)
M w  M eg  M ru
2
1
(4.30)
PDI 
Mw
Mn
(4.31)
where M eg and M ru represent the molar mass of polymer end groups (eg) and
repeating units (ru) (18 and 72 Da, respectively), M n and M w the number and weight
average molecular weights, PDI the polydispersity index, and i the i-th order moment

of the polymer chain length distribution, defined as i   j i C j .
j 1
The comparisons between model and experiments are shown in Figures 4.7 (Nitrogen
flow, constant stirring, different temperatures), 4.8 (constant vacuum and temperature,
different stirring rates) and 4.9 (constant stirring and temperature, different vacuum).
While M n and M w grows linearly in time for the reactions under Nitrogen flow
(Figure 4.7), the same evolution is quite non-linear in all the other cases. This behavior
reflects the more effective volatile (and especially water) removal under flow than
under vacuum.
The effect of stirring and pressure on the polymer average properties is also
nicely predicted: molecular weight is smaller, the higher the pressure and the lower the
stirring rate. The effect of pressure on the polymer molecular weight seems larger than
that of the stirring rate: this result is consistent with the moderate dependence of the
mass transport upon the stirring rate shown by Equation 4.27. Moreover, it is worth to
notice that, these two parameters affect the transport rate in different ways: while
stirring rate affects the transport coefficient by reducing the thickness of the boundary
78
diffusion layer, pressure acts directly on the driving force of the transport term
(Equation 4.9). For all experiments at constant temperature PDI values were quite close
and below 2, as expected for polycondensation reactions.[8]
Figure 4.6. Mole fractions of monomer and first linear oligomers for the reactions under
Nitrogen flow at different temperatures (runs 6-9): ○ 130 °C; ◊ 150 °C; □ 170 °C; x 190 °C.
Lines: model results.
79
a
b
c
d
Figure 4.7. Polymer average properties (a–b) and water (c) and lactide (d) concentrations for
the reactions under Nitrogen flow (runs 6-9): (○)130 °C, (◊) 150 °C, (□) 170 °C and (x) 190 °C.
Lines: model results.
The concentration profiles of water and lactide in melt phase are also shown in Figures
4.7, 4.8 and 4.9. Water concentration is invariably decreasing as required to establish
increasing extent of polycondensation. While large differences have been found for the
reactions at different temperatures, quite minor effect on the residual concentration of
water was observed at different stirring rates and pressures. About lactide, its
concentration profile is quite different at different reaction conditions: the cyclic dimer
exhibits a maximum value and such maximum is established at reaction extents which
correspond to number average molecular weights of about 200-300 Da. Such behavior
80
is quite peculiar and was not previously reported in the literature; it discloses new
process alternatives, where the recovery of lactide could be carried out already during
the pre-polymerization, with a significant reduction of the residence time of the prepolymer inside the reactor.
a
b
c
d
Figure 4.8. Polymer average properties (a–b) and water (c) and lactide (d) concentrations for
the reactions under vacuum at different stirring rates (runs 1, 4, 5): (○) 100 rpm, (□) 200 rpm,
(*) 400 rpm. Lines: model results.
81
a
b
c
d
Figure 4.9. Polymer average properties (a–b) and water (c) and lactide (d) concentrations for
the reactions at different pressures (runs 1-3): (○) 150 mbar, (□) 200 mbar, (*) 300 mbar. Lines:
model results.
Let us examine the model results in terms of liquid volume and cumulative
amount of condensed species. As shown in Figure 4.10 for run 4 in Table 4.1, both
quantities are nicely predicted by the model and similar agreements were found in all
reactions. It is worth to mention that other species were detected in the condensate
samples, i.e. lactide, dimer and trimer, but they were always present as traces. As
already mentioned, this result agrees with the volatility ranking reported in the
literature for these components.[11, 96]
82
a
b
Figure 4.10. (a) Volume change during the reaction (run 4). (b) Cumulative mass of volatiles:
(◊) water and (♦) monomer. Lines: model results.
Finally, let us comment the estimated values of the rate coefficients. The monomer
presents kinetic constant larger than that of longer oligomers; this finding is in
agreement with literature data on polymer degradation kinetics and it is related to the
formation of an ester bond close the polymer chain end group.[23] The same behavior
was anticipated in the previous chapter on polycondensation equilibria for lactic
acid.[88] Additionally, lactide is formed preferentially by end-biting reaction of the
linear dimer; therefore, lactide production is maximized when linear dimer production
is also maximized.
4.6 The impact of mass transport limitations on reaction kinetics
Finally, let us exploit the model prediction ability to analyse the role of the
transport resistances on the reaction evolution. This is conveniently done plotting the
calculated reaction trajectories on a “reduced” pseudo-ternary diagram, where vertices
correspond to monomer, water and all polymer species (from dimer on), respectively.
As discussed in the previous chapter,[88] the reaction path in such diagram is
83
represented by a trajectory quickly approaching the equilibrium curve if the reaction is
strongly affected by diffusion limitations; on the other hand, the reaction path remains
far from such curve (and then close to the binary sides of the triangular diagram) if the
reaction is slower compared to the removal of volatile species. Therefore, the operating
regime of the reactor is quite readily assessed looking at such trajectories at different
operating conditions.
As shown in Figure 4.11 for runs 4 and 7 of Table 4.1, the reaction trajectories
evolve from the initial state to large polymer contents quickly approaching and then
staying very close to the equilibrium curve. This is the case for the reaction carried out
under vacuum (run 4) but also for the one under Nitrogen flow (run 7), where more
effective removal of volatile species is expected. This behavior is a convincing proof of
the relevance of the mass transport limitations in all examined cases: a competition
between water removal and reaction kinetics is indeed operative and the first
phenomenon could easily be the rate determining step inside the explored range of
operating conditions. Note that the stirring rate is not as helpful as expected because of
its moderate impact on the value of the mass transport coefficient.
This is shown in Figure 4.12 for water: k x , w is weakly affected by stirring while
it decreases dramatically during the reaction due to the corresponding increase in
viscosity at increasing molecular weight. This is a confirmation that high molecular
weight cannot achieved under accessible operating conditions with reasonably small
reaction times, i.e. attractive productivity.
84
Figure 4.11. Reduced ternary system water (W) – monomer (M) – polymer (P). Lines:
equilibrium (solid line); reaction trajectory for run 4 (-.-); reaction trajectory for run 7 (--).
Experimental data: ○ run 7; □ run 4.
Figure 4.12. Calculated effect of stirring rate on the mass transport coefficient: □ 100 rpm; ○
250 rpm; ◊ 500 rpm; ■ 1000 rpm.
85
4.7 Conclusions
Lactic acid polycondensation in bulk was studied experimentally and theoretically. On
the experimental side, reactions have been performed at different conditions of
pressure, temperature and stirring rate. With respect to previous literature results, a full
characterization of the system composition in terms of water, lactide, monomer and
linear oligomers in both polymer melt and gaseous phases is provided combining
different analytical techniques.
On the modeling side, a comprehensive model of the reacting system, accounting for a
kinetic scheme involving all polycondensation reactions as well as lactide forming
reactions was developed. Transport limitations, chain length dependent reactivity and
volume change of the melt phase were considered in the model. In particular, the mass
transport coefficient was expressed as a function of product parameters (molecular
weight) and process conditions (temperature and stirring rate). All model parameters
have been evaluated from independent literature sources or by direct fitting of the
model predictions to experimental data.
The first achievement of this work is the complete set of rate constants at different
temperatures, thus contrasting the general lack of reliable values in the open literature.
As a second achievement, the significant impact of mass transport limitations at all
examined reaction conditions was indeed proved. This result is especially important
with two respects: first, the reliable evaluation of kinetic parameters in lactic acid
polycondensation needs a careful check of the operating regime, chemical or transport
limited; second, diffusion limitations should be carefully quantified when designing
large scale reactors in order to minimize residence times and maximize productivity.
86
Finally, the role of lactide forming reactions has been clarified. Even though such
reactions are indeed affecting the composition of the liquid phase at minor extent (of
course with the exception of lactide content), the major mechanism of lactide formation
was end-biting at all the investigated temperatures. Such finding could be helpful to
design the best conditions of the pre-polymerization reactor when this process step is
aimed to maximize lactide production.
87
88
Chapter 5. Kinetics of the Hydrolitic degradation
of Poly(Lactic Acid)
5.1. Introduction
In the past years, poly-lactic acid (PLA) acquired significant interest as hydrolytically
degradable, non-toxic material for carriers and devices used for drug delivery medical
applications. Degradation studies have been performed in different systems of interest,
such as nano and microparticles,[12] as well as tablets and suture threads.[13, 14]
Hydrolytic degradation affects mechanical properties and erosion mechanism of the
devices, thus strongly influencing release and targeting of the drug.[108] Moreover, its
excellent environmental compatibility combined with good mechanical properties
makes PLA one of the most attractive candidate to replace non-biodegradable oil-based
synthetic polymers in large scale production of consumables.[1, 3] Thus, degradation
kinetics is also interesting in the chemical industry for the polymer production and its
final composting. In general, polymer degradation is the result of the interplay between
chemical hydrolysis and water and oligomer diffusion.[15, 22]. To decouple these
effects, and thus to evaluate the hydrolytic degradation kinetics in the chemical regime,
degradation has been carried out in solution.[23, 24, 109-112]
Hydrolytic degradation of PLA is a strong function of pH, which can affect both
the degradation mechanism and kinetics. In particular, at neutral and basic pH it was
89
found that the degradation occurs preferentially through backbiting reactions, although
a minor contribution of random scission hydrolysis was observed.[23, 24] At acidic pH
it was shown by H-NMR measurements that the hydrolysis proceeds through a
preferential scission of the polymer end groups. In particular the kinetic constant of the
terminal groups was found to be 10 times larger than the one of the internal esters.[110,
113] The same result was obtained by Batycky et al.,[114] who found that the
difference in reaction rate between terminal and backbone esters is 4 fold. Similar
findings were reported by de Jong et al.,[23] without the evaluation of the two
degradation constants. On the other hand, Belbella et al. studied the degradation of PLA
nanospheres concluding that the degradation mechanism is a random chain scission
one.[115]
Other parameters affecting the degradation hydrolysis are temperature,
molecular weight and chain stereo-configuration. Different studies have been reported
in the literature suggesting Arrhenius-dependent kinetics, with activation energies in
the order of 10-25 kcal/mol.[116-118] On the contrary, Lyu et al. and Han et al.
reported that the degradation kinetic constant follows a Vogel–Tamman–Fulcher (VTF)
temperature dependence.[119, 120] The dependence of the degradation rate constant
upon the polymer molecular weight was investigated suggesting that the hydrolysis
constant decreases with increasing molecular weight.[121] On the contrary, Maniar et
al. reported that the rate of hydrolysis among the homologous series of oligomers
increases as the molecular weight increases.[122] Furthermore, chain stereoconfiguration, i.e. enantiomer composition, plays an important role being the
degradation faster the lower the crystallinity. For example, a maximum in hydrolysis
rate was found for a racemic polymer with a L/D composition equal to 50/50
mol%.[123]
90
The aim of this work is to develop a reliable kinetic model for PLA degradation
at acidic condition. This way, we try to clarify some of the issue listed above and in
particular to identify: i) the degradation kinetic scheme, ii) the influence of molecular
weight, iii) the dependence upon temperature and , iv) the effect of chain stereoconfiguration.
The degradation experiments were carried out at pH 2, starting from oligomers
of different chain lengths (n = 2 to 9) and chiral compositions (50% DL and 100 %LL)
within the temperature range 40 to 120 °C. As such, the experimental results cover
conditions of interest for both biomedical as well as chemical applications. The
considered oligomers are short enough to ensure complete solubility at all examined
conditions. In fact, as reported in a previous work in which description of oligomers
degradation in time has been characterized through HPLC, oligomers with less then 10
lactic acid units are fully soluble in water solution at pH=2 [71]. After employing the
aforementioned HPLC characterization, the obtained data were simulated considering
different reaction mechanisms, namely random chain scission and preferential chain
end scissions. Due to the wide experimental range of temperature considered, a reliable
evaluation of the different activation energies was possible along with a convincing
elucidation of the degradation mechanism.
5.2. Experimental part
5.2.1 Materials
L lactic acid 90% reagent grade and DL-lactic acid purum were supplied by Acros
Organics and Fluka, respectively. HPLC grade acetonitrile and orthophosphoric acid,
91
used for the HPLC analysis, were purchased from Fluka. Copper(II) sulphate
anhydrous 98% was supplied by Acros Organics. All reagents were used as received
without any further purification.
5.2.2 PLA oligomer synthesis, separation and degradation
PLA oligomers with chain lengths n = 2 to 9 were synthesized and collected following
a two steps procedure: low molecular weight PLA samples were produced by bulk melt
polymerization starting from L-lactic acid and a mixture of D and L lactic acid (50%
mol/mol). Next, the oligomers were separated through semi-preparative HPLC, using
the analytical procedure described in the next section. Namely, the polymer samples
were dissolved in acetonitrile at high concentration (0.4 g/l) and narrow fractions of
oligomers were collected. Finally, the degradation kinetics of the individual oligomers
was investigated.
The polycondensation reactions were carried out without catalyst for 10 h at 150oC in a
round bottomed glass flask under nitrogen flow. The reaction temperature was set low
enough to limit the formation of side products, such as cyclic compounds.[10] The
resulting polymers exhibited a relatively broad molecular weight distribution
(polydispersity of 1.7), and a number average molecular weight close to 500-600 Da.
It is worth noting that the oligomers collected by gradient semi-preparative HPLC are
dissolved in solutions with different acetonitrile-water compositions. In order to avoid
any error due to the presence of the organic solvent, all the collected samples were
diluted in water acidified with phosphoric acid (pH = 2), to the same volume fraction of
acetonitrile equal to about 3% (the acetonitrile content was measured by gas
chromatography analysis as described in Appendix A). This concentration of
acetonitrile was selected because appeared to affect the degradation kinetics at
negligible extent, as reported in detail in Appendix A.
92
After dilution, the oligomer concentration is low enough to avoid any backward
reaction and high enough to be easily detected by HPLC.
The hydrolysis reaction of each individual oligomer was investigated at different
temperatures in closed glass vials heated by means of an electrical oven (accurancy ±
3oC). The degradation products were characterized by RP-HPLC analysis. Samples
were collected at different times during the hydrolysis reaction and once more
characterized by HPLC as described above. To investigate the occurrence of
racemization reactions, the same samples were also analyzed by chiral chromatography.
5.2.3 Reverse Phase HPLC analysis
The concentration of the polymer chains of any given length in a polymer sample was
measured by gradient HPLC following the procedure detailed in a previous work for
the LL species[71]. As reported in Appendix A, the calibration factors were found to be
independent on the oligomer stereo configuration, and thus the same procedure is
applied for all species. The analysis was carried out using an Agilent 1200 series
apparatus, equipped with 2 Agilent Eclipse XDB C18 columns (3.9mm×150 mm,
particle size 3.5 μm) and UV detector (constant wavelength at 210 nm). The mobile
phase was a mixture of water and acetonitrile, acidified with phosphoric acid (0.1%
v/v). The column oven temperature was 40 ◦C and mobile phase flow rate was 1
mL/min. A gradient operating mode was applied, with the following gradient profile:
initial adsorbing conditions with mobile phase at 98% v/v water; after 2 min, the
acetonitrile concentration was ramped linearly to 60 % v/v in 25 min; then, it was
changed to 100% v/v and maintained constant for 5 min and finally back to 98 % v/v
water in a step change.
93
5.2.4 Chiral HPLC analysis
The separation of the isomers of L and D lactic acids has been carried out using a
Chirex 3126 (D)-penicillamin (Phenomenex) column (length 150 mm, internal
diameter 4.6 mm and 5 μm particles) mounted on the same HPLC apparatus described
above. A mixture of Copper(II) sulfate 3mM was used as eluent at flow rate of
1ml/min. As shown in Figure 5.1a, the elution times of the two isomers were identified
by injection of L-LA and the racemic mixture of D and L-LA. Since the chromatogram
of the racemic mixture showed that the ratio between the areas of the two isomers is
equal to 1, the same calibration factors were used for both species.
5.3. Results and Discussion
The hydrolytic degradation kinetics of PLA has been investigated as a function of
oligomer chain length, temperature and chiral composition. As described in Section 5.2,
oligomer mixtures were fractionated by HPLC, and the collected oligomers were
separately degraded at acidic conditions (pH = 2) and different temperatures (from 40
to 120oC). As an example, the chromatograms of the initial pentamer, LA5, and its
degradation products after 6 hours of reaction are shown in Figure 5.2. Given the
calibration factors, the concentration profiles of the initial oligomer and its degradation
products have been evaluated as a function of time as shown in Figure 5.3.
In order to verify that pH was constant during all the reactions, a preliminary
test was run by adding L-LA to an aqueous H3PO4 solution at pH 2. The concentration
of LA was 0.01 mol/l, i.e. 5 times larger than the maximum value measured after the
hydrolysis of the longest oligomer investigated. No change in pH was found, thus
confirming that pH remains constant during all the considered hydrolysis reactions.
94
It is worth noting that, since the experiments are in batch mode, the first order moment
of the molecular weight distribution (i.e. the total number of monomer units) is
constant. For all experiments in this work this condition was fulfilled with an error of ±
2%. This number provides a reliable estimate of the experimental error for all data
reported in this work.
In the following we discuss all the collected results: while the results for the LL
oligomers cover the entire temperature range mentioned above, the effect of chirality is
analyzed in a narrower temperature range (40 – 60 °C).
a
b
Figure 5.1. Chiral HPLC chromatogram of: (a) L lactic acid (dashed line) and DL lactic acid
(solid line) monomers; (b) degradation products of LL (dashed line) and DL (solid line)
oligomers with chain length equal to 5. Degradation experiments performed at 60 °C.
95
a
b
Figure 5.2. HPLC chromatograms at (a) t = 0 and (b) 6 h for the hydrolysis of LA5 at 80oC.
5.3.1 The Random Chain Scission mechanism (RCS)
According to this reaction mechanism the degradation of a PLA oligomer with chain
length n occurs by hydrolysis of the ester bonds in the polymer backbone which all
exhibit the same reactivity whatever their position. Due to the high dilution of the
sample in water, the hydrolysis reaction can be considered irreversible and the
corresponding scheme becomes:
kd
LAn  W 
 LAi  LAn i
96
(5.1)
where LAn indicates an oligomer with chain length n, kd the hydrolysis rate constant
and W a water molecule. The material balance of the generic n-th oligomer is:
dCn
 2kd CW
dt

C
f  n 1
f
 (n  1)kd CW Cn
(5.2)
where Cn is the concentration of the species with chain length n and CW the
concentration of water. This last species, being present in large excess, is considered
constant in time.
Figure 5.3. Oligomer concentrations as a function of time during the degradation of LA5 at
80oC. Experimental results: C5 (□), C4 (*), C3 (+), C2 (o), C1 (x).
In all experiments, the initial conditions were evaluated by HPLC after dilution of the
selected oligomer and a few minutes of temperature conditioning in the oven at the
selected temperature. Therefore, the degradation process never started from a solution
of the pure oligomer but from the set of initial concentrations measured by HPLC,
which therefore accounts for trace amounts of shorter oligomers formed during the
sample pre-treatment.
97
Focusing on the major component in the system (the initial oligomer), its material
balance reduces to the consumption term and can be integrated in time leading to:
C 
ln  n0   (n  1)kd CW t
 Cn 
(5.3)
and the rate coefficient kd for each individual oligomer is readily evaluated from the
experimental data independently of the degradation kinetics of the other species. The
experimental data corresponding to Equation 5.3 are shown in Figure 5.4 at two
selected temperatures and for four oligomers of different length.
a
b
Figure 5.4. Natural logarithm of the concentration ratios during the degradation at (a) 40 oC and
(b) 100 oC of oligomers with different chain lengths ( C8 (◄), C6 (◊), C4 (■), C2 (o)).
98
The linearity of the experimental data supports the assumption of negligible
autocatalytic effect: despite the increase of the concentration of carboxylic groups
during degradation, no change in the reaction rate is observed in the whole temperature
range studied. This means that at constant, acidic pH of the solution, the dissociation of
the carboxylic groups is irrelevant and non-detectable, in agreement with the results
reported in the literature for ester hydrolysis in the presence of an additional acid.[109]
The corresponding values of the constants, kd , estimated for each chain length are
reported in Figure 5.5 and Table 5.1.
It is seen that, contrary to the assumption of RCS mechanism, the value of the rate
constant kd changes with the oligomer chain length. In particular, it is larger for shorter
chains and becomes almost independent of the chain length for oligomers longer than 7
repeating units.
Table 5.1. Values of hydrolysis rate constant, kd,n, estimated at 40, 50, 60, 80, 100 and 120 oC
(l/mol/h).
kd,n . 105
(50 °C)
23.4
kd,n . 105
(60 °C)
45.4
kd,n . 102
(80 °C)
kd,n . 102
(100 °C)
kd,n . 102
(120 °C)
2
kd,n . 105
(40 °C)
8.5
0.28
0.75
2.30
3
6.0
18.1
31.7
0.13
0.44
1.69
4
4.4
12.2
23.8
0.10
0.32
1.18
5
4.0
11.1
29.7
0.07
0.26
0.86
6
3.3
8.5
17.2
0.07
0.21
0.69
7
3.2
8.5
15.1
0.04
0.17
0.65
8
2.6
6.6
13.5
0.05
0.19
0.75
9
-
-
-
0.05
0.16
0.55
Chain
length
99
a
b
Figure 5.5. kd ,n estimated at different temperature as a function of chain length: (a) ■
80 °C, ● 100 °C and ♦ 120 °C; (b) ■ 40 °C, ● 50 °C and ♦ 60 °C.
5.3.2 The Preferential Chain End Scission mechanism (PCES)
In order to overcome the difficulties of the RCS mechanism discussed above, a model
accounting for the different reactivity of the ester groups depending on their position
along the chain was adopted based on the observation of Shih.[110] In particular,
according to the Preferential Chain End Scission mechanism (PCES), two types of ester
groups with different reactivity were postulated: α-esters, the groups close to hydroxyl
100
or carboxyl chain end groups, and β-esters, all the other ester groups in the polymer
chain backbone as sketched in Figure 5.6.
Figure 5.6. Definition of α- and β-ester groups along the PLA chain.
Accordingly, the following expression of the overall degradation rate constant, kd ,n , for
a generic oligomer of length n can be proposed:
k d ,n
2kd  ( n  3)kd

n 1
n3
(5.4)
This equation is a simple average of the two rate constants weighed on the
corresponding number of reacting sites. It is worth noticing that Equation 5.4 predicts
the same behavior identified experimentally (Figure 5.4): as chain length increases, the
ratio between the numbers of α and β esters along the chain backbone decreases and,
therefore, the impact of k d (corresponding to the most reactive groups) on the overall
degradation constant becomes smaller and smaller; for long enough chains, kd ,n
becomes practically constant and equal to k d . Of course, such expression applies to
chain lengths larger than 2: the linear dimer represents an exception since, due to the
close vicinity of the chain end groups, it could in principle exhibit a different reaction
101
rate constant, kd ,2 (evaluated through equation (5.3)). In this frame, the hydrolysis
reactions of oligomers longer than 2 units are sketched as follows:

kd
LAn  W 
 LA1  LAn 1

kd
LAn  W 
 LAn i  LAi
n3
n3
(5.5)
i  2, 3.., n  2
(5.6)
The corresponding material balances are:
dCn
 2kd Cn 1Cw  2Cwkd
dt

C
f n 2
f
 2kd CwCn  (n  3)kd CwCn
n3
(5.7)
while for shorter oligomers, the following specific balances are considered:

dC1
 2kd ,2CwC2  2Cw kd  C f
dt
f 3
(5.8)

dC2
 2kd C3Cw  2Cw kd  C f  kd ,2CwC2
dt
f 4
(5.9)
The PCES mechanism involves only three parameters, kd ,2 , k d and k d , instead of the
multiple chain length specific rate coefficients of the previous RCS mechanism. The
value of k d and k d at each temperature were estimated by fitting the experimental data
of oligomers longer than two and they are listed in Table 5.2. The value of the overall
average relative error was about 13%.
As expected, k d is larger than k d in agreement with the key assumption
underlying the PCES mechanism. Both k d and k d conform to Arrhenius temperature
dependence as shown in Figure 5.7, with activation energies equal to 17.5 and 14
kcal/mol and pre-exponential factors of 8.21·107 and 1.77·105 l/mol/h, respectively.
These values are within the range of 10-25 kcal/mol were previous values reported in
the literature are also included,[116-118, 121, 124] while the proposal that the
102
degradation rate constant follows a Vogel–Tamman–Fulcher (VTF) temperature
dependence is not confirmed.[119, 124]
Table 5.2. Values of the kinetic rate constants k d and k d at 80, 100 and 120 oC (l/mol/h).
T
°C
k d 105
l/mol/h
k d 105
l/mol/h
40
4.5
2
50
12
8
60
22.5
11.8
80
84
34
100
355
123
120
1450
355
From the Arrhenius plots in Figure 5.7 it is seen that the difference between k d
and k d is due to the large difference between the pre-exponential factors more than to
that between the activation energies (larger in the case of α ester bonds). Similar
conclusions has been reached for the ester bonds hydrolysis in acidic conditions:[125]
the corresponding activation energy (involving two transition states) is in fact only
slightly affected by the atoms surrounding the ester bond, while the steric effect is
predominant in discriminating the reactivity in different solvents. In the specific case
under examination, the larger probability of hydrolysis of the α ester groups can be
attributed to the presence of two hydrophilic chain end groups (carboxylic and
hydroxylic) enhancing the rate of hydrolysis of the ester groups close to them.
Finally, the predictions of two models based on the RCS and PCES kinetic
mechanisms, respectively, are compared to the concentration values of the various
oligomers as a function of time for a selected reaction in Figure 5.8. As expected, no
103
difference between RCS and PCES models are observed for the longest oligomer
degradation. However, the PCES model gives better predictions for all shorter
oligomers. It is worth noticing that by looking only at the monomer function kinetics it
would not be possible to discriminate between these two models.
Figure 5.7. Arrhenius plot of k d (□) and k d (◊) for LL (open symbols) and DL (solid
symbols) oligomers.
5.3.3 Effect of chiral composition
The dependence of the degradation kinetics upon oligomers chiral composition was
investigated experimentally in the temperature range from 40 to 60 °C by studying the
degradation kinetics of racemic DL oligomers. The DL polymer samples were
produced by polycondensation of a mixture of D and L lactic acid 50% w/w, as
reported in section 5.2.
104
The occurrence of racemization during polycondensation has been excluded by
analyzing the degradation products of LL and DL oligomers through analytical chiral
chromatography. As an example, the chromatograms obtained in the case of LA5
hydrolysis are shown in Figure 5.1b. While in case of LL oligomer degradation only
the peak of L-LA is found, L-LA and D-LA peaks with similar areas are found for the
DL oligomer. This finding suggests that configurational rearrangements during
polycondensation and hydrolysis are negligible.
Following the same procedure applied above for the LL oligomers, the
degradation rate constants k d and k d compatible with the PCES model have been
evaluated for the DL oligomers. The values of the corresponding rate constants are
compared in Figure 5.7 with those relative to the LL oligomers. It can be seen that all
values are quite similar whatever the examined stereo-configuration, thus suggesting
that the chiral composition does not affect the degradation kinetic to any significant
extent. Experimental data obtained by studying the hydrolytic degradation of
macroscopic devices suggested that hydrolysis reactions are strongly influenced by the
isomer composition.[116] For example, Fukuzaki et al. [123] pointed out that the
hydrolytic degradation of PLA plates is faster the larger the amount of D-LA. The
highest rate of hydrolysis rate was found for a racemic PLA with L/D composition
equal to 50/50 mol%.[123] This apparent contradiction can be explained by considering
the role of mass transport resistances which are most likely significant in macroscopic
objects.
105
Figure 5.8. Concentration profiles of the different oligomers during degradation at 100 °C of
LA8. Symbols: experimental data; lines: RCS (dashed) and PCES (continuous line) models.
106
Since the degradation kinetics is a function of the local water concentration in
the polymer object,[15, 126] and water diffusion is strongly affected by the crystallinity
of the polymer, crystalline and amorphous PLA devices degrade with rather different
characteristic times. Thus, DL polymers with a majority of amorphous domains
enhances water uptake and therefore degrades faster than LL ones. However, when
transport limitations are removed, as it is the case of the aqueous solutions considered
in this work, it is found that the degradation rate constants are not affected by the
stereo-configuration of the reacting chains.
5.4. Conclusions
A comprehensive study of the hydrolysis kinetics of water soluble PLA oligomers in
solution was carried out at temperatures in the range 40 to 120 °C and acidic pH
conditions for various chain lengths, ranging from 2 to 9 repeating units. First,
degradation experiments starting from single oligomers were performed. It was found
that oligomers shorter than a critical chain length exhibit larger degradation rates than
longer ones, while, above this threshold length, the reactivity becomes independent of
chain length. In order to further investigate this behavior, a kinetic model was adopted
where the ester groups along the PLA chain are classified as α- and β-ester, being the
first ones the ester groups close to the hydroxyl and carboxyl chain end groups and the
second ones all the others, i.e. the so called preferential chain end scission mechanism.
Based on this assumption a relation is developed for evaluating the hydrolysis rate
constant of oligomers of any length as a function of only two parameters, i.e. the
hydrolysis rate constants of the ester groups α and β ( k d and k d ). For the special case
of the dimer, the corresponding hydrolysis kinetic constant is evaluated directly from
107
experimental data. This model can be applied to predict the hydrolysis of polymer
chains of any length. Activation energies of 17.5 and 14 kcal/mol and a pre-exponential
factors of 8.21·107 and 1.77·105 l/mol/h have been estimated for
k d and k d ,
respectively. All experimental data are reproduced with an average relative error of
about 13 %. The obtained data indicate that, the higher reactivity of the ester groups
close to the chain end groups with respect to those inside the oligomer chain has to be
attributed to a favorable steric effect caused by the hydrophilic nature of the chain end
groups more than to a difference in the activation energies.
Finally, it was shown that the hydrolysis kinetic is not affected by chirality
suggesting that the differences reported in the literature in the degradation of
macroscopic objects are most probably due to differences in the mass transport
resistances in turn due to different degrees of crystallinity in the polymer matrix.
108
Chapter 6. A comprehensive study on PLA
nanoparticles production by flash - nanoprecipitation
6.1
Introduction
In the last decades, degradable polymeric nanoparticles (NPs) attracted large attention
in the literature with respect to their production, functionalization, stability and
degradation path.[15, 25-28] In particular, due to their high versatility, biocompatibility
and bioavailability, they have been employed in pharmaceutical applications such as
drug delivery systems for the administration of hydrophilic as well as hydrophobic
active compounds and as targeting and imaging agent nanocarriers.[29-33] Their
pharmacological use may modify the drug’s absorption, distribution, metabolism and
excretion [127] leading to a great number of benefits. The tissue specific delivering of
drug, with a consequent improvement of drug efficacy and reduction of side effects
[128], is of enormous importance when handling with highly toxic compounds, such as
anti-cancer drugs. [129] In general, polymers used for this applications are
biodegradable polyesters, such as polylactic acid (PLA), polyglycolic acid (PGA),
polycaprolactone (PCL) and their copolymers, as well as other polyesters based
materials such as PEG block copolymers and therapeutics conjugates. [34-39]
Different methods of production using preformed polymers have been reported and can
be classified mainly as emulsion-based methods and solvent displacement techniques
or precipitation. In the first case a solution of the polymer in a good solvent is first
109
emulsified in a suitable non-solvent and then NPs precipitation is obtained by solvent
evaporation or dilution of the emulsion, leading to diffusion of the good solvent from
the dispersed phase into the continuous phase. In the case of solvent displacement
methods the polymer is dissolved in a solvent which is fully miscible with water and
particle formation occurs when the organic phase is mixed with water (non-solvent)
through spontaneous dispersion.[36] Compared to emulsion based methods, particles
formation through precipitation is accompanied by lower particle volume fraction and
thus a subsequent concentration step is required.[130] In all cases, solvent displacement
is a fundamental aspect for the final application and ultracentrifugation and
ultrafiltration followed by freeze drying are usually applied as post treatments to
remove the organic solvents and store the produced NPs. On the other hand, such
purification steps are very expensive, time demanding and limited by aggregation
phenomena during drying, especially at large production scale. Alternative solutions
have been proposed, such as are the use of supercritical fluids extraction to enhance the
organic solvent removal and hydrogen bonding coacervate precipitation (HBCP),
which, using polyelectrolytes, allows NPs concentration and drying through reversible
aggregation.[131]
In the frame of this thesis the attention is focused on the particle production by
precipitation. Despite the large number of experimental and modeling studies reported
in the literature, the mechanisms of NPs formation still need to be fully clarified.
According to one school of thought, similarly to crystallization, particles formation
occurs through nucleation, growth and aggregation phenomena.[132, 133] A second
approach is instead based on the formation of polymer rich droplets dispersed in the
non-solvent phase driven by different interfacial phenomena, i.e. spontaneous droplet
formation, spinodal decomposition, interfacial turbulence. In particular, Vitale and Katz
110
[134] proposed that a dispersion of organic phase droplets in water is formed by
homogeneous liquid-liquid nucleation when the miscibility limit of the ternary system
solute/solvent/non-solvent is crossed (binodal line) entering the metastable zone
between binodal and spinodal line also called “Ouzo region”. Brick et al.[135] reported
that when the solvent and non-solvent phases are mixed, mixing inhomogeneity results
in a first dispersion of small droplets which then by counterdiffusion of solvent and
non-solvent leads to nanoparticles formation through spinodal decomposition. Fessi et
al.[136] investigated the formation of PLA NPs by pouring a solution of polymer
dissolved in acetonitrile into water. The authors suggest that particles formation
involves interfacial hydrodynamic phenomena. At the solvent non-solvent interface a
gradient of interfacial tension determines an unbalance of forces which generates
interfacial turbulence with formation of small droplets. Polymer precipitation occurs by
solvent diffusion from the droplets to the continuous phase. This effect is referred to as
the Marangoni effect.[137] In polymer NPs formation studies, different mixing
condition have been investigated ranging from polymer solution dropping and pouring
procedures,[136, 138] to the use of high performance devices like impinging jet and
vortex mixers.[132] When mixing is done with high performance mixers, the process is
called
flash-nanoprecipitation
because
of
the
possibility
of
creating
high
supersaturation conditions over a time scale shorter than the characteristic time of
particles formation.[139]
In the frame of these considerations, this chapter deals with the precipitation of
PLA nanoparticles in a multi-inlet vortex mixer (MIVM). A systematic investigation of
the impact of selected parameters, such as polymer concentration and molecular
weight, surfactant concentration, mixer geometry and flow rates of organic and water
stream, was carried out. Moreover, alternative feeding strategies of the polymer
111
solution were tested giving new insights on the NPs precipitation process. The effect of
these operating parameters on NPs size distribution, -potential and morphology was
thoroughly characterized with various analytical techniques, i.e. dynamic light
scattering (DLS), electrophoretic mobility measurement, transmission electron
microscopy (TEM) and scanning electron microscopy (SEM). The outcomes of the
experimental study are analyzed in the light of the particles formation paths proposed in
the literature.
6.2
Materials and methods
6.2.1
Materials
For the poly-(DL-lactic acid) synthesis (hereafter referred to as PLA), DL lactide
was purchased from PURAC (The Netherlands), DL-lactic acid from Fluka (purum
~90%) and 2-ethylhexanoic acid tin (II) salt (Sn(Oct)2 95% purity) from Sigma Aldrich.
Methyl methacrylate (MMA) and Azobisisobutyronitrile (AIBN) used in PMMA
synthesis were purchased from Acros Organics. Tween® 80 was obtained from Fluka
and the solvents, THF, toluene and dichloromethane, from Sigma Aldrich. Uranyl
acetate used as staining agent for TEM imaging was purchased from Fluka. All
reagents were used as received without further purification.
6.2.2 Polymer synthesis and characterization
PLA samples were synthesized in bulk by ring opening polymerization (ROP) of
DL lactide catalyzed by SnOct2 and initiated by DL lactic acid. Since ROP of lactide is
a semi-living process characterized by reversible catalyst activation, samples with
different molecular weights were obtained by varying the catalyst to co-catalyst ratio,
112
as reported in Table 6.1 [58]. Briefly, 25 g of lactide were melted at 130 °C in a close
100 ml glass flask. The temperature was controlled by means of an external oil bath.
Then, catalyst and co-catalyst were added and the reaction was carried out overnight.
The polymer was finally purified by dissolution in dichloromethane and precipitation in
toluene in order to remove low molecular weight species such as residual monomer,
impurities and reaction side products [140].
Table 6.1. Recipes and GPC characterization for the PDLLA samples investigated. Sample Catalyst Co‐catalyst Mn PDI (g) (g) (kDa) (‐) S1 0.07 0.113 13 2.5 S2 0.07 0.056 25 2.0 S3 0.07 0.034 35 2.4 S4 0.07 0.017 89 2.1 The molecular weight of PMMA as measured by GPC was 160 kDa with PDI equal to 2.5.
Methyl methacrylate (MMA) was polymerized in bulk, adopting the same
equipment used for PLA samples. The reaction was initiated by AIBN (0.07 g in 30 ml
monomer) and run at 70 °C for 4 hours. Polymer molecular weight distributions were
characterized by SEC (Agilent, 1100 series) equipped with two detectors, ultraviolet
and differential refractive index. A pre-column and two PLgel 5 μm MIXED-C
113
columns (polymer Laboratories (USA), length of 300 mm and diameter of 7.5 mm,
measuring range: 2,000-2,000,000 Da) were employed. Chloroform was used as eluent
at a flow rate of 1 mL/min and temperature of 30°C. The molecular weights reported
are relative to poly(styrene) standards.
6.2.3
NPs flash nanoprecipitation
Polymer NPs preparation was performed by first dissolving the polymer in the
organic solvent (THF) and then mixing this solution with water (non-solvent). The
polymer weight fraction in THF ( wp ) was varied from 0.01 to 4% w/w. The process
was carried out in a multi inlet vortex mixer (MIVM) with four inlets (setup shown in
Figure 6.1 A-D). Adopting the configuration reported by Liu et al.[139], the mixer
housing was modified by insertion of a polyether ether ketone (PEEK) plate on which
the mixer geometry was designed (see Figure 6.1 B). In particular, the size of the inlet
streams, having squared cross section, was varied from 1 to 1.5 mm and in the next part
the two configurations are addressed as DISC_1 and DISC_2, respectively. Two water
and two organic streams are fed in alternate sequence in the vortex mixing chamber
where they are tangentially mixed and discharged through the outlet, (see 6.1 D) which
was connected to a metal tube. Different lengths of outlet tube, from 1 to 50 cm, were
tested. While the organic streams were fed by means of polypropylene 20 ml syringes
(B. Braun Injeckt®), 120 ml syringes (Exelmed®) were used for water.
Polytetrafluoroethylene (PTFE) capillaries with 1 mm inlet diameter were used to
connect the syringes to the mixer inlets. The flow rate of all inlet streams was
controlled by means of infusion syringe pumps (VitFit, Lambda, Switzerland). Water
and organic phase flow rates were varied in the ranges from 40 to 100 mL/min and
from 4 to 10 ml/min, respectively.
114
Figure 6.1. (A) Experimental setup configuration, (B) Zoom of MIVM, (C) PEEK inserts used,
(D) sketch of a flow inlet mixing configuration.
According to Liu et al. [139] the fluid flow regime inside MIVM can be
characterized by Re number defined as:
Re 
Qi
 vr
i 1, N
2
D
(6.1)
i
where vi is the kinematic viscosity of the ith stream,
D
is the chamber diameter (equal
to 6 mm), r is the dimension of the inlet channel (square cross sectional area with size
characteristic of the used disc) and Qi is the flow rate of the ith component.
After starting the experiment, a transition time of 1 min was employed before
sample collection to allow the system to reach steady state conditions. The sample was
then collected at the outlet of the metal tube in a beaker filled with water. This way, the
115
system was diluted by a factor 10 to prevent the occurrence of aggregation phenomena
after NPs precipitation.
6.2.4
Nanoparticles suspension characterization
NPs size distribution was characterized by Zetasizer Nano instrument (Malvern,
U.K.) using standard disposable polysterene cuvettes (Plastibrand®). The mean
hydrodynamic diameter was obtained by fitting the autocorrelation function with the
cumulant method. It is worth noting that when referring to average particles size, the average value is adopted. Polydispersity index (PDI) used to characterize the particle
distribution broadness is defined as:
PDI 
R4 R6
1
R52
(6.2)
where Ri is the ith moment of the particle size distribution. To characterize the NPs
surface charge, the electrophoretic mobility, e , was measured in the presence of
electric field using a Zetasizer Nano instrument operating in PALS (phase analysis light
scattering) mode. Consequently e was converted to the -potential using the
dispersant viscosity applying the Smoluchowski theory [141, 142]. It was verified that
the concentration of THF after sample dilution was low enough to not affect the
measurements. Gas chromatography was applied to monitor the removal of THF from
the PLA NPs latexes. The analysis was carried out using a Hewlett Packard gas
chromatograph HP6890 apparatus, equipped with a crosslinked 5% PH ME Siloxane
HP column (USA) (30 m x 0.3 mm x 0.25 µm) and TCD detector. Helium was used as
carrier gas at a flow rate of 10 ml/min. The injector and detector temperatures were 250
°C and the column temperature was maintained at 60 °C for 10 minutes and then raised
to 250 °C in 20 minutes. The calibration of the solvent peak was carried out by
116
injecting THF water mixtures with a known amount of THF. Transmission electron
microscopy (TEM) was used to evaluate the NPs morphology. One drop of the NPs
suspension was deposited on a 400 mesh copper grid covered by a Formvar®/Carbon
film supplied by Quantifoil Micro Tools GmbH. After thirty seconds the droplet was
removed and, if required, staining with uranyl acetate was carried out. Images of the
slices were made with a FEI Morgagni 268 transmission electron microscope (FEI
Company, USA). Since under some conditions flocculation occurred, the flocks were
characterized by SEM analysis. SEM pictures were recorded by a Zeiss Gemini 1530
FEG.
6.3
Results and discussions
As previously mentioned, PLA NPs production by flash nanoprecipitation in
MIVM was systematically studied by evaluating the effect of selected parameters on
the process performances. All results obtained in the experimental campaign are
discussed based on the role of mixing, polymer concentration and molecular weight,
and the effect of alternative feeding strategies of the polymer solution. The
experimental findings are analyzed in the frame of the particles formation mechanisms
proposed in the literature.
6.3.1
The role of mixing
The impact of mixing on the NPs production process has been investigated as a
function of mixer outlet tube length, mixing chamber geometry and water (W) and
organic (O) streams flow rates. In particular, the tube length was varied from 1 to 50
cm and two different discs with inlet diameters of 1 mm (DISC_1) and 1.5 mm
117
(DISC_2) were tested. The streams flow rates were changed as follows: at constant
water flow rate varying the THF one (series A: W = 100 ml/min; O = 4-8-10 ml/min ),
at constant THF flow rate varying the water one (series B: O = 10 ml/ min; W = 40-80100 ml/min) and by varying both THF and water flow rates keeping constant the ratio
between the two (series C: W= 40-80-100 ml/min; O/W = 0.1). In all these experiments,
sample S3 (Table 6.1) was used as polymer at w p equal to 0.5 % w/w. The effect of the
outlet tube length was tested with 1.5 mm inlet diameter disc and water and organic
flow rates equal to 40 and 4 ml/min, respectively. It was found that stable NPs, with potential around -50 mV, diameter of 118 ± 2 nm and PDI equal to 0.13 ± 0.02 were
produced independently on the outlet tube length, thus suggesting that NPs
precipitation is completed within the mixer. Based on this result, the experiments on
streams flow rates and mixer geometries were performed with outlet tube length equal
to 10 cm. For the different mixing conditions, the obtained results in terms of average
NPs diameter and PDI are reported in Figure 6.2 as a function of Reynolds number
evaluated as in Equation (6.1). It was found that NPs with average diameter of about
120 nm and with narrow PDI in the range of 0.08-0.13 were produced independently on
mixer geometry and water and organic flow rates, suggesting that, within the
investigated experimental range of Reynolds numbers, the nanoprecipitation process is
not controlled by mixing. This finding is in agreement with the results reported by Liu
et al.[139] on the study of the characteristic mixing time in MIVM based on the Bourne
reaction.[143] For Reynolds number larger then 2000, no mixing control condition was
established. Similar findings were also reported for poly-ε-caprolactone NPs
precipitated by means of a confined impinging jets mixer when operating at high flow
rates.[132]
118
a
b
Figure 6.2. Effect of Re on NPs size (a) and PDI (b). For all experiment polymer (S3 from
Table) was dissolved in THF at w p equal to 0.5% w/w. (○) A series, (□) B series and (◊) C
series performed using DISC_1, (♦) C series run with DISC_2.
An additional finding coming from this set of experiments is related to the effect
of the polymer concentration in the system. Being the polymer weight fraction in the
organic phase constant, the overall polymer concentration changes after mixing for
series A and B while it is constant for series C. The fact that no influence of the overall
polymer concentration on NPs size is observed is a hint for the discrimination of the
particles formation path.
119
A commonly adopted parameter used when dealing with precipitation processes
is the supersaturation parameter, S, which is defined as:
S
C
C*
(6.3)
where C and C* represent the overall polymer concentration in the system and its
maximum solubility in the specific water/organic mixture, respectively. While the
polymer concentration ( C ) is evaluated knowing the polymer weight fraction in THF
and the flow rates of THF and water streams, it is difficult to determine with accuracy
the polymer solubility limit ( C * ) since it is a specific function of polymer properties
and mixture composition in terms of solvent and non-solvent ratio. When comparing
the solubility data reported by Lince et al. [132] for poly-ε-caprolactone and those
measured by Brick et al. [135] for cyanophenyl furanone dye, it is found that, despite
the different nature of the solutes, comparable results are obtained. Therefore, the data
reported by Lince et al. [132] were used to estimate the polymer solubility limit for the
system here studied. It was found that for the A series S decreases with increasing the
THF flow rate approximately by a factor of 1.7 while for the B series S increases
approximately by a factor of 8 with increasing the water flow rate. Overall this results
in a total variation of S approximately by a factor of 14.
In the frame of the classical crystallization theory, the supersaturation parameter
directly influences the nucleation and growth rates and thus, being the flow condition
investigated such that the influence of mixing on the precipitation process is negligible,
it is expected that NPs size varies considerably for the different experiments
performed.[144] Despite the large change in supersaturation no differences in NPs
average size was found, thus suggesting that supersaturated condition is of course a
120
prerequisite for NPs precipitation but it is not the main parameter influencing the
process. It is worth noting that this conclusion is in agreement with results presented by
Fessi et al. and Brick et al..[135, 136]
As discussed in the Introduction, different literature works suggest that when
solvent and non-solvent phases are mixed, the solvent disperses in the non-solvent
phase in the form of droplets rich in polymer. Then, the NPs precipitation occurs when
the solubility limit of polymer inside the droplet is reached due to the interdiffusion of
solvent and non-solvent from the droplet to the continuous phase.[135] Notably, if the
droplet formation is governed by mixing, the initial droplet size should depend on the
hydrodynamic conditions investigated, thus showing a strong impact on the final
particles size. For example, when considering the two limiting conditions of Reynolds
number investigated, i.e. 2,000 and 12,000, the Kolmogorov microscale varies from
about 38 to 13 microns, respectively. When assuming Kolmogorov microscale as an
estimation of the minimum size of the formed droplets, one would expect also large
variation of the formed NPs. However, as can be seen from Figure 6.2, no change in
NPs size was found, thus indicating that the formation of NPs is not controlled by the
hydrodynamic conditions but by different phenomena. It is found in the literature that
droplets dispersion can occur through different interfacial phenomena, i.e. binodal or
spinodal decomposition of the mixture and unbalance of interfacial tension forces
(Marangoni effect). In all cases, the size of the formed droplets is in the nanometer
range. In the frame of these theories, the final particle size is influenced by the
concentration of polymer in the dispersed solvent droplets and thus by the initial
concentration of polymer in the organic phase. This point is further verified in the next
section.
121
a
b
Figure 6.3. Effect of PLA w p on NPs particles size distribution. (a) wp equal to ● 0.1 % w/w ,
◊ 0.25 % w/w, ■ 0.5 % w/w, o 0.75 % w/w and ♦ 1 % w/w. (b) w p equal to 0.01 % w/w:
precipitation performed in water (solid line) and in 0.01% Tween® 80 water solution (dashed
line). Water and THF flow rates were 100 ml/min and 10 ml/min, respectively.
122
a
b
Figure 6.4. Effect of PLA wp on average particle size (a) and -potential (b). Symbols:
precipitation performed in water (o) and in 0.01% Tween® 80 water solution (x).Water and
THF flow rates were 100 ml/min and 10 ml/min, respectively.
123
6.3.2
The effect of polymer concentration in the organic phase
It is reported that NPs size strongly depends on the polymer concentration in the
organic phase.[36] In order to investigate this aspect, the weight fraction of polymer in
THF was changed in the range from 0.01 to 4% w/w. All the experiments reported in
this section were run with the PLA sample S3 while the THF and water flow rates were
kept constant and equal to 10 ml/min and 100 ml/min, respectively. The obtained
results in terms of average particle diameter, size distribution and -potential are
reported in Figure 6.3 and Figure 6.4. Stable NP suspensions were produced in the w p
range from 0.1 to 1% w/w. As shown in Figure 6.3 a, within this concentration range,
the particle size distribution moves towards larger sizes when increasing the polymer
weight fraction. The average particle size changes from 63 to 162 nm and particles
shape was spherical as confirmed by TEM pictures shown in Figure 6.5.
The colloidal stability was characterized by -potential measurements. It was
found that -potential decreases from -13 to -46 mV with increasing polymer
concentration. The negative -potential is due to the presence of carboxylic chain end
groups, which during polymer precipitation redistribute on the nanoparticles surfaces.
To confirm such statement, NPs stability and -potential were monitored at different
pH values in the range from 2 to 11. As shown in Figure 6.6, the -potential increases
from -60 to 0 mV moving from high to low pH values. Particles aggregation occurs
when the number of charges on their surface is not large enough to ensure the system
stability by repulsive forces. Notably, the aggregation starts at pH equal to 3.3, a value
very close to the pKa of the carboxylic acid chain end group in PLA.[109]
124
a b Figure 6.5. TEM analysis of PLA nanoparticles produced with polymer weight fraction in THF
equal to (a) 0.25 % w/w and (b) 0.75 % w/w. Water and THF flow rates were 100 ml/min and
10 ml/min, respectively. The size bars in both figures corresponds to 200 nm.
Even though a further decrease of NPs size was expected when working at
polymer weight fraction in THF equal to 0.01% w/w, an apparent increase was
observed. By close inspection of the particle size distribution (see Figure 6.3b, solid
line), the sample exhibits monomodal distribution with average size equal to 180 nm.
This increase can be related to the formation of large clusters through NPs aggregation.
To verify this point, the precipitation was repeated in the presence of Tween 80
dissolved in water phase at a concentration equal to 0.01 % w/w. As shown in Figure
6.3b (dashed line), the measured particle size distribution is made of two populations
proving that the apparent increase in NPs average size observed at low polymer
concentration is due to NPs aggregation after precipitation.
125
Table 6.2. Effect of Tween® 80 concentration on NPs average size and PDI.
Tween® d PDI w/w nm ‐ 0.0001 % 123.9 0.13 0.001 % 122.9 0.16 0.01 % 125.1 0.107 0.05 % 124.4 0.109 0.1 % 117.5 0.161 In all experiments, polymer (S3 from Table) weight fraction in THF was equal to 0.5% w/w
and water and THF flow rates were 100 ml/min and 10 ml/min, respectively.
This aggregation behavior could affect the results discussed above for w p range
from 0.1 - 1% w/w. To verify that the increase in NP size as a function of w p is not
affected by aggregation, also these precipitation experiments were repeated in the
presence of Tween 80 (0.01% w/w in water). Moreover, the effect of surfactant
concentration was investigated at w p equal to 0.5% w/w for different concentrations of
Tween 80 in water ranging from 0.0001 to 0.1% w/w. As reported in Table 6.2 and
Figure 6.4a, minor differences in terms of NP average size were observed in all cases
when the surfactant was dissolved in the water phase, proving that aggregation occurs
only for w p lower than 0.1% w/w and validating all previous results. As shown in
Figure 6.6b, the use of the surfactant improved particle stability at low pH compared to
the case in which NPs were produced without stabilizer.
126
a
b
Figure 6.6. (♦) NPs average size and (◊) -potential as a function of pH. The PLA
sample (S3 from Table) was dissolved in THF at w p equal to 0.5 % w/w and the precipitation
was performed in water (a) and in 0.01% Tween® 80 water solution (b). Water and THF flow
rates were 100 ml/min and 10 ml/min, respectively.
127
Figure 6.7. SEM analysis of the flocks formed for PLA (S3 from Table) weight fraction in THF
equal to 2%. Water and THF flow rates were 100 ml/min and 10 ml/min, respectively. The size
bar is 200 nm.
An additional confirmation of Tween 80 adsorption on the particle surface
during precipitation is the larger -potential value measured at high pH, due to the
partial screening of the surface charges compared to the case without surfactant (Figure
6.6).
When the polymer weight fraction in THF was increased to 2 and 4% w/w, the
formation of a turbid solution (indicating the presence of NPs) and of few large flocks
floating at the top of the collecting vessel was observed. The stable suspension was
withdrawn from the sample and characterized by DLS. NPs average size and potential were 223 nm and -49 mV and 350 nm and -45 mV, respectively. Flocks
morphology was investigated by SEM (Figure 6.7): large particles are indeed present,
with size in the order of few microns, as well as a large number of small NPs with size
in the order of 300 nm, comparable to the size measured by DLS in suspension.
128
Furthermore, the particles are significantly interconnected among each other and some
of the large particles have elongated shape which can be the result of coalescence of
smaller particles or flow deformation.
In contrast with the previously reported experiments where a 14-times change of
S did not had any influence on the average NPs size (Figure 2a), in these experiments a
comparable change of S determines a large variation in the average size of the final
particles. For example by varying w p from 0.1 to 1% w/w (i.e. producing a change of S
of 10 times), particle size increases from 60 to 160 nm: this finding is in contrast with
the nucleation and growth mechanism.
It is worth to mention that, the increase in NP size at increasing concentration of
polymer in the organic phase was observed also for other polymers. Such increase was
described in the frame of the crystallization theory through a combination of nucleation
and aggregation mechanisms.[130] In particular, the increase in polymer concentration
results in higher S and a larger number of nuclei is formed. The apparent increase in NP
size is thus explained through the aggregation of those nuclei into nanometer size
clusters. Since the aggregation rate scales with the square of nuclei concentration, the
larger the nuclei concentration the larger the size of the produced clusters. On the other
hand, as proved by surfactant addition, aggregation phenomena occurs only at the
lowest polymer concentration while no effect of surfactant was found at w p larger than
0.01 %w. This behavior supports the particle formation by droplets formation and is in
contrast with the coagulative nucleation mechanism.
129
6.3.3
The effect of polymer molecular weight
As already introduced, the effect of polymer molecular weight (here the number
average molecular weight, Mn, is used) was studied in the range from 13 to 89 kDa. For
each polymer sample, NPs were produced by varying w p from 0.1 to 1% w/w which
was previously found to be a suitable range for the production of stable suspensions.
The results in terms of NP size and -potential are shown in Figure 6.8. At all the
investigated values of molecular weight, an increase of w p determines the precipitation
of larger particles. Moreover, a decrease of -potential until a plateau value of -40 mV
is observed, in agreement with the previous results. More interesting is the comparison
of average NP size at constant polymer weight fraction in THF as a function of
molecular weight. It is noticed that, there is a critical average molecular weight (Mn*)
for which NP size reaches minimum. Below such Mn* value, NP size is controlled by
the polymer swelling, which increases with decreasing Mn. On the other hand, above
Mn* nanoparticle size is controlled by the decreasing mobility of the polymer chains,
i.e. shorter chains rearrange themselves in polymer coils more easily than longer ones.
This result is in agreement with literature data reported for poly-ε-caprolactone.[132]
130
a
b
Figure 6.8. NPs average size (a) and -potential (b) as a function of polymer molecular weight.
The symbols correspond to different w p : (◊) 0.1 % w/w; (■) 0.25 % w/w; (○) 0.5 % w/w; (♦)
0.75 % w/w; (□) 1 % w/w. Water and THF flow rates were 100 ml/min and 10 ml/min,
respectively.
131
6.3.4
Alternative feeding strategies
Additional hints on the precipitation process were obtained carrying out ad-hoc
experiments in which alternative feeding strategies of the organic polymer phase were
tested. The different runs are reported in Table 6.3 as well as the measured scattered
intensity, NP average size and PDI.
A first insight is obtained by comparing the results of runs R_A and R_B. While
R_B corresponds to the standard procedure always used so far (both syringes of organic
stream filled with the THF/polymer mixture), in run R_A only one syringe was filled
with the polymer solution whereas the second one with pure solvent. No difference in
particle size and polydispersity was found for the two runs but the scattered signal
intensity (I) of R_A was half compared to the one of R_B. According to the Rayleigh–
Debye–Gans (RDG) theory, the intensity of the scattered light of a monodisperse
distribution of particles is equal to:
I ( q )  NV 2 P ( q )
(6.4)
where N refers to number of particles, V to their volume and P(q) to the form factor
evaluated at scattering wave vector q, which is defined as:
q  4π
n

 2
sin 
(6.5)
where n is the solvent refractive index,  the laser wavelength, and  the scattering
angle, equal to 173 degrees in these experiments. According to Equation 6.4, being the
particle size equal in both the experiments, I is directly related to the number of
particles which in run R_B is twice the value in run R_A. If particle formation occurs
after complete mixing in the mixer chamber, being one of the organic streams replaced
132
with pure solvent, w p decreases by a factor two and is equal to 0.25 % w/w. Thus, the
particle size expected in run R_A is smaller than that of run R_B, in agreement with the
results obtained studying the effect of w p on NP average size. On the contrary, particle
size did not change upon system dilution suggesting that particle precipitation occurs
locally at the inlet of the mixing chamber.
Table 6.3. Average NPs diameter (d), polydispersity index (PDI) and scattered signal intensity
(I) measured for the alternative feeding experiments.
run syringe 1 syringe 2 d PDI I 10‐4 nm ‐ kcps R_A PLA 7 0.5% w/w pure THF 119 0.12 2.1 R_B PLA 7 0.5% w/w PLA 7 0.5% w/w 119 0.13 4.1 R_C PLA 1% w/w PLA 0.1% w/w 199 0.23 3.7 97 0.14 1.2 R_D PLA0.5% w/w + PLA0.1% w/w R_E PLA 0.5% PLA 0.1% w/w 117 0.14 2.1 R_F PMMA 0.5% w/w PMMA 0.5% w/w ‐ ‐ ‐ R_G PLA 0.5% w/w PMMA 0.5% w/w 147 0.26 4.2 158 0.30 4.1 R_H PLA 0.5% w/w +PMMA 0.5% w/w In all experiments, water and THF flow rates were 100 ml/min and 10 ml/min, respectively.
133
To confirm this expectation, different values of the polymer weight fraction in
the two organic streams were used in run R_C, equal to 0.1 and 1% w/w, respectively.
Comparing the measured average particle sizes with the one measured in run R_B
(where the polymer concentration is close to the one expected in run R_C if complete
mixing of the streams occurs before particles precipitation), larger particles are formed.
Further experiments were carried out to prove the reproducibility of this result: namely,
two polymer/THF solutions with w p equal to 0.1 and 0.5% w/w were fed to the system
pre-mixed or separately in runs R_D and R_E, respectively. When the organic phases
were pre-mixed, the final w p was 0.3 %w/w and particles with average size of 97 nm
were produced; on the other hand, by feeding separately the polymer solutions, larger
particles were obtained (117 nm). These results prove that particle precipitation occurs
before complete mixing of all streams is achieved and thus that the characteristic time
of particle formation is smaller than the mixing time of the system. Thus, when
polymer solution with different w p are fed separately two particle populations are
expected; however, they could not be distinguished by DLS due to their relatively
similar size.
A final remark is done looking at the results reported for runs R_F, R_G and R_H
in which the effect of mixing different polymers (PMMA) was investigated. In run R_F
PMMA was fed from both syringes leading to the precipitation of a non-stable
suspension with fast formation of large aggregates which settled down at the bottom of
the collecting vial as shown in Figure 6.9.
134
Figure 6.9. NPs suspensions obtained for different polymers and feeding strategies as described
in Table 6.3. Water and THF flow rates were 100 ml/min and 10 ml/min, respectively.
More interesting are the results obtained in runs R_G and R_H in which PMMA
and PLA solutions with w p equal to 0.5% w/w were fed separately or pre-mixed,
respectively. It is worth to notice that, while in run R_G the weight fraction of PLA at
the mixing chamber inlet is equal to 0.5% w/w, in run R_H, due to the preparation of
PLA/PMMA mixture, the overall polymer weight fraction is still 0.5% w/w but equal to
0.25% w/w for each polymer. As reported in Table 6.3, no large difference was
observed in terms of particle size. By close inspection of the sample (Figure 6.9), it is
noticed that while a stable suspension is produced in run R_H, sedimentation of large
clusters is found for run R_G.
These findings suggest that, the formation of two different kinds of particles
(each kind made of one specific polymer) occurs when feeding the two polymers
separately (R_G), while particles made of both the polymers are produced (R_H) when
the two are premixed before precipitation. This point is also supported by the fact that if
two different types of particles had been formed in run R_H, cluster formation would
135
have been observed since PMMA particles were found to be unstable (as for R_F).
Accordingly, since in R_H the weight fraction of each individual polymer was 0.25%
w/w, PLA particles with average size smaller than the one observed would have been
produced (as found investigating the effect of w p on particle average size). The
ultimate proof of this concept was obtained by TEM analysis as shown in Figure 6.10.
While for run R_G the presence of small NPs and large aggregates was observed,
particles only were found for run R_H. The possibility to blend different polymers in
one particle has large applicative potential since this strategy can be used to modify the
properties of the particle surface.
a
b
Figure 6.10. TEM analysis of the nanoparticles produced in (a) R_G and (b) R_H experiments
described in Table 6.3. Water and THF flow rates were 100 ml/min and 10 ml/min,
respectively. The size bars are: (a) 200 nm and (b) 500 nm.
136
6.4 Conclusions
Nanoprecipitation of PLA particles in a multi inlet vortex mixer (MIVM) has been
investigated experimentally as a function of selected key parameters, such as mixer
geometry, flow conditions, polymer concentration and molecular weight. Dynamic
light scattering, transmission electron microscopy, scanning electron microscopy and potential measurements were used to characterize the particle size distribution,
morphology and surface charges. NPs with average size in the range from 25 to 300 nm
were produced with relatively low PDI.
It was found that the main parameter governing the process is the concentration
of polymer in the organic phase. The experimental results were analyzed in the frame
of the previously proposed mechanisms of particle formation. From our experimental
evidences, it turns out that the NP formation cannot be explained through the classical
nucleation theory as done in the literature for this kind of mixers. Instead, after mixing
the organic phase is dispersed in the form of droplets into the non-solvent and
precipitation occurs when the solubility limit of polymer into the organic phase is
reached.
Through alternative feeding strategies of the polymer-rich phase, it was shown
that when different polymers are dissolved in the organic phase, the precipitation
process leads to particles which contain both polymers. Thus, this technique is an
effective tool for the preparation of multifunctional nanoparticles by polymer blending.
137
138
Chapter 7. Synthesis of Magnetic Hetero-NanoClusters by combining Aggregation and Breakage
7.1 Introduction
The challenge of nanotechnology is currently shifting from the synthesis of
individual nanoparticles (NPs) to their assembly into larger, supra-nano, systems and
nanostructured materials. Synthetic methods are available for a broad range of materials
going from metals,[145, 146] semiconductors,[147] oxides,[148, 149] and inorganic
salts,[150] up to polymers.[151] Moreover, NPs functionalization can be carried out to
obtain specific desired surface properties, such as solubility in selected solvents,
affinity towards small molecules or larger biologicals,[40] resistance to nonspecific
adsorption,[152] etc. All these characteristics can be used to produce novel materials
suitable for various applications, including medical diagnostics,[41, 42, 153-155] drug
delivery,[156, 157] sensors,[158] electronic devices,[159] etc. Due to the complexity of
these applications individual NPs are generally not sufficient and better performances
can be obtained using assemblies of NPs, also referred to as nanuclusters (NCs), which
can be obtained through self-, controlled assembly or aggregation.[40, 160-166]
The self-assembly of nanoparticles is commonly realized by using primary
particles with opposite charges, or by addition of binding molecules like
polyelectrolites, polymers, proteins, or DNA strands.[40, 167] NPs self-assembly into
clusters is driven by a specific minimum energy configuration, which determines the
139
size and the shape of the formed clusters.[168] To increase compactness of the final
clusters the self-assembly of NPs is typically followed by solvent removal[155, 161,
169, 170] so as to obtain NCs with high compactness or with specific organization of
the NPs inside the single NC.
NCs production through aggregation process is instead realized by manipulating
electrostatic repulsive and van der Waals attractive forces between different primary
particles bearing surface charges of the same sign by varying the solution pH or the
ionic strength. To achieve clusters of the desired size the aggregation process can be
stopped by adding a suitable surfactant. Even though the aggregation kinetics can be
properly controlled,[171, 172] the major drawback of using only aggregation to form
NCs is that the produced clusters are characterized by a rather open structure, resulting
in low solid volume fraction, weak mechanical properties and irregular shape. In
addition, rather polydisperse distribution of aggregates is formed when an aggregation
mechanism is acting alone under shear conditions.
Accordingly, the aim of this work is to develop an alternative approach based
on the combination of aggregation, steric stabilization and controlled breakage to
produce NCs composed of nanoparticles with compact structure and size in the
submicrometer range. Since in this case the NCs densification is obtained by multiple
aggregation and breakup events, no solvent removal is needed to obtain very compact
internal morphology. Due to the high sensitivity of the formed clusters to the applied
stress, their size can be efficiently controlled by tuning the shear forces in the device
used to induce cluster breakup.[173] Various relative compositions of the individual
NCs, i.e. the numbers of primary particles composing a single NC, were achieved by
using nanoparticles with different sizes while keeping constant the final NCs size. The
developed methodology has been extended to the production of compact hetero-NCs
140
made of different nanoparticles, such as magnetic and polymer NPs. The obtained
results indicate that the developed technology can be used for the production of a
variety of hetero-clusters with taylor-made composition and size.
7.2 Materials and Methods
Methyl methacrylate (MMA), sodium dodecylsulphate (SDS) and potassium
persulphate (KPS) used in PMMA NPs synthesis were purchased from Acros Organics.
The surfactants used for NCs stabilization, Tween® 80 and poly-vinyl alcohol (PVA
Mowiol® 4-98), were supplied by Sigma Aldrich and Fluka, respectively. Sodium
choride (NaCl puriss. p.a., >=99.8%) and aluminium chloride (AlCl36H2O purum
p.a., >=99.0%) were purchased from Fluka. Iron(II)chloride (FeCl24H2O
ReagentPlus 99%) and acetone (spectrophotometric, purity ≥ 99.5%) were obtained
from Sigma-Aldrich. Iron(III) chloride (FeCl36H2O extra purity > 99%), was
obtained from Acros Organics. Uranyl acetate used as staining agent was supplied by
Fluka. Ammonia solution 25% w/w and poly(acrylic acid) 1800 Da were obtained from
Merck and Sigma Aldrich, respectively. All chemicals were used as received without
further purification.
7.2.1 Primary nanoparticle synthesis
Polymethyl-methacrylate (PMMA) primary nanoparticles were prepared by
monomer-starved semibatch emulsion polymerization.[174, 175] All reactions were run
in a 200 ml round bottom flask heated by an external oil bath and equipped with a
finger glass condenser, cooled by recirculation water to 15°C, to ensure no material
losses by evaporation. The reactor temperature was monitored with a standard
thermometer (accuracy ± 1oC). A three way valve placed at the top of the condenser
was used to connect the system to vacuum and nitrogen lines. Sodium dodecyl sulphate
141
(SDS) was dissolved in 100 mL deionized water. Batches of latexes with different NPs
size were prepared varying the amount of surfactant dissolved in water as reported in
Table 7.1. Due to the nature of the free radical polymerization process, oxygen was
removed from the surfactant solution by applying subsequent vacuum/nitrogen washing
cycles. The system was heated up to 70oC and then 0.08 g of initiator (KPS) was added
to the surfactant solution. Finally, 10 g of methyl methacrylate (MMA) were
continuously added to the reacting mixture at a flow rate of 6 mL/min. Monomer
addition was controlled by means of a programmable syringe pump (VIT-FIT
LAMBDA, Switzerland). When MMA addition was completed, the polymerization was
run for two more hours in order to ensure complete monomer conversion.
Table 7.1. Properties of primary nanoparticles
Latex name
SDS amount
dissolved
in 100 mL of water
Particle
diameter
-potential
Critical
coagulation
concentration
(CCC)
(g)
(nm)
(mV)
(mM)
PMMA17
1.16
17
-27
13a
PMMA40
0.32
40
-42
40a
PMMA80
0.12
80
-53.6
120a
MNP
-
27
-45
4b
a
CCC measured for NaCl
b
CCC measured for AlCl3
Magnetite nanoparticles (MNPs) were prepared through the Massart coprecipitation method.[176] In particular, 3.90 g of FeCl24H2O, 10.71 g of
FeCl36H2O and 12.0 g of poly-acrylic acid (PAA) were mixed in 180 ml of H2O. The
142
solution was heated up to 80 °C and subsequently 39.4 ml of NH3 were added leading
to the formation of a dark suspension. The reaction was carried out under mechanical
stirring in a 250 ml three necks round bottom flask equipped with a thermocouple
connected to a heating jacket to ensure temperature control. After a reaction time of 30
minutes the system was cooled down to room temperature and the product was then
precipitated in acetone and washed two times with water and acetone recovering
magnetite with a permanent magnet.[177] Finally, MNPs were redispersed in water,
magnetically filtrated and concentrated in a rotary-evaporator at 60°C and 150 mbar.
7.2.2
Nanocluster preparation
A sketch of the experimental setup is shown in Figure 7.1a. Typical aggregation
experiments started by mixing a primary particle dispersion with a salt solution
resulting in a final salt concentration three times above the critical coagulation
concentration (CCC). It is worth noting that due to the different stability of PMMA and
magnetic nanoparticles NaCl or AlCl3, respectively, were used to initiate the
aggregation process. Measured CCC values are reported in Table 7.1. All aggregation
experiments were run with a final particle volume fraction, , equal to 1  10 4 at 20oC
in a thermostated vessel (liquid volume 75 ml) connected to an external recirculating
water bath. NPs aggregation leads to the formation of large aggregates with sizes in the
micrometer range. To stop their growth, a surfactant, Tween® 80 or PVA, was added to
the system. Further, in order to reduce the size of the formed aggregates and densify
their internal structure so as to produce controlled nanoclusters, the aggregates
suspension was pumped, by means of a peristaltic pump (Watson Marlow, U.K.),
through a loop equipped with a contracting nozzle which generates high hydrodynamic
stress (see Figure 7.1a). The pump was operated in the range of flow rates from 84 to
143
598 ml/min. Hetero-NCs were prepared with the same procedure reported above
starting from a suspension containing a mixture of both PMMA and magnetic
nanoparticles.
a
Latex
Salt
Surfactant
Contracting
nozzle
Thermostated
vessel
Magnetic
bar
Figure 7.1. Illustration of the (a) laboratory device used for nano-cluster synthesis together with
(b) geometric details of the contracting nozzle.
In all cases, the final size of the produced NCs is controlled by the breakage intensity
due to the high hydrodynamic stress produced inside the contracting nozzle (see Figure
7.1b). This was characterized in details by computational fluid dynamic (CFD)
simulations using the CFD software Fluent v6.2.[178] Since a very broad range of flow
144
conditions were considered covering laminar as well as turbulent flow, a full 3D time
dependent simulation of the Navier-Stokes equation was performed. The obtained
results are summarized in Table 7.2 in terms of the hydrodynamic stress values, while
more details about the numerical procedure are reported in Appendix B.
Table 7.2. Fluodynamic operating conditions in the contracting nozzle of the experimental
setup shown in Figure 7.1 with diameter of 0.75 mm and various liquid flow rates.
Pump speed
Q
U nozzle

Renozzle
 max
(rpm)
(ml/min)
(m/s)
()
(Pa)
50
84
3.2
2373
193
75
130
4.9
3675
356
100
178
6.7
5026
535
150
264
9.9
7449
845
200
360
13.6
10162
1244
250
448
16.9
12660
1544
300
522
19.7
14746
1838
400
598
22.6
16892
2147
*
Renozzle 
4Q
, where  represents liquid density, dnozzle is the
π d nozzle 
nozzle diameter, and  is the liquid dynamic viscosity
7.2.3 Nanoparticles and Nanoclusters characterization
The original primary NPs and the resulting NCs were characterized in terms of
average value and polydispersity of the particle size distribution (PSD) by dynamic
light scattering using a Zetasizer Nano instrument (Malvern, U.K.). In all experiments,
145
the solid volume fraction of the particles was equal to 1.0  10 5 . The electrophoretic
mobility, e , of the NPs was measured in the presence of an electric field using the
Zetasizer Nano instrument operated in PALS (phase analysis light scattering) mode.
The measured values were then converted into zeta potential values using the dispersant
viscosity through Smoluchowski theory.[141, 142]
Size and structure of produced clusters were characterized by static light
scattering using a Mastersizer 2000 device (Malvern, U.K.) and a BI-200SM
instrument (Brookhaven, USA) with solid-state laser, Ventus LP532 (Laser Quantum,
U.K.) (wavelength 532 nm) equipped with a BI-9000 AT digital autocorrelator. Briefly,
the measured intensity of the scattered light, I  q  , was used to evaluate the average
structure factor of the cluster population S  q  according to:[179, 180]
S (q) 
I (q)
I (0) P (q )
(7.1)
where I  0  is the zero-angle intensity and P  q  is the form factor of the primary
particles. The scattering vector amplitude, q , is defined as:
q  4π
n

 2
sin 
(7.2)
where  is the scattering angle, n is the refractive index of the dispersing fluid and 
is the laser wavelength in vacuum. The Guinier approximation of the S  q  , which
reads as:
S q
146
 q 2 Rg2
 exp  

3

S (q)

,


for q Rg2
S (q)
1
(7.3)
was used to evaluate the root-mean square radius of gyration of the population of
aggregates according to
Rg2  Rg2
S (q)
2
 Rg,p
with the radius of gyration of the
2
primary particles given by Rg,p
 3 5 Rp2 .
A further information extracted from the light scattering measurements is the
effective fractal dimension, d f , which characterizes the internal fractal structure of the
clusters.[181] According to the Rayleigh-Debye-Gans (RDG) theory[179, 182] the
average structure factor S  q  of a population of fractal aggregates scales with q as:
S  q   q df ,
for 1 Rg  q  1 Rp
(7.4)
Therefore, by plotting S  q  vs. q in a double logarithmic plot a linear behavior with
a slope equal to d f is obtained. Depending on the aggregation process and whether
breakage is present or not values of d f in the range from 1.8 up to 2.7 can be
found.[173, 183-186] In particular, clusters grown under fully destabilized quiescent
conditions (i.e. DLCA) exhibit a very open structure characterized by a d f value
around 1.8,[183] while those formed under turbulent conditions and therefore in the
presence of strong breakage are much more compact with a d f around 2.7.[173, 185187]
In order to support the light scattering measurements, NPs and NCs were further
investigated by transmission electron microscopy (TEM) using a 400 mesh copper grid
covered by a Formvar®/Carbon film (Quantifoil Micro Tools GmbH). All samples were
prepared by depositing a single drop of the NPs/NCs suspension on a copper grid for
30s. After this time the droplet was removed and images of the slices were made with a
147
FEI Morgagni 268 transmission electron microscope (FEI Company, USA). Negative
staining with uranyl acetate was used when necessary.
7.3 Results and Discussion
To investigate the effect of primary particle size on morphology and size of the
NCs, a set of PMMA NPs with different sizes were prepared using a monomer starved
emulsion polymerization process.[174, 175] Varying the surfactant amount dissolved in
100 mL of water from 0.12 g to 1.16 g results in PMMA NPs with average size ranging
from 80 to 17 nm as reported in Table 7.1. As shown by the TEM pictures in Figure
7.2a, the produced NPs have spherical shape and are characterized by a narrow particle
size distribution with a low polydispersity index (PDI) of about 0.14 as measured by
DLS. The same analysis was carried out for the MNPs. Also in this case a narrow PSD
with an average hydrodynamic diameter of 27 nm and a PDI equal to 0.12 was
measured. The corresponding TEM image is shown in Figure 7.2b. It is worth noting
that due to the presence of COO  groups of the poly-acrylic acid used for MNPs
stabilization and the SO 4 groups originated from the surfactant and the initiator used
during the synthesis of PMMA NPs, both sets of NPs exhibit a negative -potential
ranging from -21 to -54 mV (see Table 7.1), which provides a good stability of the
colloidal dispersion.
148
(a)
(b)
Figure 7.2. a) TEM picture of PMMA primary particles with average diameter of 80 nm
prepared by starved polymerization. b) TEM picture of PAA-coated MNPs. Scale bars in (a)
and (b) corresponds to 500 and 100 nm, respectively.
The primary particles were destabilized using a salt concentration well above
the critical coagulation concentration as determined by aggregation kinetic
measurements performed under stagnant conditions. An example of aggregation kinetic
measurement is shown in Figure 7.3a where the hydrodynamic average diameter is
reported as a function of time for various salt concentrations using primary PMMA NPs
with average particle size equal to 80 nm. It can be seen that in the range of low salt
concentrations (below 80 mM) a small increase of NaCl concentration leads to a very
large increase in the initial aggregation rate, while no effect of salt concentration on the
149
aggregation rate was observed at higher concentrations (i.e., above 250 mM). Since the
former behavior is typical of reaction limited cluster aggregation[184] and the latter of
diffusion limited cluster aggregation,[183] the salt concentration value separating the
two behaviors is the salt critical coagulation concentration (CCC) and can be estimated
as illustrated in Figure 7.3b. It is worth noting that due to the high stability of the MNPs
a trivalent salt, AlCl3, was used instead of NaCl to achieve their complete
destabilization. A summary of the obtained CCC values measured for all primary
particles is reported in Table 7.1.
According to the above results, in all aggregation experiments the salt
concentration was chosen to be equal to three times the CCC values measured for the
corresponding primary NPs suspension. Immediately after salt addition, aggregation
started leading to the formation of large aggregates with size in the micrometer range.
Due to their large size, cluster breakage becomes important and a dynamic equilibrium
between aggregation and breakage is reached which determines the size of the
produced aggregates.[188] It is worth noting that in this experiment the suspension was
not pumped through the contracting nozzle shown in Figure 7.1 and therefore the
breakage is only due to stirring. At this point a sample of the suspension was gently
withdrawn from the system, diluted 10 times with water and measured by static light
scattering (SLS). An example of the structure factor, S  q  , measured for aggregates
composed of 80 nm primary PMMA NPs is shown in Figure 7.4a (see open squares)
while the data measured for the other NPs used in this work are reported in Appendix B
Figure 1. It can be seen that the produced aggregates have average gyration radius,
Rg , between 10 to 30 microns as indicated by the bending part of the S  q  .
150
200
Dh / (nm)
180
a
160
140
120
100
80
0
2
4
6
Time / (min)
8
Slope / (nm/min)
b
10
1
10
CCC
100
cNaCl / (mM)
1000
Figure 7.3. (a) Average hydrodynamic diameter as a function of time representing the
aggregation kinetics measured under stagnant conditions at various salt concentrations using
primary particles of PMMA with diameter of 80nm,  = 1.10-5. () cNaCl = 25 mM, () cNaCl =
62.5 mM, () cNaCl = 80 mM, () cNaCl = 250 mM, () cNaCl = 375 mM, () cNaCl = 800 mM.
Lines represent the initial aggregation rate. (b) Initial aggregation rates as a function of salt
concentration and definition of the critical coagulation concentration (CCC).
Furthermore, from the slope of S  q  vs. q Rg it is found that the produced
aggregates are very compact with fractal dimension, d f , in the range from 2.4 to 2.75
(solid lines in Figure 7.4b and in Appendix B Figure 1). Such high values of d f
indicates that processes competitive to aggregation, such as breakage and consequent
151
densification play a significant role and are responsible for the formation of such very
compact aggregates.[173, 185, 186]
0
S(q) / ()
10
-2
10
-4
10
-6
10
-8
10
a
-5
-4
10
-3
10
-2
10
10
q / (1/nm)
0
10
S(q) / ()
-2
10
-4
10
-2.75
q
-6
10
b
-8
10 -1
10
0
10
1
10
2
10
3
10
qRg / ()
Figure 7.4. Structure factor S  q  as a function of the wave vector q (a) and q Rg
(b) as
measured at steady state before () and after () the surfactant addition and circulating the
suspension through the contracting nozzle with the liquid flow rate equal to 84 ml/min. Used
PMMA primary nanoparticles have diameter of 17 nm.
152
The solid triangles shown in Figure 7.4a and b represent data coming from the
same experiments discussed above obtained after the addition of Tween® 80 and start
of circulating the suspension through the contracting nozzle. The first one is a steric
surfactant that reduces aggregation while the second provides a very high
hydrodynamic stress to the suspension thus increasing breakage. The result is that the
system evolves towards a different steady state characterized by much smaller
aggregate sizes as clearly indicated by the shift to the right of the structure factor values
in Figure 7.4a. In particular, it appears that clusters reduce their size from
approximately 10 micron down to approximately 150 nm referred to in the sequel as
nanoclusters (NCs). Nevertheless, their internal structure does not change significantly
as indicated by the fractal dimension values again ranging from 2.4 to 2.75 (see solid
lines in Figure 7.4b and in Appendix B Figure 1). This indicates that this is probably
the most compact structure that can be reached by combining aggregation and
breakage, and more compact ones probably require other mechanisms such as
coalescence or sintering.[189-191]
It is worth noting that through a detailed fluodynamic analysis of the individual
parts of the used experimental setup, i.e. magnetic stirring, peristaltic pump, and
contracting nozzle, it was found that the contribution of magnetic stirring and peristaltic
pump to breakage, and therefore to the final size of the NCs, is rather small. That is, the
final size of the formed NCs is exclusively controlled by the maximum hydrodynamic
stress in the contracting nozzle (see Appendix B Figure 1). Therefore in the following
the values of the maximum hydrodynamic stress generated in the contracting nozzle
(reported in Table 7.2) are considered when comparing different operating conditions.
For brevity, the details of the computational fluid dynamic computations used to
evaluate such hydrodynamic stresses are reported in Appendix B (Figures 2 and 3).
153
4
Dh / (nm)
10
a
3
10
2
10
-1
10
0
10
r / ()
1
10
b
r / ()
1
-1.07
r  dp
0.1
10
100
Particle diameter / (nm)
Figure 7.5. Effect of surfactant to primary particle mass ratio, r , on the size of formed NCs (a)
together with scaling of r as a function of primary particle diameter (b). Data obtained at
liquid flow rate in the contracting nozzle equal to 522 ml/min using surfactant Tween® 80 for
primary particles with diameter of 17 nm (), 40 nm () and 80 nm ().
Since the added surfactant amount and the hydrodynamic stress conditions are the key
parameters affecting the final NCs size further experiments were carried out to
investigate their effect. In Figure 7.5a the measured NCs sizes obtained for different
PMMA primary particles using constant liquid flow rate through the contracting nozzle
equal to 522 ml/min (and therefore constant maximum hydrodynamic stress) are shown
as a function of the surfactant to polymer mass ratio, r .
154
It can be seen that in all cases the increase of surfactant concentration results in the
reduction of the NCs size until a threshold value above which a further increase of
surfactant concentration does not affect NCs size anymore (see plateau values in Figure
7.5a). By plotting the threshold values of r obtained from Figure 7.5a as a function of
the primary particle size we found that r is linearly decreasing with the nanoparticle
diameter (see Figure7.5b). The dependency of r on the nanoparticle diameter can be
theoretically evaluated by considering that surfactant molecules can adsorb on every
primary particle present in the system and thus that the measured plateau value of r
corresponds to the total particle coverage which is function of the total particle surface
area (the contact area between particles in NC is neglected). In this frame the
theoretical value of r is equal to the ratio between particle area and volume which is
inversely proportional to the particle diameter in good agreement with the experimental
value.
In an attempt to investigate the influence of the type of surfactant, the above
experiments have been repeated using PVA instead of Tween® 80 for the production of
NCs using PMMA NPs of 17 nm. The obtained results are compared in Table 7.3 at
equal surfactant concentration, i.e. r equal to 1.3, for both Tween® 80 and PVA as a
function of the recirculation rate. It is seen that the average NCs size is independent
upon the nature of the stabilizer used. Out of these experimental findings, all the
following experiments were performed with Tween® 80 with an amount corresponding
to r equal to 1.3.
The effect of the maximum value of the hydrodynamic stress,  max , (see Table
7.2 and Appendix B) on the average NCs size is shown in Figure 7.6. It is seen that as
expected the NCs size decreases with increasing  max with scaling very similar to that
155
calculated according to Zaccone et al.[192] (see solid line in Figure 7.6). This finding
confirms that the breakup of produced NCs is solely controlled by the hydrodynamic
stress in the contracting nozzle and not by other mechanisms, e.g. cavitation.[193]
Table 7.3. Average NCs size obtained for PMMA NPs of 17 nm at different pump speed with
Tween® 80 and PVA.
Pump speed
Q
PVA
d NC
Tween 80
d NC
(rpm)
(ml/min)
(nm)
(nm)
100
178
208
205
150
264
187
167
200
360
156
160
300
522
110
118
400
598
105
112
While no significant difference is observed when changing the PMMA primary
particle diameter up to approximately 1200 Pa, for higher hydrodynamic stress values
two different behaviors are observed. For the NCs composed of the largest NPs, i.e. 80
nm, a further increase of the hydrodynamic stress does not affect the final NCs size
reaching a plateau value at 160 nm (see open triangles in Figure 7.6), while for smaller
NPs a further decrease of NCs size is observed (see solid circles Figure 7.6).
156
Diamater / (nm)
1000
100
40 2
10
3
10
Hydrodynamic stress / (Pa)
Figure 7.6. Scaling of obtained NCs diameter vs maximum hydrodynamic stress, 
max
, using
primary particles of PMMA with diameter of: 17 nm (), 40 nm (), and 80 nm (). Solid
line represents theoretical scaling after Zaccone et al.[192] using df  2.6 . In all experiments
Tween® 80 was used to stop the aggregation.
These findings can be explained through the evaluation of the number of
particles per cluster. The NCs plateau size of 160 nm is about twice as large as the
corresponding primary particle diameter, i.e., 80 nm, indicating that formed NCs are in
the form of triplets.[194] For, NCs composed of 17 nm PMMA particles the number of
primary particles in a cluster can be evaluated through the fractal scaling.[171] Using
d f  2.75 as measured by light scattering (see Figure 7.4), the number of primary
particles (N) is equal to N  110 17 
2.6
 170 . These considerations are further
supported by the TEM pictures of the NCs shown in Figure 7.7. These results clearly
indicate that the primary particle size is a key parameter to control the NCs
composition, i.e. the number of NPs composing a single NC.
157
(a)
(b)
Figure 7.7. TEM pictures of NCs composed of PMMA primary particles with diameter of 80
nm (a) and 17 nm (b) prepared at liquid flow rate equal to 522 ml/min (see Table 7.2). Scale
bar in (a) is 200 nm and in (b) is 500 nm.
We now extend the procedure discussed so far for clusters produced from a
dispersion of all identical primary NPs, i.e. homo-NCs, to the case where we start from
two dispersions of two different primary particles. The aim is to obtain compact
heterostructure with narrow size distribution and average size in the hundreds of
nanometers scale, i.e. hetero-NCs. Following the same strategy reported for homo-NCs,
the production of hetero-NCs was achieved by mixing 10 g of PMMA dispersion (10%
w/w) with average nanoparticle size equal to 40 nm with 1.5 g of MNPs dispersion
(37% w/w) with an average diameter of 27 nm. After mixing the two dispersions,
aggregation was induced by adding 10 ml of an AlCl3 solution (13 wt%), resulting in a
final salt concentration above the CCC of both the individual dispersions (Table 7.1),
thus ensuring the simultaneous destabilization of both primary NPs. After 10 minutes
under gentle stirring a sample was withdrawn and analyzed by SLS. To stop the
aggregation process 2 g of Tween® 80, corresponding to r equal to 1.3, were added to
the dispersion. Aggregates breakup was carried out in the same way as discussed
158
previously. In Figure 7.8a the structure factors of the NCs obtained before adding the
surfactant (open square) and after surfactant addition and circulating the suspension
through the nozzle (closed triangles) are shown. Similarly as for the homo-NCs, also in
this case the average cluster size decreases significantly after circulation in the
contracting nozzle from
Rg
about 30 microns to
Rg
about 300 nm, while the
internal structure remains substantially unchanged with a fractal dimension of about
2.6.
An open question remains about the composition of the NCs in terms of the two
NPs; do all the clusters contain the same fraction of them? An answer can be given by
observing the clusters behavior in the presence of magnetic and gravitational fields.
This test was performed for homo and hetero clusters with large size ( Rg
about 30
microns) obtained before surfactant addition (see Figure 7.9a) and for hetero-NCs after
breakage in the contracting nozzle (Figure 7.9b). As expected, while magnetic homo
clusters are attracted by the permanent magnet and therefore accumulate on the side
wall of the vial in the direction of the magnetic field (see Figure 7.9a-1), the PMMA
homo clusters do not present any magnetic behavior and sediment because of the
gravitational field (see Figure 7.9a-2). On the other hand, MNP/PMMA hetero clusters
are attracted by the magnet, leaving no material in suspension, thus proving that the
formed clusters are all magnetic and similar in composition (see Figure 7.9a-3). An
additional indirect proof is that the color of the hetero clusters is light brown,
suggesting a good homogenization between individual dark MNPs and white PMMA
NPs. The same magnetic behavior was found also for the smaller NCs produced after
the nozzle circulation step (see Figure 7.9b). Once more, this is an indication that the
final production step decreases the NCs size but does not affect their internal structure.
159
This finding is confirmed by the TEM pictures of the hetero clusters shown in Figure
7.10, where it is possible to distinguish between PMMA spherical nanoparticles and
MNP which have a higher contrast.
0
S(q) / ()
10
-2
10
-4
10
a
-6
10 -5
10
-4
10
-3
10
-2
10
q / (1/nm)
0
S(q) / ()
10
-2
10
-2.6
q
-4
10
b
-6
10 -1
10
0
10
1
10
2
10
qRg / ()
Figure 7.8. Value of the S  q  as a function of wave vector q (a) and q Rg
(b) for the
hetero-NCs of PMMA40 and MNP obtained at steady state before () and after () adding the
surfactant and circulating the suspension through the contracting nozzle with flow rate equal to
130 ml/min (see Table 7.2Error! Reference source not found.).
160
a)
b)
Figure 7.9. (a) Evaluation of the magnetic properties of formed large aggregates: (1)
Aggregates composed of pure magnetic primary particles, (2) aggregates composed of pure
PMMA40 primary particles, (3) aggregates composed of mixture (1:1 by mass) of magnetic
and PMMA40 primary particles. (b) Evaluation of the magnetic properties of heteronanoclusters composed of PMMA and magnetite nanoparticles. Liquid flow rate was equal to
130 ml/min
161
(a)
(b)
(c)
Figure 7.10. Example of a TEM image of magnetic hetero NCs obtained at liquid flow rate
equal to 130 ml/min. Scale bar in (a) corresponds to 200 nm while in (b) and (c) corresponds to
100 nm.
162
7.8
Conclusions
The present work is focused on the production of hetero nano-clusters (NCs)
from different primary nanoparticles through a combination of aggregation and breakup
processes. The method is based on the aggregation of completely destabilized small
primary particles into large micron size clusters by addition of a salt solution, followed
by controlled breakup of clusters in the presence of steric surfactant down to submicron
size by the hydrodynamic stresses generated in a contracting nozzle. The cluster size
and morphology was investigated by DLS and SLS and the results were confirmed by
TEM. Compact NCs characterized by high fractal dimension, ranging from 2.4 to 2.7,
and with size in the range from 100 to 300 nm were produced. Precise control was
achieved by the hydrodynamic stress generated in a contracting nozzle through which
NCs dispersion was pumped. Further, it was found that by changing the size of primary
particles it is possible to affect the relative composition of individual NCs. This was
demonstrated by the formation of NCs with comparable size composed in one case of
doublets, triplets, and quadruplets for case when very large primary particles were used,
compare to NCs composed of more than 100 primary particles when very small
primary particles were used. To include several functionalities polymeric nanoparticles
and magnetic NPs were combined resulting in magnetic hetero-NCs. Magnetic
response of such hetero-NCs provided by the MNPs proven that a random distribution
of the different NPs inside a single NC was achieved. The obtained results clearly
indicate that the developed NCs production strategy is a robust methodology and could
be applied in the synthesis of hetero-NCs made of various primary particles with great
advantages in many applications such as biomedical imaging, targeted drug delivery
and in general composites synthesis.
163
164
Chapter 8. Conclusions and Outlook
8.1 Lactic acid polycondensation
An experimental and theoretical study of the polycondensation reaction of lactic acid
has been carried out. Different aspects of the process, such as chemical equilibrium,
reaction kinetics and transport phenomena have been explored.
On the characterization side, the combination of HPLC (to measure the
composition in melt phase), GC (to analyze volatiles) and Karl-Fischer titration (to
measure water contents) provided a very detailed picture of the reacting system. At the
best of our knowledge, this is the first time that such a detailed picture of the time
evolution of the system is made available.
To identify the set of reactions and analyze their chemical equilibrium, long
time batch experiments in a broad temperature range (110 to 165 °C) have been
performed. Polycondensation and lactide forming reactions have been accounted for. In
the first case, monomer reactivity was shown to be different from that of longer linear
oligomers, while ideal behavior of the liquid mixture was well approached. In the
second case, the cyclic dimer was formed through end- and back-biting reactions of
PLA oligomers and the values of the corresponding equilibrium constants were largely
affected by the system composition, thus supporting non-ideal thermodynamic
behavior.
Reaction kinetics and transport phenomena were systematically studied in
semibatch stirred reactor under Nitrogen flow and in vacuum within the temperature
range from 130 to 190 °C. The removal rates of the most volatile components, water
165
and monomer, were experimentally investigated by varying stirring rate and pressure
thus influencing the thickness of the boundary layer and the driving force of the
process, respectively. A comprehensive kinetic model has been developed accounting
for all the involved phenomena and predicting the complete composition of both the
phases inside the reactor, melt liquid and gas. In particular, chain length dependent
kinetics and lactide forming reactions were involved in agreement with the results of
the previous equilibrium study. The mass transport coefficients were expressed as a
function of product parameters (average molecular weight) and operating conditions
(temperature and stirring rate). All model parameters have been estimated from
independent experiments and literature sources or directly by fitting the model
predictions to the experiments. Generally good agreements in terms of average polymer
properties, melt phase composition and collected amounts of volatile species have been
obtained.
The resulting set of model equations and parameter values provides a reliable,
predictive tool for process design, scale up and optimization: similar tools were not
available in the literature before for this specific polymerization system. Namely, the
relevance of mass transport limitation was quantified: this could be the rate determining
step if the selected reaction equipments do not provide enough interface area between
liquid and gas phases. The same model offers insights to major process modifications
with respect to its most conventional industrial version. In particular, the development
of novel process conditions aimed to maximize lactide production based on its selective
extraction could be envisioned.
166
8.2 Poly(lactic acid) degradation
A comprehensive study of PLA degradation through hydrolysis reactions was
carried out at acidic pH aimed to answer open issues about degradation path and
dependence of the kinetic parameters on temperature, polymer molecular weight and
chain stereoconfiguration. Oligomers of different length (from 2 to 9 repeating units,
recovered at high purity by HPLC) were hydrolyzed in batch conditions in the
temperature range from 40 to 120 °C. The experimental data were interpreted using a
kinetic model based on the “preferential chain end scission” mechanism proposed in the
literature. It was proved that the hydrolysis occurs preferentially on the ester bonds
close the polymer chain end groups (α esters) compared to the ones inside the polymer
chain (β esters). The parameter values of the Arrhenius type dependence of the kinetic
parameters upon temperature were estimated; moreover, reaction kinetics was not
affected by the chain stereoconfiguration. A specific value of this analysis is that all
kinetic analyses were performed in aqueous solution, i.e. without any influence of
diffusion phenomena. This way, and in contrast to many literature papers reporting
kinetic analysis on polymer devices, the intrinsic reaction rates could be
unambiguously determined. Therefore, the estimated kinetic parameters can be reliably
used when modeling the degradation of bulk materials, where diffusion limitations
enter into the game.
8.3 Nanoparticles and Nanoclusters production
The production of PLA nanoparticles by flash nanoprecipitation in a multi-inlet
vortex mixer has been systematically investigated as a function of mixing, polymer
concentration, polymer molecular weight and polymer feed strategy. The experimental
167
results support a particle formation mechanism by precipitation through the formation
of a dispersion of polymer rich droplets of solvent in contrast to the conventional
literature mechanism of nucleation and aggregation. Being the characteristic time of
particle formation smaller than the mixing time of the system, nanoparticle
precipitation occurs locally at the inlet of the mixing chamber. Polymer concentration
plays a major role in the process and stable particles in the range from 25 to 300 nm
were produced. This technique was shown to be effective to blend different polymers
inside each single particle and thus represents a feasible approach to the one step
preparation of multifunctional nanoparticles.
The possibility to produce multifunctional devices was also investigated
through the production of nanoclusters composed of primary nanoparticles made of
different polymers through aggregation and controlled breakage in the presence of
surfactant. Compact polymeric clusters in the size range from 100 to 300 nm have been
produced as a function of the shear applied in a contracting nozzle. The same procedure
was extended to the production of hetero magnetic nanoclusters as proof of the concept
that this methodology can be applied to obtain compact structures with heterogeneous
composition.
Due to the possibility to combine together particles made of different materials,
with different properties and loaded with different drugs, either hydrophilic or
hydrophobic, the proposed technology can be successfully adopted for the production
of drug delivery devices.
168
Appendix A
1. The effect of acetonitrile content on the hydrolysis kinetics
Another effect to be accounted for is the influence of the medium on the
hydrolysis kinetics. Namely, it has been reported that the addition of an organic
modifier to the aqueous solution affects the hydrolysis rate by changing the dielectric
constant of the medium and therefore the nature of the polymer end groups.[109] Thus,
the “true” hydrolysis kinetics in pure water is obtained by running experiments at
decreasing amounts of organic modifier and by extrapolation to pure water.[23] Even if
the water solubility of the oligomers is not an issue in this study due to their short
length, traces of acetonitrile were always present due to the way the oligomer were
fractionated. As mentioned above, in fact, after collection the samples are further
diluted with acidified water, so that the final content of acetonitrile is always about 3%
v/v.
To investigate the effect of such modifier on the degradation kinetics, a tetramer
sample was degraded at 60 °C in water/acetonitrile mixtures at different acetonitrile
contents (AC) up to 30% v/v. The degradation rate constants evaluated through
Equation 5.3 are shown in Figure A as a function of water volume fraction. It is seen
that, even though the amount of acetonitrile plays indeed a role, the effect of amount
below 3% v/v can certainly be neglected.
169
Figure A. Effect of acetonitrile content on the overall degradation kinetic constant of trimer,
k d ,4 . Experiments run at 60 °C.
2. Gas Chromatography analysis (GC)
Gas chromatography was applied to determine the volume fraction of acetonitrile in
solution. The analysis was carried out using a Hewlett Packard gas chromatograph
HP6890 apparatus, equipped with a (crosslinked 5% PH ME Siloxane) 30 m x 0.3 mm
x 0.25 µm (USA) HP column and TCD detector. Helium was used as carrier gas at a
flow rate of 10 ml/min. The injection and detector temperature were 250 °C and the
column temperature was maintained at 60 °C for 10 minutes and then raised to 250 °C
in 20 minutes. Calibration was carried out by injecting acetonitrile/water mixtures with
known composition.
170
3. HPLC calibration factors for DL oligomers
It is worth noting that the calibration procedure reported was run with LL oligomers,
while no information was reported for the DL ones. Thus, the same calibration
procedure was applied for DL species aimed to clarify the influence of the oligomer
stereo-configuration on the calibration factors ( K i ). The obtained K i values are
reported in Figure B and compared with those of LL oligomers[71].
Figure B. Calibration factor ( K i ) as a function of chain length (n). (●)LL (from [71]),
(◊)DL.
171
172
Appendix B
Fluid Flow Characterization
All CFD simulations reported were performed with the CFD software Fluent
v6.2[178] using the length and the diameter of the entrance and exit sections of the
nozzle equal to lentry  15 mm, lexit  45 mm and d entry  d exit  5.4 mm, respectively (
the nozzle sketch is presented in Figure 7.1b). Nozzle length and diameter were equal
to 0.75 mm. To properly resolve regions with large velocity gradients, in all
simulations the position of the first grid element in the axial as well as in the radial
direction was located at a distance 5.10 4  d nozzle from the nozzle edge.[195]
Depending on the operating conditions it was necessary to use 40 to 60 grid nodes
over the nozzle diameter resulting in a total number of grid nodes ranging from 1.3  106
to 1.7  106 . Since the flow far upstream of the contracting nozzle was laminar, the
boundary conditions of the inlet velocity can be computed analytically.[196] Due to the
low solid volume fraction of the suspension the fluid properties were approximated as
equal to those of water at 20C with density and viscosity equal to 998.2 kg/m3 and 1
mPa.s, respectively.
To obtain a statistically stationary solution, time dependent simulations were
started from previously calculated steady state solutions using a constant time step t
equal to L / U
nozzle
, where U
and L was selected as 1
20
nozzle
2
is the mean velocity in the nozzle
 4Q  d nozzle
d nozzle , which for the present case was equal to 0.0375 mm.
The steady state solution characterized by a non-changing mean velocity everywhere in
173
the flow was reached after approximately 20 000 time steps. After this additional
20 000 time steps were performed to collect statistics of the fluctuating velocity, ui ,
calculated at each time step as a difference between the local velocity, U i , and the
mean value, U i . To characterize the gradients of the fluctuating velocity a User
Defined Function[197] was used. Consequently the turbulent energy dissipation rate
was evaluated from:
  2 sij sij , where sij

1  ui u j


2  x j xi



The hydrodynamic stress depends on the type of flow (laminar vs. turbulent)
and the relative size of the cluster with respect to the characteristic size of the flow and
is in general given by three contributions. One contribution is due to the gradient of the
mean flow for which the corresponding hydrodynamic stress can be evaluated as:[173,
198]
5
2
 L   L
where  is the dynamic viscosity and L is the maximum positive eigenvalue of the
rate of strain tensor. As the flow in the nozzle becomes weakly or even fully turbulent,
the turbulent energy dissipation rate, determines the hydrodynamic stress. When the
cluster size is larger than the Kolmogorov microscale,  K   3   , i.e., when the
14
cluster is in the inertial subrange of turbulence, the hydrodynamic stress to which the
cluster is exposed to results from the difference in the pressure on opposite locations of
the cluster,[199] i.e., the dynamic pressure. Under these conditions the corresponding
hydrodynamic stress can be approximated as:[173]
 IS     d cluster 
174
23
where  is fluid density and dcluster is cluster size. For aggregates smaller than the
Kolmogorov microscale,  K , the corresponding hydrodynamic stress can be calculated
as:[173]
5
2
 VS  



6

Another type of hydrodynamic stress that was proposed to cause aggregate
breakup is the collapse of the vapor bubbles formed during cavitation.[193] Since in the
investigated system under all operating conditions no formation of bubbles or foam at
the exit of the nozzle was observed, this mechanism was not considered to be relevant.
Effect of shear stress on cluster size and structure
To evaluate the relative contribution of individual parts of the used setup to the
aggregate breakup, aggregates were exposed to (i) magnetic stirring only, (ii)
combination of magnetic stirring and loop equipped with peristaltic pump, and (iii) to
the whole setup when also contracting nozzle was mounted after the peristaltic pump. A
comparison of the steady state S  q  values measured for all primary particles under
different conditions is presented in Figure C a-h. For the experiments ii and iii, the flow
rate of the liquid was set equal to 130 ml/min. As expected, large aggregates are
produced when only magnetic stirring was applied while introducing the loop and
finally also the contracting nozzle a reduction of aggregate size was observed by shift
of the Guinier region of the S  q  , i.e., the bending part of S  q  , towards higher q
values. When evaluating an average
Rg
of starting aggregates obtained under the
action of magnetic stirring, by Equation 7.3, results in aggregates with Rg
ranging
175
from 10 to 30 microns, while smaller aggregates with
Rg
around 5 micron were
measured when aggregates where exposed to the shear stress generated in the peristaltic
pump. Further reduction was obtained when aggregates where exposed to the
hydrodynamic stress generated in the contracting nozzle (see Figure C). From the same
figure it can be seen that the clusters preserve their compact structure, as none of the
slopes of S  q  as a function of q Rg changed compared to the previously reported
values (solid line in Figure C b, d, f, h). This finding suggests that cluster restructuring
does not occur, which is in close agreement with a previous work where it was shown
that once aggregates reach a high values of d f around 2.7 their internal density cannot
be further increased by breakage.[173, 185] In this frame it is concluded that the stress
generated by the magnetic stirring and pump has only a small effect compare to that
produced with the contracting nozzle.
Therefore, to fully characterize the hydrodynamic stress in contracting nozzle a
full 3D time dependent CFD simulation of the flow field in the nozzle was carried out
(see previous section). An example of results obtained for liquid flow rate equal to 360
ml/min is presented in Figure D a-e. It can be seen that the flow field in the nozzle is
rather complex with laminar flow upstream and far downstream of the nozzle, and
strong increase of velocity at the nozzle entrance followed by the formation of turbulent
jet at the nozzle exit. Approximately 20 000 time steps were required to obtain time
averaged velocity profiles (see Figure D b). Same number of iterations was used to
evaluate the average profile of all hydrodynamic stresses. Contour plots of the
hydrodynamic stress generated by the mean velocity gradient,  L , the gradient of the
velocity fluctuations,  VS , and dynamic pressure,  IS , are presented in Figure D c-e,
176
respectively. It can be seen that in the case of  L the highest values can be found at the
nozzle entrance. On the other hand, as the nozzle length is rather short, turbulence
could not develop and the hydrodynamic stress related to the existence of turbulence,
 VS and  IS , reach its highest values inside the jet formed at the nozzle exit. For this
particular case  VS reaches much higher values compared to  IS .
Since a radial variation of the hydrodynamic stress is generated either at the
nozzle entrance or at its exit, a further investigation based on different particle
trajectories was performed. A comparison of hydrodynamic stress along two different
particle trajectories, one starting close to the wall upstream of the nozzle and the other
at the nozzle axis is presented in Figure E a and b. It is worth noting that the selected
particle trajectories represent two limiting cases of lowest and highest stress which NCs
would experience passing through the nozzle.[185] Taking into consideration the finite
size of NCs the starting point of the particle trajectory close to the wall was selected so
that it passes through the nozzle entrance (x-coordinate equal to zero) at a distance from
the nozzle wall equal to the diameter of produced NCs. The size of the NCs was chosen
to be equal to that measured by DLS at steady state, which for liquid flow rate equal to
360 ml/min was equal to 160 nm. From the comparison presented in Figure E, it can be
seen that the highest values of the hydrodynamic stress are located at the nozzle wall,
while at the nozzle axis approximately 3 times lower values can be found. Furthermore,
among all stresses the highest ones are those due to the mean velocity gradient (  L ).
Since the measured NCs sizes represent the steady state values, it is assumed that the
produced NCs have been at least once exposed to the highest hydrodynamic stress
present in the system, i.e.,  L close to the nozzle wall. Therefore, these values
calculated for all operating conditions investigated in this work control the NCs
177
breakup in the nozzle and are used for further analysis. A summary of maximum values
of  L , in the main text referred as  max , together with other flow field characteristics are
reported in Table 7.2.
178
0
0
S(q) / ()
10
10
-2
10
-2
-4
10
-6
10
10
-4
10
-6
10
-8
10
a
-5
1
10
-4
10
-3
10
-2
10
10
10
-3
10
S(q) / ()
0
10
1
10
2
3
10
10
-1
-3
10
-2.4
q
-5
-5
10
-7
10
10
c
-5
10
-4
10
-3
10
-2
10
0
-2
q
-4
10
e
-5
10
-4
10
-3
10
-2
10
0
3
10
f
-6
10 -1
10
0
10
1
10
-2.6
2
3
10
10
0
10
10
-2
-2
10
10
-4
q
-4
10
-6
2
10
-2
10
10
1
10
10
-4
-6
0
10
10
10
10
d
-7
10 -1
10
0
10
S(q) / ()
b
-8
10 -1
10
1
10
-1
10
S(q) / ()
-2.75
q
10
g
-5
10
-4
10
-3
10
q / (1/nm)
-2
10
h
-6
10 -1
10
0
10
1
10
qRg / (-)
2
10
-2.5
3
10
Figure C. Comparison of the S  q  plotted as a function of q (left column) and plotted as a
function of q Rg
(right column) measured at steady state after applying stirring (open
square) and applying loop with liquid flow rate was equal to 84 ml/min without (closed circle)
and with contracting nozzle mounted in the loop (open triangle). Obtained results measured for
PMMA primary particles with diameter of 17 nm (a, b), 40 nm (c, d), and 80 nm (e, f) and for
MNP (g, h).
179
(a)
(b)
(c)
(d)
(e)
Figure D. Flow field characterization inside the contracting nozzle calculated for liquid flow
rate equal to 360 ml/min (a) Actual velocity magnitude snapshot (m/s), (b) Velocity magnitude
averaged over 20 000 time steps. Contour plot of the hydrodynamic stresses due to the mean
velocity gradient  L  (c); due to the gradient of the velocity fluctuations  VS  (d), and due to
dynamic pressure  IS  (e).
180
Hydrodynamic stress / (Pa)
Hydrodynamic stress / (Pa)
1600
1400 a
1200
1000
800
600
400
200
0
600 b
500
400
300
200
100
0
-5
0
5
10
15
20
Distance from the nozzle entrance / (mm)
Figure E. Comparison of the three hydrodynamic stresses along two particle trajectories starting
at two different locations: (a) closed to the wall (see insert of Figure E(a)) and (b) at the nozzle
axis (see insert of Figure E(b)). In both figures solid line represents  L , dashed line  VS , and
dotted line  IS . In figure (a) solid and dash line were shifted up by factor 200 or 100,
respectively. In figure (b) solid and dash line were shifted up by factor 250 or 50, respectively.
Both simulations were obtained for liquid flow rate equal to 360 ml/min.
181
182
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Curriculum Vitae
Personal information:
Fabio Codari
Birth Date:
27/07/1983
Birth Place:
Rho (Milan), Italy
Nationality/ Status: Italian/ not married
Educations:
2008 – 2011 Ph. D. student in the group of Prof. Dr. M. Morbidelli at the Institute for
Chemical and Bioengineering, ETHZ Zürich.
2006 – 2007 M. Sc. in Chemical Engineering at the University Politecnico di Milano.
Grade: 110/110
2002-2006
B. Sc. in Chemical Engineering at the University Politecnico di Milano.
Grade: 99/110
1997-2001
High School Education in Chemistry at the ITIS S. Cannizzaro Rho,
Milan (Italy).
Grade: 97/100
Research, Teaching and Supervision Experiences:
2008 – 2011 Research topics: polymer and particle science.
 Experimental and modeling work on lactic acid
polycondensation. Industrial collaboration with Uhde InventaFischer (Berlin) on industrial plant simulation.
 Hydrolitic PLA degradation.
 Nanoparticle preparation by nanoprecipitation and emulsion
based process.
 Investigation of particles aggregation and breakage phenomena.
Scientific collaboration with Mario Negri Institute for
Pharmacological Research (Milan, Italy).
2008 – 2011 Supervision of M. Sc. thesis and B. Sc. works (ETH-Zürich).
2008 – 2010 Laboratory assistant in the practical course of “Homogeneous reaction
Engineering” for Chemical Engineering Students (BSc course, ETHZürich).
2008 – 2011 Responsible of security in the group of Prof. Dr. M. Morbidelli (ETHZürich).
2007
M. Sc. thesis at the Institute for Chemical and Bioengineering, ETHZ
Zürich (Switzerland), in the group of Prof. Dr. M. Morbidelli. The focus
of the work was on the characterization of PLA oligomers and lactic acid
polycondensation kinetics.
195
2005
Internship in Chemical Engineering at the Chemistry, Material and
Chemical Engineering Department “Giulio Natta”, Politecnico di
Milano, Milan (Italy) under the supervision of Prof. G. Groppi. Topic of
the research project : "Activity study of metal based catalysts in methane
combustion".
Internship at Cryovac, Passirana di Rho (Italy). Summer project in the
R&D laboratory on polymeric materials for industrial application.
2000
Pubblications
‐
F. Codari, D. Moscatelli, G. Storti and M. Morbidelli, “Characterization of low
molecular weight PLA using HPLC ”, Macromolecular Materials and
Engineering, 2010, 295, 58-66
‐
S. Lazzari, F. Codari, D. Moscatelli, M. Morbidelli, M. Salmona, L. Diomede,
“Colloidal stability of polymeric nanoparticles in biological fluids”, Journal of
Nanoparticle Research, 2012, 14, 6
‐
F. Codari, S. Lazzari, M. Soos, G. Storti, M. Morbidelli, D. Moscatelli,
“Kinetics of the Hydrolitic degradation of Poly(Lactic Acid)”, Polymer
Degradation and Stability, 2012 in press
Conferences
‐
High temperature degradation kinetic of PLA
Presentation - 8th world congress of chemical eng. 2009 (Montreal)
‐
Polymer nanoclusters preparation through aggregation and breakage processes
Presentation - AICHE 2010 (Salt Lake City)
‐
Experimental and modeling analysis of LA polycondensation
Presentation - AICHE 2010 (Salt Lake City)
‐
Experimental and modeling analysis of LA polycondensation
Invited Presentation - Hangzhou International Polymer Forum (Hangzhou,
China)
‐
Bulk melt polycondensation of lactic acid: equilibrium and kinetic behavior.
Presentation - EUPOC 2011 (Gargnano, Italy)
196
‐
PLA polycondensation kinetic
Poster - SCS 2008 (Freiburg)
‐
PLA oligomers degradation
Poster - PRE 2009 (Niagara Falls)
‐
Diffusion limitation in PLA polycondensation
Poster - PRE 2009 (Niagara Falls)
‐
Mass transport evaluation in PLA polycondensation
Poster - SCS 2010 (Zürich)
‐
Experimental and modeling analysis of LA polycondensation at equilibrium
Poster - PRE 2010 (Hamburg)
197
198

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