materials
Article
Study of the Molecular Dynamics of Multiarm Star
Polymers with a Poly(ethyleneimine) Core and
Poly(lactide) Multiarms
Frida Román *, Pere Colomer, Yolanda Calventus and John M. Hutchinson
Laboratori de Termodinàmica i Físicoquímica, TERFIQ, Departament de Màquines i Motors Tèrmics, ESEIAAT,
Universitat Politècnica de Catalunya, Barcelona Tech, Carrer Colom 11, Terrassa 08222, Spain;
[email protected] (P.C.); [email protected] (Y.C.); [email protected] (J.M.H.)
* Correspondence: [email protected]; Tel.: +34-93-739-8124; Fax: +34-93-739-8101
Academic Editor: Ming Hu
Received: 19 December 2016; Accepted: 28 January 2017; Published: 4 February 2017
Abstract: Multiarm star polymers, denoted PEIx-PLAy and containing a hyperbranched
poly(ethyleneimine) (PEI) core of different molecular weights x and poly(lactide) (PLA) arms with
y ratio of lactide repeat units to N links were used in this work. Samples were preconditioned to
remove the moisture content and then characterized by thermogravimetric analysis (TGA), differential
scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). The glass transition
temperature, Tg , is between 48 and 50 ◦ C for all the PEIx-PLAy samples. The dielectric curves
show four dipolar relaxations: γ, β, α, and α0 in order of increasing temperature. The temperatures
at which these relaxations appear, together with their dependence on the frequency, allows
relaxation maps to be drawn, from which the activation energies of the sub-Tg γ- and β-relaxations
and the Vogel–Fulcher–Tammann parameters of the α-relaxation glass transition are obtained.
The dependence of the characteristic features of these relaxations on the molecular weight of the
PEI core and on the ratio of lactide repeat units to N links permits the assignation of molecular
motions to each relaxation. The γ-relaxation is associated with local motions of the –OH groups of the
poly(lactide) chains, the β-relaxation with motions of the main chain of poly(lactide), the α-relaxation
with global motions of the complete assembly of PEI core and PLA arms, and the α0 -relaxation is
related to the normal mode relaxation due to fluctuations of the end-to-end vector in the PLA arms,
without excluding the possibility that it could be a Maxwell–Wagner–Sillars type ionic peak because
the material may have nano-regions of different conductivity.
Keywords: dielectric relaxation spectroscopy (DRS); multiarm star polymers; poly(lactide) (PLA);
poly(ethyleneimine) (PEI); differential scanning calorimetry (DSC)
1. Introduction
Cured epoxy resins are thermosets exhibiting a cross-linked structure with excellent electrical
properties, good chemical and corrosion resistance, low shrinkage, and high tensile strength and
modulus. On account of these characteristics, epoxy resins are widely used in applications such
as coatings, adhesives, and encapsulation of electronic components. To obtain an acceptable set of
properties, the oligomers or monomers of low molecular weight must be converted into a highly
cross-linked network polymer; this is achieved by means of curing agents, which involve a variety of
reaction mechanisms [1–3]. The wide range of curing agents available for their cross-linking makes the
resulting cured epoxy systems extremely versatile, and in particular there is considerable interest in
the use of dendrimers and hyperbranched polymers as cross-linking agents.
Dendritic polymers are materials with a highly branched structure. Due to the large number of
end groups, one at the end of every branch, they are highly functional. The high degree of branching
Materials 2017, 10, 127; doi:10.3390/ma10020127
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Materials 2017, 10, 127
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renders entanglement of the polymers impossible which results in low melt and solution viscosity.
Dendritic architecture may be divided into six subclasses: dendrons and dendrimers, linear-dendritic
hybrids, dendrigrafts or dendronised polymers, hyperbranched polymers, multi-arm star polymers,
and hypergrafts or hypergrafted polymers. The first three subclasses exhibit perfect structures with a
degree of branching of 1.0, while the latter three exhibit a random branched structure.
Dendrimers are molecules with a three-dimensional globular shape [4–6] and belong to the family
of highly branched molecules emanating from a central core with a large number of functional terminal
groups at their periphery. Recently, dendrimers have been used as modifiers in thermoplastic polymers
and as curing agents for thermosetting materials. For example, Tande et al [7] used ester-terminated
poly(propyleneimine) dendrimers to plasticize polyvinyl chloride (PVC), while other authors report
that poly(amidoamine) dendrimers, butyl-glycidylether-modified poly(propyleneimine) dendrimers
and others of similar molecular structures could effectively cross-link epoxy resins [8–13].
Such star-like topologies have considerable interest because of their unusual physical and
rheological properties. The properties of the final materials and their processability can be tailored as a
function of the core and arms structures, the type and amount of functional end groups, the molecular
weight, and the length and number of the polymeric arms. In previous studies, multi-arm stars with
poly(ε-caprolactone) arms using hyperbranched poly(glycidol) or poly(ethyleneimine) as a core have
been synthesized and studied as modifiers in the curing of diglycidylether of bisphenol A (DGEBA)
epoxy resin using cationic and anionic initiators as curing agents [14–16].
Recently, hyperbranched poly(ethyleneimine) has been used as a multifunctional cross-linker of
epoxy resins. The densely branched architecture and high molecular weight of poly(ethyleneimine)
create significant mobility restrictions, which have a strong effect on the glass transition temperature
and on the degree of cross-linking of the cured materials [17]. Within the last few years, multiarm
stars with poly(lactide) (PLA) arms using a poly(ethyleneimine) (PEI) of different molecular weight
(Lupasol® , BASF, Mississauga, ON, Canada) as the multifunctional core have been synthesized [18].
With an appropriate selection of PLA arms, which contain rigid esters of secondary alkyl groups in the
structural units, materials with higher glass transition temperature can be obtained, compared with the
use of similar stars with poly(ε-caprolactone) (PCL) arms with primary ester linkages. Such materials
formed by a multifunctional core of PEI of different molecular weights and multiple branches of
PLA, denoted PEIx-PLAy where x represents the molecular weight of the poly(ethyleneimine) and
y represents the ratio of lactide repeat units to N links, were used as chemical modifiers in the
anionic curing of DGEBA epoxy resins. The addition of the multiple arm stars led to homogeneous
materials with an improvement of the impact strength in comparison with the neat material, without
compromising the glass transition temperature [18].
In previous work, we studied the dielectric relaxations associated with pure PEI and blends of PEI
and DGEBA epoxy resin in the uncured state, during the curing reaction, and as a fully cured system.
The behavior of each relaxation was analyzed in order to ascertain the molecular motions and the
groups responsible for these relaxations [19]. Likewise, the molecular mobility of poly(lactide) has also
been studied, including for example the relationship between morphology and glass transition [20].
On the other hand, for the PEIx-PLAy copolymers, there has been no systematic study of the effect of,
for example, the molecular weight of the PEI core, or of the effect of the presence of the branches of
PLA and the length and density of these branches. Accordingly, in the present work the thermal and
dielectric behavior of three multiarm star polymers composed of a polyethyleneimine (PEI) core and
polylactide (PLA) arms has been studied, and has been compared with that of a commercial –NH2
terminated hyperbranched polymer, also based on polyethyleneimine but with different molecular
weights, in order to identify the contributions of the core and arm architectures to the molecular
dynamics. A schematic illustration of the molecular architecture of these star-shaped polymers is
shown in Figure 1.
Materials 2017, 10, 127
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Materials 2017, 10, 127
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Figure
Schemeof
ofmultiarm
multiarm star
PEIx-PLAy.
Figure
1. 1.Scheme
starcopolymers
copolymers
PEIx-PLAy.
Figure 1. Scheme of multiarm star copolymers PEIx-PLAy.
2. Results and Discussion
2. Results and Discussion
2. Results
Discussion
Figureand
2a,b
show the thermograms obtained by thermogravimetric analysis (TGA,
Figure 2a,b show
the
thermogramsSwitzerland),
obtained byshowing
thermogravimetric
analysis (TGA,
Mettler-Toledo
Mettler-Toledo
AG,
Schwerzenbach,
thermal degradation
behavior
of the
Figure 2a,b show
the thermograms obtained
bythethermogravimetric
analysis
(TGA,
AG, samples
Schwerzenbach,
Switzerland),
showing
the
thermal
degradation
behavior
of
the
samples
PEI2000-PLA5,
PEI2000-PLA20,
and
PEI800-PLA5.
Two
kinds
of
experiments
were
Mettler-Toledo AG, Schwerzenbach, Switzerland), showing the thermal degradation behavior of
the
performed
in
order
to
observe
the
effect
of
moisture
in
the
samples:
in
the
first
type
of
experiment,
PEI2000-PLA5,
PEI2000-PLA20,
and
PEI800-PLA5.
Two
kinds
of
experiments
were
performed
samples PEI2000-PLA5, PEI2000-PLA20, and PEI800-PLA5. Two kinds of experiments were in
samples
were
10 in
°C/min
over the
from
40 toof
600
°C;the
in the
orderthe
tooriginal
observe
the
effect
ofheated
moisture
the
samples:
in samples:
the first range
type
experiment,
original
performed
in
order
to
observe
theateffect
of
moisture
in temperature
the
in
the of
first
type
experiment,
◦
◦
second
type
of
experiment,
the
original
samples
were
first
subjected
to
an
isothermal
samples
were heated
at 10
C/min
temperature
from 40
to 600
type of
the original
samples
were
heatedover
at 10the
°C/min
over the range
temperature
range
fromC;
40in
tothe
600second
°C; in the
pre-conditioning
100
°C for 30
min,first
followed
by cooling
to
40 first
°C at subjected
20pre-conditioning
°C/min, to
before
second the
typeoriginal
of atexperiment,
the
original
samples
were
an monitoring
isothermal
experiment,
samples
were
subjected
to an
isothermal
at 100 ◦ C for
the
TGA scan on heating
from
600followed
°C◦ at 10 °C/min.
pre-conditioning
at 100 °C
for 40
30◦ to
min,
by cooling to 40 °C at 20 °C/min, before monitoring
30 min, followed by cooling to 40 C at 20 C/min, before monitoring the TGA scan on heating from
◦ C at
◦ C/min.
scan
heating from 40 to 600 °C at 10 °C/min.
40 to the
600TGA
10 on
Figure 2. Thermogravimetric results, % weight loss as a function of temperature of the samples
PEI2000-PLA20
(continuous line),
PEI2000-PLA5
(dashed
line) and PEI800-PLA5
line):
Figure
2. Thermogravimetric
results,
% weight
weight loss
temperature
of(dotted
the
samples
Figure
2. Thermogravimetric
results,
%
loss as
asaafunction
functionof of
temperature
of the
samples
(a) original samples; (b) isothermally preconditioned samples.
PEI2000-PLA20
(continuousline),
line),PEI2000-PLA5
PEI2000-PLA5 (dashed
PEI800-PLA5
(dotted
line): line):
PEI2000-PLA20
(continuous
(dashedline)
line)and
and
PEI800-PLA5
(dotted
(a) original
samples;
isothermally
preconditioned samples.
samples.
(a) original
samples;
(b) (b)
isothermally
preconditioned
Appreciable differences in the thermal degradation of the original samples and preconditioned
samples
can be seen
in theseinFigures.
In particular,
there
is a original
large difference
in the
temperature
Appreciable
differences
the thermal
degradation
of the
samples and
preconditioned
corresponding
to
2%
weight
loss
(T
D2%) between
the
original
and
the
preconditioned
samples,
as
Appreciable
differences
in
the
thermal
degradation
of
the
original
samples
and
preconditioned
samples can be seen in these Figures. In particular, there is a large difference in the temperature
shown
in
Table
1,
as
a
consequence
of
the
moisture
content
in
all
the
samples
studied.
A
comparison
samples
can be seen
in these
particular,
is and
a large
in the
temperature
corresponding
to 2%
weightFigures.
loss (TD2%In
) between
the there
original
the difference
preconditioned
samples,
as
of
Figure
shows
this(Tmoisture
content
has
more influence
on the thermal
stability
ofas
the
shown
in 2a,b
Table
1,weight
as athat
consequence
of
the
moisture
content
in
all
the
samples
studied.
A
comparison
corresponding
to 2%
loss
)
between
the
original
and
the
preconditioned
samples,
shown
D2%
PEI800-PLA5
and
PEI2000-PLA5
polymers,
whichhas
is also reflected
in the
of Tonsetstability
. In Figure
of Figure
shows
that this
moisture
content
influence
on values
thestudied.
thermal
of 2b,
the of
in Table
1, as 2a,b
a consequence
of the
moisture
contentmore
in all
the samples
A comparison
itPEI800-PLA5
can be seenand
thatPEI2000-PLA5
the star polymer
PEI800-PLA5,
freereflected
of moisture,
is thermally
more
stable 2b,
in
polymers,
which
is more
also
in the
of Tonset
. Instability
Figure
Figure
2a,b shows
that
this samples.
moisture
content
has
influence
onvalues
the thermal
of the
comparison
with
the
other
The
thermal
degradation
of
these
samples
occurs
in
two
stages.
it can be seen that the star polymer PEI800-PLA5, free of moisture, is thermally more stable in
PEI800-PLA5
and
PEI2000-PLA5
polymers,
which
is
also
reflected
in
the
values
of
T
.
In
Figure
onset
The
first stage,
is the
more The
pronounced
and occurs of
around
260 °C, occurs
corresponds
to the 2b,
comparison
withwhich
the other
samples.
thermal degradation
these samples
in two stages.
it candecomposition
be seen that the
polymer
PEI800-PLA5,
free
of moisture,
is athermally
more stable in
the star
PLA
arms.
Previous
studies and
have
shown
that PLA
is
degradable
The first stage,ofwhich
is the
more
pronounced
occurs
around
260
°C,thermally
corresponds
to the
comparison
with
the
other
samples.
The
thermal
degradation
of
these
samples
occurs
in two
polymer
as
a
consequence
of
the
presence
of
ester
groups
of
secondary
alkyl
moieties
in
the main
decomposition of the PLA arms. Previous studies have shown that PLA is a thermally degradable
◦ C,
chain,
which
can
break
by
a
thermal
β-elimination
process
in
the
temperature
interval
from
stages.
The
first
stage,
which
is
the
more
pronounced
and
occurs
around
260
corresponds
polymer as a consequence of the presence of ester groups of secondary alkyl moieties in the main to
200
to 250
°C [21,22].
The
second
around
350 °C, have
is associated
decomposition
of the
PEI
the decomposition
of the
PLA
Previous
studies
shown
that
PLA
is a thermally
degradable
chain,
which
can
break
byarms.
a stage,
thermal
β-elimination
process
inwith
thethe
temperature
interval
from
core,
as
shown
by
Acebo
et
al
[18]
and
by
ourselves
[19]
in
studies
of
the
thermal
degradation
of
PEI.
polymer
as250
a consequence
the presence
of ester
groups
of secondary
alkyl moieties
200 to
°C [21,22]. The of
second
stage, around
350 °C,
is associated
with the decomposition
ofin
thethe
PEImain
as shown
by Acebo
al [18] and
by ourselves [19]
in studies
of the
thermal degradation
PEI. 200 to
chain,core,
which
can break
by aet thermal
β-elimination
process
in the
temperature
intervaloffrom
◦
◦
250 C [21,22]. The second stage, around 350 C, is associated with the decomposition of the PEI core,
as shown by Acebo et al [18] and by ourselves [19] in studies of the thermal degradation of PEI.
Materials 2017, 10, 127
4 of 18
Table 1. Thermogravimetric analysis (TGA) results for the original and isothermally preconditioned samples.
Materials
2017, 10, 127
Sample
Heating Rate (◦ C/min)
Original Sample
T 2% (◦ C)
T onset (◦ C)
Preconditioned Sample
T 2% (◦ C)
4 of 18
T onset (◦ C)
Table
1. Thermogravimetric analysis
for the original
and isothermally
PEI2000-PLA5
10 (TGA) results
93.3
234.5
176.4 preconditioned
243.9 samples.
PEI2000-PLA20
10
114.4
243.1
166.7
240.8
Preconditioned
Sample
PEI800-PLA5
10 Rate (°C/min)
114.5Original Sample
239.8
195.1
254.3
Sample
Heating
T2% (°C) Tonset (°C) T2% (°C)
Tonset (°C)
PEI2000-PLA5
10
93.3
234.5
176.4
243.9
10
114.4 by 243.1
166.7 scanning
240.8 calorimetry (DSC,
Figure 3 PEI2000-PLA20
shows the thermogram
obtained
differential
10 of 10 ◦ C/min,
114.5 for
239.8
195.1
254.3
Mettler-ToledoPEI800-PLA5
AG), at the heating rate
the PEI2000-PLA5
sample in its original
state (upper curve). An endothermic peak at approximately 50 ◦ C followed by a shoulder is observed.
Figure 3 shows the thermogram obtained by differential scanning calorimetry (DSC,
This peak has been attributed to the glass transition of PEI2000-PLA5 influenced by the physical aging
Mettler-Toledo AG), at the heating rate of 10 °C/min, for the PEI2000-PLA5 sample in its original
effectstate
and possibly
by theAn
presence
of moisture
(slight
plasticization).
order tobyeliminate
the is
effects
(upper curve).
endothermic
peak at
approximately
50 °C In
followed
a shoulder
of physical
aging
and
humidity,
the
samples
were
subjected
to
two
different
preconditioning
processes:
observed. This peak has been attributed to the glass transition of PEI2000-PLA5 influenced by the
dynamic
and aging
isothermal.
For dynamic
preconditioning,
non-isothermal
scan was made
10 ◦ C/min
physical
effect and
possibly by
the presence of amoisture
(slight plasticization).
In at
order
to
◦
over eliminate
a temperature
range
from 0 to
150 and
C, humidity,
while for the
isothermal
preconditioning,
thedifferent
sample was
the effects
of physical
aging
samples were
subjected to two
dynamic
and isothermal.
For dynamic
a non-isothermal
held preconditioning
at 100 ◦ C for 30processes:
min, each
preconditioning
procedure
beingpreconditioning,
followed by cooling
to 0 ◦ C before
◦
scan
was
made
at
10
°C/min
over
a
temperature
range
from
0
to
150
°C,
while
for
isothermal
starting the DSC scan in which the sample is heated at a rate of 10 C/min from 0 to 150 ◦ C. For such
preconditioning,
the sample
held thermograms
at 100 °C for 30
min, each
preconditioning
procedure beinglower
preconditioned
samples,
Figure was
3 shows
(middle
curve,
dynamic preconditioning;
followed by cooling to 0 °C before starting the DSC scan in which the sample is heated at a rate of 10
curve isothermal preconditioning) in which only the glass transition of the material is observed.
°C/min from 0 to 150 °C. For such preconditioned samples, Figure 3 shows thermograms (middle
Table 2 shows the DSC results for all samples investigated. Both methods of preconditioning give
curve, dynamic preconditioning; lower curve isothermal preconditioning) in which only the glass
the same
glassoftransition
temperature
all the
samples
Thefor
preconditioned
samples have
transition
the material
is observed.inTable
2 shows
thestudied.
DSC results
all samples investigated.
◦
a glass
transition
between
3 and
5 C higher
than thetemperature
non-preconditioned
Both
methodstemperature
of preconditioning
give
the same
glass transition
in all the samples
samples as a
consequence
of the
removal of moisture.
studied. The
preconditioned
samples have a glass transition temperature between 3 and 5 °C higher
thanglass
the non-preconditioned
samples
a consequence
of the removal
of moisture.
The
transition temperature,
Tgas
, of
the three samples
tested, with
different molecular weights
The
glass
transition
temperature,
T
g
,
of
the
three
samples
tested,
with
different
molecular
of the poly(ethyleneimine) core and different degrees of polymerisation of the
lactide
arms in the
◦
◦ C in the
weights ofare
theessentially
poly(ethyleneimine)
and
of polymerisation
of the
star polymer,
the same:core
45.0
± different
1.5 C indegrees
the original
samples and
49.0lactide
± 1.0arms
in the star polymer,
areItessentially
the same:
1.5 °C
the
original samples
and 49.0is± much
1.0 °C in
preconditioned
samples.
is noted that
the Tg45.0
of ±each
of in
the
multiarm
star polymers
higher
the preconditioned samples. It is noted that the Tg of each of the multiarm star polymers is much
than those observed for the hyperbranched polymer, PEIx, which forms the core of the star polymer,
higher than those observed for the hyperbranched polymer, PEIx, which forms the core of the star
for which the Tg is −54 ◦ C for PEI2000 and −58.3 ◦ C for PEI800. The presence of the PLA arms
polymer, for which the Tg is −54 °C for PEI2000 and −58.3 °C for PEI800. The presence of the PLA
increases
glass transition
temperature
with respect
to the to
PEI
It is also
that the
arms the
increases
the glass transition
temperature
with respect
thecore.
PEI core.
It is noteworthy
also noteworthy
glassthat
transition
temperatures
obtained
for
the
PEIx-PLAy
systems
here
are
slightly
lower
than
the glass transition temperatures obtained for the PEIx-PLAy systems here are slightly lowerthose
obtained
samples
offor
PLA
alone,ofaround
57 ◦ C
[23–28],
and
closerand
to that
oftoa that
racemic
amorphous
than for
those
obtained
samples
PLA alone,
around
57 °C
[23–28],
closer
of a racemic
◦
PLA
polymer,
Tg is 47 °C [29].
PLA amorphous
polymer, for
which
the Tfor
47 Cthe
[29].
g iswhich
Figure
3. Differential
scanning
calorimetry
plots
heat(Wg
flow
) as a function
of
−1 )(Wg
Figure
3. Differential
scanning
calorimetry
(DSC)(DSC)
plots of
heatofflow
as a function
of temperature
temperature (°C), at a heating
rate of 10 °C/min, for PEI2000-PLA5 in the original and preconditioned
◦
◦
( C), at a heating rate of 10 C/min, for PEI2000-PLA5 in the original and preconditioned states.
states. The heat flow scale (y-axis) is relative, and the curves have been separated for clarity.
The heat flow scale (y-axis) is relative, and the curves have been separated for clarity.
−1
Materials 2017, 10, 127
Materials 2017, 10, 127
5 of 18
5 of 18
Table 2.
2. Differential
Differential scanning
scanning calorimetry
calorimetry (DSC)
(DSC) results
resultsfor
forthe
thedifferent
differentsamples
samplesinvestigated.
investigated.
Table
Heating Rate
Sample
Heating
Rate
(°C/min)
Sample
(◦ C/min)
10
PEI2000-PLA5
PEI2000-PLA5
10 10
PEI2000-PLA20
PEI2000-PLA20
10
10
PEI800-PLA5
PEI800-PLA5
10
PEI
800
PEI 800
10 10
PEI
2000
PEI 2000
10 10
Original
Original
sample
Sample
43.8
43.8
45.7
45.7
46.5
46.5
−58.3
−
58.3
−54.0
−
54.0
Tg (°C)
T g (◦ C)
Dynamic
Isothermal
Dynamic preconditioned
Isothermal
preconditioned
Preconditioned
Preconditioned
48.2
48.8
48.2
48.6
48.8 48.8
48.6
48.8
49.1
50.4
49.1
50.4
- - -
During the heating above the glass transition, the calorimetric curves of Figure 3 do not display
During the heating above the glass transition, the calorimetric curves of Figure 3 do not display
any exothermic peak, which would be characteristic of cold crystallization, nor any peak associated
any exothermic peak, which would be characteristic of cold crystallization, nor any peak associated
with melting. Most DSC thermograms were made over the temperature range from 0 to 150 °C, but
with melting. Most DSC thermograms were made over the temperature range from 0 to 150 ◦ C, but
additional scans were also made for the multiarm star polymers over a wider temperature range,
additional scans were also made for the multiarm star polymers over a wider temperature range,
from −65 to 180 °C, including a first scan, a quench, and a second scan. This was done to verify that
from −65 to 180 ◦ C, including a first scan, a quench, and a second scan. This was done to verify that
there was no residual glass transition of the PEI, and to demonstrate that PEI2000-PLA5, and also the
there was no residual glass transition of the PEI, and to demonstrate that PEI2000-PLA5, and also
PEI2000-PLA20 and PEI800-PLA5 systems, are amorphous and non-crystallizable, in comparison
the PEI2000-PLA20 and PEI800-PLA5 systems, are amorphous and non-crystallizable, in comparison
with quenched samples of PLA, for which cold crystallization occurs in the range 102–122 °C and the
with quenched samples of PLA, for which cold crystallization occurs in the range 102–122 ◦ C and the
endothermic peak due to melting at 148–175 °C [23,24,26,27].
endothermic peak due to melting at 148–175 ◦ C [23,24,26,27].
Dielectric Relaxation
Relaxation Spectroscopy
Spectroscopy (DRS)
(DRS)
Dielectric
In this
present
andand
discuss
the results
of dielectric
relaxation
spectroscopy
(DRS, TA
In
thissection,
section,wewe
present
discuss
the results
of dielectric
relaxation
spectroscopy
Instruments,
Inc., New
DE, USA)
on each
of of
thethethree
(PEI2000-PLA5,
(DRS,
TA Instruments,
Inc.,Castle,
New Castle,
DE, USA)
on each
three systems
systems (PEI2000-PLA5,
PEI2000-PLA20,
PEI800-PLA5)
separately,
and
then
compare
the
behaviors
in
order
to identify
identify the
the
PEI2000-PLA20, PEI800-PLA5) separately, and then compare the behaviors in order to
effects
of
the
different
molecular
structures
(PEI
core
and
PLA
arms)
and
hence
obtain
information
effects of the different molecular structures (PEI core and PLA arms) and hence obtain information
about the
the molecular
molecular relaxation
relaxation processes.
processes.
about
(1) PEI2000-PLA5
PEI2000-PLA5
(1)
Dielectric relaxation
relaxation
curves
for PEI2000-PLA5,
PEI2000-PLA20,
and preconditioned
PEI800-PLA5
Dielectric
curves
for PEI2000-PLA5,
PEI2000-PLA20,
and PEI800-PLA5
◦
preconditioned
samples
were
obtained
at
0.5
and
2
°C/min,
over
the
frequency
range
from
Hz to
samples were obtained at 0.5 and 2 C/min, over the frequency range from 0.1 Hz to 100 kHz,0.1
in order
0
00
100
kHz,the
in dielectric
order to constant
obtain the
dielectric
factor
ε", illustration,
and tan δ Figure
signals.4 shows
As an
to
obtain
ε , loss
factor εconstant
, and tanε′,δ loss
signals.
As an
illustration,
4 shows
thefor
dielectric
relaxation curves
for the PEI2000-PLA5 sample.
the
dielectricFigure
relaxation
curves
the PEI2000-PLA5
sample.
Figure
C/min over
Figure 4.4. Dielectric
Dielectric relaxation
relaxation spectroscopy
spectroscopy curves
curves (DRS)
(DRS)for
forPEI2000-PLA5
PEI2000-PLA5atat0.5
0.5◦ °C/min
over the
the
frequency
frequency range
range from
from0.5
0.5Hz
Hzto
to100
100kHz,
kHz,as
asdefined
definedin
inthe
theinset.
inset.
Four dipolar relaxations can be observed in the dielectric relaxation curves of PEI2000-PLA5:
these are labelled γ, β, α, and α′, from lowest to highest temperature. The γ-relaxation appears
Materials 2017, 10, 127
6 of 18
Materials
10, 127
6 ofthese
18
Four 2017,
dipolar
relaxations can be observed in the dielectric relaxation curves of PEI2000-PLA5:
are labelled γ, β, α, and α0 , from lowest to highest temperature. The γ-relaxation appears between −90
between −90 and −50 °C depending on the measurement frequency, shifting to higher temperature as
and −50 ◦ C depending on the measurement frequency, shifting to higher temperature as the frequency
the frequency increases. The β-relaxation is hidden at low frequencies, but appears as a shoulder at
increases. The β-relaxation is hidden at low frequencies, but appears as a shoulder at frequencies
frequencies above 500 Hz, in the temperature interval between 70 °C (0.5 kHz) and 90 °C (100 kHz),
above 500 Hz, in the temperature interval between 70 ◦ C (0.5 kHz) and 90 ◦ C (100 kHz), increasing in
increasing in temperature as the frequency increases. In order to determine approximately the
temperature
the frequency
increases.
In order
to determine
approximately
frequency
dependence
frequency as
dependence
of this
β-relaxation,
an “onset”
temperature
is foundthe
from
the intersection
of
of tangents
this β-relaxation,
an
“onset”
temperature
is
found
from
the
intersection
of
tangents
before is
and
before and after the shoulder, and is used instead of a peak temperature. The α-relaxation
after
shoulder,
and is used
instead
of a peak
temperature.
The α-relaxation
the dominant
thethe
dominant
relaxation,
the peak
temperature
increasing
from around
80 °C at theisfrequency
of
◦ C at the frequency of 1 Hz to 190 ◦ C at
relaxation,
the
peak
temperature
increasing
from
around
80
1 Hz to 190 °C at 100 kHz. A shoulder, associated with the relaxation labelled α', is observed at
100temperatures
kHz. A shoulder,
with the
is observed at different
temperatures
above
aboveassociated
the α-relaxation.
Therelaxation
relaxationlabelled
map forα',
PEI2000-PLA5
heating
ratesthe
α-relaxation.
relaxation
map for PEI2000-PLA5 at different heating rates is shown in Figure 5.
is shown in The
Figure
5.
Figure5. 5. Relaxation
Relaxation map
sample
at different
heating
rates: rates:
0.5 °C/min
Figure
mapfor
forPEI2000-PLA5
PEI2000-PLA5
sample
at different
heating
0.5 ◦(open
C/min
symbols) and 2 °C/min
(filled symbols).
◦
(open symbols) and 2 C/min (filled symbols).
It can be seen that the heating rate has virtually no influence on the relaxation behavior. An
It can be
seen that on
thetemperature
heating rate
no γinfluence
on the relaxation
behavior.
Arrhenius
dependence
canhas
be virtually
seen for the
and β-relaxations,
from which
the
Anactivation
Arrhenius
dependence
on
temperature
can
be
seen
for
the
γand
β-relaxations,
from
which
energy, averaged for the two heating rates used, was found as 50.2 ± 2.3 kJ/mol for the
theγ-relaxation
activation energy,
forfor
thethe
two
heating rates
was found
50.2 ±obtained
2.3 kJ/mol
for the
and 267averaged
± 15 kJ/mol
β-relaxation.
Theused,
activation
energyasvalues
for each
γ-relaxation
and
± 15inkJ/mol
heating rate
are267
shown
Table 3.for the β-relaxation. The activation energy values obtained for each
heatingInrate
are shown
Table 3.
contrast,
theinα-relaxation
shows a slight curvature which is characteristic of the
Vogel–Fulcher–Tammann
(VFT) equation:
In contrast, the α-relaxation
shows a slight curvature which is characteristic of the
Vogel–Fulcher–Tammann (VFT) equation:
(1)
ln (fm) =A − B/(T − T0)
ln the
(f m )maximum
= A − B/(T
T0 )δ occurs at the temperature T. The(1)
where fm is the frequency for which
in−tan
parameters A, B, and T0 of the VFT equation can be determined as follows. Selecting an initial value
where
is the frequency
for Twhich
tan δBoccurs
at the temperature
T. The parameters
of T0f m
between
Tg − 30 and
g − 70,the
themaximum
values of in
A and
are obtained
by a least squares
fit of the
A, experimental
B, and T0 of the
VFT
equation
can
determined
as follows.
Selecting
an initial
value of T
data,
together
with
thebe
degree
of fit. This
procedure
is repeated
for successive
values
of
0 between
Tg T−0 until
30 and
the values
of A and B
are obtained
by athe
least
squaresvalues
fit of the
data,
theTbest
possible
fit is obtained,
which
thus defines
required
of Texperimental
0, A, and B. The
g − 70,
values with
obtained
A, B,of
and
in this
way for PEI2000-PLA5
are:
A = 18.6 ± values
2.0, B = of
1583
314 K,
and
together
the for
degree
fit.T0This
procedure
is repeated for
successive
T0±until
the
best
T0 = 282.5
7.5 K, being
the average
of thethe
values
obtained
for of
theTdifferent
rates. Given
thatfor
possible
fit is± obtained,
which
thus defines
required
values
B. The values
obtained
0 , A, and heating
for this
sample
is 321.5
K by DSC (seeare:
Table
it can
be B
seen
that±T0314
is approximately
40 K±less
A, T
B,g and
T0 in
this way
for PEI2000-PLA5
A =2),
18.6
± 2.0,
= 1583
K, and T0 = 282.5
7.5 K,
thanthe
theaverage
calorimetric
g. Tableobtained
3 lists thefor
results
obtainedheating
for eachrates.
heating
rate.
As Twell
as
fitting
the
being
of theTvalues
the different
Given
that
for
this
sample
is
g
VFT
equation,
an
"apparent"
activation
energy,
E
app, for the α-relaxation can be determined from the
321.5 K by DSC (see Table 2), it can be seen that T0 is approximately 40 K less than the calorimetric Tg .
slope
of athe
best
fit straight
linefor
to each
the data,
which
gives
values
of 264 the
kJ/mol
241 kJ/mol
for the
Table
3 lists
results
obtained
heating
rate.
As well
as fitting
VFTand
equation,
an “apparent”
heating rates
of 2Eand, 0.5
°C/min, respectively (average value 252 ± 12 kJ/mol).
activation
energy,
app for the α-relaxation can be determined from the slope of a best fit straight line
to the data, which gives values of 264 kJ/mol and 241 kJ/mol for the heating rates of 2 and 0.5 ◦ C/min,
respectively (average value 252 ± 12 kJ/mol).
Materials 2017, 10, 127
Materials 2017, 10, 127
7 of 18
7 of 18
Table 3.3.Activation
values
Ea and
Vogel–Fulcher–Tammann
(VFT) parameters
for the different
Table
Activationenergy
energy
values
Ea and
Vogel–Fulcher–Tammann
(VFT) parameters
for the
samples studied.
different
samples studied.
Sample
Sample
α Relaxation
Relaxation
α
Relaxation β β
Relaxation
Heating
Heating
Raterate γ γ
Relaxation
Relaxation
VFT
Parameters
VFT Parameters
(◦ C/min)
(°C/min)
Eapp
(kJ/mol) A A
a (kJ/mol)
a (kJ/mol)
(K) T
Eapp
(kJ/mol)
Ea E
(kJ/mol)
Ea E
(kJ/mol)
BB(K)
T 00 (K)
(K)
PEI2000-PLA5
PEI2000-PLA5
0.5 0.5
2 2
52.5
52.5
48.0
48.0
282282
252252
241241
264264
20.3 1898
1898
20.3
16.3 1268
1268
16.3
0.5
PEI2000-PLA200.5
PEI2000-PLA20
2 2
57.2
57.2
50.8
50.8
364364
345345
169169
171171
16.2 1572
1572
16.2
13.9 1226
1226
13.9
PEI800-PLA5
PEI800-PLA5
0.5 0.5
2 2
55.1
55.1
52.3
52.3
265265
258258
187187
202202
16.8 1405
1405
16.8
13.4
13.4 809
809
PEI2000
PEI2000
0.5 0.5
2 2
42.0
42.0
41.2
41.2
86.4
86.4
99.0
99.0
78.1
78.1
63.3
63.3
25.1 4512
4512
25.1
18.7
18.7 2905
2905
PEI800
PEI800
0.5 0.5
2 2
46.2
46.2
45.8
45.8
181181
155155
71.3
71.3
66.6
66.6
22.4
22.4 3544
3544
15.5
15.5 1459
1459
PLA
PLA[28]
[28]
-
- -
39.1
39.1
- -
35.9
35.9 1840
1840
PLA[30]
[30]
PLA
-
- -
41.1
41.1
- -
- -
-
--
291
291
275
275
268
268
281
281
274
274
297
297
82
82
109
109
88
156
156
279
279
-
(2)
(2) PEI2000
PEI2000
Figure
showsthe
therelaxation
relaxation
curves
PEI2000,
poly(ethyleneimine),
obtained
the
Figure 66 shows
curves
forfor
PEI2000,
poly(ethyleneimine),
obtained
underunder
the same
same
conditions
as
for
PEI2000-PLA5,
in
order
to
compare
the
relaxation
peaks
of
both
samples
and
conditions as for PEI2000-PLA5, in order to compare the relaxation peaks of both samples and hence
hence
elucidate
their possible
these spectra
for PEI2000,
the γ-relaxation
can be
seen at
elucidate
their possible
origins.origins.
In theseInspectra
for PEI2000,
the γ-relaxation
can be seen
at around
◦
around
°Cfrequency
at the frequency
1 Hz,
and it
higher temperatures
with increasing
−90 C −90
at the
of 1 Hz, of
and
it moves
to moves
higher to
temperatures
with increasing
frequency.
frequency.
This
relaxation
peak
is
attributed
to
local
motions
of
the
–NH
2
groups
of
PEI
[19]. map
The
This relaxation peak is attributed to local motions of the –NH2 groups of PEI [19]. The relaxation
relaxation
for rates
different
heatinginrates
is 6,depicted
inlinear
Figure
6, where between
the linear
for differentmap
heating
is depicted
Figure
where the
relationship
ln(frelationship
m ) and 1/T
between
) and 1/T behavior,
indicates for
an which
Arrhenius
behavior, energy
for which
the activation
energy
associated
indicates ln(f
an m
Arrhenius
the activation
associated
with this
process
is found
with
this
process
is
found
as
41.6
±
0.4
kJ/mol
(see
Table
3),
somewhat
lower
than
but
of
the
same
as 41.6 ± 0.4 kJ/mol (see Table 3), somewhat lower than but of the same order of magnitude as
the
order
of magnitude
theγ-relaxation
activation energy
for the γ-relaxation
of kJ/mol).
PEI2000-PLA5 (50.2 ± 2.1 kJ/mol).
activation
energy forasthe
of PEI2000-PLA5
(50.2 ± 2.1
Figure 6. Dielectric
at 0.5
0.5 ◦°C/min,
Dielectric relaxation
relaxation spectroscopy
spectroscopy curves
curves for the PEI2000 sample at
C/min, for
for the
frequency range from 0.1 Hz to 100 kHz.
The
above the
the γ
γ peak,
peak,
The β-relaxation
β-relaxation of
of PEI2000,
PEI2000, aa dipolar
dipolar relaxation,
relaxation, is
is observed
observed at
at temperatures
temperatures above
appearing
first
as
a
shoulder
at
a
temperature
of
about
−40
°C
at
a
frequency
of
0.1
kHz,
and
◦
appearing first as a shoulder at a temperature of about −40 C at a frequency of 0.1 kHz, and moving
moving
higher temperatures
and becoming
more pronounced
with frequency.
increasingThis
frequency.
This
to highertotemperatures
and becoming
more pronounced
with increasing
relaxation
is
relaxation
is
associated
with
motions
of
the
lateral
branches
of
PEI
[19].
The
average
activation
associated with motions of the lateral branches of PEI [19]. The average activation energy, calculated
energy,
slope of theinlinear
in Figure
is 92.7to±the
6.3comparison
kJ/mol. In
from thecalculated
slope of thefrom
linearthe
representation
Figurerepresentation
7, is 92.7 ± 6.3 kJ/mol.
In 7,
contrast
contrast to the comparison of the γ-relaxations, this activation energy for the β-relaxation of PEI2000
is much lower than the average value for the β-relaxation of PEI2000-PLA5 (267.0 ± 14.8 kJ/mol,
Materials 2017, 10, 127
8 of 18
of theMaterials
γ-relaxations,
this activation energy for the β-relaxation of PEI2000 is much lower8 than
the
2017, 10, 127
of 18
average value for the β-relaxation of PEI2000-PLA5 (267.0 ± 14.8 kJ/mol, Table 3). This indicates
Table
3).relaxations
This indicates
the two origin:
relaxations
have arms
a different
the PLA
armsdo
in not
the exist
that the
two
havethat
a different
the PLA
in theorigin:
PEIx-PLAy
system
PEIx-PLAy system do not exist in PEI2000.
in PEI2000.
Figure 7. Relaxation map for PEI2000 at different heating rates: 0.5 °C/min (open symbols) and
Figure 7. Relaxation map for PEI2000 at different heating rates: 0.5 ◦ C/min (open symbols) and
2
°C/min (filled symbols).
2 ◦ C/min (filled symbols).
The α-relaxation, associated with the glass transition of PEI, is observed at temperatures higher
than α-relaxation,
those of the β-relaxation,
of the peakoftemperatures
obtained
for the different
The
associated and
withthe
theinverse
glass transition
PEI, is observed
at temperatures
higher
plotted in theand
relaxation
map of
7. Intemperatures
the same wayobtained
as for thefor
PEIx-PLAy
than frequencies
those of theareβ-relaxation,
the inverse
of Figure
the peak
the different
systems,are
a non-linear
relationship
is observed,
it is 7.
lessIn
well
the as
frequency
is
frequencies
plotted in
the relaxation
map though
of Figure
thedefined
same as
way
for therange
PEIx-PLAy
smaller.
If
this
behavior
is
fitted
by
the
VFT
equation,
we
obtain
the
results
shown
in
Table
3
for
the
systems, a non-linear relationship is observed, though it is less well defined as the frequency range
different heating rates used. The average results for the different heating rates are A = 21.9 ± 3.2,
is smaller. If this behavior is fitted by the VFT equation, we obtain the results shown in Table 3 for
B = 3709 ± 804 K, and T0 = 95.5 ± 12.8 K. As can be seen, the value obtained for the parameter B is very
the different
heating rates used. The average results for the different heating rates are A = 21.9 ± 3.2,
high and T0 is very low, more than 120 K below Tg, which does not seem reasonable. This is possibly
B = 3709
±
804
K, and
12.8 K.
can be seen,
value obtained
the parameter
0 = 95.5 ± range
a consequence
of anTinsufficient
of As
temperatures
andthe
frequencies
to obtainfor
reliable
values for B is
very these
high parameters.
and T0 is very
low, more
120 activation
K below energy,
Tg , which
seem reasonable.
This is
Accordingly,
thethan
apparent
Eapp,does
from not
the average
slope of a best
possibly
a consequence
of anforinsufficient
range
of temperatures
andmeans
frequencies
to obtain
reliable
fit straight
line to the data
the α-relaxation
provides
a more reliable
of comparing
the two
systems.
Forparameters.
PEI, Eapp takes
values of 78.1
andactivation
63.3 kJ/mol
for theEheating
rates
0.5 andslope
values
for these
Accordingly,
the kJ/mol
apparent
energy,
theofaverage
app , from
2
°C/min,
respectively,
the
average
value
being
70.7
±
7.4
kJ/mol.
This
is
noticeably
less
than
for
of a best fit straight line to the data for the α-relaxation provides a more reliable means ofthat
comparing
PEI2000-PLA5,
252
±
12
kJ/mol,
suggesting
a
much
higher
degree
of
co-operativity
in
the
molecular
the two systems. For PEI, Eapp takes values of 78.1 kJ/mol and 63.3 kJ/mol for the heating rates of 0.5
associated with the glass transition of the PEIx-PLAy systems.
◦ C/min,
and 2motions
respectively, the average value being 70.7 ± 7.4 kJ/mol. This is noticeably less than
The α-relaxation peak is an asymmetric peak in which the presence of a shoulder on the high
that for PEI2000-PLA5, 252 ± 12 kJ/mol, suggesting a much higher degree of co-operativity in the
temperature side can be clearly observed in Figure 6. The presence of this shoulder seems to suggest
molecular
motions associated with the glass transition of the PEIx-PLAy systems.
the existence of a relaxation peak, overlapping the dipolar α-relaxation and associated with ionic
The
α-relaxation
peak
is which
an asymmetric
peak inaswhich
the presence
shoulderby
onother
the high
charge
trapped in the
PEI,
could be labelled
an α'-relaxation.
Thisof
is asupported
temperature
side
can
be
clearly
observed
in
Figure
6.
The
presence
of
this
shoulder
seems
to
suggest
results, not shown here but to be reported in another paper, where the effect of the molecular weight
the existence
of
a
relaxation
peak,
overlapping
the
dipolar
α-relaxation
and
associated
with
of the PEI core, up to 25000, on this ionic relaxation is revealed. It is observed there that, withionic
0 -relaxation. to
increasing
weight
of the
PEI be
core,
this shoulder
the is
ionic
α'-relaxation
charge
trappedmolecular
in the PEI,
which
could
labelled
as an αcorresponding
This
supported
by other
becomes
more here
pronounced
and
is clearlyinevident
over
a wider
frequency
range.
results,
not shown
but to be
reported
another
paper,
where
the effect
of the molecular weight of
the PEI core, up to 25000, on this ionic relaxation is revealed. It is observed there that, with increasing
(3) PLA
molecular weight of the PEI core, this shoulder corresponding to the ionic α0 -relaxation becomes more
Many
dielectric
studies
of amorphous
poly(lactide)
can
be found in the literature, which show
pronounced
and
is clearly
evident
over a wider
frequency
range.
that there are three dielectric relaxations, usually designated as αn, αs, and β in order of decreasing
temperature [30]. The αn-relaxation is assigned to the normal mode relaxation due to the component
(3) PLA
of dipole vector aligned in the direction parallel to the chain contour and the fluctuation of the
Many
dielectric
amorphous
poly(lactide)
can be
found in
the literature,
which
end-to-end
vector,studies
and the of
αs-relaxation
is assigned
to the local
segmental
modes
associated with
theshow
that there
are
three
dielectric
relaxations,
usually
designated
as
α
,
α
and
β
in
order
of
decreasing
n
s, Tg, and hence is attributed
glass transition. The β-relaxation is observed at temperatures well below
temperature
[30].relaxations
The αn -relaxation
is assigned
normaltomode
relaxation
the component
to secondary
in the glassy
state, andtointhe
particular
twisting
motions due
of thetomain
chains
as there
are noaligned
flexible side
groups
on which
dipoles
attached
of dipole
vector
in the
direction
parallel
toare
the
chain [28,30].
contour and the fluctuation of the
end-to-end vector, and the αs -relaxation is assigned to the local segmental modes associated with the
glass transition. The β-relaxation is observed at temperatures well below Tg , and hence is attributed to
Materials 2017, 10, 127
9 of 18
secondary relaxations in the glassy state, and in particular to twisting motions of the main chains as
there are no flexible side groups on which dipoles are attached [28,30].
Pluta et al [27] found that the temperature dependence of the αs -relaxation follows the VFT
Equation (1) with T0 = 302 K and B = 800 K, which are stated to be in reasonable agreement with other
results [29,30]. This value of T0 , though, is only 28 K below the measured Tg of 330 K, which seems
rather low. Accordingly, we converted these values into an apparent activation energy of 354 kJ/mol
at an average temperature of 350 K, for comparison with our own results listed in Table 3. This is a
very high value for the activation energy, and it is consistent with the observation that incorporating
the PLA arms onto the PEI2000 core molecule results in a much higher activation energy for the
PEI2000-PLA5 sample in comparison with that for the PEI2000 alone. Indeed, as is shown below,
the activation energy for the glass transition increases significantly relative to the PEI core in all the
PEIx-PLAy systems studied here.
Pluta et al [27] also reported a secondary β-relaxation in PLA, with an activation energy
of 41.5 kJ/mol, in reasonable agreement with other values in the literature: 39.1 kJ/mol [28];
43.9 kJ/mol [29]; 41.1 kJ/mol [30]; 36.4 kJ/mol [31].
The γ-relaxation for PEI2000-PLA5, whose maximum is located between –90 ◦ C at 1 Hz and
◦
–50 C at 1 kHz, corresponds approximately with the temperature of the β-relaxation in PLA (–80 ◦ C) at
a frequency of 1 Hz, though the average activation energy, 50.2 ± 2.3 kJ/mol for PEI2000-PLA5,
is somewhat higher than that of the β-relaxation of PLA (36.4 to 43.9 kJ/mol, as listed above).
Accordingly, the γ-relaxation in PEI2000-PLA5 could be associated with the terminal –OH groups
of the PLA arms, with some additional hindrance resulting from the PLA being incorporated as the
arms of the star-shaped polymer. The γ-relaxation of the PEI2000, associated with terminal –NH2
groups, is also observed in the same temperature range and its activation energy (41.6 ± 0.4 kJ/mol)
is similar to that of PEI2000-PLA5. However, the γ-relaxation of PEI2000-PLA5 cannot be correlated
with the γ-relaxation of PEI2000, because the movements of the –NH2 groups should not be seen, as a
consequence of their replacement by PLA chains.
The β-relaxation of PEI2000-PLA5 is only observed above 0.5 kHz, and then only as a
superimposed shoulder, at about 80 ◦ C, on the low temperature flank of the α-relaxation. The activation
energy for the β-relaxation of PEI2000-PLA5 is 267 ± 15 kJ/mol, which is much higher than
the β-relaxation of PEI2000 (92.7 ± 6.3 kJ/mol). This suggests that this relaxation could be due
to movements of the entire chain of PLA which forms the arms of the multiarm star polymer.
The segmental motions associated with the glass transition of PLA have a VFT temperature dependence,
from which one can estimate an apparent activation energy of about 114 kJ/mol at 350 K [24,30],
approximately the same temperature as that at which the β-relaxation of PEI2000-PLA5 is observed.
The implication of this would be that these segmental motions of the PLA arms are considerably
restricted if they appear as the β-relaxation in the PEIxPLAy multiarm star polymers.
On the other hand, the α-relaxation of PEI2000-PLA5, occurring at 70 ◦ C at 1 Hz, is associated
with the glass transition of the polymer and could correspond to the αs -relaxation of the PLA
(occurring at about 60 ◦ C at 1 Hz [27]), but displaced to higher temperatures by the effect of the
PEI2000 core. The α0 -relaxation of PEI2000-PLA5 (90 ◦ C at 1 Hz) corresponds to the αN -relaxation of
the PLA (85 ◦ C at 1 Hz [27]), influenced by the PEI core [27], without excluding the possibility that
it could be a Maxwell–Wagner–Sillars type ionic peak because the material may have nano-regions
of different conductivity. Above 1 kHz, the α- and α0 -relaxations overlap and cause a unique dipolar
relaxation. As seen in Figure 5, the relationship between ln(f m ) and T −1 is practically linear, from
which the apparent average activation energy for the α0 -relaxation in the PEI2000-PLA5 is found as
263 ± 38 kJ/mol.
(4) PEI2000-PLA20
The multiarm star polymer PEI2000-PLA20 has the same structure as PEI2000-PLA5, but with the
ratio of lactide repeat units to N links now being 20 instead of five. The dielectric relaxation curves
Materials 2017, 10, 127
10 of 18
for PEI2000-PLA20 are virtually identical to those for PEI2000-PLA5. The relaxation map, shown
in Figure 8, indicates the existence of γ, β, α, and α0 relaxations, very similar to the relaxation map
Materials
2017, 10, 127 (Figure 5) but with some small displacements as a consequence of the effect
10 of of
18
for PEI2000-PLA5
increasing
the10,
number
of lactide repeat units.
Materials 2017,
127
10 of 18
Figure 8. Relaxation map for PEI2000-PLA20 at different heating rates: 0.5 °C/min (open symbols)
Figure 8. Relaxation map for PEI2000-PLA20 at different heating rates: 0.5 °C/min
(open symbols)
Figure
8. Relaxation
map for PEI2000-PLA20 at different heating rates: 0.5 ◦ C/min (open symbols)
and
2 °C/min
(filled symbols).
and ◦2 °C/min (filled symbols).
and 2 C/min (filled symbols).
The γ-relaxation (local motions of the –OH groups) is observed in PEI2000-PLA20 at
The γ-relaxation (local motions of the –OH groups) is observed in PEI2000-PLA20 at
temperatures
lower
for
PEI2000-PLA5.
Thus,
kHz,
γ-relaxationofof
The
γ-relaxation
(local
motions
the –OH groups)
is observed
inγ-relaxation
PEI2000-PLA20
atPEI2000-PLA5
temperatures
temperatures
lowerthan
thanthose
those
forof
PEI2000-PLA5.
Thus,
atat11kHz,
PEI2000-PLA5
appears
at
−48
°C
while
that
of
PEI2000-PLA20
appears
at
−53
°C
(−27
and
−37
°C
kHz,
lower
than
those
for
PEI2000-PLA5.
Thus,
at
1
kHz,
γ-relaxation
of
PEI2000-PLA5
appears
at
appears at −48 °C while that of PEI2000-PLA20 appears at −53 °C (−27 and −37 °C forfor
10 10
kHz,
◦ C while Figure
◦ C (−27
◦ C for 10
respectively),
9a,b.
The
activation
energy
is
similar
in
both
polymers
(50.2
±
2.3
kJ/mol
in
−48
that
of
PEI2000-PLA20
appears
at
−
53
and
−
37
kHz,
respectively),
respectively), Figure 9a,b. The activation energy is similar in both polymers (50.2 ± 2.3 kJ/mol in
PEI2000-PLA5
54.0
kJ/mol
20).Increasing
Increasing
the
ratio
lactide
repeat
units
to
Figure
9a,b. Theand
activation
energy
is in
similar
in both polymers
(50.2 ±
2.3
kJ/mol
in PEI2000-PLA5
PEI2000-PLA5
and
54.0±±3.2
3.2
kJ/mol
in PEI2000-PLA
PEI2000-PLA
20).
the
ratio
ofof
lactide
repeat
units
toand
N
links,
temperature
the γ-relaxation
γ-relaxation
occurs
but
doesunits
notsignificantly
significantly
affect
54.0
±
3.2reduces
kJ/mol
in
20).
Increasing
the ratio of
lactide
repeat
to
N links, affect
reduces
N
links,
reducesthe
thePEI2000-PLA
temperature at
at which
which
the
occurs
but
does
not
thethe
activation
isis also
unaffected
by the
theheating
heating
rate
(57.2kJ/mol
kJ/mol
temperature
at
whichwhich
the γ-relaxation
occurs but
does not significantly
affect
the(57.2
activation
energy,
activationenergy,
energy,
which
also relatively
relatively
unaffected
by
rate
at at
◦
0.5
°C/min
and
50.8
atat22°C/min
forheating
PEI2000-PLA20),
Table3.3.
Figure
9a,b
also
shows
that
0.5
°C/min
and
50.8kJ/mol
kJ/mol
°C/min
PEI2000-PLA20),
Table
Figure
9a,b
also
shows
thethe
which
is also
relatively
unaffected
by the
rate (57.2 kJ/mol
at
0.5 C/min
and
50.8 that
kJ/mol
at
ofthe
the
relaxationisisgreater
greater
in
PEI2000-PLA20
than
ininPEI2000-PLA5,
regardless
heating
intensity
relaxation
than
PEI2000-PLA5,
regardless
of
heating
2 ◦intensity
C/minoffor
PEI2000-PLA20),
Tablein
3.PEI2000-PLA20
Figure 9a,b also
shows
that the intensity
of the of
relaxation
is
rate
and
frequency,
this
effect
being
related
the
mobility
of
a
larger
number
of
OH
groups
present
rate
and
frequency,
this
effect
being
related
to
the
mobility
of
a
larger
number
of
OH
groups
present
greater in PEI2000-PLA20 than in PEI2000-PLA5, regardless of heating rate and frequency, this effect
in
PEI2000-PLA20
structure.
in
thethe
PEI2000-PLA20
structure.
being
related
to the mobility
of a larger number of OH groups present in the PEI2000-PLA20 structure.
(a)
(a)
(b)
(b)
Figure 9. Dielectric relaxation spectroscopy curves for the γ-relaxation for the different samples
Figure
9. Dielectric
relaxation
curves
for
samples
studied:
PEI2000-PLA5
(blackspectroscopy
circles), PEI2000-PLA20
(redγ-relaxation
squares) and
PEI800-PLA5
(blue
Figure 9.
Dielectric
relaxation
spectroscopy
curves for
for the
the
γ-relaxation
for the
the different
different samples
studied:
PEI2000-PLA5
(black
circles),
PEI2000-PLA20
(red
squares)
and
PEI800-PLA5
(blue
triangles)
at
frequencies:
(a)
1
kHz;
(b)
10
kHz.
Heating
rate:
0.5
°C/min.
studied: PEI2000-PLA5 (black circles), PEI2000-PLA20 (red squares) and PEI800-PLA5 (blue triangles)
triangles)
at frequencies:
kHz;
(b)Heating
10 kHz.rate:
Heating
rate: 0.5 °C/min.
at frequencies:
(a) 1 kHz; (a)
(b)110
kHz.
0.5 ◦ C/min.
The β-relaxation of the PEI2000-PLA20, due to movements of the entire chain of PLA, occurs as
a shoulder
at low frequencies
but develops as a peak
as the frequency
increases.chain
Figure 10
shows the as
T
he β-relaxation
β-relaxation
of
The
of the
the PEI2000-PLA20,
PEI2000-PLA20, due
due to
to movements
movements of
of the
the entire
entire chain of
of PLA,
PLA, occurs
occurs as
β-relaxation
of PEI2000-PLA5
compared
with
PEI2000-PLA20
at 100 increases.
kHz for the
heating
rate ofthe
aa shoulder
at
low
frequencies
but
develops
as
a
peak
as
the
frequency
Figure
10
shoulder at low frequencies but develops as a peak as the frequency increases. Figureshows
10 shows
0.5 °C/min.of For
PEI2000-PLA5,
a shoulder
can
be seen between
60
and 85
°C, while rate
for
β-relaxation
PEI2000-PLA5
compared
with
PEI2000-PLA20
at at
100
kHz
the β-relaxation
of PEI2000-PLA5
compared
with
PEI2000-PLA20
100
kHzfor
forthe
theheating
heating rate of
of
PEI2000-PLA20
there
is
a
clear
peak
with
a
maximum
around
75
°C.
This
is
because
the
higher
ratio
0.5 °C/min. For PEI2000-PLA5, a shoulder can be seen between 60 and 85 °C, while for
of lactide repeat
units
N links
in PEI2000-PLA20
results
in a 75
higher
glassistransition
temperature,
PEI2000-PLA20
there
is to
a clear
peak
with a maximum
around
°C. This
because the
higher ratio
and
hence
a
greater
separation
of
the
βand
α-relaxations.
The
relaxation
map,
Figure
8,
shows
that
of lactide repeat units to N links in PEI2000-PLA20 results in a higher glass transition temperature,
this β-relaxation is insensitive to the heating rate.
and hence a greater separation of the β- and α-relaxations. The relaxation map, Figure 8, shows that
this β-relaxation is insensitive to the heating rate.
Materials 2017, 10, 127
11 of 18
0.5 ◦ C/min. For PEI2000-PLA5, a shoulder can be seen between 60 and 85 ◦ C, while for PEI2000-PLA20
there is a clear peak with a maximum around 75 ◦ C. This is because the higher ratio of lactide repeat
units to N links in PEI2000-PLA20 results in a higher glass transition temperature, and hence a greater
separation of the β- and α-relaxations. The relaxation map, Figure 8, shows that this β-relaxation is
Materials 2017,
10, 127
11 of 18
insensitive
to the
heating rate.
Materials 2017, 10, 127
11 of 18
Figure
Dielectric relaxation
curves
for the
for the different
samples studied:
Figure
10.10.Dielectric
relaxationspectroscopy
spectroscopy
curves
forβ-relaxation
the β-relaxation
for the different
samples
PEI2000-PLA5, PEI2000-PLA20 and PEI800-PLA5. Frequency: 100 kHz. Heating rate: 0.5 °C/min.
studied:
PEI2000-PLA5,
PEI2000-PLA20
and
PEI800-PLA5.
Frequency:
100
kHz.
Heating
rate:
Figure 10. Dielectric relaxation spectroscopy curves for the β-relaxation for the different samples studied:
◦
0.5
C/min. PEI2000-PLA20 and PEI800-PLA5. Frequency: 100 kHz. Heating rate: 0.5 °C/min.
PEI2000-PLA5,
The α-relaxation is observed in PEI2000-PLA20 at higher temperatures than in PEI2000-PLA5,
and this difference increases with increasing frequency. For example, as seen in Figure 11, the
α-relaxation
observed
PEI2000-PLA20
The α-relaxation
is observed
in PEI2000-PLA5
PEI2000-PLA20
atathigher
thanfor
in the
PEI2000-PLA5,
α-relaxation
is observed
at 75 °C in
and
93 °C temperatures
in PEI2000-PLA20
frequency
difference
increases
with
increasing
frequency.
For
example,
as
seen
in
Figure
11, the
and
this
difference
increases
with
increasing
frequency.
For
example,
as
seen
in Figure
11,
of 1 Hz, while for 1 kHz these temperatures are 127 and 169 °C, respectively.
◦ CininPEI2000-PLA20
α-relaxation
is observed
at 75
°C◦in
PEI2000-PLA5
the
α-relaxation
is observed
at 75
C in
PEI2000-PLA5and
andatat9393°C
PEI2000-PLA20for
for the
the frequency
of 11 Hz,
Hz, while
while for
for 11 kHz
kHz these
these temperatures
temperatures are
are 127
127 and
and169
169◦°C,
respectively.
of
C, respectively.
Figure 11. Dielectric relaxation spectroscopy curves for the α-relaxation for the different samples
studied: PEI2000-PLA5 (black circles), PEI2000-PLA20 (red squares) and PEI800-PLA5 (blue
triangles), at frequencies: (a) 1 Hz; (b) 1 kHz. Heating rate: 0.5 °C/min.
Figure 11.
11. Dielectric
Dielectric relaxation
relaxation spectroscopy
spectroscopy curves
curves for
for the
the α-relaxation
α-relaxation for
for the
the different
different samples
samples
Figure
studied:
PEI2000-PLA5
(black
circles),
PEI2000-PLA20
(red
squares)
and
PEI800-PLA5
(blue is
−1
On the
relaxation map
FigurePEI2000-PLA20
8, the representation
of ln(f
m) PEI800-PLA5
vs. T for PEI2000-PLA20
studied:
PEI2000-PLA5
(blackincircles),
(red squares)
and
(blue triangles),
triangles),
at
frequencies:
(a)
1
Hz;
(b)
1
kHz.
Heating
rate:
0.5
°C/min.
◦
non-linear
for the
adjusting
the0.5
VFTC/min.
equation (1). The parameters of this equation
at frequencies:
(a)α-relaxation,
1 Hz; (b) 1 kHz.
Heatingtorate:
are given in Table 3 for the heating rates studied, the average values being: A = 15.1 ± 1.1,
−1 for PEI2000-PLA20 is
On
the relaxation
map Tin
the
representation
of ln(fresults
m) vs. T
−1 for
B On
= 1398
± 173 K, map
and
=Figure
274.58,8,±the
6.4representation
K. Comparing
PEI2000-PLA5
and is
the relaxation
in0 Figure
of the
ln(f m ) vs. Tfor
PEI2000-PLA20
non-linear
for the itα-relaxation,
adjusting
to
theheating
VFT equation
(1).
The parameters
ofequation
this equation
PEI2000-PLA20,
can
be
seen
that,
for
the
same
rate,
the
parameters
of
the
VFT
areare
non-linear for the α-relaxation, adjusting to the VFT Equation (1). The parameters of this equation
arelower
given
in Table
3 for theThe
heating
rates
studied,energy,
the average
values
being:
A = slope
15.1 of
± a1.1,
in
the
PEI2000-PLA20.
apparent
activation
calculated
from
the
average
given in Table 3 for the heating rates studied, the average values being: A = 15.1 ± 1.1, B = 1398 ± 173 K,
B best
= 1398
± 173 toK,theand
T0 = 274.5
± is
6.4Eapp
K. Comparing
the results
for PEI2000-PLA5
and
straight
experimental
data,
170.0 ± 1.2 kJ/mol
the PEI2000-PLA20,
is
and
T0 fit
= 274.5
± 6.4 K. Comparing
the
results
for=PEI2000-PLA5
andfor
PEI2000-PLA20,
it canand
be seen
PEI2000-PLA20,
it can be seen
for the same heating
rate,
parametersofofthe
the
VFT equation
lower for PEI2000-PLA20
thanthat,
for PEI2000-PLA5,
possibly
as athe
consequence
greater
flexibilityare
that, for the same heating rate, the parameters of the VFT equation are lower in the PEI2000-PLA20.
lower
inPLA20
the PEI2000-PLA20.
The apparent activation energy, calculated from the average slope of a
of the
chains.
The apparent activation energy, calculated from the average slope of a best fit straight to the
dipolar
appears
at temperatures
thefor
α-relaxation.
This relaxation
best fitThe
straight
to α′-relaxation
the experimental
data,
is Eapp = 170.0higher
± 1.2 than
kJ/mol
the PEI2000-PLA20,
and is
experimental data, is Eapp = 170.0 ± 1.2 kJ/mol for the PEI2000-PLA20, and is lower for PEI2000-PLA20
is more
visible on decreasing
the frequency
and the
rate. InofPEI2000-PLA20,
this
lower
for PEI2000-PLA20
than forboth
PEI2000-PLA5,
possibly
as heating
a consequence
the greater flexibility
than for PEI2000-PLA5, possibly as a consequence of the greater flexibility of the PLA20 chains.
relaxation
peak
is
better
defined
than
in
the
PEI2000-PLA5
due
to
the
higher
ratio
of
lactide
repeat
of the PLA20 chains.
units
N links,α′-relaxation
as shown in appears
Figure 12.
relaxation map
in than
Figure
8 shows
that there
is relaxation
a linear
Thetodipolar
atThe
temperatures
higher
the
α-relaxation.
This
−1
between
ln(fm) andboth
T over
rather limited
range
available,
from which thethis
is relationship
more visible
on decreasing
thethe
frequency
and frequency
the heating
rate.
In PEI2000-PLA20,
activation
energy
is
found
as
131.0
kJ/mol,
for
the
heating
rate
of
0.5
°C/min,
significantly
less than
relaxation peak is better defined than in the PEI2000-PLA5 due to the higher ratio of lactide
repeat
that
obtained
for
PEI
2000-PLA5
at
the
same
heating
rate.
units to N links, as shown in Figure 12. The relaxation map in Figure 8 shows that there is a linear
−1
Materials 2017, 10, 127
12 of 18
The dipolar α0 -relaxation appears at temperatures higher than the α-relaxation. This relaxation is
more visible on decreasing both the frequency and the heating rate. In PEI2000-PLA20, this relaxation
peak is better defined than in the PEI2000-PLA5 due to the higher ratio of lactide repeat units to N
links, as shown in Figure 12. The relaxation map in Figure 8 shows that there is a linear relationship
between ln(f m ) and T −1 over the rather limited frequency range available, from which the activation
energy is found as 131.0 kJ/mol, for the heating rate of 0.5 ◦ C/min, significantly less than that obtained
Materials 2017, 10, 127
12 of 18
for PEI
2000-PLA5
at the same heating rate.
Materials
2017, 10, 127
12 of 18
Figure
12.
Deconvolutionofofthe
thedielectric
dielectricrelaxation
relaxation spectroscopy curves
for
Figure
Deconvolution
forPEI2000-PLA5
PEI2000-PLA5(blue),
(blue),
Figure
12.12.Deconvolution
of the dielectric
relaxationspectroscopy
spectroscopycurves
curves
for
PEI2000-PLA5
(blue),
PEI2000-PLA20(red):
(red):experimental
experimental curves
curves (dotted
(dotted lines); fit
PEI2000-PLA20
fit (thick
(thick lines),
lines), deconvoluted
deconvolutedinto
into
PEI2000-PLA20 (red): experimental curves (dotted lines); fit (thick lines), deconvoluted into α-relaxation
α-relaxation
(thin
lines)
andα′-relaxation
α′-relaxation(dashed
(dashed lines).
lines). Frequency:
Frequency: 0.1
°C/min.
α-relaxation
(thin
lines)
and
0.1Hz.
Hz.Heating
Heatingrate:
rate:0.50.5
°C/min.
(thin lines) and α0 -relaxation (dashed lines). Frequency: 0.1 Hz. Heating rate: 0.5 ◦ C/min.
PEI800-PLA5
(5) (5)
PEI800-PLA5
(5) PEI800-PLA5
multiarmstar
starpolymer
polymerPEI800-PLA5
PEI800-PLA5 has
has the
the same
same ratio
to to
TheThe
multiarm
ratio (=
(= 5)5)ofoflactide
lactiderepeat
repeatunits
units
N links
as for
PEI2000-PLA5,
but a has
lower
molecular
weight
for therepeat
hyperbranched
The
multiarm
star
polymer
PEI800-PLA5
the
same
ratio
(=
5)
of
lactide
units
to
N
links
N links as for PEI2000-PLA5, but a lower molecular weight for the hyperbranched
poly(ethyleneimine)
core.
The
dielectric
relaxation
curves
are
similar
to
that
for
PEI2000-PLA5,
and
aspoly(ethyleneimine)
for PEI2000-PLA5, but
lower
molecular
weightcurves
for theare
hyperbranched
core.
core.a The
dielectric
relaxation
similar to that poly(ethyleneimine)
for PEI2000-PLA5, and
are shownrelaxation
in Figure 13.
The
aredielectric
shown in Figure 13. curves are similar to that for PEI2000-PLA5, and are shown in Figure 13.
Figure 13. Dielectric relaxation spectroscopy curves for PEI800-PLA5 at 0.5 °C/min for frequencies
between 0.5 Hz and 100 kHz.
Figure
Dielectricrelaxation
relaxationspectroscopy
spectroscopy curves
curves for
forfor
frequencies
◦ C/min
Figure
13.13.Dielectric
for PEI800-PLA5
PEI800-PLA5atat0.5
0.5°C/min
frequencies
between
0.5
Hz
and
100
kHz.
between
Hz and 100for
kHz.
The 0.5
γ-relaxation
PEI800-PLA5, associated with local movements of the hydroxyl groups,
appears at a slightly higher temperature than for PEI2000-PLA5 and PEI2000-PLA20, as shown in
The γ-relaxation for PEI800-PLA5, associated with local movements of the hydroxyl groups,
Figure
14: at 1 Hz and PEI800-PLA5,
2 °C/min, the γ-relaxation appears
a −90movements
°C for PEI800-PLA5,
at −95 °C for
The
γ-relaxation
with local
of the hydroxyl
groups,
appears
at a slightly for
higher temperatureassociated
than for PEI2000-PLA5
and PEI2000-PLA20,
as shown
in
PEI2000-PLA5, and at −97 °C for PEI2000-PLA20. Figure 9 compares the γ-relaxation for all three
appears
at
a
slightly
higher
temperature
than
for
PEI2000-PLA5
and
PEI2000-PLA20,
as
shown
in
Figure
14:
at
1
Hz
and
2
°C/min,
the
γ-relaxation
appears
a
−90
°C
for
PEI800-PLA5,
at
−95
°C
for
samples at two selected
frequencies: 1 kHz and 10 kHz. It is noted◦ that the magnitude of tan δ for
◦
◦
Figure
14: at 1 Hzisand
C/min,
the
γ-relaxation
appears
acompares
−90 C for
at all
−being
95three
C for
PEI2000-PLA5,
at2−97
°C for
PEI2000-PLA20.
Figure
thePEI800-PLA5,
γ-relaxation
for
PEI800-PLA5 and
intermediate
between
PEI2000-PLA20
and9 PEI2000-PLA5,
the highest value
◦ C for PEI2000-PLA20. Figure 9 compares the γ-relaxation for all three
PEI2000-PLA5,
and
at
−
97
samples
at
two
selected
frequencies:
1
kHz
and
10
kHz.
It
is
noted
that
magnitude
of
tan
δ
for
for PEI2000-PLA20. This might appear to suggest that the position of the γ-relaxation on the
PEI800-PLA5
intermediate
between
PEI2000-PLA20
and PEI2000-PLA5,
the highest
being
temperatureis scale
is determined
principally
by the average
molecular weight
of the value
PEI core,
for whereas
PEI2000-PLA20.
Thisofmight
appear to
suggest
that thebyposition
of the
γ-relaxation
on the
the intensity
the relaxation
peak
is dominated
the density
of the
PLA branches.
temperature
scale two
is determined
principally since
by the
average
molecular
weight
of will
the imply
PEI core,
However, these
effects are inter-related,
a higher
molecular
weight
PEI core
a
higher the
density
of the of
arms,
so the individual
contributions
each
cannotofbethe
distinguished
by
whereas
intensity
the and
relaxation
peak is dominated
byofthe
density
PLA branches.
these results.
map
of Figure 15since
showsa that
thismolecular
relaxation is
practically
independent
of a
However,
theseThe
tworelaxation
effects are
inter-related,
higher
weight
PEI core
will imply
Materials 2017, 10, 127
13 of 18
samples at two selected frequencies: 1 kHz and 10 kHz. It is noted that the magnitude of tan δ for
PEI800-PLA5 is intermediate between PEI2000-PLA20 and PEI2000-PLA5, the highest value being for
PEI2000-PLA20. This might appear to suggest that the position of the γ-relaxation on the temperature
scale is determined principally by the average molecular weight of the PEI core, whereas the intensity
of the relaxation peak is dominated by the density of the PLA branches. However, these two effects
are inter-related, since a higher molecular weight PEI core will imply a higher density of the arms,
Materials
10, 127
13 of 18
and
so
the2017,
individual
contributions of each cannot be distinguished by these results. The 13
relaxation
Materials 2017, 10, 127
of 18
map of Figure 15 shows that this relaxation is practically independent of the heating rate. The average
the heating rate. The average activation energy for PEI800-PLA5 is 53.7±1.4 kJ/mol, very close to
activation
energy
forThe
PEI800-PLA5
is 53.7±
1.4 kJ/mol,
very closeis to
those kJ/mol,
for PEIvery
2000-PLA5
the heating
rate.
average activation
energy
for PEI800-PLA5
53.7±1.4
close to and
those
forfor
PEIPEI
2000-PLA5
and
50.2±1.3 kJ/mol
and54.2±3.2
54.2±3.2kJ/mol,
kJ/mol,respectively.
respectively.
those
2000-PLA5
andPEI2000-PLA20,
PEI2000-PLA20,
and
PEI2000-PLA20,
50.2
±1.3 kJ/mol
and 54.2±3.250.2±1.3
kJ/mol,kJ/mol
respectively.
Figure
14. Relaxation
map for
PEI800-PLA5 (green), PEI2000-PLA5
PEI2000-PLA5 (blue)
and
PEI2000-PLA20
(pink)
Figure
14.14.
Relaxation
(blue)
and
PEI2000-PLA20
(pink)
Figure
Relaxationmap
mapfor
forPEI800-PLA5
PEI800-PLA5 (green),
(green), PEI2000-PLA5 (blue)
and
PEI2000-PLA20
(pink)
◦ C/min:
at heating
rate
2 °C/min:
α-relaxation(triangles),
(triangles), β-relaxation
(asterisks),
γ-relaxation
(rhombus).
at heating
rate
2
α-relaxation
β-relaxation
(asterisks),
γ-relaxation
(rhombus).
at heating rate 2 °C/min: α-relaxation (triangles), β-relaxation (asterisks), γ-relaxation (rhombus).
Figure 15. Relaxation map for PEI800-PLA5 at different heating rates: 2 °C/min (filled symbols) and
0.5
(open symbols).
Figure°C/min
15. Relaxation
map for PEI800-PLA5 at different heating rates: 2 °C/min (filled symbols) and
Figure 15. Relaxation map for PEI800-PLA5 at different heating rates: 2 ◦ C/min (filled symbols) and
0.5 °C/min (open symbols).
0.5 ◦ C/min
symbols).in the other samples, the β-relaxation becomes more visible at frequencies
As was(open
also observed
higher than 100 Hz for PEI800-PLA5, when it appears as a shoulder between 70 and 90 °C, as seen in
As was also observed in the other samples, the β-relaxation becomes more visible at frequencies
Figure
13. Using
the same
procedure
of determining
an “onset” temperature
for the
β-relaxation
as
As
in the
otherwhen
samples,
the β-relaxation
becomes
more
visible
at as
frequencies
higherwas
thanalso
100observed
Hz for PEI800-PLA5,
it appears
as a shoulder
between
70 and
90 °C,
seen in
was used earlier for PEI2000-PLA5, the frequency of the β-relaxation can be estimated,◦ and the
higher
than
Hzthe
forsame
PEI800-PLA5,
it appearsan
as “onset”
a shoulder
between for
70 and
90 C, as seen
Figure
13. 100
Using
procedurewhen
of determining
temperature
the β-relaxation
as in
relaxation map, Figure 15, shows an Arrhenius relationship between ln(fm) and T−1 with an average
Figure
Using
thefor
same
procedure of the
determining
temperature
β-relaxation
was
was 13.
used
earlier
PEI2000-PLA5,
frequencyanof“onset”
the β-relaxation
canforbethe
estimated,
andas
the
activation energy of 261 ± 4 kJ/mol, independent of the heating rate. This is almost identical to the
used
earlier
for
PEI2000-PLA5,
the
frequency
of
the
β-relaxation
can
be
estimated,
the
relaxation
relaxation
map,
Figure
15,
shows
an
Arrhenius
relationship
between
ln(f
m) and T−1 and
with
an
average
value for PEI2000-PLA5 (267 ± 15 kJ/mol), but both are smaller than that for PEI2000-PLA20
−1 with
activation
ofas261
±be
4 kJ/mol,
independent
of theindicate
heating
is almost
identical
tobythe
map,
Figure
15,
shows
an
relationship
between
ln(f mthat
)rate.
and
Tβ-relaxation
anisaverage
activation
(354
± 10energy
kJ/mol),
canArrhenius
seen in Table
3. The results
theThis
influenced
value
for
(267units/N
± 15 kJ/mol),
but
both
are to
smaller
than
that
for PEI2000-PLA20
energy
261PEI2000-PLA5
±of4 lactide
kJ/mol,
independent
of not
the being
heating
rate.
This
almost
identical
to weight
the value
theofcontent
repeat
link,
sensitive
theis
effect
of the
molecular
of for
(354
± 10
as 15
cankJ/mol),
be seen in
The
resultsthan
indicate
the β-relaxation(354
is influenced
by
PEI2000-PLA5
(267 ±
butTable
both3.are
smaller
that that
for PEI2000-PLA20
± 10 kJ/mol),
the
PEIkJ/mol),
core.
the
content
of
lactide
repeat
units/N
link,
not
being
sensitive
to
the
effect
of
the
molecular
weight
of of
When
comparing
the
results
for
the
β-relaxation
of
PEI800-PLA5
with
those
for
PEI2000-PLA5
as can be seen in Table 3. The results indicate that the β-relaxation is influenced by the content
the
PEI
core.
and
PEI2000-PLA20,
we
observe
that
the
β-relaxation
is
located
in
the
same
temperature
range
for
all
lactide repeat units/N link, not being sensitive to the effect of the molecular weight of the PEI core.
When comparing
results
for occurs
the β-relaxation
of PEI800-PLA5
with
PEI2000-PLA5
samples,
as shown inthe
Figure
10, but
as a shoulder
on samples with
thethose
samefor
content
of PLA,
PEI2000-PLA5,
and
PEI800-PLA5,
while
it
appears
as
a
peak
in
the
multiarm
star
polymer
of
higher
and PEI2000-PLA20, we observe that the β-relaxation is located in the same temperature range
for all
PLA
content,
PEI2000-PLA20,
for
which
the
glass
transition
is
better
separated
from
the
β-relaxation.
samples, as shown in Figure 10, but occurs as a shoulder on samples with the same content of PLA,
Figure 11a,b
show the α-relaxation
PEI800-PLA5
forin
frequencies
of 1 star
Hz and
1 kHzofand
a
PEI2000-PLA5,
and PEI800-PLA5,
while itfor
appears
as a peak
the multiarm
polymer
higher
heating
ratePEI2000-PLA20,
of 0.5 °C/min. For
frequency
of 1 transition
Hz, the α-relaxation
peak is observed
at β-relaxation.
85 °C. This
PLA
content,
forthe
which
the glass
is better separated
from the
temperature
is show
intermediate
between for
the PEI800-PLA5
peak temperatures
obtained of
for1 Hz
PEI2000-PLA5
Figure 11a,b
the α-relaxation
for frequencies
and 1 kHz and
and a
PEI2000-PLA20,
75°C
and
93
°C,
respectively.
This
behavior
is
observed
for
all
the
frequencies
used,
heating rate of 0.5 °C/min. For the frequency of 1 Hz, the α-relaxation peak is observed at 85 °C. This
Materials 2017, 10, 127
14 of 18
When comparing the results for the β-relaxation of PEI800-PLA5 with those for PEI2000-PLA5
and PEI2000-PLA20, we observe that the β-relaxation is located in the same temperature range for all
samples, as shown in Figure 10, but occurs as a shoulder on samples with the same content of PLA,
PEI2000-PLA5, and PEI800-PLA5, while it appears as a peak in the multiarm star polymer of higher
PLA content, PEI2000-PLA20, for which the glass transition is better separated from the β-relaxation.
Figure 11a,b show the α-relaxation for PEI800-PLA5 for frequencies of 1 Hz and 1 kHz and a
heating rate of 0.5 ◦ C/min. For the frequency of 1 Hz, the α-relaxation peak is observed at 85 ◦ C.
This temperature is intermediate between the peak temperatures obtained for PEI2000-PLA5 and
PEI2000-PLA20, 75◦ C and 93 ◦ C, respectively. This behavior is observed for all the frequencies used,
as shown in Figure 14, the difference being more marked as the frequency increases; however, for
the minimum frequency of 0.1 Hz, the values of the temperature of the α-relaxation peak, associated
with the glass transition of these multiarm star polymers, are substantially similar, as was observed in
the DSC results (see Table 2). The VFT parameters obtained for the PEI800-PLA5 are A = 15.1 ± 0.2,
B = 1107.1 ± 298 K, and T0 = 285.7 ± 11.4 K. These parameters are intermediate between those
for PEI2000-PLA5 (A = 18.6 ± 2.0, B = 1583.0 ± 314 K, and T0 = 282.5 ± 7.6 K) and PEI2000-PLA20
(A = 15.0 ± 1.1, B = 1398.8 ± 173 K and T0 = 274.0 ± 6.9 K), as given in Table 3. The average apparent
activation energy, Eapp, for this relaxation in PEI800-PLA5 is 194 ± 8 kJ/mol, intermediate between
those for PEI2000-PLA5 (252 ± 11 kJ/mol) and PEI2000-PLA20 (170 ± 2 kJ/mol) and higher than the
PEI800 (68.7 ± 2.6 kJ mol−1 ), see Table 3. To explain the fact that these results for PEI800 PLA5 are
intermediate between those for the other two multiarm star polymers, we consider the following.
It has been observed that the α-relaxation associated with the glass transition and the apparent
activation energies for PEI800-PLA5 are much higher than for the PEI800 core, which can be explained
by the predominant effect of the branches of PLA. The structure of the PEI800-PLA5 is much more
complex than that of PEI800 and this translates into greater difficulty of molecular movement and
consequently a higher activation energy. Comparing the multiarm star polymers with the same
PLA content but with different molecular weights for the core, we observe that the temperature at
which the α-relaxation peak appears and the activation energy for PEI800-PLA5 are higher than for
PEI2000-PLA5; this can be attributed to the reduction in the molecular weight of the PEI core giving
a structure which allows greater proximity and interaction between the branches of the PLA, and
therefore the co-operative molecular mobility associated with the branches of PLA and the PEI core
is more hindered, and as a consequence the α-relaxation is displaced towards higher temperatures.
On the other hand, as was explained in the comparative analysis of PEI2000-PLA5 and PEI2000-PLA20,
by increasing the ratio of lactide repeat units to N links, the possibilities for interaction between PLA
chains increases, and the temperature of the α-relaxation peak for PEI2000-PLA20 is greater than for
the other two multiarm star polymers, PEI800-PLA5 and PEI2000-PLA5.
The α0 -relaxation, associated with the normal mode relaxation due to fluctuations of the
end-to-end vector in the PLA arms, is more pronounced in PEI2000-PLA20, and appears as a
well-defined peak, whereas this relaxation for the other two star-shaped polymers appears as a
shoulder, as shown in Figure 12. The average activation energy for this α0 -relaxation has been
determined as 254 kJ/mol in PEI800-PLA5, virtually identical to that for PEI2000-PLA5 (263 kJ/mol),
and considerably greater than that for PEI2000-PLA20 (131 kJ/mol). This indicates a null effect of
the PEI core on this relaxation, as expected, while an increase in the ratio of lactide repeat units to N
links causes a sharp decrease in the activation energy and a better definition of the relaxation peak.
This possible assignment of this relaxation does not exclude that it could be a Maxwell–Wagner–Sillars
type ionic peak because the material may have nano-regions of different conductivity.
Finally, we compare the multiarm star polymer PEI2000-PLA5 with PEI2000 and PLA on the
relaxation map in Figure 16 in order to further clarify some of the ideas presented above. The data for
amorphous PLA have been taken from Figure 5 of Laredo et al [32], with their secondary relaxation
labelled βIII being taken as the β-relaxation. It is immediately apparent that the α-relaxation for
PEI2000 is quite different from that for PEI2000-PLA5 whereas the relaxations for PEI2000-PLA5 and
Materials 2017, 10, 127
15 of 18
amorphous PLA merge at low frequency, and have approximately the same value of T0, (as in fact
do all the multiarm star polymers, see Table 3). The α-relaxation of all the multiarm star polymers is
associated with the glass transition of the polylactide arms, with a displacement to higher temperatures
as the frequency increases as a consequence of the restriction on mobility imposed by the PEI core.
Likewise, the β-relaxation for PEI2000 can be seen to be widely separated from that of PEI2000-PLA5,
and with a much lower activation energy (see Table 3), whereas again the relaxation in the multiarm
star polymer appears to coincide with an extrapolation of the relaxation in the amorphous PLA. In fact,
Materials 2017, 10, 127
15 of 18
the β-relaxation in PEI2000-PLA5 closely superposes on the α-relaxation of the PLA in just the region in
which
the intersect
extrapolated
of theThis
PLAiswould
intersect
the α-relaxation.
This
would
withβ-relaxation
the α-relaxation.
consistent
withwith
the interpretation
made
in is
anconsistent
earlier
with
the
interpretation
made
in
an
earlier
section
that
the
β-relaxation
in
PEI2000-PLA5
was
associated
section that the β-relaxation in PEI2000-PLA5 was associated with the entire PLA chain,
and
with
the entire
chain, and
byβ-relaxation
Laredo et alin
[32]
that the β-relaxation
supports
thePLA
observation
by supports
Laredo etthe
alobservation
[32] that the
PEI2000-PLA5
displays in
PEI2000-PLA5
displays
Johari-Goldstein
Lastly,clearly
Figurethe
16wide
also shows
clearlybetween
the wide
Johari-Goldstein
characteristics.
Lastly, characteristics.
Figure 16 also shows
discrepancy
discrepancy
between
the
γ-relaxations
in
PEI2000
and
PEI2000-PLA5;
even
though
they
have
similar
the γ-relaxations in PEI2000 and PEI2000-PLA5; even though they have similar slopes and hence
slopes
andactivation
hence similar
activation
energies
3), theseare
relaxations
arewith
associated
with quite
similar
energies
(see Table
3), (see
theseTable
relaxations
associated
quite different
terminal
groups.groups.
different
terminal
◦ C/min:
Figure
Relaxationmap
mapfor
forPEI2000-PLA5
PEI2000-PLA5 (blue),
(blue), PEI2000
PEI2000 (pink),
Figure
16.16.
Relaxation
(pink), and
andPLA
PLA(green)
(green)atat2 2°C/min:
α-relaxation
(triangles),
β-relaxation
(asterisks),
γ-relaxation
(rhombus).
α-relaxation (triangles), β-relaxation (asterisks), γ-relaxation (rhombus).
3. Experimental
3. Experimental
Materials
3.1.3.1.
Materials
Multiarm star polymers were used, named generically PEIx-PLAy, where x represents the
Multiarm
star polymers were used, named generically PEIx-PLAy, where x represents the
molecular weight of the poly(ethyleneimine) and y represents the ratio of lactide repeat units to N
molecular weight of the poly(ethyleneimine) and y represents the ratio of lactide repeat units to
links. The three samples used were: PEI2000-PLA5, PEI2000-PLA20, and PEI800-PLA5, all in solid and
N links. The three samples used were: PEI2000-PLA5, PEI2000-PLA20, and PEI800-PLA5, all in solid
powder form. The samples were provided by Acebo et al (Universitat Rovira i Virgili, Tarragona,
and powder form. The samples were provided by Acebo et al (Universitat1 Rovira i Virgili, Tarragona,
Spain), who had previously made the synthesis and the characterization by H-NMR
[18].
Spain), who had previously made the synthesis
and the characterization by 1 H-NMR [18].
Polyethyleneimine (PEI) Lupasol® FG (800 g/mol) and Lupasol® PR 8515 (2000 g/mol) were
®
® PR 8515 (2000 g/mol) were
Polyethyleneimine
(PEI)
(800 of
g/mol)
and Lupasol
donated
by BASF. From
the Lupasol
molecularFG
weight
the polymer
and of the
repeating unit, average
donated
From theofmolecular
weight® of
of the
average
® PRrepeating
degreesbyofBASF.
polymerization
18.6 for Lupasol
FGthe
andpolymer
46.5 for and
Lupasol
8515 wereunit,
calculated.
® FG and 46.5 for Lupasol® PR 8515 were calculated.
degrees
of
polymerization
of
18.6
for
Lupasol
®
The relationship (NH2/NH/N) was (1/0.82/0.53) for Lupasol FG and (1/0.92/0.70) for Lupasol® PR
®
The8515,
relationship
(NH
(1/0.82/0.53)
forsecondary
Lupasol® and
FG and
(1/0.92/0.70)
and hence
the2 /NH/N)
equivalentwas
number
of primary,
tertiary
amines canfor
beLupasol
calculatedPR
8515,
hence the0.010,
equivalent
number
of primary,
andand
tertiary
amines
canand
be 0.0062
calculated
as, and
respectively,
0.00837,
and 0.0053
eq/g forsecondary
Lupasol® FG
0.0089,
0.0082,
eq/gas,
® FG and 0.0089, 0.0082, and 0.0062 eq/g for
®
respectively,
0.010,
0.00837,
and
0.0053
eq/g
for
Lupasol
for Lupasol PR 8515. Lactide (LA) was purchased from Sigma-Aldrich (Madrid, Spain).
Lupasol® PR 8515. Lactide (LA) was purchased from Sigma-Aldrich (Madrid, Spain).
3.2. Experimental Techniques
3.2. Experimental Techniques
Thermogravimetric analysis (TGA), which measures the weight loss of the sample during a
Thermogravimetric
(TGA),
which measures
the weight
of the sample
during a
programmed
heating inanalysis
a controlled
atmosphere,
was performed
in a loss
Mettler-Toledo
TGA/DSC1
equipped with
a sample
and Huber
cryostat (precision
± 0.1 °C).
TGA/DSC was TGA/DSC1
calibrated
programmed
heating
in arobot
controlled
atmosphere,
was performed
inThe
a Mettler-Toledo
using indium
a dry
air flow
200 mL/min.
the experiments
were
with a was
dry nitrogen
equipped
with awith
sample
robot
and of
Huber
cryostatAll
(precision
± 0.1 ◦ C).
Themade
TGA/DSC
calibrated
flowindium
of 200 mL/min.
using
with a dry air flow of 200 mL/min. All the experiments were made with a dry nitrogen
DSC thermograms were studied using a Mettler-Toledo DSC 821e differential scanning
flow of The
200 mL/min.
calorimeter (DSC) equipped with a sample robot and Haake EK90/MT intracooler. All DSC
experiments were performed with a dry nitrogen gas flow of 50 mL/min. The data evaluation was
performed with the STARe software (Mettler-Toledo AG, Schwerzenbach, Switzerland). The DSC
was calibrated for both heat flow and temperature using indium. A small sample of about 8–10 mg
was weighed into an aluminium pan, sealed, and immediately inserted into the DSC furnace. The
Materials 2017, 10, 127
16 of 18
The DSC thermograms were studied using a Mettler-Toledo DSC 821e differential scanning
calorimeter (DSC) equipped with a sample robot and Haake EK90/MT intracooler. All DSC
experiments were performed with a dry nitrogen gas flow of 50 mL/min. The data evaluation was
performed with the STARe software (Mettler-Toledo AG, Schwerzenbach, Switzerland). The DSC was
calibrated for both heat flow and temperature using indium. A small sample of about 8–10 mg
was weighed into an aluminium pan, sealed, and immediately inserted into the DSC furnace.
The glass transition temperature, Tg , was determined from the mid-point between the glassy and
rubbery asymptotes.
A dielectric analyzer DEA 2970 from TA Instruments was used to measure, in real time,
the dielectric signals at different frequencies. Dielectric measurements were performed using a ceramic
single-surface cell of 20 mm × 25 mm based on a coplanar inter-digitated comb-like electrode design.
The values of dielectric permittivity, ε0 , dielectric loss factor, ε00 , and tan δ (= ε00 /ε0 ) were obtained
from the resulting current. The interval of data sampling was 1 s per point. The sample was spread
on the electrode surface, covering the entire inter-digitated area. The non-isothermal measurements
were performed at 2 and 0.5 ◦ C/min in a nitrogen atmosphere with a gas flow of 500 mL/min. The ε0 ,
ε00 , and tan δ were measured in the frequency range from 0.1 Hz to 100 kHz. In order to eliminate
previous thermal history and any trace of moisture, the samples were preconditioned in the same
dielectric analyzer as follows. The samples were heated from 25 ◦ C to 100 ◦ C at a rate of 2 ◦ C/min,
held isothermally at 100 ◦ C for 30 min, and then cooled to −130 ◦ C before scanning from−130 to
180 ◦ C at the heating rates of 0.5 and 2 ◦ C/min.
4. Conclusions
We studied three multiarm star PEIx-PLAy polymers with different molecular weights for the
poly(ethyleneimine) (PEI) core (PEIx) and different ratios of lactide repeat units to N links (PLAy):
PEI800-PLA5, PEI2000-PLA5, and PEI2000-PLA20. All samples were preconditioned for 30 min at
100 ◦ C. The glass transition temperature of all samples, determined by DSC, was in the range 48–50 ◦ C,
independent of the molecular weight of the PEI core and of the ratio of lactide repeat units to N links.
The glass transition temperatures of the multiarm star polymers were much higher than those for the
PEI from which the multiarm star polymers were obtained.
The dielectric relaxation curves of all samples, for frequencies from 0.1 Hz to 100 kHz, show
four dipolar relaxations: γ, β, α, and α0 , in order of increasing temperature. The γ-relaxation for
PEI800-PLA5 appears at a slightly higher temperature than for PEI2000-PLA5 and PEI2000-PLA20,
and its peak intensity is intermediate between these other two samples. This suggests that the
γ-relaxation can be influenced by both the molecular weight of the PEI core and the density of
the multiarms, which are inter-related aspects of the molecular architecture. The relaxation map
shows that this relaxation is independent of the heating rate, and has an Arrhenius temperature
dependence, for which the average activation energy is 53.7 ± 1.4 kJ/mol, practically identical to those
found for PEI2000-PLA5 and PEI2000-PLA20, 50.2 ± 2.3 kJ/min and 54.0 ± 3.2 kJ/min, respectively.
The γ-relaxation is attributed to local motions of the terminal –OH groups of the poly(lactide) arms.
The β-relaxation becomes visible between 70 and 90 ◦ C at frequencies higher than 100 Hz for
PEI800-PLA5, but appears only as a shoulder on the α-relaxation peak. The combined effect of higher
molecular weight PEI core (PEIx) and the highest ratio of lactide repeat units to N links (PLAy) results
in the appearance of a clearly observable peak for PEI2000-PLA20. From the analysis of the relaxation
map for the β-relaxation, we conclude that this relaxation is influenced by the content of lactide repeat
units/N link and is not sensitive to the effect of the molecular weight of the PEI core. In particular, the
activation energy for PEI800-PLA5 is approximately equal to that for PEI2000-PLA5, but significantly
lower than that for PEI2000-PLA20. The β-relaxation is attributed to motions of the main chain of the
poly(lactide) arms.
The dipolar α-relaxation, of the VFT type, appears at temperatures which depend on both the
molecular weight of the PEI core and the ratio of lactide repeat units to N links. Independently of
Materials 2017, 10, 127
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frequency, the PEI core and the PLA arms have opposing effects: increasing the molecular weight of the
PEI core results in a decrease in the α-relaxation temperature (Tα PEI2000-PLA5 < Tα PEI800-PLA5),
whereas increasing the ratio of lactide repeat units to N links results in an increase in the α-relaxation
temperature (Tα PEI2000-PLA5 < Tα PEI2000-PLA20), the effect of the PLA arms being dominant
(Tα PEI800-PLA5 < Tα PEI2000-PLA20). The apparent activation energy, Eapp , for this relaxation
increases with decreasing ratio of lactide repeat units to N links while it is little influenced by the
molecular weight of the PEI core (170 ± 1.2 kJ/mol PEI2000-PLA20 < 194.3 ± 7.5 kJ/mol PEI800-PLA5
< 252.4 ± 11.3 kJ/mol PEI2000-PLA5). The α-relaxation is attributed to global molecular motions of
the assembly of PEI core and PLA arms.
The α0 -relaxation, considered here to be associated with the normal mode relaxation due to
fluctuations of the end-to-end vector in the PLA arms but recognizing also that it could be a
Maxwell–Wagner–Sillars type ionic peak, is more pronounced in PEI2000-PLA20, for which it appears
as a well-defined peak, in comparison with the other two multiarm star polymers for which it appears
only as a shoulder, approximately within the same temperature interval. This indicates a null effect of
the PEI core over this relaxation, as expected, while an increase in the ratio of lactide repeat units to N
links causes a sharp decrease in the activation energy and a better definition of the relaxation peak.
Acknowledgments:
The authors would like to thank MINECO (MAT2011-27039-CO3-03 and
MAT2014-53706-C3-3-R) for giving financial support. Likewise the authors wish to thank Cristina Acebo and
Àngels Serra (URV) for the provision of the samples of PEIx-PLAy used in this work.
Author Contributions: Frida Román, Pere Colomer and Yolanda Calventus were responsible for gathering the
experimental data, analyzed the results and prepared a first draft of the paper. John M. Hutchinson instigated and
supervised the project, directed the discussion and interpretation of the results, and prepared the final draft of
the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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