REVIEW
www.rsc.org/softmatter | Soft Matter
Progress in the characterization of synthetic (supramolecular) polymers by
analytical ultracentrifugation
Mircea Raşa and Ulrich S. Schubert*
Received 3rd February 2006, Accepted 4th May 2006
First published as an Advance Article on the web 2nd June 2006
DOI: 10.1039/b601666a
Analytical ultracentrifugation (AUC) is the leading technique for determining the molar mass,
state of association in solution, and association constants of biological macromolecules. Even
though it is little used for supramolecular polymers, this technique has already been shown to
represent one of the best options in the characterization of these systems. The use of
supramolecular assemblies in the field of nanotechnology requires the arrangement of such
systems on surfaces, from solution. Therefore, the control and investigation of solution properties
is of major importance. In this contribution we highlight the applicability and advantages of using
AUC by presenting a summary of the results of the past few years on the characterization of
various types of synthetic polymers and supramolecular polymer systems.
1. Introduction
Analytical ultracentrifugation (AUC) is a well-known technique mostly used for the characterization of proteins and
protein complexes but also of synthetic macromolecules. The
introduction of a new generation of ultracentrifuges in 1991 by
Laboratory of Macromolecular Chemistry and Nanoscience, Eindhoven
University of Technology and Dutch Polymer Institute, Den Dolech 2,
5600 MB Eindhoven, The Netherlands. E-mail: [email protected]
Mircea Raşa was born in
Timisoara (Romania) in
1967. He studied physics at
the West University of
Timisoara between 1987 and
1992 and worked towards his
PhD degree on physical properties of magnetic fluids, at
the same university, between
1996 and 1999. There he
became a lecturer, covering
several areas in physics. The
main part of his research on
magnetic fluids was done as a
researcher at the Institute for
Mircea Raşa
Complex Fluids, ‘Politehnica’
University of Timisoara. In August 2000 he moved to The
Netherlands as a postdoctoral researcher in the field of colloid
science at the Van ‘t Hoff Lab for Physical and Colloid
Chemistry at Utrecht University. Starting with October 2004,
Mircea Raşa has been working as a postdoc in the Laboratory of
Macromolecular Chemistry and Nanoscience at the Eindhoven
University of Technology, performing analytical ultracentrifugation on synthetic polymers and supramolecular complexes.
Ulrich S. Schubert was born in Tübingen in 1969. He studied
chemistry at the Universities of Frankfurt and Bayreuth (both
Germany) and the Virginia Commonwealth University, Richmond
This journal is ß The Royal Society of Chemistry 2006
Beckman opened a period of renewed theoretical and applied
research in this field. The AUC theoretical background,
methods, and typical applications are described in several
books1–5 and review articles.6–9 During the last few years,
AUC was involved in the characterization of an increasing
number of sedimenting species: various synthetic polymers,
polyelectrolyte complexes, polymers complexed via covalent
bonds, metallo-supramolecular assemblies, hybrid systems
(synthetic–natural diblock copolymers and polymer–nanoparticle systems), various kinds of colloidal particles, as well
(USA). His PhD work was
performed under the supervision
of Professor Eisenbach
(Bayreuth, Germany) and
Professor Newkome (Florida,
USA). In 1995 he obtained his
doctorate with Prof. Eisenbach.
After a postdoctoral training
with Professor Lehn at the
U n i v e r s i t e´ S t r a s b o u r g
(France) he moved to the
T e c h n i s c h e U n i v e r s i t ä t
München (Germany) to obtain
his habilitation in 1999 (with
Professor Nuyken). From 1999
Ulrich S. Schubert
to spring 2000 he held a temporal position as a professor at the Center for NanoScience at the
Universität München (Germany). Since summer 2000 he is FullProfessor at the Eindhoven University of Technology (Chair for
Macromolecular Chemistry and Nanoscience). His awards
include the Bayerischen Habilitations-Fö rderpreis, the
Habilitandenpreis of the GDCh (Makromolekulare Chemie),
the Heisenberg-Stipendium of the DFG, the Dozenten-Stipendium
of the Fonds der Chemischen Industrie and the VICI award of the
Dutch Science Organization (NWO). The major focuses of his
research interests are: organic heterocyclic chemistry, supramolecular materials, combinatorial material research, nanoscience
and tailor-made macromolecules.
Soft Matter, 2006, 2, 561–572 | 561
as in the study of chemical reactions. A summary of results
obtained on such systems with AUC in the past years is given
in section 2.2.
Cölfen and Völkel described in detail the applications of
AUC in colloid science in a couple of recent review
articles.10,11 In this paper we focus on the characterization of
metallo-supramolecular assemblies12–14 and synthetic polymers in solution by AUC and show the suitability of using
AUC for these systems. General theoretical overviews on
analytical ultracentrifugation can be found in previous review
articles.9–11
The most encountered applications of AUC are the determination of the average molar mass and the state of association, for the latter one AUC being the leading technique.
Determination of the sedimentation coefficient is the primary
method when sedimentation velocity measurements are
analyzed (see Section 2.1), which also allow the obtaining of
the diffusion coefficient, friction factor, and hydrodynamic
radius (for spherically-shaped species). AUC was proposed as
a technique for investigating the solution properties of supramolecular assemblies in 1997 by D. Schubert et al.,15 which
was followed by several examples.16–22 Such studies are
important for the applications of supramolecular assemblies
in the field of nanotechnology,23 since all larger systems and
architectures have to be assembled from solution. Consequently, the control and investigation of the state of association of the building blocks in solution is a major prerequisite.
1.1. AUC versus other techniques
Several techniques are frequently employed for the characterization of polymers to obtain the molar mass (distribution)
as well as size and structural information. Obtaining reliable
results requires confirmation by other techniques, so that AUC
is at least a candidate in all these cases.
The diffusion coefficient and hydrodynamic radius is
typically determined from dynamic light scattering (DLS).24
Polydispersity can be determined from both DLS and static
light scattering (SLS).24,25 However, in the case of metallosupramolecular assemblies, the strong absorption may be a
complicating factor in the interpretation of light scattering
data so that AUC measurements might be the preferred
approach in this case.
More problematic can be the determination of the average
molar mass and especially the state of association in solution,
as already discussed earlier (see ref. 16), which made AUC
the leading technique for such determinations. In ref. 26, for
example, it was concluded that the molar mass determination
of polyelectrolytes is often a difficult task and AUC was found
to be the most practical method for its determination in spite
of the longer time required when equilibrium measurements
are performed (see also Section 2.2). The molar mass
distribution can be determined from gel permeation chromatography (GPC)27 benefiting from a fast analysis. GPC is the
most frequently applied technique for determining the molar
mass distribution. Once the distribution is known, both the
number-average molar mass Mn and the weight-average molar
mass Mw can be calculated. However, a calibration of the
measurements is required which is problematic for new types
562 | Soft Matter, 2006, 2, 561–572
of polymeric species due to the lack of suitable calibration
standards. Moreover, column interactions might complicate
the situation if charged and/or strongly adsorbing polymers
are investigated. The Mn of metallo-supramolecular complexes
could be determined from SLS, but absorption may be a
serious drawback as already mentioned above. In a very
similar way as from SLS, Mn can be determined from small
angle X-ray scattering (SAXS) or small angle neutron
scattering (SANS) measurements. In the last case for example,
Michels et al.26 found it impossible to determine the molar
mass of polyelectrolytes. In the case of charged species,
polyacrylamide gel electrophoresis was tried but with insufficient results.26 Nuclear magnetic resonance (NMR) spectroscopy can be used to determine Mn for (linear) polymers with
defined end groups,27 but these measurements are limited to
lower molecular weights. The so-called viscosity-average molar
mass Mv can be determined from viscosity measurements
after relating Mv to the intrinsic viscosity via the so-called
Mark–Houwink equation.27 The constants in that equation,
however, have to be determined by measuring a series of
polymer samples with known Mn and Mw and narrow molar
mass distribution. Matrix assisted laser desorption/ionization
time-of-flight (MALDI-TOF) mass spectrometry allows, in
principle, an accurate determination of molar masses. It is,
however, limited to rather low molecular weight polymers
with a polydispersity index smaller than 1.2,28 while weakly
linked assemblies (via hydrogen bonding for example) can
easily break during the measurement.20
The main advantages of AUC can be summarized as
follows: it provides the absolute molar mass of species, a large
range of molar masses can be analyzed (from hundreds up to
several million g mol21), weakly linked assemblies can be
safely investigated, and interactions of the species with
matrices or surfaces are not a limiting factor. The main
disadvantages are related to the difficulty in obtaining accurate
partial specific volumes in some cases (see ref. 17 for details)
as well as to the data interpretations when a substantial
amount of information is needed (such as molar mass
distribution and concentrations in the case of associating
species). Fortunately, several numerical methods were
implemented during the past years and significantly ease such
determinations (see Section 2.1). The centrifugation time
needed for equilibrium measurements can be significantly
shortened by reduction of the filling column height.
2. Recent results
In this section we present results obtained in the last few years
on synthetic polymers and supramolecular polymer systems,
emphasizing how AUC was used to characterize these
compounds. The summary is preceded by a short introduction
to the technique and main experimental approaches.
2.1. Basic AUC methods
AUC offers several approaches for studying sedimenting
species. The sedimentation velocity measurements and sedimentation equilibrium measurements are the most used ones.
In the first case, a set of many intermediate profiles is recorded
during the sedimentation process, while in the latter the
This journal is ß The Royal Society of Chemistry 2006
sedimentation–diffusion equilibrium profile is analyzed only.
Analytical ultracentrifuges are equipped with optical systems
which measure these sedimentation profiles, absorption optics
and interference optics being common. Other experimental
approaches (e.g. density gradients, synthetic boundary
method)4,5 as well as different optical systems (such as
Schlieren optics and turbidity optics)5 have been much used.
Sedimentation equilibrium measurements are usually performed under ideal conditions so that the long-range interactions between sedimenting species as well as the macroscopic
internal field resulting from the spatial separation of free ions
and charged sedimenting species are negligible. This allows
easier determinations and requires low sample concentration
and relatively high ionic strength (if the sedimenting species
is charged). Sedimentation equilibrium measurements allow
the direct determination of average molar mass(es), state
of association, association constants (see refs 6,16 for the
fundamental equations and examples) as well as molar mass
distribution (see for example ref. 29).
Sedimentation velocity measurements performed under ideal
conditions are typically used for the determination of the
sedimentation coefficient distribution, molar mass distribution
(obtained by conversion of the sedimentation coefficient
distribution, which conversion however leads to correct results
in some particular cases only), even size distribution in the case
of spherical species,11 as well as the average diffusion or
friction coefficients (see ref. 16).
In some situations (colloids, polyelectrolytes), measurements
under ideal conditions are not possible because the systems are
not stable in the presence of salt so that non-ideal sedimentation theories must be applied (see ref. 24).
The determinations mentioned above are currently done
via numerical methods. The fundamental equation which
describes the sedimentation profiles of monodisperse species,
with sedimentation coefficient S and diffusion coefficient D,
is the Lamm equation.4,5,9 The sedimentation coefficient is
defined by S = v/(v2r), where v is the sedimentation velocity
and v2r the centrifugal acceleration. At infinite dilution, it is
given by:
M ð1{vrÞ
(1)
S~
NA f
where NA is Avogadro’s number, r is the solvent density, v̄ is
the partial specific volume, M is the molar mass and f is the
friction coefficient. S, D, and the molar mass M are linked by
the Svedberg equation,4,5,9 valid for non-interacting, ideally
sedimenting species:
S~
M ð1{vrÞ
D
RT
(2)
where T is the absolute temperature and R the gas constant.
As discussed above, the three measurable quantities S, D, and
M can be determined from ultracentrifugation only, though
some authors prefer to import the diffusion coefficient from
DLS measurements.
There are many methods for determining the sedimentation
coefficients and molar masses, and, for the case of polydisperse
species, their distribution and averages. The reader may refer
to the RASMB website for choosing the analysis software.30
This journal is ß The Royal Society of Chemistry 2006
A guide through the methods is available in literature.7 For
determining the average sedimentation coefficient, for
example, the second moment method1 and the Van Holde–
Weischet method31 can be used. More recently, it could be
obtained by fitting the sedimentation boundaries with the
numerical solutions of Lamm’s equation.31,32 The apparent
sedimentation coefficient distribution, not deconvoluted due to
diffusion, can be found using the time derivative method (the
so-called g(S*) distribution)2,3 or direct fitting of sedimentation boundary (the ls-g*(S) distribution) using numerical
solutions of the Lamm equation.34 The boundary fitting
method can be also used to find the diffusion-deconvoluted
distribution c(S) together with the average frictional ratio.34
This method allows thus the determination of an average
diffusion coefficient. The sedimentation equilibrium profiles
can be fitted with the well-known ideal exponential:
2
v ð1{vrÞMav 2 2 (3)
r {r0 zb
cðrÞ~cðr0 Þ exp
2RT
to obtain an average molar mass, or with a sum of
exponentials (3) with known masses to determine the fraction
of each species. In eqn (3), v is the angular velocity of the
rotor, r the radial coordinate, r0 a reference coordinate, and b a
free baseline parameter. Eqn (3) can be integrated over the
distribution of molar mass to yield the final function which
describes the experimental profiles. The determination of the
spectrum of either the sedimentation coefficient or the molar
mass is done using the linear least squares method.33–35
The latest and most laborious method, called global
analysis, brought additional accuracy to determinations by
analyzing a large set of data obtained at different experimental
parameters (see for example ref. 36 as well as the discussion
in ref. 32).
2.2. Summary of results
2.2.1. Supramolecular complexes. AUC, mainly used for
biological macromolecules, proved to be an effective technique
for characterizing supramolecular assemblies, as demonstrated
by D. Schubert et al.16 The goals and applications of the
analytical ultracentrifugation measurements for the characterization of supramolecular complexes in solution were clearly
defined. The description of three methods, i.e., sedimentation
velocity, sedimentation equilibrium, and transient state analysis are illustrated with results obtained on a cobalt coordination array. A couple of experimental problems were posed:
determination of the partial specific volume v̄, avoidance of the
non-ideal sedimentation, and chemical compatibility of the
sedimentation cell components with the organic solvents.
These problems were further studied in their subsequent
works. Tziatzios et al.17 discussed four methods of determining
the partial specific volume. Using the so called buoyant density
method, it was shown that v̄ is solvent dependent and biased by
salt concentration (Fig. 1b) but it is not influenced by the
hydrostatic pressure which means that the sample volume in
the sedimentation cell can be safely varied (see also the
discussion in ref. 18). The results obtained for v̄ were used for
molar mass determination of a supramolecular Co coordination array (used as a model system and presented in Fig. 1a)
Soft Matter, 2006, 2, 561–572 | 563
Fig. 1 Model system and its partial specific volume determination from AUC measurements, taken from ref. 17. a. Structure and assembly of a
Co coordination array. b. Partial specific volume determination by the buoyant density method in the absence (open symbols) and presence of
25 mM salt (solid symbols), in mixtures of acetonitrile–chloroform. The figure shows the effective molar mass Meff = Mav (1 2 v̄r) versus the
solvent density. Reprinted with permission from ref. 17. Copyright (2002) American Chemical Society.
from equilibrium measurements. The charge effects (in a nonideal sedimentation experiment) are also discussed. It was
confirmed that the primary charge effects can be easily
suppressed by adding salt, while a correction for the secondary
charge effects was found not necessary when applying the
buoyant density method. In ref. 19 Tziatzios et al. studied the
partial specific volume of a poly(ethylene glycol) (PEG)
derivative (Fig. 2a) using different solvent combinations
and two methods: the buoyant density method and digital
densimetry. An analysis of the state of association of the PEG
derivative was done: dimers (Fig. 2b), when an acetonitrile
solution was measured, and even larger aggregates, when
other solvents were used, have been observed in concentrations
up to 40%. Dimerization of functionalized PEO was studied
in ref. 20. AUC was used to compare the complexation via
Fe(II)–ligand interaction (almost complete) and hydrogen
bonding (y50%). Details about the determination of v̄ via
densitometrical methods can be found elsewhere.37
The synthesis and characterization of various terpyridine
metal complex connected polymers such as homo-dimers,
chain extended polymers, and diblock and triblock copolymers
were described by Lohmeijer.38 PEO70-[Ru2+]-PEO70 (Fig. 3a),
PEO70-[Fe2+]-PEO70, and PS20-[Ru2+]-PEO70 were subjected
to sedimentation equilibrium measurements. Effective molar
masses of both uncomplexed PEO-[ and the homo-dimers
complexed via Ru and Fe were obtained as a function of
solvent density (Fig. 3b,c). The partial specific volumes and
absolute molar masses were subsequently determined. Both
homo-dimers and mono-complexes/uncoordinated species
were detected in AUC measurements. The stability of the Fe
mono- and bis-complexes is discussed. The diblock copolymer
564 | Soft Matter, 2006, 2, 561–572
Fig. 2 Example of sedimentation equilibrium analysis done on a
model compound in ref. 19. a. The schematic representation of the
poly(ethylene glycol) derivative (the model system). b. Fit of the
experimental data assuming a monomer–dimer combination and their
calculated contributions to the experimental profile (upper plot) as well
as local fit residuals (lower plot). Reprinted from ref. 19 with kind
permission of Springer Science and Business Media.
This journal is ß The Royal Society of Chemistry 2006
Fig. 3 Complexation of PEO terpyridine-functionalized blocks via Fe and Ru ions evidenced in AUC sedimentation equilibrium experiments
shown in ref. 38. a. Schematic representation of the PEO70-[Ru2+]-PEO70 homo-dimer. b,c. Buoyant density method applied to determine the partial
specific volumes and molar masses. Reprinted from ref. 38 with kind permission of the author.
PS20-[Ru2+]-PEO70 was also subjected to sedimentation and
the equilibrium profile was fitted with a sum of two
exponentials. The dominant species (96%) was the complex
(referred to as the monomer). The dimer was believed to form
due to unspecific ionic interactions.
The average molar mass of an extended metallo-supramolecular polymer, based on an a,v-bis-terpyridine–poly(ethylene glycol) polymer linked via Ru(II) ions was
determined from sedimentation equilibrium profiles by fitting
the data with an exponential function.39 Hence, the number of
repeat units was obtained. A good agreement with the average
molar mass determined from viscosity measurements and GPC
measurements (the latter for the first time applied to such a
system) was reported.
Several metallo-supramolecular assemblies containing PS
and PEO blocks, terpyridine-end-functionalized and complexed via Ru(II) ions were analyzed from both velocity and
equilibrium sedimentation by Raşa et al.29 Different methods
of analysis were used for the determinations described in
Section 2.1. (except for association constants, which were
not addressed in this case). The results from the two types of
sedimentation experiments were compared and discussed
and the type of the average molar mass determined from
sedimentation equilibrium was clarified. It was also shown that
the type of salt used in the synthesis process of the PS20-[Ru2+]PEO70 had a strong influence on the state of association of
this complex in solution. Polymer concentration effects were
observed when all the other experimental parameters were kept
the same.
This journal is ß The Royal Society of Chemistry 2006
Michels et al.26 applied AUC for determining the molar
mass of water-soluble conjugated polyrotaxanes (an example
is shown in Fig. 4a). The determination of molar mass for
polyelectrolytes was found to be a difficult task. Their attempt
to use polyacrylamide gel electrophoresis gave unrealistically
high molecular weight. Reasonable values were obtained by
using GPC but only for two of their compounds (due to
absorption onto the column material) and when high ionic
strength was used to suppress electrostatic interactions
between the polyelectrolyte chains. The determination by
SANS was mentioned to be unsuccessful. MALDI-TOF MS
did not provide quantitative information on the molecular
weight distribution because shorter chains are desorbed more
easily. AUC proved to be the most practical method for the
average molar mass determination. Sedimentation equilibrium
measurements were performed in the presence of 6 mM salt.
The partial specific volumes of all polymers were determined
densitometrically. A generally good agreement between the
experimental and calculated values was observed. The
efficiency of the polymerization method was tested by
determining the average molar mass from AUC experiments
as a function of the nominal stoichiometry-predicted number
average degree of polymerization (Fig. 4b).
The synthesis and characterization of heteropolytungstate
clusters encapsulated in a shell of dendritically branching
surfactants were discussed by Volkmer et al.40 The characterization was done by using several techniques, including
analytical ultracentrifugation, on a dispersion of clusters in
organic solvents (toluene, THF, CHCl3). The sedimentation
Soft Matter, 2006, 2, 561–572 | 565
Fig. 4 Application of AUC to the study of polyelectrolytes. a.
Example of the idealized structure of one of the polyrotaxanes studied
in ref. 26. b. The determined average molar mass as a function
of the nominal stoichiometry-predicted number average degree of
polymerization. Deviation from ideality is observed at higher n̄NOM
values because of the accidental termination or fractionation
during purification. Reprinted from ref. 26 with kind permission of
Wiley-VCH.
velocity experiments were used to determine the hydrodynamic
radius of the cluster (decomposition and aggregation were not
observed). The sedimentation and diffusion coefficients were
determined from boundary moving and spreading, respectively, followed by extrapolation to zero concentration. In a
previous work,41 Kurth et al. synthesized and characterized
partially reduced polyoxomolybdate encapsulated in a shell of
dimethyldioctadecylammonium. The molar mass in the case of
an aqueous polyoxomolybdate solution was first determined
from velocity measurements by making use of the Svedberg
equation. The hydrodynamic radius was determined from the
diffusion coefficient and it was shown that the particles are
monodisperse. Equilibrium sedimentation was performed to
determine the apparent average molar mass. The encapsulated
clusters were dispersed in organic solvents and the particle size
distribution determined from velocity measurements indicated
solvent dependent aggregation (see Fig. 5).
The synthesis and solution characterization of coordination
polyelectrolytes used to generate molecular films were
described by Schütte et al.42 A methanol solution was
centrifuged to obtain the lower limit of molar masses in
the solution from sedimentation velocity measurements. The
polydispersity of the supramolecular polyelectrolytes was
determined from the size distribution.
2.2.2. Polyelectrolyte complexes. Beyer and Nordmeier43
studied the complexation of poly(acrylic acid) (PAA) and
poly(methacrylic acid) (PMAA) with ionene (see Fig. 6a for the
ionene structure). The sedimentation velocity measurements
566 | Soft Matter, 2006, 2, 561–572
Fig. 5 Sedimentation velocity analysis of a surfactant encapsulated
cluster done in ref. 41. a. The structure of the encapsulated cluster and
b. the particle size distribution determined using dispersions based on
three different organic solvents: i) THF, ii) toluene, iii) cyclohexane.
Reprinted from ref. 41 with kind permission of Wiley-VCH.
distinguished between uncomplexed ionene and PAA–ionene
complexes. The apparent (non-ideal) sedimentation coefficient
was determined (addition of excess salt results in unstable
complexes). A plot of the apparent sedimentation coefficient
versus the ionene fraction (Fig. 6b) provided the saturation
degree of complexation, which occurs when the apparent
sedimentation coefficient enters the saturation region.
Qualitatively similar, but quantitatively different results were
reported for PMAA–ionene in water.
Analytical centrifugation was the only technique used
to characterize PSS–PDADMAC-co-AA polyelectrolyte
complexes (PECs) by Karibyants et al. (PSS represents
poly(styrenesulfonate), DADMAC stands for diallyldimethylammonium chloride, and AA for acrylamide).44 The use of
This journal is ß The Royal Society of Chemistry 2006
Fig. 6 Example of AUC analysis of polyelectrolyte complexes, taken
from ref. 43. a. The structure of ionene used as a polycation. b. The
apparent sedimentation coefficient versus the ionene fraction for
different ethanol weight fractions in the solvent (water). The saturation
region indicates the saturation of complexation. Reprinted with
permission from ref. 43. Copyright (1999) Elsevier.
AUC was justified by the fact that this is the only method
which allows the examinations of the ratio between free
polymer (PSS) and complexed polymer, actually the main goal
of the presented investigations. First, velocity measurements
were performed to determine the concentration of free PSS,
an example being shown in Fig. 7. The effect of various
parameters such as mixing ratio, ionic strength, molecular
mass, and copolymer composition, was thoroughly investigated. By improving the solubility of the PEC (by copolymerization with AA), the sedimentation coefficients were
determined and studied as a function of initial molar mixing
ratios to identify the saturation of complexation. The model
independent ‘V analysis’ was used for the interpretation of the
sedimentation equilibrium data, since it allowed a separation
of the contribution of the components within interacting
systems. Karibyants and Dautzenberg45 studied the preferential binding of PDADMAC, a polycation, added to mixtures
of PSS and PSS–sodium poly(methacrylate) (PSS/PMA),
which are the polyanions, leading to aggregated quasisoluble complexes. Viscosimetry and UV spectroscopy were
employed in addition to AUC. The sedimentation coefficient
distribution was determined, and the absorption plateau of the
sedimentation profiles used to determine the concentration of
each component. A radial dilution correction was performed
and the Beckman software was used for obtaining the so-called
g(s*) distribution.34
Water soluble polyelectrolyte complexes were also studied
by Kochanowski et al.46 The ‘simplex’ formation (complex of
polyelectrolytes with opposite charges) is studied in the case
of 2-acrylamido-2-methylpropanesulfonic acid and acrylamide
copolymer (host component) and ionene (guest component).
The apparent sedimentation coefficients were determined and
used together with viscosity data to estimate the relative
increase in the diameters of certain simplex particles as a
function of the diameter of the host copolymer.
A number of polyelectrolyte complexes (PECs), formed
between oppositely charged polyelectrolytes, may lead to gellike networks which do not precipitate in aqueous solution.
Under certain conditions, membrane formation can occur.
A modified synthetic boundary method was applied by
Wandrey et al.47 to study the PEC membrane formation.
Poly(L-lysine)hydrochloride, poly(vinylamine)hydrochloride,
and chitosan oligomers were the polycations. The polyanion
was sodium alginate. The synthetic boundary method11 is
known as a method for studying chemical reactions and
requires special centerpieces for the sedimenting cells.48 It was
applied for the first time to study PEC membrane formation
by Wandrey and Bartkowiak.48 The principle of membrane
formation in a synthetic boundary cell is shown in Fig. 8. It is
concluded that this is a unique technique which can visualize
on-line membrane growth as well as membrane properties like
Fig. 7 Application of sedimentation velocity measurements, presented in ref. 44, to determine: a. the concentration of the free polyelectrolyte PSS
after formation of the complex, and b. the stoichiometry factors f of the components in the complex versus their molar mixing ratio X. For the case
PSS-66T–PDADMAC, the aqueous solution contained pure water (1), 0.01 N NaCl (2) and 0.1 N NaCl (3). The complex PSS–PDADMAC-coAA-47, dissolved in pure water, corresponds to (4). The solid line 5 is the calculated dependence for a 1 : 1 stoichiometry. Reprinted with permission
from ref. 44. Copyright (1997) American Chemical Society.
This journal is ß The Royal Society of Chemistry 2006
Soft Matter, 2006, 2, 561–572 | 567
Fig. 8 Principle of membrane formation experiments in a synthetic
boundary cell (view from above), taken from ref. 48. During the run,
the solvent is layered over the sample. For this purpose the two sectors
are connected with two capillaries. Component positions (upper
drawing) and the corresponding absorption scans are indicated for
the cases: a. before layering, b. during layering (membrane formation is
indicated by the black sector corresponding to absorption peak 4), c.
after layering is finished. Reprinted with permission from ref. 48.
Copyright (2001) Elsevier.
thickness, symmetry, and stability. Membrane defining characteristics are reported in ref. 49 after a systematic study
Bourdillon and Wandrey performed to observe the influence
of the polyion concentration and solution pH as well as the
influence of molar mass. In synthetic boundary experiments,
absorbance scans were used to monitor the membrane formation in time and interference scans to calculate the layering
velocity.
The time derivative concentration curves dc/dt (i.e. the
apparent sedimentation coefficient distributions) were
obtained for the hydrophobically modified polyelectrolyte
poly(maleic acid–octyl vinyl ether) (PMAOVE), the binding
surfactant sodium dodecyl ether (SDS), and various mixtures
of them having the concentration of SDS as parameter, by
Deo et al.50 The interaction between PMAOVE and SDS
was studied. Above a certain SDS concentration a change in
the distribution from monomodal to bimodal suggested the
presence of both partially and completely unfolded PMAOVE.
Further increase in the SDS concentration resulted in the
presence of unfolded PMAOVE only, as the distribution
became again monomodal, but with a different average
sedimentation coefficient.
2.2.3. Supramolecular and block copolymer micelles. In a
couple of papers (see for example refs 13,14), Gohy et al.
studied metallo-supramolecular block copolymer micelles. The
alternative to the ‘classical’ covalent block copolymers is now
the metal–ligand complex used as a supramolecular linker
between hydrophilic and hydrophobic blocks. The formation
of aqueous ‘frozen’ micelles is reported in the case of the
diblock copolymer PS20-[Ru2+]-PEO70 and the triblock copolymer, PS32-b-P2VP13-[Ru2+]-PEO70. The AUC was used as a
characterization tool for these micelles by Vogel et al.21 and
Mayer et al.22 In the latter case, an improvement in the
preparation procedure was reported in order to obtain a more
homogeneous particle population. Both sedimentation equilibrium and velocity measurements were employed. The average
micelle molar mass and subsequently the micelle composition
568 | Soft Matter, 2006, 2, 561–572
were determined from equilibrium measurements, confirming
the velocity measurement results obtained on the same system
(micelles prepared with the improved method). The diameters
obtained from AUC measurements were compared with those
from TEM measurements. The molar mass distribution of
PS20-[Ru2+]-PEO70 micelles was determined from velocity
measurements by using the Sedfit program.51 However the
conversion from sedimentation coefficient distribution
seemed to be affected by errors due to using the same friction
coefficient for all particles. A separate study was done on
PS20-[Ru2+]-PEO375.22
PIB-b-PMAA micelles were characterized using various
techniques (Fluorescence Correlation Spectroscopy (FCS),
DLS, SLS, TEM, AUC) in ref. 52 by Schuch et al.
Sedimentation velocity measurements were performed to
determine the sedimentation coefficient distribution, which
evidences more than one sedimenting species (two peaks were
observed in the sedimentation coefficient distribution as shown
in Fig. 9). Assuming different species (with different packing
densities) the packing density of the main component was
calculated from the sedimentation coefficient, by making use
of the hydrodynamic diameter obtained from DLS.
AUC equipped with absorption optics was a very useful
technique to show the transport of UV absorbing guest
molecules encapsulated in the core of PEO-b-PCL micelles
self-assembled in water.53 The polymer blocks absorb much
less than the guest molecules at 262 nm, so that the measured
sedimentation velocity profiles demonstrated the role of the
micelles as carriers for the water-insoluble encapsulated
compound.
2.2.4. Synthetic polymers in solution. The properties of
a membrane-forming polymer poly(1-trimethylgermyl-1propyne) were studied by Pavlov et al.,54 who combined the
results obtained from sedimentation velocity measurements,
translational isothermal diffusion, and viscosimetry. The
sample was fractionated and the 12 fractions plus the original
sample were studied in cyclohexane solutions. The sedimentation coefficients were calculated from the sedimentation
Fig. 9 Detection of species present in a PIB-b-PMAA micellar
solution from sedimentation coefficient analysis: the experimentally
determined sedimentation coefficient distribution in ref. 52 shows two
peaks corresponding to two species in the system. Reprinted with
permission from ref. 52. Copyright (2000) American Chemical Society.
This journal is ß The Royal Society of Chemistry 2006
boundary shift in time. Their concentration dependence was
found to be linear, which allowed a simple determination
of the coefficients at infinite dilution. The molar mass was
determined from Svedberg’s equation (eqn (2)).
A systematic study of the microemulsion polymerization
of n-butyl acrylate was done by Hammond et al.55 Light
scattering (DLS, SLS), TEM and AUC sedimentation velocity
measurements were the characterization techniques. The last
one was used for diluted microemulsion lattices to obtain the
sedimentation coefficient from the rate of movement of the
peak in the Schlieren image. The hydrodynamic radius was
obtained from the diffusion coefficient determined from DLS
measurements and compared to that obtained from the
sedimentation coefficient as well as to the z-average RMS
radius of gyration determined from SLS.
Galacturonic and mannuronic acids were coupled to
polyethyleneimine PEI or PEI-b-PEG to investigate them as
novel targeting ligands for receptor mediated gene delivery.56
The average molar masses of the polymers and functionalized
polymers were determined from AUC by converting the
average sedimentation coefficient, obtained from the corresponding distribution.
Lavrenko et al.57 determined the translational mobilities
of poly(methylhydrodimethylsiloxane) (PMS) in solution (in
chloroform and benzene respectively) by low-speed analytical
ultracentrifugation using interference optics. The dispersions
of the boundary profiles were calculated and the diffusion
coefficient was determined from the dependence of dispersion
on time. The sedimentation coefficient was estimated from
the Svedberg equation (eqn (2)) and the hydrodynamic
radius from the diffusion coefficient. The results are discussed
in detail.
2.2.5. Polymer lattices. The determination of particle size
distribution by AUC originates long time ago. A significant
development of the method based on scattered light intensity
analysis in time was reported by Mächtle in 1984 and 1988,
and described in a more recent work.58 The light passes
through the middle of a sedimentation cell and the time
dependency of intensity is interpreted using the Mie light
scattering theory to determine mass fractions and Stokes’ law
to calculate particle diameters (from the sedimentation time
between the meniscus and detector). This approach was also
used to determine the density of particles by measuring the
sedimentation time in a second solvent (heavy water). The
optical system with which any preparative ultracentrifuge can
be equipped is referred to as turbidity optics. The H2O/D2Osedimentation analysis is also presented in ref. 5.
Müller also reported in 1989 the analytical ultracentrifugation characterization on a variety of latexes used in chemical
industry using a similar turbidity detector.59 The subject is
recalled in ref. 60 where several results are given for mixtures
of fine and coarse polybutadiene particles, a mixture of
polystyrene butadiene copolymer and PS latex, and a mixture
of fine and coarse particles of polybutadiene grafted with a
mixture of monomeric styrene and acrylonitrile. A mixture of
nine monodisperse calibration lattices is shown to be resolved
(Fig. 10).61 In the case of smaller particles and samples with
lower turbidity, the turbidity optics had to be replaced by
This journal is ß The Royal Society of Chemistry 2006
Fig. 10 Resolving power of ultracentrifugation as presented in
ref. 61: a mixture of nine monodisperse calibration lattices is measured
in one cell during one run with the method proposed in ref. 59. The
differential mass distribution (left axis) and the integral mass
distribution (right axis) are plotted vs. the particle diameter.
Reprinted from ref. 61 with kind permission of Springer Science and
Business Media.
interference optics (a Beckman XL-I was used for this
purpose).61 Data analysis was discussed in this case in detail.
2.2.6. Hybrid complexes. Vandermeulen et al.62 described the
preparation and characterization (using several techniques,
including analytical ultracentrifugation) of two novel hybrid
diblock copolymers based on poly(ethylene glycol) (PEG) and
peptide sequences. Sedimentation equilibrium measurements
on aqueous solutions of both peptide and diblock copolymers
were best interpreted in terms of monomer, dimer, and
tetramer association. The degree of association of the diblock
copolymers was significantly different from that observed
when only a peptide solution was investigated: the PEG
segment of the copolymers hindered the association, leading to
a strongly increased monomer content but to less tetramer
content.
A series of peptides and mPEG-peptides conjugates have
also been synthesized by Pechar et al.63 The influence of the
hydrophilic PEG and the effect of peptide chain length on the
conformation of the peptides were studied using circular
dichroism, spectroscopy, size-exclusion chromatography, and
analytical ultracentrifugation. The molar mass was determined
from ideal equilibrium measurements by fitting the data with
the ideal single-species model.
The colloidal properties of PBMA342-b-PAEMA39 in dilute
cyclohexane solution (AEMA is 2-(acetoacetoxy)ethyl methacrylate and BMA is n-butyl methacrylate) were studied by
Krasia and Schlaad.64 This block copolymer was found to
assemble into spherical micelles. The PAEMA cores were
loaded with metal ion salts and characterization was done by
UV–vis, AUC, and AFM. The analysis of the sedimentation
coefficient distribution in the absence and in the presence of
the ferric salt evidenced the formation of a polymer–metal
complex and that the ferric salt was evenly distributed among
the aggregates.
Antonietti et al.65 synthesized PEO-b-PMAA-C12 (by partial
alkylation with dodecylamine). While PEO-b-PMAA is a
Soft Matter, 2006, 2, 561–572 | 569
Fig. 11 Example of time-dependent sedimentation analysis for PEOb-PMAA-C12–calcium phosphate aggregates at pH = 4, taken from
ref. 65. The evolution of the sedimentation coefficient distribution
indicates a primary growth process (over hours) and a transformation
into a second species in which the aggregates became denser, with a
maximum concentration after y100 h. Afterwards the concentration
decreased because of colloidal instability. Reprinted from ref. 65 with
kind permission of Wiley-VCH.
double-hydrophilic block copolymer, micellar dispersions in
water of PEO-b-PMAA-C12 have been prepared. Precipitation
of calcium phosphate was performed at different pH values.
The association between the functionalized block copolymer
and calcium phosphate occurred at pH , 4.2. In this case
AUC revealed that all polymer micelles were mineralized. The
sedimentation coefficient distribution was determined as a
function of time showing a primary growth process and, later,
bulk sedimentation of a second species (see Fig. 11).
The formation of PS-b-PEO–surfactant micellar complexes
and the synthesis of Pd and Pt nanoparticles mainly located in
the block copolymer micelles were described by Bronstein
et al.66 The micellar structures in PS-b-PEO–cetylpiridinium
chloride (CPC) aqueous solutions were characterized from
AUC sedimentograms. The increase in the amount of CPC
resulted in an increase in molar mass of both micelles and
micelle clusters showing that the CPC molecules incorporate
into the block copolymer micelles and micelle structures. In a
previous paper, Bronstein et al.67 studied the interaction of
P2VP-b-PEO (where P2VP stands for the poly(2-vinylpyridine)) with metal ions and metal nanoparticle formation.
First, the micelles in aqueous solution were studied for the
case of two block copolymers, P2VP135-b-PEO350 and P2VP41b-PEO205, by analyzing the sedimentation coefficient distribution. AUC was also used to study the interaction of Na2PdCl4
with P2VP135-b-PEO350: it showed simultaneous sedimentation
in absorption (salt) and interference optics (salt + polymer)
which leads to the conclusion that all the palladium salt is
incorporated into the micelle cores.
The linear hybrid block copolymer PS-b-PLL, where PLL
stands for poly(Z-L-lysine) was synthesized by Dimitrov et al.68
and characterized by several techniques. The sedimentation
coefficient distribution showed single sedimenting unimers. A
conversion of this distribution to molar mass distribution
showed however a Mw value smaller than the corresponding
570 | Soft Matter, 2006, 2, 561–572
Mn value measured by NMR, a result which needs further
investigation.
Several model systems containing quantum size colloidal
particles prepared in micelle cores are analyzed by Cölfen
et al.69 using combined absorbance and interference radial
scans as well as monitoring the absorbance in time at a fixed
radial position. Au particles were prepared both in PSS
microgels and in PS-b-P4VP micelles while CdS particles were
obtained by precipitation in the PS-b-P4VP micelles. First,
AUC was employed to distinguish whether the particles are
grown or aggregated crystal nuclei. AUC separation of these
two types of particles is possible when there is a density
difference between them. When the densities are nearly equal it
was shown that it is still possible to distinguish them if the
spectra of the two components are different. AUC was also
used for particle (ZnO) growth observation. This was done by
studying the time-dependent changes of the particle size
distribution. Another application was the determination of
the extinction coefficient of ZnO particles prepared in
PS-b-PMAA micelles. The necessity for the AUC approach
instead of UV–vis spectrometry is discussed. Finally an AUC
investigation of the reaction efficiency for the synthesis of
hybrid colloids is presented, showing once more the impressive
capabilities of AUC as a characterization tool for these
complex systems.
3. Conclusions and perspectives
We have highlighted results obtained in the past years on
the characterization of metallo-supramolecular assemblies by
analytical ultracentrifugation as well as of various synthetic
polymer systems. The increasing number of analyzed species
from block copolymers to supramolecular and hybrid
complexes, the large variety of methods applied for characterization to determine molar mass, sedimentation and
hydrodynamic coefficients, and the development of experimental approaches for studying, for example, functionalized
polymers or membrane formation, clearly show a strongly
ascending trend in using AUC as a characterization tool. This
was accompanied by a permanent adaptation of the analysis
software to experimental needs and implementation of new
numerical methods.
There is now much effort put into obtaining enhanced, more
accurate, and faster results in the following directions: analysis
of new species which also bring with them new experimental
challenges, using new optical systems, experimental approaches, and methods of data processing. AUC equipped with
absorption optics was shown to be a valuable tool in studying
the transport of unsoluble compounds encapsulated in micelle
cores, an application we intend to develop in the near future
due to its utility in the study of novel drug carriers.
Fluorescence and multi-wavelength detectors have already
been made. A new method of sedimentation velocity analysis,
taking into account not only size but also shape polydispersity,
can now be applied. Recent equilibrium measurements
performed on charged colloidal silica spheres70,71 revealed
the possibility of a larger area of applications if non-ideal
equilibrium sedimentation is performed on stable diluted nonassociating systems. Besides the molar mass, which can be
This journal is ß The Royal Society of Chemistry 2006
determined from the ideal part of the equilibrium profiles, the
species charge and free ion concentration could be determined
in one and the same experiment. The analysis may require,
however, more accurate theoretical models (to assure the
quantitative agreement between the theory and experiment,
not observed in the above mentioned references). The equilibrium profiles also offer the possibility of a direct determination of the equation of state by numeric integration (see
ref. 71), and of the internal macroscopic field via a theoretical
model, applications which were less exploited so far.
The effects of the internal field on the sedimentation velocity
profiles at low polymer concentration also need attention
since, to our knowledge, no studies are available yet. If in
addition concentration effects are present, the interpretation of
(non-ideal) sedimentation velocity measurements of charged
species becomes very complicated and an eventual polydispersity leads for the time being to insurmountable
numerical difficulties. Nevertheless, a concentration dependence study of the average sedimentation coefficient was
reported several times (see for example refs 40,54,72) and
modeled for uncharged monodisperse colloids and even for
charged monodisperse colloids24 because it may provide
precious information about the interactions. Currently, linear
non-ideal sedimentation behavior for monodisperse species
can be analyzed. However, the linear behavior normally
corresponds to uncharged species.
Returning to ideal sedimentation experiments, the global
analysis method developed in the past few years offers now
not only more accurate possibilities of studying the association behavior of macromolecules but also incorporation of
different types of data (e.g. DLS) for a complex analysis.
Acknowledgements
Prof. D. Schubert (J.W. Goethe – University Frankfurt) is
thanked for critically reading the manuscript and helpful
discussions. M. A. R. Meier (TU Eindhoven) is also thanked
for useful comments. This work was financially supported
by the Dutch Polymer Institute (DPI), the Nederlandse
Organisatie for Wetenschappelijk Onderzoek (NWO, VICI
award) and the Fonds der Chemischen Industrie.
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