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Friedrich-Schiller-Universität Jena 

 

 



 

Chemisch-Geowissenschaftlichen Fakultät 

 

Hydrodynamic analysis of macromolecular and 
colloidal systems by analytical 
ultracentrifugation and related methods 

 

Dissertation 
zur Erlangung des akademischen Grades 

doctor rerum naturalium (Dr. rer. nat.) 

 

vorgelegt dem Rat der Chemisch-Geowissenschaftlichen 

Fakultät der Friedrich-Schiller-Universität Jena 

 

von Master of Science Igor Perevyazko 

geboren am 26. März 1984 in Leningrad (USSR) 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gutachter: 

1. ...................................... 
2. ...................................... 


Tag der öffentlichen Verteidigung:


Table of Contents 

Documentation of Authorship ………………………………………………………………….. 4 

1. Introduction ………………………………………………………………………………... 9 

2. Hydrodynamic Methods as a Powerful Tool to Study Macromolecular and Colloidal 
Systems…………………………………………………………………………………….. 11 

3. Comprehensive Application of Velocity Sedimentation: Critical Aspects…………...…… 19 

4. Hydrodynamic Characterization of Charged Macromolecular Systems…………............... 25 

5. Polyplexes – Polyelectrolyte Complexes of DNA and Poly(ethylene imine)………..…..... 33 

6. Influence of Process and Formulation Parameters on the Formation of Polymeric 
Nanoparticles by the Solvent Displacement Method ……………………………………… 39 

7. Separation of Nanoparticles of Different Size and Composition by Density Gradient 
Centrifugation ……………………………………………………………………………... 45 

8. Summary …………………………………………………………………………………... 51 

9. Zusammenfassung …………………………………………………………………………. 53 

10. References …………………………………………………………………………………. 55 

Supplementary Information ………………………………………………………………......... 61 

Curriculum Vitae ……………………………………………………………………………….. 63 

List of Publications …………………………………………………………………………….. 65 

Acknowledgments / Danksagung ………………………………………………………………. 69 

Declaration of Authorship / Selbständigkeitserklärung ………………………………………... 71 

Publications A1-A9 …………………………………………………………………………….. 73 

 


 


Documentation of Authorship 

This section contains a list of the individual authors’ contributions to the publications reprinted 
in this thesis. 

 

1) G. M. Pavlov, I. Y. Perevyazko, O. V. Okatova, U. S. Schubert, Conformation parameters of 
linear macromolecules from velocity sedimentation and other hydrodynamic methods. 
Methods 2011, 54, 124-135. 


 

G. M. Pavlov: literature research, preparation of the manuscript 

I. Y. Perevyazko: preparation of the manuscript 

O.V. Okatova: preparation of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

2) G. M. Pavlov, I. Perevyazko, U. S. Schubert, Velocity sedimentation and intrinsic viscosity 
analysis of polystyrene standards with a wide range of molar masses. Macromol. Chem. Phys. 
2010, 211, 1298-1310. 


 

G. M. Pavlov: conceptual contribution, preparation of the manuscript 

I. Perevyazko: experimental results (velocity sedimentation and intrinsic 
viscosity measurements), preparation of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

3) I. Perevyazko, A. Vollrath, S. Hornig, G. M. Pavlov, U. S. Schubert, Characterization of 
poly(methyl methacrylate) nanoparticles prepared by nanoprecipitation using analytical 
ultracentrifugation, dynamic light scattering, and scanning electron microscopy. 
J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 3924. 


 

I. Y. Perevyazko: characterization of the nanoparticles by AUC, analysis of 
the data, preparation of the manuscript 

A. Vollrath: preparation of the nanoparticles, characterization by DLS 
and SEM, preparation of the manuscript 

S. Hornig: conceptual contribution, correction of the manuscript 

G. M. Pavlov: conceptual contribution, preparation of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

 

 


4) T. Erdmenger, I. Perevyazko, J. Vitz, G. Pavlov, U. S. Schubert, Microwave-assisted 
synthesis of imidazolium ionenes and their application as humidity absorbers. 
J. Mater. Chem. 2010, 20, 3583-3585. 


 

T. Erdmenger: syntheses, preparation of the manuscript 

I. Y. Perevyazko: analytical ultracentrifugation and viscosity measurements, 
preparation of the manuscript 

J. Vitz syntheses, preparation of the manuscript 

G. M. Pavlov: conceptual contribution, preparation of the manuscript 

U. S. Schubert revision and correction of the manuscript, supervision 

 

5) B. Happ, G. M. Pavlov, I. Perevyazko, M. D. Hager, A. Winter, U. S. Schubert, Induced charge 
effect by Co(II) complexation on the conformation of a copolymer containing a bidentate 
2-(1,2,3-triazol-4-yl)pyridine chelating unit. Macromol. Chem. Phys. 2012, 213, 1339-1348. 


B. Happ: syntheses, preparation of the manuscript 

G. M. Pavlov: analytical ultracentrifugation and viscosity measurements, 
preparation of the manuscript 

I. Y. Perevyazko: analytical ultracentrifugation and viscosity measurements, 
preparation of the manuscript 

M. D. Hager: conceptual contribution, correction of the manuscript 

A. Winter: conceptual contribution, correction of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

6) I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Höppener, S. Schubert, D. Fischer, U. S. 
Schubert, Characterization of DNA-linear PEI polyelectrolyte complexes: Formation, 
properties and composition. Langmuir 2012, 28, 16167-16176. 


 

I. Y. Perevyazko: characterization (AUC, DLS, intrinsic viscosity) of the 
polyplexes and initial polymers, analysis of the data, 
preparation of the manuscript 

M. Bauer: preparation of the polyplexes, transfection and cytotoxicity 
experiments, preparation of the manuscript 

G. M. Pavlov: conceptual contribution, correction of the manuscript 

S. Höppener: AFM investigations, preparation of the manuscript 

S. Schubert: correction of the manuscript 

D. Fischer: conceptual contribution, correction of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 


7) I. Y. Perevyazko, J. T. Delaney, A. Vollrath, G. M. Pavlov, S. Schubert, U. S. Schubert, 
Examination and optimization of the self-assembly of biocompatible, polymeric nanoparticles 
by high-throughput nanoprecipitation. Soft Matter 2011, 7, 5030-5035. 


 

I. Y. Perevyazko preparation and characterization (AUC and DLS) of the 
nanoparticles, analysis of the data, preparation of the 
manuscript 

J. T. Delaney: conceptual contribution, preparation of the nanoparticles, 
preparation of the manuscript 

A. Vollrath: preparation and characterization (SEM, DLS) of the 
nanoparticles, preparation of the manuscript 

G. M. Pavlov: conceptual contribution, preparation of the manuscript 

S. Schubert: conceptual contribution, correction of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

8) I. Y. Perevyazko, A. Vollrath, C. Pietsch, S. Schubert, G. M. Pavlov, U. S. Schubert, 
Nanoprecipitation of poly(methyl methacrylate)-based nanoparticles: Effect of the molar mass 
and polymer behavior. J. Polym. Sci., Part A: Polym. Chem. 2012, 50, 2906-2913. 


 

I. Y. Perevyazko: characterization of the initial polymers (AUC, intrinsic 
viscosity, densitometry), preparation and characterization 
(AUC, DLS) of the nanoparticles, analysis of the data, 
preparation of the manuscript 

A. Vollrath: preparation and characterization (SEM, DLS) of the 
nanoparticles, preparation of the manuscript 

C. Pietsch: synthesis and characterization (SEC) of the PMMA 
samples 

S. Schubert: correction of the manuscript 

G. M. Pavlov: conceptual contribution, preparation of the manuscript 

U. S. Schubert: revision and correction of the manuscript, supervision 

 

 

 

 

 

 

 

 

 


9) A. Vollrath, D. Pretzel, C. Pietsch, I. Perevyazko, R. Menzel, D. Weiß, S. Schubert, G. M. 
Pavlov, R. Beckert, U. S. Schubert, Preparation, cellular internalization, and biocompatibility 
of highly fluorescent PMMA nanoparticles. Macromol. Rapid Commun. 2012, 33, 1791-1797. 


 

A. Vollrath: Preparation and characterization (SEM, DLS) of the 
nanoparticles, preparation of the manuscript 

D. Pretzel: biological studies, preparation of the manuscript 

C. Pietsch: synthesis of the polymers, preparation of the manuscript 

I. Perevyazko: fractionation of the nanoparticles, characterization of the 
particles by AUC, preparation of the manuscript. 

R. Menzel synthesis of fluorescent dye 

S. Schubert conceptual contribution, correction of the manuscript 

G. M. Pavlov conceptual contribution, correction of the manuscript 

D. Weiß conceptual contribution 

R. Beckert conceptual contribution 

U. S. Schubert: conceptual contribution, revision and correction of the 
manuscript, supervision 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Declaration of the supervisor: 
(Prof. Dr. Ulrich. S. Schubert) 


1. Introduction 

 

During the last decades, macromolecular chemistry has generated numerous different 
polymeric and colloidal systems which are capable of molecular complexation and, thus, of the 
formation of a large number of architectures on the nanoscale.[1-11] To study the properties of the 
different polymer architectures, a variety of powerful methods can be applied.[12-15] One of the 
main goals of polymer characterization is to be able to predict certain physical/chemical 
properties of the systems based on their conformational characteristics. The present thesis deals 
with extracting molecular information on the conformation of macromolecules and nanoparticles 
in solution from their hydrodynamic behavior. 

Among the hydrodynamic methods applied in this thesis, a key role is reserved for 
sedimentation velocity analysis using an analytical ultracentrifuge.[16-18] Analytical 
ultracentrifugation (AUC) is a classical analytical technique that can be used to study the 
solution behavior, i.e., hydrodynamic and thermodynamic properties, of nearly any 
macromolecular and colloidal system over a wide range of solute concentrations and in a large 
variety of solvents.[19-20] However, though this technique is well-known in biochemistry and 
biophysics and uses modern instruments,[21-22] its application for studying synthetic polymers is 
rather limited up to now.[23-27] The main reason may be that the available software for the 
treatment of automatically collected sedimentation data has been developed for the study of 
globular proteins, which are characterized by high fractal dimensions (~3; like macroscopic 
particles), whereas linear macromolecules are characterized by fractal dimension between 2 and 
1 (“soft matter”) and behave, with respect to their molecular hydrodynamics, much more 
sophisticated. Consequently, special attention will be given in this thesis to the use of analytical 
ultracentrifugation and modern analytical software for studying linear macromolecules, with 
special attention to the relation between chain rigidity and conformation in solution, and to 
complex heterogeneous systems (Chapter 3). 

Besides neutral polymers, charged macromolecular systems and polyelectrolyte 
complexes offer great potentials for applications and will be discussed in Chapters 4 and 5. 
Polyelectrolytes are polymers carrying either negatively or positively charged ionizable groups. 
Electrostatic interactions lead to a behavior of polyelectrolyte solutions that differs completely 
from that of uncharged polymers. Examples of polyelectrolytes include polystyrenesulfonate, 
polyacrylic and polymethacrylic acids and their salts, DNA, as well as poly(ethylene imine) and 
polyionenes. In addition to the “classical” polyelectrolytes mentioned above, self-assembling 
systems composed of organic molecules and metal ions offer promising opportunities.[1, 28-30] The 
incorporation of metal ions enables the creation of well-defined metallo-supramolecular systems 
with unique properties. Therefore, in the Chapter 4 attention will be given to the investigation of 


polyionenes and metallo-supramolecular polyelectrolytes. The discussion will be focussed on the 
molar mass determination and the investigation of conformational changes in solution. Another 
topic studied here are cationic polymer/DNA complexes, as widely used as gene transfer vectors. 
Despite a lower transfection rate, cationic polymer-based gene delivery systems show several 
advantages as compared to viral vectors, like easy production, adjustment of size distribution or 
low immune toxicity and the possibility of composition control. For a fundamental 
understanding of the mechanism of complex formation and the transfection of the complex into 
the cell, detailed information on its composition and its variability under different conditions 
represents a prerequisite (further discussed in Chapter 5). 

In Chapters 6 and 7, the attention will be focused on the study of polymeric 
nanoparticles. Such nanoparticles have attracted great interest in the field of medicine and 
biotechnology, in particular as promising drug carrier devices. To make these nanoparticles 
suitable for drug delivery, targeting and other applications, they should have appropriate 
physico/chemical properties that also can be controlled during the production. The approach 
applied for nanoparticle formulation is based on systematically varying the processing and 
formulation parameters (concentration, solvent/non-solvent ratio, polymer molar mass, 
thermodynamic quality of the solvent) in an automated way, in order to understand their 
influence on the characteristics of the particles formed. By changing the preparation conditions, 
well-defined and, with respect to size, uniformly distributed nanoparticles can be prepared. 
However, it is also feasible to obtain such particle fractions by separation/fractionation of less 
well-defined systems. Among different fractionation methods, density gradient centrifugation is 
not only one of the oldest but also of the most efficient ones, as described in Chapter 7 for 
nanoparticles of different nature. 

In summary, the main scope of the current thesis is the detailed investigation of various 
complex macromolecular and colloidal systems by the methods of molecular hydrodynamics, in 
particular analytical ultracentrifugation, intrinsic viscosity and translational diffusion. 

 


2. Hydrodynamic Methods as a Powerful Tool to Study Macromolecular and 
Colloidal Systems 

 

Parts of this chapter have been published in: A1) G. M. Pavlov, I. Y. Perevyazko, O. V. Okatova, U. S. Schubert, 
Methods 2011, 54, 124-135; A2) G. M. Pavlov, I. Perevyazko, U. S. Schubert, Macromol. Chem. Phys. 2010, 211, 
1298-1310; A3) I. Perevyazko, A. Vollrath, S. Hornig, G. M. Pavlov, U. S. Schubert, J. Polym. Sci., Part A: Polym. 
Chem. 2010, 48, 3924-3931. 

 

The fundamental information about the molecular structure and/or conformational 
characteristics of macromolecules can be obtained either by high resolution techniques like 
X-ray crystallography, or neutron scattering, and nuclear magnetic resonance, or by using “low” 
resolution but still very informative hydrodynamic methods.[12] From the early beginnings of 
polymer science, hydrodynamic methods, such as velocity sedimentation, translational diffusion 
and viscous flow measurements, represented powerful tools for the characterization of polymers, 
nanoparticles and colloidal systems of different nature.[31-37] With respect to polymer 
characterization, the molecular information obtained will be most reliable and exhaustive when 
typical results from more than one of the mentioned methods are collected and compared, e.g., 
velocity sedimentation and translational diffusion coefficient (s and D) and intrinsic viscosity 
([.]), in particular if these coefficients can be gathered for homologous series of 
macromolecules.[12, 31, 38-39] These characteristic hydrodynamic values are related to the size (D, 
s, and [.]) and the molar mass (s and [.]) of the macromolecule as shown in the following 
equations: 

 

..=..(..-......)...... (2.1) 

..=...... (2.2) 

..=......<....>../.. (2.3) 

[..]=..<h..>../.... (2.4) 

where f is translational frictional coefficient, <h2> the mean-square end-to-end distance, NA 
Avogadro’s number, k the Boltzmann constant, (1-..0) the buoyancy factor, D the translational 
diffusion coefficient, F(L/A, d/A, e) and P(L/A, d/A, e) are the Flory hydrodynamic parameters, L 
is the chain contour length (the length of a molecular chain extended as much as possible without 
deforming its valence angels), d the diameter of the chain, A the statistical segment length, and e 
a parameter characterizing the thermodynamic quality of the polymer-solvent system. 


Picture14.tif 
Sedimentation coefficients can be determined in different ways. In the classical method, 
the displacement of the sedimentation boundary versus time of sedimentation is observed, 
followed by a calculation based on the definition s = (dr/dt)/.2r (r: distance of the boundary 
from the axis of rotation). The measured integrated distributions of the refractive index or the 
optical density versus r (Figure 2.1A) can be transformed into differential ones (Figure 2.1B), 
and the position of the maximum of the differential distribution can then be taken as the radial 
distance of the sedimentation boundary (Figure 2.1C). There are several types of software 
available for obtaining the velocity sedimentation coefficient (Figure 2.1D).[40-42] 

 

 

Figure 2.1. Results of velocity sedimentation experiments on a polystyrene standard with 
Mw = 864,000 g mol-1. (A) Superposition of the integral distribution of the polystyrene 
concentration inside the cell, collected by interference optics every 435 s. (B) Corresponding 
differential distribution of the sedimentation profiles. (C) Dependence of the .ln r on .t for the 
determination of the sedimentation coefficient. (D) Comparison of the differential distribution of 
the sedimentation coefficient obtained by different software: 1 – Sedfit c(s), 2 – Sedanal g(s). 

 

 The translational diffusion coefficient can be determined by the classical method of the 
temporal spreading of an artificially formed solution/solvent boundary[39, 43] or by dynamic light 
scattering (DLS). Moreover, using modern software for the analysis of sedimentation data, the 


diffusion coeffcient can be determined from a single sedimentation velocity experiment in terms 
of the frictional ratio value f/fsph. The diffusion coefficient is related to the size of the 
macromolecules (particles) through the Stokes-Einstein equation. In the case of spherical 
particles the frictional coefficient f, as ingressed in Eq. 2.2, is described by the Stokes equation. 
The frictional coefficient for polymer coils is well described by the Kirkwood–Riseman theory 
(Eq. 2.3).[44] The intrinsic viscosity (rotational friction) data can be extracted from measurements 
of the dynamic viscosity, in various kinds of viscometers, of polymer solutions of different solute 
concentration. There are a number of extrapolation procedures allowing determination of [.] for 
neutral macromolecules.[45-46] 
To obtain information, based on the hydrodynamic values, on the properties of individual 
macromolecules it is necessary to use dilute solutions in a wide range of concentrations 
(cmax/cmin = 3), sufficient for reliable extrapolation to c . 0. The product of the intrinsic viscosity 
and the concentration of the solute (c[.]) characterizes the degree of dilution of the solution; the 
solution is dilute if c[.] < 1. To eliminate the solvent properties, it is useful to apply the intrinsic 
values of the velocity sedimentation coefficient [s] = s0.0/(1-..0) and the translational diffusion 
coefficient [D] = D0.0/T. These values only depend on the main characteristics of a 
macromolecular component (<h2>1/2 and M). The intrinsic coefficients have a more general 
sense and allow comparing transport properties of various polymer systems independent of the 
solvent nature. The basic set of hydrodynamic values s0, ks, [.], and D0, is the initial matrix of the 
experimental data, which can be transformed into the matrix of molar masses and hydrodynamic 
invariants (A0 and ßs). The hydrodynamic invariant (A0) and sedimentation parameter (ßs) fulfill 
an important function:[37, 47-48] a low fluctuation of the A0 and ßs values around their averages 
allows to state that appropriate correlations are observed between the hydrodynamic 
characteristics obtained in independent experiments and that the experimental values obtained 
are themselves appropriate, which allows further interpretation of these data. The comparison of 
the hydrodynamic characteristics with each other and with the molar mass allows to obtain cross 
(among hydrodynamic characteristics) and canonic (among hydrodynamic characteristics and 
molar mass) Kuhn-Mark-Houwink-Sakurada (KMHS) relationships (Figure 2.2). In general, 
they may be given as follows: 

 

....=................ (2.5) 

 

where Pi is one of the hydrodynamic characteristics [.], D0, s0, and ks, and Pj is another 
hydrodynamic characteristic from this row or molar mass. The values of the scaling indexes 
allow first statements on the macromolecule’s conformation. It is important to know that in a 


Figure 2.tif
very large range of molar mass values the scaling indexes may change passing from the region of 
low molar mass to the region of very high molar mass.[49-50] 

 

Figure 2.2. Scaling (Kuhn-Mark-Houwink-Sakurada) plots for polystyrene in methylethylketone. 
The double logarithmic plots show intrinsic viscosity [.] (curve 1; bij = 0.57, Kij = 0.041), 
sedimentation coefficient s0 (curve 2; bij = 0.483, Kij = 2.78×10-15), frictional ratio (f/fsph)0 
(curve 3; bij = 0.185, Kij = 2.63×10-5), and diffusion coefficient D0 (curve 4 bij = –0.519, 
Kij = 2.65×10-4) versus molar mass. 

 

 Further interpretation of the hydrodynamic data is related to the determination of gross 
conformational parameters, such as the persistence length (a) or the statistical segment length 
(A = 2a) and the hydrodynamic diameter of the chain (d). There are several approaches to 
analyze hydrodynamic data taking into account the intrachain draining effect[43, 51-55] as well as 
intrachain excluded volume effects[56-58] for different types of polymer molecules. An example 
of the determination of the length of the Kuhn segment and the hydrodynamic diameter of the 
polymer chain, in the framework of the Gray-Bloomfield-Hearst theory (Eq. 2.6), is shown in 
Figure 2.3 for the homologous series of polystyrene macromolecules in methylethylketone 
(MEK). 

 

[..]........=..[..]......=........+........-....(..-..)(..-..)....-....+......../....×..........
-..........-..-..(..).. (2.6) 

 


Picture1.tif
The first term of Eq. 2.6 describes the non-draining limit chain behavior, and the second one is 
related to intramolecular draining effects. It is a more complete theory up to now describing the 
translational friction of linear macromolecules. 

 

 

Figure 2.3. Statistical segment (Kuhn segment) length A and hydrodynamic diameter d from 
hydrodynamic measurements on polystyrene samples in methylethylketone. 

 

 The investigations of colloidal systems by hydrodynamic methods becomes more facile 
due to the fact that compact (spherical) particles do not show any concentration dependences of 
sedimentation and diffusion coefficients. The intrinsic viscosity in this case is not far from the 
value defined by the Einstein equation and equal 2.5×. (where . is the partial specific volume). 
The characteristics of colloidal systems obtained are the particle size distribution, the average 
particle size, the polydispersity and the surface charge density. Nevertheless, the combination of 
several characterization methods is highly advantageous. The standard techniques used for the 
analysis of nanoparticles are dynamic light scattering, various types of microscopy as well as 
sedimentation velocity analysis. Microscopy gives detailed shape and morphological 
information, but due to the effects of drying and contrasting involved the particle properties can 
be different from those in the solution. DLS is a fast and relatively simple method to obtain 
important information about the size and polydispersity of the nanoparticles in solution. The 
main disadvantage of DLS is that the scattering intensity of spherical particles is proportional to 
the sixth power of the diameter or the square of the molar mass: I ~ d6 ~ M2. Thus a small amount 
of aggregates or larger particles can dominate the distribution. The resolution of AUC is 
significantly higher and less model dependent than in DLS. Measurements of a particle size 
distribution by AUC are based on the exact determination of the sedimentation coefficient 


distribution of mono- and polydisperse samples. The corresponding transformation of the s-
values into d (or the molar mass) can be done using the Svedberg and Stokes equations: 

 

..=..v....[..]..=......../........ (2.7) 

 

However, a number of problems are involved when colloids are investigated by AUC. Colloidal 
dispersions may exhibit a very broad sedimentation coefficient distribution, and small 
concentrations of large aggregates or impurities cannot be detected. Colloids can aggregate 
during the sedimentation process. Moreover, the solute particles usually carry an electrical 
charge, which often leads to non-ideal sedimentation behavior. Another common obstacle of 
AUC is that the partial specific volume (reciprocal density) of the particles is not known. To 
overcome the problem, a density variation method was developed.27,28 The method applies 
sedimentation velocity experiments of the sample performed in at least two solvents with 
different densities.[59-60] Comparing the sedimentation coefficients in the different solvents gives 
the density of the nanoparticle. 
Different methods for characterizing nanoparticle suspensions lead to different size 
distributions: Scanning force microscopy (SFM) investigations yield number average 
distributions; from velocity sedimentation, a weight average distribution can be obtained, while 
DLS usually yields z-average size distributions. To obtain an adequate correlation, the average 
values calculated from the different kinds of distributions must be used. In Figure 2.4A, a 
comparison of the nanoparticle’s weight average sizes obtained by different techniques is 
presented. 

 

Figure 2.4. (A) Comparison of weight average sizes of nanoparticles obtained by different 
techniques. The slope of the dashed line is equal to the measurement parity. (B) Correlation 
between the PDI values (dw/dn) calculated from AUC, DLS, and SEM data, and the weight-
average sizes estimated from AUC. 


A satisfactory correlation between the measurements by the different methods can be observed. 
However, at large particle sizes (> 400 nm) the deviation between the different methods is 
increased.The heterogeneity of an ensemble of nanoparticles can be characterized by the ratio of 
the different size average values (dw/dn). For a spherical particle, it is related in a simple way to 
the molar mass distribution ((dw/dn)3~Mw/Mn). Figure 2.4B demonstrates the slight increase of 
the dw/dn values with increasing diameter of the particles. 

 In summary, the algorithms of extracting molecular information on the conformation and 
properties of linear macromolecules in solution from their hydrodynamic characteristics have 
been considered. The analysis of colloidal systems was discussed using, as an example, 
polymeric nanoparticles of different size distributions. The accuracy of the determination of the 
molecular and conformational characteristics increases by a simultaneous study and comparison 
of the data obtained by different hydrodynamic methods. From sedimentation and diffusion data, 
parameters like hydrodynamic radius, molar mass, density, particle shape and shapes of the size 
distributions are available. Viscosimetric data are indispensable for a full discussion of the 
conformation of polymer chains. The influence of the intrachain excluded volume and of 
draining effects on important conformational characteristics of the macromolecules, like the 
statistical segment length or the hydrodynamic diameter of the polymer chains, was discussed. 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


3. Comprehensive Application of Velocity Sedimentation: Critical Aspects 

 

Parts of this chapter have been published in: A1) G. M. Pavlov, I. Perevyazko, U. S. Schubert, Macromol. Chem. 
Phys. 2010, 211, 1298-1310; A2) G. M. Pavlov, I. Y. Perevyazko, O. V. Okatova, U. S. Schubert, Methods 2011, 
54, 124-135. A6) I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Hoeppener, S. Schubert, D. Fischer, U. S. Schubert, 
Langmuir 2012, 28, 16167-16176. 

 

 Sedimentation velocity analysis using an analytical ultracentrifuge is a classical 
characterization technique to study various colloidal, protein as well as polymer systems due to 
its high statistical capability and versatility. Performing a quantitative analysis of the 
experimental data means determining the sedimentation coefficient, diffusion coefficient and 
partial specific volume. The fundamental equation which describes the sedimentation profiles of 
monodisperse species, with sedimentation and diffusion coefficient, is the Lamm equation:[61] 

 

........=....
....................-.............. (3.1) 

 

In an ideal case of hard, globular and non-diffusing objects, a sedimentation velocity experiment 
leads to information about the size and molar mass of species investigated. In other cases, the 
sedimentation coefficient alone reports only indirectly on the species’ molar mass. To overcome 
this problem, a number of data analysis programs for the treatment of sedimentation data have 
been developed.[40-42] One of the most widely used analysis methods is Sedfit, which is based on 
the numerical solutions of the Lamm equation (Eq. 3.1).[40] It is intended to study globular 
protein systems and scales the diffusion coefficient to the sedimentation coefficient consistent 
with the s ~ D-2 power law. In the following discussion, limitations and critical aspects of the 
analysis of the sedimentation velocity data, in particular of flexible and semi rigid polymer 
chains, by modern analytical software will be considered. 
For the purpose described, the classical system of polystyrene (PS) was chosen in a 
thermodynamically marginal solvent (methylethylketone) and a good solvent (toluene). In 
addition, samples of sodium alginate macromolecules were investigated in water at different 
ionic strengths. The molar masses were calculated by the Svedberg equation using the frictional 
ratio and the sedimentation coefficient determined by c(s) analysis implemented into Sedfit. The 
analysis of the obtained hydrodynamic characteristics shows that, for PS in MEK extrapolated to 
zero concentration, f/fsph values lead to an adequate characterization of the macromolecules 
(Table 3.1). Nevertheless, in the case of the frictional ratio, a strong concentration dependence 
((f/fsph)0 = f/fsph(1+kfc)) is observed, in particular for the high molar mass samples. Such a 
behavior cannot be explained within the limits of the usual dependence of kf = ks–2A2M, where 
A2 is the second virial coefficient. This problem was highlighted by studying PS standards in a 


thermodynamically good solvent (toluene), where the polymer coils, as compared to MEK, 
occupy a larger volume due to the increased interaction with solvent molecules. The measured 
values of the sedimentation and Gralen coefficients (ks) are in satisfactory agreement with the 
known literature data. However, it was not possible to obtain reasonable extrapolated values of 
the frictional ratio and, as a consequence, to determine the molar mass. 

 

 Table 3.1 Hydrodynamic parameters for polystyrene in MEK and toluene (*) at 20 oC. 

Mw×10-3 

g mol-1 

Msf×10-3 

g mol-1 

[s] 

ks 

f/f0 

kf 

Msf×10-3 

g mol-1* 

[s]* 

ks* 

f/f0* 

kf* 

1,760a 

1,760 

51.7 

260 

3.45 

3,450 

3,300 

37.1 

600 

7.30 

1,740 

564a 

710 

29.6 

100 

3.30 

870 

440 

22.6 

247 

3.15 

3,500 

133a 

194 

15.8 

45 

2.60 

135 

72.8 

12.7 

95 

1.69 

840 

17a 

19 

5.40 

8 

1.63 

19 

15.8 

4.70 

26 

1.64 

36 

3a 

4 

2.65 

11 

1.16 

16 

3.7 

2.50 

11 

1.00 

11 



 a Data provided by the supplier. 

 

In case of macromolecules with high equilibrium rigidity (sodium alginate molecules), 
the inability of Sedfit to adequately determinate the frictional ratio becomes more pronounced. 
The sodium alginate samples of different composition (namely LVG, MVG with 
G/M = 2.2 ± 0.1 and LVM, MVM with G/M = 0.8 ± 0.1, where G is glucuronic acid and M is 
mannuronic acid) were studied in 0.2 M NaCl (in water). The hydrodynamic characteristics 
extrapolated to zero concentration are presented in Table 3.2. In spite of the high linearity of the 
concentration dependence of f/fsph, the extrapolated values were below 1, which has no physical 
meaning. Nonetheless, the molar mass can be estimated by coupling the determined values of s0 
and [.], or s0 and ks using the following equations: 

 

......=................([..]..×[..])...... (3.2) 

........=..................([..]..×....)...... (3.3) 

 

where A0 and ßs are the hydrodynamic invariant and the sedimentation parameter. On the one 
hand, a good correlation is found between Ms. and Msks; on the other, it is clear that Sedfit does 
not provide the appropriate extrapolated value of the frictional ratio. Apparently, this is 
connected with the general scaling law for globular particles used in Sedfit: Such a model does 


not take into account excluded volume interactions or any non-ideality of the solution. The 
deviation from the behavior of globular particles increases in the following manner: Flexible 
macromolecules in .-conditions, flexible macromolecules in thermodynamically good solvents, 
and, at last, rigid macromolecules. 

 

Table 3.2. Hydrodynamic characteristics of sodium alginate molecules in aqueous 0.2 M NaCl. 

sample 

s 

S 

ks 

cm3 g-1 

(f/fsph)0 

kf 

cm3 g-1 


[.] 

cm3 g-1 

Ms,[.] 
g mol-1 

Ms,ks 
g mol-1 

LVG 

3.9 

1,040 

0.45 

37,300 

700 

210,000 

240,000 

MVG 

3.8 

740 

0.41 

46,500 

840 

270,000 

290,000 

LVM 

3.6 

1,200 

0.79 

21,000 

620 

155,000 

160,000 

MVM 

3.8 

750 

0.73 

35,000 

1,060 

280,000 

300,000 



 

To investigate the potentials and limitations of AUC for highly heterogeneous systems, 
mixtures of polystyrene standards of different modality (with two, three and five components) 
were investigated. The mass concentration of each component in the mixture was kept the same. 
As a first example, two component PS mixtures (mixture of Mw = 564,000 g mol-1 and 
Mw = 248,000 g mol-1 standards (A) and mixture of Mw = 564,000 g mol-1 and 
Mw = 17,000 g mol-1 standards (B)) will be considered. In Figure 3.1, the distributions of the 
sedimentation coefficients are compared. 

 

 

Figure 3.1. Distributions of the sedimentation coefficients and corresponding superposition of 
sedimentation profiles: (A) Mixture of Mw = 564,000 g mol-1 and Mw = 248,000 g mol-1 PS 
standards, (B) Mixture of Mw = 564,000 g mol-1 and Mw = 17,000 g mol-1 PS standards. 


The data treatment was made by c(s) analysis, assuming the same average frictional ratio 
for all components in the solution. The sedimentation coefficients of the species in the mixture 
are in satisfactory agreement with those obtained from the investigations of individual samples. 
Nevertheless, the approximation of the weight average frictional ratio does not lead to the correct 
molar mass values. However, in the case of two clearly separated regions in the sedimentation 
coefficient distribution it is usually possible to optimize two separate values of the frictional 
ratios. In such a case, c(s) distribution analysis with bimodal frictional ratio must be used. The 
obtained values of the frictional ratios show a very good correlation with the results obtained for 
individual samples. 

The analysis of the data becomes more complicated with increasing heterogeneity of the 
samples. As a further example two five-component mixtures of PS standards, corresponding to 
high (ranging from 1,760×103 g mol-1 to 194×103 g mol-1) and low (ranging from 95×103 to 
1.8×103 g mol-1) molar mass regions, were investigated by AUC. 

 

 

Figure 3.2. Characterization of five-component PS mixtures by analytical ultracentrifugation. 
Top – Superposition of sedimentation profiles (at highest concentration). Bottom – 
Corresponding differential distribution of the sedimentation coefficients. (A) Mixture of high 
molar mass and (B) low molar mass PS standards. Arrows indicate the sedimentation 
coefficients at zero concentration, obtained from experiments on a single component. 

 

Analysis of the experimental data shows that the mixture containing high molar mass 
constituents (Figure 3.2A) can be adequately characterized: (1) The mixture studied consists of 


five components with sedimentation coefficients that correspond well to the values obtained for 
the individual samples. (2) At low concentrations, the areas under the peak practically coincide, 
which testifies the uniform composition of the mixture. (3) For a component with high molar 
mass, stronger concentration dependence is observed. While for the low molar mass mixture 
(Figure 3.2B) the redistribution of the components and a shift of the sedimentation coefficients 
towards lower values were observed. Moreover, since c(s) analysis only yields average frictional 
coefficients of all species, it is not possible to determine the molar mass of the individual species 
suspended in the solution. To overcome this problem, model-independent two-dimensional size 
and shape distribution analysis (c(s,ff0)) can be used.[62] However, the estimated frictional ratios 
by c(s, ff0) of individual species in the mixture result in inadequate values of the molar mass. 
Obviously, this can be explained by the fact that for highly heterogeneous solutions the 
contribution of the diffusion from the components of different molar masses cannot be resolved 
properly. This effect becomes more pronounced for the low molar mass systems, which, in turn, 
may distort the distribution of sedimentation coefficients. 

The above arguments were further confirmed by the study of the complex formation of 
plasmid DNA (pGL3) with linear poly(ethylene imine) (PEI). The characterization of the DNA 
sample shows the presence of different DNA isoforms (linear, open circle, supercoiled DNA). 
The analysis of sedimentation data by various methods (c(s), c(s,ff0) and ls-g*(s)) results in 
identical distributions of sedimentation coefficients (Figure 3.3A top), whereas, the average 
frictional radio obtained by c(s) analysis leads to an underestimation of the molar mass 
(Msf = 2.1×106 g mol-1). At the same time, due to the very low diffusion rate of high molar mass 
DNA molecules, c(s,ff0) analysis leads to a correct value for the frictional ratio and, as a 
consequence, to a correct molar mass (Msf = (3.0 ± 0.2)×106 g mol-1). Furthermore, in 
Figure 3.3B the comparison of frictional ratios obtained by c(s) and c(s,ff0) for the DNA/PEI 
complexes at different N/P ratios (nitrogen (PEI) to phosphate (DNA) ratio) is presented. At 
relatively low N/P ratios, the polyplex solution consists of differently complexed DNA 
molecules, already formed primary polyplexes as well as their agglomerates. If c(s) analysis is 
applied for such a highly heterogeneous system, the obtained values of the average frictional 
ratio are underestimated, as shown in Figure 3.3B. With increasing N/P ratio, the total 
heterogeneity of the sample decreases since a higher amount of DNA molecules becomes fully 
complexed by PEI. At N/P ˜ 2.5, complex formation is generally completed and the solution 
mainly contains polyplexes of different sizes. As a consequence, c(s) and c(s,ff0) lead to the 
same frictional ratios (f/fsph ˜ 1). 

 


 

Figure 3.3. (A) Sedimentation velocity analysis of pGl3 DNA in water/0.05 M NaCl: 
Top – Comparison of sedimentation coefficient distributions obtained by various methods (c(s), 
c(s,ff0) and ls-g*(s)), bottom – concentration dependences of the frictional ratio, obtained by c(s) 
and c(s,ff0) methods. (B) Frictional ratio corresponding to the polyplex solutions at different 
N/P ratios; data obtained by c(s) and c(s,ff0) methods, respectively. 

 

In summary, velocity sedimentation experiments evaluated with the Sedfit software can 
be considered as a self-sufficient method for the determination of molecular characteristics of 
flexible linear polymers with narrow size distribution. Nevertheless, in the case of flexible 
macromolecules in thermodynamically good solvents as well as for molecules with high 
equilibrium rigidity the evaluation of macromolecular characteristics is complicated. In this case, 
independent measurements of the translation diffusion are required. Highly heterogeneous 
systems can be well resolved only in the case of low total diffusivity of the solution. 


4. Hydrodynamic Characterization of Charged Macromolecular Systems 

 

Parts of this chapter have been published in: A4) T. Erdmenger, I. Perevyazko, J. Vitz, G. Pavlov, U. S. Schubert, J. 
Mater. Chem. 2010, 20, 3583-3585. A5) B. Happ, G. M. Pavlov, I. Perevyazko, M. D. Hager, A. Winter, U. S. 
Schubert, Macromol. Chem. Phys. 2012, 213, 1339-1348. 

 

Polyelectrolytes play a decisive role in nature and have many applications in modern 
technology. Polyelectrolytes are represented by chains with variable equilibrium rigidity 
regulated by linear charge density, ionic strength of surrounding medium, and the structure of the 
polymer.[63-66] In the following chapter the investigation of specific types of polyelectrolyte 
molecules namely poly(ionenes) and metallo-supramolecular complexes will be discussed. 

Polyionenes, or ionenes, are ion-containing polymers that contain quaternary nitrogen 
atoms in the macromolecular main chain.[67-68] Due to the large variety of ditertiary amins and 
dihalides, a wide range of ionenes can be synthesized.[69-70] Ionenes are known to possess 
excellent mechanical properties and offer many potentional applications in emerging biomedical 
fields, like DNA delivery or antimicrobial applications.[71] Recently, imidazolium ionenes were 
utilized as quasy-solid electrolytes for solar cells[72] and as a solid support for peptide 
synthesis[73] as well as for a humidity sensors.[74] In this chapter, 4,4-imidazolium ionenes 
(poly(ionenes)) of different molar masses and with bromide counter ions, synthesized under 
microwave irradiation and conventional heating in an oil bath, were investigated by the methods 
of molecular hydrodynamics. As a first step to study the solution properties of the ionenes, 
viscosity measurements were carried out at different ionic strength in water and methanol 
(Figure 4.1A). The intrinsic viscosities were determined by applying Huggins extrapolation 
procedure (.sp/c = [.]+k[.]2c+…, where .sp is the specific viscosity and c is the concentration). 
At low polyelectrolyte concentrations, .sp/c increases as a result of the polyelectrolyte effect 
(Figure 4.1A). This effect is caused by the fact that the volume, in which the counter ions are 
spread, increases with dilution, thus reducing the screening of the charges fixed on the chain and 
strengthening their mutual repulsion. As a result, the size of the poly(ionene) increases. In this 
connection, further experiments were carried out in 0.5 M NaBr to suppress the polyelectrolyte 
effect. As expected, the intrinsic viscosity of the ionenes increases for the higher molar mass 
samples, but these changes were not in the same order of magnitude as obtained molar masses 
from 1H NMR spectroscopy (Table 4.1). Therefore, in addition, the molecular properties of 
poly(ionenes) were studied by analytical ultracentrifugation. In Figure 4.1B the distributions of 
the sedimentation coefficients of different samples of ionenes are compared. 

 

 

 


Table 4.1. Hydrodynamic parameters of 4,4-imidazolium ionenes in 0.5 M NaCl/methanol. 

sample 

s0 

S 

(f/fsph)0 

MNMR 

g mol-1 

Msf 

g mol-1 

% of 
linear 
chains 

[.] 

cm3 g-1 

ßs×10-7 

mol-1/3 

A0×1010 

ks±.k 

cm3 g-1 

B2* 

1.60 

1.49 

44,000 

3,100 

7.0 

11.1 

2.0 

3.8 

40 

B4 

1.46 

1.32 

22,000 

2,500 

11.4 

10.2 

2.1 

3.9 

40 

B6 

1.39 

1.41 

18,000 

2,100 

11.7 

12.7 

1.9 

4.3 

30 

B8 

1.25 

1.33 

13,000 

1,800 

13.8 

9.9 

2.0 

4.1 

30 

B10 

1.39 

1.30 

11,000 

2,000 

18.2 

6.5 

2.2 

3.6 

40 



* The numerical index corresponds to the mol % of benzyl bromide utilized as chain stopper. 

 

For all samples investigated, the distribution consists of a main peak (~90% of total mass) and a 
smaller peak shifted towards lower sedimentation coefficients. The molar masses were calculated 
according to the Svedberg equation (Eq. 2.1), using average values of the sedimentation 
coefficient and frictional ratio extrapolated to zero concentration. The intercorrelation between 
the obtained experimental hydrodynamic values (s0, (f/fsph)0 and [.]) was analyzed by calculating 
the values of the hydrodynamic invariant and sedimentation parameter (Table 4.1). 

 

Figure 4.1. Solution properties of ionenes: (A) Determination of the intrinsic viscosity (Huggins 
extrapolation procedure) in water and methanol at different ionic strength. (B) Comparison of 
the distributions of sedimentation coefficients of different poly(ionenes) in 0.5 M NaBr/methanol. 

 

Significant differences in obtained molar masses between AUC and 1H NMR spectroscopy were 
found. This difference may result from the formation and presence of both linear and ring 
molecules of the same molar mass in solution, which would reduce the number of free end 
groups and, therefore, lead to an overestimation of the MNMR values. In fact, the presence of 


species with relatively low and relatively high sedimentation coefficients (Figure 4.1B) can be 
related to different frictional properties of linear and ring molecules of the same molar mass. The 
hypothesis concerning the presence of linear and ring molecules in solution can be further 
supported by the determination of the mass per unit length ML of the poly(ionene) chains using 
the model of a weakly bending rod (Figure 4.2A):[51] 

 

[..]=(..../........)(......-..........+...........) (4.1) 

 

In addition, the statistical length of the Kuhn segment can be calculated in the frame of the Gray-
Bloomfield-Hearst theory (Figure 4.2B), where d is the hydrodynamic diameter of the polymer 
chain and M is the average molar mass. The obtained ML value (4.5×10-9 g mol-1 cm) is twice the 
value calculated from the chemical structure (2.3×10-9 g mol-1 cm). The composition of the 
mixture of linear/ring chains in solution can simply be estimated by comparing MNMR and Msf: 
The part of the linear chain (x) will be x = Msf/MNMR and constitutes from 7% to 18% of the total 
mass (the content of linear chains increases with the amount of benzyl bromide). 

 

 

Figure 4.2. (A) Evaluation of the mass per unit length (ML) and the hydrodynamic diameter (d) 
of the polymer chain, in the frame of a weakly bending rod model. (B) Estimation of the Kuhn 
segment length. 

 

Self-assembly of supramolecular polymers induced by transition metal ions result in the 
formation of metallo-supramolecular polyelectrolyte complexes. The positive charge of such 
complexes can be utilized in several ways to produce highly ordered structures for a variety of 
applications. Following this idea, poly(alkyl methacrylate) copolymers embedding 10% 
(sample P10) and 20% (samples P20a and P20b) bidentate 2-(1,2,3-triazol-4-yl) pyridine (trzpy) 


chelating units as comonomer in the side chains synthesized by controlled radical addition-
fragmentation chain transfer polymerization (RAFT) were treated with Fe2+, Co2+ and Eu3+ metal 
salts. The initial polymer solutions were characterized by sedimentation velocity and intrinsic 
viscosity measurements. The molar masses were calculated according to the Svedberg equation, 
using extrapolated values of the sedimentation coefficient and frictional ratio (Table 4.2). 

 

 Table 4.2. Characterization data of the investigated copolymers. 

sample 

chemical 
structure 

Ligand/
MMA 

[.] 

cm3 g-1 

s0 
S 

ks 

cm3 g-1 


f/f0 

Msf 
g mol-1 

P10 

 

10/90 

8.5±0.2 

6.9 

20 

1.43 

27,600 

P20a 

20/80 

8.8±0.1 

7.5 

5 

1.35 

32,000 

P20b 

20/80 

7.8±0.5 

5.7 

11 

1.69 

29,600 



 

 

 

 

 

 

In order to study the crosslinking process (Scheme 4.1.) caused by metal complexation, viscosity 
titration measurements were applied. The metal salts were dissolved in acetone and added 
stepwise to the polymer solution. 

 

 

Scheme 4.1. Schematic representation of the complexation of the copolymers with Fe2+ and Co2+ 
ions. 

 

Figure 4.3A shows the effect of the addition of Co2+ salt on the dynamic viscosities of P10 
copolymer. The magnitude of the dynamic viscosity at a certain salt concentration strongly 
depends on the polymer concentration. At relatively high dilution (c[.] = 0.25), only a slight 
increase in solution viscosity was observed. For higher solute concentrations (c[.] = 0.5), the 
viscosity increases exponentially upon the addition of Co2+ salts, indicating the formation of 
crosslinked structures (intermolecular complexation). Moreover, the increased ligand content in 
the macromolecular main chain (samples P20a and P20b) resulted in a considerable increase in 


the dynamic viscosity (Figure 4.3B). The addition of Fe2+ ions to the P20b polymer solution 
resulted in a similar behavior of the dynamic viscosity (Figure 4.3B), whereas titration with Eu3+ 
ions resulted in a minor viscosity increase only (Figure 4.3B). 

 

 

Figure 4.3. (A) The dynamic viscosity of the P10 copolymer as a function of Co2+ concentration 
at different degrees of dilution. (B) A comparison of the dynamic viscosities of copolymers 
containing 10% (P10) and 20% (P10a, P10b) of the ligand in the side chain after addition of 
different metal salts. 

 

The average molar mass of a crosslinked structure, at high concentration, can be estimated from 
the dynamic viscosity value using the following scaling relation: . = KhM3.4, where K is a 
constant depending on the nature of the system.[75] Based on the estimated values of the molar 
mass, the number of individual molecules forming one crosslinked unit (N) can be calculated. It 
turns out that, on the average, the unit consists of five molecules, this number slightly increasing 
with higher ligand content (Table 4.3). 

 

 Table 4.3. Characterization of crosslinked structures. 

Sample 

Ion 

.*, cP 

Mw, g mol-1 

.** 

P10 

Co2+ 

14.1 

150,000 

5 

P20a 

Co2+ 

121 

250,000 

8 

P20b 

Fe2+ 

311 

350,000 

11 

P20c 

Eu3+ 

2.2 

39,000 

1 



 * The maximum observed value. ** The number of individual molecules in 
the crosslinked unit. 

 

In the case of Eu3+ ions, the determined molar mass is close to the value of the initial polymer, 
indicating the absence of crosslinked structures. The slight increase of the viscosity at high salt 


concentration may be caused by an induced polyelectrolyte effect due to absorption of some 
metal ions on the polymer chain, followed by an expansion due to electrostatic repulsion. 
The intramolecular complexation caused by the salt addition was studied with highly 
diluted polymer solutions (c[.] ˜ 0.006) by sedimentation velocity experiments. In Figure 4.4A 
the dependence of the intrinsic sedimentation coefficient on the molar salt concentration is 
presented. Two regions can be distinguished. The first region is characterized by a significant 
decrease in the sedimentation coefficient. This can be explained by an increased proportion of 
metal ions in the polymeric chain, which leads to an electrostatic expansion of the chains and 
increased electrostatic interactions between distant macromolecules; both effects lead to an 
increase in the translational friction coefficient. This argument was further supported by the 
addition of the one-to-one ion salt NH4 PF6 to the cobalt-containing solution (P10): In this case a 
decrease in the velocity sedimentation coefficient did not occur, which means that the induced 
polyelectrolyte effect was suppressed (Figure 4.4B). In the second region, after reaching a 
minimum at csalt ˜ 0.2 × 10–3 M the value of [s] begins to increase with increasing salt 
concentration. Presumably, in this case the main effect is the screening of charges on the 
polymer chains due to the increase in ionic strength, which probably can be reached by the 
addition of any other one-to-one ion salt. For all studied systems, the intrinsic sedimentation 
coefficient increases to its maximum value of ˜ 9.5 and does not change significantly at higher 
salt concentrations. 

 

 

Figure 4.4. (A) Dependence of the intrinsic sedimentation coefficient on salt concentration for 
copolymer solutions at c = 0.0007 g·cm-3. (B) Dependence of the intrinsic sedimentation 
coefficient for P10 on the Co2+ concentration, with and without addition of NH4 PF6. 

 

 


To conclude, in the first part 4,4-imidazolium ionenes synthesized by microwave 
irradiation were characterized by the methods of molecular hydrodynamics. The results allowed 
to determine the conformational parameters of the polymer, such as mass per unit length (ML), 
hydrodynamic diameter (d) and the Kuhn segment length (A). They further showed that both 
linear and ring chain molecules are present in the solution. 

The induced charge effect following complexation of Co2+, Fe2+ and Eu3+ to the 
macromolecular main chain was studied by velocity sedimentation and viscosity measurements. 
The differentiation between intermolecular and intramolecular complexation, respectively, was 
achieved by viscosity titration experiments at different concentrations of the copolymer. The 
metal ion-induced self-assembly results in the elongation of the individual polymer coils due to 
electrostatic repulsion of the coordinated metal ions. Based on the obtained data, the amount of 
the copolymer molecules forming a crosslinked unit was calculated. 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


5. Polyplexes – Polyelectrolyte Complexes of DNA and Poly(ethylene imine) 

 

Parts of this chapter have been published in: A6) I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Hoeppener, S. 
Schubert, D. Fischer, U. S. Schubert, Langmuir 2012, 28, 16167-16176. 

 

Gene therapy can be defined as the treatment of a disease by the transfer of genetic 
material into specific cells. However, in most cases the administration of naked DNA results in 
insufficient amounts of genes reaching the nucleus.[76] To improve the delivery of DNA into the 
cell, the DNA must be protected from damage, in particular against degradation by nucleases, 
and its entry into the cell must be facilitated. Numerous efforts have been made to solve the 
problem of DNA protection and internalization by developing different delivery vehicles; the 
latter include viruses and non-viral systems based on lipidic or polymeric formulations.[77-81] 
Polyplexes, i.e. complexes of DNA and polycations, represent perspective non-viral delivery 
system with promising results both in vitro and in vivo.[82-84] The physicochemical characteristics 
of polyplexes, in particular their solubility, dimensions, and surface charge, can be varied by 
altering the composition of the complex and the chemical structure of its constituents. Among 
the numerous different polycationic agents used for the manufacturing of the polyplexes, 
poly(ethylene imine) (PEI) is considered as one of the most efficient synthetic vectors.[85-87] The 
formation of DNA/PEI complexes results from cooperative binding of the negatively charged 
DNA phosphate groups and the protonated nitrogen atoms of PEI (Figure 5.1). 

 

 

Figure 5.1. Schematic representation of the DNA/PEI complexation and the transfer of the 
complex into the cell. 

 

The properties of the resultant DNA/PEI polyplexes (average size and size-distribution, 
surface charge) as well as the molecular characteristics (chemical structure, molar mass etc.) of 
the initial components are important for an effective gene delivery.[88-95] The current study was 
designed to investigate the complexation behavior of plasmid DNA (pGL3, 4818 base pairs) and 


low molar mass linear PEI (LPEI). The thorough investigation of DNA/PEI complexation 
requires, first of all, the detailed characterization of its initial components. The DNA and PEI 
were investigated by analytical ultracentrifugation and intrinsic viscosity measurements. The 
molar masses were calculated according to the Svedberg equation (Eq. 2.1) and constitute 
Msf = 3.0×106 g mol-1 and Msf = 13.4×103 g mol-1 for the DNA and PEI molecules, respectively. 
The evolution of the DNA complexation upon the addition of different amounts of PEI 
molecules was monitored by sedimentation velocity, gel electrophoresis, light scattering and 
scanning force microscopy. In Figure 5.2A, the distributions of the sedimentation coefficients at 
different N/P ratios are presented. The addition of a small amount of PEI to the DNA solution 
(N/P < 1) resulted in a shift of the sedimentation coefficients to higher values, accompanied by a 
broadening of the distributions. The average sedimentation coefficient increased from ˜ 20 S for 
the free DNA to ˜ 160 S at N/P 0.96. 

 

 

Figure 5.2 (A) Comparison of the sedimentation coefficient distributions of polyplex dispersions 
at different N/P ratios. (B) Dependence of the weight average sedimentation coefficients of the 
polyplexes as a function on the N/P ratio. Both plots are presented in semi-logarithmic scale. 

 

The increase of the apparent sedimentation coefficient indicates the partial condensation 
of the DNA chains due to the compensation of the electrostatic charges on the DNA. Another 
reason could be the increasing size of the complex due to hydrophobic interactions of the 
complexed sites. In addition, analysis of the distributions at N/P = 1 showed the existence of 
several species, which might be attributed to free or not fully complexed DNA (with an average 
sedimentation coefficient of 24.0 ± 0.5 S) and already formed primary polyplexes containing 
only a small number of DNA molecules (sedimentation coefficient 220 ± 80 S). Further addition 
of PEI to the DNA solution (1 = N/P = 4) leads to the merging of the initially formed polyplexes 
and the formation of complexes of much larger size. This aggregation process may be due to 


Picture6.tif
interactions of accessible unbound DNA chains in one polyplex with the unbound PEI in another 
primary polyplex. On the other hand, at relatively low N/P ratios initially formed polyplexes tend 
to agglomerate due to the nearly neutral surface charge of the polyplexes. Accordingly, the 
average sedimentation coefficient was increased to maximum values of ˜ 300,000 S at N/P 2.06 
(Figure 5.2B). A further increase of the PEI content resulted in a decreasing average 
sedimentation coefficient, indicating the formation of complexes with a lower aggregation level. 
The DNA condensation by PEI, followed by complex formation, will result in changes in the 
frictional properties of the complex. The asymmetry of the complex formed can be evaluated 
from the fitted value of the frictional ratio. At a value of 1, the frictional coefficient of the solute 
macromolecule would correspond to that of a rigid sphere; the higher the value of f/fsph, the 
higher is the asymmetry of the polyplexes investigated. Analogous to the behavior of the 
sedimentation coefficient, the tendency of decreasing f/fsph with increasing N/P ratio indicates a 
DNA condensation and the formation of more compact and uniform DNA/PEI complexes 
(Figure 5.3 A). 

 

 

Figure 5.3. Double logarithmic plot of the dependence of the average frictional ratio (f/fsph) 
(A) and the average hydrodynamic diameter (B) on the initial N/P ratio. The data point on the 
Y–axis corresponds to N/P = 0 (free DNA). 

 

In the experiments described, the value of f/fsph = 1 was reached at N/P ˜ 2 and remained 
the same within the experimental error also for higher N/P ratios. Using the determined values of 
the sedimentation coefficient, the frictional ratio and the partial specific volume, the average 
hydrodynamic size of the polyplexes was calculated applying Eq. 2.7 (Figure 5.3B). At 


relatively low N/P ratios (= 1), the hydrodynamic size of the objects decreased as a result of the 
DNA condensation. The minimum value of ~29 nm was reached at N/P ˜ 0.5. The formation of 
large aggregates with sizes up to 1,000 nm occurs at N/P ˜ 2. A further increase of the PEI 
concentration in the polyplex dispersion results in a continuous decrease in particle size. At 
N/P = 10, polyplexes have an average size of about 170 ± 65 nm. 

To obtain information about the composition of the complexes, the amount of condensed 
DNA molecules in one polyplex as well as the number of PEI molecules bound to one DNA 
molecule needs to be known. Using a combination of sedimentation velocity experiments with a 
copper complex assay and preparative ultracentrifugation, the concentration of free PEI in the 
polyplex solution was determined at different N/P ratios. The amount of unbound PEI increased 
from 60.5% at N/P 6.2 to ~90.5% at N/P 57.8 (Figure 5.4A). 

 

 

Figure 5.4. (A) Experimentally determined concentration of unbound PEI in the polyplex 
dispersion in comparison to the initial PEI concentration at different N/P ratios. 
(B) Calculated concentration of bound PEI as a function of the N/P ratio. 

 

According to the fitted data, virtually all PEI is associated with DNA at N/P = 2.5. The 
concentration of the bound PEI in the dispersion can simply be calculated as the difference 
between the initial and the free PEI concentrations (Figure 5.4B). Two distinct regions are 
clearly visible. The first region corresponds to N/P ratios = 2.5 and can be attributed to the 
process of complex formation. The second region, with N/P = 6, describes the binding behavior 
of PEI to the already formed polyplexes. The continuous binding of PEI to DNA shows that the 
polyplexes are not uniformly complexed, and even at high N/P ratios some binding sites on the 
DNA molecules are still unoccupied. Based on the determined sedimentation coefficient and the 
fitted value of f/fsph, the molar mass of the polyplexes was calculated. The number of condensed 
DNA molecules in a single polyplex (N) can then be simply determined from the ratio of the 


polyplex molar mass to the molar mass of a single condensed DNA molecule with associated 
PEI molecules (Table 5.1). It is evident that the number of DNA molecules in one polyplex will 
be rather large. Apparently, this can be explained by the agglomeration of the initially formed 
polyplexes. According to images from scanning microscopy, the size of the single polyplex is 
50 ± 10 nm. Depending on the sample, the relative amount of polyplexes of such a size is 
between 3% and 12%, as estimated by AUC. In this case, the polyplex molecules will consist of 
8 to 33 condensed DNA molecules and 70 ± 25 PEI molecules. 

 

Table 5.1. Hydrodynamic characteristics and composition of the polyplexes at various N/P 
ratios 

N/P ratio 

Mpolyplex×10-9 
g mol-1* 

d 

nm* 

MDNA+PEI×10-6 
g mol-1 

. bound PEI 
molecules 

N 

dav 

 nm** 

2.5 

~630 

~1,000 

3.67 

50 

~170,000 

~1,000 

6.2 

13.0 

275 

3.67 

50 

3,540 

320 ± 50 

11.6 

1.90 

150 

3.72 

54 

510 

210 ± 60 

28.6 

0.74 

105 

4.18 

88 

180 

170 ± 65 

57.8 

0.57 

100 

4.41 

105 

130 

100 ± 5 



* The values corresponding to a single experiment at a specific N/P ratio. ** Average sizes from several 
experiments performed at the same N/P ratio. 

 

In addition to the physicochemical properties, the influence of varying polyplex N/P 
ratios on the biological activity was investigated by transfection efficiency and cytotoxity 
experiments. To protect the DNA against degradation and to enhance the transfection rate, high 
N/P ratios are required. Adequate transfection was obtained at N/P ratios = 10. The excess of 
unbound PEI probably enhanced the cellular polyplex uptake by a yet unspecified interaction 
between the cationic charged polymers and the negatively charged cell membrane.[96] In addition 
to an improved transfection rate, these interactions are also responsible for the cytotoxicity of 
cationic polymers, which could also be observed in our experiments. Compared to untreated 
cells, the total protein mass of 13.4×103 g mol-1 LPEI at N/P 25 was reduced, which is regarded 
as an indication for cytotoxicity caused by the high concentration of unbound PEI. 

 In summary, the DNA/PEI complexation was studied in detailed by various 
characterization techniques. The content of free PEI in the polyplex dispersion was determined 
over a wide range of N/P ratios. The results revealed differences in the binding behavior of PEI 
to DNA, corresponding to the different phases of complex formation. It was shown that the DNA 
is not completely condensed by the PEI, resulting in the availability of free negative charges of 
the DNA even at high N/P ratios. In addition, the number of the DNA molecules as well as those 
of the PEI molecules per single polyplex were calculated. 


 

 


6. Influence of Process and Formulation Parameters on the Formation of 
Polymeric Nanoparticles by the Solvent Displacement Method 

 

Parts of this chapter have been published in: A3) I. Perevyazko, A. Vollrath, S. Hornig, G. M. Pavlov, 
U. S. Schubert, J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 3924-3931; A7) I. Y. Perevyazko, J. T. Delaney, A. 
Vollrath, G. M Pavlov, S. Schubert, U. S. Schubert, Soft Matter 2011, 7, 5030-5035; A8) I. Y. Perevyazko, A. 
Vollrath, C. Pietsch, S. Schubert, G. M. Pavlov, U. S. Schubert, J. Polym. Sci., Part A: Polym. Chem. 2012, 50, 
2906-2913. 

 

Nanoparticles are defined as solid colloidal particles in the range of 10 to 1000 nm; the 
definition includes both nanospheres and nanocapsules. The development of functional 
nanoparticles is of major interest since it was found that the unique properties of such nanoscale 
materials allow breakthroughs in technology, bioengineering, life sciences, and many others. In 
particular, polymer-based nanoparticle dispersions offer tremendous opportunities for the 
formulation of biologically active materials, such as drugs[97-98] and transfection agents.[99] 
Polymers provide unique structural diversity and functionality to be used in the preparation of 
functional nanoparticles, such as poly(lactide-co-glycolide),[100] poly(e-caprolactone),[101] 
poly(acrylics), poly(styrene), poly(methyl methacrylate) (PMMA), and its different copolymers 
as well as various amphiphilic block copolymers.[102-104] Polymeric nanoparticles can be prepared 
applying a variety of techniques, like emulsification-solvent diffusion, salting out and 
nanoprecipitation (solvent shifting).[105] Among these preparation techniques, nanoprecipitation 
represents a very simple, convenient and mild method for the production of polymeric 
nanoparticles. The particle formation occurring by self-assembly of polymer molecules during an 
exchange of a solvent against a non-solvent that is miscible with the solvent (Figure 6.1A).[106] 

The process and mechanism of the nanoparticle formation was intensively investigated in 
the last decades.[107-109] The formation of nanoparticles via nanoprecipitation complies with the 
nucleation theory and consists of several steps like particle nucleation, molecular growing, and 
aggregation.[108-109] Stable nanoparticle suspensions are only formed under conditions which 
promote a supersaturation of polymer molecules in a ternary polymer/solvent/non-solvent system 
and a shifting into a metastable region – the Ouzo region.[104, 109-111] This region is located 
between the binodal (miscibility limit curve) and spinodal (stability limit curve) on a three-
component phase diagram based on the hydrophobic solute, the solvent, and the non-solvent 
(Figure 6.1B). 

The resulting properties of the particles primarily depend on the polymer behavior in the 
organic phase but also on the nature and ratio of the external phase as well as on the 
concentration and nature of the surfactants or other additives used.[107, 112-115] While many 
publications are available in this area, there is still no “unified theory” for predicting particle 
size, size distribution, and dispersion stability ab initio for complex systems. The experiments 


described below were carried out to investigate the process-parameter relationships for the 
preparation of nanoparticles with desired properties, based on polymers with different 
physicochemical properties. 

 

 

 

Figure 6.1. (A) Schematic representation of the nanoprecipitation process. (B) Right triangle 
three-component phase diagram at constant temperature and pressure (reprinted from, S. A. 
Vitale, J. L. Katz, Langmuir 2003, 19, 4105-4110). 

 

As a first example, poly(MMA-stat-PyMMA) nanoparticles were prepared by 
nanoprecipitation in various ways: By dropping polymer solution in water, by dropping water in 
polymer solution, and by a dialysis technique. For each preparation technique, the initial polymer 
concentration was kept the same (4 mg mL-1). The resulting average sizes and size-distributions 
of the particles formed are strongly affected by the method of preparation (Figure 6.2). It was 
generally observed that dropping polymer solution into water leads to the formation of small 
(< 100 nm), uniform nanoparticles with narrow size distribution. In contrast, dropping water into 
the polymer solution leads to the formation of larger particles, with sizes around 500 nm. The 
dialysis preparation procedure leads to ~300 nm particles with broad size distribution. 

 

 

Figure 6.2. SEM images of poly(MMA-stat-PyMMA)-based nanoparticles prepared by applying 
different precipitation methods, with the corresponding size distributions. 


Picture6.tif 
To elucidate the material relationships more rigorously, nanoprecipitation was further 
applied using high-throughput experimentation. To formulate the particles in an automated and 
reproducible manner a pipetting robot was used. Nanoprecipitation was performed in a 96 well 
plate by the fast injection of the polymer solution (or the non-solvent water) to a well containing 
water (or the polymer solution). In a first set of experiments, a dilution series of 
p(MMA-stat-MAA)2:1 ranging from 1 to 16 mg mL-1 was used (12 different solutions in acetone 
with logarithmically spread concentrations). These samples were then each combined with eight 
different proportions of water in a way that the acetone solution/water ratios varied from 0.099 to 
0.500 (again spread logarithmically). The net result was an array of 96 different formulations 
which exhibited a visually observable trend in appearance, following the changes made in the 
nanoprecipitation process (Figure 6.3A). At the lowest concentration, a faintly opalescent 
suspension was obtained; as the concentration increased, the opalescence became more apparent. 
At the highest concentration, macroscopic precipitates were evident. In Figure 6.3B, the 
corresponding average particle sizes are presented as a function of the polymer concentration and 
the solvent/non-solvent ratio. 

 

Figure 6.3. Particle suspensions of p(MMA-stat-MAA)2:1 prepared by dropping the polymer 
solution into water. (A) Image of the nanoprecipitation experiment using a pipetting robot. The 
concentration in each well is the product of the initial polymer concentration and the 
solvent/non-solvent ratio. (B) 3D-representation of the size distribution, obtained by DLS, as a 
function of the initial concentration of the polymer and the solvent to non-solvent ratio. 

 

 To study the influence of the polymers on the particle formation, nanoparticles were also 
prepared from two biocompatible polymers, namely PLGA (50:50) and dextran acetal (ac-dex) 
(degrees of substitution (DS) of cyclic acetals 1.37 and acyclic acetals 0.80). For 


Picture12.tif
p(MMA-stat-MAA)2:1 two different areas can be distinguished (Figure 6.4A): Low and 
intermediate concentrations of the polymer (1 to 6 mg mL-1) correspond to the Ouzo region, 
while at concentrations = 10 mg mL-1 particles with diameters larger than ~300 nm as well as 
macroscopic aggregates are produced, indicating the shift to the unstable region of particle 
formation. In contrast, the sizes of the ac-dex and PLGA particles increase linearly in the whole 
interval of concentrations examined. The difference could be due to the differences in 
hydrophobicity of the polymers: ac-dex as well as PLGA contain a certain amount of OH groups, 
which are assumed to be preferentially located at the particle surface. Their presence may 
stabilize the particle in addition to the surface charge, thus preventing their further growth and 
aggregation. The ratio between solvent and non-solvent has a more complex, nonlinear influence 
on the size of the particles formed (Figure 6.4B). Such a behavior can be the result of changes of 
the nucleation rate due to the increasing content of non-solvent in the solution.[104] 

 

 

Figure 6.4. (A) Nanoparticle sizes as a function of the initial polymer concentration. 
(B) Dependence of the mean sizes of the formed particles on the solvent/non-solvent ratio where 
(1) the initial polymer concentration was kept constant at 3.57 mg·mL-1, (2) the polymer 
concentration in the final mixture was kept constant at 0.1 mg·mL-1, and (3) the amount of the 
polymer in the final mixture was kept constant at 0.1 mg. 

 

 In a further study, PMMA samples of a wide range of molar masses (between 
Mw = 7,700 and 274,000 g mol-1) were investigated in two solvents (acetone and tetrahydrofuran 
(THF)). The interaction between the polymer and solvent molecules at various polymer molar 
masses was evaluated by intrinsic viscosity measurements. According to the collected data, THF 
seems to be a thermodynamically better solvent for PMMA than acetone. To maintain the same 
initial conditions for each nanoprecipitation process and assess the contribution of the different 


Picture15.tif
intrinsic viscosities, nanoparticle suspensions were prepared at the same degree of dilution (c[.]) 
from 0.004 to 0.12, corresponding to the dilute concentration regime. At first, the morphology of 
the particles formed was studied by SEM. In Figure 6.5, the SEM micrographs of nanoparticles 
based on PMMA with Mw = 39,700 g mol-1 and Mw = 278,000 g mol-1, prepared in acetone and 
THF at a degree of dilution c[.] = 0.01 and a solvent/non-solvent ratio of 0.1 respectively, are 
shown. The calculated weight average particle size constitutes 74 ± 4 nm for the preparation 
procedure in acetone and 100 ± 20 nm for the THF preparations. However, particles prepared 
from acetone solution are only uniform and spherically shaped for the lower molar mass, 
whereas with increasing molar mass less spherical particles with rough surfaces appeared. In 
contrast, particles prepared from THF solution are spherical and uniform within the whole molar 
mass range. 

 

 

Figure 6.5. SEM images of nanoparticles prepared from solutions of PMMA with different molar 
masses in acetone and THF. The particles were prepared by dropping the polymer solution into 
water. The initial polymer concentration was adjusted to obtain the same degree of dilution 
(c[.] = 0.01) of all polymer solutions. The solvent/non-solvent ratio was kept constant at 0.1. 

 

Detailed information about the size distribution of the nanoparticles was obtained by 
sedimentation velocity analysis. As expected, the particle sizes increases as the solution becomes 
more concentrated, due to higher values of the Debye parameter. The resulting comparison of the 
particle sizes (an average from AUC, DLS, and SEM data) as a function of the polymer molar 


Picture8.tif
mass is presented in Figure 6.6A. The majority of particles prepared from different molar mass 
samples at similar degree of dilution have virtually the same size. However, a slight increase of 
the average particle size with the molar mass is noticeable. It can also be concluded that, 
regardless of the solvent used, with increasing MW the particle size reaches a plateau. 
Figure 6.6B represents, in a semi-logarithmic plot, the dependence of the particle size on the 
product of molar mass M and intrinsic viscosity [.]. The parameter M[.] is reflecting the volume 
of the macromolecular coils in the initial solution. It is clear that in both cases an increase of the 
volume of the macromolecular coil leads to the formation of nanoparticles with larger sizes, 
particle size increasing approximately 2.5 to 3 times as compared to the first data point. With a 
further increase of the macromolecular volume, the size of the nanoparticles remains constant 
within the experimental error. It was generally observed that stable nanoparticle suspensions 
were only produced when c[.] = 0.1. 

 

 

Figure 6.6. (A) Dependence of the weight average particle size on the initial polymer molar 
mass of the PMMA. The nanoparticles were obtained by nanoprecipitation (at c[.] = 0.01) in 
acetone and THF. (B) Semi-logarithmic dependence of the particle size on the product of 
polymer molar mass and intrinsic viscosity. 

 

In summary, a new approach for the production of nanoparticles with predictable 
performance in an automated and reproducible manner has been demonstrated. The appropriate 
conditions to prepare particles in a wide range of sizes, depending on the way of preparation and 
initial conditions were found. Regardless of polymer molar mass, hydrodynamic volume and 
solvent quality, the formation of stable nanoparticle suspensions could only be observed with 
highly diluted polymer solutions. 

 


Picture2.tif
7. Separation of Nanoparticles of Different Sizes and Compositions by Density 
Gradient Centrifugation 

 

Parts of this chapter have been/will be published in: A9) A A. Vollrath, D. Pretzel, C. Pietsch, I. Perevyazko, R. 
Menzel, D. Weiß S. Schubert, G. M. Pavlov, R. Beckert, U. S. Schubert, Macromol. Rapid Commun. 2012, 33, 
1791-1797. F. Kretschmer, I. Y. Perevyazko, U. S. Schubert (manuscript in preparation). E. Bracht, I. Y. 
Perevyazko, U. S. Schubert, R. Brock (manuscript in preparation). 

 

The control of size and geometry of nanomaterials is important for the discovery of their 
intrinsic size/shape-dependent properties and essential for the preparation of well-defined 
materials for fundamental studies or applications. There are two general approaches to create 
uniform nanoparticles in size and/or shape. One of them is direct particle size control during the 
preparation; the other approach is the use of separation methods, as magnetic separation,[116] 
selective precipitation,[117] filtration/diafiltration,[118] electrophoresis,[119] or chromatographic 
methods[120] for attaining particle fractions with narrow shape and size distributions. Density 
gradient ultracentrifugation is a general, nondestructive and scalable separation method adapted 
from biomacromolecular separation technology; it can be used also for sorting of colloidal NPs, 
mixtures of macromolecules, supramolecular aggregates etc. according to their chemical, 
structural, and size differences.[121-127] The principle of the experiment is relatively simple: A thin 
layer of the suspension to be fractionated is placed on top of a solution representing a density 
gradient (linear or step type). When a centrifugal field is applied, the various components move 
through the gradient at different rates depending on their sizes, densities or shapes. After the 
centrifugation is completed, the particles of different size/shape will have moved to different 
positions in the centrifuge tube (Figure 7.1). 

 

 

Figure 7.1. Schematic representation of a density gradient centrifugation experiment for 
nanoparticle fractionation (reprinted from www.mun.ca). 

 


At first, the fractionation of fluorescent labeled PMMA-based nanoparticles prepared by 
the nanoprecipitation process will be considered. The PMMA copolymers were chosen as a 
model system to demonstrate that functional PMMA-based nanoparticles are well suited for 
diagnostic applications, in particular cell imaging. To study the relationship between the size of 
the particles and their biological applicability, discrete nanoparticle populations were prepared 
by centrifugation in a linear sucrose density gradient. In Figure 7.2 the results of the 
fractionation experiment are presented. Due to the existence of particles with distinctly different 
sizes in the suspension, the fractionation leads to the appearance of discrete bands, corresponding 
to particle populations of different size (Figure 7.2B). After centrifugation, fractions of the 
gradient were collected by using a peristaltic pump and a narrow tube inserted from above to the 
bottom of the centrifuge vial. The fractions containing nanoparticles were dialyzed against pure 
water and analyzed by AUC (Figure 7.2D), DLS, and SEM (Figure 7.2C). The concentration- 
and size-dependent internalization of the different particle populations were investigated by 
confocal laser scanning microscopy. In addition, the biocompatibility of the particle suspensions 
in terms of their non-toxicity was studied by XTT cytotoxicity assays and microscopic 
evaluation of viability after a live/dead staining. These results demonstrate that PMMA 
nanoparticles are attractive for applications in a biological and medical environment. 

 

 

Figure 7.2. Results of density gradient centrifugation of labeled P(MMA-stat-MAy) based 
nanoparticles. (A) Image of a centrifuge vial with the sample applied before centrifugation. (B) 
Centrifuge vial after centrifugation at 10,000 rpm for 40 min. (C) SEM images of the fractions 
collected. (D) Corresponding size distributions obtained by analytical ultracentrifugation. 

 


Recently, novel drug delivery capsules, namely lyophilisomes, were designed for 
improving the biodistribution of systemically applied (chemo)-therapeutics.[8, 128] The capsules 
are formed by phase separation comprising three stages: Freezing, annealing, and lyophilization, 
resulting in globular particles ranging from 100 to 3,000 nm (Figure 7.3). Such biocapsules may 
show a great biomedical potential due to the ability to incorporate both hydrophilic and lipophilic 
compounds. However, a major disadvantage is that the size of the capsules can only be poorly 
controlled during the preparation procedure, which results in a very broad final size-distribution. 
For biomedical applications, in particular for intravenous drug therapy, the preferable sizes of the 
capsules should be = 1,000 nm. 

 

 

Figure 7.3. Scanning electron microscopy and corresponding distribution of sedimentation 
coefficients of albumin lyophilisomes. 

 

The suspensions of lyophilisomes were fractionated by density gradient centrifugation. In 
the case of highly polydisperse systems characterized by a broad size-distribution, the 
centrifugation in a density gradient results in spreading of the initially layered band through the 
entire gradient volume, without the formation of distinct bands. The fractions were collected 
from the top of the vial by a pipette and dialyzed against pure water. Afterwards, analytical 
ultracentrifugation and dynamic light scattering were used to obtain detailed information about 
average size and size distribution. In Figure 7.4, the resulting distributions of sedimentation 
coefficients and hydrodynamic sizes are compared. Obviously, the size-distributions of most 
particles in a fraction are very narrow in comparison to the starting solution. The size of the 
particles in the collected fractions varied from 200 to 700 nm. The fractionated samples were 
further used for biodistribution and cell viability studies. 

 


albumin_fractionationl.tif 


Figure 7.4. Results of a density gradient centrifugation of albumin-based lyophilisomes: 
Analysis of the fractions by AUC (A) and DLS (B). 

 

It is clear that the physicochemical properties of nanoparticles are defined and limited by 
their physical dimensions and shapes.[129] A controlled assembly of nanoparticles by specific 
clustering of two or three particles in solution could be considered as a first-step towards scalable 
fabrication of nanodevices.[130] In the following, the separation of gold nanoparticles of different 
architectures will be examined. Citrate-stabilized gold nanoparticles were prepared via the 
Turkevich method.[131] Assembling the nanoparticles was facilitated by the addition of thio- 
functionalized oligo(o-phenylene ethynylene) linker. Depending on the amount of linker added, 
the solution changed its color from red at the lowest concentration to a dark violet at the highest 
concentration used, indicating the formation of nanoparticle clusters (dimers, trimers, tetramers, 
etc). With respect to the hydrodynamic behavior of nanoparticles and their clusters, it is clear 
that the frictional coefficient will be larger for dimers, trimers etc. than for monomers, due to an 
increased average cross section. On the other hand, dimers will have twice the molar mass of the 
monomer and this will overcompensate the increased frictional coefficients, resulting in higher 
sedimentation coefficients of dimers and higher order agglomerates in comparison to single 
particles. It can therefore be expected that the clusters could be separated by density gradient 
centrifugation. In Figure 7.5 the results of such a centrifugation are presented. The 
centrifugation resulted in the formation of two main areas corresponding obviously to the 
population of single nanoparticles (1st region) and their assemblies (2nd and 3rd region). 
Sedimentation velocity analysis (Figure 7.5B) showed reasonable shifting of the average 
sedimentation coefficients to the higher values for the later fractions. Moreover, the estimated 
frictional ratio changes from 1.0 for the first fraction to the value of 1.10 and 1.50 for the second 
and third fraction, respectively, indicating nanoparticle assemblies with higher asymmetry. 


 

Figure 7.5. Density gradient centrifugation of gold nanoparticles. (A) Images of a centrifuge 
vial with the sample applied, before and after centrifugation. (B) Corresponding distributions of 
sedimentation coefficients of the fractions collected. 

 

In summary, density gradient centrifugation was successfully applied for the separation of 
nanoparticles by taking advantage of the differences in their sedimentation rate. The method 
provides high resolution for the separation of colloid particles of different compositions, in 
different size ranges, and of different states of aggregation. The method is versatile, scalable, 
efficient, and non-destructive. 

 


 


8. Summary 

 

The methods of macromolecular hydrodynamics are powerful tools to study a large 
variety of soluble and dispersed species including diverse macromolecular systems. However, 
the application of a single method of molecular hydrodynamics alone, either velocity 
sedimentation or a determination of translational diffusion coefficient, or the evaluation of the 
value of the intrinsic viscosity does not allow to obtain exhaustive information about the 
molecular and conformational characteristics of linear macromolecules. Only complex research 
on all of the system’s fundamental hydrodynamic characteristics can lead to reliable information. 
In the present thesis, polystyrene (PS) standards in a wide interval of molar masses are used as a 
model system to put to the test and demonstrate the general procedure of analyzing the 
experimental data and of extracting conformational and molecular characteristics. 

Among the hydrodynamic methods, sedimentation velocity analysis is especially 
valuable. The progress in software development has enormously improved its potential and, in 
principle, now allows obtaining the mass data and the hydrodynamic properties of the whole 
range of macromolecular systems, including polymers and their complexes, nanoparticles etc.. 
The examination of the characteristic hydrodynamic values and comparison of them with 
literature data lead to the adequate determination the molar mass and corresponding 
conformational properties in the case of polymers with low equilibrium rigidity studied in 
marginal solvents (PS in MEK). However, in the case of polymers characterized by high 
equilibrium rigidity (sodium alginate, DNA) as well as polymers studied in thermodynamically 
good solvents (PS in toluene), the analyses become problematic due to the more pronounced 
excluded volume interactions. Nevertheless, with any type of macromolecules the simultaneous 
determination of the sedimentation and the Gralen coefficients for a homologous series were 
found to allow a complete interpretation of the sedimentation velocity data by using the concept 
of the sedimentation parameter. Furthermore, it was shown that highly heterogeneous systems 
can be safely characterized only in the case of low total diffusivity. In other cases the analysis 
may result in the shift of the values of sedimentation coefficients and a redistribution of the peak 
areas, as well as an inadequate estimation of the values for the frictional ratio. 

The charged polymeric systems, represented by 4,4-imidazolium poly(ionene)s, metallo-
supramolecular complexes as well as DNA/polycation polyplexes, have been studied by the 
methods of molecular hydrodynamics. The ionenes showed significant differences in the 
obtained molar mass as compared to NMR spectroscopy, which was explained by the formation 
of polymer macrocycles. The determined conformational parameters, like Kuhn segment length 
and mass per unit length, have confirmed the formation of ring chain molecules. Based on the 
results obtained, the content of the linear/ring chains in the solution was determined. The 


investigation of the binding behavior of poly(alkyl methacrylate) copolymers containing 
bidentate 2-(1,2,3-triazol-4-yl) pyridine ligands with different metal ions has enabled a 
differentiation between intra- and intermolecular complexation. 

Electrostatic interactions between charged macromolecules result in the formation of 
polyelectrolyte complexes. A particular type of such complexes, namely polyplexes (DNA/PEI), 
was examined. The hydrodynamic properties and the composition were studied in a wide range 
of N/P ratios. The results obtained show different binding behavior of PEI molecules to DNA 
corresponding to different phases of complex formation. Moreover, it was shown that DNA is 
not completely condensed by PEI, resulting in the availability of free negative charges on the 
DNA even at high N/P ratios. Based on the experimental data, detailed information about the 
complex composition and its changes was obtained. 

To obtain organic and inorganic nanoparticles with controllable size and shape, two main 
approaches were applied: (i) Preparation of the nanoparticles with desired properties by tuning 
and optimizing the nanoprecipitation process, and (ii) fractionation of already prepared 
nanoparticles according to their hydrodynamic properties. According to the first approach, stable 
nanoparticles of different sizes were obtained by systematically varying the process and 
formulation parameters. It was shown that the key factor during particle preparation is the 
volume fraction occupied by the polymer macromolecular coil in the initial solution. The 
morphology of the nanoparticles depends on the affinity of the polymer molecules to the solvent. 
It appeared that ‘thermodynamically good’ solvents are preferable to formulate uniform 
nanoparticles with smooth surfaces. The separation of the nanoparticles according to their 
size/shape by density gradient centrifugation represented the second approach. The polymeric 
nanoparticles, lyophilisomes as well as assemblies of inorganic gold nanoparticles, were 
fractionated by taking advantage of differences in their sedimentation rate. The analysis of the 
fractionated samples by several analytical techniques revealed a high separation efficiency of the 
method applied. 

The thesis provides insights into the field of molecular hydrodynamics methods as a tool 
for extracting conformational characteristics of complex macromolecular and colloidal systems. 
Besides describing the basic characterization procedures, fundamental structure-property and 
material relationships were established for a variety of systems. 

 


9. Zusammenfassung 

 

Hydrodynamische Verfahren stellen wichtige Methoden zur Untersuchung von 
makromolekularen Systemen in Lösung dar. Die Anwendung einzelner Verfahren, wie die 
Bestimmung der Sedimentationsgeschwindigkeit, des translatorischen Diffusionskoeffizienten 
oder der intrinsischen Viskosität, erlaubt jedoch keine vollständige Aufklärung der molekularen 
Eigenschaften von linearen Makromolekülen; nur die Kombination mehrerer hydrodynamischer 
Verfahren kann verlässliche Informationen liefern. In dieser Arbeit dienten Polystyrol-Standards 
als Modellsysteme, um die Möglichkeiten zur Interpretation der experimentellen Daten zu 
untersuchen sowie molekulare und konformative Eigenschaften der untersuchten Moleküle zu 
bestimmen. 

Unter den meistbenutzten hydrodynamischen Methoden erwies sich die 
Sedimentationsgeschwindigkeitsanalyse als besonders nützlich. Durch die enorme 
Weiterentwicklung der Software können die Massendaten und die hydrodynamischen 
Eigenschaften einer Vielzahl von makromolekularen Systemen bestimmt werden, einschließlich 
von Polymeren und deren Komplexverbindungen, Nanopartikeln etc.. In dieser Arbeit führten 
die Untersuchung charakteristischer hydrodynamischer Parameter und deren Vergleich mit 
Literaturdaten zu einer sicheren Ermittlung von Molmassen bei Polymeren mit geringer 
Gleichgewichtsstabilität (PS in MEK) und zur Bestimmung der daraus resultierenden 
konformativen Eigenschaften. Die Analyse von Polymeren mit hoher Gleichgewichtsstabilität 
(Natriumalginat, DNA) sowie die Charakterisierung von Polymeren in „thermodynamisch guten“ 
Lösungsmitteln (PS in Toluol) sind jedoch mit Problemen verbunden, da ausgeprägte 
Volumenwechselwirkungen nicht ausgeschlossen sind. Dennoch ermöglichte die simultane 
Bestimmung des Sedimentations- und des Gralen-Koeffizienten für eine homologe Reihe von 
Makromolekülen, unter Einbeziehung anderer Sedimentationsparameter, eine komplette 
Interpretation der Sedimentationsgeschwindigkeitsdaten. Darüber hinaus konnte gezeigt werden, 
dass heterogene Systeme nur dann zuverlässig charakterisiert werden können, wenn sie ein 
geringes Diffusionsvermögen aufweisen. Andernfalls kann es zu einer scheinbaren Verschiebung 
des Sedimentationskoeffizienten, einer Umverteilung der Peak-Flächen und einer fehlerhaften 
Berechnung des Reibungsverhältnisses kommen. 

Des Weiteren wurden geladene Polymersysteme, wie 4,4-Imidazolium Poly(Ionene), 
metallbasierte supramolekulare Komplexverbindungen und DNA/Polykationen, mit 
hydrodynamischen Methoden charakterisiert. Die erhaltenen Molmassen der Ionene zeigten 
signifikante Unterschiede zu den durch NMR-Spektroskopie bestimmten, was auf die Bildung 
von polymeren Makrozyklen zurückgeführt werden kann. Die Bestimmung der Kuhn-Länge und 


der Masse pro Einheitslänge bestätigten die Bildung von Ring-Ketten-Molekülen. Basierend auf 
den Ergebnissen konnte der Anteil an linearen/ringförmigen Ketten in der Lösung bestimmt 
werden. Die Untersuchung des Bindungsverhaltens von Poly(alkylmethacrylat)-Copolymeren, 
die zweizähnige 2-(1,2,3-Triazol-4-yl)Pyridin-Liganden enthalten, ermöglichte eine 
Differenzierung zwischen intra- und intermolekularer Komplexierung. 

Elektrostatische Wechselwirkungen zwischen geladenen Makromolekülen führen zur 
Bildung von Polyelektrolytkomplexen. Ein spezielles Beispiel für derartige Komplexe, nämlich 
„Polyplexe“ aus DNA und PEI, wurde untersucht. Deren hydrodynamische Eigenschaften und 
Strukturen wurden über einen weiten Bereich von N/P-Verhältnissen verfolgt. Es konnten 
unterschiedliche Phasen der Komplexbildung von PEI-Molekülen und DNA detektiert werden, 
die mit unterschiedlichem Bindungsverhalten korreliert waren. Dabei war sogar bei hohen N/P-
Verhältnissen die DNA nicht komplett von PEI-Molekülen umgeben, so dass negative Ladungen 
an der DNA zugänglich blieben. Die experimentellen Daten lieferten detaillierte Informationen 
über die Komplexzusammensetzung und deren Veränderung. 

Um organische und anorganische Nanopartikel mit enger Verteilung von Größe und 
Form zu erhalten, wurden zwei komplementäre Methoden benutzt: (i) Herstellung der 
Nanopartikel mit den gewünschten Eigenschaften durch Optimierung des Nanofällungs-
Prozesses und (ii) Fraktionierung von Nanopartikel-Populationen gemäß ihrer 
hydrodynamischen Charakteristika. Bei Ansatz (i) konnten stabile Nanopartikel der jeweils 
angestrebten Größenverteilung durch systematische Variation der Herstellungsparameter 
erhalten werden. Als Schlüsselparameter erwies sich der Volumenanteil, der mit 
Makromolekülen in der Ausgangslösung besetzt ist. Die Morphologie der Nanopartikel hing 
vorwiegend von der Lösungsmittelaffinität der Makromoleküle ab. „Thermodynamisch“ gute 
Lösungsmittel lieferten einheitliche Nanopartikel mit glatten Oberflächen. Ansatz (ii) wurde in 
Form der Dichtegradienten-Zentrifugation realisiert. Polymere Nanopartikel und Anordnungen 
von anorganischen Gold-Nanopartikeln wurden aufgrund ihrer unterschiedlichen 
Sedimentationsgeschwindigkeiten fraktioniert, wobei eine hohe Trennungseffizienz erreicht 
wurde. 

Diese Arbeit liefert Einblicke in die Anwendung von molekularen hydrodynamischen 
Verfahren als Werkzeuge zur Gewinnung von Informationen über Konformation und 
Eigenschaften komplexer makromolekularer und kolloidaler Systeme. Die grundlegenden 
Charakterisierungsverfahren werden beschrieben, und für eine Reihe von Systemen werden 
fundamentale Struktur-Eigenschaftsbeziehungen und wichtige Materialeigenschaften aufgezeigt. 

 


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Supplementary information 

 

Additional experimental section for Chapter 7 containing not yet published procedures. 

 

The materials and methods 

 

All used chemicals and solvents were purchased from Sigma-Aldrich and were used without 
further purification. The PBS solutions were received from Biochrom. Dialysis bags (molar mass 
cut off 3,500 g mol-1) were purchased from Spectra/Por. 

 

Density gradient centrifugation 

 

The fractionation of the gold nanoparticles and their assembles as well as the albumin based 
lyophilisomes was performed in a Beckman Optima L-XP ultracentrifuge (Beckman 
Instruments, Palo Alto, USA), using the swinging bucket rotor SW 41 Ti and 13.2 mL capacity 
ultracentrifuge tubes (ultra clear tubes, Beckman). The linear density gradients were prepared in 
14 mm diameter, 13.2 mL capacity ultracentrifuge tubes (ultra clear tubes, Beckman) using a 
gradient maker consisting of two chambers connected via a channel with a stopcock; the final 
gradient volume was 11.7 mL. In order to create a “pillow” for pelleting particles, 0.5 mL of 
60% w/w sucrose solution was placed on the bottom of the tube before the main gradient 
solution was loaded. The main gradient, in both cases, was obtained by mixing 5.6 mL of 10% 
w/w and 5.6 mL of 40% w/w sucrose solution in a mixing chamber by the way that the lower 
density solution was loaded first into the centrifugal tube. The gradient prepared was then stored 
for an hour at room temperature. The initial particle solution (0.6 mL) was placed on the top of 
the gradient. 

The suspensions of gold nanoparticles were fractionated at 7,500 rpm for 75 minutes. After 
centrifugation, the solution was collected by using a pipette from the top of the vial. Depending 
on the fraction each 0.5 mL or 1 mL of the solution was collected. 

The suspensions of lyophilisomes were fractionated at 3,000 rpm for 15 minutes. After 
centrifugation, the solution was collected by using a peristaltic pump and a narrow tube, inserted 
from above to the bottom of the centrifuge vial, each 1.0 mL of the solution was collected. 

To remove the sucrose gradient from the fractions collected, they were dialyzed against pure 
water. After the dialysis, the fractionated lyophilisomes solutions were adjusted to the following 
buffer: PBS, 0.5% bovine serum albumins (BSA). 

 

 

 


Analytical ultracentrifugation 

 

Sedimentation velocity experiments of the initial and fractionated solutions were performed with 
a ProteomeLab XLI Protein Characterization System analytical ultracentrifuge (Beckman 
Coulter, Brea, CA), using conventional double-sector Epon centerpieces of 12 mm optical path 
length and a four-hole rotor (An-60Ti). Rotor speed was 1,000 to 10,000 rpm, depending on the 
sample. Cells were filled with 420 µL of sample solution at initial concentration and 440 µL of 
solvent. Before the run, the rotor was equilibrated for approximately 1 h at 20 °C in the 
centrifuge. Sedimentation profiles were obtained by absorbance at . = 270 nm and . = 520 nm 
for the lyophilisomes and gold nanoparticles respectively. For the analysis of the sedimentation 
velocity data ls-g*(s) as well as c(s) methods were used. Ls-g*(s) represents the least-square 
boundary analysis, which describes sedimentation of non-diffusing species. C(s) analysis based 
on the numerical resolution of the Lamm equation assuming the same frictional ratio values for 
each s value. The value of the partial specific volume of 0.73 cm-3 g and 0.052 cm-3 g was used 
for the albumin lyophilisomes and gold nanoparticles respectively. The size of the fractionated 
particles/lyophilisomes was calculated according to the Svedberg equation. 

 

Dynamic light scattering 

 

DLS was performed on the DynaPro Plate Reader Plus (Wyatt Technology Corporation, Santa 
Barbara, CA) equipped with a 60 mV linearly polarized gallium arsenide (GaAs) laser of 
. = 832.5 nm and operating at an angle of 156°. The data were analyzed with the Dynamics 
software ver.6.10 by the method of cumulants. 

 

 

 

 

 

 

 

 

 

 

 

 


H:\MyData\Documents\foto\A_067357(2).jpg 


Curriculum Vitae 

 

 

 

Education 

 

26/03/1984 Born in Leningrad, USSR 

1991 – 2001 Primary and high school, Saint Petersburg, Russia 

2001 – 2005 Saint Petersburg state university, Russia, Faculty of 
Physics, Bachelor Degree. 

2004 – 2005 Bachelor thesis at the Department of Molecular Biophysics, 
SupervisorProf. Dr. Nina .. Kasyanenko 

Topic: “Studying of the influence of divalent metal ions on 
the conformational transitions in DNA molecule in water-
ethanol solutions” 

2005 – 2008 Saint Petersburg state university, Russia, Faculty of 
Physics, Department of Molecular Biophysics, Master 
Degree, SupervisorProf. Dr. Nina .. Kasyanenko 

Topic: “Self-organizing nanostructure on the base of DNA 
complexes with divalent metal Ions in water-ethanol 
solution” 

Since 8/2008 PhD student at the Laboratory of Organic and 
Macromolecular Chemistry (IOMC) Friedrich-Schiller-
University Jena, Supervisor Prof. Dr. Ulrich S. Schubert 

Topic: “Hydrodynamic analysis of macromolecular and 
colloidal systems by analytical ultracentrifugation and 
related methods” 


 


Publication list 

 

Peer-reviewed publications 

 

1. I. Perevyazko, A. Vollrath, S. Hornig, G. M. Pavlov, U. S. Schubert, 
Characterization of poly(methyl methacrylate) nanoparticles prepared by 
nanoprecipitation using analytical ultracentrifugation, dynamic light scattering, and 
scanning electron microscopy. J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 3924-
3931. 

2. I. Y. Perevyazko, J. T. Delaney, A. Vollrath, G. M. Pavlov, S. Schubert, 
U. S. Schubert, Examination and optimization of the self-assembly of biocompatible, 
polymeric nanoparticles by high-throughput nanoprecipitation. Soft Matter 2011, 7, 
5030-5035. 

3. I. Y. Perevyazko, A. Vollrath, C. Pietsch, S. Schubert, G. M. Pavlov, 
U. S. Schubert, Nanoprecipitation of poly(methyl methacrylate)-based nanoparticles: 
Effect of the molar mass and polymer behavior. J. Polym. Sci., Part A: Polym. 
Chem. 2012, 50, 2906-2913. 

4. I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Hoeppener, S. Schubert, 
D. Fischer, U. S. Schubert, Polyelectrolyte complexes of DNA and linear PEI: 
Formation, composition and properties. Langmuir 2012, 28, 16167-16176. 

5. G. M. Pavlov, I. Perevyazko, U. S. Schubert, Velocity sedimentation and intrinsic 
viscosity analysis of polystyrene standards with a wide range of molar masses. 
Macromol. Chem. Phys. 2010, 211, 1298-1310. 

6. T. Erdmenger, I. Perevyazko, J. Vitz, G. Pavlov, U. S. Schubert, Microwave-assisted 
synthesis of imidazolium ionenes and their application as humidity absorbers. 
J. Mater. Chem. 2010, 20, 3583-3585. 

7. G. M. Pavlov, I. Y. Perevyazko, O. V. Okatova, U. S. Schubert, Conformation 
parameters of linear macromolecules from velocity sedimentation and other 
hydrodynamic methods. Methods 2011, 54, 124-135. 

8. M. M. Bloksma, C. Weber, I. Y. Perevyazko, A. Kuse, A. Baumgärtel, 
A. Vollrath, R. Hoogenboom, U. S. Schubert, Poly(2-cyclopropyl-2-oxazoline): 
From rate acceleration by cyclopropyl to thermoresponsive properties. 
Macromolecules 2011, 44, 4057-4064. 

9. B. Happ, G. M. Pavlov, I. Perevyazko, M. D. Hager, A. Winter, U. S. Schubert, 
Induced charge effect by Co(II) complexation on the conformation of a copolymer 
containing a bidentate 2-(1,2,3-triazol-4-yl)pyridine chelating unit. Macromol. 
Chem. Phys. 2012, 213, 1339-1348. 


10. A. Vollrath, D. Pretzel, C. Pietsch, I. Perevyazko, R. Menzel, D. Weiß, S. Schubert, 
G. M. Pavlov, R. Beckert, U. S. Schubert, Preparation, cellular internalization and 
biocompatibility of highly fluorescent PMMA nanoparticles. Macromol. Rapid 
Commun. 2012, 33, 1791-1797. 

11. C. Weber, K. Babiuch, S. Rogers, I. Y. Perevyazko, R. Hoogenboom, 
U. S. Schubert, Unexpected radical polymerization behavior of oligo(2-ethyl-2-
oxazoline) macromonomers Polym. Chem. 2012, 3, 2976-2985. 

12. N. Kasyanenko, D. Mukhin, I. Perevyazko, Conformational changes of a DNA 
molecule induced by metal complexes formed in solution. Polym. Sci. Ser C 2010, 
52, 122-133. 

 

Manuscripts in preparation 

 

1. F. Kretschmer, I. Y. Perevyazko, U. S. Schubert, Synthesis, separation and 
characterization of gold nanoparticles assembled by a rigid rod linker, in preparation. 


 

2. E. Bracht, I. Y. Perevyazko, U. S. Schubert, R. Brock, Albumin based lyophilisomes 
novel protein capsules as drug delivery system, in preparation. 


 

Oral Presentations 

 

1. I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Schubert, D. Fischer, U. S. Schubert 
“Hydrodynamic study of formation and properties of PEI based polyplexes” (20th 
International Analytical Ultracentrifugation Conference, San Antonio, USA, March 
25 - 30, 2012). 
2. I. Y. Perevyazko, A. Vollrath, C. Pietsch, J. T. Delaney, S. Schubert, G. M. Pavlov, 
U. S. Schubert “High-throughput nanoprecipitation of the functional polymers: A 
new approach to developing and understanding self-assembling nanoparticles” (7th 
International Symposium Molecular Mobility and Order in Polymer Systems, 
St.-Petersburg, Russia, June 6 - 10, 2011). 
3. I. Perevyazko, A. Vollrath, C. Pietsch, S. Hornig, G. M. Pavlov, U. S. Schubert 
“Comparison of analytical ultracentrifugation, dynamic light scattering and scanning 
electron microscopy for the size determination of poly(methyl methacrylate) 
nanoparticles” (18th International AUC conference, Uppsala University, Sweden, 
September 13-18, 2009). 


 

 

 


Poster presentations 

 

1. I. Y. Perevyazko, M. Bauer, G. M. Pavlov, S. Schubert, D. Fischer, U. S. Schubert 
“Hydrodynamic study of formation and properties of PEI based polyplexes” (20th 
International Analytical Ultracentrifugation Conference, San Antonio, USA, March 
25 - 30, 2012). 
2. A. Vollrath, I. Y. Perevyazko, C. Pietsch, J. T. Delaney, S. Schubert, G. M. Pavlov, 
U. S. Schubert, “High- throughput nanoprecipitation of functional polymers” (CRS 
and NanoConSens Meeting, Jena, Germany, March 30, 2011). 
3. I. Perevyazko, G. M. Pavlov, T. Erdmenger, U. S. Schubert “Analytical 
ultracentrifugation and NMR studies of poly(4,4-imidazolium ionene)s for 
investigations about molar mass and molecular organization” (18th International 
AUC conference, Uppsala University, Sweden, September 13 - 18, 2009). 
4. I. Perevyazko, G. M. Pavlov, U. S. Schubert “Hydrodynamic investigations of 
sodium alginate at different ionic strength” (18th International AUC conference, 
Uppsala University, Sweden, September 13 - 18, 2009). 
5. I. Perevyazko, A. Vollrath, C. Pietsch, S. Horning, G. M. Pavlov, U. S. Schubert 
“Analytical ultracentrifugation for the sizing of poly(methyl methacrylate) 
nanoparticles” (44th Meeting of the German colloidal society, Hamburg, Germany, 
September 28 - 30, 2009) 
6. I. Perevyazko, G. M. Pavlov, U. S. Schubert “Velocity sedimentation of polystyrene 
standards and their mixtures of different modality” (17th International Symposium on 
Analytical Ultracentrifugation and Hydrodynamics, Newcastle, UK, 
8 - 12 September, 2008). 



 


 

Acknowledgements 

 

 Working on my PhD was a great and wonderful experience. I am indebted to 
many people helped me during the last 4 years and who contributed to the described 
work. First and foremost, I would like to express my sincere gratitude to the 
Prof. Dr. Ulrich S. Schubert, for giving me the opportunity to start as a PhD student 
within his group at the Friedrich Schiller University Jena. I would like to thank you 
for your continuous support, immense patience and great motivation you have been 
giving. Your ability to select and to approach compelling research problems, you 
great individual energy and hard work coupling with the high scientific standards set 
a remarkable example. 

Secondly, I owe sincere thankfulness to my direct research advisor Dr. George M. 
Pavlov, who guided me through the process of scientific research during the time of 
my PhD work. His supervision laid the groundwork for my understanding of the field 
of molecular hydrodynamics and the analysis of the experimental data. No doubt, I 
could never have accomplished any of the studies which have been described in this 
thesis without your critical insights, guidance, help and support. 

....... .........., . ....... ... ........ ............... . 
............. .. .... ......, . ........... . ....... .... .... ....... 
......... ..., . . ...... .... ........ “.....” ....... ............ . 
........ ........ .... ................. ....... 

Furthermore, I am very grateful to Dr. Stephanie Schubert, who has been correcting, 
improving and made a significant contribution to all of my “first author” 
manuscripts. Thank you very much as well, for the corrections and very helpful 
comments of the current thesis, without your help I would not be able to finish it in 
time. 

I am also very grateful to Prof. Dr. Dieter Schubert. Your critical comments and 
corrections for almost all of the studies that have been described in this thesis were 
very helpful and efficient. I would like to thank you as well for the correction of the 
current thesis. Moreover, I am very grateful for your assistance and useful 
discussions about the density gradient centrifugation. 

A special thank goes to Antje Vollrath, with whom I have worked on different 
projects during the whole time of my PhD. Thank you for numerous DLS and zeta 
potential measurements, nanoprecipitation experiments, helping with manuscript 
preparations and simply to be very kind all the time. 

 

 


I would like to thank Dr. Joseph T. Delany for the collaboration under the 
high-throughput nanoprecipitation approach. Your fundamental ideas served as a 
basement for the future development and application of this project. 

A big guy – Marius Bauer, I want to thank you for the very productive and efficient 
cooperation under the “polyplex” project. When it just started nobody really knew 
what will be the result, but finally it turned out into a nice piece of work. I appreciate 
very much working with you. 

Here, I also would like to thank Prof. Dr. Dagmar Fisher for her help and discussions 
about the “polyplex” project. 

Dr. Stephanie Höppener is highly acknowledged for the microscopy studies and 
corresponding discussions. Thank you very much for your cooperation and help 
under different projects. 

I would like especially thank Dr. Bobby Happ for the help with the translation of the 
summary chapter and efficient cooperation under the studies of supramolecular 
systems described in one of the chapters. 

I am very grateful to Dr. Vitaly Vogel. Thank you very much for coming here and 
teaching me the principles and all critical aspects of the density gradient 
centrifugation. 

I thank Christian Pietsch, for providing a large amounts of fine PMMA samples, 
which made possible one of the studies described in this thesis. 

I thank Florian Kretschmer for the continuous cooperation under the fractionation of 
gold nanoparticles. 

I thank Tina Erdmenger for her collaboration under the investigation of polyionens. 

I thank Etienne von Bracht for the continuous and productive cooperation under the 
lyophilisomes studies. 

Furthermore I would like to thank Renzo Paulus and Dr. Jürgen Vitz who have been 
helping with so many technical, computer and other problems that I cannot even 
remember. 

I want to thank the colleagues with whom, I shared the office space for creating nice 
and worm working atmosphere. These are Dr. Jolke Perelaer, Sebastian Wünscher, 
Michael Wagner as well as the former members Dr. Albert Libersky and Juha 
Niittynen. 

Lastly, I offer my kind regards to all of those, who might not be mentioned in person 
here, but nonetheless supported, me in any respect during the completion of this 
work. 

 


 

Declaration of Authorship / Selbständigkeitserklärung 

 

 

Ich erkläre, dass ich die vorliegende Arbeit selbständig und unter Verwendung der 
angegebenen Hilfsmittel, persönlichen Mitteilungen und Quellen angefertigt habe. 

 

I certify that the work presented here is, to the best of my knowledge and belief, original and 
the result of my own investigations, except as acknowledged, and has not been submitted, 
either in part or whole, for a degree at this or any other university. 

 

 

 

 Jena, den 22.01.2013 
(Igor Perevyazko) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

Publications A1–A9 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A1: Reprinted with permission. Copyright 2011 Elsevier 

 

A2: Reprinted with permission. Copyright 2010 Wiley-VCH 

 

A3: Reprinted with permission. Copyright 2010 Wiley-VCH 

 

A4: Reprinted with permission. Copyright 2010 The Royal Society of Chemistry 

 

A5: Reprinted with permission. Copyright 2012 Wiley-VCH 

 

A6: Reprinted with permission. Copyright 2012 American Chemical Society 

 

A7: Reprinted with permission. Copyright 2011 The Royal Society of Chemistry 

 

A8: Reprinted with permission. Copyright 2012 Wiley-VCH 

 

A9: Reprinted with permission. Copyright 2012 Wiley-VCH 


 

 

 

 

 

 

 

 

Publication A1: 

 

Conformation parameters of linear macromolecules from 
velocity sedimentation and other hydrodynamic methods 

 

 

 

Georgy M. Pavlov, Igor Y. Perevyazko, Olga V. Okatova, 
Ulrich S. Schubert 

 

Methods 2011, 54, 124-135 

 

 

 

 

 

 

 

 

 

 

 

 


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Publication A2: 

 

Velocity sedimentation and intrinsic viscosity analysis of 
polystyrene standards with a wide range of molar masses 

 

 

 

Georgy M. Pavlov, Igor Perevyazko, 

Ulrich S. Schubert 

 

Macromol. Chem. Phys. 2010, 211, 1298-1310 

 

 

 

 

 

 

 

 

 

 

 

 


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Publication A3: 

 

Characterization of poly(methyl methacrylate) 
nanoparticles prepared by nanoprecipitation using 
analytical ultracentrifugation, dynamic light scattering, and 
scanning electron microscopy 

 

 

 

Igor Perevyazko, Antje Vollrath, Stephanie Hornig, 
Georgy M. Pavlov, Ulrich S. Schubert 

 

J. Polym. Sci., Part A: Polym. Chem. 2010, 48, 3924 

 

 

 

 

 

 

 

 

 

 


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Publication A4: 

 

Microwave-assisted synthesis of imidazolium ionenes and 
their application as humidity absorbers 

 

 

 

Tina Erdmenger, Igor Perevyazko, Jürgen Vitz, 
Georgy M. Pavlov, Ulrich S. Schubert 

 

J. Mater. Chem. 2010, 20, 3583-3585 

 

 

 

 

 

 

 

 

 

 

 

 


 


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Publication A5: 

 

Induced charge effect by Co(II) complexation on the 
conformation of a copolymer containing a bidentate 
2-(1,2,3-triazol-4-yl)pyridine chelating unit 

 

 

 

Bobby Happ, Georges M. Pavlov, Igor Perevyazko, 
Martin D. Hager, Andreas Winter, Ulrich S. Schubert 

 

Macromol. Chem. Phys. 2012, 213, 1339-1348 

 

 

 

 

 

 

 

 

 

 

 


 


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Publication A6: 

 

Characterization of DNA-linear PEI polyelectrolyte 
complexes: Formation, properties and composition 

 

 

 

Igor Y. Perevyazko, Marius Bauer, Georgy M. Pavlov, 
Stephanie Höppener, Stephanie Schubert, Dagmar Fischer, 
Ulrich S. Schubert 

 

Langmuir 2012, 28, 16167-16176 

 

 

 

 

 

 

 

 

 

 

 


 


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Publication A7: 

 

Examination and optimization of the self-assembly of 
biocompatible, polymeric nanoparticles by high-throughput 
nanoprecipitation 

 

 

 

Igor Y. Perevyazko, Joseph T. Delaney, Antje Vollrath, 
Georgy M. Pavlov, Stephanie Schubert, Ulrich S. Schubert 

 

Soft Matter 2011, 7, 5030-5035 

 

 

 

 

 

 

 

 

 

 


 


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Publication A8: 

 

Nanoprecipitation of poly(methyl methacrylate)-based 
nanoparticles: Effect of the molar mass and polymer 
behavior 

 

 

 

Igor Y. Perevyazko, Antje Vollrath, Christian Pietsch, 
Stephanie Schubert, Georgy M. Pavlov, Ulrich S. Schubert 

 

J. Polym. Sci., Part A: Polym. Chem. 2012, 50, 2906-2913 

 

 

 

 

 

 

 

 

 

 

 


 


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Publication A9: 

 

Preparation, cellular internalization, and biocompatibility 
of highly fluorescent PMMA nanoparticles 

 

 

Antje Vollrath, David Pretzel, Christian Pietsch, Igor 
Perevyazko, Roberto Menzel, Dieter Weiß, Stephanie 
Schubert, Georgy M. Pavlov, Rainer Beckert, 
Ulrich S. Schubert 

 

Macromol. Rapid Commun. 2012, 33, 1791-1797 

 

 

 

 

 

 

 

 

 

 


 


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