Document [original]

Ionic co-assembly in mixtures of

polysaccharides and surfactants

vorgelegt von

Master of Science Leonardo Chiappisi

geboren in Palermo, Italien

von der Fakultät II - Mathematik und Naturwissenschaften

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

Dr.rer.nat.

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Roderich Süssmuth (Technische Universität Berlin)

Gutachter: Prof. Michael Gradzielski (Technische Universität Berlin)

Gutachter: Dr. Giuseppe Lazzara (Università degli Studi di Palermo)

Tag der wissenschaftlichen Aussprache: 23. Februar 2015

Berlin 2015

The scientist does not study nature because it is useful to do

so. He studies it because he takes pleasure in it, and he takes

pleasure in it because it is beautiful.

Henri Poincaré

Acknowledgements

This is probably the most important section of this thesis, as the work in

this form could have never seen light without the vivid environment of the

Stranski Laboratorium at the Technische Universität Berlin. There is a large

number of people which I want to acknowledge, as all of them have given

their contribution making the last years spent at the TU-Berlin a great time.

First, I want to acknowledge my supervisor, Prof. Dr. Michael Gradziel-

ski. I could find in him the right balance of supervision without being limited

in my research. Thanks for quickly answering my emails (more than 300 in

2013 and 2014), and being in general very present. I enjoyed all, well most,

of the also lengthy discussions, not only those directly concerning the current

research. I learned with him, that you can spend incredible twenty minutes

discussing about the temperature of the north sea in September.

A deep "THANKS!!!" goes to Sylvain Prévost. First, for his patience.

With incredible regularity he was answering my questions, every day, several

times per day over a period of years. To share the office with him definitely

gave a boost to my understanding of scattering experiments and the way

of extracting some useful information from weird-looking curves. I am also

thankful to Ingo, Andreas, Caro, and the many more people who helped me

in these years.

I would like also to thank Miriam and Ninh, who did a great job. It is a

joy to see when the time spent on explanations is transformed into valuable

results.

However, the Stranski-Lab is not only a great place to work at, but is

a place where I could find a number of people whom it was a pleasure to

spend also some free time with. Coffee breaks, cheese-evenings, bierchen or

windsurfing are an important part of the last years. Thanks for that and I

hope that all these activities will continue in the future.

A special thanks goes to Samantha, who every day recharges my batteries

and gives the good mood needed for enjoying life. I thank you for all, even

the shortest, moments spent together.

Finally, I would like to thank all those people who build up the foundation

on which my whole life is based. Thanks for that to my family, which has

continuously supported me, and to my school teachers. I am realizing only

now how important those lessons were.

This cumulative thesis is based on following publications:

•Paper I Complexes of oppositely charged polyelectrolytes and surfac-

tants – recent developments in the field of biologically derived polyelec-

trolytes. L. Chiappisi, I. Hoffmann and M. Gradzielski. Soft Matter,

2013,9, 3896-3909.

•Paper II An improved method for analyzing isothermal titration calori-

metry data from oppositely charged surfactant polyelectrolyte mix-

tures. L.Chiappisi, D. Li, N. J. Wagner, M. Gradzielski. The Journal of

Chemical Thermodynamics,2014,68, 48-52. Supporting information

available at dx.doi.org/10.1016/j.jct.2013.08.027

•Paper III Form factor of cylindrical superstructures composed of glob-

ular particles. L. Chiappisi, S. Prévost, M. Gradzielski. Journal of Ap-

plied Crystallography,2014,47, 827-834. Supporting information avail-

able at dx.doi.org/10.1107/S1600576714005524/fs5062sup1.pdf

•Paper IV Chitosan/Alkylethoxy Carboxylates: A Surprising Vari-

ety of Structures. L. Chiappisi, S. Prévost, I. Grillo, M. Gradzielski.

Langmuir,2014,30, 1778-1787. Supporting information available at

http://pubs.acs.org/doi/suppl/10.1021/la404718e

•Paper V From Crab Shells to Smart Systems: Chitosan–Alkylethoxy

Carboxylate Complexes. L. Chiappisi, S. Prévost, I. Grillo, M. Gradziel-

ski. Langmuir,2014,30, 10608-10616. Supporting information avail-

able at http://pubs.acs.org/doi/suppl/10.1021/la502569p

•Paper VI Towards bioderived intelligent nanocarriers for controlled

pollutant recovery and pH-sensitive binding. L. Chiappisi, M. Simon,

M. Gradzielski. ACS applied Materials & Interfaces,2015,7, 6139-

6145. Supporting information available at http://pubs.acs.org/doi/

suppl/10.1021/am508846r

•Paper VII Co-assembly in Chitosan – Surfactant mixtures: thermo-

dynamics, structures and applications. L. Chiappisi, M. Gradzielski

Advances in Colloid and Interfaces,2015,220, 92-107.

Herewith I ensure that the manuscripts were written by myself with the

support of Prof. Dr. Michal Gradzielski, except for Paper I, where my

contribution was focused on section 4. All experiments presented in the

manuscripts were carried out by myself when not explicitly mentioned in the

thesis. The data analysis was also performed by myself.

iii

While performing the research with focus on polysaccharide / surfactant mix-

tures, I had the opportunity to come in contact with various quite different

topics. Giving a contribution concerning scattering experiments (small-angle

neutron scattering, static and dynamic light scattering), rheology measure-

ments, and self-assembly of surfactants and polymers in general, the following

additional papers were published in peer-reviewed journals.

1. Chiappisi, L.; Lazzara, G.; Milioto, S.; Gradzielski, M. A Quantitative

Description of Temperature Induced Self-Aggregation Thermograms

Determined by Differential Scanning Calorimetry. Langmuir 2012, 28,

17609–17616.

2. Kaur, G.; Chiappisi, L.; Prévost, S.; Schweins, R.; Gradzielski, M.;

Mehta, S. K. Probing the Microstructure of Nonionic Microemulsions

with Ethyl Oleate by Viscosity, ROESY, DLS, SANS, and Cyclic Voltam-

metry. Langmuir 2012, 28, 10640–10652.

3. Inal, S.; Chiappisi, L.; Kölsch, J. D.; Kraft, M.; Appavou, M.-S.;

Scherf, U.; Wagner, M.; Hansen, M. R.; Gradzielski, M.; Laschewsky,

A.; et al. Temperature-Regulated Fluorescence and Association of

an Oligo(ethyleneglycol)methacrylate-Based Copolymer with a Con-

jugated Polyelectrolyte-The Effect of Solution Ionic Strength. J. Phys.

Chem. B 2013, 117, 14576–14587.

4. Inal, S.; Kölsch, J. D.; Chiappisi, L.; Janietz, D.; Gradzielski, M.;

Laschewsky, A.; Neher, D. Structure-Related Differences in the Tempe-

rature-Regulated Fluorescence Response of LCST Type Polymers. J.

Mater. Chem. C 2013, 1, 6603.

5. Inal, S.; Kölsch, J. D.; Chiappisi, L.; Kraft, M.; Gutacker, A.; Janietz,

D.; Scherf, U.; Gradzielski, M.; Laschewsky, A.; Neher, D. Temperature-

Regulated Fluorescence Characteristics of Supramolecular Assemblies

Formed By a Smart Polymer and a Conjugated Polyelectrolyte. Macro-

mol. Chem. Phys. 2013, 214, 435–445.

6. Schwarze, M.; Chiappisi, L.; Prévost, S.; Gradzielski, M. Oleylethoxy-

carboxylate - An Efficient Surfactant for Copper Extraction and Sur-

factant Recycling via Micellar Enhanced Ultrafiltration. J. Colloid In-

terface Sci. 2014, 421, 184–190.

7. Wu, C.; Strehmel, C.; Achazi, K.; Chiappisi, L.; Dernedde, J.; Lensen,

M. C.; Gradzielski, M.; Ansorge-Schumacher, M. B.; Haag, R. Enzy-

matically Cross-Linked Hyperbranched Polyglycerol Hydrogels as Scaf-

folds for Living Cells. Biomacromolecules 2014, 15, 3881-3890.

8. Schwarze, M.; Gross, M.; Buchner, G.; Kapitzki, L.; Chiappisi, L.;

Gradzielski, M. Micellar Enhanced Ultrafiltration of Metal Cations

with Oleylethoxycarboxylate. Journal of membrane science. 2015,

478, 140-147.

It should be mentioned here, that the results concerning the use of oleyl-

ethoxycarboxylates for metal recovery (Papers 6 and 8) are based on the

stimuli-responsive behaviour of alkyl oligoethyleneoxide carboxilic acids. Their

investigation was a relevant part of the thesis and discussed in detail within

the broader field of mixtures with oppositely charged chitosan (Papers IV,

V, and VI) .

Contents

1 Introduction 1

2 Overview on charged polysaccharide – surfactant mixtures

Related to: Soft Matter,2013,9, 3896-3909. 7

3 Thermodynamics of polymer – surfactant mixtures

Related to: J. Chem. Therm.,2014,68, 48-52. 12

4 Structures in stiff-polymer – macroion mixtures

Related to: J. App. Cryst.,2014,47, 827-834. 17

5 Structural variety in chitosan/alkyl oligoethyleneoxide car-

boxylic acid complexes.

Related to: Langmuir,2014,30, 1778-1787 & Langmuir,

2014,30, 10608-10616. 21

6 Uses of Chitosan/Alkyl oligoethyleneoxide carboxylic acid

complexes

Related to: ACS Appl. Mater. Interfaces,2015,7, 6139–

6145. 30

7 Conclusions

Related to: Adv. Colloid Interf. Sci.,2015,220, 92–107. 36

References 39

A Appendix 48

A.1 Satake-Yang ITC fit ....................... 48

A.2 Sasfit form factor for N-core-shell ellipsoids aligned within a

cylinder .............................. 51

List of symbols and abbreviations 53

Abstract

In this thesis, the co-assembly of ionic polysaccharides and oppositely charged

surfactants is investigated, with particular attention on chitosan – alkyl oligo-

ethyleneoxide carboxylic acid mixtures.

The goal of the work is to evidence how the chemical structure of the polysac-

charides influences the binding behaviour of oppositely charged surfactants

and to determined how it affects the resulting structures. A main focus on

modified cellulose and chitosan is given. An approach for extracting the

most important thermodynamic binding parameters, e.g., free energy, en-

thalpy and entropy, from isothermal titration calorimetry is presented and

successfully applied to mixtures of cationically modified cellulose and dode-

cyl sulfate. Moreover, a scattering form factor which is able to describe the

scattering pattern typically found in mixtures of stiff ionic polysaccharide

and globular macroions is derived.

In addition to the general behaviour of polysaccharide – surfactant mix-

tures, a comprehensive and detailed investigation of chitosan – alkyl oli-

goethyleneoxide carboxylic acid complexes is presented. Different aspects of

these mixtures were explored with a main focus on their structural diversity

and on the possibility of controlling them by pH and surfactant molecular

architecture. A surprisingly high variety is obtained by changing the de-

gree of ionization of the surfactant via pH, therefore directly affecting the

strength of interaction with the oppositely charged polymer. The already

large spectrum of accessible structures can be further widened by choosing

amphiphiles with appropriate length of hydrophilic and hydrophobic blocks,

therefore controlling the spontaneous curvature of the surfactant aggregate.

The large control over the possible structures and functionality can fi-

nally be exploited for the formulations of multifunctional systems which can

find application in different fields. As demonstrative examples, their use of

these mixtures as efficient and selective recovery system for organic and inor-

ganic pollutants is demonstrated. Moreover, a simple, one-step layer-by-layer

functionalization of solid surfaces is performed.

In summary, ionic polysaccharide – surfactant mixtures are highly com-

plex systems, being a great challenge to understand, and having a large

potential in different fields.

Zusammenfassung

Die vorliegende Dissertation beschäftigt sich mit der Selbstaggregation von

entgegengesetzt geladenen Polysacchariden und Tensiden, mit einen Schwer-

punkt auf Mischungen aus Chitosan und Alkyl-oligoethylenoxid Carboxyl-

säuren. Insbesondere wurde der Einfluss der chemischen Struktur der Poly-

saccharide, vor allem Chitosan und modifizierte Zellulose, auf das Bindungs-

verhalten von entgegengesetzt geladenen Tenside und auf die resultierenden

Strukturen untersucht. Ein verbesserter Ansatz, um die wichtigsten thermo-

dynamischen Parameter des Bindungsprozesses, z.B., freie Enthalpie, Entro-

pie und Enthalpie, aus isothermer Titrationskalorimetrie zu bestimmen, wird

vorgestellt. Der hergeleitete Formalismus wurde dann erfolgreich angewandt,

um die Bindung von Dodecylsulfat an kationisch-modifizierte Zellulose zu

beschreiben. Desweiteren, würde ein neuer Streuformfaktor hergeleitet, um

typische Streukurven aus Mischungen von steifen geladenen Polysacchariden

und kugelförmigen Makroionen zu beschreiben.

Nachdem das allgemeine Verhalten von Mischung aus Polysacchariden

und Tensiden untersucht wurde, wird eine detaillierte und umfassende Un-

tersuchung von Chitosan und Alkyl-oligoethylenoxid Carboxylsäuren prä-

sentiert. Diese Mischungen wurden aus mehreren Blickwinkeln betrachtet,

mit dem Hauptfokus auf deren strukturelle Vielfalt und die Möglichkeit,

diese durch pH Änderungen oder über die molekular Struktur der Tenside

zu kontrollieren und zu steuern. Die Mischungen von Chitosan und Alkyl-

oligoethylenoxid Carboxylsäuren, die globulare Mizellen bilden, zeigen eine

überraschend große strukturelle Vielfalt, die stark vom Ionisierungsgrad der

Tenside abhängt. Diese Vielfalt an Strukturen kann noch erweitert werden,

indem Tenside mit unterschiedlichen Packungsparametern verwendet wer-

den. Um dies zu erreichen, können Tenside mit unterschiedlichen Längen der

hydrophilen und hydrophoben Blöcke ausgewählt werden.

Die weitreichende strukturelle Kontrolle kann zur Formulierung von mul-

tifunktionellen Systemen genutzt werden. Als Beispiele werden deren Anwen-

dung für eine selektive und effiziente Rückgewinnung organischer und anorga-

nischer Schadstoffe gezeigt, sowie die einfache ein-Schritt-Multischichtfunkti-

onalisierung von festen Oberflächen.

Somit wird gezeigt, dass Mischungen aus entgegengesetzt geladenen Po-

lysacchariden und Tenside hoch komplexe Systeme sind, deren Verständnis

zwar eine Herausforderung darstellt aber ein großes Potential in verschie-

densten Anwendungsbereichen birgt.

Because we don’t think about future generations,

they will never forget us.

Henrik Tikkanen

Introduction

All breakthrough in human life-quality was associated with the mastering of

widespread techniques, e.g., the controlled use of fire, the discovery of agri-

culture or the development of automated machines. The technical progress,

however, is strictly linked to the ability to process raw materials, being them

stones, wood or metals. The effect on everyday life arising from these pro-

gresses were so strong, that the history of mankind is divided in ages named

after the ability to process stone, bronze, or iron.

Similarly, given the enormous impact which polymers have on our every-

day life, the term “age of plastic” was coined to describe the 20th century.1

Despite polymers have been in use since thousands of years, it was just in

1920 that the existence of high molecular weight molecules was described.2

For these discoveries Hermann Stuadinger was awarded with the Nobel Prize

in chemistry in 1953.3Since then the understanding of polymer chemistry

and physics has dramatically increased, as well as their spreading in modern

civilization. Already in 1941, Yarsley and Couzens predicted how polymer-

based objects will be ubiquitous in our everyday life:1

“This plastic man will come into a world of colour and bright

shining surfaces where childish hands find nothing to break, no

sharp edges, or corners to cut or graze, no crevices to harbour dirt

or germs. [...] As he grows he cleans his teeth and brushes his

hair with plastic brushes, clothes himself with in plastic clothes,

writes his first lesson with a plastic pen and does his lessons in a

book bound with plastic.” (Yarsley & Couzens, 1941)

The predictions of Yarsley and Couzens became dramatically true and

nowadays synthetic polymers are present in every single aspect of modern life.

The reason can easily be found in the ease of processing synthetic polymers:

objects with virtually every desired shape, with a broad range of mechanical

properties, covering the whole spectrum of colours can be manufactured at

low cost and in large quantities. Though, all these advantages do not come

without side effects, which were elegantly summarized by Hopewell et al.:4

“Around 4 per cent of world oil and gas production, a non-re-

newable resource, is used as feedstock for plastics and a further

3–4% is expended to provide energy for their manufacture. A

major portion of plastic produced each year is used to make dis-

posable items of packaging or other short-lived products that are

discarded within a year of manufacture. These two observations

alone indicate that our current use of plastics is not sustainable.

In addition, because of the durability of the polymers involved,

substantial quantities of discarded end-of-life plastics are accumu-

lating as debris in landfills and in natural habitats worldwide.”

(Hopewell et al., 2009)

Accordingly, within the perspective of a sustainable economy there is an

increasing search for alternative polymers, which are obtained from renewable

resources and/or are easily degradable. We can distinguish between biopoly-

mers and bio-based polymers (often referred to as bioplastics). According to

the IUPAC definition:5

Biopolymer: Macromolecule (including proteins, nucleic acids,

and polysaccharides) formed by living organisms.

and

Bio-based polymer: [Polymer] derived from the biomass or

issued from monomers derived from the biomass.

In both cases, advantages and disadvantages can be pointed out. Biopoly-

mers, as they are directly formed by living organisms are found in a highly

complex environment and their purification is an essentially complex task,

limiting in several cases the large scale production. These polymers are in-

herently biodegradable, though long times might be required. Differently,

bio-based polymers are synthetic polymers prepared from monomers with

biological origin, or chemical modifications of biopolymers. The term "bio-

based" indicates only the renewable origin of the macromolecules and does

not imply any biodegradability. For instance, the fermentation of glucose is

a major source for bio-monomers, e.g., lactic, succinic or glutammic acid.6If

on one hand the efficiency of the fermentation processes is increasing due to

new genetically modified bacterial strains, the separation of the final prod-

ucts from the fermentation broth is still a major challenge.7Moreover, in my

personal opinion, the use of food stock such as corn or sugar cane represent

an essential ethical limitation for the use of bio-based polymers as environ-

mentally friendly alternative for petrochemicals. An alternative is given by

the fermentation of agricultural waste products. Although the yield is lower

when compared to the use of corn, agricultural waste does not require extra

land and water consumption.8

Over billions of years, nature has developed a large number of highly

complex molecules with the aim of executing very different functions: low-

molecular weight surfactants (mostly phospholipids) spatially delimit the liv-

ing cell and its compartments; oligo- and poly-peptide chains act as catalysts,

transporters or structural elements; the genetic information is safeguarded

and trasmitted by nucleic acids. Carbohydrates, which are found in a large

range of molecular weights, from monosaccharides (ca. 180 g mol−1), disac-

charides (ca. 340 g mol−1), oligosaccharides (500 – 1500 g mol−1) and polysac-

charides (Mw up to several MDa), cover very different functions: starch and

glycogen are the principal energy storages in animals and plats, cellulose and

chitin are the main structural elements of plants and arthropods. Oligosac-

charides, present in glycoproteins and glycolipids, serve as markers for cellular

recognition.

These are just few examples of how nature employs carbohydrates. It is

fascinating to note the width of functions which molecules with a rather

similar chemical structure can cover. Accordingly, carbohydrates represent

the largest fraction of biopolymers, with cellulose and chitin being the most

abundant polysaccharides in nature (estimated annual production of cellulose

by photosynthesis is of 1011 tons9).

Chitin (poly-β(1-4)–D–N-acetylglucosamine) and cellulose (poly-β(1-4)–

D–glucose) are the main structural elements in plants and arthropods, i.e.,

insects, arachnids, and crustaceans. These polymers are chemically rather

similar, the C2 hydroxyl group of cellulose is exchanged with an N-acetyl-

amine moiety (see chemical formulas in Fig. 1.1) in chitin. It is interesting

to note that, despite the strong and evident differences between a tree and a

shrimp, nature has used the same recipe to provide them with a strong struc-

tural element. Although cellulose has been used since the beginning of human

history, e.g., cotton and paper, its first description from a chemical perspec-

Figure 1.1 Chemical structure of, from top to bottom, chitin, chitosan and cellu-

lose.

tive appeared only in 183810 (well before the concept of macromolecule was

established). Chitin was first identified in 1929.11

Both cellulose and chitin are practically insoluble in water, despite their

constituent units glucose and N-acetylglucosamine are highly soluble, 50 and

25 wt%, respectively. The low solubility of the macromolecules is the result

of a complex interplay of forces, e.g., hydrophobic interactions, hydrogen

bridging and van der Waals interactions.12 Moreover, both polymers show a

high tendency to crystallize and, in their natural environment, are found as

a mixture of crystallites and amorphous regions.13,14

A clear advantage resulting from the numerous functional groups on the

saccharidic backbone is the high variety in chemical modifications which can

be performed on cellulose and chitin,14–17 in particular, to overcome their

insolubility in water. For instance, non-ionic cellulose esters, e.g., methyl-

and hydroxypropyl cellulose, are soluble in cold water. At a first glance,

it might seem contradicting that the substitution of an hydrophilic group

(−OH) with an hydrophobic one (−OMe) increases the solubility of the

polymer. This effect can be explained considering the increased free energy

of the solid compound, in which favourable hydrogen bridges are broken and

the crystallinity disrupted. The most common water-soluble derivative of

chitin is chitosan (see chemical formula in figure 1.1). Chitosan is obtained

from the partial or complete deacetylation of chitin, either via enzymatic or

alkaline deacetylation.

Our everyday life is not only heavily influenced by non-ionic polymers,

but also by polyelectrolytes, i.e., polymers with ionizable repeating units,

Figure 1.2 Schematic description of possible arrangements in surfactant – poly-

electrolyte complexes depending on the polyelectrolyte stiffness and surfactant sol-

ubility and packing parameter. Adapted from Soft Matter,2013,9, 3896-3909.

are equally important. The behaviour of this class of polymers drastically

differs from that of nonionic polymers in several aspects. The difference

can be ascribed to the presence of N associated counterions for each polymer

chain, with N being the number of charges on the polymer. The most obvious

consequence of the presence of counterions is a dramatic increase of solubility

of a polyelectrolyte in solvents with a high dielectric constant as compared

to its nonionic counterpart. Moreover, electrostatic interactions are, in many

cases, the dominant forces which control the properties of these systems.

In a number of cases, a synergistic use of polyelectrolytes and surfactants

is desired, e.g., in paints or detergency, in which rheological control of the

formulation, provided by the polyelectrolyte, has to be combined with the

solubilization power and surface activity of surfactants. Accordingly, mix-

tures of polyelectrolytes and surfactants have been subject of studies since a

long time.18,19 The enormous range of properties which can be achieved in

surfactant – polyelectrolyte complexes (SPECs) can be easily envisioned con-

sidering the virtually endless number of combinations of polymers and surfac-

tants, the different conditions of concentration, ionic strength, pH, tempera-

ture, etc., in which these mixtures are prepared. A schematic representation

of few possible structures is given in Fig. 1.2 (adapted from Paper I). It

exceeds the goal of this thesis to discuss the large range of physico-chemical

properties observed in such mixtures. However, there are some general points

of polyelectrolyte – surfactant mixtures which are useful to be discussed to-

gether with the peculiarities of employing charged polysaccharides, as done

in the next chapter.

From time immemorial, man has desired to compre-

hend the complexity of nature in terms of as few

elementary concepts as possible.

Abdus Salam

Overview on charged polysaccharide –

surfactant mixtures

Related to: Soft Matter,2013,9, 3896-3909.

The behaviour of polyelectrolyte – surfactant mixtures strongly depends on

a number of parameters. In addition to some intrinsic properties arising

from the specific chemical nature of the polymer and of the surfactant, some

general points of relevance are:

•Mixing ratio The mixing ratio, i.e., the relative amount of surfac-

tant and polymer units, is probably the most important parameter

governing the behaviour of such mixtures. The mixing ratio is in most

cases defined as the ratio of nominal charges of surfactant and polyelec-

trolyte, i.e., Z= [Surf.]/[PE], or viceversa. The use of nominal charges

provides an alternative for the use of real charges, which are in many

cases difficult to access.

Around equimolarity, i.e., Z= 1, phase separation usually occurs, as

the counterions, which provide to a large extent the solubility of the

single compounds, are no longer associated with the macroions. The

system can separate into two clear liquid phases (coacervation or asso-

ciative phase separation) or into a solid precipitate in equilibrium with

a clear solution (precipitation). In both cases, the complex rich phases

are mesoscopically ordered and can be used as a starting point for the

preparation of highly structured and responsive solid materials.20–23

In the polyelectrolyte excess regime, i.e., for Z < 1, a particularly com-

plex behaviour is observed, with a number of very different structures

formed and properties observed, which depend on the chemical nature

of the components and on the experimental conditions. In this region

of the phase diagram, strong structural changes are observed when Zis

approaching one, as a result of the mutual neutralization. Several cases

are reported in which the viscosity of the system increases over orders

of magnitude upon approaching the phase boundary as a consequence

of an extended network formation with polyelectrolyte – surfactant mi-

celles forming high energy knots.24–27

In the surfactant excess regime, i.e., for Z > 1, single polymer chains

decorated by surfactant micelles are usually found. These solutions

are, in most cases, clear and low-viscous. Despite being less interesting

from a structural point of view, they deserve attention in a number of

household products, which are mostly formulated in this region of the

phase-diagram.28

•Charge density of polyelectrolyte The charge density of the poly-

mer is a second parameter of major importance affecting the behaviour

of mixtures with oppositely charged surfactants. In a primary instance,

the charge density affects the polymer conformation, due to the electro-

static contribution to the persistence length (this point will be discussed

in detail later in this chapter). Moreover, the binding constant found

for a large number of SPECs varies with a ξ2power-law, ξbeing the

linear charge density of the polymer.29 This empirical observation can

be linked to the electrostatic repulsion Ueper unit length lwhich varies

with the square of the charge density:

Ue∝1

r=nee2

rl =ξ2(2.1)

with e0,r, and nebeing the elementary charge, the spacing between

them, and the number of charges per unit length, respectively. The

charge density is then given by e0/r or nee0/l.

Moreover, the polymer charge density also affects the conformational

entropy contribution to the adsorption free energy. In particular, the

conformation of free polymer in solution is that associated with the

highest entropy; when the polymer is adsorbed onto the macroion (a

soft or hard charged colloid), every contact point represents a constraint

reducing the overall polyelectrolyte conformational entropy. Large charge

separation distances (when compared to the Kuhn length) are causing a

minor entropic loss when compared to densely charged polyelectrolytes.

It has to be pointed out here, that the entropic losses from the reduced

conformational freedom of the polymer and from the association of sev-

eral macroions into one complex are largely compensated by the release

of counterions. Accordingly, in most cases the formation of surfactant

– polyelectrolyte complexes is an entropically favoured process.

•Molecular weight of polyelectrolyte The molecular weight of the

polyelectrolyte has a remarkable effect on the solubility, on the rhe-

ological properties, and to a certain extent on the structures found

in polyelectrolytes – surfactant complexes. The higher the molecular

weight of the polymer, the lower the entropy of mixing of the complex

salt with the solvent, thereby simply decreasing the solubility of the

SPECs.30

As mentioned before, the addition of surfactant to a polyelectrolyte so-

lution may lead to a substantial increase in viscosity as a result of the

formation of an extended network. A necessary condition is, however,

that the overlap concentration is reached. This last point is easily ac-

complished by employing polyelectrolytes on saccharidic basis, as they

are mostly characterized by rather high molecular weights, e.g., which

reaches several MDa.

•Total concentration The total concentration also affects the macro-

scopic behaviour of polyelectrolyte – surfactant mixtures. However,

given the complexity of the system, it is everything but trivial to high-

light some general effects. A first important aspect is that the addition

(or removal) of solvent, alters the ionic strength and therefore the elec-

trostatic interactions. Moreover, a dilution of the systems increases the

translational entropy of the solutes. In certain cases this can lead to

the counter-intuitive phenomenon of phase-separation upon dilution of

polyelectrolyte – surfactant complexes.31

As mentioned before, the polymer conformation within the complex is

one of the main structural directing forces, in addition to the spontaneous

curvature of the surfactant aggregates. Moreover, similarly to a puzzle, the

stability of the complexes largely depends on the spatial compatibility of

the different “pieces”, i.e., given by persistence lengths, curvatures, charge

densities, etc.. With this in mind, remarkable differences between synthetic

polyelectrolytes and ionic polysaccharides can be evidenced examining the

effect of electrostatics on the polymer conformation. For most practical uses,

the electrostatic interaction in aqueous environment has to be considered.

The spatial range of interaction is best described with two quantities: the

Bjerrum length λB, i.e., the distance at which the energy of interaction of

two point charges equals their thermal energy, and the Debye length δ, i.e.,

the distance at which the electrostatic potential has decayed of a factor of e.

λB=kBT

4πε0εr

(2.2)

δ=skBTε0εr

2NAe2

0I(2.3)

with kB, T, ε0,εr, and NAbeing the Boltzmann constant, the temperature,

the vacuum dielectric constant, the relative dielectric constant of the medium,

and the Avogadro number, respectively. The ionic strength Iis given by

I=X

ciz2

i(2.4)

where ciis the concentration of the ith species carrying a charge of zie0. The

Bjerrum and Debye lengths in water, at 300 K and at 0.15 mol L−1ionic

strength (physiological conditions) are λB= 0.72 and δ= 0.78 nm, respec-

tively. The fact that they are so close allows a fine tuning of electrostatic

interactions in the sub-nm range, which seems to be a condition for the ex-

istence of higher forms of life.

The persistence length lpof charged polymers can be expressed as the sum

of the contributions of an intrinsic persistence length li

pand an electrostatic

persistence length le

p:32,33

lp≈li

p+le

p(2.5)

The former depends on the rigidity of the polymer backbone, the latter arises

from the electrostatic repulsion between the charged units and accordingly,

varies with the degree of ionization and/or ionic strength.

Most synthetic polyelectrolytes are based on vinyl monomers, e.g., polyacrylic

acids, poly styrenesulfonate, with a rather flexible backbone (lpof polyethy-

lene is 0.65 nm34) and an average charge spacing of 0.25 nm. On the contrary,

polysaccharides are characterized by a stiff backbone35–37 (li

p= 5 −20 nm)

and a spacing between charges of 0.5 nm for the case of one charge on ev-

ery glucosidic unit. Usually, the charge density is lower resulting in ca. 0.1

– 0.05 charges per nanometer. In summary, the conformation of synthetic

polyelectrolytes is mostly determined by the electrostatic contribution to the

persistence length while those of polysaccharides is rather given by their

intrinsic stiffness.

In co-assembled complexes with oppositely charged surfactants, the elec-

trostatic contribution to the persistence length can be neglected in first ap-

proximation as most of the charges are compensated. Accordingly, one ob-

serves a strong reduction in persistence length for synthetic polyelectrolytes

(lp∼le

p) while little variation takes place for ionic polysaccharides (lp∼li

p).

The first consequence is that flexible (synthetic) polyelectrolytes show a

higher affinity to curved surfaces when compared to ionic polysaccharides

with a high intrinsic persistence length. Differently, ionic polysaccharides

have a higher affinity towards flat surfaces, due to the minor conformation

entropy loss upon adsorption. The effect of the high intrinsic persistence

length of polysaccharides on the binding process and on the resulting struc-

tures in mixtures with oppositely charged surfactants will be discussed in

detail in Chapters 3and 4, respectively.

A theory is the more impressive the greater the sim-

plicity of its premises, the more different kinds of

things it relates, and the more extended its area of

applicability.

Albert Einstein

Thermodynamics of polymer –

surfactant mixtures

Related to: J. Chem. Therm.,2014,68, 48-52.

The thermodynamic description of polyelectrolyte – surfactant mixtures is

a fundamental part of a comprehensive understanding of their behaviour.

In this chapter, an approach for extracting the most important thermo-

dynamic parameters characterizing polyelectrolyte–surfactant mixtures from

calorimetric experiments is provided. The function, which best connects the

experimentally accessible information to thermodynamic quantities, such as

Gibbs free energy, is the binding isotherm Θ. The binding isotherm is usually

referred to as the ”curve of the amount of ligands adsorbed as a function of

the concentration or partial pressure of the ligand at a fixed temperature.” 38

The first expression for an adsoprtion isotherm was given by Freundlich in

1909 and is purely based on empirical observations:39

Θ = a p1/b (3.1)

where aand bare system specific parameters, and pthe pressure/concentra-

tion of the adsorbing molecule. Irvin Langmuir first derived an expression

for an adsorption isotherm based on the assumption that the adsorbed and

free gaseous molecules are in a dynamic equilibrium:40,41

Θ = Kp

1 + Kp(3.2)

with K being the equilibrium constant of the binding process. This expression

is derived assuming no interaction between adsorbed molecules, i.e., K is

independent from Θ. The binding constant immediately then leads to the

standard Gibbs free energy of binding through

∆G◦=−RTln K (3.3)

The basic ideas derived in the early 20th century are valid also for com-

plex polyelectrolyte/surfactant mixtures, although clear differences have to

be considered. First, there is a strong interaction between the adsorbed sur-

factant molecules, primarily hydrophobic interactions. Secondly, the poly-

mer “binding sites” cannot always be modelled as a two-dimensional lattice

of identical binding sites. Moreover, a number of additional equilibria, e.g.,

micellization or micelle/polyelectrolyte binding may have to be considered.

In the simplest, but still realistic approach, the polymer is modelled as a

one-dimensional array of binding sites and only nearest neighbor interactions

between the surfactant molecules are considered. Such an approach leads to

the commonly known Satake-Yang binding isotherm,42 named after Satake

and Yang which derived the expression reported in Eq. 3.4 in 1976. However,

the same problem had been solved six years earlier by Gerhard Schwarz.43

The model is based on the presence of three equilibria: the non-cooperative

binding with equilibrium constant K, the cooperative binding with equilib-

rium constant Ku and the equilibrium between non-cooperatively and coop-

eratively bound surfactant, with u being the cooperativity parameter.

Θ = 1

2 1 + KuCf−1

p(KuCf−1)2+ 4KCf!(3.4)

Cfis the free surfactant concentration. A schematic representation of the

three equilibria is given in Fig. 3.1.

The Satake-Yang model, with its assumptions of a linear array of binding

sites and a 1:1 stoichiometry, is particularly suited for the description of

polysaccharide – surfactant mixtures for the following reasons:

•The intrinsic persistence length is larger than the unit repeating dis-

tance, validating the assumption of linear array, at least on the length

scale of neighbour interactions.

Figure 3.1 Schematic representation of the cooperative and non-cooperative bind-

ing as well as the transition between cooperatively and non-cooperatively bound

surfactant molecules. Reprinted from J. Chem. Therm.,2014,68, 48-52, Copy-

right 2014, with permission from Elsevier.

•The 1:1 stoichiometry, i.e., one surfactant binds to one binding site,

can be supported with simple geometrical considerations. The area per

charge of a surfactant molecule and that of a saccharide unit are com-

parable. For instance, the headgroup area of sodium dodecyl sulfate is

found to be between 60 and 55 Å2, with a ionic strength between 25 and

200 mM, respectively.44 In the crystalline form, i.e., when all charges

are compensated, an effective headgroup area of 19.4 Å2is found.45

Similar areas per charge are also found in ionic polysaccharides. Con-

sidering that a saccharide unit occupies an area of 5×5Å2, an area

per charge of 25 and 75 Å2is found, provided every or every third unit

is charged.

Within the Satake-Yang formalism, three states for the surfactant molecules

are foreseen: free, non-cooperatively and cooperatively bound. Similarly, the

polyelectrolyte binding site can be free, non-cooperatively and cooperatively

occupied. The fraction of occupied binding sites which in Eq. 3.4; the fraction

of bound sites which are non-cooperatively occupied is given by43

χ=KCf

λ2

1−Θ

Θ(3.5)

with λ0being

λ0= 0.51 + KuCf+q(KuCf−1)2+ 4KCf(3.6)

Any variation of an extensive property Xof the system can be expressed as:

dX=X

Xidni(3.7)

Figure 3.2 Binding heat (on the left) of sodium dodecyl sulfate to a cationiccally

modified cellulose (JR-400) as a function of total surfactant concentration for dif-

ferent total binding site concentration. Lines are best fit curves obtained using Eq.

3.10. On the right, the resulting binding isotherms are reported.

where niand Xiare the moles and the partial molar quantity of the ith

species. A comprehensive description of the system should take into account

all six species present (in addition to the solvent), three states for the surfac-

tant and three states for the polymer binding sites. However, Eq. 3.7 can be

simplified, if the changes of the partial molar quantities of the solvent and

the polymer binding sites are included in those of the surfactant:

dX=Xfdnf+Xncdnnc +Xcdnc(3.8)

with the pedices f,nc and crepresenting the free, non-cooperatively and

cooperatively bound surfactant, respectively. With this premise, the heat

exchanged during the binding process, which can be measured by isotherm

titration experiments, is given by:

Q=Hfdnf+Hncdnnc +Hcdnc≃∆nfHf+ ∆nncHnc + ∆ncHc(3.9)

The same approach can be used for the description of other experimentally

accessible quantities, e.g., the volume determined by densitometric experi-

ments. In Paper II, from Eqs. 6 to 13 the derivation of an analytical ex-

pression for the description of ITC experimental data for systems following

the Satake-Yang model is reported (see Paper II for symbols) that yields:

Q=Cp(dΘ/dCf)

Cp(dΘ/dCf)+1∆H−Θ∆∆H◦(dχ/dΘ)(3.10)

Table 3.1 Thermodynamic binding parameters obtained for the adsorption of

sodium dodecyl sulfate on a cationically modified cellulose (JR-400) for different

polymer concentrations. The binding site concentration Cpis given in 10−3mol

L−1, the standard binding free energies and enthalpies in 103J mol−1and the

standard binding entropies in J K−1mol−1.

Cp∆G◦

nc ∆G◦

c∆∆G◦∆H◦

nc ∆H◦

c∆∆H◦∆S◦

nc ∆S◦

c∆∆S◦

0.1 -29.3 -33.9 -4.6 5.0 -8.3 -13.3 111 83 -28

0.5 -26.9 -33.3 -6.4 8.8 -5.9 -14.7 116 89 -27

0.8 -27.5 -33.9 -6.4 5.9 -5.8 -11.7 108 91 -17

A python-written program to perform the fitting procedure is given in

Appendix A.1. The application of the model derived to sodium dodecyl sul-

fate binding to a cationically modified cellulose (JR-400) is shown in Fig. 3.2.

The model is able to describe all the features of the calorimetric signal. Ac-

cordingly, non-cooperative and cooperative binding heats and constants can

be determined (see Table 3.1 and Table 1 of Paper II), shading light on

the thermodynamic origin of the binding process. Moreover, the adsorption

isotherms can be easily obtained from the binding constants using Eq. 3.10

(example curves reported in Fig. 3.2, right).

For a total polymer unit concentration of 0.8 mM, a non-cooperative

and cooperative binding enthalpy of respectively 5.9 and -5.8 kJ mol−1were

found, leading to a ∆∆H◦=−11.7kJ mol−1. This value is in good agree-

ment with the micellization enthalpy found for sodium dodecyl sulfate in

water at 35 ◦C,46 corroborating the hypothesis of hydrophobic interactions

among the surfactant tails as origin of the cooperativity. Moreover, both co-

operative and non-cooperative adsorption process are entropically favoured,

with ∆S◦

nc = 108 J K−1mol−1and ∆S◦

c= 91 J K−1mol−1. While the cooper-

ative binding entropy is expected to be positive, due to the release of bound

counterions and water, the positive ∆S◦

nc indicates that the vertical surfac-

tant – polyelectrolyte interactions are not solely of electrostatic origin. It

has to be mentioned here, that the non-cooperative adsoprtion process takes

place at low surfactant concentration, where the uncertainty in the titration

experiments is highest and in which a correct account for dilutions heats is

not trivial. In addition to accurate experimental values obtained at low sur-

factant concentrations, titrations performed at different temperatures which

reveal also the variations in heat capacity, would help in the interpretation

of the data.

On Mondays, Wednesdays, and Fridays we use the

wave theory; on Tuesdays, Thursdays, and Satur-

days we think in streams of flying energy quanta or

corpuscles.

William Henry Bragg

Structures in stiff-polymer – macroion

mixtures

Related to: J. App. Cryst.,2014,47, 827-834.

As discussed in Chapter 2, ionic polysaccharides retain their stiffness also

within the complex with oppositely charged surfactants. The most obvious

consequence is that, provided the inverse curvature of the macroion is smaller

than the intrinsic persistence length of the polysaccharides, an efficient wrap-

ping does not take place. An favourable complexation can, however, be

obtained when a stiff polymer and small globular particles co-assemble in

superstructures with cylindrical symmetry.

Several examples of polysaccharide complexes with charged soft and hard

macroions with one-dimensionally ordered suprastructrues can be found in

literature.47–51 In Fig. 4.1 a cryo-TEM image of suprastructures obtained in

10 nm silica nanoparticles / chitosan mixtures is shown.50

In addition to electron microscopy, the fine details of such structures

can be evidenced by small-angle neutron and X-ray scattering, provided a

suitable model is available. In particular, due to the low-contrast conditions

of polysaccharides with respect to D2O and H2O (for SANS and SAXS), in

many cases the contributions of the polymers to the scattering curves are

weak and in a first instance negligible.49,50 Accordingly, these structures can

be described with a model of N-aligned spherical (or spheroidal) particles

Figure 4.1 Cryo-TEM image of 0.01 g/L Chitosan and 10 g/L 10 nm silica

nanoparticles, acetic acid buffer at 0.5 M total acetic acid and pH = 4.58 (top).

Schematic representation of the structures found in solution, with characteris-

tic lengths (bottom). Adapted with permission from ACS Macro Lett., 2012, 1,

(Fig. 4.2, top). However, contrast variation experiments, in particular in

neutron scattering, allow to focus also on the behaviour of the stiff polymer

in the complex. For this case, a more complex model of N-aligned particles

contained in a cylinder is needed (Fig. 4.2, bottom). Both models were

derived in Paper III and applied to chitosan – alkyl oligoethyleneoxide

carboxylic acid mixtures (Paper IV and V). Briefly, the scattering form

factor of a cluster of Nobjects is given by:53

P(q, N) = *

k=1

Ak(q)e−i~q·~rk

2+(4.1)

where Ak(q)is the scattering amplitude of the kth particle, located at a

position ~rk;~q is the scattering vector with modulus of:

q=2πnsin θ

2

λ(4.2)

with n being the refractive index (n = 1 for neutrons) and θthe scattering

angle. The angle brackets represent the spatial average over all possible

orientations. Eq. 4.1 can be solved applying the Euler relation for complex

numbers and leads to the following solution for the case of Naligned identical

particles, characterized by a scattering amplitude Aob(q):52

P(q, N) = 1−cos (z N)

1−cos zA2

ob(q, α)(4.3)

Figure 4.2 Schematic representation of the model on Naligned spheres, spaced

by a distance D (top) and of Naligned spheres, spaced by a distance D, contained

in a cylinder of radius Rcand length Lc(bottom). Adapted from Ref. 52 with

permission of the International Union of Crystallography.

with z=qD cos α, where Dis the modulus of the particle center-to-center

distance vector ~

Dand αis the angle formed by ~q and ~

For the case of Naligned identical particles, characterized by a scattering

amplitude Aob(q), contained in a cylinder with scattering amplitude Acyl(q),

the scattering intensity is:52

Itot(q, N) = INob−Nob(q, N) + ICyl−Cyl(q) + INob−Cyl(q, N)(4.4)

where INob−Nob(q, N)is obtained as the product of Eq. 4.3 and (ρob −ρcyl)2.

ICyl−Cyl(q)is given by:

I(q)Cyl−Cyl =(ρcyl −ρ)2A2

cyl(q, α)(4.5)

and

INob−Cyl(q, N) = 2(ρob −ρcyl)(ρcyl −ρ)hAob(q, α)Acyl(q, α)g(N, z)i(4.6)

with

g(N, z) = cos z N

2sin z N +z

2−sin z

2hsin z

2i−1(4.7)

Features of the resulting curves are, from high to low-q, an increase in

intensity, arising from the form factor of the spheroidal particle; the appear-

ance of an asymmetric correlation peak at qp≃2π/D, whose intensity and

sharpness increases with increasing number of particles, and a large q−1-

Figure 4.3 On the left, the normalized particle scattering form factor and effective

structure factor, defined in Eq. 6 of Paper III, are reported as a function of the

magnitude of the scattering vector, q, for objects with increasing number of spheres

with radius of 3 nm with N= 1, 2, 3, 5 and 10 spaced by a center-to-center distance

Dof 8 nm. On the right, normalized particle scattering form factor from an object

made up of ten spheres of radius 3 nm, with D= 8 nm included in a cylinder

with radius of 3 nm and length L=N·D= 80 nm, is reported for different

contrast conditions as a function of q. Scattering contrasts are in arbitrary units.

A schematic representation of the objects is given in the inset. Reproduced with

permission of the International Union of Crystallography.

regime arising from the 1-dimensional symmetry of the object which persists

till q≃2π/Lc. Typical scattering curves are reported in Fig. 4.3 (and in

Figures 2 and 7 of Paper III), which show the sensitivity of the obtained

scattering curves to Nand the contrast conditions. In particular the latter

renders SANS experiments very interesting to characterize such structures.

It is noteworthy, that the shape of the aligned objects is not limited to

spheres, but every particle sharing a rotational axis with the cylinder can

be used. For instance, the model was applied to the complexes formed by

chitosan and alkyl oligoethyleneoxide carboxylic acids, self-assembling into

core-shell ellipsoidal micelles.48,49 A detailed description of these systems is

given in next Chapter.

There is strength in numbers. When the bricks stick

together, great things can be accomplished.

Steve Klusmeyer

Structural variety in chitosan/alkyl

oligoethyleneoxide carboxylic acid

complexes.

Related to: Langmuir,2014,30, 1778-1787 &

Langmuir,2014,30, 10608-10616.

In the previous chapters some peculiarities of polysaccharides were evidenced,

in particular the effect on the binding process in mixtures with surfactants

and on the resulting structures. Virtually all naturally occurring ionic polysac-

charides are negatively charged, e.g., hyaluronate, carrageenans, alginate,

etc.. Still, when working with mixtures of polyelectrolytes and oppositely

charged surfactants, the use of polycations has several advantages, the most

important being the lower toxicity of anionic surfactants, as compared to

their cationic counterparts.

Nature does not provide cationic polysaccharides in large quantities. How-

ever, chitosan can be readily obtained from chitin, the second most abundant

biopolymer after cellulose. Chitin is mostly extracted from crustaceans shells,

i.e., a waste product of the food industry whose availability is estimated at

ca. 60,000 - 80,000 tons per year.54 Given the definitions in the first chap-

ter, chitosan is not a biopolymer but rather a bioderived polymer, although

few fungi can synthesize chitosan directly.55,56 It maintains the character-

istics of biopolymers, e.g., renewable origin, high biodegradability and low

toxicity for complex life forms. In addition, its pronounced antiinflammatory

and antibacterial activities made this polymer particularly interesting for the

medical industry.57,58

Accordingly, the interaction of chitosan with oppositely charged surfac-

tants has attracted large interest in the past decades. Unfortunately, com-

plexes of chitosan and strong anionic surfactants, e.g., sodium dodecyl sul-

fate, are characterized by a pronounced low solubility.59–66 While this prop-

erty can be exploited for the preparation of highly stable capsules,59,63 it

limits the field of uses of such mixtures.

A higher solubility of the complexes can be achieved by choosing a more

hydrophilic surfactant. In addition, the use of a surfactant which shows a

stimuli-responsive behaviour is a key requirement for the formulation of re-

sponsive supramolecular complexes. These considerations led to the choice

of alkyl oligoethyleneoxide carboxylic acids. The used surfactants are, here-

after abbreviated as CiEjAc, with i and j being the number of carbon atoms

and ethyleneoxide moieties, respectively; Ac represents one CH2COOH unit.

This class of surfactants shows a higher solubility as aliphatic acids, a pH-

dependent behaviour given by the carboxylic headgoup, and a responsiveness

towards temperature given by the oligoethyleneoxide moieties. A further ad-

vantage is given by the large choice of hydrophilic and hydrophobic block

lengths, which allows to largely vary the packing parameter and the solubil-

ity of the surfactant.

In this work, surfactants with different alkyl chain length (C8, C12, and

C18:1), and varying number of ethyleneoxide units (2.5 – 10) were employed

at different pH conditions (3.5 – 5.0). This pH-range was chosen as the de-

gree of ionization of the surfactant is largely changed while that of chitosan

remains almost constant (see Fig. 5.1). A summary of physico-chemical prop-

erties of the surfactants, i.e., critical micelle concentration, headgroup area

requirement, packing parameter, etc., is given in Table 2 of Paper V.

The small-angle neutron scattering patterns arising from mixtures of chi-

tosan with C12E10Ac, C8E5Ac, and C12E4.5Ac at pH = 4, and with C18:1E9Ac

at different pH are reported in Fig. 5.2 (or Fig. 7 of Paper IV and Fig. 3 of

Paper V). In all cases, strong structural changes are observed either when

the degree of ionization of the surfactant is changed or by changing its molec-

ular structure. In particular, C18:1E9Ac and C12E10Ac, and C8E5Ac form

globular micelles at the given experimental conditions; C12E4.5Ac is found

as a mixture of cylindrical and vesicular aggregates.67 All experiments were

carried out in a 0.2 M acetic acid buffer, in excess of chitosan. The mixing

ratio, Z, is defined as the ratio of surfactant molecules over the glucosamine

Figure 5.1 On the left, degree of ionization of a 1 wt% C18:1E9Ac (open circles)

and of a 1 wt% chitosan solution (open squares) in H2O as a function of pH obtained

from potentiometric titration. The box indicates the investigated pH range.

units of chitosan.

Effect of surfactant molecular architecture The choice of C12E10Ac,

C8E5Ac, and C12E4.5Ac allows a systematic investigation of the effect of the

surfactant on the resulting structures. First, the surfactant solubility is var-

ied keeping the packing parameter constant, C12E10Ac vs. C8E5Ac, and,

secondly, the surfactant curvature is changed keeping the solubility constant

C12E10Ac vs. C12E4.5Ac (see parameters reported in Table 2 of Paper V).

Small-angle neutron and light scattering experiments reveal a similar be-

haviour for all globular micelles at pH = 4.0: at low surfactant concentration

the polymer chains are loosely decorated by surfactant micelles; at interme-

diate surfactant concentration the formation of linearly ordered aggregates is

observed and their scattering pattern can be described with the models de-

rived in Chapter 4; a further addition of surfactant causes the 1D structures

to collapse into a core-shell suprastructure with a core formed by densely

packed micelles surrounded by a stabilizing chitosan chain.

Highly different scattering patterns are obtained when chitosan and a

vesicle-forming surfactant (C12E4.5Ac) are mixed. The curves are character-

ized by a large q−2-law (typical for systems with a 2-dimensional extension,

e.g., bilayers), the presence of a correlation peak at qp= 0.095nm−1, and

a sudden change in slope at q∼0.09nm−1. The curves can be described

with a model of multiwalled vesicles in the presence of cylindrical surfac-

tant aggregates (see details in Paper V). The one-step formation of such

Figure 5.2 Top: SANS intensities for mixtures of C12E10Ac, C8E5Ac and

C12E4.5Ac and chitosan at 0.3 wt% chitosan at different Z= [−]/[+] and pH

= 4. Straight lines represent best fits according to different models (see Paper

V). Curves are scaled by successive factors of 3. Reprinted with permission from

Bottom: SANS intensity as a function of magnitude qof the scattering vector for

mixtures of C18:1E9Ac and chitosan at 0.3 wt% chitosan at different pH and chi-

tosan to surfactant ratio Z= [−]/[+]. Straight lines represent best fits according

to different models (see Paper IV). Curves are scaled by successive factors of 30,

10 and 20 for curves at pH 3.5, 4.0 and 5.0, respectively. Reprinted with permission

Figure 5.3 Structural phase diagram of mixtures of chitosan – C18:1E9Ac micelles

as a function of pH and mixing ratio and constant chitosan concentration of 0.3

wt% (in a 0.2 mol kg−1acetate buffer). Full lines represent the ranges of the

different structural arrangements. Adapted with permission from Langmuir,2014,

multiwalled vesicles can be exploited for a polymer-surfactant layer-by-layer

surface modification, as shown in Chapter 6. The corresponding scattering

patterns are reported in the upper part of Fig. 5.2 and in Paper V.

In summary, the spontaneous shape of the surfactant aggregate is retained

within the complex, and chitosan provides a framework for the supramolecu-

lar aggregation. Moreover, the surfactant spontaneous structure is also found

when the complexes are separated out of solution, which were analysed by

small-angle X-ray scattering (see Fig. 5 of Paper V). This provides an easy

route for the formulation of solid materials, with an high mesoscopic order

controlled by the molecular structure of the surfactant.

Effect of pH Varying the pH of the solution between pH 3.5 and 5.0 di-

rectly affects the degree of ionization of the surfactant with little changes in

that of the chitosan (see Fig. 5.1). Moreover, for the case of C18:1E9Ac the

micellar structure shows only minimal changes upon pH increase within the

investigated pH-range.68 These premises allow for the investigation of the

effect of the strength of the surfactant/polymer interaction on the resulting

structures with minimal side effect interferences. From the scattering curves

shown in Fig. 5.2 (bottom), and the light scattering results reported in Paper

Figure 5.4 SANS intensity as a function of magnitude qof the scattering vector

for mixtures of C12E4.5Ac and chitosan at 0.3 wt% chitosan at different pH and

chitosan to surfactant ratio Z= [−]/[+] = 0.5. On the right the curves are scaled

by successive factors of 3. Experiments were performed on D11 at the Institut

Laue-Langevin with a wavelength of λ= 6 Å, sample-to-detector distances of 1.2,

8 and 20 m with respective collimation of 5.5, 8.0 and 20.5 m.

IV, a comprehensive structural phase diagram can be constructed (see Fig.

5.3). As explained in detail in Paper IV, this structural evolution is a direct

consequence of the delicate balance of forces, which are either pH-dependent

(the binding of surfactant micelles and polymer chain) or pH-independent,

such as the bending of the stiff chitosan. The transition between the dif-

ferent structures can be employed for the formulation of highly responsive

delivery/recovery systems as shown in the next Chapter.

Even stronger structural changes are observed by pH-changes in chitosan

– C12E4.5Ac mixtures,with Z= [−]/[+] = 0.5as reported in Fig. 5.4 (Un-

published data). With increasing pH, one observes:

•An increase in scattering intensity at low-q, with a jump between pH

4.0 and 4.3.

•The scattering curves measured at higher pH are approaching a plateau

at low-q.

•An evident increase of the correlation peak at q≈0.9nm−1. The peak

becomes also broader and shifts to smaller qvalues with increasing pH.

•A decrease in scattering intensity at intermediate scattering vectors

(0.02 < q/nm−1<0.06), as commonly found for objects with increas-

ing compactness (and therefore showing minor fluctuations in the scat-

tering length density at a length scale of 2π/q).

To interpret these results it has to be recalled that C12E4.5Ac aggregates

themselves undergo strong structural changes with increasing pH.67 At low

pH a mixture of cylinders and large vesicles is found. The vesicles decrease in

size with increasing pH. Above pH 4.5 a transition towards globular micelles

is found. As shown before, multiwalled vesicles are formed at Z= 0.5and

pH = 4. With this premises, the scattering curves presented in Fig. 5.4 can

be interpreted as follows:

•At pH = 3.8, chitosan and C12E4.5Ac weakly interact. A mixture of

cylindrical aggregates and vesicles with low bilayer multiplicity is prob-

ably formed, as indicated by the relatively high scattering at interme-

diate q, and the presence of a little pronounced correlation peak at

q∼0.9nm−1.

•Upon increase of the pH, the interactions become stronger, the cor-

relation peak becomes more pronounced, the scattering intensity at

intermediate qdecreases while that at low-qincreases. Moreover, at

pH 4.3, objects with a rather well defined size are formed, as indicated

by the oscillations at q∼0.1nm−1. Presumably, multiwalled vesi-

cles, with increased bilayer multiplicity and decreasing size are formed

between pH 4.0 and 4.3.

•The curves recorded at higher pH (4.6 and 5.3) show a pronounced

broadening of the correlation peak and a shift towards smaller q, which

could arise from a transition from a 2-dimensional order (stacked lamel-

lae) to a 3-dimensional one (densely packed micelles). The transition

of the surfactant aggregates from a bilayer structure towards globular

aggregates upon increasing degree of ionization was shown by other

authors to occur at pH 4.5.67

Effect of ionic strength It was shown in several studies that the total

ionic strength strongly affects the ionic co-assembly of polymers and surfac-

tants.66,69,70 The general effect is a weakening of the surfactant – polymer

interactions,66,69 due to a screened electrostatic interaction and to a reduced

entropic gain from counterion release. Accordingly, several examples show

that upon reaching rather high ionic strengths (ca. 1 M) the complexes can

be dissolved into their components.70 Moreover, an increasing ionic strength

may also alter the structural behaviour of the complexes,70 either as a con-

sequence of dehydration of the supraaggregates or because it alters the cur-

vature of the surfactant aggregate.

Figure 5.5 SANS intensity as a function of magnitude qof the scattering vector

for mixtures of C18:1E9Ac and chitosan at 0.3 wt% chitosan at pH = 4, increasing

chitosan to surfactant ratio Z. Acetic acid concentration was 0 mM. Curves are

scaled by successive factors of 1.5. Experiments were performed on D11 at the

Institut Laue-Langevin with a wavelength of λ= 6 Å, sample-to-detector distances

of 1.2, 8 and 20 m with respective collimation of 5.5, 8.0 and 20.5 m.

The effect of the total ionic strength on the co-assembly of chitosan and

C18:1E9Ac was investigated by preparing mixtures at different buffer con-

centration or by the addition of sodium chloride. Apparently contradicting

results are found in these mixtures. In Fig. 5.5 the scattering patterns of

chitosan – C18:1E9Ac, with a total concentration of acetic acid of 0 mM and

at pH = 4.0 adjusted with a minimal amount of HCl are shown. The depen-

dence of the molecular weight from the mixing ratio for complexes prepared

at different buffer concentration is shown in Fig. 5.6. These results indicate

that the addition of salt simply shifts the co-assembly process towards lower

mixing ratios, without affecting the observed structures.

Further insight is obtained when the dependence of the molecular weight

of the complex is reported as a function of the added salt concentration (see

Fig. 5.6 right). A similar behaviour, showing a maximum binding affinity is

reported for other polyelectrolyte – protein71,72 or polyelectrolyte – surfactant

complexes.73–75 The non-monotonic trend indicates that more than one effect

influences the co-assembly process.

As mentioned before, at high ionic strength the interaction between sur-

factant micelles and polyelectrolyte is strongly reduced as a consequence of

the decreasing electrostatic interactions and entropy gain of freeing the coun-

Figure 5.6 On the left, the molecular weight as determined from light scattering

curves (for details refer to the experimental section of Paper IV) for mixtures of

C18:1E9Ac and chitosan at 0.3 wt% chitosan at pH = 4 at different chitosan to

surfactant ratio Zand acetic acid concentration. pH was adjusted by addition of

HCl. On the right, the molecular weight determined for mixtures of C18:1E9Ac

and chitosan at 0.3 wt% chitosan, pH = 4.5, Z= [−]/[+] = 0.2, acetic acid

concentration of 0 mM and variable sodium chloride concentration is reported.

Experiments were performed by Ninh Tran Dang during his “Forschungspraktikum”

supervised by the author.

terions. Differently, an explanation for the salt-induced co-assembly is not

trivial and the arguments reported in literature are system-specific72,73,75 and

cannot be applied to these mixtures. An initial hypothesis is that the vertical

micelle – polymer interaction steadily decreases with increasing salt concen-

tration; however, for the formation of large, dense supramolecular aggregates

a collapse of the decorated polymer chains is needed. This collapse might

be hindered by the micelle– micelle or polymer–polymer electrostatic repul-

sions and can take place only above a certain ionic strength. This example

demonstrates the complexity of this systems, with a multitude of relevant

forces influencing the co-assembly process.

As shown in the next chapter, these systems can be exploited for different

purposes by employing surfactants with the most suitable packing parameters

and controlling the co-assembly process via pH.

A complex system that works is invariably found to

have evolved from a simple system that worked.

John Gall

Uses of Chitosan/Alkyl

oligoethyleneoxide carboxylic acid

complexes

Related to: ACS Appl. Mater. Interfaces,2015,7,

6139–6145.

The high structural variety found in mixtures of chitosan and oppositely

charged alkyl oligoethyleneoxide carboxylic acid forming globular micelles is

summarized in the phase diagram reported in Fig. 5.3 and in Paper IV.

The variation of the block length of the surfactants (at a given a packing

parameter p∼0.3) does shift the structural phase boundaries but not their

overall behaviour.

By varying the pH from 3.5 to 5.5, keeping the total acetic acid/acetate

concentration of 0.2 mol kg−1, chitosan concentration of 0.3 wt%, and Z=

[−]/[+] = 0.2constant, all structures formed in mixtures with C18:1E9Ac are

probed. In particular, the mobility of the surfactant micelles is expected

to strongly decrease with increasing pH, as they become incorporated into

the supramolecular complex. Their mobility on a time and space scale of

ms and µm can be probed by fluorescence correlation spectroscopy (FCS),

provided a fluorescent dye is permanently solubilized within the micellar core.

Figure 6.1 On the left: fluorescence autocorrelation functions with 5 nM Nile

red recorded for chitosan - C18:1E9Ac mixtures, with Z= [−]/[+] = 0.2, constant

chitosan concentration of ∼0.3 wt% and variable pH (top) and for C18:1E9Ac

1 wt% solutions at variable pH (bottom). On the right: ratio of fast and slow

diffusion coefficients (top) and relative amplitude of the fast mode as a function of

pH (bottom). FCS experiments were performed by Miriam Simon in collaboration.

This was achieved by using Nile Red, whose binding constant to C18:1E9Ac

is estimated to be 1.5±0.2µM−1. The obtained correlation functions are

reported in Fig. 6.1 and in Paper VI. The incorporation of the surfactant

micelles in the complex can be clearly seen in the appearance of a second, slow

mode for pH >4. Moreover, the transition between the different structural

phase regions can be seen in the change of slope of the relative amplitudes

of the slow and the fast mode on pH (see Fig. 6.1).

This pH-dependent binding/release of the surfactant micelles can be ex-

ploited for the formulation of release and recovery systems. In particular,

the use of chitosan – C18:1E9Ac complexes for the recovery of organic and in-

organic pollutant is presented in Paper VI. The recovery mechanism works

Figure 6.2 On the top, photos of chitosan - C18:1E9Ac solutions containing Su-

dan Red (10 µM) and methylene blue (10 µM) with Z= [−]/[+] = 0.2, chitosan

concentration of ∼0.3 wt% and variable pH, before and after centrifugation are

reported. On the bottom, the corresponding UV-Vis spectra are given.

as follows: i) the target compound is bound to the surfactant micelle or

solubilized within its hydrophobic core; ii) given the pH is sufficiently high,

the micelles are incorporated in the supramolecular complex and iii) can be

centrifuged out of solution. This mechanism becomes clearly visible, when

chitosan – C18:1E9Ac complexes are employed for the separation of a mixture

of an hydrophobic (Sudan red) and hydrophilic (methylene blue) dye. After

centrifugation, an initially purple solution is separated into a red precipitate

and a blue supernatant, as shown in Figure 6.2. This process can be applied

also to metal ions bound to the surfactant headgroup or involved in an hy-

drophobic complex with an appropriate ligand, as demonstrated in detail in

Paper VI. The whole process is highly selective, with respect both to the

Figure 6.3 Top, frequency shift ∆fand dissipation changes ∆Dfor different

overtones during layer formation from chitosan – C12E4.5Ac, with chitosan con-

centration of 0.3 wt% and Z= [−]/[+] = 0.4is reported. Bottom, AFM images of

the QCM-D crystal before adsorption (0 min), after equilibration with the complex

solution (∼100 min), and after water rinse (∼600 min). QCM-D measurements

were performed on a E1 instrument from Q-Sense, at 25.00(2) ◦C and with a flow

rate of 0.1 mL min−1. For the experiments a Q-Sense QSX303 crystal was used.

The fit with the Voigt-model was performed with the Q-Tools suite provided by

Q-Sense, using a film density of 1.2 g cm−3, and a solvent density and viscosity of

0.997 g cm−3and 0.9 mPas, respectively. AFM scans were performed on a Cypher

AFM (Asylum Research) in air and tapping mode by Jana Lutzki.

hydrophilicity of the pollutant (in the case of organic molecules) as well as

to the metal type and valence (in the case of heavy metals). For the latter

case, the affinity can be tuned by the addition of an appropriate ligand.

The multiwalled vesicles, found in chitosan – C12E4.5Ac mixtures, can

be envisioned as carrier for hydrophilic molecules with release times which

depend on the wall thickness, i.e., on the mixing ratio. However, another

interesting approach is their use as precursors for “layer-by-layer” function-

alization of surfaces. The simple idea consists of adsorbing the multilayered

vesicles on a surface with their subsequent rupture and coverage of the sur-

face. The adsorption process can be followed by quartz crystal microbalance

with dissipation monitoring (QCM-D) and the morphology of the surface at

different stages by atomic force microscopy (AFM). A preliminary experi-

ment is shown in Fig. 6.3 and serves as a proof of principle.

The used protocol foresees an initial period in which the layer is in con-

tact with the multiwalled vesicle solution, followed by a rinsing period with

the buffer solution in which the complexes were prepared, and, finally, a rinse

with pure water. When the crystal is in contact with the chitosan–C12E4.5Ac

solution, one observes a strong decrease in frequency and increase in dissi-

pation, coupled with a strong splitting of the overtones (see Fig. 6.3 top).

Such a behaviour is commonly found during the adsorption of vesicles,76 as

they are large and soft (high ∆fand ∆Dsignals) and inhomogeneous in the

z-direction (splitting of the overtones). The AFM image taken at this stage

clearly shows the presence of spherical particles with a radius of ca. 200 nm,

in perfect agreement with the structural picture of the multiwalled vesicles

obtained by SANS and given in Paper V.

The subsequent rinse with buffer solution causes an increase in frequency

and decrease in dissipation, together with a reduced splitting of the signals,

indicating a pronounced mass loss, which can be ascribed to the rupture of

the vesicles and the formation of a homogeneous multilayer on the surface. A

layer thickness of ∼30 nm is obtained when the QCM-D signal is described

with the Voigt model for viscoelastic films.77 This value is in good agreement

with an expected film made up of 5 chitosan – surfactant layers, each 6 nm

thick (see Table 3 in Paper V). The final rinse with water, where chitosan is

insoluble while the surfactant is highly charged, causes a a further mass loss.

The signals of the frequency shift from the different overtones are perfectly

superimposed, while a small albeit significant splitting is observed in the

dissipation signal, with the higher overtones showing a smaller dissipation.

This indicates the presence of an hydrophobic outermost layer, given by the

neutral chitosan chains. AFM images confirm the presence of a highly homo-

geneous layer on the crystal surface. The analysis of the QCM-D with both

the Sauerbrey and Voigt model indicates the presence of a 3 nm thick layer,

suggesting the removal of the multilayer. Future work is planned foreseeing

the optimization of the adsoprtion protocol as well as the confirmation of the

presence of a multilayered structure by X-ray (or neutron) reflectometry.

Life is the art of drawing sufficient conclusions from

insufficient premises.

Samuel Butler

Conclusions

Related to: Adv. Colloid Interf. Sci.,2015,220,

92–107.

Finally, after having introduced the general behaviour of ionic polysaccharide

– surfactant mixtures and investigated in detail the mixtures of chitosan and

alkyl oligoethyleneoxide carboxylic acids, a general overview of the behaviour

of chitosan and small amphiphiles systems is given in Paper VII.

To summarize, oversimplifying certain aspects, it can be stated that for

mixtures of ionic polysaccharides (and in particular of chitosan) and oppo-

sitely charged amphiphiles, the polymer only provides a stiff supramolecular

skeleton for the aggregation of self-assembled amphiphilic molecules. The

structure of the surfactant aggregate is solely determined by the ratio of

headgroup size and hydrophobic volume, i.e., the surfactant packing param-

eter within the complex.

The structural characterization of chitosan and alkyl oligoethyleneoxide

carboxylic acids reported in Paper IV and Paper V has shown that globu-

lar micelles are incorporated into the complex, with a supramolecular order

depending on the strength of the interaction. Similarly, the bilayer struc-

ture of C12E4.5Ac is retained within the complex, where multiwalled vesi-

cles are formed. A seemingly contradicting result is given, for instance, by

mixtures of the cationically modified cellulose JR-400 and sodium dodecyl

Figure 7.1 Schematic phase behaviour and structures of chitosan – carboxylic acid

mixtures, depending on the solution pH and hydrophobicity of the organic acid.

sulfate,26,78 where a sphere-to-rod transition for the surfactant aggregate is

observed upon complexation. This transition can be explained by an appar-

ent high ionic strength felt by the surfactant within the complex, i.e., with

most of its charges being continuously compensated by those of the polymer,

and therefore, by a reduced headgroup requirement which leads to the ob-

served sphere-to-rod transition (as also found in pure alkyl sulfates or alkyl

trimetylammonium solutions).79,80

The importance of the hydrophobic interactions can be evidenced in mix-

tures of chitosan and aliphatic carboxylic acid, whose phase behaviour is

schematically reported in Fig. 7.1. The longer the alkyl chain of the car-

boxylic acid the stronger the hydrophobic interactions are. For instance,

no aggregation is observed with short chain carboxylic acids (n(C)≤5)81

as the necessary cooperative hydrophobic interaction is missing; mesostruc-

tured complexes are obtained with fatty acids with intermediate chain length

C11:1;82–84 and, chitosan stabilized emulsions are formed for highly hydropho-

bic fatty acids (n(C)>16).85,86

Similar results as those reported for chitosan/C12E4.5Ac mixtures are also

found in systems where chitosan is mixed with phospholipid vesicles. Its

addition promotes the formation of multilamellar vesicles and increases the

membrane stiffness.87,88 Moreover, the membranes become more resistant

against pH, salt or temperature jumps.89,90

Polysaccharides are a great tool which nature wisely employed for the

fulfilment of highly different tasks. Their behaviour is therefore obviously

complex. In this work, the focus was put on cellulose-based polysaccharides

and chitosan. Both classes of polymers show an almost identical arrange-

ment of functional groups (with the exception of an amine substituting an

hydroxylic unit for cellulose/chitosan) and some common, peculiar charac-

teristics were evidenced. For instance, the spacing between the charges and

the intrinsic persistence length, elegantly agree with the Bjerrum length at

physiological conditions. The first consequence is a strong tendency of these

polymers to imprint a one-dimensional order to the resulting supramolecular

aggregates (provided the curvature of the macroion is high enough to avoid

an efficient adsorption). A second consequence arising from the chemical

structure of the polymer is the complex interplay of interactions with other

colloids. While the behaviour of many synthetic polyelectrolytes in mixtures

with oppositely charged surfactant aggregates (or nm to µm sized objects

in a more extended view) can be explained considering few effects, e.g., en-

tropic effects arising from counterion release or polymer conformation loss,

hydrophobic and dispersion interactions, the behaviour of polysaccharides is

more complex. In addition to the just mentioned effects, specific interactions

arising from the particular arrangements of functional groups do play a role.

Concluding, in the perspective of a sustainable economy, the use of biopoly-

mers and bioderived polymers as an alternative to petro-based compounds

is an unavoidable step, which, however, has to be coupled with a rational

use of new materials and an efficient recycling process. In this regard, an

added value of chitosan is its derivation from a waste product, crustaceans

shells, which may limit in the future use on very large scales. However, the

availability of chitin is nowadays orders of magnitude higher than its request.

Differently, the availability of cellulose is virtually endless.

Finally, despite the highly complex behaviour of ionic polysaccharide –

surfactant mixtures is far from being understood completely, reasonable ex-

planations for a number of observations can be made, but accurate predic-

tions are not (yet) possible. For example, some open questions directly linked

to this work are: why do chitosan – sulfated surfactant complexes show such

a low solubility? Why do polysaccharides with similar length collapse upon

addition of surfactants while others gel? Why do chitosan – carboxylated

surfactant mixtures seem to easily reach thermodynamic equilibrium while

chitosan – sulfated surfactant do not? These, and many more questions are

still open making polysaccharide – surfactant mixtures an interesting topic

for further fundamental and applied research.

The dwarf sees farther than the giant, when he has

the giant’s shoulder to mount on.

Samuel Taylor Coleridge

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Appendix

A.1 Satake-Yang ITC fit

import scipy

import sc ip y . optimize , sc ip y . s pe c ia l , sci py . s t a t s

from math import sqrt

import matplotlib

import matplotlib . pyplot as plt

from numpy import loadtxt

from numpy import savetxt

from pylab import ∗

from scipy . optimize import fsolve

from scipy . optimize import curve_fit

#K i s the non−c oo perat iv e binding constant

#Ku i s the coo pe rat iv e bindin g constant

#DHNC i s the non−cooper ative binding enthalpy

#DHC i s the co ope ra tiv e binding enthalpy

#CP i s t o t a l binding s i t e concentration

#Ctot i s the t o t a l su r f acta nt concentration

#Cf i s th e f r e e s u r f a ct a n t co nc en tr at io n

#This f un ct io n i s obtained by combining the adsoprtion isotherm with

#the mass balance equation . I t i s used by Sig () to determine Theta

#as a function of the t o t a l su r fact an t concentration .

def func (x , Ctot , CP, K, u ) :

S = x−0.5∗(1+(K∗u∗( Ctot−CP∗x)−1)/

sq rt ((1−K∗u∗( Ctot−CP∗x))∗∗2+4∗K∗( Ctot−CP∗x ) ) )

return S

def Sig ( Ctot , Ku, u , DHNC, DHC) :

CP = 2 .

K = Ku/u

#Determines the f r e e s u r f a ct a n t concentrat ion from t he b in ding isotherm

#and mass balance

Theta = f s o l v e ( func , Ctot / 1.5 , args =(Ctot , CP, K, u ))

#Ca lcula te s CF from the mass balance

Cf = Ctot−CP∗Theta

#lambda0 , ei ge nv al ue from weight matrix

lamb = 1 . + s qr t ((K∗Cf∗Theta )/(1. −Theta ) )

#f r a c t i o n of non−c o o p e r a t i v e l y bound s u r f a c ta n t

chi = ( Cf∗(1. −Theta )∗K)/( Theta∗lamb ∗∗2)

#new v a r i a b l e

s = K∗u∗Cf

#f i r s t d e r i v a t i v e of t he ta with r es pe ct to cf

Theta1cf = 0 . 5 ∗( ( u∗K)/ sqrt ( ( s −1)∗∗2+4∗s /u)−

(( s −1)∗(2∗u∗K∗( s −1)+4∗K))/(2∗s qr t (( s −1)∗∗2+4∗s /u ) ∗∗3))

#s e t of dummy fu nct io ns to c a l c u l a t e c h i1 cf

a1 = −(4.0∗Cf∗Theta1cf∗K)/( Theta ∗( s qrt ((1−s )∗∗2+4∗s /u)+s +1)∗∗2)

a2 = −(4.0∗Cf∗(1−Theta )∗Theta1cf∗K)/

(Theta∗∗2∗( s qrt ((1−s )∗∗2+4∗s /u)+s +1)∗∗2)

a3 = +(4.0∗(1−Theta )∗K)/( Theta ∗( sq rt ((1−s )∗∗2+4∗s /u)+s +1)∗∗2)

a4 = −(8.0∗Cf∗(1−Theta )∗K∗((4∗K−2∗u∗K∗(1−s ))/

(2∗sq rt ((1−s )∗∗2+4∗s /u))+u∗K))/

(Theta∗( sqr t ((1−s )∗∗2+4∗s /u)+s +1)∗∗3)

#f i r s t d e r i v a t i v e of chi with re sp ec t to Cf

c h i 1 c f = a1 + a2 + a3 + a4

#mean enthalpy of adsorption

DHm=DHNC∗chi+(1−chi )∗DHC

#c a l or i me t ri c s i g n a l

return CP∗(Theta1cf∗DHm + Theta ∗(DHNC−DHC)∗c h i 1 c f )/

(CP∗Theta1cf+1)

#Reads from the f i l e the t o t a l su r f act an t concentration

#and the binding heat

Ctot , Y = loadtxt ( ’ input . dat ’ , unpack=True )

#I n i t i a l guess of the f i t t i n g parameters

#in the order as the appear in Sig ()

guess = [ 2 . , 510. , 1000. , 2000. ]

params = guess

#Fit command . Cal cu lat es the set of b e st f i t t i n g parameters

#and t h e i r covariance matrix . Standard d ev iat io n i s obtai ned

#as the square root of the val ues on the diagonal .

params , params_covariance = curve_fit ( Sig , Ctot , Y, guess )

#pri n t params #Prints in terminal the parameter matrix

#pri n t params_covariance #Prints in terminal the covariance matrix

Ctotcalc = arange (0 . 0 02 ,2 , 0 .00 2 )

# In the f o l l o w i n g l i n e s the experim ent al data and

#b es t f i t t i n g curve are p l o t t e d

matplotlib . rcParams [ ’ axes . unicode_minus ’ ] = False

f i g = p lt . f i g u r e ()

ax = f i g . add_subplot (111)

ax . set_xscale ( ’ log ’ )

ax . plo t ( Ctot , Sig ( Ctot , params [ 0 ] , params [ 1 ] , params [ 2 ] , params [ 3 ] ) )

ax . plo t ( Ctot , Y, ’ o ’ )

pl t . show ()

#End of the program

savetxt ( ’ Sig . out ’ , Sig ( Ctot , params [ 0 ] , params [ 1 ] ,

params [ 2 ] , params [ 3 ] ) )

savetxt ( ’ Ctot . out ’ , Ctot )

A.2 Sasfit form factor for N-core-shell ellipsoids

aligned within a cylinder

#include " i ncl ude / private . h"

#include <sasfit_error_ff .h>

// d efi ne s ho r tc ut s f or l o c a l parameters / v a r i a b l e s

#define A param−>p [ 0 ] // Rotational ax is

#define B param−>p [ 1 ] // Equ a t i o r ial a xis

#define T param−>p [ 2 ] // S h e l l t h ic k ne s s

#define D param−>p [ 3 ] //Border−to−border distance

#define N param−>p [ 4 ] //Number of m i c e l l e s in the c y l i nd e r

#define RHO_P param−>p [ 5 ] //SLD of the p a r t i c l e core

#define RHO_S param−>p [ 6 ] //SLD of the p a r t i c l e s h e l l

#define RHO_C param−>p [ 7 ] //SLD of the cylin d e r

s c a l a r s a sf i t_ f f_ c hi t os a n_ e ll i ps o id s _f 1 ( s c a l a r x , sasfit_param ∗param )

{

SASFIT_ASSERT_PTR(param ) ; // a s s e r t p oi n te r param i s v a l i d

double pr e f a c el e l , p r e f a c c y l e l ;

double Q = param−>p [MAXPAR−1];

double vcyl = param−>p [MAXPAR−8];

double R = param−>p [MAXPAR−6];

double L = param−>p [MAXPAR−7];

// End importing parameters

double xc = Q∗sqrt ( gsl_pow_2 (A∗x ) + gsl_pow_2 (B)∗(1.0 −x∗x ) ) ;

double xs = Q∗sqrt (gsl_pow_2 ( (A+T)∗x ) + gsl_pow_2 (B+T)∗(1.0 −x∗x ) ) ;

double vc = 4. 0/3.0∗M_PI∗A∗B∗B;

double vs = 4 .0 /3.0∗M_PI∗(A+T)∗(B+T)∗(B+T) ;

double y = Q∗(D+2.∗(A+T))∗x ;

double fc = vc ∗(RHO_P−RHO_S) ∗3.0∗( s in ( xc)−xc∗cos ( xc ))/ gsl_pow_3( xc ) ;

double f s = vs ∗(RHO_S−RHO_C)∗3.0∗( s i n ( xs)−xs ∗cos ( xs ))/ gsl_pow_3 ( xs ) ;

double f c y l = vcyl ∗RHO_C∗4.0∗gsl_sf_bessel_J1(Q∗R∗sq rt (1.0 −x∗x ))∗

si n (Q∗L∗x/2.0)/(Q∗Q∗R∗s qr t (1.0 −x∗x )∗L∗x ) ;

prefacelel = (1.−cos (y∗N))/(1. −cos (y ) ) ;

p r e f a c c y l e l = cos ( y∗N/2.)∗si n (y∗(N+1)/2.)/ si n ( y /2.) −1.;

double Ael el = gsl_pow_2 ( f c+f s )∗prefacelel ;

double Acylcyl = gsl_pow_2( f c y l ) ;

double Acylel = f c y l ∗( fc+f s )∗p r e f a c c y l e l ;

return Aelel + Acylcyl + 2.∗Acylel ;

}

s c a l a r sa sf it _f f_ cs _e ll ip so id _i n_ cy l ( s c a l a r q , sasfit_param ∗param)

{

SASFIT_ASSERT_PTR(param ) ; // a s s e r t p oi n te r param i s v a l i d

SASFIT_CHECK_COND1( ( q < 0 . 0 ) , param , "q(%lg ) < 0" ,q ) ;

SASFIT_CHECK_COND1( (A < 0 . 0 ) , param , "A(%lg ) < 0" ,A) ;

SASFIT_CHECK_COND1( (B < 0 . 0 ) , param , "B(%l g ) < 0" ,B) ;

SASFIT_CHECK_COND1( (T < 0 . 0 ) , param , "T(%lg ) < 0" ,T) ;

SASFIT_CHECK_COND1( (D < 0 . 0 ) , param , "D(%lg ) < 0" ,D) ;

SASFIT_CHECK_COND1( (N < 0 . 0 ) , param , "N(%lg ) < 0" ,N) ;

double R = B + T; // Radius of the c y l i n d e r

double L = N∗(2∗(A+T) + D) ; // Length of the c y l i nder

double Vcyl = M_PI∗R∗R∗L; // Volume of the cyli n d e r

param−>p [MAXPAR−1] = q ;

param−>p [MAXPAR−6] = R;

param−>p [MAXPAR−7] = L ;

param−>p [MAXPAR−8] = Vcyl ;

s c a l a r r es ;

r es = s a s f i t _ i n t e g r a t e ( 0 . 0 , 1 . 0 , sa sf it _f f_ ch it os an _e ll ip so id s_ f1 , param ) ;

// r ad i al average of o b j e ct with N p a r t i c l e s

return res ;

}

List of symbols and abbreviations

δDebye length

∆D Dissipation change

∆f Frequency shift

∆HcCooperative binding heat

∆Hnc Non-cooperative binding heat

λWavelength

λBBierrum length

Ku Cooperative binding constant

K Non-cooperative binding constant

n Refractive index

ΘBinding isotherm

θScattering angle

ε0Vacuum permittivity

εrRelative permittivity

CfFree surfactant concentration

e0Elementary charge

IIonic strength

kBBoltzmann constant

lpPersistence length

pElectrostatic contribution to the persistence length

pIntrinsic persistence length

NAAvogadro constant

qModulus of the scattering vector

UeElectrostatic potential energy

ZMixing ratio

AFM Atomic force microscopy

DLS Dynamic light scattering

FCS Fluorescence correlation spectroscopy

PE Polyelectrolyte

QCM-D Quartz crystal microbalace with dissipation monitoring

R Gas constant

SANS Small-angle neutron scattering

SAXS Small-angle x-ray scattering

SLS Static light scattering

SPEC Surfactant – Polyelectrolyte complex

T Absolute temperature

Full-text manuscripts are available online as follows:

•Paper I Complexes of oppositely charged polyelectrolytes and surfac-

tants – recent developments in the field of biologically derived poly-

electrolytes. L. Chiappisi, I. Hoffmann and M. Gradzielski. Soft Mat-

ter,2013,9, 3896-3909. Available at http://dx.doi.org/10.1039/

c3sm27698h.

•Paper II An improved method for analyzing isothermal titration calori-

metry data from oppositely charged surfactant polyelectrolyte mix-

tures. L.Chiappisi, D. Li, N. J. Wagner, M. Gradzielski. The Jour-

nal of Chemical Thermodynamics,2014,68, 48-52. Available at http:

//dx.doi.org/10.1016/j.jct.2013.08.027.

•Paper III Form factor of cylindrical superstructures composed of glob-

ular particles. L. Chiappisi, S. Prévost, M. Gradzielski. Journal of

Applied Crystallography,2014,47, 827-834. Available at http://dx.

doi.org/10.1107/S1600576714005524.

•Paper IV Chitosan/Alkylethoxy Carboxylates: A Surprising Vari-

ety of Structures. L. Chiappisi, S. Prévost, I. Grillo, M. Gradzielski.

Langmuir,2014,30, 1778-1787. Available at http://dx.doi.org/10.

1021/la404718e.

•Paper V From Crab Shells to Smart Systems: Chitosan–Alkylethoxy

Carboxylate Complexes. L. Chiappisi, S. Prévost, I. Grillo, M. Gradziel-

ski. Langmuir,2014,30, 10608-10616. Available at http://dx.doi.

org/10.1021/la502569p.

•Paper VI Towards bioderived intelligent nanocarriers for controlled

pollutant recovery and pH-sensitive binding. L. Chiappisi, M. Simon,

M. Gradzielski. ACS applied Materials & Interfaces,2015,7, 6139-

6145. Available at http://dx.doi.org/10.1021/am508846r.

•Paper VII Co-assembly in Chitosan – Surfactant mixtures: thermo-

dynamics, structures and applications. L. Chiappisi, M. Gradzielski

Advances in Colloid and Interfaces,2015,220, 92-107. doi: Available

at http://dx.doi.org/10.1016/j.cis.2014.10.013.