Collapse of polymer brushes grafted onto planar ... - Wageningen UR

Frontis - Wageningen International Nucleus for Strategic 

Expertise 

Chain molecules at interfaces: SCF Theory and Experiments 

A symposium to the memory of Jan Scheutjens 

Conveners: Gerard J. Fleer and Frans A.M. Leermakers, Laboratory of Physical 

Chemistry and Colloid Science, Wageningen University

Contributors 

Dr. Victor Amoskov Institute of Macromolecular Compounds 

31 Bolshoy pr. V.O., St. Petersburg 

199004 

Russia 

Dr. ir. Peter Barneveld Wageningen University, Laboratory of 

Physical Chemistry and Colloid Science 

Dreijenplein 6, 6703 HB Wageningen 

The Netherlands 

Dr. ir. Klaas Besseling Wageningen University, Laboratory of 




Prof. Kurt Binder Johannes-Gutenberg Universität, Inst. für 

Physik 

Postfach 3980, D-6500 Mainz 01 

Germany 

Dr. Edgar Blokhuis Leiden Institute of Chemistry 

P.O. Box 9502 , 2300 RA Leiden 


Dr. Oleg Borrisov Wageningen University, Laboratory of 




Ir. Wouter Bosker Wageningen University, Laboratory of 




Ir. Mireille Claessens Wageningen University, Laboratory of 



Prof. dr. Martien Cohen 

Stuart 

Prof. dr. Terence 

Cosgrove 


Wageningen University, Laboratory of 




University of Bristol, School of Chemistry 

Cantock's Close , Bristol BS8 1TS 

United Kingdom 

Dr. Kostas Daoulas ICE/HT-FORTH 

Stadiou Street, Platani, GR 26500 Patras 

Greece 

Dr. Arie de Keizer Wageningen University, Laboratory of 




Dr. Renko de Vries Wageningen University, Laboratory of 




Prof. dr. Gerard Fleer Wageningen University, Laboratory of 




Telephone: +7-812-3288542 

Fax: +7-812-3286869 

Email: vic@avm.macro.pu.ru 

Telephone: +31-317-484962 

Fax: +31-317-483777 

Email: peter@fenk.wag-ur.nl 

Telephone: +31-317 484243 

Fax: +31-317-483777 

Email: 

klaas.besseling@fenk.wau.nl 

Telephone: - 

Fax: 49-6131-392991 

Email: 

binder@shiel.physik.uni-mainz.de 

Telephone: +31-71-5274542 

Fax: +31-71-5274397 

Email: 

e.blokhuis@chem.leidenuniv.nl 

Telephone: +31-317-482178 

Fax: +31-317-483777 

Email: 

Telephone: +31-317-482277 

Fax: +31-317-483777 

Email: 

wouter.bosker@fenk.wau.nl 

Telephone: +31-318-483710 

Fax: +31-317-483777 

Email: mireille@fenk.wau.nl 

Telephone: +31-317-482178 

Fax: +31-317-483777 

Email: martien@fenk.wag-ur.nl 

Telephone: +44-117-9287663 

Fax: +44-117-9250612 

Email: 

terence.cosgrove@bris.ac.uk 

Telephone: +30-610-965219 

Fax: +30-610-965223 

Email: 

daoulas@physics.upatras.gr 

Telephone: +31-317-416368 

Fax: +31-317-483777 

Email: arie@fenk.wau.nl 

Telephone: +31-317-484561 

Fax: +31-317-483777 

Email: devries@fenk.wau.nl 

Telephone: +31-317-482275 

Fax: +31-317-483777 

Email: fleer@fenk.wag-ur.nl

Prof. dr. Hans Fraaije Leiden University 

P.O. Box 9502, 2300 RA Leiden 


Ana Belen Jodar-Reyes University of Granada 

Dpto. Fisica Aplicada, Facultad de 

Ciencias, Fuent, Granada 18071 

Spain 

Prof. Toshihiro Kawakatsu Tohoku University 

Department of Physics, Tohoku 

University, Aza-Aoba, Sendai 980-8578 

Japan 

Dr. Leonid Klushin American University of Beirut, Department 

of Physics 

P.O.Box 11-0236, Beirut 1107 2020 

Lebanon 

Dr. Hiroya Kodama Mitsubishi Chemical Corporation 

Naruse 2-17-1-17-105, Machida 194-0044 

Japan 

Dr. Luuk Koopal Wageningen University, Laboratory of 




Andriy Kyrylyuk Ph.D. Leiden University 

P.O..Box 9502, 2300 RA Leiden 


Yansen Lauw M.Sc. Wageningen University, Laboratory of 




Dr. ir. Frans Leermakers Wageningen University, Laboratory of 




Prof. dr. Per Linse University of Lund, Dept. Physical 

Chemistry 1 

Chemical Centre, P.O. Box 124, S-22100 

Lund 

Sweden 

Drs. Kateryna Lyakhova Leiden University 



Prof. dr. Hans Lyklema Wageningen University, Laboratory of 




Dr. Vlasis Mavrantzas ICE/HT-FORTH 

Stadiou Street, Platani, GR 26500 Patras 

Greece 

Mihai Morariu University of Groningen 

Nijenborgh 4, 9742 AG Groningen 


Martin Olsson University of Lund Chemical Centre 

P.O. Box 124, S-22100 Lund 

Sweden 

Telephone: +31-71-5274243 

Fax: +31-71.5274243 

Email: 

j.fraaije@chem.leidenuniv.nl 

Telephone: +34-958-246175 

Fax: +34-958-243214 

Email: ajodar@ugr.es 

Telephone: +81-22-2176438 

Fax: +81-22-2176438 

Email: 

kawakatu@cmpt.phys.tohoku.ac.j 

p 

Telephone: 

Fax: +961-1-744461 

Email: leo@aub.edu.lb 

Telephone: +81-45-9633263 

Fax: +81-45-9633947 

Email: kodama@rc.m- 

kagaku.co.jp 

Telephone: +31-317-482629 

Fax: +31-317-483777 

Email: koopal@fenk.wau.nl 

Telephone: +31-71-527 4438 

Fax: +31-71 527 4537 

Email: 

a.kiriluk@chem.leidenuniv.nl 

Telephone: +31-317-485594 

Fax: - 

Email: yansen.lauw@fenk.wau.nl 

Telephone: +31-317 482268 

Fax: +31-317-483777 

Email: frans@fenk.wau.nl 

Telephone: +46-46-2228151 

Fax: +46-46-2224413 

Email: per.linse@fkem1.lu.se 

Telephone: +31-71-527 4438 

Fax: +31-71-5274397 

Email: 

e.lyakhova@chem.leidenuniv.nl 

Telephone: +31-317-482279 

Fax: +31-317-483777 

Email: hans.lyklema@fenk.wag- 

ur.nl 

Telephone: +30-610-965214 

Fax: +30-610-965223 

Email: vlasis@iceht.forth.gr 

Telephone: +31-50 363 4517 

Fax: +31-50-3634400 

Email: m.d.morariu@chem.rug.nl 

Telephone: +46-46-2221536 

Fax: +46 46-2224413 

Email: 

Martin.Olsson@fkem1.lu.se

Dr. Martijn Oversteegen Utrecht University 

Padualaan 8, 3584 CH Utrecht 


Dr. Johan Pluyter International Flavors and Fragrances 

1515 State Highway 36, Union Beach, NJ 

07735 

USA 

Prof. Raj Rajagopalan University of Florida 

Dept of Chemical Engineering, Gainesville 

Florida 32611-6005 

USA 

Dr. Bart Reuvers Akzo Nobel Dep. CoRA 

Velperweg 76, P.O. Box 9300 

6800 SB Arnhem 


Prof. Randal Richards IRC in Polymer Science 

University of Durham, Durham DH1 3LE 

United Kingdom 

Prof. Thomas Russell University of Massachusetts 

Polymer Science & Engineering 

Amherst Mass. 01003 

USA 

Prof. Sam Safran Weizmann Institute of Science 

Herzel Street, Rehovot 76100 

Israel 

Ir. Sonja Scheinhardt- 

Engels 

Wageningen University, Laboratory of 




Prof. dr. Michael Schick University of Washington 

Dept. of Physics, Seattle WA 98195-1560 

USA 

Prof. Alexander Semenov Moscow State University 

Physics Department, Moscow 119992 

Russia 

Dr. Agur Sevink Leiden University , Gorlaeus labs, 



Prof. Yitzhak Shnidman Polytechnic University 

6 MetroTech Center, Brooklyn, NY 11201 

USA 

Dr. Nadezhda Shusharina University at Buffalo - SUNY 

303 Furnas Hall, Dept. of Chemical 

Engineering, Buffalo, NY 14260-4200 

USA 

Drs. Karl Isak Skau Leiden Institute of Chemistry 

P.O. Box 9502 , 2300 RA Leiden 


Prof. dr. Alexander 

Skvortsov 

Chemical Pharmaceutical Academy, 

Prof. Popova 14 , St. Petersburg 197022 

Russia 

Telephone: +31-30 253 2540 

Fax: +31-30-2533870 

Email: 

m.oversteegen@chem.uu.nl 

Telephone: +1-732 335-2496 

Fax: +1-32-3352591 

Email: johan.pluyter@iff.com 

Telephone: +1-352-3920868 

Fax: +1-352-3929513 

Email: Raj@ChE.UFL.edu 

Telephone: +31-26-3663415 

Fax: +31-26-3665827 

Email: 

Bart.Reuvers@AkzoNobel.com 

Telephone: +44-191-3743153 

Fax: +44-191-3744651 

Email: 

r.w.richards@durham.ac.uk 

Telephone: +1-413-5771516 

Fax: +1-413-5771510 

Email: 

russell@mail.pse.umass.edu 

Telephone: +972-8-9343362 

Fax: +972-8-9344138 

Email: 

sam.safran@weizmann.ac.il 

Telephone: +31-317-482277 

Fax: +31-317-483777 

Email: Sonja.Engels@fenk.wau.nl 

Telephone: 

Fax: 

Email: 

schick@mahler.phys.washington. 

edu 

Telephone: 

Fax: 

Email: 

semenov@polly.phys.msu.su 

Telephone: +31-71-5274233 

Fax: +31-71-5274397 

Email: 

a.sevink@chem.leidenuniv.nl 

Telephone: +1-718-260-3785 

Fax: +1-509-5617203 

Email: shnidman@poly.edu 

Telephone: +1-716-6452911 

Fax: +1-716-6452238 

Email: ns33@eng.buffalo.edu 

Telephone: +31-71-5274542 

Fax: +31-71-5274397 

Email: 

k.skau@chem.leidenuniv.nl 

Telephone: 

Fax: 

Email:

Prof. Ullrich Steiner University of Groningen 

Nijenborgh 4, 9747 AG Groningen 


Prof. Igal Szleifer Purdue University 

Dept. Of Chemistry, West Lafayette, 

IN 47907-1393 

USA 

Prof. Doros Theodorou National Technical University of Athens 

School of Chemical Engineering, 

Department of Mate, GR 15780Athens 

Greece 

Prof. dr. Theo van de Ven Paprican/McGill 

3420 University Street, Montreal QC H3A 

2A7 

Canada 

Ir. Jos van den Oever Wageningen University, Laboratory of 




Ir. Jasper van der Gucht Wageningen University, Laboratory of 



Dr. ir. Katinka van der 

Linden 


E.I. Dupont de Nemours 

Antoon Spinoystraat 6, B-2800 Mechelen 

Belgium 

Dr. Marcel van Eijk CP Kelco 

Ved Banen 16, DK-4623 Lille Skensved 

Denmark 

Dr. Rene van Roij Utrecht University, Institute for Theoretical 

Physics 

Postbus 80.195, 3508 TD Utrecht 


Dr. Ad van Well IRI, Delft University of Technology 

Mekelweg 15, 3639 JB Delft 

María Eugenia Velázquez- 

Sánchez M. Sc. 

Dipl. Phys. Ludger 

Wenning 


Technical University of Eindhoven 

Helix STO 2.41, 5600 MB Eindhoven 


Johannes-Gutenberg Universität, Inst. für 

Physik 

Postfach 3980, D-6500Mainz 01 

Germany 

Prof. Mark Whitmore Memorial University of Newfoundland 

Department of Physics, St. Johns NF A1B 

3X7 

Canada 

Prof. Katya Zhulina 135 Sheffield Lane, McMurray, PA15317 

USA 

Dr. Pacelli Zitha Delft University of Technology 

Mijnbouwstraat 120, 2625 LK Delft 


Telephone: +31-50-3637888 

Fax: +31-50-3634400 

Email: u.steiner@chem.rug.nl 

Telephone: +1-765-494-5255 

Fax: +1-765-494-0239 

Email: igal@purdue.edu 

Telephone: +30-10-7723157 

Fax: +30-10-7723184 

Email: doros@central.ntua.gr 

Telephone: +1-514-3986177 

Fax: +1-514-398 6256 

Email: theo.vandeven@mcgill.ca 

Telephone: +31-317-484776 

Fax: +31-317-483777 

Email: 

Jos.vandenOever@fenk.wag-ur.nl 

Telephone: +31-317-482585 

Fax: +31-317-483777 

Email: jasper@fenk.wau.nl 

Telephone: +32-15-441615 

Fax: +32-15-441510 

Email: katinka.van-der- 

linden@bel.dupont.com 

Telephone: +45-56165895 

Fax: +45-56169446 

Email: 

marcel.vaneijk@cpkelco.com 

Telephone: +31-30-2537579 

Fax: +31-30-2535937 

Email: r.vanroij@phys.uu.nl 

Telephone: +31-15-2784738 

Fax: +31-15-2788303 

Email: vanwell@iri.tudelft.nl 

Telephone: +31-40-2473132 

Fax: +31-40-2445619 

Email: M.velazquez- 

sanchez@tue.nl 

Telephone: +49-6131-3925151 

Fax: +49-6131-3925441 

Email: wenning@uni-mainz.de 

Telephone: +1-709-7378832 

Fax: +1-709-7378739 

Email: markw@physics.mun.ca 

Telephone: 

Fax: 

Email: kzhulina@hotmail.com 

Telephone: +31-15-2788437 

Fax: +31-015-2781189 

Email: p.l.j.zitha@citg.tudelft.nl

Dr. Andre Zvelindovsky Leiden University 

P.O.Box 9502, 2300 RA Leiden 


Telephone: +31-71-5274234 

Fax: +31-71-5274537 

Email: 

a.zvelindovsky@chem.leidenuniv. 

nl

Preface 

Self-consistent field modelling has played a key role in the increase of our knowledge of chain 

molecules at interfaces. This is a topic where the disciplines of physics, chemistry, biology and 

technology meet. Typical keywords are: 

• Statics and dynamics of long and short polymers in solution and at interfaces (coil, globule, helix, 

flower, living polymers) 

• Self-organization of (bio-)amphiphiles into micelles, membranes, vesicles 

• Surface modification, copolymer, polyelectrolyte and polyampholyte adsorption, brushes 

• Colloidal stabilization, wetting, capillary condensation, nucleation 

• (Micro-)emulsions, phase separation, curved interfaces 

• Polymer blends, structure (pattern) formation in polymer melts. 

Without exception all these topics have direct technological applications and consequences. 

The Wageningen School to model inhomogeneous systems was started by the seminal work of the 

late Jan Scheutjens. In August 2002 it was ten years ago that Jan Scheutjens died. This symposium 

was dedicated to his memory. Experts in the field of chain molecules at interfaces were invited to 

come together to evaluate the state of the art. Progress on numerical, analytical, scaling aspects as 

well as new insights resulting from "theory-guided" experiments was considered. The aim of the 

symposium was to assess the possibilities and challenges for the near and more distant future. The 

symposium was held from 25 to 28 August 2002 in the Wageningen International Conference Centre.

Chain Molecules at Interfaces: SCF Theory and Experiment: a summary 

The symposium "Chain Molecules at Interfaces: SCF Theory and Experiment" was organized 

by Frontis - Wageningen International Nucleus for Strategic Expertise, in collaboration with 

the Laboratory of Physical Chemistry and Colloid Science (LPCCS) of Wageningen 

University and with financial support by the Royal Netherlands Academy of Sciences, to 

commemorate Jan Scheutjens, who died ten years ago in a car accident. The importance of 

the self-consistent field (SCF) theory for mesoscopic physics can be compared with the 

importance of quantum mechanics for theoretical physics. Jan Scheutjens was one of the 

designers of the SCF theory, and the Wageningen LPCCS has built up a strong international 

position in this field. Ten years ago Gerard Fleer and his co-workers pledged to take care of 

Jan Scheutjens' heritage. The attendance of so many of the world's most recognized 

scientists at this symposium proves that this field of research is still thriving at Wageningen 

University. 

The participants were unanimous in their judgement that this symposium was extremely 

interesting; they were enthusiastic about the wealth of problems that can successfully be 

attacked by the SCF theory. The approach by Scheutjens (and Fleer) is still seen as a 

flexible tool to study complex problems involving chain molecules and concentration 

gradients. There was no doubt about the historic importance of Jan Scheutjens in the 

development of this theory. 

The symposium brought together various disciplines within physical chemistry. Theoretical 

modelling was the issue that united all those who attended the symposium, not only through 

typically theoretical approaches, but also in various experimental aspects. The wide range of 

subjects that was covered may be deemed unique. New experimental data on polymers at 

surface boundaries were discussed in relation with modern developments in modelling of 

them. The emphasis was on equilibrium analyses, but also their dynamic modelling was 

discussed. Many of these systems have a direct technological relevance. In addition the 

modelling of self-assembling systems was thoroughly discussed. This topic has an obvious 

biological component. It is not surprising, therefore, that various speakers who usually find 

themselves in very different parts of science met each other for the first time during this 

symposium. These meetings can be characterized as "cross-pollinations" and must be 

considered one of the successes of the symposium. Without doubt Wageningen was put on 

the map once again as a centre for SCF modelling, not only in polymer physics, but also in 

areas of relevance to biophysics. 

The symposium was attended by ca 60 scientists. The 14 invited keynote speakers all had 

one hour for their presentations, including discussion. Five additional speakers, selected on 

the basis of their submitted poster abstracts, were each given 30 minutes for oral 

presentations. The limited number of participants has certainly contributed to the often very 

lively discussions that followed the thorough and generally excellent presentations. Also the 

LPCCS's PhD students were allowed and able to take part in the discussions, which, of 

course, were continued after the formal sessions. The relatively many posters were the 

subject of lively discussions during breaks. 

The participants represented many countries: Canada (2), Denmark (1), Germany (3), 

Greece (3), Israel (1), Japan (2), Lebanon (1), Russia (3), Spain (1), Sweden (2), United 

Kingdom (2), United States (8) and The Netherlands (ca 30). The importance of the SCF 

method is recognized more strongly abroad than in The Netherlands; Wageningen University 

is better known in this field outside the Dutch borders than at home. A limited number of 

participants (5) came from industry. 

Experimental aspects of polymers at boundaries were discussed by T. Russel (how to place 

nano-sized rods perpendicular to a surface), T. Cosgrove (neutron scattering on surfaces

covered by polymers), and R. Rajagopalan (surface force measurements of polymer-coated 

layers). Theoretical counterparts were F. Leermakers (accounting for intramolecular 

interactions), L. Klushin (adsorption transition of copolymers), M. Whitmore (polymer 

brushes), and A. Semenov (analytical theory for adsorption of semi-flexible macromolecules). 

Computer simulations for polymers in confined spaces (wetting and capillary condensation) 

were presented by K. Binder. D. Theodorou discussed a method to use SCF results as input 

for simulations. Various aspects of dynamic modelling of concentrated polymer systems 

(melts) were treated by J. Fraaije, T. Kawakutsu and Y. Snidman. The emphasis was here on 

generating and understanding mesoscopic patterns that can only be made by a dynamical 

path. In this area theory and experiment come surprisingly close to each other. A contribution 

by V. Mavrantzas linked the classical adsorption theory with flow fields. P. Linse gave an 

overview of the modelling of self-assembling behaviour of non-ionogenic soap molecules. R. 

van Roij discussed the theory of rod-like particles (molecules) and their behaviour in confined 

spaces. Biologically oriented topics were brought forward by I. Szleifer (protein molecules at 

surfaces), S. Safran (self-assembling networks), and M. Schick (theory of vesicle fusions). 

The research done in the Laboratory of Physical Chemistry and Colloid Sciences at 

Wageningen has very close relations with the subjects discussed during the symposium. 

This was particularly clear through the many poster presentations of Wageningen graduate 

students. Some keywords describing the width of the research are: bending moduli of 

membranes and stability of vesicles, modelling of pores in membranes and SCF modelling of 

lipid bi-layers, stiffness of worm-like micelles, self-assembling polymers at surfaces, wetting 

of a poly-electrolyte brush, allophobic and autophobic behaviour of a polymer melt on a 

brush, brushes made of polysaccharides, and the steady-state modelling of surfaces in a 

polymer solution. 

In conclusion the symposium has been very successful. Undoubtedly its results will have 

great impact on future research at Wageningen. New contacts were made and old ones 

renewed. Wageningen has confirmed or even strengthened its position in a large number of 

disciplines in mesoscopic (bio)physics.

INTERACTIONS BETWEEN BOVINE SERUM ALBUMIN AND BILE SALTS: 

A THERMODYNAMIC INVESTIGATION 

M.L. Antonelli, A. Palacios, C. La Mesa 

Dipartimento di Chimica, Università di Roma la Sapienza, 

P.le A. Moro 5, 00185, Rome, Italy 

email: marta.antonelli@uniroma1.it 

ABSTRACT 

Due to its ubiquitous nature, albumin is found in significant amounts in almost all human, or mammal, tissues. 

As such it is responsible for the complex phenomena associated to the formation of human bile, both hepatic 

and colecystic ones. In such tissues the composition and the overall amount of albumin and bile acid salts is 

dictated by certain rules. 

Most bile acid salts occurring in the humans interact with albumin by a combination of electrostatic and 

hydrophobic contributions. There is experimental evidence of a small selectivity between albumin and different 

bile acid salts (conjugated or not, mono, di- or tri-hydroxy derivatives, etc.) based on a relative hydrophobicity 

scale of the different bile acid salts. 

To check this hypothesis a thermodynamic investigation of the interactions between bovine serum 

albumin (BSA) and Sodium Taurodeoxycholate, (NaTDC), has been performed. The investigation deals with 

batch dilution calorimetric studies, activity coefficients findings (inferred by freezing point depression data) 

and surface tension behaviour. Studies have been performed at 25°C. The concentrations investigated cover 

a wide range of protein to surfactant ratios [1]. In this way information from the observed effects may be 

useful to quantify the energetics of binding phenomena in biologically relevant systems [2]. The data have 

been interpreted in terms of competition between NaTDC binding onto the protein and micelle formation. 

References 

1. Nielsen, A.D., Borch, K., Westh, P., 2000. Biochim. Biophys. Acta, 1479, 321-331. 

2. Samso, M, Daban, J:R., Hansen, S., Jones, G.R., 1995. Eur. J. Biochem., 212, 818-824.

FIRST-ORDER WETTING TRANSITION AT FINITE CONTACT ANGLE 

F.A.M. Leermakers, J. Maas and M.A. Cohen Stuart 

Laboratory of Physical Chemistry and Colloid Science, Wageningen University, 

Dreijenplein 6, 6703 HB Wageningen, The Netherlands 

email: frans@fenk.wau.nl 

ABSTRACT 

The wetting of a polymer brush by a melt of similar chains can have a window of complete wetting. In this 

case there is a classical allophobic wetting transition, at low grafting density σ , and an autophobic one at 

high σ . However, when the melt chains are much longer than the brush chains, the contact angle α goes 

through a non-zero minimum where ∂α ∂σ 

/ has a jump. An SCF analysis and experimental observations 

indicate a double-well disjoining pressure curve, consistent with a novel first-order wetting transition at finite 

α . The meta-stable contact angle can become zero. This is important information in order to understand the 

kinetics of dewetting. The results show that the classical wetting theory must be extended in order to account 

for incomplete wetting (i.e. wetting transitions at finite contact angle).

WETTING OF AN ANNEALED POLYELECTROLYTE BRUSH, A NUMERICAL SCF STUDY 

F.A.M. Leermakers 1) , A. Mercurieva 2) , E.B. Zhulina 2) , T.M. Birshtein 2) 

1) Laboratory of Physical Chemistry and Colloid Science, Wageningen University, 


2) 

Institute of Macromolecular Compounds of the Russian Academy of Sciences, 

199004, St. Petersburg, Russia 


ABSTRACT 

In this poster we will discuss the wetting properties of an annealed polyelectrolyte brush in an oil-salted water 

system. The ionic strength is chosen as the control parameter. The salted water interacts with the solid 

substrate as well as with the annealed brush. The first type of interaction has a short-range character; the 

other one is long range (at least proportional to the brush height). One can envision wetting transitions due to 

both interactions. The two wetting transitions appear to be of the first-order type and interfere with each other. 

The pre-wetting lines associated to these transitions cross and a triple point is found. At this triple point three 

(microscopic) film thicknesses coexist. There can only be one wetting transition and therefore one part of one 

of the pre-wetting lines is meta-stable in between a hidden wetting transition and the triple point. The other 

pre-wetting line is attached to the true wetting transition and has a kink at the triple point.

MOLECULAR SCF MODELLING OF PORES IN LIPID BILAYERS 

M.A.C. Roelen, F.A.M. Leermakers, M.M.A.E. Claessens, M.A. Cohen Stuart 




ABSTRACT 

The stability of bilayer systems, e.g. lipid vesicles, under tension is determined by the ease with which rupture 

nuclei form. A molecular self-consistent-field theory with the discretisation scheme of Scheutjens and Fleer is 

applied to obtain structural and thermodynamical information on perforated (flat) bilayers. It is found that the 

critical tension on the bilayer for the long wavelength perturbation is much higher than the tension needed to 

rupture the bilayer if a small spherical hole is allowed for.

FIRST-ORDER ADSORPTION TRANSITION OF MINORITY CHAINS IN A BRUSH 

A.N. Skvortsov 1) , A.A. Gorbunov 2) , F.A.M. Leermakers 3) , G.J. Fleer 3) 

1) Chemical Pharmaceutical Academy, 

Prof. Popova 14, 197022, St. Petersburg, Russia 

2) Institute for highly pure biopreparations 

Pudozhskaya 7, 197110 St Petersburg Russia 




ABSTRACT 

The adsorption transition of homopolymers onto a flat solid-liquid interface is known to be second order. The 

surface field is typically a short-range well near the surface. In this poster we consider polymer adsorption 

onto a surface that is decorated by a polymer brush. Now the surface field felt by adsorbing chains is more 

complex. Besides a short-range attraction, there is a long-range repulsive region. The range of the repulsive 

part of the surface potential is given by the brush height and the strength of the repulsion (which is of the 

excluded-volume type) is only a function of the grafting density. The adsorption transition becomes first-order 

in the thermodynamic limit. Simple scaling arguments are presented.

COLLAPSE OF POLYMER BRUSHES GRAFTED ONTO PLANAR OR CONVEX SURFACE 

V.M. Amoskov, T.M. Birshtein, A.A. Mercurieva 

Institute of Macromolecular Compounds, Academy of Science of Russia, 

31, Bolshoy pr., V.O., St-Petersburg, 199004, Russia 

email: vic@avm.macro.pu.ru 

ABSTRACT 

The collapse of polymer brushes is investigated. Four types of the polymer systems are considered: (1) 

polyelectrolyte brushes in poor solvent, (2) non-ionizable and ionizable brushes in binary solvents, (3) 

brushes with n-cluster interactions and (4) thermotropic LC brushes. Both an asymptotic analytical analysis 

(for chain length N →∞) 

and exact numerical computations (for finite N) are applied for investigating these 

systems in a self-consistent field (SCF) framework. The SCF numerical calculations are carried out using the 

formalism developed by J.Scheutjens and G.Fleer in their classical works. 

For the brushes of planar geometry it has been stated that under suitable external and internal conditions, 

collapse in all of these systems can occur as a first order phase transition. The solvent quality (system 1), the 

fraction of better solvent (system 2), the energy of isotropic interactions (system 3) and the energy of anisotropic 

interaction (system 4) are the parameters that govern corresponding phase transitions. The brushes 

grafted onto convex curved surfaces are also investigated. It is found that for the brushes grafted onto 

external cylindrical or spherical surfaces (combs, stars, micelles and so on), collapse may also occur as a 

first order phase transition. 

Though investigated polymer systems differ in the interactions as well as in the grafting type, it is shown 

that a number of features are similar for the phase transitions observed in all of them. 

At small (or large) enough values of the governing parameter, anyone of the systems under consideration 

exists only in a single-phase state, namely, in extended (or collapsed) state. However, there is an intermediate 

range of the governing parameter values where the swollen and the collapsed microphases may 

coexist, such a state being usually referred as a micro-segregated brush (MSB). It is noteworthy that a more 

compact phase is typically located in the neighborhood of the grafting surface, while the swollen phase is at 

the periphery. If the brush is in the biphasic state, its chains are never partly collapsed and partly extended: 

on the contrary, the chains are strictly divided into two groups that are either fully collapsed or fully extended. 

The fraction of the chains responsible for one or another sublayer in the brush depends on the value of the 

corresponding governing parameter. Collapsed chains never participate in the formation of the swollen layer, 

thus decreasing the effective grafting density for the remaining chains and allowing their existence in the 

swollen state. The free end distribution for any brush in MSB state is bimodal. All these effects are 

irrespective of the grafting surface type. 

At relatively small values of the grafting densities and finite values of the number of segments N in each 

chain, the brush collapse takes place in a jump-like manner, that being typical of the first order phase 

transitions. The size of nuclei of the collapsed phase is defined as H ~ N δ and grows with the chain length N 

slower than the brush size. Hence the first order phase transitions cannot exist at the limit of N →∞.

MD AND SCF ON BILAYERS OF SOPC AND SDPC 

F.A.M. Leermakers 1) , N.K. Balabaev 2) , A.L. Rabinovich 3) 



2) Institute of Mathematical Problems of Biology, Russian Academy of Sciences, 

Pushchino, Moscow Region, 142292, Russia 

3) Institute of Biology, Karelian Research Center, Russian Academy of Sciences, 

Pushkinskaja str 11, Petrozavodsk, 185610, Russia 

ABSTRACT 

Structural features of two lipid bilayer membranes composed of mono-unsaturated 1-stearoyl-2-oleoyl-snglycero-3-phosphatidylcholine 

SOPC and 1-stearoyl-2-docosahexaenoyl-sn-glycero-3-phosphatidylchol 

SDPC have been evaluated by an all-atom Molecular Dynamics simulation and compared to results 

obtained from a detailed numerical SCF method. SCF is computationally approximately 10.000 times 

more efficient than MD. The two methods appear complementary. The MD gives more details. In SCF it is 

possible to vary parameters. It is found that unsaturated lipid tails are effectively shorter (end-to-end 

distance. They reduce the interdigitation of tails into opposite monolayers (they modify the coupling 

between the two monolayers). Both MD and SCF predict equilibrium area per molecule close to the 

experimental data.

SURFACE FORCES, SUPRAMOLECULAR POLYMERS, AND DIRECTIONALITY 

J. van der Gucht 1,2) , N.A.M. Besseling 1) , M.A. Cohen Stuart 1) 

1) 



2) 

Dutch Polymer Institute, 

Postbus 902, 5600 AX Eindhoven, The Netherlands 

email: klaas@fenk.wau.nl 

ABSTRACT 

Interactions between surfaces, e.g. of dispersed colloidal particles are crucial in all heterogeneous soft 

matter.(1) Supramolecular equilibrium polymers (sometimes denoted as living polymers) are polymeric chains 

formed by reversible, non-covalent association of special small molecules.(2) The main purpose of this 

presentation is to point out the relevance of the symmetry of the monomers for their behaviour at surfaces. 

Monomers that are symmetric in the sense that their two binding sites are self-complementary form nondirectional 

chains, but monomers with mutually complementary binding sites, often denoted as donor and 

acceptors sites (or as host and guest, lock and key) form directional chains. In solution or in bulk this 

difference will not lead to any difference in behaviour. However, in the presence of surfaces, and especially 

when two surfaces approach each other, the directionality of the monomers and the ensuing chains may be 

crucial. 

Figure 1. Non-directional chains between two surfaces (a), and directional chains between two similar surfaces that bind 

preferentially to the acceptor binding sites of the monomers (b). 

Phenomenological Landau analysis indicates that non-directional equilibrium polymers always yield attractive 

surface forces, but that directional equilibrium polymers may yield repulsion between surfaces that binds 

preferentially either the donors or the acceptors. More detailed information is deduced from a lattice model 

analysed in a Bethe-Guggenheim approximation. The strength and the range of the surface force, and their 

concentration dependencies is predicted to be different for the directional and the non-directional cases. 

These principles may explain certain observations on heterogeneous systems, and might be used to 

manipulate the properties of such systems. 

References 

1. J. Israelachvili, Intermolecular and Surface Forces, Academic Press, 1991. 

2. A. Ciferri, Supramolecular Polymers, Marcel Dekker, 2000. 

3. J. van der Gucht, N.A.M. Besseling, M.A. Cohen Stuart, 2002. Surface forces, supramolecular polymers, 

and inversion symmetry. J. Am. Chem. Soc. 124, 6202-6205.

PHASE TRANSITIONS OF BINARY POLYMER MIXTURES CONFINED BETWEEN COMPETING 

SURFACES 

K. Binder, M. Müller 

Institut für Physik, Johannes-Gutenberg-Universität Mainz, 

Staudinger Weg 7, 55099 Mainz, Germany 

e-mail: kurt.binder@uni-mainz.de; marcus.mueller@uni-mainz.de 

ABSTRACT 

A symmetrical polymer blend (chain lengths NA = NB = N ) is considered in a thin film geometry, treating the 

case where one surface preferentially attracts component A, while the other surface attracts component B. 

This situation leads to an interesting competition between lateral versus perpendicular phase separation 

between an A-rich and a B-rich phase, which is studied both with the self-consistent field theory and with 

Monte Carlo simulations of the bond fluctuation model on the simple cubic lattice [1-5]. 

For simplicity, the case of “antisymmetric walls” (same strength of the surface forces) is emphasized, while 

the general case of asymmetric surfaces is treated only briefly. It is argued that the increase of the Flory- 

Huggins χ parameter that drives phase separation in the bulk (if χ > χcb 

= 2/N in the mean field limit) 

leads to a rounded transition from a uniformly mixed state to a stratified structure in the thin film geometry (an 

A-rich phase is separated from the B-rich phase by a single interface, while in the case of “symmetric” walls 

which both attract the same component a stratified structure with two interfaces parallel to the walls results). 

Only for a distinctly larger value χc (D), controlled by the strength of the wall-monomer interactions and 

related to the wetting transition of a semi-infinite polymer blend, is a sharp phase transition encountered, 

related to lateral phase separation. For the case where in the semi-infinite geometry one has first-order 

wetting, the thin film shows a triple point, and two critical points appear as remnants of prewetting criticality. 

For asymmetric surfaces forces, the triple point can merge with one of the critical points, and a phase 

diagram with a single critical point remains. Also tricritical phenomena in thin films may occur. Ginzburg 

criteria are developed for a discussion of the validity of the mean field description. Finally, also some 

comments on related experiments [6] are made. 

References 

1. Müller, M. and Binder, K., 1998. Macromolecules 31, 8323. 

2. Müller, M, Binder, K. and Albano, E. V., 2000. Europhys. Lett 49, 724. 

3. Müller, M, Binder, K. and Albano, E. V., 2000. Physica A279, 188. 

4. Müller, M, Albano, E. V. and Binder, K., 2000. Phys. Rev. E62, 5281. 

5. Müller, M. and Binder, K., 2001. Phys. Rev. E63, 021602. 

6. Kerle, T, Klein, J. and Binder, K., 1996; 1999. Phys. Rev. Lett. 77, 1318; Europ. Phys. J. B7, 401.

SWEET BRUSHES: SYNTHESIS AND INTERFACIAL BEHAVIOUR OF POLYSTYRENE- 

POLYSACCHARIDE DI-BLOCK COPOLYMERS 

W.T.E. Bosker 1) , K. Ágoston 2) , M.A. Cohen Stuart 1) , W. Norde 1) , J.W. Timmermans 2) , 

T.M. Slaghek 3) 

1) Department of Physical Chemistry and Colloid Science, Wageningen University, 


2) Agrotechnological Research Institute ATO, 

Wageningen UR, 6700 AA Wageningen, The Netherlands 

3) TNO Nutrition and Food Research, 

3704 HE Zeist, The Netherlands 

email: bosker@fenk.wau.nl 

ABSTRACT 

Research has revealed that coating surfaces with hydrophilic polymer brushes can prevent or reduce protein 

adsorption and hence retard biofouling. In biological systems the use of natural polymers may be preferred 

and polysaccharides seem to be the most plausible candidate. Linear block copolymers of polystyrene and 

polysaccharide were synthesized using a block synthesis method with amino terminated polystyrene and 

sodium cyanoborohydride as reducing agent. Different types of polysaccharides, dextrans and maltodextrins, 

with various molecular weights were used. 

IR spectroscopy indicated a successful coupling. Yields are 75 to 95 wt%. Interfacial pressure measurements 

of monolayers of the copolymers showed hysteresis between successive compression and expansion 

cycles. This is, to a large extent, due to the slow adsorption/desorption of the polysaccharide chains at the 

air-water interface and the formation of aggregates of copolymer at the interface, mainly by H-bonding 

between adjacent polysaccharide chains. When the time scale of compression and expansion is increased 

the hysteresis becomes smaller and reaches a time independent level, demonstrating a permanent change in 

conformation of the copolymers. The relaxation time for hysteresis is 85 minutes. Interfacial pressure 

isotherms differ from theoretical polymer brush model predictions. The deviation is attributed to the relative 

short length of the polysaccharide chains.

STABILITY OF CHARGED LIPID VESICLES: EXPERIMENTS AND SCF-CALCULATIONS 

M.M.A.E. Claessens, B.F. van Oort, F.A.M. Leermakers 



email: mireille@fenk.wau.nl 

ABSTRACT 

The unilamellar vesicle is a stable state for both anionic DOPG and zwitterionic DOPC bialyers in salt 

solutions. The equilibrium size of these vesicles strongly depends on the ionic strength and the type of salt 

solution. Molecularly realistic self consistent field calculations show that single component vesicles have no 

spontaneous curvature. The predictions for the mean bending moduli kc correlate well with the experimentally 

found trends in vesicle radii. This gives rise to the hypothesis that the vesicles are entropically stabilized.

EFFECT OF MIXING OF TWO CHARGED PHOSPHOLIPIDS ON VESICLE SIZE AND 

MEAN BENDING MODULI 

M.M.A.E. Claessens, B.F. van Oort, F.A.M. Leermakers 



email: mireille@fenk.wau.nl 

ABSTRACT 

The mean bending modulus, kc, of a bilayer of a surfactant mixture is expected to depend on the 

composition. It is usually assumed that kc decreases towards the equimolar composition. As the the 

size of entropically stabilized vesicles is related to kc, a decrease in kc will result in smaller vesicles. 

Previously we showed that both the anionic DOPC and the zwitterionic DOPG form vesicles that are 

stabilized by undulation entropy. Mixtures of these bilayer forming phospholipids indeed have a 

decreased equilibrium size compared to the pure component vesicles. SCF calculations were used 

to obtain kc for mixtures of chared surfactants. The predictions for kc correlate well with the experimentally 

found trends in vesicle radii. The changes in kc are not only due to the mixing of lipids, 

variations in charge density also affect kc.

VOLUME FRACTION PROFILES OF ADSORBED POLYMER LAYERS 

T. Cosgrove 1) , J. Marshall 1) , J. Hone 1) , F. Leermakers 2) , T.M. Obey 1) , J. Marshall 1) 

1) University of Bristol, School of Chemistry, 

Cantock’s Close, Bristol BS8 1TS, United Kingdom 

2) Laboratory of Physical and Colloid Chemistry, Wageningen University, 

Dreijenplein 6, 6703 BC Wageningen, The Netherlands 

email: terence.cosgrove@bris.ac.uk 

ABSTRACT 

Volume fraction profiles for adsorbed polymers are central to the understanding and manipulation of colloidal 

dispersions. Small-angle neutron scattering has proven to be an elegant method for determining the shape of 

the volume fraction profile though there are some difficulties in dealing with concentration fluctuations. In this 

presentation we shall develop the SANS methods for both on and off contrast scattering and use it together 

with scaling and mean field theories to provide the most detailed shapes yet for adsorbed polymer layers on 

colloidal particles. The improvement in these methods due to better resolution in particle size and momentum 

transfer (Q) has made it possible to expand the studies to look at complex formation at interfaces with 

surfactants and sugars. 

Results and Discussion 

-1 

I(Q) /cm 

1 

0.1 

0.01 

Q /Å -1 

0.01 0.1 

Figure 1 Figure 2 

(z) φ 

0.1 

0.01 

0.001 

112.1 K PEO Exponential Profiles 

112.1 K PEO Scaling Profiles 

112.1 K PEO Scheutjens-Fleer Profiles 

0 50 100 150 200 250 

Figure 1 shows the scattering obtained from a deuterated polystyrene latex with adsorbed polyethylene oxide 

(110K Mw) suspended in water that has the same scattering length density as the latex. Under these 

circumstances the latex is essentially invisible. However, unlike earlier data we observe strong oscillation in 

the scattering from the polymer layer. This is partly due to preparing a very monodisperse latex (radii 

625 ± 20 Ã and 443 ± 10 Ã) and by obtaining higher Q resolution on the D22 camera at Grenoble and NG3 at 

NIST. The data have been fitted using an exponential volume fraction profile with fluctuations (solid line) and 

without fluctuations (dashed line) both smeared for Q resolution. It is clear that fluctuations do contribute to 

the scattering and without suitable safeguards fitting the data without fluctuations can be problematical. 

z /Å 

R g 112.1 K PEO

Figure 2 show a semi-log comparison of volume fraction profiles obtained from fits to the on-contrast layer 

scattering (black lines) and interference scattering (red lines) for 112 kD PEO at full surface coverage. The 

calculated radius of gyration (Rg) for 112 kD PEO is also shown. Three different functional forms have been 

chosen to fit the data, an exponential (as in Figure 1), a scaling profile and a profile generated by a modified 

Scheutjens Fleer (SF) theory. The profiles in the last case overlap completely. Further examples will be 

shown and the results indicate that up to ca 100k Mw the SF model can quantitatively predict the scattering 

data. Beyond this molecular weight as tails become progressively more extended and dilute the scattering 

becomes progressively less sensitive to the layer extent. 

Other systems that will be discussed include grafted and physically adsorbed PEO layers complexing with 

surfactants and cyclodextrins. Figure 3 below shows the volume fraction profiles for a grafted PEO layer and 

the effect of addition of α-cyclodextrin. Cyclodextrin forms spontaneous inclusion complexes with PEO in 

solution that are insoluble and precipitate. In the case of a grafted layer geometric constraints would prevent 

a complete complexation( the cyclic sugar threads on to the chain starting at one end). The data here show 

that these complexes can form at interfaces, causing the chains to stiffen and expand. 

Volume fraction 

0.4 

0.3 

0.2 

0.1 

0.0 

Increased CD 

concentration 

5.7Å αααα cyclodextrin 

0 100 200 

z/Å 

300 400 

References 

1. Fleer, G.J., Cohen Stuart, M.A., Scheutjens, J.M.H.M., Cosgrove, T., Vincent, B. Polymers at Interfaces, 

Chapman and Hall, London, 1993. 

2. Auvray, L., Auroy, P. Neutron, X-Ray and Light Scattering; Linder, P. and Zemb, T., Eds., Elsevier 

Science Publishers, B.V., Amsterdam, 1991. 

3. Hone, J.H.E., Cosgrove, T., Saphiannikova, M., Obey, T.M., Crowley, T.L., 2002. Langmuir 18, 855-864.

DETAILED ATOMISTIC MONTE CARLO SIMULATION OF GRAFTED POLYMER MELTS: 

THERMODYNAMIC, CONFORMATIONAL AND STRUCTURAL PROPERTIES 

K.Ch. Daoulas, V.G. Mavrantzas 

Institute of Chemical Engineering and High-Temperature Chemical Processes, 

ICE/HT-FORTH, GR 26500, Patras, Greece 

email: daoulas@physics.upatras.gr 

ABSTRACT 

The thermodynamic and conformational properties of polymer melts grafted on a solid substrate as obtained 

from detailed, atomistic Monte Carlo simulations with the end-bridging algorithm are presented. The interface 

between a basal graphite plane (as well as a non-interacting hard surface) and a bulk polyethylene (PE) melt, 

a few or all chains of which are grafted on the plane, has been studied. Three different PE melts, of mean 

molecular length C78, C156 and C250, have been investigated, at grafting densities ranging from 0.54 nm –2 to 

2.62 nm –2 . For melts composed of grafted and free chains, it is observed that, at moderate to high surface 

densities (σ ≥ 1 nm –2 ), the region close to the substrate is fully occupied by segments belonging to grafted 

chains, which are forced by their chemical grafting to have their first segment on the interface. As the grafting 

density increases, free chains are progressively expelled from the surface region, in agreement with scaling 

arguments and the predictions of a lattice-based self-consistent mean-field (SCF) theory. For melts grafted 

on a graphite plane, it is also seen that the local melt density in the region closest to the interface is 

systematically higher than in the bulk, exhibiting distinct local maxima due to polymer adsorption. Results for 

the chain conformation tensor demonstrate that chains are significantly stretched in the direction 

perpendicular to the surface, even for moderate surface densities. For the C250 PE melt at a grafting density 

σ = 1.31 nm –2 , for example, the average chain dimension perpendicular to the interface is 1.9 times larger 

than its equilibrium value in the bulk. The profile of the chain end density is also seen to exhibit universal 

behavior in agreement with the predictions of the SCF theory. Additional results concerning the mean chain 

conformational path, the structure of the interfacial area for both systems studied (fully grafted and mixtures 

of grafted and free chain systems) and their 2 H NMR spectra are also presented. Further, the dependence of 

all these properties on chain polydispersity will be assessed.

MODELING OF STATIONARY POLYMER DIFFUSION: APPLICATIONS OF A NON- 

EQUILIBRIUM SCF-METHOD 

S.M. Scheinhardt-Engels, F.A.M. Leermakers and G.J. Fleer 



email: sonja@fenk.wau.nl 

ABSTRACT 

We present a few applications of the Mean Field Stationary Diffusion (MFSD) method. This method allows 

the study of diffusion in polymer systems driven by (for example) a concentration gradient. We do not follow 

the evolution of the system towards the stationary state, but we obtain immediately the stationary state itself, 

which is the situation that there is no accumulation of material anywhere in the diffusion layer. The method 

has the Scheutjens-Fleer result for equilibrium inhomogeneous polymer solutions as its limit when gradients 

in chemical potential vanish. We show volume fraction profiles of such stationary polymer systems. In the 

case of ‘color’ diffusion, where there are no interactions between the diffusing substances, the strong influence 

of mobility-differences is immediately seen. If there are intermolecular interactions, an interface 

between diffusing substances may develop even for χ χ 

< critical . The flux-expressions of the MFSD method 

are used to obtain simple analytical approximations for the coexistence curves of polymer mixtures. We show 

that these approximations are more accurate than other analytical approximations. Finally, we present some 

results on diffusion through a barrier, where we employ the possibility to monitor the polymer conformations.

A SCF STUDY OF INHOMOGENEOUS ADSORPTION OF NON-IONIC SURFACTANTS 

ON HYDROPHOBIC SURFACES 

A.B. Jódar-Reyes, J.L. Ortega-Vinuesa, A. Martín-Rodríguez, F.A.M. Leermakers 

University of Granada, Dpto. Fisica Aplicada, Facultad de Ciencias, Fuent, 

Granada, 18071, Spain 

email: ajodar@ugr.es 

ABSTRACT 

The structure of non-ionic surfactant layer adsorbed on a hydrophobic surface is studied by means the 

SCF-A. The possibility of formation of surface aggregates instead of homogeneous layers is included. 

Applying the one-gradient version of this theory in combination with the two-gradient one, we could 

follow the evolution of the adsorption process for several lengths of the PEO head. A branched 

hydrocarbon tail model that has an important effect on micellisation and adsorption results is also 

used. Theoretical results are compared to the experimental adsorption isotherms of Triton X-100 and 

Triton X-405 onto a polystyrene Latex dispersion. The process including inhomogeneous adsorption is 

closer to the experimental results than the homogeneous one.

THEORY AND SIMULATION OF BILAYER MEMBRANE FUSION: 

FREE ENERGY AND STRUCTURE OF INTERMEDIATES 

K. Katsov 1) , M. Schick 1) , M. Mueller 2) 

1) Department of Physics, University of Washington, U.S.A. 

2) Institut für Physik, Johannes-Gutenberg-Universität, Mainz, Germany 

email: schick@mahler.phys.washington.edu 

ABSTRACT 

We combine Monte Carlo simulations and SCF theory to study the microscopic mechanism of bilayer 

membrane fusion. Bilayers are composed of single chain amphiphiles in an excess homopolymer solvent. 

The fusion mechanism we observe in simulations is very different from a widely accepted "stalk" hypothesis. 

Instead of the radial stalk expansion into a hemifusion diaphragm with subsequent fusion pore formation, we 

observe very strong bilayer destabilization after the first local connections (stalks) are formed. This 

destabilization leads to a local rupture of the membranes in the vicinity of the stalk with a following sealing off 

of the formed microscopic holes by propagation of the initial connection (stalk). 

The observed mechanism is supported by our SCFT calculations of the structure and free energy of 

different intermediates that could be involved in the fusion process. The structures that we are able to study 

within the SCFT include bilayer edge, 3- and 4-junctions, point and linear stalks and some transition states. 

We calculate both relative stability of the intermediates and barriers encountered along the alternative fusion 

reaction paths. We also address the problem of mixed bilayers and find relatively strong deviations from the 

ideal mixing. 

The obtained results allow us to make very definite predictions that can be checked experimentally. This 

includes, e.g. the effect of tension and amphiphile architecture on the fusion rate, and the fact that the 

membrane fusion is a leaky process.

DYNAMIC EXTENSION OF THE SELF-CONSISTENT FIELD THEORY OF 

INHOMOGENEOUS POLYMER SYSTEMS 

T. Kawakatsu 

Department of Physics, Tohoku University, 

Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan 

email: kawakatu@cmpt.phys.tohoku.ac.jp 

ABSTRACT 

1. Introduction 

Self-consistent field (SCF) theory is one of the useful techniques for studying mesoscopic structures of 

inhomogeneous polymer systems, such as phase separating polymer blends, polymer films on solid 

surfaces, and polymer brushes (Fleer 1993, Matsen 1996). Combined with a numerical evaluation of the 

polymer path integral, i.e. canonical statistical weight of the chain conformation, this theory well reproduces 

the equilibrium domain structures and segment density profiles. Despite of such success in 

equilibrium systems, extensions to dynamic non-equilibrium systems have not completely understood yet. 

In the present study, we propose several techniques to introduce dynamic processes into the SCF theory, 

and evaluate their usefulness and efficiency. 

2. Dynamic SCF method for weakly non-equilibrium systems 

The dynamic extension of the SCF theory has been initiated by Fraaije (Fraaije 1993) by combining 

the SCF theory with the Fick’s law of segment diffusion driven by the gradient of the chemical potential. 

To obtain the chemical potential, the system is assumed to be in local equilibrium, which is essential for 

the use of the path integral formalism. Using this technique, one can calculate the ordering processes in 

phase separating polymer blends or block copolymer systems. For example, we can reproduce the phase 

diagram of a mixture of long and short block copolymers that shows complex domain structures (Morita 

2002). Using the segment interaction parameters and the block ratio (the ratio between the lengths of the 

two blocks) as input parameters, the dynamic SCF calculation gives a quantitatively correct phase 

diagram and domain structures including metastable transient structures. 

The success of these dynamic SCF simulations owes to the weak non-equilibrium nature of the 

phenomena, which is crucial to the use of the path integral formalism of the polymer chain conformation. 

3. Highly non-equilibrium systems -- Rheological properties -- 

As in the case of a sheared polymer melt, an external deformation force makes the chain conformation 

strongly stretched. In such a situation, the assumption of the local equilibrium becomes unreliable. To 

overcome this difficulty, we extend the path integral formalism by introducing the bond orientation tensor, 

and combined it with the reptation dynamics (Kawakatsu 2001, Shima 2002). In this formalism, the 

polymer path integral Q ( s, r; s′ , r ' ) , i.e. the statistical weight of a subchain between the s -th and s′ -th 

segments whose ends are found at r and r ′ , is given by 

∂ 

1 

Q( s, r; s′ , r') = ∇∇: { A( s, r) Q( s, r; s′ , r') } −∇⋅{ u( s, r) Q( s, r; s′ , r') } −βV( 

r) Q( s, r; s′ , r ') 

, 

∂s 

2 

where u( s, 

r ) and A( s, 

r ) are the average and covariance of the distribution of the s -th bond vector, 

and V ( r ) is the self-consistent field. The temporal evolutions of u( s, 

r ) and A( s, 

r ) are determined by 

the reptation theory and the Navier-Stokes equation (Kawakatsu 2001, Shima 2002). A similar treatment 

has recently been used by Fredrickson (Fredrickson, 2002). 

We applied this method to a sheared two parallel plates on which melt brushes are grafted. Due to the 

disentanglement between the two brushes, the shear stress and the density profile of the segments 

changes as is shown in Figure 1. Such a behavior is consistent with a microscopic Monte Carlo 

simulation using a many chain system.

Figure 1. Time evolution of the shear stress and the change in the segment density profile. 

4. Conclusions 

We have proposed a new method to simulate rheological properties of the dense polymer systems using 

SCF technique. By applying it to sheared polymer brushes, we demonstrated its usefulness. This technique 

could also be applied to many non-equilibrium phenomena in dense polymer systems, such as 

adhesion, phase separation, and so on. 

References 

1. Fleer, G.J., Cohen Stuart, M.A., Scheutjens, J.M.H.M., Cosgrove, T., and Vincent, B. Polymers at 

Interfaces. Chapman & Hall, 1993. 

2. Fraaije, J.G.E.M., 1993. Dynamic density functional theory for microphase separation kinetics of block 

copolymer melts. J. Chem. Phys., 99 (11), 9202-9212. 

3. Fredrickson, G., Dynamics and rheology of inhomogeneous polymeric fluids. A complex Langevin 

approach, preprint. 

4. Kawakatsu, T., 2001. Mesoscale modellings of multiphase polymer systems using density functional 

approaches, The Knowledge Foundation’s 2 nd International Conference on “Multiscale modeling – 

Bridging the gap between atomistic and mesoscales –“, Boston, 2001. 

5. Matsen, M. and Bates, F., 1996. Unifying weak- and strong-segregation block copolymer theories. 

Macromolecules, 29 (4), 1091-1098. 

6. Morita, H., Kawakatsu, T., Doi, M., Yamaguchi, D., Takenaka, M., and Hashimoto, T., 2002. 

Competition between micro- and macrophase separations in a binary mixture of block copolymers. A 

dynamic density functional study. Macromolelues, in press. 

7. Shima, T., Kuni, H., Okabe, Y., Doi, M., Yuan, X.-F., and Kawakatsu, T., 2002. Self-consistent field 

theory of viscoelastic behavior of inhomogeneous dense polymer systems, Macromolecules, 

submitted.

ADSORPTION OF PERIODIC AND RANDOM AB COPOLYMERS 

L. Klushin 1,2) , E. Maraachlian 1) , A. Skvortsov 3) 

1) American University of Beirut, Department of Physics, Beirut, Lebanon 

2) 

Institute for Macromolecular Compounds, Russian Academy of Sciences, 

St. Petersburg, Russia 

3) 

Chemical-Pharmaceutical Academy, St. Petersburg, Russia 

email: leo@aub.edu.lb 

ABSTRACT 

The goal of this work is to compare the effects of composition for random and periodic (multiblock) AB 

copolymers on their localization at liquid-liquid and solid-liquid interfaces. Recently, it was extensively 

demonstrated that random monomer distribution promotes localization of copolymers at liquid-liquid 

interface as compared to periodic copolymers of the same average composition [1-3]. Here we 

investigate the effects of composition on adsorption at a planar solid surface. The energy of contact for 

a monomers A with the surface is ε , while the surface is assumed to be inert for monomers B 

(ε = 0 ). The energy of interaction per monomer averaged over composition is thus ε = f ε , where f 

B 

is the fraction of A monomers. An ideal lattice chain model is used to calculate numerically the thermodynamic 

average energy per segment and to determine the critical point of adsorption. We also 

calculate the average thickness of the adsorbed layer. 

For regular copolymers (periodic composition) in the range 1≤f ≤0.3, 

the critical point of 

adsorption is defined up to high accuracy by the composition average energy f ε = ε (homo) where 

c c 

ε (homo) is the critical energy for a homopolymer. This is in agreement with the earlier results of Di 

c 

Marzio et.al. [4]. We find that the dependence of the number of contacts and the thickness of the 

adsorbed layer on ε in the vicinity of the critical point is well described by the analytical expressions 

for a homopolymer with the effective energy per monomer ε . 

For adsorption of random copolymers at a solid-liquid surface, a theory based on replica treatment 

[5] predicts the critical adsorption energy to be lower than expected from simple composition average 

arguments mentioned above, the deviation being especially prominent around f = 0.5. Our numerical 

calculations for chains of polymerization index up to N = 10 4 show that the difference in the critical 

energy between regular and random copolymers is quite negligible in the composition range 

1≤f ≤0.5. 

We develop an alternative analytical theory based on the trial potential approach 

introduced in [3] that supports this result. 

For lower values of f, (f < 0.2), the critical energy of adsorption for random copolymers becomes 

noticeably lower than that for periodic chains. Both critical energies deviate significantly from the 

simple composition average prediction. For periodic copolymers, the order parameter and the thickness 

of the adsorbed layer as functions of ( ε − εс) εcare 

still well described by “effective homopolymer” 

expressions. For random copolymers, this description fails. 

References 

1. Sommer, J.-U., Daoud, M., 1995. Europhys. Let. 32, 407. 

2. Dai, C.-A., et.al., 1994; 1995. Phys. Rev. Lett. 73, 2472; 74, 2837. 

3. Chen, Z.Y., 1999; 2000. J. Chem. Phys. 111, 5603; 112, 8665. 

4. Di Marzio, E.A., Guttman, C.M., Ma, A., 1995. Macromolecules 28, 2930. 

5. Gutman, L., Chakraborty, A., 1995. J. Chem. Phys. 103, 10733.

SALT EFFECT TO RAYLEIGH DROPLETS OF HYDROPHOBIC POLYELECTROLYTES 

H. Kodama 

Mitsubishi Chemical Corporation, 

Naruse 2-17-1-17-105, Machida, 194-0044, Japan 

email: kodama@rc.m-kagaku.co.jp 

ABSTRACT 

A finite size droplets (aggregates) of weakly charged polyelectrolytes in poor solvents are analyzed in 

terms of mean-field Poisson-Boltzmann + Edwards approach. The standard chemical potential per 

chain is calculated as a function of the number of polyelectrolyte molecules in a droplet for a given salt 

concentration, and the droplet size distribution is computed. It will be shown that a classical Rayleightype 

argument [1] breaks down because of the counterion condensations. For low salt concentration, a 

finite size droplets can stably exist, while infinite aggregates emerge (macrophase separation) for high 

salt concentration. 

A simulation program "SUSHI" in the "OCTA" system (http://octa.jp) is used to perform the above 

calculations. 

Reference 

Joanny, J. F. and Leibler, L., 1990. J. Phys. France 51 545.

ELECTRIC FIELD VERSUS SURFACE ALIGNMENT IN CONFINED FILMS OF A BLOCK 

COPOLYMER MELT 

A.V. Kyrylyuk, G.J.A. Sevink, A.V. Zvelindovsky, J.G.E.M. Fraaije 

Leiden University, 

P.O.Box 9502, 2300 RA Leiden, The Netherlands 

email: a.kiriluk@chem.leidenuniv.nl 

ABSTRACT 

The dynamics of alignment af a block copolymer microstructure in thin films in the presence of an 

external electric filed has been studied numerically. We considered in detail a symmetric diblock 

copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density 

functional method, derived from the generalized time-dependent Ginzburg-Landau theory. We allow 

for a slight compressibility by adding a Helfand penalty function to the free energy. We investigated 

the effect of an electric filed on block copolymers under the assumption that the dipolar interaction 

induced due to the fluctuations of composition pattern is a dominant mechanism of electric field 

induced domain alignment. As a result, depending on the ratio between electric filed and interfacial 

interactions, perpendicular, parallel or intermediate (mixed) final lamellar structures were obtained. 

The intermediate mixed structures remains to be stable, though these structures do not correspond to 

the minimum of the free energy. While alignment process, the mesophases passes through 

fascinating states of coexistence of several lamellae clusters with different orientations.

MACROMOLECULES AT INTERFACES, A FLEXIBLE THEORY FOR HARD SYSTEMS 

F.A.M. Leermakers 




ABSTRACT 

On January 11 1985 Jan Scheutjens defended his thesis entitled “Macromolecules at interfaces, a flexible 

theory for hard systems”. In this thesis the Scheutjens-Fleer self-consistent field SF-SCF theory is presented 

and applied mainly, but not exclusively, to homopolymers at interfaces. It condensed the work done over a 

period of about 10 years in close harmony with Gerard Fleer and several MSc students of whom I was one, 

into a booklet of 168 pages. In retrospect one can say that Jan re-invented (almost single-handedly) the selfconsistent-field 

method. In the early days (before 1980) there was no knowledge in laboratory of Physical 

Chemistry and Colloid Science in Wageningen about comparable approaches in quantum mechanics. Also 

the close relation of his work to the Edwards diffusion equation was not known. The work has long been (and 

still is) associated to lattice models. The reason for this is clear, because the deep understanding of the 

theory was based on counting conformations and interactions of polymer chains on a lattice. The goal of this 

lecture is to prove that the discretisation scheme of Scheutjens (and Fleer) of the self-consistent field 

equations for polymer adsorption is even today a very powerful, flexible tool to obtain better insights in hard 

systems such as macromolecules at interfaces. I will do this in the context of the state of the art 10 years ago 

(when Jan passed away). 

I will discuss a new self-consistent-field method, that better than in the classical SF-SCF approach, 

accounts for the intra-molecular excluded-volume effects of the polymer molecules. The method that has 

been developed together with Ph.D’s Jan van Male and Jos van den Oever, features translationally constraint 

molecules in a two-gradient cylindrical coordinate system. The equilibrium between chains in the bulk and 

near the surface can only be established by hand. For this the accurate evaluation of appropriate thermodynamic 

quantities is necessary. A selection of applications will be discussed. 

Homopolymer adsorption 

The theory of homopolymers at solid–liquid interfaces was the first problem considered by Jan 

Scheutjens. It also turns out to be (numerically) one of the hardest problems. The adsorption-desorption 

transition in polymer adsorption is smooth. It is shown that the polymer conformation near the adsorption 

transition transforms from the coil to the pancake. The radius scales as R ∝ α 

g N , whereα ≈ 0.6 for the coil 

and α = 3 / 4 for the pancake. 

Ten years ago, the self-similar scaling in the central region of the polymer adsorption profile was basically 

understood (Van der Linden worked in close cooperation with the Strasbourg group on this issue) from a 

ground-state approximation. However, the mean-field power law ϕ ( ) ∝ −2 

z z that was found in the limit of long 

chains and strong adsorption, of course deviated from the prediction of De Gennes: ϕ ( ) ∝ −4/3 

z z . The failure 

was often attributed to the fact that ‘correlations’ were neglected. The new method (still being a mean-field 

theory) is in reasonable agreement with the result of De Gennes.

Polyelectrolyte adsorption 

Van der Steeg in our group considered polyelectrolyte adsorption in the limit of electrostatic interactions 

only. She showed that polyelectrolytes are attracted to an oppositely charged surface. The gain in entropy of 

the small ions is the driving force for this. The strongest adsorption and the highest adsorbed amount, was 

found in the limit of low ionic strength. In the absence of non-electrostatic interactions no charge overcompensation 

was found. Accounting for intramolecular excluded-volume effects shows that this result 

should be reconsidered: I will report on the overcompensation of the surface charge that is found for 

polyelectrolyte stars electrostatically attracted to an oppositely charged surface (work together with Zhulina). 

Copolymer (protein analogues) near interfaces 

Jan Scheutjens was extremely interested in biological applications. The work on lipid bilayer membranes 

was just one example. I will show how the new approach can be used to obtain interesting results for the 

adsorption of charged partially collapsed copolymers (protein analogues) adsorbing on charged surfaces. 

This work is done in collaboration with Jos van den Oever who carefully worked out the electrostatics in a 

two-gradient approach for systems in which the dielectric permittivity is not homogeneous. 

The effects of tails of adsorbed polymers on the colloidal stability 

The effect of polymers on the colloidal stability and the importance of tails were probably the two main 

insights often pushed by Jan Scheutjens. However, at full equilibrium, the interaction induced by the polymer 

chains was found to be purely attractive. Now we know that this result shows that in fact the loops dominate 

the pair interaction. Only recently Semenov showed that there is a very small repulsive contribution of the 

tails that can be seen when the surfaces are a distance H ≈ R g apart. Together with Jan van Male I 

considered the adsorption of homopolymers on a surface onto which short chains were grafted. This ‘fur’ 

layer suppresses short loops. As a consequence tails dominate the adsorbed layer characteristics. In this 

case it is possible to obtain purely repulsive interaction potential for homopolymer adsorbing in full 

equilibrium. If time allows I will address this issue as well. It is already found for the classical SF-SCF theory. 

It is necessary to mention that our group still benefits from what Jan Scheutjens left behind. The best way 

to illustrate this is to mention that the SCF equations can usually only be solved numerically. Jan Scheutjens 

wrote a generic solver based on a Newton-like minimization algorithm optimized to tackle these ill-behaving 

functions. This solver is the hart of the computer program SFBox that has been used to generate results 

presented in this lecture. For good order, Jan van Male did most of the implementations of this unique 

program making use of many ‘old’ tricks.

APPLICATION OF HETEROGENEOUS LATTICE MEAN-FIELD THEORY APPLIED TO 

SYSTEMS WITH INTERNAL DEGREES OF FREEDOM, POLYELECTROLYTES, AND 

CAPILLARY INDUCED PHASE SEPARATION 

P. Linse 

Center for Chemistry and Chemical Engineering, Lund University, 

P.O. Box 124, S-221 00 Lund, Sweden 

email: per.linse@fkem1.lu.se 

ABSTRACT 


The impact of the ideas in the seminal papers by Jan Scheutjens and Gerard Fleer (SF) presented 1979 

and 1980 (Scheutjens 1979, Scheutjens 1980) can hardly be exaggerated. Today, about 200 papers have 

been published containing calculations based on their ideas, and ca. 10 doctoral theses have been devoted 

to developments and applications of the theory by SF. 

The start of my acquaintance with the SF-theory appeared in the second half of the 80:ies, when the 

original papers of SF came in my hand. At that time, I gave the PhD student Mikael Björling the task to merge 

the SF-theory with another idea of representing polymers with internal states. Since then, the original SFtheory 

and its later numerous extensions have been one of the main theoretical tool in my research. 

Throughout, we have close contacts with the Wageningen group and heavily utilized their developments. 

The aim of my presentation is to (i) provide an overview of the developments and applications made in the 

Lund group during the last decade and to give a more in-dept account of three different areas, (ii.a) systems 

with internal states, (ii.b) polyelectrolytes, and (iii.c) capillary induced phase separation. 

2. Overview 

The SF-theory has been, and is still, used in our laboratory to provide a deepen understanding of polymer 

in solution. The focus has been to apply the theory on systems currently under experimental investigation. In 

many occasions, it has been an extremely valuable tool for improving the analysis of experimental results. 

However, the results of the SF-theory has also been employed to examine scaling predictions and been 

confronted with results from Monte Carlo simulations. 

The overview will contain examples covering phase diagram of ethylene oxide (EO) and propylene oxide 

(PO) containing polymers and copolymers, micellization of corresponding copolymers, adsorption of these 

copolymers at interfaces/surfaces, partitioning of proteins in polymer two-phase systems, forces between 

solid surfaces mediated by block copolymers. In addition, significant effort has been made to investigate the 

phase behavior in polymer mixtures containing polyelectrolytes, adsorption of polyelectrolytes to solid 

surfaces, and the self-association of charged block copolymers. Moreover, examples of properties of novel 

charged block copolymers grafted at a solid support will be provided. 

3. Systems with internal degrees of freedom 

An important class of polymers as poly(propylene oxide) (PEO) display an decreasing solubility in water 

upon a temperature increase. This behavior is not captured by the standard Flory-Hugins theory for polymer 

solutions. Instead of using an ad-hoc temperature dependent χ-parameter, Gunnar Karlström introduced on 

the basis of quantum mechanical calculations the concept of internal states (Karlström 1985). With this 

concept, a framework for describing the reverse temperature dependence was established. Despite that still a 

few parameters needs to be fitted, here to the phase diagram of PEO in aqueous solution, this approach 

provides a mechanism and understanding for the reverse temperature dependence.

An important step in our theoretical developments was the fusion of the SF-theory (at that time 

generalized by Olav Evers et al. (Evers 1990) to arbitrary number of components, copolymers etc) with the 

concept of internal states (Linse 1991). This theoretical foundation was then extensively utilized to in great 

detail describe the self-association of PEO-PPO-PEO block copolymers, the role of composition (Linse 

1993a), sphere-to-rod transition (Linse 1993b), impurities (Linse 1994a), and polydispersity (Linse 1994b) as 

well as the appearance of lyotropic liquid crystalline phases (Noolandi 1996, Svensson 1999) and the 

adsorption to surfaces and interfaces (Tiberg 1991, Malmsten 1992, Linse 1997). These predictions were 

made with essentially no fitted parameters of the actual systems. All parameters used (except those involving 

solid surfaces) were taken from previous studies, where they were determined by fitting to phase diagrams of 

simple solutions of homopolymers. 

4. Polyelectrolytes 

The properties of homogeneous systems containing polyelectrolytes can be successfully addressed by 

extending the Flory-Huggins theory and, similarly, properties of heterogeneous systems containing 

polyelectrolytes can be dealt within the SF-theory. In the former case, the simplest but yet powerful approach 

is to enforce charge neutrality of the individual phases being in equilibrium (Gottschalk 1998). In the latter 

case, the SF-theory was extended with the Poisson equation (Böhmer 1991), and typically the electrostatics 

are described on the same level as in the Poisson-Boltzmann equation, although subjected to an 

descretization implied by the layers. 

Examples of predictions of the phase behavior of solutions polyelectrolyte and mixtures of polymers based 

on the extended Flory-Huggins theory will be given (Gottschalk 1998). Thereafter, the some selected 

properties of polyelectrolytes adsorbed or grafted to solid surfaces will be presented (Shubin 1995, Linse 

1996, Shusharina 2001). 

5. Capillary induced phase separation 

The capillary condensation may appear in many shapes and contexts. A few years ago, it displayed still 

another one. Experimentally, it was discovered (Freyssingeas 1998) that a mixture of two polymers close to a 

segregative phase separation may give rise to a very long-range attraction between to surfaces inserted in 

the polymer mixture. The range of attraction exceeds far the polymer extension and has a thermodynamic 

origin and arises from a capillary induced phase separation (CIPS) (Wennerström 1998). 

Lattice mean-field calculations have been performed and provided an enhanced understanding of this 

phenomenon. An account of the long-range attraction associated with CIPS will be given (Joabsson 2002). 

Here, the lattice mean-field theory provided convicting argument supporting previous analytic explanation of 

the long-range attraction. Presently, similar calculations are performed on polydisperse polymer solutions and 

solution of a single polymer. 

References 

1. Böhmer, M.R., Koopal, L.K. and Lyklema, J., 1991. Micellization of ionic surfactants. Calculations based 

on a self-consistent field lattice model. J. Phys. Chem., 1991, 9569. 

2. Evers, O.A., Scheutjens, J.M.H.M. and Fleer, G.J., 1990. Statistical thermodynamics of block copolymer 

adsorption. 1. Formulation of the model and results for the adsorbed layer structure. Macromolecules, 

23, 5221. 

3. Freyssingeas, E., Thuresson, K., Nylander, T., Joabsson, F. and Lindman, B., 1998. A surface force, 

light scattering, and osmotic pressure study of semidilute aqueous solutions of ethyl(hydroxyethyl) 

cellulose - long-range attraction forces between two polymer coated surfaces. Langmuir, 14, 5877. 

4. Gottschalk, M., Linse, P. and Piculell, L., 1998. Phase stability of polyelectrolyte solutions as predicted 

from lattice mean-field theory. Macromolecules, 31, 8407. 

5. Joabsson, F. and Linse, P., 2002. Capillary-induced phase separation in mixed polymer solutions. A 

lattice mean-field calculation study. Langmuir, 106, 3827. 

6. Karlström, G., 1985. A new model for upper and lower critical solution temperature in poly(ethylene 

oxide) solutions. J. Phys. Chem., 89, 4962. 

7. Linse, P., 1993a. Micellization of poly(ethylene oxide)-poly(propylene oxide) block copolymers in 

aqueous solution. Macromolecules, 26, 4437.

8. Linse, P., 1993b. Phase behavior of poly(ethylene oxide)-poly(propylene oxide) block copolymers in 

aqueous solution. J. Phys. Chem., 97, 13896. 

9. Linse, P., 1994a. Micellization of poly(ethylene oxide)-poly(propylene oxide) block copolymer in aqueous 

solution: Effect of polymer impurities. Macromolecules, 27, 2685. 

10. Linse, P., 1994b. Micellization of poly(ethylene oxide)-poly(propylene oxide) block copolymers in 

aqueous solution: Effect of polymer polydispersity. Macromolecules, 27, 6404. 

11. Linse, P., 1996. Adsorption of weakly charged polyelectrolytes at oppositely charged surfaces. Macromolecules, 

29, 326. 

12. Linse, P. and Björling, M., 1991. Lattice theory for multicomponent mixtures of copolymers with internal 

degrees of freedom in heterogeneous systems. Macromolecules, 24, 6700. 

13. Linse, P. and Hatton, T.A., 1997. Mean-field lattice calculations of ethylene oxide and propylene oxide 

containing homopolymers and triblock copolymers at the air/water interface. Langmuir, 13, 4066. 

14. Malmsten, M., Linse, P. and Cosgrove, T., 1992. Adsorption of peo-ppo-peo block copolymers at silica. 

Macromolecules, 25, 2474. 

15. Noolandi, J., Shi, A.-C. and Linse, P., 1996. Theory of phase behavior of poly(oxyethylene)-poly- 

(oxypropylene) - poly(oxyethylene) triblock copolymers in aqueous solutions. Macromolecules, 29, 5907. 

16. Scheutjens, J.M.H.M. and Fleer, G.J., 1979. Statistical theory of the adsorption of interacting chain 

molecules. 1. Partition function, segment density distribution and adsorption isotherms. J. Phys. Chem., 

83, 1619. 


molecules. 2. Train, loop, and tail size distributions. J. Phys. Chem., 84, 178. 

18. Shubin, V. and Linse, P., 1995. Effect of electrolytes on adsorption of cationic polyacrylamide on silica: 

Ellipsometric study and theoretical modeling. J. Phys. Chem., 99, 1285. 

19. Shusharina, N.P. and Linse, P., 2001. Oppositely charged polyelectrolytes grafted onto planar surfaces: 

Mean-field lattice theory. Eur. Phys. J. E6, 147. 

20. Svensson, M., Alexandridis, P. and Linse, P., 1999. Phase behaviour and microstructure in binary block 

copolymer/selective solvent systems: Experiment and theory. Macromolecules, 32, 637. 

21. Tiberg, F., Malmsten, M., Linse, P. and Lindman, B., 1991. Kinetic and equilibrium aspects of block 

copolymer adsorption. Langmuir, 7, 2723. 

22. Wennerström, H., Thuresson, K., Linse, P. and Freyssingeas, E., 1998. Long range attractive surface 

forces due to capillary-induced polymer incompatibility. Langmuir, 14, 5664.

MORPHOLOGIES IN THIN TRIBLOCK COPOLYMER FILMS 

K.S. Lyakhova 1) , A. Horvat 2) , G.J.A. Sevink 2) , A.V. Zvelindovsky 1) , R. Magerle 2) , 

J.G.E.M. Fraaije 1) 

1) 

Soft Condensed Matter Group, Leiden Institute of Chemistry, 

P.O. Box 9502, 2300 RA Leiden, The Netherlands 

2) 

Physicalishe Chemie II, University Bayreuth, 

D-95440 Bayreuth, Germany 

email: e.lyakhova@chem.leidenuniv.nl 

ABSTRACT 

The physics behind morphology formation in thin block copolymer films is not well understood. Recent 

experiments with free polystyrene- polybutadiene-polystyrene (SBS) films (in collaboration with Bayreuth 

University) result in complex morphologies, with terrace formation at integer domain distance film heights and 

connecting structures that are not present in bulk. In an article recently published [1], we compared these 

experiments with DDFT simulations for a geometry confined between two hard walls and symmetric polymerwall 

interaction. We identified two important parameters, the width of the slit and the surface interaction, and 

two relevant mechanisms: frustration and surface reconstruction. The experiments and the simulations match 

perfectly. In the present study, we extend our simulations to the more general case of asymmetric polymerwall 

interactions. The resulting asymmetry in surface reconstruction, combined with frustration, leads to a 

much richer phase diagram with many so-called hybrid structures. We compare the results to the symmetric 

phase diagram, and identify, similar to the symmetric case, the relevant mechanisms. 

Reference 

Knoll, A., Horvat, A., Lyakhova, K.S., Kraush, G., Sevink, G.J.A., Zvelindovsky, A.V., Magerle, R., 2002. 

Physical Review Letters 89 (3), 035501.

MODELING INTERFACIAL EFFECTS ON THE CONFORMATION AND RHEOLOGY OF 

POLYMER SOLUTIONS THROUGH A HIERARCHICAL, CONTINUUM MODEL 

V.G. Mavrantzas 1) , A.N. Beris 1,2) 

1) 

Institute of Chemical Engineering and High-Temperature Chemical Processes, 

ICE/HT-FORTH, GR 26500, Patras, Greece 

2) 

University of Delaware, Department of Chemical Engineering, 

Newark, DE 19716, U.S.A. 

email: vlasis@iceht.forth.gr 

ABSTRACT 

The Hamiltonian formulation of transport phenomena is employed to study the behavior of polymer solutions 

near a solid surface under both equilibrium (static) and nonequilibrium (flowing) conditions. The methodology 

is hierarchical and derives macroscopic flow equations which, through the use of selected internal variables, 

couple with the system microstructure. The bridging of the different length scales in the problem is achieved 

through the specification of the system Hamiltonian for which a microscopic model (at the level of Kuhn 

segments) is invoked. The macroscopic equations are derived through a two-fluid Hamiltonian model and 

consist of: (a) the concentration equation for the polymer component, (b) the momentum equation for the 

average fluid velocity, and (c) the constitutive equation for the stress-strain rate relationship which is a 

generalized Oldroyd-B model accounting for flow inhomogeneities. Under equilibrium conditions, the 

governing equations reduce to a minimization problem for the free energy of the system; this results into the 

well known equilibrium condition that the chemical potentials of all chain conformations in the interfacial area 

should be equal. However, the proposed methodology is more general and allows extending equilibrium 

considerations under flowing conditions, as well. In both cases, chain conformational characteristics near the 

solid boundary is taken into account through the solution of a diffusion equation for the chain propagator. 

Flow field effects are accommodated in the model by allowing the propagator to further depend on the 

Cauchy-Green strain tensor. Results are presented in two Parts for two cases: (a) the homopolymer 

adsorption problem and (b) the flow of a polymer solution past a non-interacting solid surface. In the first case 

(Part I), our model reduces to the continuum analogue of the original Scheutjens-Fleer lattice model, with 

which a thorough comparison is presented. In the second case (Part II), our model calculates selfconsistently 

the velocity profile in the interfacial area, and predicts the development of an apparent slip 

velocity near the wall of length scale commensurate with the size of the flowing polymer molecules.

HIERARCHICAL STRUCTURE FORMATION AND PATTERN TRANSFER INDUCED BY AN 

ELECTRIC FIELD 

M.D. Morariu 1) , N.E. Voicu 1) , E. Schaeffer 2) , U. Steiner 1) 

1) Polymer Physics, Rijksuniversiteit Groningen, 

Nijenborgh 4, 9747 AG, Groningen, The Netherlands 

2) Max Planck Institute of Molecular Cell Biology and Genetics, 

Pfotenhauerstrasse 108, 01307 Dresden, Germany 

email: u.steiner@chem.rug.nl 

ABSTRACT 

Fabrication of smaller and smaller surface structures is a current trend in materials science. Many different 

techniques were developed during the past years such as photolithography, microcontact printing, imprint 

lithography and electrically induced structure formation. We present here a new concept of pattern formation 

that make use of a sequence of instabilities. The technique is based on the process of destabilizing the 

surface of polymer films. By imposing a lateral variation of the force field, we are able to direct the instability 

to replicate a master pattern with high precision and 100% reproducibility. 

Electrohydrodynamic (EHD) instabilities have received considerable attention [1] and surface instabilities 

were studied using a variety of liquids. The triggering factor was the experimental observations of the rupture 

of a liquid surface by an external applied electric field. [2,3] Two different cases can be distinguished: [4-6] 

(i) Accumulation of charges at the interface due to a difference in the conductivities between liquid-air or 

liquid-liquid interface; and (ii) induction of polarization charges due to the external electric field. In the case of 

two polymeric liquids, the electrostatic pressure is smaller at the interface due to a lower difference in the 

dielectric constants and the dynamics is slowed down because of the viscous coupling and the dissipation in 

the second liquid layer. While these effects weaken the instability, the decrease in the interfacial tension 

enhances it. 

The control of patterns on sub-micrometer lateral length scales is of considerable technological interest. 

Since in our experiment the wavelength of the instability is on the order of microns, we were able to control 

the resulting pattern by using topographically structured electrodes. Any conventional lithographic technique 

[7] is sufficient to produce a master pattern that can be multiply used. A replicated structure is shown in fig. 1. 

Figure 1. The replicated topography and the subsequent structure that surrounds the main structure.

Using this patterned electrode, we induce a lateral anisotropy in the electric field. The instability is focused 

towards regions of highest fields and the final structure is a replica of the master pattern. In our experiments, 

due to the use of a polymer bilayer, a hierarchical pattern is formed. The first instability replicated the topography 

of the upper electrode. A subsequent instability creates a polymer structure that surrounds the main 

structure. In conclusion we have developed here a new non–optical lithographic technique, that can produce 

structures on sub-100 nm lateral scales. The method is very simple and does not need special equipment or 

materials. By tuning the system parameters, such as the applied voltage (U), distance between capacitor 

plates (d) or polymer film thickness and imposing a lateral non-uniformity in the electric field by using a 

patterned master electrode, we can produce hierarchical structures with high aspect ratio. 

References 

1. Tonks, L., 1935. Phys.Rev. 48, 562. 

2. Melcher, J.R. and Smith Jr., C.V., 1969 Phys. Fluids 12, 778. 

3. Melcher, J.R., 1961. Phys. Fluids 4, 1348. 

4. Melcher, J.R., 1963. MIT Press, Cambridge, Mass. 

5. Reynolds, M., 1965. Phys. Fluids 8, 161. 

6. Swan, J.W. 1987. Proc. R. Soc. (London) 62, 38. 

7. Xia, Y., Rogers, J.A., Paul, K.E. and Whitesides, G.M., 1999. Chem.Rev. 99, 1823.

CAPILLARY-INDUCED FORCES BETWEEN PARTICLES IN POLYMER SOLUTIONS NEAR 

PHASE SEPARATION 

M. Olsson, F. Joabsson, P. Linse, L. Piculell 

Physical Chemistry 1, Center for Chemistry and Chemical Engineering, 

Lund University, P.O. Box 124, S-221 00 Lund 

email: Martin.Olsson@fkem1.lu.se 

ABSTRACT 

Capillary-induced phase separation (CIPS) leads to a long-ranged attractive force between two surfaces 

immersed in a bulk solution. The formation of a new phase in the gap between the surfaces is driven by a 

lower surface energy for the new (capillary) phase compared to the bulk phase. The decrease in free energy 

is larger at shorter separations between the particles than for longer ones. An important condition for CIPS to 

arise is that the particle-free solution has to be close to phase separation. 

CIPS forces are known to affect particle aggregation in mixed solvents and in polymer blends as well as 

protein aggregation in biological membranes. We have instead looked at polymer solutions with added 

colloidal dispersed particles both experimentally and theoretically. Previous surface force measurements 

have showed that CIPS occurs in mixed polymer solutions as well as in quasi-binary polymer solutions [1,2]. 

A complementary experimental study [3] for the mixed polymer system displays phase separation at 

compositions far into the one-phase area for the original phase diagram, when colloidal particles are added. 

To investigate more generally the parameters affecting CIPS for the mixed polymer system, a theoretical 

mean-field lattice study has been done [4]. This study shows that CIPS occurs close to phase separation for 

the system and is affected by parameters like the molecular weight of the polymer, the affinity of the polymer 

to the surface, the composition of the sample and the distance between the particles. A recent study [5] 

shows that CIPS can also appear in quasi-binary solutions. This has also been shown experimentally. 

References 

1. Freyssingeas, E., Thuresson, K., Nylander, T., Joabsson, F., Lindman, B., 1998. Langmuir 14, 5877-5889. 

2. Wennerström, H., Thuresson, K., Linse, P., Freyssingeas, E., 1998. Langmuir 14, 5664-5666. 

3. Joabsson, F., Calatayu, A., Thuresson, K., Piculell, L., submitted. Journal of Physical Chemistry B. 

4. Joabsson, F. and Linse, P. “Capillary-Induced Phase Separation in Mixed Polymer Solutions. A Lattice 

Mean-Field Calculation Study”, manuscript. 

5. Olsson, M., Linse, P., Piculell, L. “Capillary-Induced Phase Separation in Binary and Quasi-binary Solutions. 

A Lattice Mean-Field Calculation Study”, manuscript.

span the gap between the electrodes. Throughout the course of growth, the characteristic wavelength 

remains invariant. The characteristic length scale coupled with the sharpening of the peaks of the fluctuations 

gives rise to a hexagonal packing of the cylinders laterally. 

By replacing the air gap with a second fluid or polymer layer between the electrodes reduces the energetic 

cost of generating interfacial area by replacing the surface energy with an interfacial energy. In general, the 

interfacial energy is approximately one order of magnitude smaller than the surface energy. This translates 

into a reduction in the characteristic fluctuation wavelength. The experimentally measured wavelengths are in 

excellent agreement with the predictions. Theoretically, significant changes are unexpected, but a significant 

decrease is observed. While unexpected, this represents a tremendous advantage for end-use of this 

phenomenon.

POLYMER-MEDIATED FORCES: OPTICAL TENSIOMETRY AND OPTICAL FORCE 

MICROSCOPY 

R. Rajagopalan 

Department of Chemical Engineering, University of Florida, 

Gainesville, Florida 32611-6005, USA 

email: Raj@ChE.UFL.edu 

ABSTRACT 

Introduction 

Intensive research over the last two decades has established that polymer adsorption on surfaces is far 

more subtle than previously recognized (Scheutjens 1985; Fleer 1993). Whether interaction between polymer-laden 

surfaces is attractive or repulsive depends on the amount of polymer between the two surfaces 

and on the precise conformational details of the adsorbed chains, a fact that is all the more important in the 

case of physisorbed layers, especially under “starved” (undersaturated) conditions. The latter situation is of 

particular interest in a number of practical contexts, as physisorbed polymer layers under less-than-saturation 

conditions are often the rule in colloid stabilization or in polymer interfaces of biomedical and biological 

interest. The structure of adsorbed polymer chains (especially the role of tails) has been debated since the 

early work of Scheutjens and Fleer and has been clarified to some extent only recently by Semenov and 

coworkers (e.g., Semenov 1996), who revisited this problem in the last few years using an extension of the 

ground state dominance approximation within a mean-field framework, and by Fleer and coworkers 

(1999a,b), who developed an analytical approximation for the numerical mean-field theory and related it to 

the approach of Semenov and coworkers. Simultaneously, a parallel effort to study interaction forces 

between polymer layers using simulations has also been initiated (Jimenez 1998, 2000). Although these 

simulations are based on self-avoiding random walk chains and therefore cannot be compared directly (or, 

used to “test”) mean-field theories, such simulations do provide a way to assess how mean-field approximations 

perform relative to realistic chains. Despite the approximations or simplifications involved, the 

Scheutjens-Fleer (SF) lattice mean-field theory provides an important framework for studying polymer/ 

interface systems that are not amenable to scaling theories and to the Edwards-equation-based analytical 

mean-filed formulations. In particular, the SF theory allows one to examine low-molecular-weight polymers 

and chains of complicated molecular architecture. 

The extensive work available in the literature based on mean-filed theories and simulations have also set 

the stage for systematic experimental measurements of polymer-mediated forces down to the level of single 

chains. The extension to single chains implies that one should be able to measure forces of the order of tens 

of femtoNewtons – a level of sensitivity not readily accessible through atomic force microscopy (AFM). 

However, the required level of sensitivity and resolution (in force) can be achieved if one uses optical 

tweezers to hold and manipulated polymer chains and as force transducers. In this talk, we describe an 

optical force microscope (analogous to an AFM), in which a probe particle held by a diffraction-limited optical 

trap is used in place of the cantilever of an atomic force microscope. Examples of static and dynamic 

measurements and related possibilities will be described. 

Optical Force Microscopy 

As well-known, members of the family of scanning probe microscopes differ from each other with respect 

to the type of probe used and the type of substrate/probe interaction that is used as the basis of the measurement. 

The sensitivity of the force measurement and the resolution of the distances depend on the 

characteristics of the probe and the probe/substrate interactions, among others. The stiffness of a typical 

AFM cantilever is typically of the order of 1000 pN/nm, but cantilevers with stiffnesses in the neighborhood of 

1 pN/nm can be fabricated. Nevertheless, when dealing with soft interfaces such as a polymer layer, it is

desirable to use a probe with a much lower spring constant. The use of a spherical particle held in place by 

an optical trap was first suggested as a probe about a decade back by Ghislain and Webb (Ghislain 1993) to 

meet the need for probes of very low stiffness for measuring single-molecule force measurements at the pico- 

Newton level in biology and biophysics. The focused laser beam in this case acts as an optical “tweezer” to 

hold and spatially manipulate the probe. Such an optical trap, known as a tweezer trap, behaves like a linear 

spring, and the particle and the trap replace the AFM cantilever in the measurement. The above arrangement 

is also more compatible with optical microscopy, and a combination of the two allows one to perform simultaneous 

videomicroscopy on the specimen under examination. A scanning probe microscope based on the 

above principle is known as an optical force microscope (OFM). More recent developments and applications 

of optical manipulation of colloids and polymers are available in a forthcoming book (Rajagopalan 2003). 

The tweezer trap functions as a harmonic spring in the axial (z) as well as in the lateral (x and y) 

directions. For example, in the z-direction (normal to the interacting surface), which is the only one we shall 

consider here, one may write the trap potential φtr as φtr = (ktr/2)(z−ztr) 2 , where z is the distance along the axis 

of the beam, ztr is the location of the trap center and ktr is the “stiffness” of the trap potential. Similar 

approximations can be written for the lateral directions. As in the case of an AFM cantilever, the above 

spring-like function of the trap allows one to use the trap as a force transducer to determine any external 

force exerted on the probe particle, as has been demonstrated by a number of investigators (see, for 

example, Dogariu 2000 and Rajagopalan 2003 and references therein). Moreover, as the trap stiffness can 

be adjusted by changing the power of the trap laser to magnitudes of the order of 0.001 pN/nm (about four 

orders of magnitude smaller than the typical stiffness of the cantilevers of AFMs), the use of tweezer traps 

allows one to measure very small forces directly and to image “soft” polymer interfaces. 

Measurement of Polymer-Mediated Forces 

Lack of space does not permit a detailed discussion of the method and measurements here and details 

may be found elsewhere (Dogariu 2000; Rajagopalan 2003). In this talk, we shall present illustration of the 

use of an OFM for measuring electrical double-layer forces, force between a planar surface and a colloidal 

particle with physisorbed polymer chains (poly(ethylene oxide) and polyacrylic acid) on both surfaces, and 

single-chain elasticity. Possibilities for examining the dynamic response of the polymer layer to an oscillating 

probe particles and “microrheology” of polymer layers will also be illustrated. 

References 

1. Dogariu, A.C. and Rajagopalan, R., 2000. Optical Tweezers as Force Transducers: The Effects of 

Focusing the Trapping Beam through a Dielectric Interface. Langmuir 16, 2770-2778. 

2. Fleer, G., Cohen Stuart, M., Scheutjens, J., Cosgrove, T., and Vincent, B., Polymers at Interfaces, London: 

Chapman and Hall, 1993. 

3. Fleer, G.J., van Male, J. and Johner, A., 1999a. Analytical Approximation to the Scheutjens-Fleer Theory 

for Polymer Adsorption from Dilute solution. 1. Trains, Loops, and Tails in terms of Two Parameters: The 

Proximal and Distal Lengths. Macromolecules, 32, 825-844. 

4. Fleer, G.J., van Male, J. and Johner, A., 1999b. Analytical Approximation to the Scheutjens-Fleer Theory 

for Polymer Adsorption from Dilute solution. 2. Adsorbed Amounts and Structure of the Adsorbed Layer, 

Macromolecules, 32, 845-862. 

5. Ghislain, L.P. and Webb, W.W., 1993. Scanning Force Microscope Based on an Optical Trap, Opt. Lett., 

18, 1678-1680. 

6. Jimenez, J. and Rajagopalan, R., 1998. A New Simulation Method for the Determination of Forces in 

Polymer/Colloid Systems. Euro. Phys. J. B, 5, 237-243. 

7. Jimenez, J., deJoannis, J., Bitsanis, I. and Rajagopalan, R., 2000. Interaction between Undersaturated 

Polymer Layers: Computer Simulations and Numerical Mean-Field Calculations. Macromolecules, 33, 

8512-8519. 

8. Rajagopalan, R. and Dogariu, A.C., Eds., Optical Manipulation of Particles and Macromolecules, Cambridge: 

Cambridge Univ. Pr., 2003. 

9. Scheutjens, J. and Fleer, G.J., 1985, Interaction between Two Adsorbed Polymer Layers. Macromolecules 

18, 1882-1900. 

10.Semenov, A.N., Bonet-Avalos, J., Johner, A., and Joanny, J.-F., 1996. Adsorption of Polymer Solutions 

onto a Flat Surface. Macromolecules 29, 2179-2196.

DENT720CONTROLLING POLYMERS AT INTERFACES ON THE NANOSCOPIC AND 

MACROSCOPIC LEVELS 

T.P. Russell 

Polymer Science and Engineering Department, University of Massachusetts, 

Amherst, MA 01003 USA 

email: russell@mail.pse.umass.edu 

ABSTRACT 

Developing routes to manipulate the behavior of polymers at interfaces is key in designing and developing 

devices base on thin polymer films. Block copolymers offer a wealth of self-assembling, ordered, nanoscopic 

morphologies that have tremendous potential as lithographic templates, high-density porous media or as 

scaffolds for nanoscopic devices. Realizing the full potential of these materials in bulk or thin film applications, 

however, mandates control over the spatial orientation of the structures. External fields can be used to this 

end. These may be passive, as with interfacial interactions, or active, as with mechanical shear. In liquid 

crystal displays, for example, electric fields are used to control molecular alignment and, hence, the optical 

properties of the device. Much less attention has been devoted to amorphous systems where the 

anisotropies on the molecular level are small. Block copolymers are an exception where mechanical shear 

and electric fields have been used to produce well-ordered arrays of nanoscopic domains. However, in thin 

copolymer films, the orientation of the structures normal to the surface introduces an interesting twist. In 

particular, there is a competition between the applied electric field and interfacial interactions that gives rise to 

a threshold field strength that must be exceeded to fully align the morphology. This threshold field strength 

has revealed a novel means of determining differences in the interfacial energies of the components 

comprising the copolymer. 

Producing well-ordered thin films can take hours to achieve or there are restrictions on the film thickness. 

Both present barriers to their end-use. Here, a very rapid route is described by which the cylindrical 

microdomains of an asymmetric diblock copolymer of polystyrene, PS and polyethyleneoxide, PEO, denoted 

P(S-b-EO) can be oriented normal to the surface of a film over very large areas. Results are shown where, 

within seconds, arrays of nanoscopic cylindrical domains of PEO are produced in a glassy PS matrix in films 

with thickness several times the period of the copolymer. This was found over a wide range in molecular 

weight, allowing control over the size of the cylindrical domains and the areal density of the arrays. In 

addition, since PEO is water soluble, the oriented arrays of nanoscopic cylinders opening a novel route 

towards water permeable membranes with well-defined channel sizes. 

An electric field applied normal to an interface, due to the gradient in the dielectric constant across the 

interface, produces a field gradient that translates into an electrostatic pressure that amplifies thermal 

fluctuations. Surface and interfacial energies, on the other hand, act to minimize the interfacial area and, 

therefore, tend to suppress the growth of the fluctuations. A linear stability analysis taking these opposing 

forces into account yields a preferential wavelength of fluctuations that is amplified with a characteristic 

relaxation time. Optical microscopy studies on homopolymer films between two electrodes with and air gap 

between the polymer surface and the upper electrode show the growth of theses fluctuations which, 

ultimately lead to the formation of solid cylinders of the polymer spanning the gap between the two 

electrodes. The average separation distance between adjacent cylinders and the characteristic growth rate of 

the cylinders agree surprisingly well with linear theoretical arguments. Studies from the early stages of the 

growth of the fluctuations show features that a reminiscent of spinodal phase separation in polymer mixtures. 

An interconnected fluctuation pattern is observed on the surface with a characteristic length scale. With time 

the fluctuations sharpen significantly, grow in height until, finally, they form cylinders of solid polymer that

span the gap between the electrodes. Throughout the course of growth, the characteristic wavelength 

remains invariant. The characteristic length scale coupled with the sharpening of the peaks of the fluctuations 

gives rise to a hexagonal packing of the cylinders laterally. 

By replacing the air gap with a second fluid or polymer layer between the electrodes reduces the energetic 

cost of generating interfacial area by replacing the surface energy with an interfacial energy. In general, the 

interfacial energy is approximately one order of magnitude smaller than the surface energy. This translates 

into a reduction in the characteristic fluctuation wavelength. The experimentally measured wavelengths are in 

excellent agreement with the predictions. Theoretically, significant changes are unexpected, but a significant 

decrease is observed. While unexpected, this represents a tremendous advantage for end-use of this 

phenomenon.

ENTROPIC NETWORKS IN POLYMERS AND MICROEMULSIONS 

A. Zilman, S. A. Safran 

Weizmann Institute of Science, 

Rehovot, Israel 76100 

email: sam.safran@weizmann.ac.il 

ABSTRACT 

Self-assembling networks and branched structures are common in both natural and synthetic materials and 

form under a variety of equilibrium and non-equilibrium conditions. Here, we review the theory of the structure 

and thermodynamic properties of equilibrium networks of cylindrical micelles [1], microemulsions [2] and selfassembling 

polymeric gels [3]. In all these systems, the networks consist of self-assembling, locally, onedimensional 

objects (e.g., polymer chains in the case of a gel, cylindrical micelles or microemulsions or 

chains of dipolar colloids [4]). The study of network phases is of both theoretical [5] and practical interest. 

From the practical point of view, network forming amphiphiles and sol-gel systems are at the core of many 

industrial, biological and bio-medical applications. The existence of junctions and their dynamics is important 

in understanding the rheology of worm-like micelles. Network formation may also be responsible for the 

unusual "closed loop" phase diagrams of microemulsions and dipolar liquids. Cryo-electron microscopy [1] 

shows clear evidence of coexisting network phases in dilute microemulsions. In many of the systems 

mentioned above, the chains themselves are self-assembled in an equilibrium manner from a large number 

of monomers. 

We begin with a simple estimate of the density and free energy contribution of ends and junctions in a 

system of self-assembling chains or tubes and show that the junction entropy introduces an effective 

attraction (negative second-virial coefficient) that can lead to phase separation. The relationship of this 

thermodynamic transition to the topological, connectivity transition (percolation or gelation) can be predicted 

in a unified manner using a modification of the n = 0 spin-model for polymers .The extension of these ideas 

to systems with crosslinks (e.g. actin gels) is also discussed and the theoretical phase diagrams are 

compared with recent experiments [6]. Finally, we show how entropic phase separation can also explain 

recent observations [7] in a combined system of telechelic polymers and microemulsions that form network 

structures. 

References 

1. Berheim-Groswasser, A., Tlusty, T., Safran, S.A., Talmon, Y., 1999. Langmuir 15, 5448; Bernheim-Grosswasser, 

A., Wachtel, E., Talmon, Y., 2000. Langmuir 16, 4131. 

2. Tlusty, T, Safran, S.A., Strey, R., 2000. Phys. Rev. Lett. 84, 1244. 

3. Zilman, A. and Safran, S.A., submitted. 

4. Tlusty, T, Safran, S.A., 2000. Science 290, 1328. 

5. Drye, T., Cates, M.E., 1992. J. Chem. Phys. 96, 1367; Zilman, A., Safran, S.A., Phys. Rev. E, in press. 

6. Tempel, M., Isenberg, G., Sackmann, E., 1996. Phys. Rev. E 54, 1802. 

7. Filali, M., Ouazzani, M.J., Michel, E., Aznar, R., Porte, G. Appell, J., 2001. J. Phys. Chem B, 105, 10528.

MEMBRANE FUSION: RESULTS FROM SIMULATION AND SELF-CONSISTENT FIELD 

THEORY 

Michael Schick 

Department of Physics, University of Washington, 

Box 351560, Seattle, WA 98195-1560, U.S.A. 

email: schick@mahler.phys.washington.edu 

ABSTRACT 

Our group has been studying self assembly in systems of block copolymer and of biological lipids, as there is 

much similarity in the phase behavior of the two. Our studies have focussed on defects in these systems. In 

the first part of my talk, I will discuss various grain boundaries in lamellar phases of block copolymers, work 

which was accomplished utilizing self-consistent field theory only, and in the Fourier representation. In the 

second part, I will discuss our work on the mechanism of membrane fusion, which was carried out utilizing 

both Monte Carlo simulations and self-consistent field theory in real-space representation. 

Grain Boundaries 

Grain boundaries in smectics, such as the lamellar phases of block copolymers, are easier to study than 

those in crystalline solids due to the lack of in-plane order in the smectics. Matsen first showed how scft in the 

Fourier representation could be applied to symmetric-tilt grain boundaries. A notable feature was the 

occurrence of a symmetry-breaking transition as a function of tilt angle. We have extended these studies to 

include twist grain boundaries and, most recently, T-junctions. Symmetric tilt grain boundaries and Tjunctions 

both can connect lamellar grains of different orientations. Presumably the frequency with which one 

observes one or the other depends upon their relative free energy. Our motivation was a series of 

experiments which showed that T-junctions did not occur very often in a system consisting of block 

copolymer only. However the addition of homopolymer significantly increased their occurrence. Our studies 

showed that in the system of copolymer only, there was only a small range of angles over which the free 

energy of the T-junction was less than that of the symmetric tilt grain boundary. However this range of angles 

increases appreciably with the addition of homopolymer. Of additional interest is the appearance of a 

morphological change as the angle between grains approaches 180 degrees. This change is rather similar to 

that which occurs in the symmetric tilt boundaries.Membrane FusionAlthough the fusion of membranes is an 

enormously important biological process, it is poorly understood. One knows that specialized proteins are 

needed to bring two fluctuating membranes close to one another, a process which puts the membranes 

under tension. Beyond this, little is known. Almost all theories begin with an initial state consisting of a 

cylindrically symmetric stalk, a localized region in which the lipids of each of the proximate lipid layers 

rearrange to form a continuous hydrophobic region joing the hydrophobic cores of the two bilayers. The final 

fusion pore, whose hydrophilic region traverses both bilayers, is also cylindrically symmetric. It has been 

assumed by all theories that all intermediate states in the fusion process were equally symmetric. We 

investigated this process by Monte Carlo simulation and found the process took a completely different 

symmetry-broken route. Knowing the form of the intermediate, we have used self consistent field theory to 

calculate the free energy barriers along previously assumed paths and the one we found. Our calculations 

help us understand why the path we did see is the one we should have seen.

ADSORBED POLYMER LAYERS: LOOPS, TAILS AND STIFFNESS. 

A.N. Semenov 

Physics Department, Moscow State University, 

Moscow 119992, Russia 

email: semenov@polly.phys.msu.su 

ABSTRACT 

Polymer adsorption is a remarkable phenomenon that is widely used to modify properties of surfaces and 

interfaces. I will review theoretical results on the structure of adsorbed polymer layers focusing on the role of 

loops and tails on the one hand, and the chain stiffness on the other hand. 

1. Adsorbed layers formed by flexible polymers 

Self-similar structure of saturated polymer layers adsorbed from a good solvent onto an attracting surface 

was elucidated by De Gennes long ago [1]: in the central region (at the distances z from the surface longer 

than the molecular extrapolation length b but shorter than the coil size R) the monomer concentration decay 

as φ = z −a 

, where a = 4/3( a = 2 in the marginal solvent regime). The layer can be viewed as a system of 

loops of different lengths (chains sections starting and terminating at the adsorbing surface). 

More recently it was shown [2,3,4] that loops do not dominate everywhere in the central region: the 

contribution of tails (chain sections starting at the surface and terminating in the bulk) is important at 

distances z > z * , where z * is a length-scale that is much longer than the monomer size, but much shorter 

than the coil size R ( u z* N , where u = 1/ 2 in good solvent and u = 1/ 3 in marginal solvent). Hence two 

subregions: the inner sublayer z < z * formed by loops, and the outer sublayer z > z * dominated by tails (the 

tail subregion resembles a layer of broadly polydisperse end-grafted chains). Hence a significant portion of 

the adsorbed layer contains mostly tail monomers. It is remarkable that this conclusion was first obtained in 

the numerical studies by J. Scheutjens, G. Fleer and their co-workers [5,6] and then stayed unexplained for a 

long while. 

The tail sublayer is considerably thicker than the loop layer (at a given distance z from the surface). This 

results in a surprising behavior: monomer concentration at the given point z ( z >> b) in a saturated layer of 

shorter chains (N1) may be higher (by a large factor ~ 10) than concentration in a layer of longer chains (N2) 

provided that z * (N1) < z < z * (N2). The effect of polymer tails is responsible for a number of important 

effects. The `thicker' tail sublayer is relatively less permeable: it is rather difficult for an unadsorbed chain to 

penetrate through this layer, the main mechanism of penetration being often end-entry (rather than hairpin 

entry) [7]. Two saturated adsorbed layers repel each other when their tail sublayers are overlapping (at the 

distances z* < h< R). This is in contrast with the well-known normal behavior: attraction due to bridging by 

polymer fragments which is predicted at shorter distances (in the regime of loops) [8]. 

2. Adsorption of a stiff worm-like macromolecule 

Polymers with stiff backbone (including many biological polymers) show a rather different adsorption 

behavior as compared to that characteristic of flexible chains [9]. I present a theoretical description of 

adsorption of a single semiflexible chain onto a flat surface. Both scaling and quantitative approaches are 

discussed. A self-similar monomer concentration profile cx ( )~ z −4/3 is predicted near the surface (when the 

distance to the surface z is much smaller than the chain persistence length / 2 ). The typical conformation of 

a weakly adsorbed chain can be viewed as a sequence of alternating 2-dimensional (flat) and 3-dimensional 

blobs forming a double-layer structure: a thin contact layer (of molecular thickness d, d

the transition temperature T * when τ = 1 −T 

*/ T is smaller than ( d / ) −4/3; 

otherwise (at larger τ ) the lion's 

share of the chain is staying in the d-layer very close to the surface. The adsorption transition is continuous 

although it looks like a discontinuous (first-order) transition outside a narrow region around the adsorption 

temperature, τ > ( d / ) −4/3. 

References 

1 De Gennes, P.G., 1981. Macromolecules 14, 1637. 

2 Semenov, A.N., Joanny, J.F., 1995. Europhys.Lett. 29, 279. 

3 Semenov, A.N., Joanny, J.F., Johner, A. Polymer Adsorption: mean-field theory and ground state dominance 

approximation. In: Theoretical and Mathematical Models in Polymer Science, Chapter 2, pp.37-81 

(Ed. A. Grosberg, Academic Press, Boston, 1998). 

4 Johner, A., Bonet-Avalos, J., Van der Linden, C.C., Semenov, A.N., Joanny, J.F., 1996. Macromolecules 

29, 3629. 

5 Scheutjens, J., Fleer, G., 1980. J. Phys.Chem. 84, 178. 

6 Scheutjens, J., Fleer, G. In: The Effect of Polymers on Dispersion Properties, Th.F. Tadros Ed., Academic 

Press, New York, 1982. 

7 Semenov, A.N., Joanny, J.-F., 1995. J. de Physique 5, 859. 

8 Semenov, A.N., Joanny, J.F., Johner, A., Bonet-Avalos, J., 1997. Macromolecules 30, 1479. 

9 Van der Linden, C.C., Leermakers, F.A.M., Fleer, G.J., 1996. Macromolecules 29, 1172.

MEAN-FIELD THEORY PREDICTION OF PHASE BEHAVIOR OF ABC TRIBLOCK 

COPOLYMER IN SELECTIVE SOLVENT 

N.P. Shusharina 1) , P. Alexandridis 1) , S. Balijepalli 2) , H.J.M. Gruenbauer 3) 

1) Department of Chemical Engineering, University at Buffalo, 

The State University of New York, Buffalo, New York 14260-4200, U.S.A. 

2) New Product & Mathematical Modeling Group, Corporate R&D, 

The Dow Chemical Co., Midland, MI 48674, U.S.A. 

3) New Business Development, Dow Benelux N.V., 

4530 AA Terneuzen, The Netherlands 

email: ns33@eng.buffalo.edu 

ABSTRACT 

A mean-field lattice theory is applied to predict the self-assembly into ordered structures of ABC triblock 

copolymers in selective solvent. More specifically, the composition-temperature phase diagram has been 

constructed for the system (C)14(PO)12(EO)17/water, where C stands for methylene, PO for propylene oxide 

and EO for ethylene oxide. The model predicts thermotropic phase transitions between the ordered 

hexagonal, lamellar, reverse hexagonal, and reverse cubic phases, as well as the disordered phase. The 

thermotropic behavior is a result of the temperature dependence of water interaction with EO- and POsegments. 

The lyotropic effect (caused by changing the solvent concentration) on the formation of different 

structures has been found weak. The structure in the ordered phases is described by analyzing the species 

volume fraction profiles and the end segment and junction distributions. A "triple-layer" structure has been 

found for each of the ordered phases, with each layer rich in C-, PO-, and EO-segments, respectively. The 

electrolyte effects on the macroscopic phase behavior are also considered. The addition of NaCl is found to 

sharpen the thermotropic phase transition and shift them to lower temperatures compared to the salt-free 

case. The parameters describing interactions between different species are obtained from simple experiments, 

and thus this model can be useful in capturing the effects of various electrolytes on non-ionic 

surfactants phase behavior.

PROTEIN ADSORPTION ON SURFACES WITH GRAFTED POLYMERS 

Igal Szleifer 

Department of Chemistry, Purdue University, 

West Lafayette, IN 47907, USA 

email: igal @ purdue.edu 

ABSTRACT 

Introduction 

Protein adsorption plays a key role in a variety of biological processes and it is very important in many 

biotechnological processes. For example, when a foreign body is put in contact with the blood stream, large 

blood proteins e.g. fibrinogen, adsorb to the surface of the material. This protein adsorption is necessary for 

the following adhesion of platelet and the possibility of surface induced thrombosis. It has been shown that 

when the surface adsorption of fibrinogen is below a certain threshold, platelet adhesion does not occur. 

Therefore, one of the important steps in increasing biocompatibility in a material is by preventing the 

adsorption of blood proteins into the surface of the material. Another important example in which protein 

adsorption plays a key role is in the design of biosensors. In some of these cases it is necessary to obtain an 

ordered array of enzymes. Further, the proteins should adsorb in their biological active conformation for 

proper functioning of the device. These two examples show the importance of protein adsorption. However, in 

one case it is necessary to induce protein adsorption while in the other it is important to prevent the 

adsorption of the macromolecules. 

Protein adsorption is a very complex process since it involves very large energy scales. Typical van der 

Waals interactions between surfaces and proteins are in the order of tens to hundred times the thermal 

energy. Further, proteins are highly heterogeneous molecules that have the ability to change their conformation 

upon adsorption on the surface. This change of conformation is induced by the presence of an 

inhomogeneous interaction field due to surface. Another complexity arises from the fact that in general 

proteins have charged amino acids and therefore electrostatic interactions play a key role on the adsorption 

behavior. 

In this talk we will discuss the ability of grafted polymer layers to control protein adsorption. This is aimed 

to use grafted polymers as surface modifiers that can be tuned to prevent protein adsorption or in other cases 

to control the kind of protein conformation that adsorbs on the surface. We will show our theoretical studies of 

how different types of grafted polymers can be used to tune the adsorption process. Our theoretical approach 

is based on a generalization of a molecular mean-field theory that has been very successful to describe the 

properties of tethered polymers. For example, the theory is capable to quantitatively describe the pressurearea 

isotherms of polystyrene-poly ethylene oxide (PS-PEO) diblock copolymers spread at the water-air 

interface. We have also shown that the predictions of the theory are in excellent quantitative agreement with 

experimental observations of the structure of PEO molecules grafted on surfaces with rigid collagen 

molecules. Furthermore, we will also show that the predictions of the theory are in very good agreement with 

experimental observations for the adsorption isotherms of lysozyme and fibrinogen on surfaces with grafted 

PEO. These comparisons have been done over a very large range of polymer chain length, from short 

oligomers to long PEO molecules. 

Thermodynamic vs. Kinetic Control of Protein Adsorption 

Due to the very large energy scales involved on the adsorption of proteins it is important to understand the 

equilibrium and kinetic process. When a surface is modified by grafting polymer molecules the modified 

surface-protein interactions give rise to changes in both the kinetics of adsorption as well as the equilibrium 

amount of proteins adsorbed. The question is then what type of control is necessary depending on the type of

application. For example, in the case of biocompatible materials it is important to obtain thermodynamic 

prevention of protein adsorption, since the biomaterial is expected to be in contact with the blood stream for 

long periods of time. However, in the case of drug carriers, control of the kinetics of adsorption is enough, 

since in this case one is interested in preventing protein adsorption on the time scale that the drug is 

delivered to the target cell. 

We will show our theoretical studies on both the kinetic and thermodynamic control of protein adsorption. 

Most of our studies are on model PEO molecules since these are the polymers that have been most 

extensively used experimentally. PEO is a water-soluble polymer that also has affinity for hydrophobic 

surfaces. Therefore, the structure of the polymer layer and thus, its ability to control protein adsorption 

depends upon the polymer-surface interactions. 

Overall we find that when the polymers are attracted to the surfaces the polymer layer is more effective for 

the thermodynamic control of protein adsorption than surfaces that do not attract the polymer. For the kinetic 

control the opposite is true. Namely, surfaces with polymers that are not attracted to them exert a stronger 

steric repulsion to approaching proteins than surfaces with attracting polymers. In all cases polymer surface 

coverage is the most important parameter to prevent protein adsorption. As the surface coverage increases, 

the ability of the polymer to prevent protein adsorption increases. At fixed polymer surface coverage, the 

equilibrium adsorption of proteins is independent of polymer molecular weight once the thickness of the brush 

is larger than the size of the protein. However, increasing chain length at fixed surface coverage results in an 

exponential increase of the time scale for adsorption. This is the result of the increased range and strength of 

the effective surface-protein interactions as polymer molecular weight increases. 

The kinetic process of protein adsorption on surfaces with grafted polymers will be shown to be rather 

complex. This is due to the fact that as proteins adsorb the polymer layer is deformed and therefore, the 

interactions that the proteins arriving from solution feel changes with time. 

The changes in the adsorption process due to the ability of the proteins to change their conformation upon 

adsorption will be described in detail as well as the effect of charges on the proteins, polymers and surfaces. 

References 

Most of the work presented in this talk appears in the following publications. 

1. Szleifer, I., 1997. "Protein Adsorption on Surfaces with Grafted Polymers: A Theoretical Approach", Biophysical 

J. 72, 595-612. 

2. Szleifer, I., 1997. “Protein Adsorption on Tethered Polymer Layers: Effect of Polymer Chain Architecture 

and Composition”, Physica A 244, 370-388. 

3. Szleifer, I., 1997. “Polymers and Proteins: Interactions at Interfaces: Current Opinion in Solid State and 

Materials Science 2, 337-344. 

4. McPherson, T., Kidane, A., Szleifer, I. and Park, K., 1998. “Prevention of Protein Adsorption by Tethered 

PEO Layers: Experiments and Single Chain Mean Field Analysis”. Langmuir 14, 176-186. 

5. Satulovsky, J., Carignano, M.A. and Szleifer, I., 2000. “Kinetic and Thermodynamic Control of Protein 

Adsorption”. Proc. Nat. Acad. Sci. 97, 9037-9041. 

6. Carignano M.A. and Szleifer, I., 2000. “Prevention of Protein Adsorption by Flexible and Rigid Chain 

Molecules”, Colloids and Surfaces B: Biointerfaces 18, 169-182. 

7. Szleifer I. and Carignano, M.A., 2000. “Tethered Polymer Layers: Phase Transitions and Reduction of 

Protein Adsorption”. Feature Article in: Macromolecular Rapid Communications 21, 423-448. 

8. Carignano M.A. and Szleifer, I., 2002. “Adsorption of Model Charged Proteins on Charged Surfaces with 

Grafted Polymers”. Mol. Phys. (in press). 

9. Fang Fang and Szleifer, I., 2002. “Effect of Molecular Structure on the Adsorption of Protein on Surfaces 

with Grafted Polymers”. Langmuir 18, 5497-5510.

MODELLING STRUCTURE AND ADHESION AT POLYMER-POLYMER INTERFACES 

D.N. Theodorou 

School of Chemical Engineering, National Technical University of Athens, 

GR-15780 Athens, Greece and ICE/HT-FORTH, GR-26500 Patras, Greece 

email: doros@central.ntua.gr 

ABSTRACT 

Copolymers are remarkably effective in improving adhesion between immiscible polymers, or between 

polymers and solid substrates on which the polymer chains do not adsorb strongly. Predicting the molecular 

organisation and mechanical response upon deformation of polymer/polymer and polymer/solid interfaces 

strengthened with copolymers can serve as a basis for the “molecular engineering” design of materials with 

optimal interfacial properties. 

Using the work of Scheutjens and Fleer (Scheutjens 1979) as a starting point, we have developed a 

lattice-based self-consistent field (SCF) theory for capturing the molecular-level structure of interfaces formed 

by polymer melts in contact with other polymer melts or solid substrates, in the absence or presence of 

copolymers. Real polymer and copolymer chains are mapped onto the model representation invoked in the 

theory in a manner that respects their mass density in the homogeneous bulk, their contour length, and their 

conformational stiffness (characteristic ratio). The propagation of conformations is envisioned as a secondorder 

Markov process, involving an energetic penalty for chain bending. Interaction (χ) parameters between 

dissimilar segments, when needed, are obtained from fitting binary interfacial widths between the 

corresponding polymer melts. 

Application of the theory to interfaces between polystyrene (PS) and poly(methyl methacrylate) (PMMA) 

(Fischel 1995) in the presence of a symmetric PS-PMMA diblock copolymer gave segment density profiles in 

very favourable agreement with neutron reflectivity measurements (Russell 1991). The end-segment, mean 

square junction-to-end distance normal to the interface, shape parameter, and bond-order parameter profiles 

indicate that copolymer chains are significantly stretched under experimental conditions. For fixed surface 

density of the copolymer, with increasing block length, a broad transition from reflected random coil to “brush” 

behaviour occurs over the region where the block radii of gyration are 1.2 to 1.7 times the mean interchain 

spacing. At very high surface densities, the copolymer can no longer reside as a monolayer at the surface. 

Surface-phase equilibrium calculations predict that patches of trilayer will appear when the volume of 

copolymer per unit surface is roughly three times the block unperturbed root mean square radius of gyration. 

This predicted appearance of structures more complex than a monolayer at the surface is consistent with the 

emergence of off-specular scattering in neutron reflectivity measurements. It suggests an upper limit to the 

degree of mechanical strengthening of the interface by addition of larger amounts of block copolymer, as 

seen experimentally. 

Our SCF theory, in parallel with neutron reflectivity measurements, has been applied to probe interfaces 

between PS of molar mass 186 kg/mol and polished silicon wafer substrates (SiO2), in the presence of 

diblock copolymers of poly(2-vinyl pyridine) (PV2P) and PS as adhesion promoters (Retsos 2002). In these 

systems, prepared from the melt, the PV2P (“anchor”) block of the copolymer adsorbs strongly on the 

surface, while the “dangling” PS block mixes with the PS homopolymer. The molar mass of the dangling 

block, which was deuterated and therefore visible in the experiments, was kept constant at 75 kg/mol, while 

that of the anchor block was varied systematically between 3.4 and 102 kg/mol. The dangling block profile 

was found to exhibit a maximum, which decreases in height and moves away from the surface as the length 

of the anchor block is increased. Results from the SCF calculation are in very good agreement with the 

experiment. The anchoring block is not flat (pancakelike) as often assumed, but forms a layer of thickness

10-50 Å, which increases with the block length. Both experiments and theory reveal evidence for the 

existence of three regimes regarding the configuration of the dangling blocks: a “wet brush” regime, a 

“mushroom” regime, and a broad transition regime in between. 

SCF calculations can serve as a starting point for predicting mechanical failure at interfaces subjected to 

large-scale deformations. A hierarchical simulation approach has been designed for this purpose. Using as 

input the chemical constitutions and relative amounts of chain species present at the interface, the 

composition profiles and conformational characteristics for all these species are first calculated by SCF 

theory (Terzis 2000a). The statistical weights derived from the model are then used within a Monte Carlo 

procedure to generate large ( ≈ 0.1 µm-sized) three-dimensional computer “specimens” of the interfacial 

region. In these specimens the material is represented, in a coarse-grained sense, as a network of 

entanglement points. Each entanglement point is shared by two chains. Each chain is defined by the 

positions of its ends and of all entanglement points it traverses, as well as by its contour lengths between 

these points (Terzis 2000b). A coarse-grained free energy function incorporating excluded volume, dispersion 

attraction, and conformational entropy contributions is written for the network. An efficient numerical 

procedure is invoked for finding local minima of this free energy function with respect to the positions of all 

chain ends and entanglement points, and thereby imposing the condition of mechanical equilibrium. 

Deformation of the network to fracture (Figure 1) at prescribed temperature and strain rate is simulated 

through a kinetic Monte Carlo procedure, which tracks elementary events of chain slippage across 

entanglements, chain disentanglement, chain reentanglement, and chain rupture (Terzis 2002). This 

hierarchical procedure has been applied to study interfaces between polypropylene (PP) and polyamide 6 

(PA6) compatibilised with the reaction product between maleic anhydride-functionalised PP (PP-g-MA) and 

PA6. Such interfaces can be viewed as consisting of a homopolymer (free PP) next to an impenetrable solid 

surface (PA6), onto which are grafted chains of the same chemical constitution as the homopolymer (endgrafted 

PP). The effects of the surface density of grafted PP and of the molecular weight distribution of free 

PP and grafted PP have been explored. It is clearly seen that increasing the surface grafting density does not 

necessarily enhance adhesion. For high surface grafting densities, a “brush” of grafted PP builds up next to 

the PA6 surface; as a consequence, the region over which grafted and free PP chains interentangle is of 

limited width. For monodisperse grafted PP of molar mass 40 kg/mol in a free PP matrix of molar mass 60 

kg/mol, optimal adhesion (a maximum in the work required to destroy the interface) is seen at 0.1 grafted 

chains/nm 2 . 

TRUE STRESS (MPa) 

250 

200 

150 

100 

50 

1% per sec 

10% per sec 

0 

1 2 3 4 

DRAW RATIO 

Figure 1: Shapshots and stress-draw ratio curves from tensile deformation computer experiments carried out on 

network specimens modelling the PP/PP-g-MA/PA6 interface. Grafted and free PP chains are shown in red and 

green, respectively. The stress-strain curves have been obtained at two strain rates for a surface grafting density of 

0.10 chains/nm 2 . The specimen, of initial dimensions 45 nm × 45 nm × 70 nm, contained 1300 chains.

References 

1. Fischel, L.B. and Theodorou, D.N., 1995. Self-consistent field model of the polymer/diblock copolymer/ 

polymer interface. J. Chem. Soc. Faraday Trans., 91 (16), 2381-2402. 

2. Retsos, H., Terzis, A.F., Anastasiadis, S.H., Anastassopoulos, D.L., Toprakcioglu, C., Theodorou, D.N., 

Smith, G.S., Menelle, A., Gill, G.E., Hadziioannou, G., Gallot, Y., 2002. Mushrooms and brushes in thin 

films of diblock copolymer/homopolymer mixtures. Macromolecules, 35(3), 1116-1132. 

3. Russell, T.P., Anastasiadis, S.H., Menelle, A., Felcher, F.P., Satija, S.K., 1991. Segment density 

distribution of symmetric diblock copolymers at the interface between two homopolymers as revealed by 

neutron reflectivity. Macromolecules, 24(7), 1575-1582. 


molecules 1. Partition function, segment density distribution, and adsorption isotherms. J. Phys. Chem., 

83(12), 1619-1635. 

5. Terzis, A.F., Theodorou, D.N., Stroeks, A., 2000. Entanglement network of the polypropylene/polyamide 

interface. 1. Self-consistent field model. Macromolecules, 33(4), 1385-1396. 


interface. 2. Network generation. Macromolecules, 33(4), 1397-1410. 


interface. 3. Deformation to fracture. Macromolecules, 35(2), 508-521.

NEUTRON REFLECTIVITY STUDY OF POLY(STYRENE MALEIC ANHYDRIDE) ON THE 

WATER-AIR INTERFACE 

C. Malardier-Jugroot 1) , T.G.M. v.d. Ven 1) , M.A. Whitehead ) , R. Richardson 2) , T. Cosgrove 2) 

1) Department of Chemistry, McGill University, Montreal, Canada 

2) School of Chemistry, University of Bristol, United Kingdom 

email: theo.vandeven@mcgill.ca 

ABSTRACT 

Poly(styrene maleic anhydride) (SMA) is an interesting alternating copolymer, used in paper treatment 

applications. Previous studies showed interesting behavior of SMA in aqueous solutions, characterized by 

self-association, depending on pH and ionic strength. The neutron reflectivity study was performed to see if 

surface properties show similar interesting behavior. 

The results for the ethyl esters in DO 2 were indistinguishable from the reflectivity of pure DO, 2 indicating 

that the adsorption layer is very thin. The data can be accurately fitted to the theoretical reflectivity of DO, 2 

using a surface roughness of 2-3 Å. 

The neutron reflectivity data on the ethyl ester of SMA in NRW showed surprisingly little effect on pH. The 

2 

data were analyzed by plotting 

RQ vs. Q. A linear relation was obtained from which the adsorbed amount 

Γ and the adsorption layer thickness δ can be obtained from the intercept and the slope respectively. We 

found an interesting relaxation effect for the reflectivity of the ethyl ester SMA at pH 7, absent at other pH’s. 

The results obtained after 4 hours were significantly different from the initial data. With time, Γ decreased 

from 1.34 to 1.11 mg/m 2 and δ decreased from 12.6 to 9.6 Å (for the ethyl deuterated ethyl ester of SMA). 

The adsorption at pH 3 was identical to the relaxed adsorption at pH 7. The styrene deuterated compound 

always showed a slightly higher adsorbed amount compared to the ethyl deuterated one: Γ = 1.2 and 1.1 

mg/m 2 resp. 

The results at pH 13 showed that the ethyl ester of SMA was partially hydrolyzed, resulting in a reflectivity 

profile close to that of SMA at the same pH. 

The adsorbed amounts for SMA were found to be extremely low, both for pH 7 and pH 13, with adsorbed 

amounts of 0.38 and 0.24 mg/m 2 resp. The thickness of the adsorption layer was in the range 13 – 16 Å.

MULTIDOMAIN CONFORMATIONS OF RANDOM HETEROPOLYMERS 

J.M.P. van den Oever 

Laboratory of Physical Chemistry and Colloid Science, 


email: oever@fenk.wau.nl 

ABSTRACT 

Polymer molecules can attain various random-coil and compact structures in solution and at interfaces. 

The polymer's primary structure and its environment determine which conformation is prevalent. The 

influence of primary structure on stability and higher structure is an area of intensive research, especially 

in protein science. A novel two gradient SCF model is used to study various types of heteropolymers. In 

this method the complete partition function of the polymer system is calculated. Intramolecular excluded 

volume is taken into account partially. The average conformations of molecules under consideration are 

obtained in the form of volume fraction profiles. Random copolymer sequence space has been sampled 

by investigating molecules of varying length and monomer ratio. The number of domains attained in 

equilibrium was observed and summarized in a sequence space diagram. Random heteropolymers with 

pH-dependant characteristics mimicing those of proteins have been studied in a wide pH-range. We see 

that some molecules form multiple domains when going to extreme pH values. Domain formation can also 

be observed in heteropolymers approaching an oppositely charged surface.

COIL-SIZE OSCILLATORY PACKING IN POLYMER SOLUTIONS NEAR A SURFACE 

J. van der Gucht, N.A.M. Besseling, J. van Male, M.A. Cohen Stuart 



email: jasper@fenk.wau.nl 

ABSTRACT 

Depletion of polymers at a surface has been studied extensively before. Theories predict that the segment 

concentration profile decreases monotonously with decreasing distance to the surface 1,2) . Furthermore it is 

generally accepted that the only relevant lengthscale above the overlap concentration is the “blob size”. The 

coil size is believed to be irrelevant in this regime 1,2) . We have performed detailed calculations of the density 

profile of nonadsorbing polymers near a surface, using the theory developed by Scheutjens and Fleer 1) . Our 

results indicate that there is a damped oscillatory contribution to the density profile. Both the period of the 

oscillations and the decay length are proportional to the size of the individual coils and are independent of the 

polymer concentration, also above the overlap concentration. This indicates that the size of the individual 

coils is still a relevant lengthscale above the overlap concentration. The oscillations are associated with a 

liquid-like layering of polymer coils near the surface. In dilute solutions no oscillations are observed, because 

the decay length of the oscillations is smaller than the depletion correlation length. This is similar to the 

behaviour of simple fluids, where the Fisher-Widom line marks the transition from monotonic to oscillatory 

decay of the density correlation function 3) . The Fisher-Widom line in polymer solutions is proportional to the 

overlap concentration. On the oscillatory side of the Fisher-Widom line the interaction energy between two 

plates immersed in a solution of nonadsorbing polymers is an oscillatory function of the separation distance. 

The size of the oscillations is too small to be detected experimentally, but the effect is expected to be 

stronger in for example branched polymer solutions. As indicated by Evans et al. the oscillations might be of 

importance in, for example, wetting phenomena 4) . 

References 

1. Fleer, G.J., Cohen Stuart, M.A., Scheutjens, J.M.H.M.; Cosgrove, T., Vincent, B. Polymers at Interfaces. 

Chapman and Hall: London, 1993. 

2. De Gennes, P.G., Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, London. 

3. Fisher, M.E., and Widom, B., 1969. J. Chem. Phys. 50, 3756. 

4. Evans, R., Leote de Carvalho, R.J.F., Henderson, J.R. and Hoyle, D.C., 1993. J. Chem. Phys., 100, 591.

SUPRAMOLECULAR COORDINATION POLYMERS: CHAINS AND RINGS 

J. van der Gucht 



email: jasper@fenk.wau.nl 

ABSTRACT 

Bifunctional monomers were synthesized, consisting of two ligand groups bridged by a short spacer. With 

metal ions, these molecules can form coordination polymers. This can be monitored by measuring the 

viscosity. For linear chains one expects a maximum in the visocity at a 1:1 ratio of metal to monomers. At low 

concentrations however, a dip is measured there. This dip can be explained using a simple model for 

equilibrium polymerization into rings and chains, which predicts that short rings dominate at low 

concentrations at a 1:1 ratio, causing a minimum in the average length, and, hence, in the viscosity.

ASSOCIATION BEHAVIOUR OF GLUCITOL AMINE GEMINI SURFACTANTS 

SELF-CONSISTENT-FIELD THEORY AND MOLECULAR DYNAMICS SIMULATIONS 

M. van Eijk, M. Bergsma, S.-J. Marrink 

CP Kelco, 

Ved Banen 16, Lille Skensved, 4623, Denmark 

email: marcel.vaneijk@cpkelco.com 

ABSTRACT 

The association behaviour of a number of glucitol amine gemini surfactants has been investigated by means 

of molecular dynamics and self-consistent-field calculations. We have shown that the titratable head group of 

the surfactant is responsible for a micelle-to-membrane transition when changing the pH. Furthermore, the 

association structure of this group of surfactants is shown to be very sensitive to ionic strength. The 

combination of a charged head group, a spacer, and the hydrophilic glucitol side chains is responsible for the 

possible structural transitions in the associates as a function of ionic strength and pH.

INFLUENCE OF POLYMERS ON THE BENDING MODULI OF BILAYERS 

J. van Male, F.A.M. Leermakers 



email: vanmale@fenk.wau.nl 

ABSTRACT 

Surfactant bilayers have a low surface tension. The rigidity of bilayers determines the phase behavior of the 

bilayer membranes. We investigated the effect of homopolymers on the bending moduli of bilayer membranes 

by numerical self-consistent field calculations. Adsorbing polymers increase the mean bending 

modulus k c , resulting in stiffer bilayers and decrease the Gaussian bending modulus k , disfavoring handles 

between the membranes. Overall, adsorbing polymers stabilize the bilayers. Calculations that approximate 

the membrane as an inert solid wall give opposite results. This shows that the membrane should be explicitly 

taken into account.

INTERFACES, WETTING, AND CAPILLARY NEMATISATION IN COLLOIDAL ROD 

SUSPENSIONS 

R. van Roij 

Institute for Theoretical Physics, Utrecht University, 

Postbus 80.195, 3508 TD, Utrecht, The Netherlands 

email: r.vanroij@phys.uu.nl 

ABSTRACT 

We study the thermodynamics and structure of interfaces and films in colloidal hard-rod fluids within an 

Onsager-like density functional theory. For a one-component system, we find complete wetting near a hard 

wall and capillary nematisation (with a capillary critical point) in a slit confined by two hard walls. For binary 

mixtures of hard rods we study the planar interfaces of coexisting isotropic and nematic phases. We calculate 

the surface tension, the interface-induced biaxiality, and the density and order parameter profiles through the 

interface. In the case that the bulk phase diagram exhibits an isotropic-nematic-nematic (I-N1-N2) triple point, 

we find complete wetting of the I-N2 interface by N1 upon approach of the triple point. This triple-point wetting 

is an entropy-driven analogue of e.g. surface melting of a metal upon approach of the melting temperature. 

References 

1. Van Roij, R., Dijkstra, M. and Evans, R., 2000. Europhys. Lett. 49, 350. 

2. Shundyak, K. and van Roij, R., 2002. Phys. Rev. Lett. 88, 205501.

SPINODAL DECOMPOSITION IN BINARY POLYMERIC BLENDS 

M.E. Velázquez-Sánchez, P.D. Anderson, P.G.T. van der Varst, G. de With 

Technische Universiteit Eindhoven, 

Postbus 513, 5600 MB Eindhoven, The Netherlands 

email: M.velazquez-sanchez@tue.nl 

ABSTRACT 

This work aims to predict the morphology development in films, on a substrate, made from binary polymeric 

blends that undergo phase separation via a spinodal decomposition mechanism. From thermodynamics it is 

possible to predict the spinodal and binodal regions of a system, once the Flory-Huggins interaction 

parameter is known; however to know how the morphology develops as a function of time, the diffusion 

equation must be solved. A diffuse-interface model that couples the thermodynamics and the hydrodynamics 

of a binary system is used. As an input, this model uses a chemical potential where the wall interaction and 

the non-local effects in the enthalpy and the entropy are taken into account. Preliminary results show that the 

introduction of the wall potential plays an important role in the development of the spinodal decomposition, 

resulting in a more complex morphology, where formation of macroscopic layers close to the substrate is 

obtained. Additionally, the growth rate of concentration fluctuations is significantly influenced by the wall.

EXPERIMENTAL AND THEORETICAL BEHAVIOUR OF END-TETHERED POLYMERS FROM 

THE MUSHROOM TO THE BRUSH LIMITS 

M.D. Whitmore 1) , M. Pépin 1) , M.S. Kent 2) , G. Grest 2) , J. Douglas 3) 

1) 

Dept. of Physics and Physical Oceanography, Memorial University of Newfoundland, 

St. John's, NF, Canada, A1B 3X7 

2) Sandia National Laboratory, 

Albuquerque, NM 87185, U.S.A. 

3) 

Polymers Division, National Institute of Science and Technology, 

Gaithersburg, MD 20899, U.S.A. 

email: markw@physics.mun.ca 

ABSTRACT 

We present systematic experimental results on the thickness of end-tethered polymer layers in good and Θ 

solvents. These results clearly show that most experimental systems fall between the mushroom and brush 

regimes. We then show that numerical self-consistent field theory, which uses appropriate values for 

monomer and solvent volumes and statistical segment lengths, provides quantitative agreement with 

experiment in these ranges. We go on to introduce a new parameter for characterizing the tethered-layer 

coverage, and use it to propose a unified description of these systems that applies from the mushroom 

regime, through the intermediate regime where most experiments occur, to deep into the brush limit, for 

layers in both good and Θ solvents. The analysis is based on a generalization of the asymptotic SCF theory, 

numerical SCF theory, Monte Carlo and molecular dynamics simulations, and the experimental data.

PERSISTENCE LENGTH OF WORM-LIKE MICELLES OF NON-IONIC SURFACTANTS 

Y. Lauw, F.A.M. Leermakers 



email: yansen@fenk.wau.nl 

ABSTRACT 

The persistence length of worm-like micelles is calculated by using two-gradient self-consistent field (SCF) 

theory within a cylindrical coordinates system. The CnEm non-ionic surfactants are used and forced into a 

toroidal-shaped micelles. This leads to a persistent length l p which scales with the tail length n as l x 

p ∞ n in 

which x is about 2.5. Furthermore the calculated bending energy at high total curvatures J, shows a deviation 

that can be attributed to a higher order term proportional to J 3 .

COMPLEXATION OF POLYELECTROLYTES AND POLYAMPHOLYTES WITH CHARGED 

OBJECTS 

E.B. Zhulina 

Institute of Macromolecular Compounds of the Russian Academy of Sciences, 

199004 St.Petersburg, Russia 

email: kzhulina@hotmail.com 

ABSTRACT 


Charged polymers are capable of aggregating and forming complexes of various morphologies in solutions. 

The equilibrium structure and the thermodynamic stability of the aggregates are determined by a 

number of factors: the distribution of charges on macromolecules, the polymer concentration, the pH and the 

ionic strength of the solution, etc. In this lecture we focus on two different systems: (1) the complexes of 

random polyampholytes with charged spherical particles and (2) ionized polymer micelles interacting with 

oppositely charged polyions. We analyze the equilibrium properties of the complexes by using the scaling 

model and the numerical Scheutjens and Fleer self-consistent-field model (Fleer 1993). We demonstrate that 

in spite of evident differences between the two systems, the soluble complexes exhibit similar features in a 

range of conditions. Namely, in the salt-free dilute solutions, they can be envisioned as effectively neutral 

star-like polymers. 

2. Interaction of polyampholytes with charged spherical particles 

We consider a water solution of long polyampholyte molecules, each comprising N >> 1 monomers of size 

a. The chains are flexible, and the Bjerrum length lB is on the order of the monomer size, IB≅a.The positive 

and negative charges are distributed in a random fashion along the chain. The respective fractions f + and f− 

of charged monomers are assumed to be almost equal ( f+ ≈ f− = f ) and small ( fN 2

For small particles with radius R < R ≅ 1/2 

o aN , the two effects give rise to the novel “pseudo-star” 

conformation of polyampholyte chain (Zhulina 2001). Here, the equilibrium structure of the complex is 

determined by the interplay of three factors: the polarization of the loops, the stretching of the loops, and the 

ternary contacts between monomers (theta-solvent conditions). The analysis (Zhulina 2001; Dobrynin 2001) 

indicates that in the pseudo-star conformation, the loops have a bimodal distribution. The smaller loops of 

size ~ R decorate the particle (the core of the pseudo-star). The larger loops of size H ~ aN1/2( Q2f ) −1/ 

6 form 

the “branches” of the pseudo-star. The number of branches P ~( Q2f ) 2/3 does not depend on chain length N 

and is determined solely by particle charge Q and degree of chain ionization f. 

In excess of polyampholyte molecules in the bulk solution, each complex is comprised of many chains. 

One can envision such a situation as formation of a semi-dilute adsorbed layer near the charged particle. The 

structure of the adsorbed layer (the polymer density profile, the distribution of loops, etc.) depends on the 

particle size and the surface charge density. For small particles with R < R ≅ 1/2 

o aN , the internal part of the 

adsorbed layer is found in the pseudo-star conformation. (It contains P chains each forming a single branch 

of the pseudo-star). The polymer density profile cr ()~ P1/2r −1 

decays inversely proportional to the distance r 

from the particle. The exterior part of the layer is formed by the less polarized chains (“poles” stretched in the 

electric field of spherical symmetry). For very large particles, adsorption occurs as on a planar surface 

(Dobrynin 1999). We calculate the adsorption isotherms for particles of different sizes and obtain the 

thickness of the adsorbed layer as a function of bulk polymer concentration. The results are compared with 

the experimental data on adsorption of gelatin. 

3. Interaction of ionized micelles with oppositely charged polyions 

We consider the association of an ionized quenched polymer micelle with an oppositely charged polyion. 

The star-like micelle consists of a neutral core and a charged corona. The respective degrees of ionization of 

the corona and of the polyion, α and β, are assumed to be relatively small to ensure the stability (solubility) of 

the complex. The number of polymer chains in the micelle is fixed, and the length of the polyion varies. An 

analytical self-consistent-field model indicates that when the polyion is long enough, the complex is virtually 

electroneutral as a whole (Simmons 2001). The compensating amount of oppositely charged polyion is 

dragged inside the micelle to release the small counterions from the corona. The structure of the equilibrium 

complex is rationalized in terms of the effective second ( v eff ) and third ( w eff ) virial coefficients of monomermonomer 

interactions, v = + α β 2 

eff v (1 / ) + χα/ β and w = + α β 3 

eff w (1 / ) . Here, v and w are the actual virial 

coefficients of monomer-monomer interactions of the corona chains, and χ is the Flory interaction parameter. 

We then use the numerical Scheutjens and Fleer model to explore the structure of the micelle/polyion 

complex in more detail. By performing calculations at various values of v, α, β, χ, and different amounts of 

added polyion, we demonstrate that the equilibrium properties of the complex can be rationalized in terms of 

the theory of neutral star-like polymers. We also focus on the effect of charge distribution on the polyion and 

consider three different cases: (1) a homopolymer with the smeared distribution of charge, (2) a diblock 

copolymer with a charged and a neutral block, and (3) a multi-block copolymer. Although the fine details of 

polyion distribution in the micelle/polyion complex are different in the three cases, the Scheutjens and Fleer 

model confirms the essential electroneutrality of the complex. The numerical findings are in reasonable 

agreement with predictions of the analytical self-consistent-field theory. 

Acknowledgements 

The results presented in this lecture were obtained in collaboration with Dr. Andrey Dobrynin (UNC), Prof. 

Michael Rubinstein (UNC), Chris Simmons (UT), Prof. Steve Webber (UT), Dr. Jan van Male (WU) and Dr. 

Frans Leermakers (WU). The financial support from the National Science Foundation USA (grants DMR- 

9973300 and DMR-9730777) and NWO Project 047.009.016 “Self-Organization and Structure of Bionanocomposites” 

is greatly acknowledged.

References 

1. Dobrynin, A.V., Obukhov, S.P. and Rubinstein, M., 1999. Long-Range Mutichain Adsorption of Polyampholytes 

on a Charged Surface. Macromolecules, 32(17), 5689-5700. 

2. Dobrynin, A.V., Zhulina, E.B. and Rubinstein, M., 2001. Structure of Adsorbed Polyampholyte Layers at 

Charged Objects. Macromolecules, 34(3), 627-639. 

3. Fleer, G.J., Cohen Stuart, M.A., Scheutjens, J.M.H.M., Cosgrove, T. and Vincent, B. Polymers at Interfaces, 

Chapman & Hall, 1993. 

4. Simmons, C., Webber, S.E. and Zhulina, E.B., 2001. Association of Ionized polymer Micelles with 

Oppositely Charged Polyelectrolytes. Macromolecules 34 (14), 5053- 5066. 

5. Zhulina, E.B., Dobrynin, A.V. and Rubinstein, M., 2001. Adsorption of a Polyampholyte on a Charged 

Spherical Particle. Eur. Phys. J. E , 5(1), 41-49. 

6. Zhulina, E.B., Dobrynin, A.V. and Rubinstein, M., 2001. Adsorption Isotherms of Polyampholytes at 

Charged Spherical Particles .J. Phys. Chem. B, 105(37), 8917-8930.

MEAN-FIELD THEORY FOR THE ADSORPTION OF FLEXIBLE POLYMERS DURING FLOW 

THROUGH GRANULAR POROUS MEDIA 

P. L.J. Zitha 

Delft University of Technology, Department of Applied Earth Sciences, 

Mijnbouwstraat 120, 2628 RX Delft, The Netherlands 

email: p.l.j.zitha@citg.tudelft.nl 

ABSTRACT 

We have developed a mean-field theory for the adsorption of flexible polymers during flow through granular 

porous media. There exist two situations (Fig. 1): (a) At low velocity gradients (weak flows) the chains retain 

the coil conformation and adsorb according to the classic layer mode. The adsorption density w increases 

with time θ, first according to a linear kinetic equation leading to an exponential saturation law 

w( θ) = w e[1−exp( 

θ / τ)] 

and then following a non-linear kinetic process. The transition from the linear to the 

non-linear regimes is associated with the development of a strong reptation barrier scaling like w 9/4 , when 

the adsorbed chains begin to overlap. This occurs at a well-defined critical adsorption density w* 

corresponding to the critical overlap concentration for the bulk polymer solution. (b) At high velocity gradient 

(strong flow), the coiled chains coexist with strongly stretched ones giving rise to a bi-modal adsorption: the 

coiled chains adsorb according to the layer mode while the long (stretched) ones bridge over the smallest 

pores (bridging adsorption). These two adsorption modes are strongly correlated and the corresponding 

adsorption densities w and z obey a system of coupled non-linear kinetic equations. The transition from linear 

to non-linear regimes occurs now at a concentration v* = ( w + κ z ) , where κ is the fraction of segments of the 

bridging chains that are in the adsorbed layer. Remarkably, the mechanical trapping of the stretched chains 

overcomes the reptation barrier when bridging adsorption is consecutive to layer adsorption. 

Figure 1. Cross-section of a pore showing the adsorbed layer (hydrodynamic thickness εH) and one bridging chain. Two 

portions of the bridging chain (degree of polymerisation Nb,1 and Nb,2) penetrate the adsorbed layer while the central 

portion (degree of polymerization Nb,c) is exposed to flow.

Collapse of polymer brushes grafted onto planar ... - Wageningen UR

Create successful ePaper yourself

Delete template?

Save as template?