M. Watzlawek

Phase Diagram of Star Polymer Solutions

The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density.

Freezing and clustering transitions for penetrable spheres

We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction between micelles in a solvent [C. Marquest and T. A. Witten, J. Phys. France 50, 1267 (1989)]. The phase diagram of these penetrable spheres is investigated using a combination of cell- and density functional theory for the solid phase together with simulations for the fluid phase. The system displays unusual phase behavior due to the fact that, in the solid, the optimal configuration is achieved when certain fractions of lattice sites are occupied by more than one particle, a property that we call ‘clustering’. We find that freezing from the fluid is followed, by increasing density, by a cascade of second-order, clustering transitions in the crystal.

The anomalous structure factor of dense star polymer solutions

The core-core structure factor of dense star polymer solutions in a good solvent is shown theoretically to exhibit an unusual behaviour above the overlap concentration. Unlike usual liquids, these solutions display a structure factor whose first peak decreases with increasing density while the second peak grows. The scenario repeats itself with the subsequent peaks as the density is further enhanced. For low enough arm numbers , various different considerations lead to the conclusion that the system remains fluid at all concentrations.

Triplet interactions in star polymer solutions

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration.

Polydisperse star polymer solutions

We analyze the effect of polydispersity in the arm number on the effective interactions, structural correlations, and phase behavior of star polymers in a good solvent. The effective interaction potential between two star polymers with different arm numbers is derived using scaling theory. The resulting expression is tested against monomer-resolved molecular dynamics simulations. We find that the theoretical pair potential is in agreement with the simulation data in a much wider polydispersity range than other proposed potentials. We then use this pair potential as an input in a many-body theory to investigate polydispersity effects on the structural correlations and the phase diagram of dense star polymer solutions. In particular, we find that a polydispersity of 10%, which is typical in experimental samples, does not significantly alter previous findings for the phase diagram of monodisperse solutions.

Neither Gaussian chains nor hard spheres - star polymers seen as ultrasoft colloids

In dense solution high functionality star polymers show ordering phenomena which give rise to a well-pronounced peak in the static structure factor, S exp(Q), observed by small-angle neutron scattering. The concentration dependence of S exp (Q) gives evidence for unusual phase behaviour as predicted by theory. In addition, the dynamics of the star polymer solutions is dominated by an increasing amount of structural arrest with increasing concentration. The mean square displacement obtained from neutron spin-echo spectroscopy is compared to the blob size obtained from dynamic light scattering. Thermal energy enables each star core to perform restricted motion over a spatial extent equal to the blob size of the surrounding dense star polymer solution.

Enhanced structural correlations accelerate diffusion in charge-stabilized colloidal suspensions.

Theoretical calculations for colloidal charge-stabilized suspensions and hard-sphere suspensions show that hydrodynamic interactions yield a qualitatively different particle concentration dependence of the short-time self-diffusion coefficient. The effect, however, is numerically small and hardly accessible by conventional light-scattering experiments. By applying multiple-scattering decorrelation equipment and a careful data analysis we show that the theoretical prediction for charged particles is in agreement with our experimental results from aqueous polystyrene latex suspensions.

Phase transitions in colloidal suspensions and star polymer solutions

Possibilities of fluid-solid and solid-solid phase transformations in colloidal suspensions and star polymer solutions are reviewed. We start from given interparticle pair potentials and predict the corresponding phase diagrams using computer simulations and density functional theory. When possible, the results are compared with experimental data. In particular, we discuss a cascade of freezing transitions for confined colloids and re-entrant melting and anisotropic solid phases for star polymer solutions.

Colloids with polymer stars: the interaction

Abstract We derive the short distance interaction of star polymers in a colloidal solution. We calculate the corresponding force between two stars with arbitrary numbers of legs f1 and f2. We show that a simple scaling theory originally derived for high f1, f2 nicely matches with the results of elaborated renormalization group analysis for f1 + f2 ≤ 6 generalizing and confirming a previous conjecture based only on scaling results for f1 = f2 = 1, 2.

Phase transitions in soft matter systems

We review recent work on fluid-solid and solid-solid phase transitions in soft matter systems such as colloidal suspensions and star polymer solutions. Starting from a given interparticle pair potential we predict the corresponding phase diagrams using computer simulations, cell theory, and density functional theory. When possible, the results are compared with experimental data. In particular, we discuss the following aspects: a cascade of freezing transitions for confined colloids, stable one-component quasicrystals for charged colloids, reentrant melting and anisotropic solid phases for star polymer solutions and reentrant nematic ordering for suspensions of the tobacco-mosaic virus.