Polymers at interfaces and in colloidal dispersions.

This review is an extended version of the Overbeek lecture 2009, given at the occasion of the 23rd Conference of ECIS (European Colloid and Interface Society) in Antalya, where I received the fifth Overbeek Gold Medal awarded by ECIS. I first summarize the basics of numerical SF-SCF: the Scheutjens-Fleer version of Self-Consistent-Field theory for inhomogeneous systems, including polymer adsorption and depletion. The conformational statistics are taken from the (non-SCF) DiMarzio-Rubin lattice model for homopolymer adsorption, which enumerates the conformational details exactly by a discrete propagator for the endpoint distribution but does not account for polymer-solvent interaction and for the volume-filling constraint.

Analytical phase diagrams for colloids and non-adsorbing polymer.

We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett.

Analytical phase diagram for colloid-polymer mixtures.

We present a theoretical analysis of the phase behavior of colloid-polymer mixtures which applies to all polymer/colloid size ratios q. It accounts for the crossover from a constant length scale R (radius of gyration) in the colloid limit (small q) to the concentration-dependent correlation length xi in the protein limit (q>1). We obtain predictions that fully agree with observations and simulations.

Critical endpoint and analytical phase diagram of attractive hard-core Yukawa spheres.

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J.

Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution.

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field.