Theoretical Studies of Particle/Polymer Mixtures

Abstract

This thesis reports a theoretical study of polymers in the presence of particles. An analytical theory is used to describe the potential of mean force between spheres for the case where the polymer molecular weight dispersity is described by the Schulz-Flory distribution. Exact results are derived for systems where the particle radius (RS) is small in comparison to the radius of gyration (Rg) of the polymer molecules. Numerical results are obtained in the case of particles immersed in a solution of polymers. It is shown that when q = Rg/RS ≥ 10 a spherical approximation can be used to describe the potential of mean force. This result has significant consequences on the many-body interactions mediated by polymers between particles in the particle/polymer mixtures. The theory is then applied to study the phase behaviour of particle/polymer mixtures in electrolyte solutions wherein the particles are charged. Thus the particles have a combination of depletion attraction and screened electrostatic repulsion. We show that a generalized potential of mean force is an accurate and computationally efficient means by which to treat this system. In addition to the two studies above, we also consider the case of an equilibrium polymer consisting of associating co-monomers. We generalize the density functional theory of polymers to describe this scenario and study the case where the polymer is in the vicinity of an attractive surface. Interestingly, A surface phase transition is observed in ideal polymers, which is suppressed when monomers exclude each other. We use this theory to model the formation of linear peptide aggregates on the surfaces of particles. In particular, we consider a specific model for an amyloidal peptide responsible for Alzheimer disease. The thesis concludes with a discussion on possible theoretical developments in the future.