Phase transitions in Polyelectrolyte systems[HBNI Th56]

Abstract

Polyelectrolytes (PEs) are polymers whose monomers contain ionizable groups that dissociate in polar solvents, releasing charged counterions into the solvent, thereby making the polymer backbone charged. The thermodynamic properties of a PE is different from that of a neutral polymer because of the interplay between the long-range Coulomb interactions and short-range excluded volume interactions. For low linear charge densities of the polymer backbone, thermal fluctuations dominate over electrostatic interactions, and the counterions will be uniformly distributed in the solution. For high linear charge densities, electrostatic interactions dominate thermal fluctuations, and the counterions condense on the PE chain. As the linear charge density is increased from low values to high values, the system undergoes a series of phase transitions. This thesis studies different phases of three different PE systems, and the transitions between them. The first system is a single flexible PE chain in a solvent containing explicit counterions. In this system, the author identifies the counterion condensation and the condensed counterion mediated collapse of the PE chain as phase transitions. It is argued, against the existence of intermediate phases between the extended and collapsed phases. The second system is a collection of similarly charged rod-like PE chains in the presence of neutralizing counterions. In this system, the aggregation of PE chains induced by condensed counterions is studied, and it is related to the extended-collapsed transition of a single flexible PE chain. The third system that is considered, is a two-dimensional charged disc surrounded by freely moving oppositely charged counterions, and it is studied in both the canonical and microcanonical ensembles. The Coulomb interactions in PE systems are long-ranged, i.e., they decay slower than r(−d) for r ≫ 1, where r is the inter-particle separation and d is the dimension of the system. A possible consequence is the inequivalence of different statistical ensembles. By comparing the thermodynamics obtained from the analytical solutions in the canonical and microcanonical ensembles, it is shown that the ensembles are identical for the counterion condensation on a two-dimensional charged disc.