Theory of solutions of semiflexible polyelectrolytes

The main objective of this dissertation is to rationalize the wide spectrum of physical behaviors displayed by polyelectrolyte solutions using the simplest concepts available today. This goal has been achieved by constructing mathematical models that describe the observed behaviors quantitatively. Specifically, we have considered the dependences of the radius of gyration, correlation length, effective interaction, phase diagram, solution and single-chain structure factors, isotropic-nematic transition and orientational order on molecular weight, stiffness of the polymer backbone, salt and monomer concentration, degree of ionization and hydrophobicity of the polymer chain. Our calculations predict a rich thermodynamic behavior for polyelectrolyte solutions. We have found that the electrolytic nature of the polymer shifts the phase diagram (χ − &phis;) upwards with respect to the one of the neutral system. This prediction is independent of the stiffness of the polymer backbone. The extent of the shift depends on the charge density of the polymer backbone and salt concentration. In addition, an increase of salt concentration moves the phase diagram closer to the one of neutral polymers. We also predict a radical change in the nature of the phase diagram when the stiffness of the polymer backbone is increased. In the flexible chain limit the phase diagram describes the coexistence between two isotropic phases and displays an UCST (critical point). In the rod limit, the phase diagram describes the coexistence between an isotropic and a nematic phase (first order phase transition). By changing the stiffness of the polymer backbone we studied how the transition from one regime into the other one occurs. The results point to the existence of a tricritical point and coexistence between two isotropic phases or one isotropic and one nematic depending on the temperature of the solution. The isotropic-nematic transition was also studied. The main result is a decrease of the monomer concentration at which the transition takes place with increasing salt concentration. This last result implies a stabilization of the isotropic phase by the electrostatic interaction. Other results related to the thermodynamic, scattering and single-chain behaviors were studied and are analyzed in this dissertation