Self-consistent field theory for polyelectrolytes and its applications

In this work, we have developed a self-consistent field theory (SCFT) for polyelectrolytic systems and studied four important problems of contemporary interest: microphase separation in the melts of charged-neutral diblock copolymers, confinement effects on flexible polyelectrolytes, counterion adsorption on single flexible polyelectrolyte chain and the origin of translocation barriers in polyelectrolytic systems. Using the theory, we have been able to capture the effects of the degree of ionization, salt concentration, electrostatic and the excluded volume interaction strengths, degree of polymerization, role of architecture and solvent quality on these polyelectrolytic systems. Within saddle-point approximation, the polyelectrolyte chain configuration is described as a walk in the presence of fields coming from the excluded volume interactions and the other effects such as incompressibility in addition to the electrostatic potential. The electrostatic potential, on the other hand, is obtained from Poisson-Boltzmann like equation. So, in contrast to the SCFT for neutral polymers, there are two coupled non-linear equations namely modified diffusion equation describing the walk in the fields and the Poisson-Boltzmann equation, which have to be solved self-consistently. In this work, we have developed various numerical schemes to solve these coupled non-linear sets of equations. Furthermore, comparison of the SCFT results with a previous developed variational theory for polyelectrolytes has been carried out. Also, systematic expansions around the saddle-point results have been carried out to capture the effects of the density fluctuations of the small ions in the systems