title: Thermodynamics of Polyelectrolyte Solutions and Polymer Crystallization
Creators: name: Adhikari, Sabin
Publisher: name: University of Massachusetts Amherst
Year: 2019

description: Polymeric systems exhibit interesting macroscopic properties under different thermodynamic conditions and are prevalent in both biology and synthetic world. How a system of polymers behaves under different thermodynamic conditions is determined by the interplay of different possible interactions such as short-ranged Van der Waals and long-ranged electrostatic interactions and the entropy of individual components present in the system. This work is mostly focused on the theoretical study of the thermodynamic phase behaviors of charged polymers in solutions. We use the methods of both analytical theory and numerical computations in order to find the free energies and then the thermodynamically most stable states of systems under consideration. Our topics of interest in this work include phase separation of solutions of oppositely charged polyelectrolytes (also known as complex coacervation), interfacial tension in polyelectrolyte complex coacervates, orientations of rigid polyelectrolytes
in solutions and the statistics of amorphous chains in polymer semi-crystals.

We develop a new free energy expression to study the phase behaviors of polyelectrolyte complex coacervates, complementing numerous existing theories and construct phase diagrams to predict the effect of experimental variables in the phase behavior. We explore in detail on both the upper critical solution (UCST) and the lower critical solution (LCST) behavior and compare the theoretical predictions with experiments. The constructed phase diagrams predict that salt and asymmetry in polycation-polyanion content suppress complex coacervation. We also show that a solution can exhibit UCST or LCST depending upon the temperature dependencies of the solvent{polymer interaction parameter and the solvent dielectric constant. These predictions are in qualitative agreements with experiments. Further, by using this new free energy, we numerically compute the interfacial tension between the interface of a polyelectrolyte complex coacervate phase and a coexisting aqueous dilute phase. We predict that the interfacial tension decreases with increasing the salt concentration and it increases with increasing the polyelectrolyte chain length. Next, we study the thermodynamics of charged rods in solution, focusing on the effect of electrostatic interactions among the rods in determining their relative orientations. We show that electrostatic repulsion among the rods tends to stabilize the solution against the isotropic-nematic phase transition/separation. Finally, we study the statistics of ties and loops in the amorphous regions of polymer crystals. Here the focus is on determining the fraction of ties, it is because of their relevance in determining the mechanical properties of semicrystalline polymers. We calculate the fraction of ties and loops by calculating the partition sum of the amorphous region by using the field-theoretic techniques in statistical mechanics. We show that the fraction of ties increases with increasing the chain length and it decreases with increasing the thickness of the amorphous region.