(670h) Field-Theoretic Modeling of Neutral Solvent Effects on Diblock Copolymer Self-Assembly

Access to clean drinking water is of great importance, but only developed nations can implement cutting-edge seawater desalination technology at scale. One reason for this expense is poor selectivity of commercial membranes, necessitating multiple passes and post-treatments to fully rid input streams of impurities. One promising alternative material for these membranes is copolymers. These “polymer alloys” could potentially solve the issue of selectivity due to their unique self-assembly. Under specific conditions, these copolymers form heterogeneous microphases, which can result in monodisperse percolation pathways. These pathways can take the form of cylindrical domains (cylindrical phase) or a percolation network (gyroid phase). Control over the phase formed allows for control over the pathway architecture, which then determines the permeation properties of a given membrane. During synthesis, however, these membranes are exposed to different temperature and solvent conditions. During use, a solvent gradient develops, since one side of the membrane is exposed to a highly concentrated slurry and the other is exposed to pure water. These variations in environment can cause a variety of phases to self-assemble, some of which may lead to desirable, selective water purification membranes.

To understand the role of these environmental conditions, it is important to establish how varying degrees of solvent selectivity affect the phase behavior of diblock copolymers. This study can be done efficiently using computational methods. In this work, we develop a field-theoretic Monte Carlo simulation of semiflexible polymers, incorporating chemical incompatibility between monomers. This simulation generates equilibrium structures of copolymer solutions at a range of interaction parameters, and we have extended the simulation to be able to study solvents of varying selectivity. We also develop software packages capable of structure factor and heat capacity analyses, to identify phases and phase transitions. Recent efforts focus on diblock copolymer solutions in neutral solvent. We have found order-disorder and order-order transitions for diblock copolymers of a range of block sizes. This work elucidates the conditions for the self-assembly of a variety of microphases, including lamellar, perforated lamellar, and cylindrical phases.

These simulation results can be compared to predictions from self-consistent field theory. Previous work has studied the phase behavior of copolymer solutions with free-energy expressions expanded to quadratic order in concentration fluctuations. From this analysis, order-disorder and order-order phase transitions are predicted. However, we find significant deviations from these quadratic-order theoretical predictions and simulation results. This inconsistency is due to higher-order fluctuation effects. We correct for this by expanding the phase free-energy expressions to quartic order in concentration fluctuations. We develop a code base to find higher order vertex functions which contribute to the free energy, then leverage these theoretical predictions to aid in our comparison between simulation and theory. Finding agreement between these two domains instills greater confidence in our predictions of polymer phase behavior and will enable us to predict membrane architecture and properties more accurately.