Molecularly derived field theories have greatly advanced our understanding of the self-assembly behavior of polymeric fluids. The most common approach in these theories is the mean-field approximation, also known as self-consistent field theory (SCFT), which has successfully predicted and described a wide range of behaviors in inhomogeneous polymers. Field-theoretic simulations (FTS) go beyond the mean-field level, providing a numerical framework to capture various mesoscopic phenomena in polymer systems. This thesis presents advancements that enhance the design of FTS simulations, extend FTS to a broader range of polymeric fluids, enable studies of dynamical behavior, and improve the ease of FTS parameterization.
First, I compare two FTS approaches: the exact complex Langevin method and the partial saddle point approximation (PSPA). This work clarifies the conditions under which the PSPA is applicable, specifically in cases where fluctuations from the reference single-species system are negligible.
Second, I develop density-explicit FTS, which allows for a broader range of non-bonded interactions. New algorithms and schemes enable FTS simulations using this density-explicit formalism, which is accurate in dense systems but not in dilute systems. Nonetheless, we demonstrate the efficacy of this approach across a wide range of simple and polymeric fluids.
Third, I present fully fluctuating dynamical simulations generalizable to multi-species and multi-component systems. By leveraging a chain rule relationship between density and exchange fields, we develop an efficient external potential dynamics (EPD) method. This EPD approach enables stable and efficient stochastic evolution, demonstrated here on triblock copolymer melts and binary and ternary melt blends.
Finally, I propose methodologies for parameterizing polymer field theories by estimating $\chi$ parameters using high-throughput experimental data. Historically, the semi-analytical random-phase approximation (RPA) has served to link experimental parameters with polymer-field theories. Our approach involves two main components: (1) using machine learning techniques to predict phase diagrams and (2) iteratively solving RPA to achieve optimal parameter mapping. In this work, we demonstrate these methodologies in the presence of measurement error and validate them using real experimental datasets.
