A multi-species exchange model for fully fluctuating polymer field theory simulations

TL;DR

This paper introduces a multi-species exchange model that extends complex Langevin simulations to multi-component polymer systems, enabling stable and accurate fluctuation studies in complex polymer blends.

Contribution

The paper develops a multi-species exchange model that allows stable complex Langevin simulations for multi-component polymer field theories, expanding the scope of fluctuation analysis.

Findings

Demonstrated stability and accuracy in simulations of triblock and tetrablock terpolymer melts.

Enabled complex Langevin simulations for multi-component polymer systems.

Expanded the applicability of fluctuation studies in multiblock/multi-species polymers.

Abstract

Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing composition fluctuations. The models commonly used can be grouped into two categories, namely {\it species} models and {\it exchange} models. Species models involve integrations of functionals that explicitly depend on fields originating both from species density operators and their conjugate chemical potential fields. In contrast, exchange models retain only linear combinations of the chemical potential fields. In the two-component case, development of exchange models has been instrumental in enabling stable complex Langevin (CL) simulations of the full complex-valued theory. No comparable stable CL approach has yet been established for field theories of the species type. Here we introduce an extension of the exchange model to an arbitrary number of components, namely the multi-species exchange (MSE) model, which greatly expands the classes of soft material systems that can accessed by the complex Langevin simulation technique. We demonstrate the stability and accuracy of the MSE-CL sampling approach using numerical simulations of triblock and tetrablock terpolymer melts, and tetrablock quaterpolymer melts. This method should enable studies of a wide range of fluctuation phenomena in multiblock/multi-species polymer blends and composites.