Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

TL;DR

This paper develops a microscopic theoretical framework to coarse-grain diblock copolymer liquids into simplified models, accurately predicting phase behavior and matching simulations without adjustable parameters.

Contribution

It introduces a novel integral-equation-based coarse-graining method for diblock copolymers, linking microscopic details to mesoscopic descriptions.

Findings

Accurate analytical correlation functions for copolymer pairs.

Prediction of microdomain segregation driven by temperature.

Quantitative agreement with molecular dynamics simulations in the athermal regime.

Abstract

A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed, based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to provide a mesoscopic description of the diblock copolymer system at the level of block centers of mass, and at the level of polymer centers of mass. Analytical forms of the total correlation functions for block-block, block-monomer, and center-of-mass pairs are obtained for a liquid of structurally symmetric diblock copolymers as a function of temperature, density, chain length, and chain composition. The theory correctly predicts thermodynamically-driven segregation of diblocks into microdomains as a function of temperature ($chi$ parameter). The coarse-grained description contains contributions from density and concentration fluctuations, with the latter becoming dominant as temperature decreases. Numerical calculations for the block coarse-grained total correlation functions, as a function of the proximity of the system to its phase transition, are presented. Comparison with united atom molecular dynamics simulations are carried out in the athermal regime, where simulations and theory quantitatively agree with no need of adjustable parameters.