Theory of the center-of-mass diffusion and viscosity of microstructured and variable sequence copolymer liquids

TL;DR

This paper develops a microscopic dynamical theory to understand how sequence, interactions, and density influence the diffusion and viscosity of concentrated multiblock copolymer solutions, revealing microemulsion-like structures and dynamical slowing down.

Contribution

It introduces a new theoretical framework combining PRISM and force autocorrelation analysis to predict copolymer dynamics based on microstructure and sequence effects.

Findings

Sequence and attraction strength significantly slow down mass transport.

Microdomain ordering leads to increased collisional friction.

Dynamical slowing down correlates with microemulsion-like internal structures.

Abstract

Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates have been regarded as homogeneous isotropic liquids. However, in analogy with some synthetic copolymer systems, our recent theoretical research has demonstrated that model biomolecular condensates can exhibit a microemulsion-like internal structure, contingent upon the specific sequence, inter-chain site-site interactions, and concentrated phase polymer density. In this study, we present a microscopic dynamical theory for the self-diffusion constant and viscosity of concentrated unentangled A/B regular multiblock copolymer solutions. Our approach integrates static equilibrium local and microdomain scale structural information obtained from PRISM integral equation theory and the time evolution of the autocorrelation function of monomer scale forces at the center-of-mass level that determine the polymer diffusion constant and viscosity in a weak caging regime far from a glass or gel transition. We focus on regular multi-block systems both for simplicity and for its relevance to synthetic macromolecular science. The impact of sequence and inter-chain attraction strength on the slowing down of copolymer mass transport and flow due to local clustering enhanced collisional friction and retardation of motion due to emergent microdomain scale ordering are established. Analytic analysis and metrics employed in the study of biomolecular condensates are employed to identify key order parameters that quantity how attractive forces, packing structure, multiblock sequence, and copolymer density determine dynamical slowing down above and below the crossover to a fluctuating polymeric microemulsion state.