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Biomolecular condensates formed through the phase separation of proteins andnucleic acids are widely observed, offering a fundamental means of organizingintracellular materials in a membrane-less fashion. Traditionally, thesecondensates have been regarded as homogeneous isotropic liquids. However, inanalogy with some synthetic copolymer systems, our recent theoretical researchhas demonstrated that model biomolecular condensates can exhibit amicroemulsion-like internal structure, contingent upon the specific sequence,inter-chain site-site interactions, and concentrated phase polymer density. Inthis study, we present a microscopic dynamical theory for the self-diffusionconstant and viscosity of concentrated unentangled A/B regular multiblockcopolymer solutions. Our approach integrates static equilibrium local andmicrodomain scale structural information obtained from PRISM integral equationtheory and the time evolution of the autocorrelation function of monomer scaleforces at the center-of-mass level that determine the polymer diffusionconstant and viscosity in a weak caging regime far from a glass or geltransition. We focus on regular multi-block systems both for simplicity and forits relevance to synthetic macromolecular science. The impact of sequence andinter-chain attraction strength on the slowing down of copolymer mass transportand flow due to local clustering enhanced collisional friction and retardationof motion due to emergent microdomain scale ordering are established. Analyticanalysis and metrics employed in the study of biomolecular condensates areemployed to identify key order parameters that quantity how attractive forces,packing structure, multiblock sequence, and copolymer density determinedynamical slowing down above and below the crossover to a fluctuating polymericmicroemulsion state.

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