Theory of polymer diffusion in polymer-nanoparticle mixtures: effect of nanoparticle concentration and polymer length

TL;DR

This paper develops a microscopic, parameter-free theory for polymer diffusion in polymer-nanoparticle mixtures, capturing how diffusion depends on nanoparticle concentration and polymer length, and revealing entanglement-like dynamics.

Contribution

It introduces a first-principles theoretical framework combining Langevin, mode-coupling, and polymer physics for polymer diffusion in nanocomposites, explicitly incorporating system-specific structures.

Findings

Polymer diffusion decreases with increasing nanoparticle concentration.

Diffusion exhibits power-law decay with polymer length at high nanoparticle density.

The theory accurately predicts the dependence of diffusion on system parameters.

Abstract

The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for polymer diffusion in the mixtures based on a combination of generalized Langevin equation, mode-coupling approach, and polymer physics ideas. The parameter-free theory has an explicit expression and remains tractable on pair correlation level with system-specific equilibrium structures as input. Taking a minimal polymer-NP mixture as an example, our theory correctly captures the dependence of polymer diffusion on NP concentration and average interparticle distance. Importantly, the polymer diffusion exhibits a power law decay as the polymer length increases at dense NPs and/or long chain, which marks the emergence of entanglement-like motion. The work provides a first-principle theoretical foundation to investigate dynamic problems in diverse polymer nanocomposites.