Role of cross-links in bundle formation, phase separation and gelation of long filaments

TL;DR

This paper models how cross-links influence the formation, phase separation, and gelation of long filament solutions, revealing entropy-driven transitions and structural changes such as bundle formation.

Contribution

It introduces a mean field model predicting entropy-induced phase separation and structural transitions in cross-linked filament solutions, including bundle formation.

Findings

Entropy of junctions induces effective attraction between filaments.

Phase separation into a network and dilute phase occurs at mean field level.

Rigid rods form bundles at low temperatures due to entropy interplay.

Abstract

We predict the thermodynamic and structural behavior of solutions of long cross-linked filaments. We find that at the mean field level, the entropy of self-assembled junctions induces an effective attraction between the filaments that can result in a phase separation into a connected network, in equilibrium with a dilute phase. A connected network can also be formed in a non-thermodynamic transition upon increase of the chain, or cross link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network, to anisotropic bundles of rods tightly bound by cross links, that is triggered by the interplay between the configurational entropy of the cross-link distribution among the rods, and the rotational and translational entropy of the rods.