Gellation of rigid filament networks

TL;DR

This paper models the gelation process of rigid rod networks, analyzing how cross-linking evolves over time with different cross-link compliances, revealing key asymptotic behaviors.

Contribution

It introduces a mathematical model for rigid rod gelation considering both point-like and compliant cross-links, providing analytical expressions for cross-linking dynamics.

Findings

Number of cross-links approaches ~3.53 for point-like cross-links.

With compliant cross-links, cross-linking grows logarithmically over time.

The model captures the influence of cross-link compliance on gelation dynamics.

Abstract

We consider a model for gelation of rigid rods, in which rods that are initially placed at random undergo diffusion, and form cross-links when they collide. In the limit of point-like cross-links, the number N of croslinks per rod approaches N ~ 3.53. In a model with compliant cross-links of maximum length l_c, N(t) increases with time as N(t) ~ const. + cL^2 l_c ln(t), where c is concentration and L is rod length.