Shear-stress fluctuations in self-assembled transient elastic networks

TL;DR

This study numerically investigates shear-stress fluctuations in self-assembled transient elastic networks, establishing efficient methods to determine the shear-stress relaxation modulus across liquid to solid transition regimes.

Contribution

It generalizes previous work on permanent networks by providing a simple average method to compute the shear-stress relaxation modulus for transient networks across different topological states.

Findings

The shear-stress relaxation modulus can be efficiently determined using a simple average involving the shear stress mean-square displacement.

The relation between $G(t)$ and shear-stress autocorrelation function $C(t)$ is analyzed, with bounds on the number of configurations needed.

The study bridges the understanding of shear-stress fluctuations from liquid to solid states in transient network models.

Abstract

Focusing on shear-stress fluctuations we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With $\Delta dt$ being the sampling time and $t_*(f) \sim 1/f$ the Maxwell relaxation time (set by the spring recombination frequency $f$) the dimensionless parameter $\Delta x = dt/t_*(f)$ is systematically scanned from the liquid limit ($\Delta dx \gg 1)$ to the solid limit ($\Delta x \ll 1$) where the network topology is quenched and an ensemble average over $m$ independent configurations is required. Generalizing previous work on permanent networks it is shown that the shear-stress relaxation modulus $G(t)$ may be efficiently determined for all $\Delta x$ using the simple-average expression $G(t) = \mu_A - h(t)$ with $\mu_A = G(0)$ characterizing the canonical-affine shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is compared to the standard expression $G(t) = C(t)$ using the (rescaled) shear-stress autocorrelation function $C(t)$. Lower bounds for the $m$ configurations required by both relations are given.