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arXiv · 1606.06487

Shear-stress fluctuations in self-assembled transient elastic networks

J. P. Wittmer·I. Kriuchevskyi·A. Cavallo·H. Xu·J. Baschnagel
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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.

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BibTeXRIS

J. P. Wittmer, I. Kriuchevskyi, A. Cavallo, H. Xu, J. Baschnagel. 2016-06-21. Shear-stress fluctuations in self-assembled transient elastic networks. https://doi.org/10.1103/physreve.93.062611

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