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arXiv · 1304.3500

Fluctuation-stabilized marginal networks and anomalous entropic elasticity

Matthew Dennison·Michael Sheinman·Cornelis Storm·Fred C. MacKintosh
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Abstract

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show that thermal networks exhibit a non-zero shear modulus $G$ well below the isostatic point, and that this modulus exhibits an anomalous, sublinear dependence on temperature $T$. At the isostatic point, $G$ increases as the square-root of $T$, while we find $G \propto T^{\alpha}$ below the isostatic point, where ${\alpha} \simeq 0.8$. We show that this anomalous $T$ dependence is entropic in origin.

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Matthew Dennison, Michael Sheinman, Cornelis Storm, Fred C. MacKintosh. 2013-04-11. Fluctuation-stabilized marginal networks and anomalous entropic elasticity. https://doi.org/10.1103/physrevlett.111.095503

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