The Elastic Behavior of Entropic "Fisherman's Net"

Details The Elastic Behavior of Entropic "Fisherman's Net" The Elastic Behavior of Entropic "Fisherman's Net"

2000-04-17

arxiv.org/abs/cond-mat/0004276v1

Eur. Phys. J E, 3 (2000) 253

Physics

Condensed Matter

Statistical Mechanics

submitted to the European Physical Journal E-Soft Matter. 6 pages. 4 figures

Scientific paper

10.1007/s101890070017

A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio $\gamma$ between the maximal and actual extensions of the net. When the net is very stretched ($\gamma\sim 1$), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems, coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is more loose ($\gamma\sim 3$).

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