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Soft Matter and Biological Physics

Eur. Phys. J. E 3, 253-258

The elastic behavior of entropic "fisherman's net''

O. Farago - Y. Kantor

School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69 978, Israel
farago@orion.tau.ac.il

Received 9 February 2000 and Received in final form 14 May 2000

Abstract
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 ( $\gamma\sim1$), 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 looser ( $\gamma\sim 3$).

PACS
62.20.Dc Elasticity, elastic constants - 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 65.50.+m Thermodynamic properties and entropies

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