Entropic Elasticity of Two-Dimensional Self-Avoiding Percolation Systems Academic Article uri icon

abstract

  • The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction $p$ of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters $a$ the rigidity threshold is insensitive to $a$ and indistinguishable from the percolation threshold ${p}_{c}$. Close to ${p}_{c}$, the shear modulus behaves as $({p\ensuremath{-}p}_{c}{)}^{f}$, where the exponent $f\ensuremath{\simeq}1.3$ is independent of $a$ and is similar to the conductivity exponent in random resistor networks.

publication date

  • January 1, 2000