Entropic elasticity of two-dimensional self-avoiding percolation systems

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-p(c))(f), where the exponent f approximately 1. 3 is independent of a and is similar to the conductivity exponent in random resistor networks.