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Soft Matter and Biological Physics
Eur. Phys. J. E 11, 61-64 (2003)
DOI: 10.1140/epje/i2003-10006-x

3d Monte Carlo simulation of site-bond continuum percolation of spheres

M. Rottereau, J.C. Gimel, T. Nicolai and D. Durand

Polymères Colloïdes Interfaces, CNRS UMR6120, Université du Maine, F-72085 Le Mans cedex 9, France


(Received 10 March 2003 / Published online: 21 May 2003)

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ( $\phi_{\rm e}$), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres $1-\phi_{\rm e}$ is the porosity. The bond percolation threshold ( $p_{\rm b}$) can be described in terms of $\phi_{\rm e}$ by a simple analytical expression: $\log(\phi_{\rm e})/\log(\phi_{\rm ec})+\log(p_{\rm b})/\log(p_{\rm bc})=1$, with $p_{\rm bc}=0.12$ independent of the bond range and $\phi_{\rm ec}$ a constant that decreases with increasing bond range.

64.60.Ak - Renormalization-group, fractal, and percolation studies of phase transitions.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003