Journal of Statistical Physics

, Volume 44, Issue 5, pp 793-827

First online:

Geometry of random sequential adsorption

  • Einar L. HinrichsenAffiliated withDepartment of Physics, University of Oslo, Blindem
  • , Jens FederAffiliated withDepartment of Physics, University of Oslo, Blindem
  • , Torstein JøssangAffiliated withDepartment of Physics, University of Oslo, Blindem

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By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.

Key words

Random sequential adsorption random disk packing correlations pore size distribution Voronoi-Dirichlet network