The effect of a hard wall on the clustering and continuum percolation of a hard spheres fluid is studied using Monte Carlo simulations and connectedness theory. We calculate an averaged pair-connectedness function which is the probability density of finding two particles in the same cluster and separate by a distance under the assumption that one of them is fixed at a distance from the wall. We also obtain the mean size for the cluster containing the fixed sphere and the critical percolation density at which it becomes macroscopically large. Monte Carlo results allow us to conclude that, for given number density and connectedness distance, the wall causes the decrease of and the increase of in comparison with those found for the bulk in the absence of the wall. Both effects diminish with increasing The simulation data also show that, in the presence of the wall, the clusters are eccentric with cylindrical symmetry, slightly flattened in the region of contact with the wall. The theoretical calculations involve the solution for of an integral equation. It is derived from the one proposed some time ago by Giaquinta and Parrinello to obtain the average of the ordinary pair correlation function in the presence of the hard wall [J. Chem. Phys. 78, 1946 (1983)]. Integrating the pair-connectedness function over we have whose divergence determines the theoretical critical density. The results so obtained are in satisfactory agreement with Monte Carlo data.
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22 February 1999
Research Article|
February 22 1999
Clustering and continuum percolation of hard spheres near a hard wall: Monte Carlo simulation and connectedness theory
Luis A. Pugnaloni;
Luis A. Pugnaloni
Instituto de Fı́sica de Lı́quidos y Sistemas Biológicos (IFLYSIB)-UNLP-CONICET, cc. 565—(1900) La Plata, Argentina
Grupo de Aplicaciones Matemáticas y Estadı́sticas de la Facultad de Ingenierı́a, (GAMEFI)—Departamento de Fisicomatemática, Facultad de Ingenierı́a, Universidad Nacional de La Plata, La Plata, Argentina
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Fernando Vericat
Fernando Vericat
Instituto de Fı́sica de Lı́quidos y Sistemas Biológicos (IFLYSIB)-UNLP-CONICET, cc. 565—(1900) La Plata, Argentina
Grupo de Aplicaciones Matemáticas y Estadı́sticas de la Facultad de Ingenierı́a, (GAMEFI)—Departamento de Fisicomatemática, Facultad de Ingenierı́a, Universidad Nacional de La Plata, La Plata, Argentina
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J. Chem. Phys. 110, 4028–4034 (1999)
Article history
Received:
October 13 1998
Accepted:
November 19 1998
Citation
Luis A. Pugnaloni, Fernando Vericat; Clustering and continuum percolation of hard spheres near a hard wall: Monte Carlo simulation and connectedness theory. J. Chem. Phys. 22 February 1999; 110 (8): 4028–4034. https://doi.org/10.1063/1.478284
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