Bimodality of cluster-size distribution and condensation in a finite Lennard-Jones system

Gibbs, Julian H. ; Bagchi, Biman ; Mohanty, Udayan (1981) Bimodality of cluster-size distribution and condensation in a finite Lennard-Jones system Physical Review B, 24 (6). pp. 2893-2902. ISSN 0163-1829

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Official URL: http://prb.aps.org/abstract/PRB/v24/i6/p2893_1

Related URL: http://dx.doi.org/10.1103/PhysRevB.24.2893

Abstract

The complete summation of Mayer's expression for the canonical-ensemble partition function for a finite number N of particles, in terms of reducible cluster integrals bk (1≤k≤N), is performed with a recursion formula. The bk required for this are themselves obtained by use of the same technique in the summation of Mayer's expression for them, in the volume-independent case, in terms of star (i.e., irreducible cluster) integrals ßj (1≤j≤k-1). Below the critical temperature the results, obtained with use of all the star integrals that have been evaluated for the Lennard-Jones potential, display features indicative of vapor condensation at appropriate densities, i.e., bimodality in the size distribution of Mayer's mathematical clusters and remarkable constancy (for small N) in the pressure isotherms. Thus the lower-order star integrals alone suffice for the appearance of the phenomenon of vapor condensation in the theoretical results. Indeed the first star integral β1 alone (corresponding to a "tree approximation" for the cluster integrals bk) is found to suffice. This suggests that the cooperative essence of the first-order transition from vapor to liquid is to be attributed primarily to a cascade in chain branching.

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