Exact matrix computation of the statistical mechanics of a cell model of hard sphere phase behaviour

Murrell, John N, Dunne, Lawrence J, Manos, George and Rekabi, Mahdi (2006) Exact matrix computation of the statistical mechanics of a cell model of hard sphere phase behaviour. Chemical Physics Letters, 421 (1-3). pp. 47-51. ISSN 0009-2614

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Abstract

The analytical prediction of the shape of isotherms for hard spheres obtained by computer simulation and experiments has a number of challenging features [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10]. Amongst these is the rationalisation of the well-known steps in the isotherms of hard spheres reproduced in Fig. 1 (taken from [1]). In this Letter, we address a closely related issue and present an almost exact calculation of the statistical mechanics of a cell model of a strip of hard spheres with nearest neighbour exclusion and next nearest neighbour repulsion. To our knowledge, there does not seem to be any analytical treatment of a lattice model, which reproduces the essential trends in the isotherms shown in Fig. 1. Indeed, the origin of the horizontal region in the isotherms remains controversial. Because of the restriction to a lattice of cells the model which we present below is not an exact representation of an assembly of hard spheres but the connection is close. The cell fluid model has states to represent hard spheres undergoing loss of configurational freedom from compression. Vacant sites or holes are introduced to allow for incomplete filling of the cell sites. The model gives steps in isotherms similar to those observed experimentally and obtained by computer simulation for hard spheres. However, the transitions only approach being first-order at low temperatures. Our theory treats the short-range behaviour introduced by hard core exclusion effects exactly within our model and captures the essential features of the very unusual isotherm structure. In particular, the very unusual isotherm shape and the temperature independence of PV/kT are reproduced by the model. The essential achievement of the exact treatment of our limited model is that it clearly shows that entropy loss associated with packing can cause an almost horizontal region in an isotherm.

Item Type: Article
Additional Information: Collaborative theoretical paper in which JM directed important elements of the theoretical work at Sussex in collaboration with DLJ and RM
Schools and Departments: School of Life Sciences > Chemistry
Depositing User: EPrints Services
Date Deposited: 06 Feb 2012 19:53
Last Modified: 12 Jun 2012 12:25
URI: http://sro.sussex.ac.uk/id/eprint/22735
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