New PDF release: Liquid State Physics: A Statistical Mechanical Introduction

By Clive A. Croxton

ISBN-10: 0511753489

ISBN-13: 9780511753480

ISBN-10: 0521114349

ISBN-13: 9780521114349

ISBN-10: 0521201179

ISBN-13: 9780521201179

First released in 1974, Dr Croxton's e-book takes the reader from a attention of the early ways that the kinetic concept of gases used to be changed and utilized to the liquid kingdom, via a classical thermodynamic strategy, to the fashionable cluster-diagrammatic quantum and statistical mechanical innovations. He comprises chapters at the improvement and numerical answer of the fundamental equations concerning the atomic constitution to the pair capability, at the nature of the liquid floor, at the machine simulation schemes and on shipping methods and irreversibility within the liquid section.

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Additional info for Liquid State Physics: A Statistical Mechanical Introduction (Cambridge Monographs on Physics)

Sample text

DVN. 5) is just as intractable as the initial equations for the configurational integrals. 6) CLS 34 LIQUID STATE PHYSICS Making the usual assumption of pairwise additivity of the total potential, we may write the first few terms as follows: +... + ... 9) Wlt^ (2-5-5) we see that it is just — fip(8Q>12/dr^g^r). e. for/ = 3 to N. 11) simplifies to As remarked above, there are (N— 2) similar integrals, which factor just cancels that in the denominator. 3) obtained by a physical derivation. It should be pointed out that thus far the BGY relation is exact in as far as the assumption of a pairwise decomposable total potential THE CORRELATION FUNCTIONS 35 is valid.

The cancellation is, however, rather more complete in the case of the rigid sphere fluid than in a Lennard-Jones system where the coefficients 8m are not exclusively positive or negative over their entire range. This accounts for the slightly less satisfactory nature of the superposition approximation in the LJ case (cf. fig. 1). 8 The Kirkwood equation (K) In the derivation of the BGY equation the effect of an elementary displacement of one particle in the group upon the correlation of that group was investigated.

However, it is unique in one respect in that the BGY equation in the superposition approximation ceases to yield convergent or physically acceptable solutions at densities, whilst high, are still appreciably less than those appropriate to a solid phase. It was this feature which, solved for hard spheres by Kirkwood, Maun and Alder(14), led Alder and Wainwright(15) and Wood and Jacobson(16) to perform molecular dynamic simulations to find quite clear evidence of a phase transition at about the density the BGY equation ceased to be integrable.

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Liquid State Physics: A Statistical Mechanical Introduction (Cambridge Monographs on Physics) by Clive A. Croxton


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