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Sixth and Seventh Virial Coefficients for the Parallel Hard‐Cube Model

dc.contributor.authorHoover, William G.en_US
dc.contributor.authorDe Rocco, Andrew G.en_US
dc.date.accessioned2010-05-06T21:48:11Z
dc.date.available2010-05-06T21:48:11Z
dc.date.issued1962-06-15en_US
dc.identifier.citationHoover, William G.; De Rocco, Andrew G. (1962). "Sixth and Seventh Virial Coefficients for the Parallel Hard‐Cube Model." The Journal of Chemical Physics 36(12): 3141-3162. <http://hdl.handle.net/2027.42/70209>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70209
dc.description.abstractA procedure for calculating virial coefficients for parallel hard lines, squares, and cubes is outlined, and the sixth and seventh virial coefficients are computed for these models. The essential step in the evaluation of the star integrals lies in the recognition of the fact that only a few ``subintegrals'' contribute to each virial coefficient, relative to the total number of labeled star integrals. Both the sixth and seventh virial coefficients are negative for hard cubes, a fact interesting from the point of view of phase transitions. Approximations to the excess entropy are given for squares and cubes.The procedure for the star integrals is extended to the calculation of approximations to the pair distribution function and the potential of the mean force. These functions are calculated through the fourth approximation for hard lines, squares, and cubes.The topological graphs needed for the above investigations, together with the values of the related integrals in one dimension, are displayed.en_US
dc.format.extent3102 bytes
dc.format.extent1257014 bytes
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dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleSixth and Seventh Virial Coefficients for the Parallel Hard‐Cube Modelen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, The University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70209/2/JCPSA6-36-12-3141-1.pdf
dc.identifier.doi10.1063/1.1732443en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreferenceH. D. Ursell, Proc. Cambridge Phil. Soc. 23, 685 (1927); J. E. Mayer and M. G. Mayer, Statistical Mechanics (John Wiley & Sons, Inc., New York, 1940).en_US
dc.identifier.citedreferenceD. König, Theorie der Endlichen und Unendlichen Graphen (Chelsea Publishing Company, New York, 1950); C. Berge, Théorie des graphes et ses applications (Dunod, Paris, 1958); R. J. Riddell, dissertation, University of Michigan, 1951; G. W. Ford, dissertation, University of Michigan, 1954.en_US
dc.identifier.citedreferenceR. J. Riddell, reference 2.en_US
dc.identifier.citedreferenceM. Born and K. Fuchs, Proc. Roy. Soc. (London) A166, 391 (1938).en_US
dc.identifier.citedreferenceB. T. Geilikman, Proc. Acad. Sci. U.S.S.R. 70, 25 (1950).en_US
dc.identifier.citedreferenceR. W. Zwanzig, J. Chem. Phys. 24, 855 (1956).en_US
dc.identifier.citedreferenceR. J. Riddell and G. E. Uhlenbeck, J. Chem. Phys. 21, 2056 (1953).en_US
dc.identifier.citedreferenceH. N. V. Temperley, Proc. Phys. Soc. (London) B70, 536 (1957).en_US
dc.identifier.citedreferenceW. G. Hoover and A. G. DeRocco, J. Chem. Phys. 34, 1059 (1961).en_US
dc.identifier.citedreferenceL. Tonks, Phys. Rev. 50, 955 (1936).en_US
dc.identifier.citedreferenceR. J. Riddell, reference 2.en_US
dc.identifier.citedreferenceZ. W. Salsburg, R. W. Zwanzig, and J. G. Kirkwood, J. Chem. Phys. 21, 1098 (1953).en_US
dc.identifier.citedreferenceThese stars, together with all other graphs of less than eight points may be found in “Diagrams of All Seven Point Graphs” by F. Harary and D. W. Crowe, Project R287, Horace H. Rackham School of Graduate Studies, University of Michigan (mimeographed; supplied to the authors, with many corrections, by G. W. Ford), 1953; a list of smaller graphs was prepared by F. Harary, also in 1953. F. Harary and R. Z. Norman plan to include a complete list of these graphs in a book now in prepration.en_US
dc.identifier.citedreferenceThe integral appearing in (22) is taken from a notebook belonging to G. E. Uhlenbeck, who kindly lent it to the authors; see E. T. Whittaker and G. N. Watson, Modern Analysis (Cambridge University Press, London, 1958), 4th ed., p. 123.en_US
dc.identifier.citedreferenceSee J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 157; B5B5 for hard spheres is known only approximately: A. W. Rosenbluth and M. N. Rosenbluth, J. Chem. Phys. 22, 881 (1954).en_US
dc.identifier.citedreferenceG. W. Ford, dissertation, University of Michigan, 1954.en_US
dc.identifier.citedreferenceB. J. Alder and T. E. Wainwright, J. Chem. Phys. 33, 1447 (1960).en_US
dc.identifier.citedreferenceR. J. Riddell, reference 2, p. 96.en_US
dc.identifier.citedreferenceFor a derivation see T. L. Hill, Statistical Mechanics (McGraw‐Hill Book Company, Inc., New York, 1956), p. 221.en_US
dc.identifier.citedreferenceJ. E. Mayer and E. W. Montroll, J. Chem. Phys. 9, 2 (1941); see also J. de Boer, Repts. Progr. Phys. 12, 305 (1949).en_US
dc.identifier.citedreferenceJ. de Boer, reference 20, p. 340; J. O. Hirschfelder et al., reference 15, p. 147.en_US
dc.identifier.citedreferenceJ. de Boer, reference 20, p. 364.en_US
dc.identifier.citedreferenceJ. de Boer, reference 20, p. 358.en_US
dc.identifier.citedreferenceM. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).en_US
dc.identifier.citedreferenceJ. E. Mayer, J. Phys. Chem. 43, 71 (1939).en_US
dc.owningcollnamePhysics, Department of


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