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  • Print publication year: 2014
  • Online publication date: November 2014

6 - Off-lattice models

Summary

NVT ensemble and the virial theorem

The examination of the equation of state of a two-dimensional model fluid (the hard disk system) was the very first application of the importance sampling Monte Carlo method in statistical mechanics (Metropolis et al., 1953), and since then the study of both atomic and molecular fluids by Monte Carlo simulation has been a very active area of research. Remember that statistical mechanics can deal well analytically with very dilute fluids (ideal gases), and it can also deal well with crystalline solids (making use of the harmonic approximation and perfect crystal lattice periodicity and symmetry), but the treatment of strongly correlated dense fluids (and their solid counterparts, amorphous glasses) is much more difficult. Even the description of short range order in fluids in a thermodynamic state far away from any phase transition is a non-trivial matter (unlike the lattice models discussed in the last chapter, where far away from phase transitions the molecular field approximation, or a variant thereof, is usually both good enough and easily worked out, and the real interest is generally in phase transition problems).

The discussion in this chapter will consider only symmetric particles; for the consideration of hard rods, spherocylinders, etc., the reader is referred elsewhere (Frenkel and Smit, 1996).

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References
Alder, B. J. and Wainwright, T. E. (1962), Phys. Rev. 127, 359.
Alejandre, J., Tildesley, D. J., and Chapela, G. A. (1995), J. Chem. Phys. 102, 4574.
Allen, M. P. (1996), in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, eds. Binder, K. and Ciccotti, G. (Società Italiana di Fisica, Bologna), p. 255.
Asakura, S. and Oosawa, F. (1954), J. Chem. Phys. 12, 1255.
Baschnagel, J., Qin, K., Paul, W., and Binder, K. (1992), Macromolecules 25, 3117.
Baumgärtner, A. (1984), Ann. Rev. Phys. Chem. 35, 419.
Baumgärtner, A. and Binder, K. (1981), J. Chem. Phys. 75, 2994.
Bernard, E. P. and Krauth, W. (2011), Phys. Rev. Lett. 107, 155704.
Bernard, E. P. and Krauth, W. (2012), Phys. Rev. E 86, 017701.
Bernard, E. P., Krauth, W., and Wilson, D. B. (2009), Phys. Rev. E 80, 056704.
Binder, K. (1982), Phys. Rev. A 25, 1699.
Binder, K. (1994), Adv. Polymer Sci. 112, 181.
Binder, K. (ed.) (1995), Monte Carlo and Molecular Dynamics Simulations in Polymer Science (Oxford University Press, New York and Oxford).
Binder, K. and Landau, D. P. (1989), in Advances in Chemical Physics: Molecule-Surface Interaction, ed. Lawley, K. P. (Wiley, New York), p. 91.
Binder, K., Block, B., Das, S. K., Virnau, P., and Winter, D. (2011), J. Stat. Phys. 144, 690.
Bruce, A. D., Jackson, A. N., Ackland, G. J., and Wilding, N. B. (2000), Phys. Rev. E 61, 906.
Bruce, A. D., Wilding, N. B., and Ackland, G. J. (1997), Phys. Rev. Lett. 79, 3002.
Caillot, J. M. (1992), J. Chem. Phys. 96, 1455.
Catlow, C. R. A. (ed.) (1992), Modelling of Structure and Reactivity in Zeolites (Academic Press, London).
Ceperley, D., Chester, C. V., and Kalos, M. H. (1977), Phys. Rev. B 16, 3081.
Consta, S., Wilding, N. B., Frenkel, D., and Alexandrowicz, Z. (1999), J. Chem. Phys. 110, 3220.
Dadobaev, G. and Slutsker, A. I. (1981), Sov. Phys. Solid State 23, 1131.
Das, S. K. and Binder, K. (2011), Molec. Phys. 109, 1043.
Davies, G. T., Eby, K., and Colson, J. P. (1970), J. Appl. Phys. 41, 4316.
De Gennes, P. G. (1979), Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca).
De Miguel, E. and Jackson, G. (2006), Molec. Phys. 104, 3717.
Deb, D., Wilms, D., Winkler, A., Virnau, P., and Binder, K. (2012), Int. J. Mod. Phys. C 23, 1240011.
Degiorgio, V. and Corti, M. (eds.) (1985), Physics of Amphiphiles: Micelles, Vesicles and Microemulsions (North-Holland, Amsterdam).
Dress, C. and Krauth, W. (1995), J. Phys. A 28, L597.
Dünweg, B., Stevens, M., and Kremer, K. (1995), in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, ed. Binder, K. (Oxford University Press, New York and Oxford), p. 125.
Eisenriegler, E., Kremer, K., and Binder, K. (1982), J. Chem. Phys. 77, 6296.
Ermak, D. L. (1975), J. Chem. Phys. 62, 4189.
Errington, J. R. (2003), Phys. Rev. E 67, 012102.
Errington, J. R. (2004), J. Chem. Phys. 120, 3130.
Fasnacht, M., Swendsen, R. H., and Rosenberg, J. M. (2004), Phys. Rev. E69, 056704.
Frenkel, D. and Smit, B. (1996), Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, New York).
Gaines, G. L. Jr. (1996), Insoluble Monolayers at Liquid-Gas Interfaces (Intersciences, New York).
Greengard, L. and Rokhlin, V. (1987), J. Comp. Phys. 73, 325.
Grzelak, E. M. and Errington, J. R. (2010), J. Chem. Phys. 132, 224702.
Haas, F. M., Hilfer, R., and Binder, K. (1996), J. Phys. Chem. 100, 15290.
Halperin, B. I. and Nelson, D. R. (1978), Phys. Rev. Lett. 41, 121.
Houlrik, J., Landau, D. P., and Knak Jensen, S. (1994), Phys. Rev. E 50, 2007.
Jackson, A. N., Bruce, A. D., and Ackland, G. J. (2002), Phys. Rev. E 65, 036710.
Jaster, A. (1998), Europhys. Lett. 42, 277.
Karaborni, S. and O’Connell, J. P. (1990), J. Phys. Chem. 94, 2624.
Kim, Y. C, Fisher, M. E., and Luijten, E. (2003), Phys. Rev. Lett. 91, 065701.
Kofke, D. A. and Cummings, P. T. (1997), Molecular Phys. 92, 973.
Kosterlitz, J. M. and Thouless, D. J. (1973), J. Phys. C 6, 1181.
Kremer, K. and Binder, K. (1988), Computer Phys. Rep. 7, 259.
Kremer, K. and Grest, G. S. (1990), J. Chem. Phys. 92, 5057.
Kremer, K. and Grest, G. S. (1995), in Binder, K. (1995), p. 194.
Landau, D. P. (1991), in Phase Transitions and Surface Films 2, eds. H. Taub, G. Torzo, H. J. Lauter, and S. C. Fain, Jr., p. 11.
Landau, L. D. and Lifshitz, E. M. (1980), Statistical Physics, 3rd edn, Part 1 (Pergamon Press, Oxford).
Liu, J. and Luijten, E. (2004), Phys. Rev. Lett. 92, 035504.
Lodge, T. P., Rotstein, N. A., and Prager, S. (1990), in Advances in Chemical Physics, Vol. 79, eds. Prigogine, I. and Rice, S. A. (Wiley, New York), p. 1.
Martonak, R., Paul, W., and Binder, K. (1996), Computer Phys. Commun. 99, 2.
Martonak, R., Paul, W., and Binder, K. (1997), J. Chem. Phys. 106, 8918.
Mavrantzas, V. G. (2005), in Handbook of Materials Modelling, Vol. I: Methods and Models, ed. Yip, S. (Springer, Berlin).
McDonald, I. R. (1972), Mol. Phys. 23, 41.
Metropolis, N. et al. (1953), J. Chem. Phys. 21, 1087.
Milchev, A. and Binder, K. (1996), Macromolecules 29, 343.
Milchev, A. and Binder, K. (1997), J. Chem. Phys. 106, 1978.
Milchev, A. and Binder, K. (2001), J. Chem. Phys. 115, 983.
Milchev, A., Dimitrov, D. I., and Binder, K. (2008), Polymer 49, 3611.
Milchev, A., Paul, W., and Binder, K. (1993), J. Chem. Phys. 99, 4786.
Mon, K. K. and Griffiths, R. B. (1985), Phys. Rev. A31, 956.
Mooij, G. C. A. M., Frenkel, D., and Smit, B. (1992), J. Phys. Condens. Matter 4, L255.
Müller, M. and Binder, K. (1995), Macromolecules 28, 1825.
Müller, M. and de Pablo, J. J. (2006), in Computer Simulations in Condensed Matter: From Materials to Chemical Biology, eds. Ferrario, M., Ciccotti, G., and Binder, K. (Springer, Heidelberg), vol. 1, p. 67.
Nelson, D. R. and Halperin, B. I. (1979), Phys. Rev. B 19, 2457.
Nijmeijer, M. J. P. and Weis, J. J. (1995), Phys. Rev. Lett. 75, 2887.
Nijmeijer, M. J. P., Bruin, C., Bakker, A. F., and van Leeuwen, M. J. M. (1990), Phys. Rev. A 42, 6052.
Norman, G. E. and Filinov, V. S. (1969), High Temp. (USSR) 7, 216.
Owicki, J. C. and Scheraga, H. A. (1977), Chem. Phys. Lett. 47, 600.
Panagiotopoulos, A. Z. (1987), Molecular Physics 61, 813.
Panagiotopoulos, A. Z. (1995), in Observation Prediction and Simulation of Phase Transitions in Complex Fluids, eds. Baus, M., Rull, L. F. and Ryckaert, J. P. (Kluwer Academic Publ., Dordrecht), p. 463.
Pandey, R. B., Milchev, A., and Binder, K. (1997), Macromolecules 30, 1194.
Pangali, C., Rao, M., and Berne, B. J. (1978), Chem. Phys. Lett. 55, 413.
Patrykiejew, A., Sokolowski, S., Zientarski, T., and Binder, K. (1995), J. Chem. Phys. 102, 8221.
Patrykiejew, A., Sokolowski, S., Zientarski, T., and Binder, K. (1998), J. Chem. Phys. 108, 5068.
Paul, W., Binder, K., Heermann, D. W., and Kremer, K. (1991), J. Phys. II (France) 1, 37.
Paul, W., Yoon, D. Y., and Smith, G. D. (1995), J. Chem. Phys. 103, 1702.
Pearson, D. S., Verstrate, G., von Meerwall, E., and Schilling, F. C. (1987), Macromolecules 20, 1133.
Pollock, E. L. and Glosli, J. (1996), Comput. Phys. Commun. 95, 93.
Presber, M., Dünweg, B., and Landau, D. P. (1998), Phys. Rev. E 58, 2616.
Privman, V. (1988), Phys. Rev. Lett. 61, 183.
Rao, M. and Berne, B. J. (1979), Mol. Phys. 37, 455.
Rector, D. R., van Swol, F., and Henderson, J. R. (1994), Molecular Physics 82, 1009.
Rosenbluth, M. N. and Rosenbluth, A. W. (1955), J. Chem. Phys. 23, 356.
Rossky, P. J., Doll, J. D., and Friedman, H. L. (1978), J. Chem. Phys. 69, 4628.
Rouse, P. E. (1953), J. Chem. Phys. 21, 127.
Rovere, M., Heermann, D. W., and Binder, K. (1990), J. Phys. Cond. Matter 2, 7009.
Ryckaert, J. P. (1996), in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, eds. Binder, K. and Ciccotti, G. (Società Italiana di Fisica, Bologna), p. 725.
Sariban, A. and Binder, K. (1987), J. Chem. Phys. 86, 5859.
Scheringer, M., Hilfer, R., and Binder, K. (1992), J. Chem. Phys. 96, 2296.
Schilling, T. and Schmid, F. (2009), J. Chem. Phys. 131, 231102.
Schmid, F., Stadler, C., and Lange, H. (1998), in Computer Simulation Studies in Condensed-Matter Physics X, eds. Landau, D. P., Mon, K. K., and Schüttler, H.-B. (Springer, Berlin), p. 37.
Siepmann, J. I. and Frenkel, D. (1992), Mol. Phys. 75, 90.
Smit, B. (1988), Phys. Rev. A 37, 3481.
Smit, B. (1995), J. Phys. Chem. 99, 5597.
Smit, B., Esselink, K., Hilbers, P. A. J., van Os, N. M., Rupert, L. A. M., and Szleifer, I. (1993), Langmuir 9, 9.
Sokal, A. D. (1995), in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, ed. Binder, K. (Oxford University Press, New York and Oxford), p. 47.
Theodorou, D. N. (2002), in Bridging Time Scales: Molecular Simulations for the Next Decade, eds. Nielaba, P., Mareschal, M., and Ciccotti, G. (Springer, Berlin).
Viduna, D., Milchev, A., and Binder, K. (1998), Macromol. Theory and Simul. 7, 649.
Vink, R. L. C. and Horbach, J. (2004), J. Chem. Phys. 121, 3253.
Virnau, P. and Müller, M. (2004), J. Chem. Phys. 120, 10925.
Von Gottberg, F. K., Smith, K. A., and Hatton, T. A. (1997), J. Chem. Phys. 106, 9850.
Weber, H., Marx, D., and Binder, K. (1995), Phys. Rev. B 15, 14636.
Werner, A., Schmid, F., Müller, M., and Binder, K. (1997), J. Chem. Phys. 107, 8175.
Widom, B. (1963), J. Chem. Phys. 39, 2808.
Wilding, N. (2006), in Computer Simulations in Condensed Matter: From Materials to Chemical Biology, eds. Ferrario, M., Ciccotti, G., and Binder, K. (Springer, Heidelberg), vol. 1, p. 39.
Wilding, N. B. (1997), J. Phys. Condensed Matter 9, 585.
Wilding, N. B. (2001), Am. J. Phys. 69, 1147.
Wilding, N. B. and Binder, K. (1996), Physica A 231, 439.
Wilding, N. B. and Bruce, A. D. (2000), Phys. Rev. Lett. 85, 5138.
Wilding, N. B. and Landau, D. P. (2003), in Bridging Time Scales: Molecular Simulations for the Next Decade, eds. Nielaba, P., Marechal, M., and Ciccotti, G. (Springer, Heidelberg).
Wittmer, J. P., Beckrich, P., Meyer, H., Cavallo, A., Johner, A., and Baschnagel, J. (2007), Phys. Rev. E 76, 011803.
Yoon, D. Y., Smith, G. D., and Matsuda, T. (1993), J. Chem. Phys. 98, 10037.
Young, A. P. (1979), Phys. Rev. B 19, 1855.
Zollweg, J. A. and Chester, G. V. (1992), Phys. Rev. B 46, 11187.