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2
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0001193912
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The interactions in a charge-stabilised colloidal suspension can be modelled by a Yukawa potential with a positive tail, See, e.g
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E.J. Meijer and D. Frenkel (1991) The interactions in a charge-stabilised colloidal suspension can be modelled by a Yukawa potential with a positive tail Phys. Rev. Lett. 67 1110. See, e.g.
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33749444319
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For a different formulation of the constant-pressure ensemble, see
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N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.N. Teller and E. Teller (1953) J. Chem. Phys. 21 1087.
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28
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0018446914
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See also, D. Henderson (Eds), San Diego: Marcel Decker, Our treatment draws freely on the classic review article by
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R. Evans and R. Evans (1979) Adv. Phys. 28 143. See also D. Henderson (Eds) Fundamentals of Inhomogeneous Fluids San Diego: Marcel Decker Our treatment draws freely on the classic review article by
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Evans, R.1
Evans, R.2
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10644250257
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extended to finite temperatures by, It was first applied to classical systems by, See Section 3.4. The principle was established for the ground state of the electron gas by
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P. Hohenberg, W. Kohn, N.D. Mermin, C. Ebner, W.F. Saam and D. Stroud (1964) Phys. Rev. 136 B864. extended to finite temperatures by Phys. Rev. 137 It was first applied to classical systems by Phys. Rev. A 14 226. See Section 3.4. The principle was established for the ground state of the electron gas by
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3042758616
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New York: Oxford University Press, See, e.g
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D. Chandler (1987) Modern Statistical Mechanics. New York: Oxford University Press 16. See, e.g.
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Modern Statistical Mechanics
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Chandler, D.1
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0000761438
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For a listing of many of the proposed equations and an assessment of their relative merits, see
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Mulero, A.1
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36849106010
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The Carnahan-Starling equation of state was later generalised to hard-sphere mixtures by
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G.A. Mansoori, N.F. Carnahan, K.E. Starling and T.W. Leland (1971) J. Chem. Phys. 54 1523. The Carnahan-Starling equation of state was later generalised to hard-sphere mixtures by
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56
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0345045853
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The HNC approximation was developed independently by several workers. For some historical background, see
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J.S. Rowlinson (1965) Rep. Prog. Phys. 28 169. The HNC approximation was developed independently by several workers. For some historical background, see
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Rowlinson, J.S.1
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58
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7544220942
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The PY equation was originally derived in a very different way by
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J.K. Percus and G.J. Yevick (1958) Phys. Rev. 110 1. The PY equation was originally derived in a very different way by
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Phys. Rev.
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Percus, J.K.1
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0000568606
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See also, Analytical expressions covering the range x = 1 to 5 are given by
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W.R. Smith, D. Henderson, J. Chang and S.I. Sandler (1970) Mol. Phys. 19 411. See also Mol. Phys. 81 735. Analytical expressions covering the range x = 1 to 5 are given by
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Smith, W.R.1
Henderson, D.2
Chang, J.3
Sandler, S.I.4
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67
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30244472523
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The implementation of certain theories also requires a knowledge of the hard-sphere y(r) inside the hard core, a parametrisation of which is given by
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L. Verlet, J.J. Weis, E.W. Grundke and D. Henderson (1972) Phys. Rev. A 5 939. Mol. Phys. 24 269. The implementation of certain theories also requires a knowledge of the hard-sphere y(r) inside the hard core, a parametrisation of which is given by
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Phys. Rev. A
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Verlet, L.1
Weis, J.J.2
Grundke, E.W.3
Henderson, D.4
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73
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0001876948
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This result was first derived by
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J.E. Mayer and E. Montroll (1941) J. Chem. Phys. 9 2. This result was first derived by
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Mayer, J.E.1
Montroll, E.2
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81
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0030239698
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For examples of this approach, see
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C. Caccamo (1996) Phys. Rep. 274 1. For examples of this approach, see
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Caccamo, C.1
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0001638742
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Note that the "bridge function" in these and related papers is sometimes defined, in the present notation, as −d(r)
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E. Enciso, F. Lado, M. Lombardero, J.L.F. Abascal and S. Lago (1987) J. Chem. Phys. 87 2249. Note that the "bridge function" in these and related papers is sometimes defined, in the present notation, as −d(r).
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Enciso, E.1
Lado, F.2
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90
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84926805355
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See note 14. The hard-sphere bridge function has also been parametrised as a function of packing fraction by
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A. Malijevský and S. Labík (1987) Mol. Phys. 60 663. See note 14. The hard-sphere bridge function has also been parametrised as a function of packing fraction by
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Malijevský, A.1
Labík, S.2
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0001527611
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C. Caccamo, G. Pellicane, D. Costa, D. Pini and G. Stell (1999) Phys. Rev. E 60 5533.
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Phys. Rev. E
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0002830358
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For later developments see, e.g
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E. Waisman, J.S. Høye and L. Blum (1973) Mol. Phys. 25 45. J. Stat. Phys. 16 399. For later developments see, e.g.
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J. Talbot, J.L. Lebowitz, E.M. Waisman, D. Levesque and J.J. Weis (1986) J. Chem. Phys. 85 2187.
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0542374369
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For the extension to three dimensions, see
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M. Kac, G.E. Uhlenbeck, P.C. Hemmer and N.G. van Kampen (1963) J. Math. Phys. 4 216. Phys. Rev. 135 362. For the extension to three dimensions, see
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0001608409
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For a discussion of the relationship between the two expansions, see
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G. Stell (1971) J. Chem. Phys. 55 1485. For a discussion of the relationship between the two expansions, see
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See, e.g
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C. Caccamo (1996) Phys. Rep. 274 1. See, e.g.
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2nd edn., New York: John Wiley
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Statistical Mechanics
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Huang, K.1
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0000897048
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(Ising model) and, (Lennard-Jones fluid), See, e.g
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A.M. Ferrenberg, D.P. Landau and N.B. Wilding (1991) Phys. Rev. B 44 5081. (Ising model) and Phys. Rev. E 52 602. (Lennard-Jones fluid) See, e.g.
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2nd edn., Singapore: John Wiley, For introductory treatments, see the book by
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For a description of the numerical implementation, see, See, e.g
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HRT has also been successfully generalised to binary systems. See, e.g
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D. Pini, M. Tau, A. Parola and L. Reatto (2003) Phys. Rev. E 67 046116. HRT has also been successfully generalised to binary systems. See, e.g.
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Session XLVIII, J. Charvolin, J.F. Joanny, J. Zinn-Justin (Eds), Singapore: Elsevier, For a more detailed treatment of the material discussed in this section, see
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2342581048
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It also played a central role in early theoretical work on the wetting transition. See
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D. Henderson (Eds), Amsterdam: Marcel Dekker, For a critical survey of different approximations, see
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R. Evans (1991) D. Henderson (Eds) Fundamentals of Inhomogeneous Fluids Amsterdam: Marcel Dekker For a critical survey of different approximations, see
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The detailed calculation for a different but related system (parallel hard cubes) is given by
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J.A. Cuesta and Y. Martínez-Ratón (1997) J. Chem. Phys. 107 6379. The detailed calculation for a different but related system (parallel hard cubes) is given by
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Cuesta, J.A.1
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0001629016
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See also
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New York: John Wiley, Some of the material discussed in Chapters 7 to 9 is dealt with at greater length in a number of specialised texts
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B.J. Berne and R. Pecora (1976) Dynamic Light Scattering. New York: John Wiley Some of the material discussed in Chapters 7 to 9 is dealt with at greater length in a number of specialised texts.
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Dynamic Light Scattering
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New York: Clarendon Press
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R.M. Mazo (2002) Brownian Motion. New York: Clarendon Press
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84882142771
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3rd edn, New York: Cambridge University Press, When g(d) = 1, (7.2.2) reduces to the result obtained by solution of the Boltzmann equation in a first-order approximation; higher-order corrections are of order 2%. See, e.g
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S. Chapman and T.G. Cowling (1970) The Mathematical Theory of Non-Uniform Gases. 3rd edn New York: Cambridge University Press 258. When g(d) = 1, (7.2.2) reduces to the result obtained by solution of the Boltzmann equation in a first-order approximation; higher-order corrections are of order 2%. See, e.g.
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Chapman, S.1
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0035826416
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Comparison of molecular-dynamics results for the Lennard-Jones fluid with an extended form of Enskog theory reveals a different behaviour at intermediate densities. See
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K. Miyazaki, G. Srinivas and B. Bagchi (2001) J. Chem. Phys. 114 6276. Comparison of molecular-dynamics results for the Lennard-Jones fluid with an extended form of Enskog theory reveals a different behaviour at intermediate densities. See
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Deviations from gaussian behaviour increase rapidly as a liquid is supercooled: see, e.g
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3rd edn., New York: Cambridge University Press, Cambridge: McGraw-Hill, For a simplified discussion of the Boltzmann and Enskog equations see, e.g
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S. Chapman, T.G. Cowling, T.M. Reed and K.E. Gubbins (1970) The Mathematical Theory of Non-Uniform Gases. 3rd edn. New York: Cambridge University Press 308. Applied Statistical Mechanics Cambridge: McGraw-Hill For a simplified discussion of the Boltzmann and Enskog equations see, e.g.
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0000410757
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For inelastic x-ray scattering and references to earlier scattering experiments on liquid metals see, e.g., A particularly comprehensive neutron-scattering study is that of liquid Rb by
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The conclusions of this paper were later confirmed, with much higher precision, by simulations of a lattice-gas model for which the equations of motion can be solved exactly: see
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This classification is due to
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W.E. Britton, B.W. Downs, J. Downs (Eds), Vienna: Wiley Interscience
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The terms non-ergodicity parameter or Edwards-Anderson parameter are also used, the latter by analogy with a related problem in spin glasses
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For a review of the properties of the OCP, see
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The Raman spectra of molten salts can also be analysed in terms of fluctuations in mass and charge densities: see ref. 24
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New York: Cambridge University Press, The oscillatory behaviour at large separations is linked to a logarithmic singularity in the dielectric function. See
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T.E. Faber (1972) An Introduction to the Theory of Liquid Metals. New York: Cambridge University Press 28. The oscillatory behaviour at large separations is linked to a logarithmic singularity in the dielectric function. See
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Faber, T.E.1
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329
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The potential used in the simulations was derived from an empty-core pseudo-potential with a core radius obtained by fitting to the height of the first peak in the experimental structure factor: Anento, N., Canales, M. and Gonzez, L.E., unpublished results. See also
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M. Canales, L.E. Gonzàlez and J.A. Pàdro (1994) Phys. Rev. E 50 3656. The potential used in the simulations was derived from an empty-core pseudo-potential with a core radius obtained by fitting to the height of the first peak in the experimental structure factor: Anento, N., Canales, M. and Gonzez, L.E., unpublished results. See also
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331
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For a review of experimental results on liquid metals, see
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Oxford: Clarendon Press, For a discussion of the properties of the spherical harmonics and their use in liquid-state theory, see ref. 1, particularly Appendix A
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The general procedure is described by
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We follow in outline the arguments of
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P.A. Madden and D. Kivelson (1984) Adv. Chem. Phys. 56 467. We follow in outline the arguments of
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The same result follows directly from the Stillinger-Lovett sum rules (10.2.17) See
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The same formalism can be used for systems other than polymers: see, For a review, see
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Oxford: Oxford University Press, Note that the assumption of ideality is made solely for the purpose of computing the single-chain structure factor
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M. Rubinstein and R.H. Colby (2003) Polymer Physics. Oxford: Oxford University Press Note that the assumption of ideality is made solely for the purpose of computing the single-chain structure factor.
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later expanded upon by, The derivation given in the text follows the method of Sullivan and Gray. See also, This remarkable fact was first pointed out by
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D. Chandler, D.E. Sullivan, C.G. Gray, G.P. Morriss and J.W. Perram (1978) Faraday Disc. Chem. Soc. 66 74. and later expanded upon by Mol. Phys. 42 443. Mol. Phys. 43 669. The derivation given in the text follows the method of Sullivan and Gray. See also This remarkable fact was first pointed out by
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0000020246
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TIP5P is one of a series of "transferable intermolecular potentials" devised for the simulation of water in different environments
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M.W. Mahoney and W.L. Jorgensen (2000) J. Chem. Phys. 112 8910. TIP5P is one of a series of "transferable intermolecular potentials" devised for the simulation of water in different environments.
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