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Part B: Condensed Matter Physics

Morphological thermodynamics for hard bodies from a controlled expansion

ORCID Icon, ORCID Icon & ORCID Icon
Pages 2614-2635 | Received 25 Oct 2019, Accepted 11 Feb 2020, Published online: 18 Mar 2020

References

  • R. Evans, The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids, Adv. Phys. 28 (1979), pp. 143–200.
  • Y. Rosenfeld, Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing, Phys. Rev. Lett. 63 (1989), pp. 980–983.
  • P.-M. König, R. Roth and K.R. Mecke, Morphological thermodynamics of fluids: shape dependence of free energies, Phys. Rev. Lett. 93 (2004), p. 160601.
  • R. Roth, Y. Harano, and M. Kinoshita, Morphometric approach to the solvation free energy of complex molecules, Phys. Rev. Lett. 97 (2006), p. 078101.
  • H. Hansen-Goos, R. Roth, K.R. Mecke, and S. Dietrich, Solvation of proteins: linking thermodynamics to geometry, Phys. Rev. Lett. 99 (2007), p. 128101.
  • J.F. Robinson, F. Turci, R. Roth, and C.P. Royall, Morphometric approach to many-body correlations in hard spheres, Phys. Rev. Lett. 122 (2019), p. 068004.
  • J.F. Robinson, F. Turci, R. Roth, and C.P. Royall, Many-body correlations from integral geometry, Phys. Rev. E. 100 (2019), p. 062126.
  • M. Oettel, H. Hansen-Goos, P. Bryk, and R. Roth, Depletion interaction of two spheres – Full density functional theory vs. morphometric results, Europhys. Lett. 85 (2009), p. 36003.
  • D.J. Ashton, N.B. Wilding, R. Roth, and R. Evans, Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory, Phys. Rev. E 84(6) (2011), p. 061136.
  • B.B. Laird, A. Hunter, and R.L. Davidchack, Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces, Phys. Rev. E 86 (2012), p. 060602(R).
  • E.M. Blokhuis, Existence of a bending rigidity for a hard-sphere liquid near a curved hard wall: validity of the Hadwiger theorem, Phys. Rev. E 87 (2013), p. 022401.
  • I. Urrutia, Bending rigidity and higher-order curvature terms for the hard-sphere fluid near a curved wall, Phys. Rev. E 89 (2014), p. 032122.
  • H. Hansen-Goos, Communication: non-Hadwiger terms in morphological thermodynamics of fluids, J. Chem. Phys. 141 (2014), p. 171101.
  • A. Reindl, M. Bier, and S. Dietrich, Implications of interface conventions for morphometric thermodynamics, Phys. Rev. E 91 (2015), p. 022406.
  • G. Leithall and M. Schmidt, Density functional for hard hyperspheres from a tensorial-diagrammatic series, Phys. Rev. E 83(2) (2011), p. 021201.
  • G. Parisi and F. Zamponi, Mean-field theory of hard sphere glasses and jamming, Rev. Mod. Phys. 82(1) (2010), pp. 789–845.
  • W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Für Naturforschung C 28 (1973), pp. 693–703.
  • H. Reiss, H.L. Frisch, and J.L. Lebowitz, Statistical mechanics of rigid spheres, J. Chem. Phys. 31(2) (1959), pp. 369–380.
  • H. Reiss, H.L. Frisch, E. Helfand, and J.L. Lebowitz, Aspects of the statistical thermodynamics of real fluids, J. Chem. Phys. 32(1) (1960), pp. 119–124.
  • S. Korden, Deriving the Rosenfeld functional from the virial expansion, Phys. Rev. E 85(4) (2012), p. 041150.
  • M. Marechal, S. Korden, and K. Mecke, Deriving fundamental measure theory from the virial series: consistency with the zero-dimensional limit, Phys. Rev. E 90(4) (2014), p. 042131.
  • D.A. Klain and G.-C. Rota, Introduction to Geometric Probability (Lezioni Lincee), Cambridge, Cambridge University Press, 1997.
  • L.A. Santaló, Integral Geometry and Geometric Probability. 2nd ed., Cambridge Mathematical Library, Cambridge, Cambridge University Press, 2004.
  • W. Blaschke, Integralgeometrie 13. Zur Dinematik, Math. Z. 41 (1936), pp. 465–478.
  • W. Blaschke, Vorlesungen über Integralgeometrie, vol. 47, Tuebner, Berlin, 1937.
  • L.A. Santaló, Integralgeometrie 5. Über das kinematische Mass im Raum, Actual. Sci. Ind. 357 (1936). https://www.worldcat.org/title/integralgeometrie-5-uber-das-kinematischemass-im-raum/oclc/680002837
  • L. Tonks, The complete equation of state of one, two and three-Dimensional gases of hard elastic spheres, Phys. Rev. 50 (1936), pp. 955–963.
  • M.S. Wertheim, Fluids of hard convex molecules, Mol. Phys. 83 (1994), pp. 519–537.
  • J.-P. Hansen and I.R. McDonald, Theory of Simple Liquids With Applications to Soft Matter. 4th ed. Elsevier, Cambridge, Massachusetts, 2013.
  • A. Santos, A Concise Course on the Theory of Classical Liquids, vol. 923, 1st ed., Springer International Publishing, Cham, 2016.
  • A. Isihara, Determination of molecular shape by osmotic measurement, J. Chem. Phys. 18 (1950), pp. 1446–1449.
  • H. Hansen-Goos and R. Roth, Density functional theory for hard-sphere mixtures: the White bear version mark II, J. Phys. Condens. Matter 18 (2006), pp. 8413–8425.
  • J.A. Cuesta, Y. Martinez-Raton, and P. Tarazona, Close to the edge of fundamental measure theory: A density functional for hard-sphere mixtures, J. Phys. Condens. Matter 14 (2002), pp. 11965–11980.
  • Y. Rosenfeld, M. Schmidt, H. Löwen, and P. Tarazona, Dimensional crossover and the freezing transition in density functional theory, J. Phys. Condens. Matter 8(40) (1996), pp. L577–L581.
  • M.S. Wertheim, Exact solution of the percus-yevick integral equation for hard spheres, Phys. Rev. Lett. 10(8) (1963), pp. 321–323.
  • J.L. Lebowitz, Exact solution of generalized percus-Yevick equation for a mixture of hard spheres, Phys. Rev. 133 (1964), pp. A895–A899.
  • P. Tarazona and Y. Rosenfeld, From zero-dimension cavities to free-energy functionals for hard disks and hard spheres, Phys. Rev. E 55 (1997), pp. R4873–R4876.
  • N.F. Carnahan and K.E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51(2) (1969), pp. 635–636.
  • R.L. Davidchack, B.B. Laird, and R. Roth, Parameterising the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall, Mol. Phys. 113 (2015), pp. 1091–1096.
  • E.W. Montroll and J.E. Mayer, Statistical mechanics of imperfect gases, J. Chem. Phys. 9 (1941), pp. 626–637.
  • M.S. Wertheim, Fluids of hard convex molecules II. two-point measures, Mol. Phys. 89 (1996), pp. 989–1004.
  • M.S. Wertheim, Fluids of hard convex molecules III. the third virial coefficient, Mol. Phys. 89 (1996), pp. 1005–1017.
  • R. Kodama, R. Roth, Y. Harano, and M. Kinoshita, Morphometric approach to thermodynamic quantities of solvation of complex molecules: extension to multicomponent solvent, J. Chem. Phys. 135(4) (2011), p. 045103.
  • J.A. Gualtieri, J.M. Kincaid, and G. Morrison, Phase equilibria in polydisperse fluids, J. Chem. Phys. 77 (1982), pp. 521–536.
  • P.B. Warren, Combinatorial entropy and the statistical mechanics of polydispersity, Phys. Rev. Lett. 80(7) (1998), pp. 1369–1372.
  • P. Sollich and M.E. Cates, Projected free energies for polydisperse phase equilibria, Phys. Rev. Lett. 80 (1998), pp. 1365–1368.
  • P. Sollich, P.B. Warren, and M.E. Cates, Moment Free Energies for Polydisperse Systems, in Advances in Chemical Physics (I. Prigogine and S. A. Rice, eds.), pp. 265–336, Hoboken, NJ, John Wiley & Sons, Inc., 2001.

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