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Mean-field description of the structure and tension of curved fluid interfaces

Kuipers, J.

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Kuipers, J. (2009, December 16). Mean-field description of the structure and tension of curved fluid interfaces. Retrieved from https://hdl.handle.net/1887/14517

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[1] S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954).

[2] A. Vrij, Pure Appl. Chem. 48, 471 (1976).

[3] S. Pickering, J. Chem. Soc. 91, 2001 (1907).

[4] S. Guillot, F. Bergaya, C. de Azevedo, F. Waarmont, and J. Tranchant, J. Coll.

Interface Science 333, 565 (2009).

[5] P. S. Laplace, Trait´e de m´echanique c´eleste, Suppl´ement au dixi`eme livre, sur l’action capillaire (Courcier, Paris, 1806).

[6] T. Young, “An essay on the cohesion of fluids,” Philos. Trans. R. Soc. 95, 65 (1807).

[7] S. D. Poisson, Novelle th´eorie de l’action capillaire (Bachelier, Paris, 1831).

[8] K. Fuchs, Rep. Phys. 24, 141 (1888).

[9] S. D. Poisson, Novelle th´eorie de l’action capillaire (Bachelier, Paris, 1831).

[10] J. D. van der Waals, Thermodynamische Theorie der Capillariteit in de Onder- stelling van Continue Dichtheidsverandering (Verh. K. Akad. Wet., Amsterdam, 1893).

[11] L. Landau and E. Lifshitz, “On the theory of the dispersion of magnetic per- meability in ferromagnetic bodies,” Phys. Z. Sowjetunion 8, 153 (1935).

[12] J. Cahn and J. Hilliard, J. Chem. Phys. 28, 258 (1958).

[13] J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17, 338 (1949).

[14] J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).

[15] J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1982).

[16] J. Yvon, “Note sur un calcul de perturbation en m´echanique statistique,” Nuovo Cimento (Suppl.) 9, 144 (1958).

104

(3)

BIBLIOGRAPHY 105

[17] T. Morita and K. Hiroike, Prog. Theor. Phys. 25, 537 (1961).

[18] J. L. Lebowitz and J. K. Percus, J. Math. Phys. 4, 116 (1963).

[19] N. D. Mermin, Phys. Rev. A 137, 1441 (1965).

[20] C. Ebner and W. F. Saam, Phys. Rev. A 14, 2264 (1975).

[21] J. Gibbs, On the equilibrium of hetereogeneous substances in The Scientific Papers of J. Willard Gibbs (Green, London, 1906), Vol. I, p. 55.

[22] R. C. Tolman, J. Chem Phys. 17, 333 (1949).

[23] W. Helfrich, Z. Naturforsch. C 28, 693 (1973).

[24] H. Deuling and W. Helfrich, Blood Cells 3, 713–720 (1977).

[25] S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces and Mem- branes (Addison-Wesley, Reading, MA, 1994).

[26] W. M. Gelbart, A. Benshaul, and D. Roux, in Micelles, Membranes, Microemul- sions and Monolayers, D. Henderson, ed., (Springer-Verlag, New York, 1994).

[27] J. R. Henderson, in Fundamentals of Inhomogeneous Liquids, D. Henderson, ed., (Dekker, New York, 1992).

[28] E. M. Blokhuis and D. Bedeaux, Heterog. Chem. Rev. 1, 55 (1994).

[29] H. Kellay and J. Meunier, J. Phys. Cond. Matter 8, A49 (1996).

[30] J. W. Gibbs, Collected Works (Dover, New York, 1961).

[31] L. Granasy, J. Chem Phys. 109, 9660 (1998).

[32] K. Koga, X. C. Zeng, and A. K. Shchekin, J. Chem Phys. 109, 4063 (1998).

[33] D. W. Oxtoby, in Fundamentals of Inhomogeneous Fluids, D. Henderson, ed., (Dekker, New York, 1992).

[34] M. P. A. Fisher and M. Wortis, Phys. Rev. B 29, 6252 (1984).

[35] P. Phillips and U. Mohanty, J. Chem Phys. 83, 6392 (1985).

[36] S. J. Hemingway, J. R. Henderson, and J. S. Rowlinson, Faraday Sympos. Chem.

16 (1981).

[37] J. S. Rowlinson, J. Phys. A 17, L357 (1984).

[38] M. A. Anisimov, Phys. Rev. Lett. 98, 35702 (2007).

(4)

[39] M. Iwamatsu, J. Phys.: Cond. Matter 6, L173 (1994).

[40] A. E. van Giessen, E. M. Blokhuis, and D. J. Bukman, J. Chem. Phys. 108, 1148 (1998).

[41] J. Barrett, J. Chem. Phys. 111, 5938 (1999).

[42] V. G. Baidakov and G. S. Boltachev, Phys. Rev. E 59, 469 (1999).

[43] T. V. Bykov and X. C. Zeng, J. Chem. Phys. 111, 3705 (1999).

[44] T. V. Bykov and X. C. Zeng, J. Chem. Phys. 111, 10602 (1999).

[45] I. Napari and A. Laaksonen, J. Chem. Phys. 114, 5796 (2001).

[46] M. P. Moody and P. Attard, J. Chem. Phys. 115, 8967 (2001).

[47] M. P. Moody and P. Attard, Phys. Rev. Lett. 91, 056104 (2003).

[48] V. G. Baidakov and G. S. Boltachev, J. Chem. Phys. 115, 8967 (2001).

[49] V. G. Baidakov, G. S. Boltachev, and G. G. Chernykh, Phys. Rev. E 70, 011603 (2004).

[50] M. J. Haye and C. Bruin, J. Chem. Phys. 100, 556 (1994).

[51] H. E. Bardouni, M. Mareschal, R. Lovett, and M. Baus, J. Chem. Phys. 113, 9804 (2000).

[52] S. H. Park, J. G. Weng, and C. L. Tien, Int. J. of Heat and Mass Transf. 44, 1849 (2001).

[53] A. E. van Giessen and E. M. Blokhuis, J. Chem. Phys. 116, 302 (2002).

[54] Y. A. Lei, T. Bykov, S. Yoo, and X. C. Zeng, J. Am. Chem. Soc. 127, 15346 (2005).

[55] R. Lovett and M. Baus, J. Chem. Phys. 120, 10711 (2004).

[56] J. R. Henderson and P. Schofield, Proc. R. Soc. Lond. A 380, 211 (1982).

[57] P. Schofield and J. R. Henderson, Proc. R. Soc. Lond. A 379, 231 (1982).

[58] E. M. Blokhuis and D. Bedeaux, J. Chem. Phys. 97, 3576 (1992).

[59] J. R. Henderson, in Fluid Interfacial Phenomena, C. A. Croxton, ed., (Wiley, New York, 1986).

[60] J. S. Rowlinson, J. Phys. Cond. Matter 6, A1 (1994).

(5)

BIBLIOGRAPHY 107 [61] E. M. Blokhuis, H. N. W. Lekkerkerker, and I. Szleifer, J. Chem. Phys. 112,

6023 (2000).

[62] T. G. Triezenberg and R. Zwanzig, Phys. Rev. Lett. 28, 1183 (1972).

[63] A. O. Parry and C. J. Boulter, J. Phys.: Cond. Matter 6, 7199 (1994).

[64] E. M. Blokhuis, J. Groenewold, and D. Bedeaux, Mol. Phys. 96, 397 (1999).

[65] Statistical Mechanics of Membranes and Surfaces, D. Nelson, T. Piran, and S.

Weinberg, eds., (World Scientific, Singapore, 1988).

[66] L. S. Bartell, J. Chem. Phys. 105, 11615 (2001).

[67] E. M. Blokhuis and D. Bedeaux, Mol. Phys. 80, 705 (1993).

[68] J. Groenewold and D. Bedeaux, Physica A 214, 356 (1995).

[69] A. Laaksonen and R. McGraw, Europhys. Lett. 35, 367 (1996).

[70] O. S. Marchuk and V. M. Sysoev, J. Mol. Liquids 105, 121 (2003).

[71] F. J. Wegner, Phys. Rev. B 5, 4529 (1972).

[72] M. E. Fisher and G. Orkoulas, Phys. Rev. Lett. 85, 696 (2000).

[73] J. Lebowitz, Phys. Fluids 3, 64 (1960).

[74] J. Henderson, Mol. Phys. 50, 741 (1983).

[75] D. E. Sullivan, Phys. Rev. B. 20, 3991 (1979).

[76] P. Tarazona and R. Evans, Mol. Phys. 52, 847 (1984).

[77] R. Evans, in Liquids at Interfaces, J. Charvolin, J. F. Joanny, and J. Zinn- Justin, eds., (Noord-Holland, Amsterdam, 1990).

[78] A. Samborski, J. Stecki, and A. Poniewierski, J. Chem. Phys. 98, 8958 (1993).

[79] A. Poniewierski and J. Stecki, J. Chem. Phys. 106, 3358 (1997).

[80] P. Bryk, R. Roth, K. R. Mecke, and S. Dietrich, Phys. Rev. E. 68, 031602 (2003).

[81] J. R. Henderson, J. Chem. Phys. 116, 5039 (2002).

[82] M. P. A. Fisher and M. Wortis, Phys. Rev. B. 29, 6252 (1984).

[83] E. M. Blokhuis and D. Bedeaux, Physica A 184, 42 (1992).

(6)

[84] G. Gompper and S. Zschocke, Europhys. Lett. 16, 731 (1991).

[85] G. Gompper and S. Zschocke, Phys. Rev. A 46, 4386 (1992).

[86] F. van Swol and J. R. Henderson, Phys. Rev. A 40, 2567 (1989).

[87] S. L. Carnie and D. Y. C. Chen, J. Chem. Phys. 74, 1293 (1981).

[88] Y. Burak, D. Andelman, and H. Orland, Phys. Rev. E 70, 016102 (2004).

[89] T. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).

[90] R. Lovett and M. Baus, J. Chem. Phys. 95, 1991 (1991).

[91] N. F. Carnahan and K. E. Starling, Phys. Rev. A 1, 1672 (1970).

[92] H. Nakanishi and M. Fisher, Phys. Rev. Lett. 49, 1565 (1982).

[93] P. G. de Gennes, Macromolecules 14, 1637 (1981).

[94] P. G. de Gennes, Macromolecules 15, 492 (1982).

[95] E. Eisenriegler, Polymers near Interfaces (World Scientific, Singapore, 1993).

[96] A. E. van Giessen, D. J. Bukman, and B. Widom, J. Colloid Interface Sci. 192, 257 (1997).

[97] A. O. Parry and R. Evans, Mol. Phys. 65, 455 (1988).

[98] R. Evans, R. Roth, and P. Bryk, Europhys. Lett. 62, 815 (2003).

[99] R. Evans, J. R. Henderson, and R. Roth, J. Chem. Phys. 121, 12074 (2004).

[100] M. C. Stuart and R. Evans, Phys. Rev. E 71, 011602 (2005).

[101] J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17, 338 (1949).

[102] J. W. Cahn, J. Chem. Phys. 66, 3367 (1977).

[103] C. Ebner and W. F. Saam, Phys. Rev. Lett. 38, 1486 (1977).

[104] G. F. Teletzke, L. E. Scriven, and H. T. Davis, J. Coll. Interface Sci. 87, 550 (1981).

[105] R. E. B. Jr., L. E. Scriven, and H. T. Davis, Faraday Symp. of Chem. Soc. 16, 169 (1981).

[106] R. Pandit and M. Wortis, Phys. Rev. B. 5, 3226 (1982).

[107] H. Nakanishi and M. E. Fisher, J. Chem. Phys. 78, 3279 (1983).

(7)

BIBLIOGRAPHY 109 [108] K. Binder, in Phase Transitions and Critical Phenomena, C. Domb and J. L.

Lebowitz, eds., (Academic, London, 1983), Vol. 8.

[109] S. Leibler and L. Peliti, Phys. Rev. B 29, 1253 (1983).

[110] D. J. Durian and C. Franck, Phys. Rev. Lett. 59, 555 (1987).

[111] F. van Swol and J. R. Henderson, Phys. Rev. A 43, 2932 (1991).

[112] S. Dhawan, M. E. Reimel, L. E. Scriven, and H. T. Davis, J. Chem. Phys. 94, 4479 (1990).

[113] S. Perkovi´c, E. M. Blokhuis, and G. Han, J. Chem. Phys. 102, 1 (1995).

[114] L. D. Landau and E. M. Lifshitz, in Statistical Physics, 3rd ed., ed., (1980), Vol. 5.

[115] D. E. Sullivan and M. M. T. da Gama, in in Fluid Interfacial Phenomena, A.

Croxton, ed., (Wiley, New York, 1986).

[116] R. Evans, in Fundamentals of Inhomogeneous Fluids, D. Henderson, ed., (Dekker, New York, 1992).

[117] D. E. Sullivan, Phys. Rev. B 20, 3991 (1979).

[118] R. Evans and P. Tarazona, J. Chem. Phys. 80, 587 (1984).

[119] M. J. P. Nijmeijer, A. F. Bakker, C. Bruin, and J. M. J. van Leeuwen, Physica A 160, 166 (1989).

[120] E. M. Blokhuis and J. Kuipers, J. Chem. Phys. 126, 54702 (2007).

[121] R. L. Burden, J. D. Faires, and A. C. Reynolds, in Numerical Analysis, 2nd ed., ed., (Prindle, Wever & Schmidt, New York, 1981).

[122] D. M. Kroll and T. F. Meister, Phys. Rev. B. 31, 392 (1984).

[123] G. F. Teletzke, L. E. Scriven, and H. T. Davis, J. Chem. Phys 78, 1431 (1983).

[124] R. Evans, Mol. Phys. 42, 1169 (1981).

[125] C. Ebner, W. F. Saam, and D. Stroud, Phys. Rev. A 14, 2264 (1976).

[126] J. E. Lane, T. H. Spurling, B. C. Freasier, J. W. Perram, and E. R. Smith, Phys. Rev. A 20, 2147 (1979).

[127] D. G. A. L. Aarts and H. N. W. Lekkerkerker, J. Phys. Cond. Matter 16, S4231 (2004).

(8)

[128] D. G. A. L. Aarts, J. H. Wiel, and H. N. W. Lekkerkerker, J. Phys. Cond.

Matter 15, S245 (2003).

[129] H. de Hek and A. Vrij, J. Coll. Interface Sci. 70, 592 (1979).

[130] P. R. Sperry, J. Coll. Interface Sci. 99, 1984 (1984).

[131] A. P. Gast, C. K. Hall, and W. B. Russel, J. Coll. Interface Sci. 96, 251 (1983).

[132] H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, and P. B. Warren, Euro- phys. Lett. 20, 559 (1992).

[133] A. Johner, J. F. Joanny, S. D. Orrite, and J. B. Avalos, Europhys. Lett. 56, 549 (2001).

[134] E. Scholten, R. Tuinier, and H. N. W. Lekkerkerker, Langmuir 18, 2234 (2002).

[135] E. H. A. de Hoog and H. N. W. Lekkerkerker, J. Phys. Chem. B 103, 5274 (1999).

[136] D. G. A. L. Aarts, M. Schmidt, and H. N. W. Lekkerkerker, Science 304, 847 (2004).

[137] E. Scholten, L. M. C. Sagis, and E. van der Linden, J. Phys. chem. B 108, 12164 (2004).

[138] R. L. C. Vink, J. Horbach, and K. Binder, J. Chem. Phys. 122, 134905 (2005).

[139] M. Dijkstra, J. M. Brader, and R. Evans, J. Phys. Cond. Matter 11, 10079 (1999).

[140] M. Hagen and D. Frenkel, J. Chem. Phys. 101, 4093 (1994).

[141] J. M. Brader and R. Evans, Europhys. Lett. 49, 678 (2000).

[142] J. A. Barker and D. Henderson, J. Chem. Phys. 47, 2856 (1967).

[143] N. F. Carnahan and K. E. Starling, J. Chem. Phys. 51, 635 (1969).

[144] J. K. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958).

[145] L. Verlet and J. J. Weis, Phys. Rev. A 5, 939 (1972).

[146] K. R. Hall, J. Chem. Phys. 57, 2252 (1972).

[147] J. M. Kincaid and J. J. Weis, Mol. Phys. 34, 931 (1977).

[148] W. R. Smith and D. Henderson, Mol. Phys. 19, 411 (1970).

[149] R. H. Fowler, Proc. R. Soc. Lond. A 159, 229 (1937).

(9)

BIBLIOGRAPHY 111

[150] F. P. Buff, R. A. Lovett, and F. H. Stillinger, Phys. Rev. Lett. 15, 621 (1965).

[151] J. D. Weeks, J. Chem. Phys. 67, 3106 (1977).

[152] D. Bedeaux and J. D. Weeks, J. Chem. Phys. 82, 972 (1985).

[153] E. J. Meijer and D. Frenkel, J. Chem. Phys. 100, 6873 (1994).

[154] P. Bolhuis and D. Frenkel, J. Chem. Phys. 101, 9869 (1994).

[155] M. Dijkstra, J. M. Brader, and R. Evans, J. Phys. Cond. Matter 11, 10079 (1999).

[156] H. N. W. Lekkerkerker and B. Widom, Physica A 285, 483 (2000).

[157] J. M. Brader and R. Evans, Physica A 306, 287 (2002).

[158] S. M. Oversteegen and H. N. W. Lekkerkerker, Physica A 310, 181 (2002).

[159] M. Fuchs and K. S. Schweizer, J. Phys. Cond. Matter 14, R239 (2002).

[160] J. M. Brader, R. Evans, M. Schmidt, and H. L¨owen, J. Phys. Cond. Matter 14, L1 (2002).

[161] M. Dijkstra and R. van Roij, Phys. Rev. Lett. 89, 208303 (2002).

[162] W. K. Wijting, N. A. M. Besseling, and M. A. C. Stuart, Phys. Rev. Lett. 90, 196101 (2003).

[163] W. K. Wijting, N. A. M. Besseling, and M. A. C. Stuart, J. Phys. Chem. B 107, 10565 (2003).

[164] D. G. A. L. Aarts, R. P. A. Dullens, H. N. W. Lekkerkerker, D. Bonn, and R.

van Roij, J. Chem. Phys. 120, 1973 (2004).

[165] A. Bellemans, Physica 28, 493 (1962).

[166] D. G. A. L. Aarts, R. Tuinier, and H. N. W. Lekkerkerker, J. Phys. Cond.

Matter 14, 7551 (2002).

[167] B. P. Binks and R. Murakami, Soft Matter 5, 865 (2006).

[168] J. Banhart, Adv. Eng. Matter 8, 781 (2006).

[169] S. Sacanna, W. K. Kegel, and A. P. Philipse, Phys. Rev. Lett. 98, 158301 (2007).

[170] F. Gautier, M. Destribats, R. Pierrer-Cornet, J.-F. Dech´ezelles, J. Giermanska, V. H´eroguez, S. Ravaine, F. Leal-Calderon, and V. Schmitt, Phys. Chem. 9, 6455 (2007).

(10)

[171] E. R¨uckenstein and R. Krishnan, J. Coll. Interface Sci. 71, 321 (1979).

[172] B. v. Szyskowski, Z. Physik. Chem. 64, 385 (1908).

[173] I. Langmuir, Pure Appl. Chem. 40, 1361 (1918).

[174] J. Stauff, Z. Physik. Chem. 10, 24 (1957).

[175] Physical Chemistry of Surfaces, A. W. Adamson, ed., (Wiley, New York, 1990), No. 5th ed.

[176] E. J. Verwey, P. W. Haayman, and F. C. Romeijn, J. Chem. Phys. 15, 181 (1947).

[177] E. R¨uckenstein, Chem. Phys. Lett. 57, 517 (1978).

[178] W. F. Kegel, Private communication (2009).

[179] Nonionic Surfactants, M. Schick, ed., (Dekker, New York, 1967).

[180] E. M. Blokhuis and D. Bedeaux, J. Chem. Phys. 97, 3576 (1992).

[181] L. Sch¨afer, Excluded Volume Effects in Polymer Solutions (Springer, Heidelberg, 1999).

[182] E. W. Weisstein, “Circle-Circle Intersection,” http://mathworld.wolfram.com/

Circle-CircleIntersection.html(Accessed July 1, 2009).

[183] E. W. Weisstein, “Sphere-Sphere Intersection,” http://mathworld.wolfram.

com/Sphere-SphereIntersection.html (Accessed July 1, 2009).

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