The lattice gas model in the molecular-statistical theory of equilibrium systems

Russian Journal of Physical Chemistry A

Volumn 79, Issue 12, 2005, Pages 1903-1920

  Tovbin, Yu K ^a  

^a KARPOV INSTITUTE OF PHYSICAL CHEMISTRY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; LATTICE CONSTANTS; MATHEMATICAL MODELS; STATISTICAL METHODS;

CALIBRATION FUNCTIONS; EQUILIBRIUM SYSTEMS; PHASE STATE EFFECTS;

PHASE EQUILIBRIA;

EID: 31044449172     PISSN: 00360244     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (179)

1. J. W. Gibbs, Thermodynamics. Statistical Mechanics (Nauka, Moscow, 1982), p. 9 [in Russian].
2. R. Kubo, Thermodynamics: An Advanced Course with Problems and Solutions (North-Holland, Amsterdam, 1968; Mir, Moscow, 1970).
3. I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans and Green, London, 1954; Nauka, Novosibirsk, 1966).
4. J. W. Gibbs, Thermodynamics. Statistical Mechanics (Nauka, Moscow, 1982), p. 350 [in Russian].
5. R. Fowler and E. A. Guggenheim, Statistical Thermodynamics: A Version of Statistical Mechanics for Students of Physics and Chemistry (Macmillan, Cambridge, U.K., 1949; Inostrannaya Literatura, Moscow, 1949).
6. R. Kubo, Statistical Mechanics: an Advanced Course with Problems and Solutions (North-Holland, Amsterdam, 1965; Mir, Moscow, 1967).
7. K. Huang, Statistical Mechanics (New York: Wiley, 1963; Mir, Moscow, 1966).
8. N. N. Bogolyubov, in Studies in Statistical Mechanics, Ed. by J. de Boer and G. E. Uhlenbeck (Moscow, Gostekhizdat, 1946; Wiley, New York, 1961).
9. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954; Inostrannaya Literatura, Moscow, 1961).
10. T. L. Hill, Statistical Mechanics: Principles and Selected Applications (McGraw-Hill, New York, 1956; Inostrannaya Literatura, Moscow, 1960).
11. C. A. Croxton, Liquid State Physics: A Statistical Mechanical Introduction (Cambridge Univ., Cambridge, 1974; Mir, Moscow, 1979).
12. J. E. Mayer and M. Goeppert-Mayer, Statistical Physics, 2nd ed. (Wiley, New York, 1977; Mir, Moscow, 1980).
13. S. Ono and S. Kondo, Molecular Theory of Surface Tension in Liquids (Springer, Berlin, 1960; Inostrannaya Literatura, Moscow, 1963).
14. L. Onsager, Phys. Rev. 65, 117 (1944).
15. C. Domb, Adv. Phys. 9, 149, 245 (1960).
16. M. E. Fisher, Math. Phys. 4, 278 (1963).
17. R. J. Baxter, Exactly Solved Model in Statistical Mechanics (Academic, London, 1982; Moscow: Mir, 1985).
18. J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. London, Ser. A 163, 53 (1937).
19. J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. London, Ser. A 165, 1 (1938).
20. J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. London, Ser. A 169, 317 (1939).
21. I. Z. Fisher, Statistical Theory of Liquids (Fizmatgiz, Moscow, 1961) [in Russian].
22. G. A. Martynov, Fundamental Theory of Liquids: Method of Distribution Functions (A. Hilger, Bristol, 1992).
23. G. A. Martynov, Classical Statistical Mechanics: Fundamental Theories of Physics (Kluwer, Dordrecht, 1997), Vol. 89.
24. I. P. Bazarov, Statistical Theory of Crystalline State (Mosk. Gos. Univ., Moscow) [in Russian].
25. I. P. Bazarov and P. N. Nikolaev, Correlation Theory of Crystal (Mosk. Gos. Univ., Moscow, 1981) [in Russian].
26. I. P. Bazarov and E. V. Gevorkyan, Statistical Theory of Solid and Liquid Crystals (Mosk. Gos. Univ., Moscow, 1983) [in Russian].
27. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954; Inostrannaya Literatura, Moscow, 1958).
28. A. A. Maradudin, Theoretical and Experimental Aspects of the Effects of Point Defects and Disordered on the Vibrations in Crystals (Academic, New York, 1966; Mir, Moscow, 1968).
29. G. Leibfried, Bestrahlungseffekte in Festkorpern; eine Einfuhrung in die Theorie (Teubner, Stuttgart, 1965; Gos. Izd. Fiz. Mat. Lit., Moscow, 1963).
30. M. A. Krivoglaz and A. A. Smirnov, Theory of Ordering Alloys (Gos. Izd. Fiz.-Mat. Lit., Moscow, 1958) [in Russian].
31. A. A. Smirnov, Theory of Interstitial Alloys (Nauka, Moscow, 1979) [in Russian].
32. P. Tarasona, Phys. Rev. A 31, 2575 (1985).
33. E. Bruno, U. M. B. Marconi, and R. Evans, Physica A (Amsterdam) 141, 187 (1987).
34. P. Tarasona, U. M. B. Marconi, and R. Evans, Mol. Phys. 60, 573 (1987).
35. S. Sokolowski and J. Fischer, Mol. Phys. 71, 393 (1990).
36. Monte Carlo Methods in Statistical Physics, Ed. by K. Binder, Vol. 36 of Topics in Current Physics (Springer, Berlin, 1984)
37. Monte Carlo Methods in Statistical Physics, Ed. by K. Binder, Vol. 7 of Topics in Current Physics (Springer, Berlin, 1979; Mir, Moscow, 1982).
38. D. Nicolson and N. G. Parsonage, Computer Simulation and The Statistical Mechanics of Adsorption (Academic, New York, 1982).
39. E. N. Brodskaya and E. M. Piotrovskaya, Rasplavy 2 (1), 29 (1988).
40. W. A. Steele, Chem. Rev. 93, 2355 (1993).
41. A. G. Grivtsov, in Method of Molecular Dynamics in Physical Chemistry, Ed. by Yu. K. Tovbin (Nauka, Moscow, 1996), p. 16 [in Russian].
42. G. Zgrablich, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Ed. by W. Rudzinski, W. A. Steele, and G. Zgrablich, Vol. 104 of Studies in Surface Science and Catalysis (Elsevier, Amsterdam, 1997), p. 373.
43. L. D. Gelb, K. E. Gubbins, R. Radhakrishman, and M. Rep. Sliwinska-Bartkowiak, Prog. Phys. 62, 1573 (1999).
44. A. V. Neimark, P. I. Ravilovich, and A. Vishnyakov, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 62A, R1493 (2000).
45. Yu. K. Tovbin, Izv. Ross. Acad. Nauk, Ser. Khim., No. 12, 2763 (2004).
46. Yu. K. Tovbin, Theory of Physical Chemistry Processes at a Gas/Solid Interface (Nauka, Moscow, 1990; CRC, Boca Raton, 1991).
47. Yu. K. Tovbin, Zh. Fiz. Khim. 55 (2), 273 (1981).
48. M. E. Fisher, The Nature of Critical Points (Univ. Colorado, Boulder, 1965; Mir, Moscow, 1968).
49. E. W. Montroll, in Statistical Physics, Phase Transitions, and Superfluidity, Ed. by M. Chretien (Gordon and Breach, New York, 1968; Mir, Moscow, 1973).
50. Yu. V. Shulepov and E. V. Aksenenko, Lattice Gas (Naukova Dumka, Kiev, 1981) [in Russian].
51. J. A. Barker, Lattice Theories of the Liquid State (Pergamon, Oxford, 1963).
52. M. I. Shakhparonov, Introduction to Molecular Theory of Solutions (Cos. Izd. Tekh.-Teor. Lit., Moscow, 1956) [in Russian].
53. I. Prigogine, Molecular Theory of Solutions (Interscience, New York, 1957; Metallurgiya, Moscow, 1990).
54. N. A. Smirnova, Molecular Theories of Solutions (Khimiya, Leningrad, 1987) [in Russian].
55. A. G. Morachevskii, N. Ā. Smirnova, E. M. Piotrovskaya, et al., Thermodynamics of Liquid-Vapor Equilibrium Ed. by A. G. Morachevskii (Khimiya, Leningrad, 1989) [in Russian].
56. T. L. Hill, J. Chem. Phys. 17, 762 (1949).
57. Yu. K. Tovbin, Poverkhnost': Fizika, Khimiya, Mekhanika, No. 9, 15 (1982).
58. Yu. K. Tovbin, Dokl. Akad. Nauk SSSR 306, 888 (1989).
59. Yu. K. Tovbin, Zh. Fiz. Khim. 64, 865 (1990).
60. M. Jaroniec and R. Madey, Physical Adsorption on Heterogeneous Solids (Elsevier, Amsterdam, 1988).
61. W. Rudzinski and D. H. Everett, Adsorption of Gases on Heterogeneous Surfaces (Academic, London, 1992).
62. H. Kramers and G. H. Wannier, Phys. Rev. 60, 252 (1941).
63. W. Kinzel, W. Selke, and K. Binder, Surf. Sci. 121, 13 (1982).
64. B. Derrida, L. de Seze, and J. Vannimenus, in Lecture Notes in Physics (Springer, Berlin, 1981), Vol. 149, p. 46.
65. Yu. K. Tovbin, Khim. Fiz. 15, 75 (1996).
66. Yu. K. Tovbin, Zh. Fiz. Khim. 70, 700 (1996)
67. [Russ. J. Phys. Chem. 70, 650 (1996)].
68. Yu. K. Tovbin, Langmuir 13, 979 (1997).
69. Yu. K. Tovbin, Zh. Fiz. Khim. 72, 775 (1998)
70. [Russ. J. Phys. Chem. 72, 675 (1998)].
71. Yu. K. Tovbin, A. G. Petukhov, and D. V. Eremich, Zh. Fiz. Khim. 79, 1310 (2005)
72. [Russ. J. Phys. Chem. 79, 1302 (2005)].
73. V. A. Pindyurin, S. Yu. Surovtsev, and Yu. K. Tovbin, Zh. Fiz. Khim. 60, 1471 (1986).
74. S. Yu. Surovtsev, V. A. Pindyurin, and Yu. K. Tovbin, Zh. Fiz. Khim. 60, 1465 (1986).
75. R. Kikuchi and S. G. Brush, J. Chem. Phys. 47, 195 (1967).
76. P. J. Rundrotas, S. Lapinskas, and A. Rosengren, Phys. Rev. B: Condens. Matter 56, 6486 (1997).
77. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 5: Statistical Physics 2nd ed. (Nauka, Moscow, 1964; Pergamon, Oxford, 1980).
78. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Clarendon, Oxford, 1971; Mir, Moscow, 1973).
79. K. G. Wilson and J. Kogut, Phys. Rep. 12C, 75 (1974) (Mir, Moscow, 1975).
80. S. Ma, Modern Theory of Critical Phenomena (Benjamin, Reading, Mass., 1976; Mir, Moscow, 1980).
81. T. Niemeijer and J. M. J. van Leeuwen, Physica A (Amsterdam) 71, 17 (1974).
82. A. A. Tarasenko and A. A. Chumak, Poverkhnost': Fizika, Khimiya, Mekhanika, No. 11, 98 (1989).
83. Yu. K. Tovbin, Zh. Fiz. Khim. 72, 2254 (1998)
84. [Russ. J. Phys. Chem. 72, 2053 (1998)].
85. Yu. K. Tovbin, A. B. Rabinovich, and E. V. Votyakov, Izv. Akad. Nauk, Ser. Khim., No. 9, 1531 (2002).
86. Yu. K. Tovbin and A. B. Rabinovich, Langmuir 20, 6041 (2004).
87. B. E. Boehm and D. E. Martire, J. Chem. Phys. 67, 1961 (1977).
88. Yu. K. Tovbin, Izv. Akad. Nauk, Ser. Khim., No. 3, 458 (1997).
89. Yu. K. Tovbin, Khim. Fiz. 17 (6), 140 (1998).
90. J. A. Barker, J. Chem. Phys. 20, 1526 (1952).
91. S. Chandrasekhar, Liquid Crystals (Cambridge Univ., Cambridge, 1977; Mir, Moscow, 1980).
92. E. A. Guggenheim, Mixtures (Clarendon, Oxford, 1952).
93. A. R. Miller, The Theory of Solutions of High Polymers (Clarendon, Oxford, 1948).
94. P. J. Flory, Principle of Polymer Chemistry (Cornell Univ. Press, New York, 1953).
95. Yu. K. Tovbin, Izv. Akad. Nauk, Ser. Khim., No. 8, 1467 (1999).
96. Yu. K. Tovbin, L. K. Zhidkova, and V. N. Komarov, Izv. Akad. Nauk, Ser. Khim., No. 5, 752 (2001).
97. N. A. Smirnova, Kolloidn. Zh. 41, 1152 (1979).
98. N. P. Tumanyan and A. G. Shakhatuni, Armyanskii Khim. Zh. 35, 103 (1982).
99. Yu. K. Tovbin, M. M. Senyavin, and E. P. Sokolova, Zh. Fiz. Khim. 77, 714 (2003)
100. [Russ. J. Phys. Chem. 77, 636 (2003)].
101. W. G. Hoover, B. J. Alder, and F. H. Ree, J. Chem. Phys. 41, 3528 (1964).
102. E. P. Sokolova and N. P. Tumanyan, Liq. Cryst. 27 (6), 813 (2000).
103. K. Mitra and A. R. Allant, J. Phys. C: Solid State Phys. 12, 2261 (1979).
104. V. A. Vernov and W. A. Steele, Fundamentals of Adsorption IV (Kodansha, Tokyo, 1993), p. 695.
105. J. G. Kirkwood, J. Chem. Phys. 18, 380 (1950).
106. Z. W. Salsburg and J. G. Kirkwood, J. Chem. Phys. 20, 1538 (1952).
107. I. A. Barker and D. Henderson, Rev. Mod. Phys. 46 (4), 587 (1976).
108. J. E. Mayer and G. Careri, J. Chem. Phys. 20, 1001 (1952).
109. L. A. Rott, Statistical Theory of Molecular Systems (Nauka, Moscow, 1979) [in Russian].
110. Yu. K. Tovbin, Doctoral Dissertation in Chemistry (Karpov Institute of Physical Chemistry, Moscow, 1985).
111. Yu. K. Tovbin, in Theoretical Methods for Describing the Properties of Solutions: Interschool Collection of Scientific Works (Ivanovo, 1987), p. 44 [in Russian].
112. Yu. K. Tovbin, Zh. Fiz. Khim. 46, 1239 (1974).
113. Yu. K. Tovbin, Teor. Eksp. Khim. 10 (3), 258 (1974).
114. Yu. K. Tovbin, Teor. Eksp. Khim. 12 (2), 196 (1976).
115. C. V. Heer, Statistical Mechanics, Kinetic Theory, and Stochastic Processes (Academic, New York, 1972; Mir, Moscow, 1976).
116. A. M. W. Verhagen, J. Chem. Phys. 53 (3), 2223 (1970).
117. E. R. Cowley, J. Chem. Phys. 71, 458 (1979).
118. E. R. Cowley and J. A. Barker, J. Chem. Phys. 73, 3452 (1980).
119. I. C. Sanchez and R. H. Lacombe, J. Chem. Phys. 80, 2353 (1976).
120. A. Z. Panagiotopoulos, J. Chem. Phys. 112, 7132 (2000).
121. M. A. Floriano, E. Caponetti, and A. Z. Panagiotopoulos, Langmuir 15, 3143 (1999).
122. Yu. K. Tovbin, Langmuir 15, 6107 (1999).
123. V. V. Gvozdev and Yu. K. Tovbin, Izv. Akad. Nauk, Ser. Khim., No. 6, 1109 (1997).
124. E. A. Moelwyn-Hughes, Physical Chemistry (Pergamon, London, 1961; Inostrannaya Literatura, Moscow, 1962).
125. F. Chernushi and H. Eyring, J. Chem. Phys. 7, 547 (1939).
126. S. Ono, Mem. Fac. Eng. Kyushi. Univ. 10, 190 (1947).
127. H. M. Peek and T. L. Hill, J. Chem. Phys. 18, 1252 (1950).
128. J. S. Rowlinson and C. F. Curtiss, J. Chem. Phys. 19, 1519 (1951).
129. Yu. K. Tovbin, Zh. Fiz. Khim. 69, 118 (1995).
130. Yu. K. Tovbin, M. M. Senyavin, and L. K. Zhidkova, Zh. Fiz. Khim. 73, 304 (1999)
131. [Russ. J. Phys. Chem. 73, 245 (1999)].
132. Yu. K. Tovbin, Appl. Surf. Sci. 196, 71 (2002).
133. I. Prins and H. Petersen, Physica A (Amsterdam) 3, 147 (1936).
134. Ya. I. Frenkel', Kinetic Theory of Liquids (Akad. Nauk SSSR, Moscow, 1945) [in Russian].
135. V. K. Fedyanin, in Surface Phenomena in Liquids (Leningr. Gos. Univ., Leningrad, 1975), p. 232 [in Russian].
136. O. Yu. Batalin, Yu. K. Tovbin, and V. K. Fedyanin, Zh. Fiz. Khim. 53, 3020 (1979).
137. N. M. Plakida, in Statistical Physics and Quantum Field Theory (Nauka, Moscow, 1973), p. 238 [in Russian].
138. V. A. Zagrebnov and V. K. Fedyanin, Teor. Mat. Fiz. 10, 127 (1972).
139. V. K. Fedyanin, in Theoretical Methods for Describing the Properties of Solutions: Interschool Collection of Scientific Works (Ivanovo, 1987), p. 40 [in Russian].
140. Z. Rac and M. F. Collins, Phys. Rev. B: Condens. Matter 20, 229 (1980).
141. S. P. J. Rodrigues and F. M. S. S. Fernandes, J. Phys. Chem. 98, 3917 (1994).
142. B. V. Egorov, V. N. Komarov, Yu. E. Markachev, and Yu. K. Tovbin, Zh. Fiz. Khim. 74, 882 (2000)
143. [Russ. J. Phys. Chem. 74, 778 (2000)].
144. Yu. K. Tovbin and V. N. Komarov, Zh. Fiz. Khim. 75, 562 (2001)
145. [Russ. J. Phys. Chem. 75, 490 (2001)].
146. V. N. Komarov and Yu. K. Tovbin, Teplofiz. Vys. Temp. 41 (2), 1 (2003)
147. [High Temp. 41 (2), 181 (2003)].
148. Yu. K. Tovbin, Zh. Fiz. Khim. 61, 2711 (1987).
149. Yu. K. Tovbin and V. N. Komarov, Zh. Fiz. Khim. (in press).
150. R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids (The Reestimation and Correlation) (McGraw-Hill, New York, 1966).
151. J. Levelt, Physica A (Amsterdam) 26 (6), 361 (1960).
152. V. A. Rabinovich, A. A. Vasserman, V. I. Nedostup, and L. S. Veksler, Thermal Properties of Neon, Argon, Krypton, and Xenon (Standartgiz, Moscow, 1976) [in Russian].
153. Tables of Physical Values: A Handbook, Ed. by I. K. Kikoin (Atomizdat, Moscow, 1976) [in Russian].
154. S. L. Rivkin, Thermodynamic Properties of Gases: A Handbook (Energoatomizdat, Moscow, 1987) [in Russian].
155. V. V. Sychev, A. A. Vasserman, and A. D. Kozlov, Thermodynamic Properties of Nitrogen (Izd. Standartov, Moscow, 1977) [in Russian].
156. V. V. Sychev, A. A. Vasserman, and A. D. Kozlov, Thermodynamic Properties of Methane (Izd. Standartov, Moscow, 1984) [in Russian].
157. J. P. P. Ramalho, A. B. Rabinovich, D. V. Yeremich, and Yu. K. Tovbin, Appl. Surf. Sci. (in press).
158. Yu. K. Tovbin and E. V. Votyakov, Fiz. Tverd. Tela 42, 1158 (2000)
159. [Phys. Solid State 42, 1192 (2000)].
160. Yu. K. Tovbin and E. V. Votyakov, Zh. Fiz. Khim. 75, 721 (2001)
161. [Russ. J. Phys. Chem. 75, 640 (2001)].
162. Yu. K. Tovbin, Zh. Fiz. Khim. 70, 1783 (1996)
163. [Russ. J. Phys. Chem. 70, 1655 (1996)].
164. G. A. Martynov, Usp. Fiz. Nauk 169, 595 (1999).
165. G. N. Sarkisov, Usp. Fiz. Nauk 169, 625 (1999).
166. O. V. Kiselev and G. A. Martynov, in Theoretical Methods for Describing the Properties of Solutions: Interschool Collection of Scientific Works (Ivanovo, 1987), p. 29 [in Russian].
167. A. V. Klinov, G. S. D'yakonov, and S. G. D'yakonov, Zh. Fiz. Khim. 78, 602 (2004)
168. [Russ. J. Phys. Chem. 78, 503 (2004)].
169. P. Verwer and F. Leusen, Rev. Comput. Chem. 12, 327 (1998).
170. V. Matsumoto, S. Saito, and I. Ohmine, Nature (London) 416, 409 (2002).
171. D. K. Belashchenko and R. N. Pavlov, Zh. Fiz. Khim. 78, 2013 (2004)
172. [Russ. J. Phys. Chem. 78, 1777 (2004)].
173. V. L. Kuz'min, Teor. Mat. Fiz. 28, 389 (1976).
174. G. A. Martynov, I. Odvarkova, and A. Malijevsky, Zh. Fiz. Khim. 78, 1375 (2004)
175. [Russ. J. Phys. Chem. 78, 1202 (2004)].
176. J. H. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972; Mir, Moscow, 1976).
177. E. N. Eremin, Fundamentals of Chemical Kinetics (Vysshaya Shkola, Moscow, 1976) [in Russian].
178. Yu. K. Tovbin and V. K. Fedyanin, Kinet. Katal. 19 (4), 989 (1978).
179. Yu. K. Tovbin, Zh. Fiz. Khim. 55, 284 (1981).