Ion association and electrical conductance minimum in Debye-Hueckel-based theories of the hard sphere ionic fluid

Journal of Chemical Physics

Volumn 113, Issue 2, 2000, Pages 762-770

  Weingärtner, Hermann ^a   Weiss, Volker C ^b,c   Schröer, Wolffram ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF BREMEN   (Germany)

^c Department of Population Medicine and Diagnostic Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DISSOCIATION; ELECTRIC CONDUCTIVITY OF LIQUIDS; IONS; ISOTHERMS; MATHEMATICAL MODELS; MONTE CARLO METHODS; PARTICLE SIZE ANALYSIS; PERMITTIVITY; PHASE TRANSITIONS; SPHERES;

DEBYE-HUECKEL THEORY; ION ASSOCIATION; IONIC FLUID;

FLUIDS;

EID: 0141472177     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.481822     Document Type: Article

References (75)

1. (a) R. R. Singh and K. S. Pitzer, J. Chem. Phys. 92, 6775 (1990);
2. (b) K. S. Pitzer, J. Phys. Chem. 99, 13070 (1995);
3. T. Narayanan and K. S. Pitzer, J. Chem. Phys. 102, 8118 (1995).
4. (a) H. Weingärtner, S. Wiegand, and W. Schroer, J. Chem. Phys. 96, 848 (1992);
5. (b) H. Weingärtner, M. Kleemeier, S. Wiegand, and W. Schröer, J. Stat. Phys. 78, 169 (1995);
6. M. Kleemeier, S. Wiegand, W. Schröer, and H. Weingärtner, J. Chem. Phys. 110, 3085 (1999).
7. (a) K. C. Zhang, M. E. Briggs, R. W. Gammon, and J. M. H. Levelt Sengers, J. Chem. Phys. 97, 8692 (1992);
8. (b) S. Wiegand, M. E. Briggs, J. M. H. Levelt Sengers, M. Kleemeier, and W. Schröer, ibid. 109, 9038 (1998).
9. M. E. Fisher, J. Stat. Phys. 75, 1 (1994).
10. G. Stell, J. Stat. Phys. 78, 197 (1995).
11. Y. Levin and M. E. Fisher, Physica A 225, 164 (1996).
12. Y. Zhon, S. Yeh, and G. Stell, J. Chem. Phys. 102, 5785 (1995).
13. B. Guillot and B. Guissani, Mol. Phys. 87, 37 (1996).
14. V. C. Weiss and W. Schröer, J. Chem. Phys. 108, 7747 (1998).
15. H-L. Friedman and B. Larsen, J. Chem. Phys. 70, 92 (1979).
16. P. J. Camp and G. N. Patey, Phys. Rev. E 60, 1063 (1999).
17. H. Weingärtner, T. Merkel, J.-P. Conwen, H. Glasbrenner, and S. Käshammer, Ber. Bunsenges. Phys. Chem. 95, 1579 (1991).
18. D. R. Schreiber, M. C. P. de Lima, and K. S. Pitzer, J. Phys. Chem. 91, 4087 (1987).
19. H. Weingärtner and W. Schröer, Dielectric Properties and Electrical Conductivity of Ionic Systems Near Critical Points, in Steam, Water, and Hydrothermal Systems: Physics and Chemistry at the Needs of Industry, edited by P. Tremaine, P. G. Hill, D. E. Irish, and P. V. Balakrishnan (NRC, Ottawa, 2000).
20. R. M. Fuoss and C. A. Kraus, J. Am. Chem. Soc. 55, 2378 (1933).
21. B. Gestblom and J. Songstad, Acta Chem. Scand. B41, 396 (1987).
22. A long time ago Kraus stated that for any system with association at low salt concentration, the association number must necessarily possess a maximum at some concentration. See, e.g., C. A. Kraus, J. Phys. Chem. 60, 129 (1956).
23. N. Bjerrum, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 7, 1 (1926); see also H. Falkenhagen and W. Ebeling, in Ionic Interactions, edited by S. Petrucci (Academic, New York, 1971), Vol. 1, Chap. 1.
24. N. Bjerrum, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 7, 1 (1926); see also H. Falkenhagen and W. Ebeling, in Ionic Interactions, edited by S. Petrucci (Academic, New York, 1971), Vol. 1, Chap. 1.
25. (a) W. Ebeling, Z. Phys. Chem. (Leipzig) 238, 400 (1968);
26. (b) W. Ebeling and M. Grigo, Ann. Phys. (Leipzig) 37, 21 (1980).
27. W. Ebeling and M. Grigo, J. Solution Chem. 11, 151 (1982).
28. (a) Beronius and co-workers have used FK theory for analyzing conductance data from numerous studies, see e.g., T. Lindbäck and P. Beronius, Acta Chem. Scand. A34, 709 (1980), and references cited therein;
29. other representative examples are (b) Z. Chen and M. Hojo, J. Phys. Chem. B 101, 10896 (1997), and references cited therein;
30. M. Salomon and M. C. Uchiyama, J. Solution Chem. 16, 21 (1987);
31. J. Barthel, R. Gerber, and H.-J. Gores. Ber. Bunsenges. Phys. Chem. 88, 616 (1984).
32. R. M. Fuoss and C. A. Kraus, J. Am. Chem. Soc. 57, 1 (1937).
33. M. J. Gillan, Mol. Phys. 49, 421 (1983).
34. K. S. Pitzer and D. R. Schreiber, Mol. Phys. 60, 1067 (1987).
35. M. Grigo, J. Solution Chem. 11, 529 (1982).
36. H. Weingärtner, H. Nadolny, and S. Käshammer, J. Phys. Chem. B 103, 4738 (1999). and references cited therein.
37. A. M. Sukhotin, Russ. J. Phys. Chem. 34, 19 (1960); see also the remarks in Ref. 11.
38. E. A. S. Cavell and P. C. Knight, Z. Phys. Chem., Neue Folge 57, 331 (19681.
39. H. L. Friedman, J. Phys. Chem. 66, 1595 (1962).
40. Fisher and Levin noted that their critical point (see Table 1) is in good agreement with MC data, which at that time suggested that ρ*ν ≅ 0.03. (Refs. 4, 6). Since then, MC predictions of the critical density have changed by more than a factor of two towards higher density.
41. (a) J. M. Caillol, D. Levesque, and J. J. Weis, J. Chem. Phys. 107, 1565 (1997);
42. (b) G, Orgoulas and A. Z. Panagiotopoulos, ibid. 110, 1581 (1999);
43. J. Valleau and G. Torrie, ibid. 108, 5169 (1998).
44. For attempts to incorporate DI interactions into MSA theory see the socalled PMSA2 theory of Stell and co-workers (Ref. 7). DD interactions at the MSA level have been considered in a Born-type theory by Guillot and Guissani (Ref. 8).
45. D. M. Zuckerman, M. E. Fisher, and B. P. Lee, Phys. Rev. E 56, 6569 (1997).
46. M. E. Fisher and D. Zuckerman, J. Chem. Phys. 109, 7961 (1998).
47. G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, Jr., J. Chem. Phys. 54, 1523 (1971).
48. B. Smit, K. Esselink, and D. Frenkel, Mol. Phys. 87, 159 (1996).
49. l = 0.052 62 (WS). We find α ≅ 0.002 759 (FL) and 0.011 247 (WS) for the weakly conducting phase, and α = 0.246 301 (FL) and 0.901 292 (WS), for the strongly conducting phase.
50. See, e.g., A. K. Covington and T. Dickinson, The Physical Chemistry of Organic Solvent Systems (Plenum. New York, 1973), Chap. 5.
51. Conductance minima have been observed far above the upper limit quoted here, but have generally been attributed to specific short-range interactions. For conductance minima at higher reduced temperatures see for example, M. Hojo, T. Ueda, M. Nishimura, H. Hamada, M. Matsui, and S. Umetani, J. Phys. Chem. B 103, 8965 (1999).
52. (a) J. M. Caillol and J. J. Weis, J. Chem. Phys. 102, 7610 (1995);
53. (b) J. M. Caillol, ibid. 102, 5471 (1995).
54. Much more is known about the converse problem: various properties which are determined by chemical equilibria show a critical anomaly with a l(l · α) temperature dependence, where α ≅ 0.11 is the exponent of the heat capacity [J. C. Wheeler, Phys. Rev. A 30, 648 (1984)]. Such an anomaly has also been reported for the conductivity of demixing ionic systems [A. Oleinikova and M. Bonetti. Phys. Rev, Lett. 83, 2985 (1999); E. M. Andersen and S. C. Greer, Phys. Rev. A 30, 3129 (1984)].
55. Much more is known about the converse problem: various properties which are determined by chemical equilibria show a critical anomaly with a l(l · α) temperature dependence, where α ≅ 0.11 is the exponent of the heat capacity [J. C. Wheeler, Phys. Rev. A 30, 648 (1984)]. Such an anomaly has also been reported for the conductivity of demixing ionic systems [A. Oleinikova and M. Bonetti. Phys. Rev, Lett. 83, 2985 (1999); E. M. Andersen and S. C. Greer, Phys. Rev. A 30, 3129 (1984)].
56. Much more is known about the converse problem: various properties which are determined by chemical equilibria show a critical anomaly with a l(l · α) temperature dependence, where α ≅ 0.11 is the exponent of the heat capacity [J. C. Wheeler, Phys. Rev. A 30, 648 (1984)]. Such an anomaly has also been reported for the conductivity of demixing ionic systems [A. Oleinikova and M. Bonetti. Phys. Rev, Lett. 83, 2985 (1999); E. M. Andersen and S. C. Greer, Phys. Rev. A 30, 3129 (1984)].
57. P. Pfeuty and G. Tolouse, Introduction to the Renormalization Croup and to Critical Phenomena (Wiley, London, 1977), and references cited therein.
58. R. B. Griffith and J. C. Wheeler. Phys. Rev. A 2, 1047 (1970), and references cited therein.
59. 4He liquid-liquid transition at its critical point; see, e.g., M. Blume, V. J. Emery, and R. B. Griffiths. Phys. Rev. A 4, 1071 (1971).
60. Y. Levin, X. J. Lee, and M. E. Fischer, Phys. Rev. Lett. 73, 2716 (1994).
61. J. M. Caillol and D. Levesque, Phys. Rev. 33, 499 (1986).
62. J. S. Høye and G. Stell, J. Stat. Phys. 89, 177 (1975).
63. A. Z. Panagiotopoulos and S. K. Kumar, Phys. Rev. Lett. 83, 2981 (1999).
64. G. Stell, NATO ASI Ser., Ser. C 529, 71 (1999).
65. For a review see M. A. Anisimov and J. V. Sengers, in Supercritical Fluids: Fundamentals and Applications, edited by E. Kiran, P. G. Debenedetti, and C. J. Peters (Kluwer, Dordrecht, 2000).
66. P. Chieux, J.-F. Jal, L. Hili, J. Dupuy, F. Leclercq, and P. Damay, J. Phys. IV C5, 13 (1991).
67. G. Meier, D. Schwahn, K. Mortensen, and S. Janssen, Europhys. Lett. 22, 577 (1993).
68. J. Jacob, A. Kumar, M. A. Anisimov, A. A. Povodyrev, and J. V. Sengers, Phys. Rev. E 58, 2188 (1998).
69. V. C. Weiss, W. Schröer, and H. Weingärtner (unpublished).
70. See, e.g., S. C. Greer, Int. J. Thermophys. 9, 761 (1988). and references cited therein.
71. S. J. Kennedy and J. C. Wheeler, J. Chem. Phys. 78, 953 (1983).
72. J. C. Wheeler and P. Pfeuty, J. Chem. Phys. 74, 6415 (1981).
73. S. Greer, J. Phys. Chem. B 102, 5413 (1998).
74. J. Dudoivitz, K. F. Freed, and J. Douglas, J. Chem. Phys. 111, 7116 (1999).
75. G. Stell, G. N. Patey, and J. S. Høye, Adv. Chem. Phys. 48, 183 (1981).