Electrostatics and hydration in the theory of ion exchange
DOI:
https://doi.org/10.17308/sorpchrom.2026.26/13692Keywords:
ионный обмен; константа обмена; сорбционный потенциал; инверсия селективности; гидратация; набухаемость; коэффициент диффузииAbstract
The paper provides a brief overview of the problems of the modern theory of ion exchange. Their main disadvantages are related to the large number of empirical parameters used. The ion exchange model was further developed, based on expanded concepts of ion interactions, including Coulomb, dipole, and hydrogen bonds. The equation for the binding energy is reduced to a canonical form in the form of the basic Coulomb term, the product of the standard ion exchanger potential and the counterion charge. This representation, obtained by applying the Taylor series expansion, makes sense up to small contributions of factors depending on the characteristics of the environment. The paper provides quantitative relations for ion exchange efficiency coefficients, the parameters of which are the potentials and swelling of ion exchangers, the size, charge and nature of counterions. It is shown that the value of the selectivity coefficients, along with the size of the counterions (which follows from the electrostatic picture), is influenced by the ability of ions to hydrate, which is expressed in the so–called hydrate defect - the number of water molecules soaked by the ion during the transition to the ion exchanger phase. The phenomenon of ion exchanger selectivity inversion is discussed as a result of a certain combination of Coulomb interaction and hydration effects. It is shown that the contribution of the hydration factor to the ion exchange energy is determined by the hydrate number of the counterion and the ionexchanger swelling coefficient. A nonempirical model of the ion hydrate shell is proposed, taking into account the ion's ability to strengthen or destroy the local structure of the medium. The influence of the structural characteristics of crosslinked polymers on the volume of swollen ionexchanger is considered and a pattern is derived linking the swelling coefficient and the proportion of the crosslinking agent.
The theoretical conclusion is confirmed by experimental data for styrene ionexchangers. Equations for the ion exchange constants of strong ionexchangers are derived. Using the example of a highly acidic cation exchanger, the correspondence of calculated and experimental values in the description of chromatographic retention is shown. For the first time, using the developed model without using suitable parameters, the description of intradiffusion coefficients in an ion exchange system is considered, which is consistent with the results of well-known Soldano experiments and explains them.
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1. Nikol`skij B.P., Paramonova V.I. Uspexi ximii. 1939; 8: 1535-1567. (In Russ.)
2. Senyavin M.M., Rubinshtejn R.N., Venicianov E.V., Galkina N.K., Komarova I.V., Nika-shina V.A. Osnovy` rascheta i optimizacii ionoobmenny`x processov. M.: Nauka, 1972: 175 p. (In Russ.)
3. Helfferich F. Ion Exchange. NY: McGraw-Hill, 1962: 624 p.
4. Reihenberg D., Selectivity of Ion Exchange, In: Ion Exchange: A Series of Advances / Ed. by Marinsky J.A. NY: Buf-falo, 1966; 1: 423 p. Ch.2.
5. Rieman W., Walton H.F. Ion Ex-change in Analytical Chemistry. Oxford: Pergamon Press, 1970: 310 p.
6. Gregor H.P., Bregman J.I. J. Colloid Sci., 1951; 6: 323-347.
7. Marinsky J.A. Interpretation of Ion-Exchange Phenomena. In: Ion Exchange: A Series of Advances / Ed. by Marinsky J.A. NY: Buffalo, 1966. Vol. 1. 423 p. Ch.1.
8. Eisenman G. Biophys. J., Suppl., 1962; 2(2): 259-323.
9. Harris F.E., Rice S.A. J. Chem. Phys., 1956; 24: 1258.
10. Nicholls A., Honig B.,. J. Comp. Chem., 1991; 12(4): 435-445
11. Ohtaki H., Radnai T. Chem. Rev., 1993; 93: 1157-1204. Ch. II, C
12. Suresh S.J., Naik V.M. J. Chem. Phys., 2002; 116(10): 4212-4220
13. Bakker H.J. Chem. Rev., 2008; 108(4): 1456-1473
14. Onsager L. J. Am. Chem. Soc., 1936; 58: 1486-1493
15. Kirkwood J.G. J. Chem. Phys., 1939; 7: 911-919
16. Frohlich H. Theory of dielectrics; dielectric constant and dielectric loss, Ox-ford: Clarendon; 1949. 180 p.
17. Frenkel` Ya.I., Kineticheskaya te-oriya zhidkostej, L.: Nauka, 1975. 592 p. (In Russ.)
18. Shellman J.A. J. Chem. Phys., 1957; 26: 1225-1230
19. Hasted J.B., Ritson D.M., Collie C.H. J. Chem. Phys., 1948; 16: 1-21.
20. Hasted J.B., Chapman and Hall, 1973. 302 p.
21. Robinson R.A., Stokes R.H., Elec-trolyte Solutions. London: Butterworths Sci. Publ., 1959. 559 p.
22. Mehler E. L., Eichele G. Biochem-istry, 1984; 23: 3887-3891.
23. Hingerty B.E., Ritchie R.H., Ferrell T.L. Biopolymers, 1985; 24: 427-439.
24. Vasilyev V. J. Comput. Chem., 2002; 23: 1254-1265.
25. Mallik B., Masunov A., Lazaridis Th. J. Comp. Chem., 2002; 23: 1090-1099.
26. Hinton J.F., Amis E.S. Chem. Rev., 1971; 71: 627-674.
27. Zhou J., Lu X., Wang Y., Shi J. Fluid Phase Equilibria, 2002; 194–197: 257-270.
28. Marcus Y., Chem. Rev., 2009; 109(3): 1346-1370.
29. Chen H., Ruckenstein E. J. Phys. Chem. B, 2015; 119: 12671-12676.
30. Liu Ch., Min F., Liu L., Chen J. Chem. Phys. Let., 2019; 727: 31-37.
31. Marcus Y., Biophys. Chem., 1994; 5l: 111-127.
32. Baldanov M.M., Mokhosoev M.V., Tanganov B.B. Doklady AN SSSR, 1989; 308: 106-110.
33. Suresh S.J., Satish A.V., Choudhary A. J. Chem. Phys., 2006; 124: Art. 074506.
34. Smith J.D., Saykally R.J., Geissler P.L. J. Am. Chem. Soc., 2007; 129: 13847-13856.
35. Mancinelli R., Botti A., Bruni F., Ricci M.A., Soper A.K. Phys. Chem. Chem. Phys., 2007; 9: 2959-2967.
36. Freeman D.H., Seatchard G. J. Phys. Chem., 1965; 69(1): 70-74.
37. Babayan I. I., Tokmachev M. G., Ivanov A. V., Ferapontov N. B. J. Anal. Chem., 2019; 74(8): 834-838.
38. Kudukhova I.G., Rudakov O.B., Rudakova L.V., Ferapontov N.B. Sorbtsionnye i khromatograficheskie protsessy, 2010; 10(4): 589-594.
39. Schroeder P.V. Z. Phys. Chem., 1903; 45U(1): 75-117.
40. Davankov V.A., Pastukhov A.V. J. Phys. Chem. B, 2011; 115: 15188-15195.
41. Roldughin V.I., Karpenko-Jereb L.V., Colloid Journal, 2017; 79(4): 532-539.
42. Freger V. J. Phys. Chem. B, 2009; 113: 24-36.
43. Shaposhnik V.A. Sorbtsionnye i khromatograficheskie protsessy, 2020; 20(1): 48-53.
44. Khamizov R.Kh., Dolgonosov A.M. Sorbtsionnye i khromatograficheskie protsessy, 2020; 20(5): 641-646.
45. Shaposhnik V.A., Sorbtsionnye i khromatograficheskie protsessy, 2021; 21(2): 285-290.
46. Khamizov R.Kh. Sorbtsionnye i khromatograficheskie protsessy, 2021; 21(4): 600-605.
47. Dolgonosov A.M. Sorbtsionnye i khromatograficheskie protsessy, 2021; 21(4): 606-609.
48. Dolgonosov A.M., Garbar A.M., Zhurn. Fiz. Khimii, 1986; 60(1): 199-200.
49. Dolgonosov А.М., Senjavin М.М., Voloschik I.N. Ionnyj obmen I ionnaja khromatografija. М.: Nauka, 1993. 222 p.
50. Dolgonosov A.M., Khamizov R.Kh., Krachak A.N., Prudkovskiy A.G., Macroscopic model for multispecies ion-exchange kinetics, React. Funct. Polym., 1995; 28: 13-20.
51. Dolgonosov A.M., Khamizov R.Kh., Krachak А.N., Prudkovskij A.G., Kolotilina N.K. Sorbtsionnye i khromato-graficheskie protsessy, 2014; 14(5): 724-734
52. Dolgonosov A.M. Russ. J. Phys. Chem., 2022; 96(10): 2252-2258.
53. Dolgonosov A.M. Russ. J. Phys. Chem., 2022; 96(11): 2515-2522.
54. Dolgonosov A.M. Theor. Chem. Accounts, 2022; 141: Art. 47.
55. Dolgonosov A.M., Sorbtsionnye i khromatograficheskie protsessy, 2025; 25(1): 5-16.
56. Dolgonosov A.M. Sorbtsionnye i khromatograficheskie protsessy, 2024; 24(5): 662-671.
57. Dolgonosov A.M., Khamizov R.Kh. Sorbtsionnye i khromatograficheskie protsessy, 2025; 25(2): 140-145.
58. Landau L.D., Pitaevskii L.P., Lifshitz E.M. Electrodynamics of Continu-ous Media. Volume 8. Course of Theoreti-cal Physics, Butterworth-Heinemann, 1984: 460 p. Ch. II.
59. Frisch H.L., Sonnenblick E., Vys-sotsky V.A., Hammersley J.M. Rev., 1961; 124: 1021-1022.
60. Stauffer D., Aharony A., Introduc-tion to percolation theory, London: Taylor & Francis, 1992. 192 p.
61. Marcus Y., J. Chem. Soc. Faraday Trans., 1991; 87: 2995-2999.
62. Haynes W.M., Lide D.R. (Eds.). CRC Press, 2014. 2704 p.
63. Sidey V. Acta Cryst. B, 2016; 72: 626-633.
64. Freeman D.H. Buffalo, 1966; 1: 423 p. Ch.6.
65. Dolgonosov A.M., Khamizov R.Kh., Kolotilina N.K. J. Anal. Chem., 2019; 74(4): 382-392.
66. Soldano B.A. Ann NY Acad Sci. 1953 Nov 11; 57(3): 116-124.
67. Dean J.A. (Ed.) McGraw-Hill, 1999. 1424 p.
