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Ionic Soft Matter: Modern Trends in Theory and Applications pp 199–231Cite as

Macroions in Solution

Theory, experiment, and computer simulations

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 206))

Abstract

In this chapter we review models and theories suitable for studying polyelectrolytes in solution. The theories were applied to various problems: a) the first is the catalytic effect on the reaction between small ions of the same charge sign, caused by addition of a polyelectrolyte to an electrolyte solution. In the next example b) we studied the stability of polyelectrolyte solutions. For highly charged systems, and/or in presence of multivalent counterions, computer simulations and recent experimental data predict clustering of macroions. The new computer simulation data support the assumption that a partial neutralization of macroions is the first step in the process of macroion clustering. In the third example c) we considered low-charge polyelectrolytes where the effects of solvent seemed to be important. We present results for a new model of a polyelectrolyte solution with the chain-like polyions where the solvent molecules, approximated as two fused charged hard spheres, are explicitly included in the calculation. This model yields osmotic pressure results in good qualitative agreement with experiment. In the last example d) we consider the Donnan membrane equilibrium in protein solutions. The theory is used to analyze experimental data for the Donnan pressure in solutions of various proteins.

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References

  1. Dautzenberg, H., Jaeger, W., Kötz, J., Philipp, B., Seidel, Ch., and Steherbina, D. (1994). Polyelectrolytes: Formation, Characterization and Application. Germany, Munich: Hanser Publ.

    Google Scholar 

  2. Frisch, K.C., Klempner, D., and Patsis, A.V. (1976). Polyelectrolytes. CT.

    Google Scholar 

  3. Hara, M. (1993). Polyelectrolytes: Science and Technology. New York: Marcel Dekker Inc.

    Google Scholar 

  4. Hunkeler, D., and Wandrey, C. Polyelectrolytes: Research, development, and applications. Chimia, 2001, 55, No. 3, p. 223–227.

    Google Scholar 

  5. Manning, G.S., and Ray, J. Counterion condensation revisited. Journal of Biomolecular Structure & Dynamics, 1998, 16, No. 2, p. 461–476.

    Google Scholar 

  6. Radeva, T. (2001). Physical Chemistry of Polyelectrolytes. New York: Marcel Dekker Inc.

    Google Scholar 

  7. Schmitz, K.S. (1993). Macroions in Solution and Colloidal Suspension. New York: VCH.

    Google Scholar 

  8. Bhuiyan, L.B., Vlachy, V., and Outhwaite, C.W. Understanding polyelectrolyte solutions: macroion condensation with emphasis on the presence of neutral co-solutes. International Reviews in Physical Chemistry, 2002, 21, No. 1, p. 1–36.

    Article  ADS  Google Scholar 

  9. Dolar, D. (1966). Polyelectrolytes, Riedel D. Dordrecht.

    Google Scholar 

  10. Vlachy, V. Ionic effects beyond Poisson-Boltzmann theory. Annual Review of Physical Chemistry, 1999, 50, p. 145–165.

    Article  ADS  Google Scholar 

  11. Bratko, D., and Vlachy, V. Distribution of counterions in the double-layer around a cylindrical polyion. Chemical Physics Letters, 1982, 90, No. 6, p. 434–438.

    Article  ADS  Google Scholar 

  12. Wandrey, C., Hunkeler, D., Wendler, U., and Jaeger, W. Counterion activity of highly charged strong polyelectrolytes. Macromolecules, 2000, 33, No. 19, p. 7136–7143.

    Article  ADS  Google Scholar 

  13. Špan, J., Bratko, D., Dolar, D., and Feguš, M. Electrical transport in polystyrenesulfonate solutions. Polymer Bulletin, 1983, 9, No. 1–3, p. 33–39.

    Google Scholar 

  14. Drifford, M., Dalbiez, J.P., Delsanti, M., and Belloni, L. Structure and dynamics of polyelectrolyte solutions with multivalent salts. Berichte der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics, 1996, 100, No. 6, p. 829–835.

    Google Scholar 

  15. Gröhn, F., and Antonietti, M. Intermolecular structure of spherical polyelectrolyte microgels in salt-free solution. 1. quantification of the attraction between equally charged polyelectrolytes. Macromolecules, 2000, 33, No. 16, p. 5938–5949.

    Article  ADS  Google Scholar 

  16. Vesnaver, G., Kranjc, Z., Pohar, C., and Škerjanc, J. Free enthalpies, enthalpies, and entropies of dilution of aqueous-solutions of alkaline-earth poly(styrenesulfonates) at different temperatures. Journal of Physical Chemistry, 1987, 91, No. 14, p. 3845–3848.

    Article  Google Scholar 

  17. Arh, K., Pohar, C., and Vlachy, V. Osmotic properties of aqueous ionene solutions. Journal of Physical Chemistry B, 2002, 106, No. 38, p. 9967–9973.

    Article  Google Scholar 

  18. Vesnaver, G., Rudež, M., Pohar, C., and Škerjanc, J. Effect of temperature on the enthalpy of dilution of strong poly-electrolyte solutions. Journal of Physical Chemistry, 1984, 88, No. 11, p. 2411–2414.

    Article  Google Scholar 

  19. Arh, K., and Pohar, C. Enthalpies of dilution of aqueous ionene solutions. Acta Chimica Slovenica, 2001, 48, No. 3, p. 385–394.

    Google Scholar 

  20. Keller, M., Lichtenthaler, R.N., and Heintz, A. Enthalpies of dilution of some polycation solutions and exchange enthalpies of polycation counterions. Berichte der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics, 1996, 100, No. 6, p. 776–779.

    Google Scholar 

  21. Wall, T.F., and Berkowitz, J. Numerical solution to the Poisson-Boltzmann equation for spherical polyelectrolyte molecules. Journal of Chemical Physics, 1957, 26, p. 114–122.

    Article  ADS  Google Scholar 

  22. Fuoss, R.M., Katchalsky, A., and Lifson, S. The potential of an infinite rod-like molecule and the distribution of the counter ions. Proceedings of the National Academy of Sciences of the United States of America, 1951, 37, p. 579–589.

    Article  ADS  MATH  Google Scholar 

  23. Bratko, D., and Dolar, D. Ellipsoidal model of poly-electrolyte solutions. Journal of Chemical Physics, 1984, 80, No. 11, p. 5782–5789.

    Article  ADS  Google Scholar 

  24. Bratko, D., and Vlachy, V. An application of the modified Poisson-Boltzmann equation in studies of osmotic properties of micellar solutions. Colloid and Polymer Science, 1985, 263, No. 5, p. 417–419.

    Article  Google Scholar 

  25. Linse, P., Gunnarson, G., and Jönsson, B. Electrostatic interactions in micellar solutions-a comparison between Monte-Carlo simulations and solutions of the Poisson-Boltzmann equation. Journal of Physical Chemistry, 1982, 86, No. 3, p. 413–421.

    Article  Google Scholar 

  26. Rebolj, N., Kristl, J., Kalyuzhnyi, Yu.V., and Vlachy, V. Structure and thermodynamics of micellar solutions in isotropic and cell models. Langmuir, 1997, 13, No. 14, p. 3646–3651.

    Article  Google Scholar 

  27. Wennerström, H., Jönsson, B., and Linse, P. The cell model for poly-electrolyte systems-exact statistical mechanical relations, Monte-Carlo simulations, and the Poisson-Boltzmann approximation. Journal of Chemical Physics, 1982, 76, No. 9, p. 4665–4670.

    Article  ADS  Google Scholar 

  28. Deserno, M., and Holm, C. Theory and simulations of rigid polyelectrolytes. Molecular Physics, 2002, 100, No. 18, p. 2941–2956.

    Article  ADS  Google Scholar 

  29. Nishio, T., and Minakata, A. Effects of ion size and valence on ion distribution in mixed counterion systems of a rodlike polyelectrolyte solution. 2. mixed-valence counterion systems. Journal of Physical Chemistry B, 2003, 107, No. 32, p. 8140–8145.

    Article  Google Scholar 

  30. Bell, G.M., and Levine, S. (1966). Chemical Physics of Ionic Solutions, p. 409–461. New York: Wiley.

    Google Scholar 

  31. Das, T., Bratko, D., Bhuiyan, L.B., and Outhwaite, C.W. Polyelectrolyte solutions containing mixed valency ions in the cell model: A simulation and modified Poisson-Boltzmann study. Journal of Chemical Physics, 1997, 107, No. 21, p. 9197–9207.

    Article  ADS  Google Scholar 

  32. Hribar, B., Krienke, H., Kalyuzhnyi, Yu.V., and Vlachy, V. Dilute solutions of highly asymmetrical electrolytes in the primitive model approximation. Journal of Molecular Liquids, 1997, 73, No. 4, p. 277–289.

    Article  Google Scholar 

  33. Linse, P. Highly asymmetric electrolyte-comparison between one-component and 2-component models at different levels of approximations. Journal of Chemical Physics, 1991, 94, No. 5, p. 3817–3828.

    Article  ADS  Google Scholar 

  34. Reščič, J., Vlachy, V., Outhwaite, C.W., Bhuiyan, L.B., and Mukherjee, A.K. A Monte Carlo simulation and symmetric Poisson-Boltzmann study of a four-component electrolyte mixture. Journal of Chemical Physics, 1999, 111, No. 12, p. 5514–5521.

    Article  ADS  Google Scholar 

  35. Liu, Y.C., Chen, S.H., and Itri, R. Ion correlations and counter-ion condensation in ionic micellar solutions. Journal of Physics-Condensed Matter, 1996, 8, No. 25A, p. A169–A187.

    Article  ADS  Google Scholar 

  36. Belloni, L. Electrostatic interactions in colloidal solutions — comparison between primitive and one-component models. Journal of Chemical Physics, 1986, 85, No. 1, p. 519–526.

    Article  ADS  Google Scholar 

  37. Vlachy, V., and Prausnitz, J.M. Donnan equilibrium-hypernetted-chain study of one-component and multicomponent models for aqueous polyelectrolyte solutions. Journal of Physical Chemistry, 1992, 96, No. 15, p. 6465–6469.

    Article  Google Scholar 

  38. Derjaguin, B.V., and Landau, L. Theory of stability of highly charged lyophobic sols and adhesion of highly charged particles in solutions of electrolytes. Acta Phys. Chem. USSR, 1941, 14, p. 633–662.

    Google Scholar 

  39. Verwey, E.J.W., and Overbeek, J.Th.G. (1948). Theory of the Stability of Lyophobic Colloids. New York: Elsevier.

    Google Scholar 

  40. Hayter, J.B., and Penfold, J. An analytic structure factor for macroion solutions. Molecular Physics, 1981, 42, No. 1, p. 109–118.

    Article  ADS  Google Scholar 

  41. Kalyuzhnyi, Yu.V., Reščič, J., and Vlachy, V. Analysis of osmotic pressure data for aqueous protein solutions via a one-component model. Acta Chimica Slovenica, 1998, 45, No. 2, p. 194–208.

    Google Scholar 

  42. Jiang, J.W., Blum, L., Bernard, O., and Prausnitz, J.M. Thermodynamic properties and phase equilibria of charged hard sphere chain model for polyelectrolyte solutions. Molecular Physics, 2001, 99, p. 1121–1128.

    Article  ADS  Google Scholar 

  43. Jiang, J.W., Liu, H.L., Hu, Y., and Prausnitz, J.M. A molecular-thermodynamic model for polyelectrolyte solutions. Journal of Chemical Physics, 1998, 108, No. 2, p. 780–784.

    Article  ADS  Google Scholar 

  44. Stevens, M.J., and Kremer, K. The nature of flexible linear polyelectrolytes in salt-free solution-a molecular-dynamics study. Journal of Chemical Physics, 1995, 103, No. 4, p. 1669–1690.

    Article  ADS  Google Scholar 

  45. Collins, K. D. Charge density-dependent strength of hydration and biological structure. Biophysical Journal, 1997, 72, No. 1, p. 65–76.

    ADS  Google Scholar 

  46. Bernard, O., and Blum, L. Thermodynamics of a model for flexible polyelectrolytes in the binding mean spherical approximation. Journal of Chemical Physics, 2000, 112, No. 16, p. 7227–7237.

    Article  ADS  Google Scholar 

  47. Blum, L., Kalyuzhnyi, Yu.V., Bernard, O., and Herrera-Pacheco, J.N. Sticky charged spheres in the mean-spherical approximation: A model for colloids and polyelectrolytes. Journal of Physics — Condensed Matter, 1996, 8, No. 25A, p. A143–A167.

    Article  ADS  Google Scholar 

  48. Kalyuzhnyi, Yu.V. Thermodynamics of the polymer mean-spherical ideal chain approximation for a fluid of linear chain molecules. Molecular Physics, 1998, 94, p. 735–742.

    Article  ADS  Google Scholar 

  49. Kalyuzhnyi, Yu.V., and Cummings, P.T. Multicomponent mixture of charged hard-sphere chain molecules in the polymer mean-spherical approximation. Journal of Chemical Physics, 2001, 115, p. 540–551.

    Article  ADS  Google Scholar 

  50. Kalyuzhnyi, Yu.V., and Cummings, P.T. Multicomponent mixture of charged hard-sphere chain molecules in the polymer mean-spherical approximation (vol 115, pg 540, 2001). Journal of Chemical Physics, 2002, 116, p. 8637–8637.

    Article  ADS  Google Scholar 

  51. Kalyuzhnyi, Yu.V., and Stell, G. Solution of the polymer msa for the polymerizing primitive model of electrolytes. Chemical Physics Letters, 1995, 240, p. 157–164.

    Article  ADS  Google Scholar 

  52. Protsykevytch, I.A., Kalyuzhnyi, Yu.V., Holovko, M.F., and Blum, L. Solution of the polymer mean spherical approximation for the totally flexible sticky two-point electrolyte model. Journal of Molecular Physics, 1997, 73, No. 4, p. 1–20.

    Google Scholar 

  53. von Solms, N., and Chiew, Y.C. Analytical integral equation theory for a restricted primitive model of polyelectrolytes and counterions within the mean spherical approximation. i. thermodynamic properties. Journal of Chemical Physics, 1999, 111, No. 10, p. 4839–4850.

    Article  ADS  Google Scholar 

  54. von Solms, N., and Chiew, Y.C. Analytical integral equation theory for a restricted primitive model of polyelectrolytes and counterions within the mean spherical approximation. ii. radial distribution functions. Journal of Chemical Physics, 2003, 118, No. 9, p. 4321–4330.

    Article  ADS  Google Scholar 

  55. Wertheim, M. S. Fluids with highly directional attractive forces. 3. multiple attraction sites. Journal of Statistical Physics, 1986, 42, No. 3–4, p. 459–476.

    Article  MathSciNet  ADS  Google Scholar 

  56. Liao, Q., Dobrynin, A.V., and Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions: Osmotic coefficient and counterion condensation. Macromolecules, 2003, 36, No. 9, p. 3399–3410.

    Article  ADS  Google Scholar 

  57. Zhang, B., Yu, D.H., Liu, H.L., and Hu, Y. Osmotic coefficients of polyelectrolyte solutions, measurements and correlation. Polymer, 2002, 43, No. 10, p. 2975–2980.

    Article  Google Scholar 

  58. Dymitrowska, M., and Belloni, L. Integral equation theory of flexible polyelectrolytes. ii. primitive model approach. Journal of Chemical Physics, 1999, 111, No. 14, p. 6633–6642.

    Article  ADS  Google Scholar 

  59. Hofmann, T., Winkler, R.G., and Reineker, P. Integral equation theory approach to rod-like polyelectrolytes: Counterion condensation. Journal of Chemical Physics, 2001, 114, No. 22, p. 10181–10188.

    Article  ADS  Google Scholar 

  60. Friedman, H. L. (1985). A Course on Statistical Mechanics. Prentice-Hall: Englewood Cliffs.

    Google Scholar 

  61. Rasaiah, J. C. (1988). The Liquid States and its Electrical Properties. New York: Plenum.

    Google Scholar 

  62. Vlachy, V., Ichiye, T., and Haymet, A.D.J. Symmetrical associating electrolytes — gcmc simulations and integral-equation theory. Journal of the American Chemical Society, 1991, 113, No. 4, p. 1077–1082.

    Article  Google Scholar 

  63. Belloni, L. A hypernetted chain study of highly asymmetrical poly-electrolytes. Chemical Physics, 1985, 99, No. 1, p. 43–54.

    Article  ADS  Google Scholar 

  64. Vlachy, V., Marshall, C.H., and Haymet, A.D.J. Highly asymmetric electrolytes — a comparison of Monte-Carlo simulations and the HNC integral-equation. Journal of the American Chemical Society, 1989, 111, No. 12, p. 4160–4166.

    Article  Google Scholar 

  65. Blum, L. (1980). Theoretical Chemistry; Advances and Perspectives. New York: Academic Press.

    Google Scholar 

  66. Blum, L., and Hoye, J.S. Mean spherical model for asymmetric electrolytes.2. Thermodynamic properties and pair correlation-function. Journal of Physical Chemistry, 1977, 81, No. 13, p. 1311–1317.

    Article  Google Scholar 

  67. Harvey, A.H., Copeman, T.W., and Prausnitz, J.M. Explicit approximations to the mean spherical approximation for electrolyte systems with unequal ion sizes. Journal of Physical Chemistry, 1988, 92, No. 22, p. 6432–6436.

    Article  Google Scholar 

  68. Sanchez-Castro, C., and Blum, L. Explicit approximation for the unrestricted mean spherical approximation for ionic-solutions. Journal of Physical Chemistry, 1989, 93, No. 21, p. 7478–7482.

    Article  Google Scholar 

  69. Simonin, J.P., Bernard, O., and Blum, L. Real ionic solutions in the mean spherical approximation. 3. osmotic and activity coefficients for associating electrolytes in the primitive model. Journal of Physical Chemistry B, 1998, 102, No. 22, p. 4411–4417.

    Article  Google Scholar 

  70. Kalyuzhnyi, Yu.V., and Vlachy, V. Integral-equation theory for highly asymmetric electrolyte-solutions. Chemical Physics Letters, 1993, 215, No. 5, p. 518–522.

    Article  ADS  Google Scholar 

  71. Kalyuzhnyi, Yu.V., Vlachy, V., Holovko, M.F., and Stell, G. Multidensity integralequation theory for highly asymmetric electrolyte-solutions. Journal of Chemical Physics, 1995, 102, No. 14, p. 5770–5780.

    Article  ADS  Google Scholar 

  72. Holovko, M.F., and Kalyuzhnyi, Yu.V. On the effects of association in the statisticaltheory of ionic systems-analytic solution of the PY-MSA version of theWertheim theory. Molecular Physics, 1991, 73, No. 5, p. 1145–1157.

    Article  ADS  Google Scholar 

  73. Kalyuzhnyi, Yu.V., Holovko, M.F., and Vlachy, V. Highly asymmetric electrolytes in the associative mean-spherical approximation. Journal of Statistical Physics, 2000, 100, No. 1–2, p. 243–265.

    Article  MATH  Google Scholar 

  74. Kalyuzhnyi, Yu.V., Blum, L., Holovko, M.F., and Protsykevytch, I.A. Primitive model for highly asymmetric electrolytes. associative mean spherical approximation. Physica A, 1997, 236, No. 1–2, p. 85–96.

    Article  ADS  Google Scholar 

  75. Kalyuzhnyi, Yu.V., and Cummings, P.T. Solution of the polymer Percus-Yevick approximation for the multicomponent totally flexible sticky 2-point model of polymerizing fluid. Journal of Chemical Physics, 1995, 103, No. 8, p. 3265–3267.

    Article  ADS  Google Scholar 

  76. Baumgartner, E., and Fernandez-Prini, R. (1976). Polyelectrolytes, p. 1–33. Westport: Technomic, CT.

    Google Scholar 

  77. Morawetz, H. Chemical reaction rates reflecting physical properties of polymer solutions. Accounts of Chemical Research, 1970, 3, No. 10, p. 354–360.

    Article  Google Scholar 

  78. Morawetz, H. Revisiting some phenomena in polyelectrolyte solutions. Journal of Polymer Science part B-Polymer Physics, 2002, 40, No. 11, p. 1080–1086.

    Article  ADS  Google Scholar 

  79. Morawetz, H., and Shaffer, J.A. Characterization of counterion distribution in polyelectrolyte solutions. ii. the effect of the distribution of electrostatic potential on the solvolysis of cationic esters in polymeric acid solution. Journal of Physical Chemistry, 1963, 67, p. 1293–1297.

    Google Scholar 

  80. Morawetz, H., and Vogel, B. Catalysis of ionic reactions by polyelectrolytes. reaction of pentaamminechlorocobalt(iii) ion and pentaamminebromocobalt(iii) ion with mercuric ion in poly(sulfonic acid) solution. Journal of the American Chemical Society, 1969, 91, No. 3, p. 563–568.

    Article  Google Scholar 

  81. Rodenas, E., Dolcet, C., and Valiente, M. Simulations of micelle-catalyzed bimolecular reaction of hydroxide ion with a cationic substrate using the nonlinearized Poisson-Boltzmann equation. Journal of Physical Chemistry, 1990, 94, No. 4, p. 1472–1477.

    Article  Google Scholar 

  82. Wensel, T.G., Meares, C.F., Vlachy, V., and Matthew, J.B. Distribution of ions around DNA, probed by energy-transfer. Proceedings of the National Academy of Sciences of the United States of America, 1986, 83, No. 10, p. 3267–3271.

    Article  ADS  Google Scholar 

  83. Tapia, M.J., and Burrows, H.D. Cation polyelectrolyte interactions in aqueous sodium poly(vinyl sulfonate) as seen by Ce3+ to Tb3+ energy transfer. Langmuir, 2002, 18, No. 5, p. 1872–1876.

    Article  Google Scholar 

  84. Tapia, M.J., Burrows, H.D., Azenha, M.E.D.G., Miguel, M.G., Pais, A.A.C.C., and Sarraguca, J.M.G. Cation association with sodium dodecyl sulfate micelles as seen by lanthanide luminescence. Journal of Physical Chemistry B, 2002, 106, No. 27, p. 6966–6972.

    Article  Google Scholar 

  85. Keizer, J. Theory of rapid biomolecular reactions in solution and membranes. Accounts of Chemical Research, 1985, 18, No. 8, p. 235–241.

    Article  Google Scholar 

  86. Reščič, J., and Vlachy, V. (1994). Ion-ion correlation in the electrical double layer around a cylindrical polyion, pages 24–33. Washington: ACS, DC.

    Google Scholar 

  87. Reščič, J., Vlachy, V., Bhuiyan, B.L., and Outhwaite, C.W. Theoretical study of catalytic effects in micellar solutions. submitted to Langmuir, 2004.

    Google Scholar 

  88. Ise, N. When does like like like? microscopic inhomogeneity in homogeneous ionic systems. Proceedings of the Japan Academy Series B-Physical and Biological Sciences, 2002, 78, No. 6, p. 129–137.

    Article  Google Scholar 

  89. Ito, K., Yoshida, H., and Ise, N. Void structure in colloidal dispersions. Science, 1994, 263(5143), No. 4, p. 66–68.

    ADS  Google Scholar 

  90. Larsen, A.E., and Grier, D.G. Like-charge attractions in metastable colloidal crystallites. Nature, 1997, 385, No. 6613, p. 230–233.

    Article  ADS  Google Scholar 

  91. Matsuoka, H., Harada, T., Kago, K., and Yamaoka, H. Exact evaluation of the salt concentration dependence of interparticle distance in colloidal crystals by ultra-small-angle x-ray scattering.2. the universality of the maximum in the interparticle distance salt concentration relationship. Langmuir, 1996, 12, No. 23, p. 5588–5594.

    Article  Google Scholar 

  92. Ohshima, A., Konishi, T., Yamanaka, J., and Ise, N. “Ordered” structure in ionic dilute solutions: Dendrimers with univalent and bivalent counterions. Physical Review E, 2001, 6405, No. 5, p. 051808.

    Article  ADS  Google Scholar 

  93. Zhang, B., Liu, H.L., and Hu, Y. Attraction between like-charge particles. Progress in Chemistry, 2001, 13, No. 1, p. 1–9.

    Google Scholar 

  94. Quesada-Perez, M., Gonzalez-Tovar, E., Martin-Molina, A., Lozada-Cassou, M., and Hidalgo-Alvarez, R. Overcharging in colloids: Beyond the Poisson-Boltzmann approach. ChemPhysChem, 2003, 4, No. 3, p. 235–248.

    Google Scholar 

  95. Spalla, O. Long-range attraction between surfaces: existence and amplitude? Current Opinion in Colloid & Interface Science, 2000, 5, No. 1–2, p. 5–12.

    Article  Google Scholar 

  96. Hribar, B., and Vlachy, V. Evidence of electrostatic attraction between equally charged macroions induced by divalent counterions. Journal of Physical chemistry B, 1997, 101, No. 18, p. 3457–3459.

    Article  Google Scholar 

  97. Hribar, B., and Vlachy, V. Clustering of macroions in solutions of highly asymmetric electrolytes. Biophysical Journal, 2000, 78, No. 2, p. 694–698.

    Article  ADS  Google Scholar 

  98. Hribar, B., and Vlachy, V. Macroion-macroion correlations in presence of divalent counterions. Journal of Physical chemistry B, 2000, 104, No. 17, p. 4218–4221.

    Article  Google Scholar 

  99. Hribar, B., and Vlachy, V. Macroion-macroion correlations in the presence of divalent counterions. effects of a simple electrolyte. Acta Chimica Slovenica, 2000, 47, No. 2, p. 123–131.

    Google Scholar 

  100. Hribar, B., and Vlachy, V. Properties of polyelectrolyte solutions as determined by the charge of counterions. Revista de la Sociedad Quimica de Mexico, 2000, 44, p. 11–15.

    Google Scholar 

  101. Hribar, B., and Vlachy, V. Monte Carlo study of micellar solutions with a mixture of mono-and trivalent counterions. Langmuir, 2001, 17, No. 6, p. 2043–2046.

    Article  Google Scholar 

  102. Spohr, E., Hribar, B., and Vlachy, V. Mechanism of macroion-macroion clustering induced by the presence of trivalent counterions. Journal of Physical chemistry B, 2002, 106, No. 9, p. 2343–2348.

    Google Scholar 

  103. Spohr, E., Hribar, B., and Vlachy, V. unpublished results, 2004.

    Google Scholar 

  104. Linse, P. Structure, phase stability, and thermodynamics in charged colloidal solutions. Journal of Chemical Physics, 2000, 113, No. 10, p. 4359–4373.

    Article  ADS  Google Scholar 

  105. Reščič, J., and Linse, P. Gas-liquid phase separation in charged colloidal systems. Journal of Chemical Physics, 2001, 114, No. 22, p. 10131–10136.

    Article  ADS  Google Scholar 

  106. Allen, M.P., and Tildesley, D.J. (1989). Computer Simulation of Liquids. Oxford: Clarendon Press.

    Google Scholar 

  107. Blaul, J., Wittemann, M., Ballauff, M., and Rehahn, M. Osmotic coefficient of a synthetic rodlike polyelectrolyte in salt-free solution as a test of the Poisson-Boltzmann cell model. Journal of Physical Chemistry B, 2000, 104, No. 30, p. 7077–7081.

    Article  Google Scholar 

  108. Deserno, M., Holm, C., Blaul, J., Ballauff, M., and Rehahn, M. The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment. European Physical Journal E, 2001, 5, No. 1, p. 97–103.

    Article  ADS  Google Scholar 

  109. George, A., and Wilson, W.W. Predicting protein crystallization from a dilutesolution property. Acta Crystallographica Section D-Biological Crystallography, 1994, 50, p. 361–365.

    Article  Google Scholar 

  110. Haynes, C.A., Tamura, K., Korfer, H. R., Blanch, H. W., and Prausnitz, J.M. Thermodynamic properties of aqueous alpha-chymotrypsin solutions from membrane osmometry measurements. Journal of Physical Chemistry, 1992, 96, No. 2, p. 905–912.

    Article  Google Scholar 

  111. Reščič, J., Vlachy, V., Jamnik, A., and Glatter, O. Osmotic pressure, small-angle x-ray, and dynamic light scattering studies of human serum albumin in aqueous solutions. Journal of Colloid and Interface Science, 2001, 239, No. 1, p. 49–57.

    Article  Google Scholar 

  112. Vilker, V.L., Colton, C.K., and Smith, K.A. The osmotic-pressure of concentrated protein solutions-effect of concentration and ph in saline solutions of bovine serum-albumin. Journal of Colloid and Interface Science, 1981, 79, No. 2, p. 548–566.

    Article  Google Scholar 

  113. Allahyarov, E., Lowen, H., Hansen, J.P., and Louis, A.A. Nonmonotonic variation with salt concentration of the second virial coefficient in protein solutions. Phys. Rev. E, 2003, 67, No. 5, p. 051404.

    Article  ADS  Google Scholar 

  114. Haas, C., Drenth, J., and Wilson, W.W. Relation between the solubility of proteins in aqueous solutions and the second virial coefficient of the solution. Journal of Physical Chemistry B, 1999, 103, No. 14, p. 2808–2811.

    Article  Google Scholar 

  115. Kalyuzhnyi, Yu.V., and Vlachy, V. Study of a model polyelectrolyte solution with directional attractive forces between the macroions. Journal of Chemical Physics, 1998, 108, No. 18, p. 7870–7875.

    Article  ADS  Google Scholar 

  116. Jimenez-Angeles, F., and Lozada-Cassou, M. Simple model for semipermeable membrane: Donnan equilibrium. Journal of Physical Chemistry B, 2004, 108, No. 5, p. 1719–1730.

    Article  Google Scholar 

  117. Piazza, R. Protein interactions and association: an open challenge for colloid science. Current Opinion in Colloid & Interface Science, 2004, 8, No. 6, p. 515–522.

    Article  Google Scholar 

  118. Vlachy, V., Hribar-Lee, B., Kalyuzhnyi, Yu.V., and Dill, K.A. Short-range interactions: from simple ions to polyelectrolyte solutions. Current Opinion in Colloid & Interface Science, 2004.

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000, Ljubljana, Slovenia

    V. Vlachy, B. Hribar Lee & J. Reščič

  2. Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011, Lviv, Ukraine

    Yu. V. Kalyuzhnyi

Authors
  1. V. Vlachy
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  2. B. Hribar Lee
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  3. J. Reščič
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  4. Yu. V. Kalyuzhnyi
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Editors and Affiliations

  1. Brigham Young University, Provo, USA

    Douglas Henderson  & Andrij Trokhymchuk  & 

  2. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    Myroslav Holovko  & Andrij Trokhymchuk  & 

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Vlachy, V., Lee, B.H., Reščič, J., Kalyuzhnyi, Y.V. (2005). Macroions in Solution. In: Henderson, D., Holovko, M., Trokhymchuk, A. (eds) Ionic Soft Matter: Modern Trends in Theory and Applications. NATO Science Series II: Mathematics, Physics and Chemistry, vol 206. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3659-0_8

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