Adsorption of large ions from an electrolyte solution: a modified Poisson–Boltzmann equation

Abstract The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson–Boltzmann equation that takes into account the volume excluded by the ions in addition to the electrostatic interactions is presented. In a formal lattice gas formalism the modified Poisson–Boltzmann equation can be obtained from a mean-field approximation of the partition function. In an alternative phenomenological approach, the same equation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of steric repulsion, a simple case of a single, highly charged, flat surface is discussed. This situation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is expressed in terms of the surface charge density and the size of the ions. It is shown that when these effects are important a saturated layer is formed near the surface. A modified Grahame equation relating the ion concentration at the surface to the surface charge density is obtained.

[1]  R. Podgornik,et al.  Inhomogeneous coulomb fluid. A functional integral approach , 1988 .

[2]  S. Marčelja,et al.  A theoretical and experimental study of forces between charged mica surfaces in aqueous CaCl2 solutions , 1990 .

[3]  M. Sastry,et al.  Adsorption of multivalent ions on charged Langmuir monolayers , 1997 .

[4]  Olivares,et al.  Violation of the electroneutrality condition in confined charged fluids. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  R. J. Hunter.  Foundations of Colloid Science , 1987 .

[6]  Netz,et al.  Complexation Behavior of Polyampholytes and Charged Objects. , 1998, Macromolecules.

[7]  P. Chaikin,et al.  Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory , 1984 .

[8]  M. Eigen,et al.  The Thermodynamics of Electrolytes at Higher Concentration , 1954 .

[9]  李幼升,et al.  Ph , 1989 .

[10]  S. Marčelja,et al.  Double-layer interaction in the primitive model and the corresponding Poisson-Boltzmann description , 1986 .

[11]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[12]  G. S. Manning.  Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. III. An Analysis Based on the Mayer Ionic Solution Theory , 1969 .

[13]  E. Verwey,et al.  Theory of the stability of lyophobic colloids. , 1955, The Journal of physical and colloid chemistry.

[14]  B. Ninham,et al.  Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. I. Counterions only , 1988 .

[15]  Nir Ben-Tal,et al.  Statistical mechanics of a Coulomb gas with finite size particles: A lattice field theory approach , 1995 .

[16]  Henri Orland,et al.  Quantum Many-Particle Systems , 1988 .

[17]  R. Bishop,et al.  Quantum many-particle systems , 1990 .

[18]  M. Fisher.  The story of coulombic critiality , 1994 .

[19]  S. Marčelja,et al.  Charge reversal seen in electrical double layer interaction of surfaces immersed in 2:1 calcium electrolyte , 1993 .

[20]  A. Kornyshev,et al.  Conductivity and space charge phenomena in solid electrolytes with one mobile charge carrier species, a review with original material , 1981 .

[21]  R. Podgornik.  An analytic treatment of the first-order correction to the Poisson-Boltzmann interaction free energy in the case of counterion-only Coulomb fluid , 1990 .

[22]  S. Lamperski,et al.  A modified Poisson-Boltzmann analysis of the solvent primitive model electrical double layer , 1996 .

[23]  S. Yariv,et al.  Physical Chemistry of Surfaces , 1979 .

[24]  David Andelman,et al.  Electrostatic Properties of Membranes: The Poisson-Boltzmann Theory , 1995 .

[25]  Hydration interactions: aqueous solvent effects in electric double layers , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  S. Marčelja,et al.  Double layer interactions in mono‐ and divalent electrolytes: A comparison of the anisotropic HNC theory and Monte Carlo simulations , 1992 .

[27]  Christian Holm,et al.  Fraction of Condensed Counterions around a Charged Rod: Comparison of Poisson−Boltzmann Theory and Computer Simulations , 2000 .

[28]  D. Henderson.  RECENT PROGRESS IN THE THEORY OF THE ELECTRIC DOUBLE LAYER , 1983 .

[29]  Gerald S. Manning,et al.  Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties , 1969 .

[30]  B. Ninham,et al.  Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. II. Symmetric electrolyte , 1988 .

[31]  D. Deamer,et al.  Electrical double layers at the oil/water interface. , 1996, Progress in surface science.

[32]  Rob D. Coalson,et al.  Systematic ionic screening theory of macroions , 1992 .

[33]  H. Orland,et al.  Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation , 1997, cond-mat/9803258.

[34]  F. W. Wiegel,et al.  Introduction to path-integral methods in physics and polymer science , 1986 .

[35]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[36]  Wigner-Seitz model of charged lamellar colloidal dispersions , 1997, cond-mat/9703193.

[37]  C. Tanford.  Macromolecules , 1994, Nature.