Electrolytes and the Electric Double Layer

II. Analysis of the double layer 22 A. Spherical solutes 23 1. Double layer moments 23 2. Asymptotic analysis 24 B. Isolated planar solutes 26 1. Wall-ion Ornstein-Zernike equation 26 2. Asymptotics of the isolated planar double layer 28 3. Algebraic correlations along a wall 30 C. Analysis of interacting charged walls 33 1. Wall-wall Ornstein-Zernike equation 33 2. The Derjaguin approximation 34 3. Asymptotics of overlapping planar double layers 35 D. Other solute geometries 36 1. Cylinders 36 2. Membranes and pores 40 3. Dumb-bells 42

[1]  Mihaly Mezei,et al.  The Potentials of Mean Force of Sodium Chloride and Sodium Dimethylphosphate in Water : An Application of Adaptive Umbrella Sampling , 1995 .

[2]  M. Record,et al.  Polyelectrolyte Theories and their Applications to DNA , 1982 .

[3]  Derek Y. C. Chan,et al.  Interaction free energy between identical spherical colloidal particles : the linearized Poisson-Boltzmann theory , 1993 .

[4]  B. Ninham,et al.  Erratum: Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. I. Counterions only [J. Chem. Phys. 88, 4987 (1988)] , 1990 .

[5]  B. Jancovici.  Classical Coulomb systems near a plane wall. II , 1982 .

[6]  J. Kirkwood,et al.  Statistical Mechanics of Liquid Solutions. , 1936 .

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

[8]  L. L. Lee.  Chemical potentials based on the molecular distribution functions. An exact diagrammatical representation and the star function , 1992 .

[9]  D. A. Mcquarrie,et al.  On the second-moment condition of Stillinger and Lovett , 1977 .

[10]  M. Klein,et al.  Molecular dynamics investigation of a Newtonian black film , 1992 .

[11]  B. Ninham,et al.  Range of the screened coulomb interaction in electrolytes and double layer problems , 1978 .

[12]  R. Nieminen,et al.  Theory of inhomogeneous fluids , 1981 .

[13]  M. Klein,et al.  An Ewald summation method for planar surfaces and interfaces , 1992 .

[14]  L. Verlet,et al.  On the theory of classical fluids-III , 1962 .

[15]  Swapan K. Ghosh,et al.  Electric double layer at a metal/electrolyte interface: A density functional approach , 1995 .

[16]  Derek Y. C. Chan,et al.  Computation of forces between spherical colloidal particles : nonlinear Poisson-Boltzmann theory , 1994 .

[17]  C. Woodward,et al.  Monte Carlo simulations of an electric double layer , 1990 .

[18]  S. Carnie.  On sum rules and Stillinger–Lovett conditions for inhomogeneous Coulomb systems , 1983 .

[19]  Numerical solution of two new integral equations for the electrical double layer , 1988 .

[20]  J. Lebowitz,et al.  Perfect Screening for Charged Systems , 1982 .

[21]  J. Lebowitz,et al.  Mean Spherical Model Integral Equation for Charged Hard Spheres I. Method of Solution , 1972 .

[22]  L. Belloni,et al.  Surface charging process in colloidal suspensions: A new statistical approach , 1991 .

[23]  N. Ashcroft,et al.  Exact integral equations for the distribution functions of liquids and liquid mixtures , 1992 .

[24]  P. Attard.  Spherically inhomogeneous fluids. I. Percus–Yevick hard spheres: Osmotic coefficients and triplet correlations , 1989 .

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

[26]  D. A. Mcquarrie,et al.  The electrical double layer in the Born-Green-Yvon equation , 1981 .

[27]  D. Lévesque,et al.  Computation of interface density profiles by density functional theories: application to the two-dimensional one-component plasma , 1982 .

[28]  A. Augousti,et al.  Solvation forces in a model fluid mixture of ions and dipoles , 1984 .

[29]  S. Marčelja,et al.  Correlation and image charge effects in electric double layers , 1984 .

[30]  J. W. Halley,et al.  Molecular dynamics simulation of water beween two ideal classical metal walls , 1989 .

[31]  P. Attard.  Lennard‐Jones bridge functions and triplet correlation functions , 1991 .

[32]  Douglas A. Lauffenburger,et al.  NUMERICAL SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION FOR A MEMBRANE-ELECTROLYTE SYSTEM , 1994 .

[33]  A. Fetter.  Electrodynamics and thermodynamics of a classical electron surface layer , 1974 .

[34]  P. Bolhuis,et al.  Attractive double layer forces from hard-core correlations , 1993 .

[35]  P. Attard.  Long-range attraction between hydrophobic surfaces , 1989 .

[36]  L. Scriven,et al.  A three-component model of the electrical double layer , 1992 .

[37]  P. Linse.  Highly asymmetric electrolyte: Comparison between one‐ and two‐component models at different levels of approximations , 1991 .

[38]  B. L. Tembe,et al.  Ionic association in model 2–2 electrolyte solutions , 1980 .

[39]  Goldstein,et al.  Electric double layers near modulated surfaces. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[40]  L. White.  On the deryaguin approximation for the interaction of macrobodies , 1983 .

[41]  S. Marčelja,et al.  Electrolyte solutions between uncharged walls , 1987 .

[42]  J. A. Barker,et al.  Fourth Virial Coefficients for the 12–6 Potential , 1962 .

[43]  S. Levine,et al.  Modified Poisson-Boltzmann equation and free energy of electrical double layers in hydrophobic colloids , 1966 .

[44]  A. Alastuey.  Solvable Models of Coulomb Systems in Two Dimensions , 1987 .

[45]  J. Kirkwood,et al.  The Statistical Mechanical Basis of the Debye–Hüekel Theory of Strong Electrolytes , 1954 .

[46]  Douglas Henderson,et al.  The Ornstein-Zernike equation for a fluid in contact with a surface , 2002 .

[47]  J. Valleau,et al.  Water‐like particles at surfaces. II. In a double layer and at a metallic surface , 1987 .

[48]  Groot.  Density-functional theory for inhomogeneous electrolytes. , 1988, Physical review. A, General physics.

[49]  H. Wennerström,et al.  Electrical double layer forces: a Monte Carlo study , 1984 .

[50]  Ye,et al.  Ionic solution in a molecular polar solvent , 1978 .

[51]  B. Halle.  Orientation‐dependent electrical double‐layer interactions. I. Rodlike macroions of finite length , 1995 .

[52]  A. Wonderen,et al.  Equilibrium properties of a multi-component ionic mixture , 1987 .

[53]  N. H. March,et al.  Asymptotic form of correlation functions in classical fluids and in liquid helium 4 , 1965 .

[54]  M. Plischke,et al.  Pair and singlet correlation functions of inhomogeneous fluids calculated using the Ornstein-Zernike equation , 1988 .

[55]  D. J. Mitchell,et al.  An exact but linear and Poisson—Boltzmann-like theory for electrolytes and colloid dispersions in the primitive model , 1992 .

[56]  P. Nielaba,et al.  A local HNC/HNC approximation for the 2:2‐RPM electrolytes at a charged wall , 1986 .

[57]  G. Patey,et al.  Hypernetted‐chain closure with bridge diagrams. Asymmetric hard sphere mixtures , 1990 .

[58]  L. Blum.  Structure of the electric double layer , 2007 .

[59]  H. Wennerström,et al.  The cell model for polyelectrolyte systems. Exact statistical mechanical relations, Monte Carlo simulations, and the Poisson–Boltzmann approximation , 1982 .

[60]  Robert Ivkov,et al.  Colloid stability: The forces between charged surfaces in an electrolyte , 1991 .

[61]  D. Hoyle,et al.  Asymptotic decay of correlations in liquids and their mixtures , 1994 .

[62]  Ursenbach,et al.  Interaction free energy between planar walls in dense fluids: An Ornstein-Zernike approach with results for hard-sphere, Lennard-Jones, and dipolar systems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[63]  Carlo Caccamo,et al.  An improved closure for the Born–Green–Yvon equation for the electric double layer , 1986 .

[64]  S. Marčelja,et al.  Surface interactions in simple electrolytes , 1988 .

[65]  V. Pandharipande,et al.  Three-body correlations in liquidHe4 , 1982 .

[66]  D. J. Mitchell,et al.  Dressed ion theory for bulk symmetric electrolytes in the restricted primitive model , 1995 .

[67]  L. B. Bhuiyan,et al.  A modified Poisson-Boltzmann analysis of the electric double layer around an isolated spherical macroion , 1991 .

[68]  B. Ninham,et al.  The structure of electrolytes at charged surfaces: The primitive model , 1981 .

[69]  I. Snook,et al.  The grand canonical ensemble Monte Carlo method applied to the electrical double layer , 1980 .

[70]  Attard,et al.  Continuum electrostatic interactions between planar lattices of dipoles and the possible relevance to the hydration force. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[71]  K. Sharp,et al.  Macroscopic models of aqueous solutions : biological and chemical applications , 1993 .

[72]  D. Wei,et al.  On the existence of exact conditions in the theory of electrical double layers , 1992 .

[73]  P. Dehaven,et al.  Generalized van der Waals theories for surface tension and interfacial width , 1973 .

[74]  G. Stell,et al.  Fluids with Long-Range Forces: Toward a Simple Analytic Theory , 1977 .

[75]  D. Chan,et al.  The structure of electrolytes at charged surfaces: Ion–dipole mixtures , 1980 .

[76]  B. Bagchi,et al.  Exotic dielectric behavior of polar liquids , 1989 .

[77]  F. Stern,et al.  Properties of Semiconductor Surface Inversion Layers in the Electric Quantum Limit , 1967 .

[78]  L. Belloni.  Self‐consistent integral equation applied to the highly charged primitive model , 1988 .

[79]  H. T. Davis,et al.  A nonlocal free-energy density-functional approximation for the electrical double layer , 1990 .

[80]  Tarazona.  Erratum: Free-energy density functional for hard spheres , 1985, Physical review. A, General physics.

[81]  T. Kennedy.  Debye-Hückel theory for charge symmetric Coulomb systems , 1983 .

[82]  B. Jönsson,et al.  The interaction between charged aggregates in electrolyte solution. A Monte Carlo simulation study , 1984 .

[83]  S. Levine,et al.  Theory of the electric double layer using a modified poisson–boltzman equation , 1980 .

[84]  J. A. Barker,et al.  Liquid argon: Monte carlo and molecular dynamics calculations , 1971 .

[85]  D. A. Mcquarrie,et al.  The effect of discrete charges on the electrical properties of membranes. II. , 1975, Journal of theoretical biology.

[86]  G. S. Rushbrooke,et al.  On triplet potentials in the theory of classical fluids , 1967 .

[87]  J. Badiali.  Structure of a polar fluid near a wall. Exact asymptotic behavior of the profile, relation with the electrostriction phenomena and the Kerr effect , 1989 .

[88]  D. Lévesque,et al.  A comparison between computer simulation and theoretical results for ionic solutions , 1987 .

[89]  P. Federbush,et al.  Surface effects in Debye screening , 1985 .

[90]  S. Rice,et al.  An accurate integral equation for the pair and triplet distribution functions of a simple liquid , 1981 .

[91]  D. A. Mcquarrie,et al.  A self-consistent calculation of the free energy and electrostatic potential for a cylindrical polyion. , 1973, Journal of theoretical biology.

[92]  D. Heyes,et al.  Molecular dynamics computer simulation of surface properties of crystalline potassium chloride , 1977 .

[93]  F. Oosawa.  Interaction between parallel rodlike macroions , 1968 .

[94]  S. J. Zhu,et al.  Theoretical simulation for identical bands , 2005 .

[95]  M. Baus.  On the compressibility of a one-component plasma , 1978 .

[96]  E. Díaz‐Herrera,et al.  Three‐point extension hypernetted chain, conventional hypernetted chain, and superposition approximations: Numerical results for the force between two plates , 1990 .

[97]  J. Lebowitz,et al.  Equilibrium Properties of a System of Charged Particles , 1968 .

[98]  W. Ellis.  Inhomogeneous correlation functions for a planar membrane model neuron , 1994 .

[99]  John Lekner,et al.  Summation of Coulomb fields in computer-simulated disordered systems , 1991 .

[100]  P. Nielaba,et al.  Packing of ions near an electrolyte-electrode interface in the HNC/LMSA approximation to the RPM model , 1985 .

[101]  S. Levine,et al.  Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer , 1981 .

[102]  J. Hansen,et al.  Statistical mechanics of dense ionized matter. V. Hydrodynamic limit and transport coefficients of the classical one-component plasma , 1975 .

[103]  R. Zwanzig,et al.  Fluctuation Theory of Surface Tension , 1972 .

[104]  B. Montgomery Pettitt,et al.  Alkali halides in water: Ion–solvent correlations and ion–ion potentials of mean force at infinite dilution , 1986 .

[105]  Keith Refson,et al.  Computer simulation of interlayer water in 2:1 clays , 1991 .

[106]  D. J. Mitchell,et al.  Dressed‐ion theory for electrolyte solutions: A Debye–Hückel‐like reformulation of the exact theory for the primitive model , 1994 .

[107]  P. Richmond.  Electrical forces between particles with arbitrary fixed surface charge distributions in ionic solution , 1974 .

[108]  M. Wertheim,et al.  Correlations in the liquid–vapor interface , 1976 .

[109]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[110]  P. Rossky,et al.  Corrections to the HNC equation for associating electrolytes , 1983 .

[111]  C. Woodward,et al.  A Monte Carlo simulation study of the interaction between charged colloids carrying adsorbed polyelectrolytes , 1991 .

[112]  B. Ninham,et al.  Van der Waals Forces in Electrolytes , 1972 .

[113]  W. Su,et al.  Polar molecules in planar interfaces. Role of the triplet direct correlation function in the asymptotic behavior of the profile , 1990 .

[114]  V. Vlachy,et al.  Electrolytes in charged micropores , 1989 .

[115]  J. Andrew McCammon,et al.  Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation , 1993 .

[116]  P. Attard.  Integral equations and closure relations for the bridge function and for the triplet correlation function , 1990 .

[117]  P. Sloth,et al.  Hard, charged spheres in spherical pores. Grand canonical ensemble Monte Carlo calculations , 1992 .

[118]  B. Jancovici,et al.  Time-dependent correlations in an inhomogeneous one-component plasma , 1985 .

[119]  B. Jönsson,et al.  Monte Carlo simulations of colloidal stability—beyond the Poisson—Boltzmann approximation , 1991 .

[120]  L. Scriven,et al.  Interactions between primitive electrical double layers , 1992 .

[121]  G. Torrie,et al.  Molecular solvent model for an electrical double layer: Reference hypernetted‐chain results for ion behavior at infinite dilution , 1988 .

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

[123]  L. Blum,et al.  Mean spherical model for asymmetric electrolytes. 2. Thermodynamic properties and the pair correlation function , 1977 .

[124]  H. Totsuji.  Surface properties of classical one-component plasma , 1986 .

[125]  Henderson,et al.  Limiting law for ion adsorption in narrow planar pores. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[126]  S. J. Miklavic.  Mean-Field Potential for Heterogeneous Electrical Double Layers, with Application to the Surface Pressure of Charged Monolayers , 1995 .

[127]  B. Derjaguin,et al.  Untersuchungen über die Reibung und Adhäsion, IV , 1934 .

[128]  B. Jönsson,et al.  Electric double layer forces in the presence of polyelectrolytes , 1989 .

[129]  Denton,et al.  Weighted-density-functional theory of nonuniform fluid mixtures: Application to the structure of binary hard-sphere mixtures near a hard wall. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[130]  J. Kirkwood.  Statistical Mechanics of Fluid Mixtures , 1935 .

[131]  F. Stillinger,et al.  Theory of the Diffuse Double Layer , 1960 .

[132]  S. Marčelja,et al.  Inhomogeneous Coulomb fluids with image interactions between planar surfaces. I , 1985 .

[133]  Clifford E. Woodward,et al.  Conformation of surface-bound polyelectrolytes. II, A Monte Carlo study of medium-length lattice chains , 1990 .

[134]  G. N. Patey,et al.  Ionic solution near an uncharged surface with image forces , 1981 .

[135]  W. Russel,et al.  The electrostatic repulsion between charged spheres from exact solutions to the linearized poisson-boltzmann equation , 1983 .

[136]  H. Ohshima,et al.  Donnan potential and surface potential of a charged membrane. , 1985 .

[137]  J. Joanny,et al.  Electrostatic Interactions, Curvature Elasticity, and Steric Repulsion in Multimembrane Systems , 1990 .

[138]  B. Ninham,et al.  Asymptotic Behavior of the Pair Distribution Function of a Classical Electron Gas , 1968 .

[139]  G. Torrie.  Negative differential capacities in electrical double layers , 1992 .

[140]  M. Kinoshita,et al.  Structure of the metal‐electrolyte solution interface: Theoretical results for simple models , 1995 .

[141]  C. Hall,et al.  Structural properties of mixtures of highly asymmetrical electrolytes and uncharged particles using the hypernetted chain approximation , 1994 .

[142]  G. Stell.  Extension of the Ornstein-Zernike Theory of the Critical Region. II , 1970 .

[143]  G. Patey,et al.  A theoretical study of the solid–electrolyte solution interface. I. Structure of a hard sphere ion–dipole mixture near an uncharged hard wall , 1988 .

[144]  J. Perram,et al.  Electrostatic lattice sums for semi-infinite lattices , 1979 .

[145]  L. Degrève,et al.  Monte Carlo simulation for a symmetrical electrolyte next to a charged spherical colloid particle , 1993 .

[146]  M. Grimson,et al.  Linear and non-linear theories of solvation forces in fluids , 1981 .

[147]  E. Guàrdia,et al.  Mean force potential for the calcium–chloride ion pair in water , 1993 .

[148]  D. Bratko,et al.  MODIFIED POISSON-BOLTZMANN THEORY APPLIED TO LINEAR POLYELECTROLYTE SOLUTIONS , 1995 .

[149]  Max L. Berkowitz,et al.  Computer simulation of a water/membrane interface , 1991 .

[150]  M. Fushiki.  An anisotropic hypernetted chain approximation for the spherical cell model , 1989 .

[151]  P. Linse.  Accurate solution of a highly asymmetric electrolyte: Molecular dynamics simulation and integral equation , 1990 .

[152]  D. Chan,et al.  The stillinger—lovett condition for non-uniform electrolytes , 1981 .

[153]  B. Ninham,et al.  Undulations of charged membranes , 1990 .

[154]  P. Linse,et al.  A Monte Carlo study of the electrostatic interaction between highly charged aggregates. A test of the cell model applied to micellar systems , 1983 .

[155]  M. Baus.  Long range correlations along an interfacial electric double layer , 1983 .

[156]  F. Stillinger,et al.  General Restriction on the Distribution of Ions in Electrolytes , 1968 .

[157]  M. Fisher,et al.  Decay of Correlations in Linear Systems , 1969 .

[158]  A. L. Loeb.  An interionic attraction theory applied to the diffuse layer around colloid particles. I , 1951 .

[159]  S. Levine,et al.  The discrete-ion effect in ionic double-layer theory , 1967 .

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

[161]  B. Jönsson,et al.  A simple analysis of ion–ion correlation in polyelectrolyte solutions , 1990 .

[162]  S. Levine,et al.  Statistical thermodynamics of concentrated colloidal solutions. Part 2.—General theory of the double-layer forces on a colloidal particle , 1958 .

[163]  F. Booth.  The Solution of Some Potential Problems in the Theory of Electrolytes , 1951 .

[164]  H. Friedman,et al.  Theory of mixed electrolyte solutions and application to a model for aqueous lithium chloride-cesium chloride , 1970 .

[165]  J. Barber,et al.  Mixed Valency counterions between charged walls: an investigation using Monte Carlo simulation and comparison with Poisson−Boltzmann theory , 1989 .

[166]  S. Marčelja,et al.  Double-layer ion correlation forces restrict calcium-clay swelling , 1988 .

[167]  S. Toxvaerd.  Perturbation Theory for Nonuniform Fluids: Surface Tension , 1971 .

[168]  L. B. Bhuiyan,et al.  The cylindrical electric double layer in the modified Poisson-Boltzmann theory , 1994 .

[169]  J. Wiechen.  A theory for the structure and thermodynamics of molten Li/K Cl , 1986 .

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

[171]  M. Tosi,et al.  Small-angle scattering from molten salts , 1979 .

[172]  F. Lado.  Hypernetted-chain solutions for the two-dimensional classical electron gas , 1978 .

[173]  G. Saville,et al.  Effective pair potentials in fluids in the presence of three-body forces , 1970 .

[174]  M. Lozada-Cassou,et al.  Hypernetted chain approximation for the distribution of ions around a cylindrical electrode. II. Numerical solution for a model cylindrical polyelectrolyte , 1985 .

[175]  G. W. Robinson,et al.  Structure and dynamics of liquid water between plates , 1991 .

[176]  Yaoqi Zhou,et al.  Nonlocal integral‐equation approximations. I. The zeroth order (hydrostatic) approximation with applications , 1990 .

[177]  Lars Onsager,et al.  The Surface Tension of Debye‐Hückel Electrolytes , 1934 .

[178]  C. Woodward,et al.  A density functional theory for dipolar hard spheres at charged solid-liquid interfaces , 1987 .

[179]  A. Delville.  Structure of liquids at a solid interface: an application to the swelling of clay by water , 1992 .

[180]  Simulation of Confined Primitive Electrolytes: Application of a New Method of Summing the Coulomb Field , 1992 .

[181]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Solutions. I , 1951 .

[182]  Bradley K. Alpert,et al.  A Fast Algorithm for the Evaluation of Legendre Expansions , 1991, SIAM J. Sci. Comput..

[183]  J. P. Valleau,et al.  Electrical double layers. 4. Limitations of the Gouy-Chapman theory , 1982 .

[184]  J. Lebowitz,et al.  An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall , 1979 .

[185]  M. Dharma-wardana,et al.  Analysis of the structure factor of dense krypton gas: Bridge contributions and many-body effects , 1984 .

[186]  J. Lebowitz,et al.  Sum rules for inhomogeneous Coulomb systems , 1981 .

[187]  S. Marčelja,et al.  Inhomogeneous Coulomb fluids with image interactions between planar surfaces. III. Distribution functions , 1988 .

[188]  L. B. Bhuiyan,et al.  An improved modified Poisson–Boltzmann equation in electric-double-layer theory , 1983 .

[189]  G. Ramanathan,et al.  The cell model for polyelectrolytes with added salt , 1985 .

[190]  V. Vlachy,et al.  Salt exclusion from charged and uncharged micropores , 1990 .

[191]  L. Reatto,et al.  Integral equation for the structure of fluids in presence of three‐body forces: Krypton, argon, and models for complex mixtures , 1987 .

[192]  J. Andrew McCammon,et al.  The structure of liquid water at an extended hydrophobic surface , 1984 .

[193]  I. Benjamin,et al.  Solvation of Na+ and Cl− at the water–platinum (100) interface , 1991 .

[194]  G. Torrie,et al.  Reference hypernetted-chain theory for dipolar hard spheres at charged surfaces , 1989 .

[195]  Debye screening for jellium and other Coulomb systems , 1983 .

[196]  A Katchalsky,et al.  The Potential of an Infinite Rod-Like Molecule and the Distribution of the Counter Ions. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[197]  G. Patey,et al.  Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles Integral equation results with application to liquid water , 1982 .

[198]  B. Ninham,et al.  Electrostatic potential between surfaces bearing ionizable groups in ionic equilibrium with physiologic saline solution. , 1971, Journal of theoretical biology.

[199]  L. Scriven,et al.  Non-local free-energy density-functional theory applied to the electrical double layer , 1990 .

[200]  J. Rasaiah,et al.  The adsorption of dipoles at a wall in the presence of an electric field: The RLHNC approximation , 1980 .

[201]  J. L. Parker,et al.  Oscillatory solvation forces : a comparison of theory and experiment , 1992 .

[202]  M. Tosi,et al.  Hydrodynamic correlation functions for molten salts , 1976 .

[203]  P. Vieillefosse,et al.  Fluctuations de charge et de masse dans un sel fondu binaire a la limite hydrodynamique , 1977 .

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

[205]  S. Sokołowski.  Adsorption of hard spheres via the non-uniform Percus-Yevick equation , 1983 .

[206]  D. Bratko,et al.  Distribution of counterions in the double layer around a cylindrical polyion , 1982 .

[207]  D. Henderson.  Formulas for the solvation force between colloidal particles obtained from the Ornstein–Zernike relation , 1992 .

[208]  D. Chan,et al.  Correlations in inhomogeneous Coulomb systems , 1984 .

[209]  G. Torrie,et al.  Molecular solvent model for an electrical double layer: Reference hypernetted‐chain (RHNC) results for solvent structure at a charged surface , 1988 .

[210]  A. Augousti,et al.  Integral equations and the pressure at the liquid-solid interface , 1984 .

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

[212]  D. A. Mcquarrie,et al.  Ionic size effects on the force between planar electrical double layers , 1993 .

[213]  Y. Kuo,et al.  Exact solution to linearized Poisson-Boltzmann equation: Ion-penetrable membranes bearing nonuniformly distributed fixed charges , 1995 .

[214]  B. Ninham,et al.  The bending modulus of ionic lamellar phases , 1991 .

[215]  X. Artru,et al.  Weakly coupled classical Coulomb systems near a cylindrical wall , 1983 .

[216]  J. Sweeney,et al.  Gradient theory of the electric double layer at hydrocarbon–water interfaces , 1987 .

[217]  S. Marčelja,et al.  Interaction of surfaces carrying grafted polyelectrolytes , 1988 .

[218]  G. Patey.  The interaction of two spherical colloidal particles in electrolyte solution. An application of the hypernetted‐chain approximation , 1980 .

[219]  M. Lozada-Cassou.  Hypernetted chain theory for the distribution of ions around a cylindrical electrode , 1983 .

[220]  J. Kirkwood,et al.  On the Theory of Strong Electrolyte Solutions , 1934 .

[221]  D. Bratko,et al.  Electric double layer interactions in reverse micellar systems: A Monte Carlo simulation study , 1990 .

[222]  E. Díaz‐Herrera,et al.  Three point extension for hypernetted chain and other integral equation theories: Numerical results , 1990 .

[223]  S. Feller,et al.  The structure of electrolytes in cylindrical pores , 1993 .

[224]  J. Valleau,et al.  Water‐like particles at surfaces. I. The uncharged, unpolarized surface , 1987 .

[225]  H. Gregor,et al.  Coulombic reactions of polyelectrolytes with counterions of different sizes , 1977 .

[226]  J. Springer,et al.  Integral equation solutions for the classical electron gas , 1973 .

[227]  Ursenbach,et al.  Long-range attractions between solutes in near-critical fluids. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[228]  B. Ninham,et al.  Curvature elasticity of charged membranes , 1989 .

[229]  E. A. Mason,et al.  Nonadditivity of Intermolecular Forces: Effects on the Third Virial Coefficient , 1966 .

[230]  M. Lozada-Cassou,et al.  Exact numerical solution to the integral equation version of the Poisson—Boltzmann equation, for two interacting spherical colloidal particles , 1992 .

[231]  P. Higgs,et al.  Enhanced membrane rigidity in charged lamellar phases , 1990 .

[232]  D. Brydges.  A rigorous approach to Debye screening in dilute classical coulomb systems , 1978 .

[233]  D. A. Mcquarrie,et al.  Calculation of the force between planar electrical double layers containing counterion mixtures , 1993 .

[234]  M. Stevens,et al.  Density Functional Theory of Ionic Screening: When Do Like Charges Attract? , 1990 .

[235]  M. Plischke,et al.  The primitive model of the electric double layer: nonsymmetric electrolytes , 1989 .

[236]  S. Marčelja.  Electrostatics of membrane adhesion. , 1992, Biophysical journal.

[237]  J. P. Valleau,et al.  Electrical double layers. I. Monte Carlo study of a uniformly charged surface , 1980 .

[238]  D. Chan,et al.  The statistical mechanics of the electrical double layer: Stress tensor and contact conditions , 1981 .

[239]  B. Jönsson,et al.  Interaction and conformation of polyelectrolyte chains adsorbed on neutral surfaces , 1993 .

[240]  C. W. Outhwaite.  Modified Poisson–Boltzmann equation in electric double layer theory based on the Bogoliubov–Born–Green–Yvon integral equations , 1978 .

[241]  Herbert Morawetz,et al.  The counterion distribution in solutions of rod‐shaped polyelectrolytes , 1951 .

[242]  D. A. Mcquarrie,et al.  A variational solution to the hypernetted chain equations applied to the electrical double layer , 1992 .

[243]  S. Dungan,et al.  Electrostatic Interactions between a Charged Sphere and an Oppositely Charged, Deformable Interface , 1994 .

[244]  J. Henderson,et al.  Liquid‐state integral equations at high density: On the mathematical origin of infinite‐range oscillatory solutions , 1992 .

[245]  M. Lozada-Cassou,et al.  The force between two planar electrical double layers. Some numerical results , 1986 .

[246]  B. Jönsson,et al.  Electrostatic fluctuation interactions between neutral surfaces with adsorbed, mobile ions or dipoles , 1988 .

[247]  H. Davis,et al.  Simulations of solvent effects on confined electrolytes , 1993 .

[248]  Free energy in the statistical theory of fluids , 1990 .

[249]  Swapan K. Ghosh,et al.  A nonlocal density‐functional theory of electric double layer: Charge‐asymmetric electrolytes , 1994 .

[250]  A. Soper,et al.  The structure of interlayer water in a hydrated 2:1 clay , 1990 .

[251]  L. Blum,et al.  Mean spherical model for asymmetric electrolytes , 1975 .

[252]  M. Vertenstein,et al.  A theory of electrolyte solutions near a polarizable surface , 1987 .

[253]  Ph. A. Martin.  Sum rules in charged fluids , 1988 .

[254]  M. Tosi,et al.  Structure and thermodynamic properties of molten alkali chlorides , 1984 .

[255]  A. Delville.  Structure and properties of confined liquids: a molecular model of the clay-water interface , 1993 .

[256]  S. Marčelja,et al.  Perturbation of hydrogen bonding in water near polar surfaces , 1985 .

[257]  D. Bratko,et al.  Monte Carlo simulation of hydrophobic interaction , 1987 .

[258]  D. Henderson,et al.  Some exact results and the application of the mean spherical approximation to charged hard spheres near a charged hard wall , 1978 .

[259]  M. Teubner.  On the applicability of the HNC approximation to highly charged polyelectrolytes , 1981 .

[260]  D. Henderson,et al.  Mixtures of hard ions and dipoles against a charged wall: The Ornstein–Zernike equation, some exact results, and the mean spherical approximation , 1981 .

[261]  J. Henderson.  Compressibility route to solvation structure , 1986 .

[262]  J. Lebowitz,et al.  A sum rule for an inhomogeneous electrolyte , 1981 .

[263]  J. Ennis.  Spontaneous curvature of surfactant films , 1992 .

[264]  G. Patey,et al.  On the molecular theory of aqueous electrolyte solutions. II. Structural and thermodynamic properties of different models at infinite dilution , 1988 .

[265]  R. Kjellander,et al.  Electric double-layer properties calculated in the anisotropic reference hypernetted chain approximation , 1994 .

[266]  S. Marčelja,et al.  Attractive double-layer interactions between calcium clay particles , 1988 .

[267]  F. Stillinger,et al.  Ion‐Pair Theory of Concentrated Electrolytes. II. Approximate Dielectric Response Calculation , 1968 .

[268]  M. Tosi,et al.  Restricted primitive model for electrical double layers: Modified HNC theory of density profiles and Monte Carlo study of differential capacitance , 1986 .

[269]  Phil Attard,et al.  Critical comments on the nonlocal dielectric function employed in recent theories of the hydration force , 1990 .

[270]  J. Hubbard,et al.  Molecular dynamics study of a dipolar fluid between charged plates. II , 1986 .

[271]  D. Grahame.  The electrical double layer and the theory of electrocapillarity. , 1947, Chemical reviews.

[272]  M. Kinoshita,et al.  Structure and properties of the metal–liquid interface , 1994 .

[273]  G. S. Manning.  Limiting laws and counterion condensation in polyelectrolyte solutions. IV. The approach to the limit and the extraordinary stability of the charge fraction. , 1977, Biophysical chemistry.

[274]  D. Bratko,et al.  The structure of a model ionic melt in a planar slit , 1991 .

[275]  F. Stillinger,et al.  Ion‐Pair Theory of Concentrated Electrolytes. I. Basic Concepts , 1968 .

[276]  L. Belloni.  A hypernetted chain study of highly asymmetrical polyelectrolytes , 1985 .

[277]  Phil Attard,et al.  The interaction between macroparticles in molecular fluids , 1990 .

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

[279]  R. Nieminen,et al.  Structural properties of a nonuniform classical fluid near a solid substrate , 1984 .

[280]  Solvated chloride ions at contact , 1987 .

[281]  S. Levine,et al.  THEORY OF A MODIFIED POISSON-BOLTZMANN EQUATION. I. THE VOLUME EFFECT OF HYDRATED IONS , 1960 .

[282]  A. Wonderen,et al.  Equilibrium properties of a multi-component ionic mixture II. Fluctuations formulas , 1987 .

[283]  P. Attard,et al.  The electrical double layer in wall-wall hypernetted chain approximation with bridge functions , 1993 .

[284]  S. Nordholm,et al.  Generalized van der Waals theory. III. The prediction of hard sphere structure , 1980 .

[285]  D. Grahame.  Diffuse Double Layer Theory for Electrolytes of Unsymmetrical Valence Types , 1953 .

[286]  S. Marčelja,et al.  Interaction of charged surfaces in electrolyte solutions , 1986 .

[287]  Barry W. Ninham,et al.  Role of solvent structure in solution theory , 1977 .

[288]  Lars Onsager,et al.  Theories of Concentrated Electrolytes. , 1933 .

[289]  G. Gunnarsson,et al.  Electrostatic interactions in micellar solutions. A comparison between Monte Carlo simulations and solutions of the Poisson-Boltzmann equation , 1982 .

[290]  I. Snook,et al.  Finite ion size effects in the electrical double layer—A Monte Carlo study , 1981 .

[291]  C. Caccamo,et al.  Burn–Green–Yvon (BGY) equation for the electric double layer in the dilute solution regime: A ‘‘nonlocal’’ closure , 1987 .

[292]  Ghosh,et al.  Weighted-density-functional theory of nonuniform ionic fluids: Application to electric double layers. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[293]  R. Evans,et al.  The decay of correlations in ionic fluids , 1994 .

[294]  R. Kjellander,et al.  A study of anisotropic pair distribution theories for Lennard-Jones fluids in narrow slits , 1990 .

[295]  Attard.  Asymptotic analysis of primitive model electrolytes and the electrical double layer. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[296]  G. Torrie,et al.  Electrical double layers. II. Monte Carlo and HNC studies of image effects , 1982 .

[297]  D. J. Mitchell,et al.  Interactions between electro-neutral surfaces bearing mobile charges , 1987 .

[298]  Michele Parrinello,et al.  Structure and dynamics of simple ionic liquids , 1979 .

[299]  P. Rossky,et al.  Ionic atmosphere of rodlike polyelectrolytes. A hypernetted chain study , 1984 .

[300]  A. Kornyshev.  Nonlocal screening of ions in a structurized polar liquid — new aspects of solvent description in electrolyte theory , 1981 .

[301]  D. Chan,et al.  Double Layer Forces between Heterogeneous Charged Surfaces , 1994 .

[302]  D. Lévesque,et al.  Numerical simulations of homogeneous and inhomogeneous ionic systems: An efficient alternative to the Ewald method , 1991 .

[303]  E. Matijević,et al.  Double-layer interactions of unequal spheres. Part 1.—The effect of electrostatic attraction with particles of like sign of potential , 1985 .

[304]  C. Woodward,et al.  The interaction of charged surfaces with grafted polyelectrolytes: a Poisson-Boltzmann and Monte Carlo study , 1990 .

[305]  B. Derjaguin,et al.  Theory of a “two-dimensional electrolyte solution” , 1977 .

[306]  Paul C. Martin.  Sum Rules, Kramers-Kronig Relations, and Transport Coefficients in Charged Systems , 1967 .

[307]  B. Bagchi,et al.  Microscopic expression for frequency and wave vector dependent dielectric constant of a dipolar liquid , 1989 .

[308]  P. Tarazona,et al.  A density functional theory of melting , 1984 .

[309]  J. Henderson.  Mean field integral equation theories of liquid-vapour coexistence , 1984 .

[310]  T. L. Hill.  Approximate calculation of the electrostatic free energy of nucleic acids and other cylindrical macromolecules. , 1955, Archives of biochemistry and biophysics.

[311]  Peter J. Rossky,et al.  Ionic distributions near polyelectrolytes. A comparison of theoretical approaches , 1985 .

[312]  D. Bratko,et al.  Electrical double layer interactions with image charges , 1986 .

[313]  L. Nordenskiöld,et al.  EVALUATION OF THE ELECTROSTATIC OSMOTIC PRESSURE IN AN INFINITE SYSTEM OF HEXAGONALLY ORIENTED DNA MOLECULES. A MONTE CARLO SIMULATION STUDY , 1991 .

[314]  J. Lebowitz,et al.  On the properties of inhomogeneous charged systems , 1983 .

[315]  G. Torrie,et al.  Molecular solvent model for an electrical double layer: Reference hypernetted chain results for potassium chloride solutions , 1989 .

[316]  M. Lozada-Cassou.  The force between two planar electrical double layers , 1984 .

[317]  D. Lévesque,et al.  Surface density profile of the one-component plasma , 1983 .

[318]  Max Born,et al.  A general kinetic theory of liquids I. The molecular distribution functions , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[319]  Kierlik,et al.  Density-functional theory for inhomogeneous fluids: Adsorption of binary mixtures. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[320]  J. Rasaiah,et al.  Nonlinear effects in polar fluids: A molecular theory of electrostriction , 1981 .

[321]  D. A. Mcquarrie,et al.  A variational approach to the theory of ionic solutions , 1976 .

[322]  B. Jönsson,et al.  The ionic correlation contribution to the free energy of spherical double layers , 1988 .

[323]  B. Halle,et al.  Ion Distributions in Lamellar Liquid Crystals. A Comparison between Results from Monte Carlo Simulations and Solutions of the Poisson-Boltzmann Equation , 1980 .

[324]  D. Hoyle,et al.  Asymptotic decay of liquid structure: oscillatory liquid-vapour density profiles and the Fisher-Widom line , 1993 .

[325]  M. Plischke,et al.  Pair correlation functions and density profiles in the primitive model of the electric double layer , 1988 .

[326]  D. J. Mitchell,et al.  The force between two charged dielectric half spaces immersed in an electrolyte , 1974 .

[327]  J. Deutch,et al.  The Structure of Dielectric Fluids. III. Interaction between Impurities and Dielectric Saturation in Polar Fluids , 1972 .

[328]  D. Bratko.  Hypernetted chain approximation for ion distribution in reverse micelles , 1990 .

[329]  P. Tarazona,et al.  Free-energy density functional for hard spheres. , 1985, Physical review. A, General physics.

[330]  G. Patey,et al.  On the molecular theory of aqueous electrolyte solutions. I. The solution of the RHNC approximation for models at finite concentration , 1988 .

[331]  Ye,et al.  Statistical mechanics of polar systems: Dielectric constant for dipolar fluids , 1974 .

[332]  B. Ladanyi,et al.  Wave vector dependent static dielectric properties of associated liquids: Methanol , 1990 .