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Expressions are derived for the force and energy of the double-layer interaction between two parallel similar plates with arbitrary surface charge densities or surface potentials at arbitrary separations in an electrolyte solution, by taking into account the finite ion size effect on the basis of the full expression of the activity coefficients of electrolyte ions derived by Carnahan and Starling. The results for two models of the double-layer interaction, that is, the constant surface potential and constant surface charge density models, are given. It is shown that in the constant surface potential model, at large plate separations, the magnitudes of the double-layer interaction force and energy increase as the total ion volume fraction increases but this tendency reverses at small plate separations, while in the constant surface charge density model, they always increase as the total ion volume fraction increases.ᅟ [ABSTRACT FROM AUTHOR]

A theory of counterion condensation around a spherical colloidal particle in a salt-free medium containing only counterions developed by Imai and Oosawa as reported by Busseiron Kenkyu 52:42, 1952 ibid. 59:99, 1953) and later by Ohshima (J Colloid Interface Sci 247:18, 2002) is extended to incorporate the ion size effect on the basis of the modified Poisson-Boltzmann equation using the Carnahan-Starling activity coefficient of counterions. The potential distribution depends on the particle surface charge, the particle volume fraction, and the average counterion volume fraction. It is shown that for a dilute particle suspension, the counterion condensation occurs, leading to a decrease in the particle surface potential when the following two conditions are both satisfied: (i) the scaled particle surface charge is greater than the logarithm of the inverse of the particle volume fraction and (ii) the average counterion volume fraction is much smaller than the particle volume fraction. [ABSTRACT FROM AUTHOR]

Approximate expressions for the surface charge density/surface potential relationship and double-layer potential distribution are derived for a spherical or cylindrical colloidal particle in an electrolyte solution. The obtained expressions are based on an approximate form of the modified Poisson-Boltzmann equation taking into account the ion size effects through the Carnahan-Starling activity coefficients of electrolyte ions. We further derive approximate expression for the effective surface potentials of a spherical or cylindrical particle and for the electrostatic interaction energy between two spherical or cylindrical particles on the basis of the linear superposition approximation. [ABSTRACT FROM AUTHOR]

A simple algorithm is presented for solving the modified Poisson-Boltzmann equation for the electric potential around a planar charged surface in contact with an electrolyte solution, which takes into account the effects of ionic size on the basis of ionic activity coefficient given by Carnahan and Starling (J Chem Phys (1969) 51: 635). An approximate analytic expression for the surface charge density/surface potential relationship is derived. [ABSTRACT FROM AUTHOR]

A simple algorithm is presented for obtaining an approximate analytic solution to the cylindrical Poisson-Boltzmann equation for the electric double layer potential distribution in a charged cylindrical narrow pore filled with an electrolyte solution. Agreement with the exact numerical solution is excellent for low-to-moderate values of the pore surface potential when the pore radius is less than the Debye length. The obtained results are thus considerably better approximations than those previously obtained by Martynov and Avdeev (Colloid J 44: 626-632 (1983)). Approximate analytic expressions are also derived for the relationship between the pore surface charge density and the pore surface potential. [ABSTRACT FROM AUTHOR]

Asymptotic expressions for the electrostatic interaction energy between two weakly charged spheroidal particles (prolate and oblate) with uniform surface potential or surface charge density at large separations in an electrolyte solution are derived on the basis of the linear superposition approximation. The electrostatic interaction between two spheroids is found to be the screened Coulomb interaction between two hypothetical point particles with orientation-dependent charges. Explicit interaction energy equations, which are expressed in terms of spheroidal wave functions, are given for four particular configurations of two similar spheroids, that is, side-to-side prolates, end-to-end prolates, side-to-side oblates, and end-to-end oblates. Comparison is also made with results obtained using Derjaguin's approximation. Electrostatic interaction between two spheroids [Display omitted] • Asymptotic expressions for the electrostatic interaction energy between two spheroidal particles are derived. • Constant surface potential and charge density cases are considered. • Side-to-side prolates, end-to-end prolates, side-to-side oblates, and end-to-end oblates are considered. [ABSTRACT FROM AUTHOR]

Abstract: Transcendental equations, which avoid integration of the nonlinear Poisson–Boltzmann equations, are presented for obtaining the relationship between the Donnan potential and surface potential of a cylindrical soft particle (i.e., a polyelectrolyte-coated cylindrical particle) in a symmetrical electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear cylindrical Poisson–Boltzmann equations both inside and outside the polyelectrolyte layer. [Copyright &y& Elsevier]

Abstract: A simple numerical method, which does not involve numerical integration of the Poisson–Boltzmann equations, is presented for obtaining the relationship between the Donnan potential and surface potential of a spherical soft particle (i.e., a polyelectrolyte-coated particle) in a symmetrical electrolyte solution. We assume that a soft particle consists of the particle core of radius a covered with an ion-penetrable surface layer of polyelectrolytes of thickness d and that ionized groups of valence Z are distributed at a uniform density of N in the polyelectrolyte layer and the relative permittivity takes the same value in the regions outside and inside the polyelectrolyte layer. The Donnan potential and surface potential are determined by the values of a, d, Z, N, and the Debye–Hückel parameter κ of the electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear spherical Poisson–Boltzmann equations for the both regions inside and outside the polyelectrolyte layer. [Copyright &y& Elsevier]

Abstract: Surface potential of lipid membranes made of phosphatidylcholine (PC) and one of the phosphoinositides (PPI); PI, PIP or PIP2, was studied by using the electrophoretic mobility of these lipid membrane vesicles, and a theoretical model of the surface potential developed for these membranes containing PPIs. By using the measured ζ-potential for the PI/PC membranes and a well-known surface potential theory, the inositol ring of the PI molecule was found to extend into the aqueous phase approximately normal to the membrane surface for various PI/PC ratios investigated. The outer edge of the inositol ring is located at about 5.2Å from the phosphate group conjugated with the glycerol of the phospholipids. The inositol group was slightly tilted from the membrane normal direction. For both PIP/PC and PIP2/PC membranes, the analyses of surface potential using the measured ζ-potential values and the surface potential theory which was developed for these membranes gave consistent results with respect to the slipping layer distance from the second surface charge layer. The conclusion is that the experimental data can be fairly well resolved by using a linearized Poisson–Boltzmann surface potential equation set up for a PPI/PC membrane model up to a certain concentration of PPI in PC membranes. Our theoretical model made for these membrane surface potentials seems to be reasonable for analysis of electrical surface phenomena for these PPI/PC membranes containing small concentrations of PPI molecules. [Copyright &y& Elsevier]