Numerical Solution of the Poisson–Boltzmann Equation for a Spherical Cavity

López-Garcı́a, J.J.; Horno, J.; Grosse, Constantino

doi:10.1006/jcis.2002.8396

Cited by 10 publications

(5 citation statements)

References 20 publications

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“…Many attempts have been made in the past to derive an approximate solution to a Poisson-Boltzmann equation for surfaces of various types and geometries under various conditions. [2][3][4][5][6][7][8][9][10][11] For a salt-free dispersion, although the corresponding Poisson-Boltzmann equation becomes simpler because only counterions are present in the liquid phase, deriving an exact analytical solution is still nontrivial. Ohshima 12 was able to obtain a surface charge density-surface potential relationship for a spherical colloidal particle, the potential near a charged spherical colloidal particle, 13 and the potential around a polyelectrolyte-coated spherical particle.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Analytical Expressions for the Electrical Potential in a Cavity Containing Salt-Free Medium

et al. 2007

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The electrical potential in a closed surface such as a cavity containing counterions only is derived for the cases of constant surface potential and constant surface charge density. The results obtained have applications in, for example, microemulsion-related systems in which ionic surfactants are introduced to maintain the stability of a dispersion and electroosmotic flow-related analysis. An analytical expression for the electrical potential is derived for a planar slit, and the methodology used is modified to derive approximate analytical expressions for spherical and cylindrical cavities. The higher the surface potential, the better the performance of these expressions. For the case where the surface potential is above ca. 50 mV, the performance of the approximate analytical expressions can further be improved by multiplying a correction function.

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Section: Introductionmentioning

confidence: 99%

“…Other than this case, a Poisson−Boltzmann equation needs to be solved either numerically or semianalytically. Many attempts have been made in the past to derive an approximate solution to a Poisson−Boltzmann equation for surfaces of various types and geometries under various conditions. − …”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Expressions for the Electrical Potential in a Cavity Containing Salt-Free Medium

et al. 2007

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“…According to Gouy−Chapman theory, the equilibrium electrical potential can be described by the so-called Poisson−Boltzmann equation. , Unfortunately, the only exactly solvable case of this equation is for a single, infinite planar surface of constant potential immersed in a dispersion containing symmetric electrolytes. Other than that, it needs be solved numerically, semianalytically, or approximately. − Often, the condition of low surface potential is assumed so that the original Poisson−Boltzmann equation can be linearized, which can be readily solved for simple geometries.…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Expressions for the Electrical Potential between Two Planar, Cylindrical, and Spherical Surfaces

Hsu

Tseng

2006

J. Phys. Chem. B

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Approximate analytical expressions for the electrical potential of planar, cylindrical, and spherical surfaces are derived for the case in which the dispersion medium contains counterions only. On the basis of the results for single surfaces, those for two identical surfaces can be derived. The curvature effect of a surface on the electrical potential distribution can be neglected when the order of its radius exceeds approximately 100 times the thickness of the corresponding double layer. If this effect needs to be considered, it can be taken into account by multiplying a correction function by the electrical potential of a planar surface. The electrical potential at the center between two derived surfaces is readily applicable to the evaluation of the electrostatic force per unit area between two surfaces, or the osmotic pressure. For the same set of parameters, the magnitudes of the osmotic pressure for various types of surfaces rank as follows: planar surface > cylindrical surfaces > spherical surfaces.

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“…The membrane bears uniform surface charge distributions on both sides. In view of this fixed surface charge, the internal medium acquires a volume distribution of free charge of opposite sign. − This charge can be thought of as due to counterions trapped inside the membrane when the vesicle is formed or as the result of an electric current slowly leaking through the membrane until the equilibrium state is reached.…”

Section: Numerical Calculationsmentioning

confidence: 99%

Numerical Calculation of the Dielectric and Electrokinetic Properties of Vesicle Suspensions

Grosse

Zimmerman

2005

J. Phys. Chem. B

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The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant zeta potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.

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Numerical Solution of the Poisson–Boltzmann Equation for a Spherical Cavity

Cited by 10 publications

References 20 publications

Approximate Analytical Expressions for the Electrical Potential in a Cavity Containing Salt-Free Medium

Approximate Analytical Expressions for the Electrical Potential in a Cavity Containing Salt-Free Medium

Approximate Analytical Expressions for the Electrical Potential between Two Planar, Cylindrical, and Spherical Surfaces

Numerical Calculation of the Dielectric and Electrokinetic Properties of Vesicle Suspensions

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