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The electrostatic potential of spherical polyelectrolytes in aqueous solution. (English) Zbl 0645.31009

The electrostatic potential in systems of spherical polyelectrolytes is determined by superposition of spherically symmetric solutions of the linearized Poisson-Boltzmann equation. The case of constant surface potential is investigated in detail. Higher-order approximations are given by use of a generalization of the addition theorem for modified Bessel functions.

MSC:

31B15 Potentials and capacities, extremal length and related notions in higher dimensions
35A35 Theoretical approximation in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
70C20 Statics
92C50 Medical applications (general)
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References:

[1] Enos, Force Balance in Systems of Spherical Polyelectrolytes, J. Colloid and Interface Sci. 52 pp 289– (1975) · doi:10.1016/0021-9797(75)90202-7
[2] Ohlenbusch , H.-D. The Electrostatic Potential in Systems of Spherical Polyelectrolytes. Lecture presented at the ”Seminar über spezielle Probleme der statistischen Physik” RWTH Aachen. 28. 6. 1983
[3] Overbeek, Theory of the Stability of Lyophobic Colloids (1948)
[4] Watson, A Treatise on the Theory of Bessel Functions (1922) · JFM 48.0412.02
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