Approximate analytical expressions for electrical potential distribution and surface charge density/surface potential relationship for planar, cylindrical, and spherical entities immersed in a general electrolyte solution

New analytical expressions for electrical potential distribution and surface charge density/surface potential relationship (σ/ψ0) are derived by approximately solving a Poisson–Boltzann equation describing the electrical potential distribution around a colloidal particle with planar, cylindrical, or spherical shape and immersed in a general electrolyte solution. Application scopes of these new expressions are limited to small reduced radius of the colloidal particle, and are complementary with those of previous expressions available in literature, which advisably apply for larger reduced radius without solitary exception. For the new expressions for σ/ψ0 relationship, the accuracy is summarized as follows: in the case of the cylindrical colloidal particle and if top limit of a reduced surface potential is fixed as 5.5, top limits of a reduced colloidal radius are respectively not larger than 0.1, 0.034 and 0.008 for 3:1, 2:1 and 1:1 type electrolyte solutions; whereas in the case of the spherical colloidal particle and if top limit of the reduced surface potential is fixed as 6.5, top limits of the reduced colloidal radius are, respectively, not larger than 0.49, 0.39, and 0.29 for 3:1, 2:1 and 1:1 type electrolyte solutions. In the case of the planar colloidal particle immersed in a general electrolyte solution, an exact expression for (σ/ψ0) relationship is obtained.

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► We advance new approach for solving analytically and approximately a Poisson–Boltzmann equation.
► Analytical expressions for electrical potential in a general electrolyte solution are obtained.
► New exact equality linking σ/ψ0 relationship and electrical potential distribution is acquired.