Approximate Analytical Solutions Of Poisson-Boltzmann Equation And Their Applications In The Colloidal Electrostatic Stability

Poisson-Boltzmann (PB) equation plays an important role in stability analysis of the charged colloids. As the PB equation is a nonlinear differential equation, strict and analytical solutions to it can be available only in some special cases. Although numerically solving the PB equation is simple and feasible, analytical expressions are not available in this way, and therefore, it is necessary to approximately and analytically solve the PB equation with reasonable accuracy.In this dissertation, with help of several methods such as homotopy perturbation approach, least square method, high potential approximation and extensions of the Debye-Huckel approximation, we mainly solve approximately and analytically the PB equation for single planar, spherical, cylindrical colloidal particle or reverse micelle immersed in a general electrolyte solution. Accuracies of the approximate analytical solutions obtained are confirmed by comparing with the "exact" numerical solutions. Through the homotopy perturbation method and least square method we get the approximate analytic solutions, which satisfied the smaller particle size (x0≤0.5) and the lower surface potential (y0≤7.5). With help of high potential approximation method we obtain some higher potential (y0≥10.0) solutions, which more suitable for the produce and living.And then, the effects of the solution parameters on particle surface charge density, surface free energy density, and absorption coefficient are discussed according to the electrical potential distributions obtained. Finally, applying the well-known DLVO theory, we calculate the interactions between two parallel plates of the same electrical potential immersed in a general electrolyte solution, and simply discuss the statbility of charged colloids. In this dissertation involve38graphs, 17tables and75references.