Poisson Boltzmann Theory And Its Application In Colloid Science

Poisson-Boltzmann(PB) theory plays an important role in colloid science. Investigating the physical properties of colloid solution quantitatively needs to solve the PB equation, but, nonlinearity of the PB equation enables only a few cases analytically solvable and the process is rather difficult. Although numerical solution is feasible, it is difficult to explain the physical picture according to numerical results; thus, approximate analytical expression is of importance in this regard. This dissertation aims at obtaining approximate and analytical expressions of the PB equation in the cases of planar, cylindrical, and spherical colloids immersed in general electrolyte solution. According to the electric potential distribution function obtained, we discuss surface charge density/surface electrical potential relationship, surface free energy density and adsorption coefficient of colloidal particle; accuracy test and error analysis are conducted subsequently.In this paper, we advocate to use iteration method and piecewise linear interpolation method to obtain the approximate and analytical solutions of the PB equation for a general electrolyte solution. The essence of the iteration method is to approximate free term with a polynomial, and then, linearize the PB equation with the linear solutions. Implementation of the iteration method is simple, and the solution will tend to be more precise with increasing of the iteration times, but the structure of the solution will eventually become more complicated. Thus, it is not necessary to carry out the iteration process too many times, and the calculations indicate that one iteration is enough. Accuracy test of the iteration method shows that percentage relative errors (PRE) of both scaled surface charge density and scaled surface free energy density are less than2when scaled surface potential y0≤9.5; the PREs of both scaled potential and scaled surface free energy density are less than3when scaled radius x0≤1.5and scaled surface potential y0≤4.5, respectively. Essence of the piecewise linear interpolation method is to approximate the free term with a polygonal line, and then, obtain a solution with the same structure as that of the linear PB equation. This method simplifies mathematical structure of the solution from the iteration method, and the accuracy will be improved as the segment number increases. Accuracy test of the piecewise linear interpolation method shows that the PREs of both the scaled surface charge density and scaled surface free energy density are less than2.6when the scaled surface potential y0≤9.5; the PRE of the scaled potential is less than5when the scaled radius x0≤1.5and scaled surface potential y0≤6.5, respectively; the PRE of the scaled adsorption coefficient is less than4when scaled radius x0≤1.5and scaled surface potential y0≤4.5, respectively. These results are superior to those reported in recent literatures.