Study On The Interaction Between Electric Double Layers Of Colloid Particles With Iteration Method In Functional Theory

By introducing the functional theory into the solution of Poisson-Boltzmann(PB)equation, the comparison with Debye-Hückel (DH) method was given, and simultaneously relative error of functional solution was also obtained. The radius and surface potential of the cylinder particle were obtained with the graphical approach, and the changes with the linear charge density, the temperature of the system, the concentration of ions, the charge number and the dielectric constant were also showed. The charge density of cylinder particle was calculated accurately, and the change with radius, surface potential was studied. The changes with distance of activity coefficient of ions, osmotic coefficient of solvent were also given. Based on the equivalent condenser model with the same center of the particle, the relation of the cylindrical thickness with the parameters: the concentration of ions, the linear charge density, the system temperature, the charge number of ion and the dielectric constant was shown. And simultaneously the surface potentials obtained from the abovementioned thickness and the DH reciprocal length respectively were compared. Moreover, the ecumenical expression for surface charge density of spherical electric double layer was also presented. By introducing the functional theory into the calculation of electric double layer (EDL) interaction, the interaction energies of two parallel plates were calculated at low, moderate and high potentials respectively. With numerical method as reference, the calculated values were compared with the two existing methods, namely the DH and Langmuir methods, which were the same with very low and very high potential conditions respectively.The results further confirmed that the DH approximation was reasonable at low potentials and that, conversely, the use of the iterative method in the functional theory to solve the EDL PB equation of a cylindrical particle was also favorable and better than DH approximation without any restriction. The superiority of disposing electric double layer structure by functional theory can been seen by calculating the radius and surface potential of the cylinder particle straightly, while the radius and surface potential can been regarded as parameters for DH approximation. And the cylindrical thickness solved by functional theory was even more accorded with physical definition of electric double layer thickness. By introducing the functional theory into the calculation of electric double layer (EDL) interaction, the DH and Langmuir methods were applicable just for the critical potentials, performing poorly in the intermediate potential. Whereas the functional approach not only had much simple expression of the EDL interaction energy, but also performed well in the entire range of potentials.