Computer simulation of electrical conductivity of colloidal dispersions during aggregation

The computation approach to the simulation of electrical conductivity of colloidal dispersions during aggregation is considered. We use the two-dimensional diffusion-limited aggregation model with multiple-seed growth. The particles execute a random walk, but lose their mobility after contact with the growing clusters or seeds. The two parameters that control the aggregation are the initial concentration of free particles in the system p and the concentration of seeds psi. The case of psi=1, when all the particles are the immobile seeds, corresponds with the usual random percolation problem. The other limiting case of psi=0, when all the particles walk randomly, corresponds to the dynamical percolation problem. The calculation of electrical conductivity and cluster analysis were done with the help of the algorithms of Frank-Lobb and Hoshen-Kopelman. It is shown that the percolation concentration phi(c) decreases from 0.5927 at psi=1 to 0 at psi -> 0. Scaling analysis was applied to study exponents of correlation length nu and of conductivity t. For all psi > 0 this model shows universal behavior of classical 2d random percolation with nu approximate to t approximate to 4/3. The electrical conductivity sigma of the system increases during aggregation reaching up to a maximum at the final stage. The concentration dependence of conductivity sigma(phi) obeys the general effective medium equation with apparent exponent t(a)(psi) that exceeds t. The kinetics of electrical conductivity changes during the aggregation is discussed. In the range of concentration p(c)(psi)< p < 0.5927 the time of percolation cluster formation tau(c) decreases with increasing phi.