Experimental and theoretical aspects on cluster size distribution of latex particles flocculating in presence of electrolytes and water soluble polymers

Abstract

The size distribution of negatively charged polystyene latex particles flocculated in the presence of 0.15 M NaCl or in the presence of poly(4-vinylpyridine) was measured using an automatic particle counter. The time evolutions of the size distribution are well described at large time by the formulas:

$$\begin{gathered}c(g,t) = t^{ - 2} \psi (gt^{ - 2} ) \hfill \\N(t) \sim t^{ - 2} , \hfill \\\end{gathered}$$

, c(g, t) being the number of flocs containing g primary colloids at time t, and N(t) is the total number of flocs of any size, z is a scaling exponent and the function ω does not depend explicitly on time. These laws are in agreement with the theoretical predictions based either on Smoluchovski’s equation assuming a dynamic scaling argument, or on Monte-Carlo simulations on a three-dimensional lattice. If the flocculation occurs in the presence of an excess of electrolyte, z is equal to 1, however if P4VP is the flocculating agent, the value of z is related to the polymer concentration. The kinetics are discussed on the basis of the structure of the collision frequency in Smoluchovski’s equations:

. K(g, n) defines a rate constant. The total number of collisions of g- and n-sized flocs is K(g, n) C _g C _n , C _g C _n being the number of these flocs per unit volume. In this equation R _g , R _n and D _g , D _n are, respectively, the radius of gyration, and the diffusion coefficients of g- and n-sized flocs. This simple expression holds well for an excess of electrolyte situation or at a polymer concentration were flocculation proceeds at a fast rate; Expression of K(g, n) ensures z=1. At low and large polymer concentrations, we have z<1, which is interpreted on the basis of a model of the colloid interface in the presence of adsorbed polymer.