Particles Growing in Solutions: Depletion Forces and Instability of Homogeneous Particle Distribution
Crystallites, droplets and amorphous precipitates growing from supersaturated solution are surrounded by zones, which are depleted with respect to the molecules they are built of. If two such particles of colloidal size are separated by a distance comparable to their diameters, then the depletion within the gap between particles is deeper than that at the outer portion of the particles. This will cause depletion attraction between the particles should appear. It may cause particle coagulation and decay of the originally homogeneous particle distribution into a system of clouds within which the particle number density is higher, separated by the region of the lower number density. Stability criterion, Q = 4 pi R(exp 3)c/3 >> 1, was analytically found along with typical particle density distribution wavevector q = (Q/I)(exp 1/2)(a/R)(exp 1/4). Here, R and a are the particle and molecular radii, respectively, c is the average molecular number density in solution and I is the squared diffusion length covered by a molecule during a typical time characterizing decay of molecular concentration in solution due to consumption of the molecules by the growing particles.