Spontaneous nucleation of monodisperse silver halide particles from homogeneous gelatin solution I: silver chloride

Theoretical formulae for the final number density of the generated stable nuclei per unit volume, n∞, and duration of nucleation period, tN, in the homogeneous system for the formation of monodispersed particles have been derived based on a nucleation model, in which a concept of growth-limited nucleation in the mass balance for consumption of furnished solute is introduced: n∞=Q0Vm/υ̇ and tN=υ0/υ̇, where Q0 is the supply rate of the solute, Vm is the molar volume of the solid, and υ0 and υ̇ are the initial particle volume and mean volumic growth rate of the stable nuclei during the nucleation period, respectively. This theory has been developed to offer a theoretical background for the size control of monodispersed particles in closed systems. The equations were experimentally examined in the spontaneous nucleation of a monodisperse AgCl system containing silver ions as a gelatin complex, chloride ions, and diethyl sulfate, in which silver ions were gradually released from the gelatin by reduction of pH with hydrolysis of diethyl sulfate and the change of silver ion concentration was automatically monitored with a Ag2S-coated Ag electrode to follow the change of supersaturation for nucleation and growth of AgCl particles. In this experiment, the LaMer diagram has actually been visualized. Typical results are υ̇=2.62×103 nm3 s−1, υ0=6.18×102 nm3, and tN=0.236 s under the standard conditions at 25°C. The maximum supersaturation ratio, Sm, was found to be 3.56 under the standard conditions at 25°C, leading to the radius and free energy of formation of a stable nucleus at the maximum supersaturation as rm*=1.66 nm and ΔGm*=1.16×10−18 J, respectively. Effects of the content of diethyl sulfate, initial concentration of KCl, and reaction temperature on Sm, rm*, ΔGm*, υ̇, υ0, n∞, and tN were also examined.