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 n uclei per unit volume, n(infinity), and duration of nucleation period, t(N) , in the homogeneous system for the formation of monodispersed particles ha ve been derived based on a nucleation model, in which a concept of growth-l imited nucleation in the mass balance for consumption of furnished solute i s introduced: n(infinity) = Q(0)V(m)/(upsilon)over dot and t(N) = upsilon(0 )/upsilon, where Q(0) is the supply rate of the solute, V-m is the molar vo lume of the solid, and upsilon(0) and upsilon are the initial particle volu me 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 syste ms. The equations were experimentally examined in the spontaneous nucleatio n of a monodisperse AgCl system containing silver ions as a gelatin complex , chloride ions, and diethyl sulfate, in which silver ions were gradually r eleased from the gelatin by reduction of pH with hydrolysis of diethyl sulf ate 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 dia gram has actually been visualized. Typical results are (upsilon)over dot = 2.62 x 10(3) nm(3) s(-1), upsilon(0) = 6.18 x 10(2) nm(3), and t(N) = 0.236 s under the standard conditions at 25 degrees C. The maximum supersaturati on ratio, S-m, was found to be 3.56 under the standard conditions at 25 deg rees C, leading to the radius and free energy of formation of a stable nucl eus at the maximum supersaturation as r(m)* = 1.66 nm and Delta G(m)* = 1.1 6 x 10(-18) J, respectively. Effects of the content of diethyl sulfate, ini tial concentration of KCl, and reaction temperature on S-m, r(m)*, Delta G( m)*, (upsilon)over dot, upsilon(0), n(infinity), and t(N) were also examine d. (C) 2000 Elsevier Science B.V. All rights reserved.