Journal of Physical Chemistry B, Vol.109, No.46, 21664-21668, 2005
Relationship between supersaturation ratio and supply rate of solute in the growth process of monodisperse colloidal particles and application to AgHr systems
Supersaturation ratio, S, has been theoretically related to the supply rate of solute, Q, from growth rate and mass-balance equations in the quasi-steady state in the growth process of isotropic monodisperse particles. The derived equation, (S - 1) = (1/D + 1/kr)(Q/beta C(0)nr) + 2V(m)gamma/rRT, suggests a linear dependence of S on Q under constant n and r, where D is the diffusion coefficient, k is the rate constant for surface-reaction, C-0 is the solubility, n and r are the number and radius of growing particles, respectively, V-m is the molar volume of particles, R is the gas constant, T is the absolute temperature, and beta is the shape factor defined by beta equivalent to (1/r(2)) dv/dr, where v is the volume of an individual particle. The equation was applied to the analysis of growth kinetics and determinations of critical supersaturation ratio in monodisperse AgBr particles in the controlled double-jet system with the assistance of a potentiometric supersaturation measurement. In both cubic and octahedral particles, growth rates were completely limited by diffusion and surface-reaction at pBr (equivalent to -log[Br-]) 3.0 and 1.0, respectively, while the growths were intermediate of them at pBr 2.0 and 4.0. The growth parameters, DC0 and kC(0), were experimentally determined. Also, critical supersaturation ratio was estimated as 1.28 as an average in the present study.