In many studies of precipitation, the length of the nucleation period is commonly invoked as the primary control parameter for forming uniform particles in a reaction involving homogeneous nucleation and growth (l-3). In the model originally proposed by LaMer and Dinegar (14) for the mechanism of formation of sulfur sols, uniform size distributions result if all the particles are formed in a short burst of nucleation, and then particle growth occurs by a mechanism where large particles increase in diameter slower than smaller particles (as occurs when growth is limited by diffusion to the particle surface). Despite the influence this model has had on studies of inorganic particle precipitation chemistry, the model has seen little corroboration and indeed has been brought into question for the sulfur sol for which it was developed (15). While the LaMer mechanism would undoubtedly result in uniform particles, finding systems meeting the conditions required for the model to hold has been elusive.
In recent years studies on the formation of polymer latex particles have provided an alternative mechanism whereby uniform particles can result from a homogeneous nucleation, precipitation reaction. In emulsion polymerization, an insoluble monomer is mixed with water and a water soluble free radical initiator added. Final particle size depends on reaction temperature, reagent concentration and parameters controlling the colloidal stability of the growing particles (i.e., ionic strength and pH). The initial locus of the reaction is in the aqueous phase. Oligimers grow to a size where they become insoluble and undergo a sol to gel transition. Due to their relatively low concentration, this transition involves only few polymer molecules and the gel phase grows by aggregation. The charge on the primary particles is small but as the aggregation process proceeds, the charge per particle grows. As a consequence, aggregation rates between particles of equal size decrease but the rate of aggregation of particles of dramatically different size increases. The result is a bimodal particle (or gel phase) size distribution with one peak located at the primary particle size and the second peak containing particles that are stable to mutual coagulation and grow by scavenging smaller particles. Upon aggregation, the gel phase particles coalesce and thus the particles are able to retain a spherical shape. As the reaction proceeds the growing particles reach a constant number density. These colloidally stable particles swell with monomer and the locus of the reaction is transferred from the aqueous phase to the inside of the particle phase. Uniformity is achieved through control of the colloidal stability of the primary particles and aggregates of these particles (6-8).
A second organic analogy to the precipitation of inorganic particles occurs in dispersion polymerization. Here a solvent is chosen where the monomer is soluble but the polymer is not. The reaction is initiated and proceeds through polymerization until the oligimers grow to a size where they undergo a phase transition and precipitate to form polymer and solvent rich phases. Uniform particles are achieved through the addition of steric stabilizers that control the aggregation of the growing gel phase (9).
The major distinction between the model of kMer and that developed for uniform latex particles lies in the incorporation of colloidal stability of small particles. The LaMer model assumes that each nucleus is colloidally stable and survives at the end of the reaction at the center of a particle. The aggregation models argue that while stabilizing such small particles is difficult, aggregation does not necessarily result in a broad particle size distribution. In developing schemes for control of particle size distribution, the result of accepting that colloidal stability can play an important role is that rather than focussing attention on the length of the nucleation period, one becomes very concerned about the colloidal properties of the growing particles.
In this paper we review our studies on the formation of uniform precipitates through the hydrolysis and condensation of titanium and silicon alkoxides. Our work has been aimed at elucidating whether uniformity is the result of the details of the chemistry or if particle size distributions can be controlled by physico-chetnical means. In particular we focus on experiments probing the length of the nucleation period in these systems and the effects of parameters controlling particle interaction potentials. We find that for the systems studied, the nucleation period appears to be a substantial fraction of the entire reaction period and that particle size is largely controlled by parameters related to particle interaction potentials. These results suggest that there are strong links between the physical chemistry underlying the formation of uniform latex particles and that controlling particle size distributions of hydrous metal oxide precipitates (10- 14)