A mesoscopic model of nucleation and Ostwald ripening/stepping: Application to the silica polymorph system

Precipitation is modeled using a particle size distribution (PSD) approach for the single or multiple polymorph system. A chemical kinetic-type model for the construction of the molecular clusters of each polymorph is formula ted that accounts for adsorption at a heterogeneous site, nucleation, growt h, and Ostwald ripening. When multiple polymorphs are accounted for, Ostwal d stepping is also predicted. The challenge of simulating the 23 order of m agnitude in cluster size (monomer, dimer, ..., 10(23)-mer) is met by a new formalism that accounts for the macroscopic behavior of large clusters as w ell as the structure of small ones. The theory is set forth for the surface kinetic controlled growth systems and it involves corrections to the Lifsh itz-Slyozov, Wagner (LSW) equation and preserves the monomer addition kinet ics for small clusters. A time independent, scaled PSD behavior is achieved both analytically and numerically, and the average radius grows with R-ave proportional to t(1/2) law for smooth particles. Applications are presente d for the silica system that involves five polymorphs. Effects of the adsor ption energetics and the smooth or fractal nature of clusters on the nuclea tion, ripening, and stepping behavior are analyzed. The Ostwald stepping sc enario is found to be highly sensitive to adsorption energetics. Long time scaling behavior of the PSD reveals time exponents greater than those for t he classical theory when particles are fractal. Exact scaling solutions for the PSD are compared with numerical results to assess the accuracy and con vergence of our numerical technique. (C) 2000 American Institute of Physics . [S0021-9606(00)70123-1].