The fluctuation kinetics of formation of nanoparticles: Particle-size distribution

A stochastic simulation of the growth of particles on a uniform cubic lattice was performed by the Monte Carlo method. Changes in the width of the distribution (M (w) /M (n) ) as the size of particles increased were extremal in character. Distribution narrowing occurred much more slowly than in classic polymerization. An empirical equation relating the number of free vacancies of a growing particle and its mean size was obtained. The introduction of a stabilizer deactivating free vacancies of a growing particle caused the appearance of a critical phenomenon. At stabilizer concentrations higher than critical, large-sized particles could not form. At stabilizer concentrations close to critical, the particle-size distribution was bimodal. This resulted in an anomalously larger distribution width.