A distribution kinetics model of self-assembly: Effects of coalescence and solvent evaporation

Self-assembly from a metastable state often occurs by nucleation accompanied by nanoparticle growth and eventually by Ostwald coarsening. By developing a population balance model for growth and coarsening, we here determine the dynamics of self-assembled cluster size distributions (CSDs) in two or three dimensions. The governing equations are solved numerically and the asymptotic coarsening stage reveals a power-law increase in average particle mass as the CSD evolves to a (minimum) polydispersity index of unity for both 2-D and 3-D phase transitions. By incorporating solvent evaporation to simulate drying-mediated self-assembly of nanoparticles, the model yields a temporal power law relationship with exponent 1/4 for the average 2-D domain radius, in agreement with experimentally observed behavior. The power law relationships can also be obtained by varying the coalescence rate and the power on mass in rate coefficient expressions. (c) 2005 Elsevier B.V.. All rights reserved.