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.