Heterogeneous Model for Precursor-Mediated Nanoparticle Growth in Polymer Film

The inorganic nanoparticle growth within a polymer matrix is due to generation of the elementary species, the monomers, because of decomposition of the precursor compounds. The nucleation of the nanoparticles can be either homogeneous or heterogeneous. The model for heterogeneous nucleation and growth considered in this paper with some natural assumptions can explain experimentally observed exposure dependence of the UV-initiated CdS nanoparticle growth in poly-(methyl methacrylate) (PMMA). The constraints on the values of the parameters imposed by the assumptions are discussed. Analytical solutions for the dynamics of the particle size distributions are obtained by reduction of the set of ordinary differential equations to the partial differential equation. The dependences of the particle size distributions on the parameters involved are found. This allows modeling the evolution of the optical absorption spectrum of the nanocomposite material due to nanoparticle growth.