Development of a phenomenological scaling law for fractal aggregate sintering from molecular dynamics simulation

A simple modification to the Frenkel sintering law is developed for nanoparticle fractal aggregates, based on molecular dynamics (MD) simulations. The fractal aggregates investigated consist of up to 110 primary particles, with primary particles of 2.5 nm in diameter, and the fractal dimension of 1 (wire), 1.9 (complex), and 3 (compact). In addition simple prototype L- and T-shape aggregate were considered. We found that L-shape aggregates behaved similar to straight chains and thus did not impact the overall sintering time. By contract T-shape aggregate sintering kinetics was controlled by the longest contiguous branch in the system (i.e. effective primary branch length). We found that sintering of fractal aggregates is a combination of local sintering processes of line-, L- and T-shape structures. As expected, sintering time increases with increasing mass of the aggregate and with decreasing the fractal dimension. The sintering times normalized by the primary particle diameter showed a universal relationship which depends only on the number of particles in an aggregate and its fractal dimension. The MD results were found to be qualitatively consistent with a continuum viscous flow model, and was used as the basis from which a phenomenological sintering law for fractal aggregates could be derived. The phenomenological model is a power law modification of the Frenkel sintering equation to include a dependence on the number of particles in a fractal aggregate and fractal dimension:t=tFrenkel*(N-1)0.68∧Df.t=tFrenkel*(N-1)0.68∧Df.This relationship is amenable for use in phenomenological aerosol models that might include sintering effects.