Late-stage phase separation: Dynamics, spatial correlations, and structure functions

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Abstract
Particle coarsening in the late stage was investigated using numerical simulations. The multiparticle diffusion problem was solved using a multipole expansion method which is valid to an arbitrary order of the expansion. The simulations were performed using both monopole and monopole plus dipole approximations. We found that the monopole approximation yields a good description of the diffusion field up to a volume fraction of approximately 0.1. Beyond this volume fraction, particle migration induced by interparticle diffusional interactions plays an important role. The simulations were performed using two different initial spatial distributions. Despite the different initial states of the system, we find that the spatial correlation functions evolve to unique scaled time independent forms. These spatial correlation functions show that depletion zones exist between small particles and that the density of small particles near large particles is less than that of a random spatial distribution. A scaled time independent structure function similar to that observed experimentally was found. The slope of the structure function in a log-log plot is close to 4 at small wave numbers and is -4 at very large wave numbers. Oscillations in the structure function, which are related to the spherical shape and size distribution of particles, are present at large wave numbers. The rate constant of the cubic growth law and the scaled particle size distribution are also determined.