Light scattering of phase separated systems by nucleation-growth mechanisms: a model based on the Fast Fourier Transform

The problem of simulating light scattering patterns of polymerization induced phase separation processes by the mechanism of nucleation and growth is addressed with the objective of reducing the number of computations required to carry out the simulation. A method, based on the Fast Fourier Transform (FFT), that takes advantage of the spherical nature of the phase separated domains, is proposed. Contrary to the case in which the spherical particles are randomly placed in arbitrary locations in the scattering volume, the proposed computational scheme requires the locations not to be arbitrary but to belong to a previously defined equally spaced grid. This last constraint determines levels of resolution in which the simulation can be performed. The FFT based method is tested with a morphology previously generated with a model of the phase separation process. The light scattering pattern corresponding to this morphology, mainly represented through the particle size distribution of the spherical separated domains, has been simulated at different levels of resolution of the grid placed in the scattering domain and of the sizes of the domains. It has been found that the original morphology represented by a distribution with 17 different sizes can be approximated by a smaller number, while keeping the total volume of particles the same, without a noticeable loss of precision. This, together with the fact that the computations can be performed at different levels of resolution, gives the chance to explore an important number of approximations to the problem, many of which produce, using the proposed method, results that are comparable to those obtained at higher levels of resolution, with the advantage of requiring a smaller number of computations.