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

Abstract

SUMMARY: 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.

Mechanism and Kinetics of Phase Separation in a Gelatin/Maltodextrin Mixture Studied by Small-Angle Light Scattering

“…Above 38 °C, up to the binodal temperature, the initial monotonic decrease in intensity of the scattering function with scattering vector, which is expected from a low volume fraction of spatially uncorrelated polydisperse spheres, shows that nucleation and growth was the phase separation mechanism in that temperature range. That a peak developed at a nonzero scattering vector in the latter case supports previous numerical and experimental findings of a peak in the scattering function caused by the NG mechanism. ,,− However, the present results show that the NG peak can be distinguished from the SD peak by its different behavior. The three main differences are the different profile of the evolution of the peak height with time, the initial movement of the NG peak to higher scattering vectors, and the lower coarsening exponents from the NG peak.…”

“…The presence of a peak in NG colloidal and polymer systems above a certain droplet volume fraction has been explained by the presence of a depletion layer around the droplets 3,41-46 that causes further nucleation to occur in preferred regions. When the droplet volume fraction is high enough, this effect leads to a correlated morphology. ,− , The development of a correlated morphology in the NG samples once a certain droplet volume fraction has been attained accounts for the experimental observation of the development of the peak in the scattering pattern at some time after the first droplets have nucleated. The scattered intensity is proportional to the size and number of the scattering objects and the density difference between them and the surrounding medium.…”

“…Since the composition of the phases is fixed at the time of nucleation, the gradual increase of the scattered intensity for the NG samples results from the increasing number of scattering objects in the system as nucleation continues. The decreasing spacing between the increasing number of droplets therefore accounts for the initial movement of the peak in the scattering function to higher scattering vectors. − In contrast, the peak height evolves differently for the SD samples because in this case the number of scattering objects is fixed at the start of phase separation but the phase compositions rapidly change, although the absence of dynamic scaling in the system precludes a straightforward analysis of the values. Moreover, because the SD structure can only coarsen, the peak in the SD samples can only move toward lower scattering vectors, as observed.…”

“Delayed” Phase Separation in a Gelatin/Dextran Mixture Studied by Small-Angle Light Scattering, Turbidity, Confocal Laser Scanning Microscopy, and Polarimetry

“…If the volume fraction of droplets is sufficiently high, some degree of correlation will exist between their positions that will cause a peak, whose position is representative of the droplet spacing, to appear in the SALS pattern. The presence of a peak in the SALS pattern for the nucleation and growth mechanism has been predicted and observed in colloidal and polymer systems, − including a liquid/liquid gelatin/maltodextrin mixture near the binodal temperature . Once nucleation has stopped, coarsening leads to the increase in droplet size that causes the scattering peak to move to lower scattering angles, as observed.…”

Complex coacervation between β-lactoglobulin and Acacia gum: A nucleation and growth mechanism

“…It was important at this stage to understand why a correlation peak appeared in scattering patterns significantly after the beginning of demixing, at a pH where particles were really present in BLG/AG dispersions. The presence of a peak in a nucleating and growing system can be explained either by the presence of a depletion layer around particles (with a local density lower than the surrounding medium density) or a high particle volume fraction [34,35,[40][41][42]. The first mechanism leads to a correlated morphology.…”