Scaling of the Kinetics of Slow Aggregation and Gel Formation for a Fluorinated Polymer Colloid

Abstract

The aggregation and gelation kinetics in moderately concentrated (0.004 </= phi(0) </= 0.1) colloidal dispersions of fluorinated polymer particles has been studied. The aggregation was adjusted to proceed slowly enough to allow a convenient characterization of the kinetics through static and dynamic light scattering on quenched and diluted samples. A population balance model based on second-order aggregation rates is developed to compute the time evolution of the cluster mass distribution, from which we calculate the values of the average radii and structure factor measured by light scattering, so as to allow a direct comparison between measured and calculated quantities. The model suggests the introduction of a dimensionless time which allows the scaling of all the aggregation data on unique master curves defined by only two parameters: the exponent of the power-law aggregation kernel, lambda, and the aggregate fractal dimension, d(f). The predicted master curves were observed experimentally, which confirms the validity of the aggregation model and allows the unique determination of the kinetic and structural parameters of the aggregation process. The cluster growth behavior, although significantly slower than DLCA, shows power-law kinetics rather than the exponential one typical of RLCA and the cluster structure is characterized by an unexpectedly small fractal dimension, d(f) = 1.7. The occurrence of gelation has been characterized using small amplitude oscillatory shearing to monitor the time evolution of the elastic modulus. It is found that also these curves, together with the gel time value, scale with the stability ratio of primary particles for a given solid volume fraction. We further use the model to calculate the cumulative occupied volume fraction of the growing aggregates and quantify in this way the increasing space filling, which is solid volume fraction dependent. The experimentally determined dimensionless gel times, which are also solid volume fraction dependent, scale then directly with the dimensionless time to reach a certain degree of the space filling in the model. This finding suggests that, like the aggregation kinetics, the gelation kinetics is governed by a second-order rate process.

Assessment of gel formation in colloidal dispersions during mixing in turbulent jets

“…This value can be found in the literature only for the dispersions of equally sized spheres assuming certain geometrical arrangement of the closed packing. The maximum packing fraction ranges from 0.524 to 0.74 for simple cubic and hexagonal close-packed arrangement, respectively, which is in good agreement with results of Sandk€ uhler et al 37,38 where gel formation under static conditions was observed when / occ reaches value around 0.5. Because all mentioned values are of a similar magnitude and because arrangement of the particles in the aggregate is close to random packing in what follows we will use the value of / m equal to 0.63 found by McGeary 39 from settling experiment.…”

“…As it was shown by Sandk€ uhler et al, 37,38 the occupied volume fraction can be efficiently used to determine the condition when aggregating clusters interconnect and form a network in the whole available volume and therefore can strongly affect the flow and turbulence fields in the coagulator.…”

“…On one side, when aggregation is controlled by Brownian mechanism, the divergence of viscosity is caused by volume filling with interconnection of fractal aggregates 38,44 and can be detected by calculating the value of occupied volume fraction using Eq. 24.…”

“…It is worth noting that for the cases when no coupling of PBE with hydrodynamic is considered values of / occ between 0.5 to one are commonly considered as conditions for local gelation. 37,38,44 Since our case such coupling was considered conditions of viscosity divergence would corresponds to the point where / occ 5/ m 50:63. Therefore, presented result corresponds to the case very close to the gelation.…”

Nanoemulsion stability: Experimental evaluation of the flocculation rate from turbidity measurements

“…The latex particles have the size of a few hundred nanometers, and are almost neutrally buoyant. As a result of these advances, the morphology of the aggregates was linked to the aggregation rate [36,37,38], and some mathematical properties of the flocculation rate were quantified thanks to the dynamic scaling of the population balance equation for irreversible aggregation [38,39,40,41,42,43,44]. From these studies, a general form of the flocculation rate between aggregates of sizes i and j was deduced [45]:…”