Detailed model of the aggregation event between two fractal clusters.
ABSTRACT A model has been developed for describing the aggregation process of two fractal clusters under quiescent conditions. The model uses the approach originally proposed by Smoluchowski for the diffusion-limited aggregation of two spherical particles but accounts for the possibility of interpenetration between the fractal clusters. It is assumed that when a cluster diffuses toward a reference cluster their center-to-center distance can be smaller than the sum of their radii, and their aggregation process is modeled using a diffusion-reaction equation. The reactivity of the clusters is assumed to depend on the reactivity and number of their particles involved in the aggregation event. The model can be applied to evaluate the aggregation rate constant as a function of the prevailing operating conditions by simply changing the value of the particle stability ratio, without any a priori specification of a diffusion-limited cluster aggregation, reaction-limited cluster aggregation, or transition regime. Furthermore, the model allows one to estimate the structure properties of the formed cluster after the aggregation, based on the computed distance between the aggregating clusters in the final cluster.
- European Urology Supplements 10/2011; 10(7):462-462. · 3.37 Impact Factor
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ABSTRACT: The fractal dimension (D f) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reaction-limited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.Colloid and Polymer Science 290(11). · 2.41 Impact Factor
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ABSTRACT: We present a population balance model for enzyme deactivation and aggregation kinetics with a limited number of physically relevant parameters and use this model to analyse the experimental data for thermal inactivation of jack bean urease. The time dependence of the relative enzymatic activity was found to follow the second order kinetics, which was consistent with pre-equilibrated folding/unfolding of the native enzyme, followed by irreversible cluster–cluster aggregation of the non-native enzyme resulting in gradual and permanent loss of enzymatic activity. Monomer–cluster aggregation scenario was considered but was not consistent with the observed kinetic order of monomer disappearance at longer times. We analysed time evolution of the average hydrodynamic radius obtained from dynamic light scattering measurements and by fitting these data with our model, we were able to estimate the value of the unfolding equilibrium constant with a reasonable accuracy (Kc≈0.05 at 80°C). We were also able to make order of magnitude estimates of the maximum number of enzyme molecules in the aggregated clusters (hundreds) as well as the aggregation rate constant of the non-native enzyme.Chemical Engineering Science 01/2011; · 2.61 Impact Factor