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We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration value: d = d0 f + a , with d0 f = 1.80 ± 0.01, a = 0.91 ± 0.03 and = 0.51 ± 0.02, and where is the volume fraction of the colloidal particles. In our second procedure, we get the d via the particle-particle correlation function gcluster(r) and the structure function Scluster(q) of individual clusters. We first show that the stretched exponential law gcluster(r) = Ard –3e–(r/) gives an excellent fit to the cutoff of the g(r). Here, A, a and are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function Scluster (q), using its Fourier transform relation with gcluster(r) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d extracted from this plot coincides with the d of the stretched exponential law. The concentration dependence of this new estimate of d, using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r), of the whole system. A recipe is given on how to obtain approximately this g(r) from a knowledge of the S(q), up to a certain maximum q value.  相似文献   
2.
The structure and aggregation kinetics of three-dimensional clusters composed of two different monomeric species at three concentrations are thoroughly investigated by means of extensive, large-scale computer simulations. The aggregating monomers have all the same size and occupy the cells of a cubic lattice. Two bonding schemes are considered: (a) the binary diffusion-limited cluster-cluster aggregation (BDLCA) in which only the monomers of different species stick together, and (b) the invading binary diffusion-limited cluster-cluster aggregation (IBDLCA) in which additionally monomers of one of the two species are allowed to bond. In the two schemes, the mixed aggregates display self-similarity with a fractal dimension d(f) that depends on the relative molar fraction of the two species and on concentration. At a given concentration, when this molar fraction is small, d(f) approaches a value close to the reaction-limited cluster-cluster aggregation of one-component systems, and when the molar fraction is 0.5, d(f) becomes close to the value of the diffusion-limited cluster-cluster aggregation model. The crossover between these two regimes is due to a time-decreasing reaction probability between colliding particles, particularly at small molar fractions. Several dynamical quantities are studied as a function of time. The number of clusters and the weight-average cluster size display a power-law behavior only at small concentrations. The dynamical exponents are obtained for molar fractions above 0.3 but not at or below 0.2, indicating the presence of a critical transition between a gelling to a nongelling system. The cluster-size distribution function presents scaling for molar fractions larger than 0.2.  相似文献   
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