Simulations of colloidal aggregation with short- and medium-range interactions (original) (raw)
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Structure function and fractal dimension of diffusion-limited colloidal aggregates
Physical Review E, 1998
On a three-dimensional lattice and at different concentrations we perform extensive numerical simulations of diffusion-limited colloidal aggregation ͑DLCA͒. In a previous work, we showed that the fractal dimension d f of the DLCA aggregates in the flocculation limit presents a square root type of dependence with the initial colloidal concentration. The d f was obtained from the slope of a standard log-log plot of the number of particles versus size of the formed aggregates. In this work we confirm the concentration dependency using the particle-particle correlation function g(r) and the structure function S(q) of individual aggregates. We demonstrate that the g(r)ϭAr d f Ϫ3 e Ϫ(r/) a , where A, a, and are parameters characteristic of the aggregates, and aϾ1. This stretched exponential law gives an excellent fit to the cutoff of the g(r). The structure function reveals the d f from the slope of a log-lot plot of S(q) versus q for high q values. We also analyze g(r) and S(q), at different times during the reaction, for the whole aggregating system composed of many clusters of different sizes. We observe that the d f calculated from the g(r) agrees well with that obtained from individual clusters. However, caution should be observed to extract a d f from the corresponding S(q). Our results indicate that for finite concentrations a d f systematically larger than the true value is obtained from such analysis. ͓S1063-651X͑98͒12404-2͔
Scaling of the Structure Factor in Fractal Aggregation of Colloids: Computer Simulations
Journal of Colloid and Interface Science, 1996
In the volume fraction range (0.005,0.08), we have obtained the temporal evolution of the structure factor S(q), in extensive numerical simulations of both diffusion-limited and reaction-limited colloid aggregation in three dimensions. We report the observation of scaling of this structure function in the diffusion-limited case, analogous to a spinodal decomposition type of scaling. By comparing S(q) with the pair correlation function between particles, we were able to identify the peak in the structure factor as arising from the correlations between particles belonging to nearest-neighbor clusters. The exponents a′ and a′′ that relate the position and the height of the maximum in S(q) vs. time, respectively, were also obtained and shown to differ somewhat from the spinodal decomposition exponents. We also found a terminal shape for S(q) that corresponds to a close packing of the clusters after gelation. Moreover, this picture was shown to be valid in a concentration range larger than the one suggested in recent experiments. Although the S(q) for reaction-limited colloid aggregation does not show a pronounced peak for the earlier times, eventually the peak stretches and becomes higher than in the diffusion-limited case. The S(q) curves, however, do not present the scaling shown for diffusion-limited aggregation.
Langmuir, 2002
A theoretical model for the interaction between colloidal particles trapped at the air-water interface is proposed in order to explain experimental aggregation results. Kinetic and structural aspects of 2D aggregation processes point out the long-range nature of the particle interactions. These interactions have been modeled by means of monopolar and dipolar repulsive forces, which depend on the monopole and dipole surface fractions at the emergent part of the colloidal particles, fmon and fdip, respectively. Brownian dynamics simulations have been used to fit the model to experiment results using the fractal dimension d f and the kinetics exponent z as comparative parameters. Simulation results show that dipolar interaction controls aggregation at high subphase salt concentration whereas the monopolar interaction determines aggregation at low salt concentrations. Moreover, results show that f mon is the main parameter controlling kinetics in 2D aggregation and, hence, a critical coagulation concentration (CCC) can be defined from the salt concentration at which the monopole fraction becomes zero, f mon) 0.
Concentration effects on two- and three-dimensional colloidal aggregation
Physica A: Statistical Mechanics and its Applications, 2002
By means of extensive numerical simulations of di usion-limited colloidal aggregation in two and three dimensions, we have found the concentration dependence of the structural and dynamical quantities. Both on-and o-lattice simulations were used in 2D to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned two-and-a-half orders of magnitude, in both dimensionalities. In two dimensions, it was found that the cluster fractal dimension di erence from the zero-concentration value shows a linear increase with the concentration, while this increase is of a square root type for the three-dimensional case. For the exponent z, deÿning the increase of the weight-average cluster size as a function of time, the di erence from the zero-concentration value in three dimensions is again of a square root type increase with concentration, while in two dimensions this increase goes as the 0.6 power of the concentration. We give arguments for the drastic change in the power laws for the case of the fractal dimension, when going from two to three dimensions, and for the small change for the case of the kinetic exponent z. We also present the master curves for the scaling of the cluster size distribution and their dependence on concentration, in both dimensionalities.
Influence of the potential range on the aggregation of colloidal particles
Physica A: Statistical Mechanics and its Applications, 2007
This work is a theoretical contribution to the understanding of the aggregation process in dilute colloidal suspensions. We employ Brownian dynamics simulations, with homodisperse solid spherical particles, neglecting hydrodynamic interactions between the particles. We study the influence of the shape of the interaction potential on the aggregation process and in particular the effect of an increase of the attraction range with regard to the DLVO potential. It is concluded that it can change either the aggregates shape and the aggregation kinetics. We show that the fractal properties, the cluster size distribution and the average cluster size prove to be capable of characterizing those effects, at least in the simulations, with two well-separated attraction ranges.
Colloidal Aggregation Induced by Long Range Attractions
Langmuir, 2004
The structure of colloidal clusters formed by long-range attractive interactions under diluted conditions is studied by means of Monte Carlo simulations. For a not-too-long attraction range, clusters show selfsimilar internal structure with lower density than that typical for diffusive aggregation. For long-range interactions, low κ, nonfractal clusters are formed (dense at short scales but open at long ones). The dependence on the volume fraction shows that more-compact clusters are grown the higher the colloidal density for diffusive aggregation and attraction-driven aggregation in the fractal regime. The whole trend is explained in terms of the interpenetration among aggregates. In attraction-driven aggregations, the interpenetration of clusters competes with aggregation in the tips of the clusters, causing low-density clusters.
Cluster Morphology of Colloidal Systems With Competing Interactions
Frontiers in Physics, 2021
Reversible aggregation of purely short-ranged attractive colloidal particles leads to the formation of clusters with a fractal dimension that only depends on the second virial coefficient. The addition of a long-ranged repulsion to the potential modifies the way in which the particles aggregate into clusters and form intermediate range order structures, and have a strong influence on the dynamical and rheological properties of colloidal dispersions. The understanding of the effect of a long-ranged repulsive potential on the aggregation mechanisms is scientifically and technologically important for a large variety of physical, chemical and biological systems, including concentrated protein solutions. In this work, the equilibrium cluster morphology of particles interacting through a short-ranged attraction plus a long-ranged repulsion is extensively studied by means of Monte Carlo computer simulations. Our findings point out that the addition of the repulsion affects the resulting cl...
Two-Dimensional Colloidal Aggregation: Concentration Effects
Journal of Colloid and Interface Science, 2002
Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration φ, following the law: d f = d fo + aφ c. For the on-lattice simulations the fractal dimension in the zero concentration limit, d fo , was 1.451 ± 0.002, while for the off-lattice simulations the same quantity took the value 1.445 ± 0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633 ± 0.021 and 1.046 ± 0.032, while for the off-lattice simulations they were 1.005 ± 0.059 and 0.999 ± 0.045, respectively. For the exponents z and z , defining the increase of the weight-average (S w (t)) and number-average (S n (t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z = z o + bφ d and z = z o + b φ d. For the on-lattice simulations, z o , b, and d were equal to 0.593 ± 0.008, 0.696 ± 0.068, and 0.485 ± 0.048, respectively, while for the off-lattice simulations they were 0.595 ± 0.005, 0.807 ± 0.093, and 0.599 ± 0.051. In the case of the exponent z , the quantities z o , b , and d were, for the on-lattice simulations, equal to 0.615 ± 0.004, 0.814 ± 0.081, and 0.620 ± 0.043, respectively, while for the off-lattice algorithm they took the values 0.598 ± 0.002, 0.855 ± 0.035, and 0.610 ± 0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d f = d fo + a φ c , with d fo = 1.560 ± 0.004, a = 0.342 ± 0.039, and c = 1.000 ± 0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S w (t) and S n (t) in the aggregation regime considered, and no exponents z and z were defined. We argue however that for sufficiently long periods of time
Physical Review E, 1996
We have performed extensive numerical simulations of diffusion-limited ͑DLCA͒ and reaction-limited ͑RLCA͒ colloid aggregation to obtain the dependence on concentration of several structural and dynamical quantities, among them the fractal dimension of the clusters before gelation, the average cluster sizes, and the scaling of the cluster size distribution function. A range in volume fraction spanning two and a half decades was used for this study. For DLCA, a square root type of increase of the fractal dimension with concentration from its zero-concentration value was found:
Dynamic scaling and fractal structure of small colloidal clusters
We studied the aggregation of small colloidal polystyrene spheres during the limiting growth regime of diffusion-limited aggregation. The number-average mean cluster size and the fractal dimension of the aggregates were obtained by dynamic and static light scattering (DLS and SLS). The experimental results are interpreted using the spatial and dynamic scaling formalism. The homogeneity exponent u was used to identify the aggregation mechanism. An unexpected cluster size scaling was observed for early aggregation stages. This feature allowed the use of spatial and dynamic scaling concepts as an alternative method for determining the Smoluchowski rate constant k 11 .