Aggregation processes in colloids: Computer simulations

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloid aggregation were performed to obtain the concentration dependence of the fractal dimension of the clusters before gelation, the average cluster sizes, and the scaling of the cluster size distribution. For DLCA, a square root type of increase of the fractal dimension from its zero-concentration value was found by three different methods: mass to radius of gyration relation, {dollar}M sim Rsbsp{lcub}g{rcub}{lcub}dsb{lcub}f{rcub}{rcub}{dollar}, short distance decay of the pair correlation function of isolated clusters, {dollar}g(r) = A rsp{lcub}dsb{lcub}f{rcub}-3{rcub} esp{lcub}-(r/xi)sp{lcub}a{rcub}{rcub},{dollar} and from the scattering function of isolated clusters. It is demonstrated that this dependence cannot be obtained from a direct analysis of the scattering function of the full aggregation bath. A recipe was proposed to be used by scattering researchers to extract the fractal dimension from the inversion of the scattering function. Both the exponent z and {dollar}zprime{dollar} that define the power law increase of the weight-average cluster size {dollar}Ssb{lcub}w{rcub}{dollar} and of the number-average cluster size {dollar}Ssb{lcub}n{rcub}{dollar} with time present a square root type increase with concentration. The cluster size distribution function scales as {dollar}Nsb{lcub}s{rcub}(t) approx Nsb{lcub}o{rcub}Ssbsp{lcub}w{rcub}{lcub}-2{rcub}f(s/Ssb{lcub}w{rcub}){dollar} where {dollar}Nsb{lcub}o{rcub}{dollar} is the number of initial colloidal particles, s the size of the clusters, and f is a concentration dependent function displaying an asymmetric bell shape in the limit of zero concentration. For RLCA the fractal dimension also presents a square root type of increase with concentration. An exponential increase of the average cluster sizes ({dollar}Ssb{lcub}w{rcub} {lcub}rm and{rcub} Ssb{lcub}n{rcub}{dollar}) with time was confirmed for a substantial range of the aggregation time. For longer times {dollar}Ssb{lcub}w{rcub}{dollar} departs from the exponential increase with time crossing over to a power law increase. The scaling is similar to the DLCA case but now a power law decay of the function f defines a new exponent {dollar}tau{dollar}, which displays a slight concentration dependence around {dollar}tau{dollar} = 1.5.