Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (te). te is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is df=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of te transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension df=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction

Depletion from a hard wall induced by aggregation and gelation

Diffusion-limited cluster aggregation and gelation of hard spheres is simulated using off-lattice Monte Carlo simulations. A comparison is made of the wall-particle correlation function with the particle-particle correlation function over a range of volume fractions, both for the initial system of randomly distributed spheres and for the final gel state. For randomly distributed spheres the correlation functions are compared with theoretical results using the Ornstein-Zernike equation and the Percus-Yevick closure. At high volume fractions (φ > 40%) gelation has little influence on the correlation function, but for φ < 10% it is a universal function of the distance normalized by correlation length (ξ) of the bulk. The width of the depletion layer is about 0.5ξ. The concentration increases as a power law from the wall up to r ≈ ξ, where it reaches a weak maximum before decreasing to the bulk value

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter

3d Monte Carlo simulation of site-bond continuum percolation of spheres

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ($\phi_{\rm e}$), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres $1-\phi_{\rm e}$ is the porosity. The bond percolation threshold ($p_{\rm b}$) can be described in terms of $\phi_{\rm e}$ by a simple analytical expression: $\log(\phi_{\rm e})/\log(\phi_{\rm ec})+\log(p_{\rm b})/\log(p_{\rm bc})=1$, with $p_{\rm bc}=0.12$ independent of the bond range and $\phi_{\rm ec}$ a constant that decreases with increasing bond range

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction (0.5\mbox{--}49\%) and time. At volume fractions below $5\%$, the gel structure is fractal on small length scales with $d_{\rm f} = 1.8$. g(r) shows a weak minimum at the correlation length ($\xi$), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given $t/t_{\rm g}$, where $t_{\rm g}$ is the gel time, it is a universal function of $r/\xi$. At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity

Monte Carlo simulation of particle aggregation and gelation: I. Growth, structure and size distribution of the clusters

Lattice and off-lattice Monte Carlo simulations of diffusion-limited cluster aggregation and gelation were done over a broad range of concentrations. The large-scale structure and the size distribution of the clusters are characterized by a crossover at a characteristic size ($m_{\rm c}$). For $m < m_{\rm c}$, they are the same as obtained in a dilute DLCA process and for $m \gg m_{\rm c}$ they are the same as obtained in a static percolation process. $m_{\rm c}$ is determined by the overlap of the clusters and decreases with increasing particle concentration. The growth rate of large clusters is a universal function of time reduced by the gel time. The large-scale structural and temporal properties are the same for lattice and off-lattice simulations. The average degree of connectivity per particle in the gels formed in off-lattice simulations is independent of the concentration, but its distribution depends on the concentration