Reversible-growth model: Cluster-cluster aggregation with finite binding energies

A reversible-growth model is built by modifying the cluster-cluster aggregation model with a finite interparticle attraction energy -E. When E is ∞, the aggregation is described by the ordinary cluster-cluster aggregation model. Within our model, particles as well as clusters are performing Brownian motion according to the rate 1/${\tau }_D$, and the unbinding takes place according to (1/${\tau }_R$)$e^{\mathrm{-}\Delta E/T}$, where ΔE is the energy change due to the unbinding, T is the room temperature, and ${\tau }_R$ is the time constant associated with the unbinding. The Boltzmann constant is taken to be unity. By changing E and ${\tau }_R$/${\tau }_D$, we are able to change the aggregation behavior over a wide range from ramified clusters to compact ones. Moreover, due to a finite E, ramified aggregates may become compact at a later time. We show that the initially fractal aggregates can remain fractal objects during restructuring while the fractal dimension D increases with time. At large E, D can stay at some value that is larger than the value of the cluster-cluster aggregation model and can remain unchanged for a long time. At a given time, D increases drastically with decreasing E from the value of the cluster-cluster aggregation model when E≤3T. The curve of the estimated sedimentation density versus E resembles that of D versus E and agrees with the experiments.