Reversible Cluster Aggregation and Growth Model for Graphene Suspensions

We present a reversible cluster aggregation model for 2-D macromolecules represented by line segments in 2-D; and, we use it to describe the aggregation process of functionalized graphene particles in an aqueous SDS surfactant solution. The model produces clusters with similar sizes and structures as a function of SDS concentration in agreement with experiments and predicts the existence of a critical surfactant concentration (C_crit) beyond which thermodynamically stable graphene suspensions form. Around C_crit, particles form dense clusters rapidly and sediment. At C ≪ C_crit, a contiguous ramified network of graphene gel forms which also densifies, but at a slower rate, and sediments with time. The deaggregation–reaggregation mechanism of our model captures the restructuring of the large aggregates towards a graphite-like structure for the low SDS concentrations.