Centrifugation theory revisited: Understanding and modelling the centrifugation of 2D nanosheets

Size selection of liquid-dispersed 2D nanomaterials is a prerequisite for size-dependent studies in earlier stage research and for their targeted application in commercial settings. Centrifugation is the most widespread method for reliably sorting suspensions of polydisperse 2D nanosheets according to size. However, whilst centrifugation is effective, no a priori models are available to predict the outcome of centrifugation, making time consuming iterative experiments necessary. Here we present a simple model for the behaviour of 2D nanosheets during centrifugation and benchmark its predictions against experiments. This model uses simple expressions, specific to 2D particles, for the hydrodynamic radius, effective density and viscous resistance to generate the equation of motion of individual nanosheet during centrifugation. Critically, the equation of motion is then used to predict nanosheet size distributions within centrifugation products. This in turn leads to equations for easily measurable properties such as mean and maximum nanosheet sizes obtained during centrifugation-based fractionation. Comparison with experimental data demonstrates the robustness of this model for a range of 2D materials and solvent systems, and its ability to describe quite subtle effects. These results will enable more tailored size selection of nanosheets for specific applications and offer new mechanistic insights to optimise exfoliation conditions.