Toward Nanomechanical Models of Liquid-Phase Exfoliation of Layered 2D Nanomaterials: Analysis of a π - peel Model

In liquid-phase exfoliation for the production of 2D nanomaterials fluid forces are used to gently overcome adhesive interlayer forces, leading to single- or few-layer 2D nanomaterials. Predicting accurately the critical fluid shear rate for exfoliation is a crucial challenge. By combining notions of fluid mechanics and fracture mechanics, we analyze a mathematical model of exfoliation, focusing on the pi - peel regime in which bending forces are much smaller than the applied hydrodynamic forces. We find that in this regime the shear rate is approximately proportional to the adhesion energy, independent of the bending rigidity of the exfoliated sheet, and inversely proportional to the size a of a (assumed pre-existing) material flaw. The model appears to give values comparable to those obtained in wet ball milling, but to overestimate the shear rate values reported for turbulent exfoliation (by rotor mixing or microfluidization). We suggest that for turbulent exfoliation a "cleavage model" may be more appropriate, as it gives a stronger dependence on a and smaller critical shear rates.