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

Abstract

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 analyse a mathematical model of exfoliation, focusing on the − 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 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 and smaller critical shear rates. Figure 1: Optimising liquid-phase exfoliation processes (left, reproduced with permission from Ref. (Paton, 2014)) requires models to link large-scale flow variables to the micromechanics of exfoliation.Optimising liquid-exfoliation processes requires addressing a delicate balance: the mechanical stresses applied to the particles by the fluid must be sufficiently high to delaminate the particles, but not much higher. Excessive stresses can fragment the nanosheets, producing small area sheets of low intrinsic value, or damage the sheets (Johnson, 2015). Reaching the right stress level is thus paramount. However, particle-level stresses cannot be controlled directly. What can be controlled are large scale flow variables, such as the mixing power or, equivalently, the average shear rate the suspension is subject to. These are the macroscopic variables that can be controlled by the user in the production process. It would be highly valuable if analytical formulas relating these macroscopic variables to microscopic exfoliation thresholds and timescales were available. Developing these formulas requires an understanding of the flow physics and deformation mechanics at the particle level (Fig. 1).Quite surprisingly, despite the growing importance of liquid-phase processing in the production of graphene and other 2D nanomaterials, the development of theoretical models for liquidphase exfoliation is at its infancy. Two theoretical models have appeared recently which seem to be relevant. An exfoliation model based on a sliding deformation was proposed by Chen et al. (Chen, 2012), and later extended by Paton et al (Paton, 2014). In this model, the shear forces exerted by the fluid are assumed to balance the rate at which the total surface energy (including solid-solid, solid-liquid and liquid-liquid interaction energy) changes with respect to the sliding distance. The model was used to describe the dependence of the critical shear rate for exfoliation on ...

Effect of hydrodynamic slip on the rotational dynamics of a thin Brownian platelet in shear flow

“…Finally, alignment is an essential ingredient to impart superior properties to nanocomposite materials. Surface modifications producing substantial slip could be used to align particles produced from the exfoliation of 2-D layered materials, which can be easily produced on mass scales by liquid-phase exfoliation (Botto 2019;Gravelle et al 2020;Salussolia et al 2020) and have therefore potential for applications. Because the ideal infinite Péclet number regime may not be achievable in practice, our results provide theoretical guidelines for deciding in which cases slip will have a dominant effect on the alignment of plate-like nanoparticles in the presence of Brownian motion.…”

“…Finally, alignment is an essential ingredient to impart superior properties to nanocomposite materials. Surface modifications producing substantial slip could be used to align particles produced from the exfoliation of 2-D layered materials, which can be easily produced on mass scales by liquid-phase exfoliation (Botto 2019; Gravelle et al. 2020; Salussolia et al.…”

Liquid exfoliation of multilayer graphene in sheared solvents: A molecular dynamics investigation

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How to unloop a self-adherent sheet

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