Quantifying the Exfoliation Ease Level of 2D Materials via Mechanical Anisotropy

The isolation of 2D materials from mother bulks into nanoscale is of vital importance for fulfilling their applications in many technological fields. Among known methods, mechanical exfoliation is one of the most widely utilized ways due to its simplicity. For a given 2D material, both its interlayer and its intralayer bonding strengths need to be taken into account for understanding the exfoliation process as the former dominates the ease level for cleaving adjacent molecular layers while the latter regulates the ability to resist cracking. In this regard, strong intralayer but weak interlayer bonding interactions respectively lead to large and thin nanosheets and, hence, facile exfoliation (and vice versa). As the bonding forces can be directly reflected through elastic properties of materials, here we propose to use the ratio between the in-plane and out-of-plane elastic modulus (E) as a universal index, A_In/Out (= E_In‑plane/E_{Out‑of‑plane}), to quantify the ease level of a 2D material’s mechanical exfoliation. Such ratios, which can be facilely obtained from routine computational and mechanical experiments, could provide useful information for estimating suitable exfoliation methods of 2D materials.