Accurate Measurement of the Cleavage Energy of Graphite

Abstract: The basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene, and carbon nanotubes. The CE is equal to twice the surface energy and is closely related to the interlayer binding energy and exfoliation energy of graphite. Nonetheless, a wide range of values for these properties have been reported and no consensus has yet emerged as to their magnitude. Here, we report the first direct, accurate experimental measurement of the CE of graphite using a novel method based on the recently discovered self-retraction phenomenon in graphite. The measured value, 0.37 +/- 0.01 J/m2 for the incommensurate state of bicrystal graphite, is nearly invariant with respect to temperature (from 22{\deg}C to 198{\deg}C) and bicrystal twist angle, and insensitive to impurities (from the atmosphere). The cleavage energy for the ideal ABAB graphite stacking, 0.39 +/- 0.02 J/m2, is calculated based upon a combination of the measured CE and a theoretical calculation. These experimental measurements are ideal for use in evaluating the efficacy of competing theoretical approaches.

• The paper presents the first direct experimental measurement of graphite's cleavage energy using a self-retraction method.
• The paper demonstrates that the measured cleavage energy remains constant (0.37 ± 0.01 J/m²) despite variations in temperature and twist angle.
• The paper refines theoretical models by providing empirical data that enhance predictions for interlayer interactions in layered materials.

Experimental Measurement of Cleavage Energy in Graphite

The accurate measurement of graphite's cleavage energy (CE), a crucial parameter influencing the characteristics of graphite, graphene, and carbon nanotubes, occupies a central role in materials science research. This paper documents the first direct experimental evaluation of CE through a novel methodology, providing empirical clarity in an area long dominated by theoretical estimation and indirect measurements yielding disparate values. The recorded CE for the incommensurate state of bicrystal graphite stands at 0.37 ± 0.01 J/m², exhibiting little variation across temperatures and twist angles.

Graphite is characterized by its hexagonal, layered crystalline structure, where each layer is a monatomic graphene sheet. The intralayer bonds in graphite are robust due to sp² bonding, while the much weaker van der Waals forces govern interlayer interactions. This disparity results in unique thermal, electrical, and mechanical properties, making graphite and its derivatives subject to extensive research attention. Despite this interest, however, the clear quantification of interlayer interactions has eluded consensus.

The paper utilizes the self-retraction phenomenon to measure the CE directly, assessing the force required to shear two rotated single crystal graphite flakes under superlubric conditions. The shear force readings enable the calculation of cleavage energy, providing insight into interlayer surface interactions. Additionally, the CE obtained for ABAB stacked graphite accounts for a value of 0.39 ± 0.02 J/m², derived from a combination of experiments and theoretical back-calculations.

The implications of these results are significant both practically and theoretically. Experimentally determined cleavage energies offer a benchmark for evaluating and refining computational methods used in the prediction of van der Waals interactions in similar two-dimensional materials. By confirming that the graphite CE is invariant with respect to external conditions, such as temperature and twist angle, the durability of graphite's structural properties in various conditions can be better understood and exploited in applications demanding material reliability.

The investigation further evaluates the theoretical framework of interlayer bonding, leveraging the Peierls-Nabarro model to complement empirical data. This model allows for a granular perspective on grain boundary energies, revealing the grain boundary's role in contributing to graphite's overall stability. These results, suggesting minimal impact of twist angles on cleavage energy within a practical range, indicate that the dominant factor remains the interlayer bonding itself rather than structural alignment.

In conclusion, this work delineates a precise framework for understanding graphite's cleavage energy, thereby aiding the predictive accuracy of theoretical calculations in layered materials and reinforcing the importance of empirical data within the materials science domain. The research substantiates that experimental and theoretical enhancements in predicting material behavior can propel technological advancements and expedite new applications involving graphite and its allotropes. Future developments might focus on exploring additional environmental variables or testing further structural modifications, such as strain effects, thereby further sharpening the material science toolset.