Liquid phase exfoliation is a commonly used method to produce 2D nanosheets from a range of layered crystals. However, such nanosheets display broad size and thickness distributions and correlations between area and thickness, issues that limit nanosheet application potential. To understand the factors controlling the exfoliation process, we have liquid-exfoliated 11 different layered materials, size-selecting each into fractions before using AFM to measure the nanosheet length, width, and thickness distributions for each fraction. The resultant data show a clear power-law scaling of nanosheet area with thickness for each material. We have developed a simple nonequilibrium thermodynamics-based model predicting that the power-law prefactor is proportional to both the ratios of in-plane-tearing/out-of-plane-peeling energies and in-plane/out-of-plane moduli. By comparing the experimental data with the modulus ratio calculated from first-principles, we find close agreement between experiment and theory. This supports our hypothesis that energy equipartition holds between nanosheet tearing and peeling during sonication-assisted exfoliation.

Chair of Applied Physical Chemistry University of Heidelberg Im Neuenheimer Feld 253 69120 Heidelberg Germany

Department of Inorganic Chemistry University of Chemistry and Technology Prague Technická 5 166 28 Prague 6 Czech Republic

School of Physics and CRANN and AMBER Research Centers Trinity College Dublin The University of Dublin Dublin 2 Ireland

Theory and Simulation of Materials École Polytechnique Fédérale de Lausanne CH 1015 Lausanne Switzerland

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