Equipartition of Energy Defines the Size-Thickness Relationship in Liquid-Exfoliated Nanosheets

TL;DR

This study reveals that energy equipartition governs the size-thickness relationship in liquid-exfoliated nanosheets, supported by experimental data and thermodynamic modeling, advancing understanding of nanosheet exfoliation mechanisms.

Contribution

The paper introduces a thermodynamics-based model linking nanosheet size and thickness to energy ratios, validated by experimental data across multiple layered materials.

Findings

Power-law scaling of nanosheet area with thickness observed.

Model predicts the size-thickness relationship based on energy ratios.

Close agreement between experimental data and theoretical predictions.

Abstract

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.