Elastic Bending Modulus of Single-Layer Molybdenum Disulphide (MoS2): Finite Thickness Effect

TL;DR

This paper derives an analytic formula for the elastic bending modulus of single-layer MoS2, accounting for finite thickness effects, and finds it significantly higher than graphene's, highlighting the influence of out-of-plane interactions.

Contribution

The paper introduces a novel analytic approach to calculate the bending modulus of SLMoS2 without defining a thickness, emphasizing finite thickness effects and out-of-plane interactions.

Findings

Bending modulus of SLMoS2 is 9.61 eV, much higher than graphene's 1.4 eV.

Finite thickness and out-of-plane interactions significantly increase the bending modulus.

The derived value aligns with thin shell theory and experimental elastic constants.

Abstract

We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2.