PDMS—A Versatile Platform for Determining Young’s Modulus in Ultrathin 2D Materials

The elastic modulus, or Young’s modulus, is a critical mechanical property that influences material suitability for various applications. This extends to 2D materials such as graphene, transition metal dichalcogenides (TMDs), boron nitride, talc, and others. However, conventional indentation techniques, effective for bulk materials, face challenges when applied to ultrathin 2D materials due to substrate effects. An alternative method involves the fabrication of well-defined circular holes on a rigid substrate, where the 2D material flake is deposited and a subsequent nanoindentation experiment is carried out at the center of the suspended 2D membrane [1]. Although successful, such procedure requires sophisticated lithography and transfer techniques which may hinder its wide applicability.<br/>Here, to address this issue, we propose an innovative approach using polydimethylsiloxane (PDMS) as a compliant substrate for atomic force microscopy-based force curves. Our method relies on an analytical model for plate deformation on an elastic foundation initially developed by Timoshenko and Woinowsky-Krieger in the late 1950s [2]. By measuring three easily accessible parameters—the flake thickness, applied force, and resulting deformation—we accurately determine the Young’s modulus of ultrathin materials [3]. Remarkably, this approach yields excellent agreement with existing literature for various tested 2D materials, including graphene, TMDs, and talc.<br/>PDMS serves as an ideal choice for the compliant substrate due to its widespread use in mechanical exfoliation and transfer of 2D material flakes. Moreover, PDMS possesses a well-known or easily measurable Young’s modulus (a requirement for our analytical model). The simplicity of our approach allows researchers to measure force curves directly on freshly exfoliated flakes while still on the PDMS surface, streamlining Young’s modulus determination.<br/>As the variety of ultrathin materials continues to expand, our proposed platform holds significant promise. By making Young’s modulus determination accessible and efficient, we contribute to the rapid development of applications for these remarkable materials.<br/><br/>Acknowledgements: The authors are thankful to Fapemig, CNPq, Capes, Rede2D, INCT NanoCarbono and LCPNano-UFMG for financial and infrastructural support.<br/><br/>References:<br/>[1] – C. Lee, X. Wei, J. W. Kysar and J. Hone; <i>Science</i> <b>321</b> 385–8 (2008).<br/>[2] – S. Timoshenko and S. Woinowsky-Krieger, <i>Theory of plates and shells</i>, McGraw Hill, NY (1959).<br/>[3] – L. de Avila and B. R. A. Neves, <i>submitted</i>.