Bubble-Induced Strong Thermal Contraction For Graphene

The thermal expansion coefficient of van der Waals layered structures is of crucial importance in governing the dependability and longevity of advanced optoelectronic equipment. Bubbles are commonly found within layered structures, yet their impact on the thermal expansion coefficient of the structure is still not well understood. We derive an analytical formula that describes the influence of bubbles on the variation in length, utilizing both the elastic membrane theory and the improved van der Waals gas state equation. The results demonstrate that as the temperature increases, bubbles can induce significant thermal contraction in few-layer graphene structures. The analytical predictions are validated through molecular dynamic simulations, confirming the accuracy and reliability of the proposed model. These findings hold significant value in enhancing our understanding of the dependability and durability of functional equipment that relies on van der Waals layered structures.