Abstract
An accurate description for the shape of the graphene bubbles is essential for research and application of these gas bubbles in tuning electronic, magnetic, and optical properties of the two-dimensional nano materials. The present work reveals that the structural parameters of the bubble can not be described by the theoretical model based on the ideal gas law, which underestimates the structure parameters by 48%. The invalidity of the ideal gas law is due to the extremely large pressure of the gas inside the bubble that can be as high as 1 gigapascal, far beyond the applicability condition of the ideal gas law. To capture this effect, we develop an improved van der Waals equation with the quadratic nonlinear term of the gas density, which is found to provide an accurate description for the shape of the bubble. Further molecular dynamics simulations show high coincidence with the above van der Waals equation model for both graphene bubbles and MoS2 bubbles.
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