Analytical methods for the mechanics of graphene bubbles

Abstract

When placing a graphene membrane on a substrate, gas molecules may be trapped underneath to form bubbles. The size of a graphene bubble (e.g., diameter and height) depends on the number of gas molecules that are trapped, the elastic properties of graphene, and the interfacial adhesion between graphene and the substrate. A mechanics analysis of such graphene bubbles is conducted via membrane and nonlinear plate theories, so that the interfacial adhesion can be determined directly from measurements of the bubble size. A comparison of the results from these two models establishes that the membrane analysis is sufficient for relatively large bubbles. The adhesion energy of mechanically exfoliated graphene on silicon oxide is extracted from two reported data sets using the simple membrane theory, and the values range from 0.097 to 0.43 J/m2. Moreover, the strain distribution of the graphene bubbles and transport of gas molecules among the bubbles are discussed.