Statistical Mechanics of Graphene Membranes and Ribbons

Abstract: Classical mechanics of thin solid rods and plates has been studied for centuries, and yet thin solid structures remain an active area of research to this day because geometrical nonlinearities in such structures lead to many unusual phenomena. These nonlinearities are also responsible for interesting behavior on the microscopic scale, where thermal fluctuations become important. It is well known that in the presence of thermal fluctuations, microscopically thin 1D rods, such as DNA and other polymers, form random coils. Since the late 1980's, it has also been clear that thermal fluctuations in microscopically thin elastic 2D membranes fundamentally alter the large distance physics and result in a strongly scale-dependent bending rigidity and Young's modulus. However, direct experimental evidence on the single membrane level was lacking until the McEuen group at Cornell recently demonstrated these effects by bending free-standing graphene sheets. Motivated by these experiments, I present a study of long narrow graphene ribbons, which behave like 1D flexible polymers, but retain many remarkable features of 2D membranes. Such studies are very useful for understanding the mechanics of microscale graphene kirigami structures, which can be used to construct flexible electronics, very sensitive force sensors and micro-actuators.