The Statistical Mechanics of Graphene Membranes and Ribbons
by
David R. Nelson(Harvard University)
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Europe/Stockholm
122:026
122:026
Description
Understanding deformations of macroscopic thin plates and shells has a
long and rich history, culminating with the Foeppl-von Karman equations
in 1904. These highly nonlinear equations are characterized by a
dimensionless coupling constant (the "Foeppl-von Karman number") that
can easily reach vK = 10^7 in an ordinary sheet of writing paper.
Since the late 1980's, it has been clear that thermal fluctuations in microscopically thin elastic membranes fundamentally alter the long
wavelength physics, leading to a negative thermal expansion coefficient, and a strongly scale-dependent bending energy and Young's modulus.
Recent experiments from the McEuen group at Cornell that twist and bend
individual atomically-thin free-standing graphene sheets (with vK =10^13!) call for a theory of the mechanical deformation of thermally
excited membranes with large Foeppl-von Karman number. We present here results for the bending and pulling of thermalized graphene ribbons and tabs in the cantilever mode.*
*Work done in collaboration with Andrej Kosmrlj
