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“Physics and Astronomy Colloquium- David Nelson”
October 9, 2017 @ 3:30 pm - 5:00 pm
UNC-CH Physics and Astronomy Colloquium
David Nelson, Lyman Laboratory of Physics, Harvard University
“Perforations, Curvature and Thermal Fluctuations in Free-Standing Graphene”
Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, 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. However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics. We discuss the remarkable properties of free-standing graphene sheets (with vK = 10^13!) at room temperature, where enhancements of the bending rigidity by factors of ~4000 compared to T = 0 values have now been observed. Thermalized elastic membranes can undergo a crumpling transition when the microscopic bending stiffness is comparable to kT. We argue that the crumpling temperature can be dramatically reduced by inserting a regular lattice of laser-cut perforations. These expectations are confirmed by extensive molecular dynamics simulations, which also reveal a remarkable “frame crumpling transition” triggered by a simple large hole inserted into a graphene sheet. We show finally that thin amorphous spherical shells with a background Gaussian curvature are inevitably (in the absence of a stabilizing pressure difference) crushed by thermal fluctuations beyond a critical size, of order 160nm for graphene at room temperature.