2016-09-29
11:00 at HIT E 41.1

Thermalized sheets and shells: curvature matters

David R. Nelson

Lyman Laboratory of Physics, Harvard University

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 = 107 in an ordinary sheet of writing paper. However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by exper- iments from the McEuen group at Cornell that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 1013). We review here the remarkable properties of thermalized sheets, where enhancements of the bending rigidity at T = 300 K by factors of ∼ 5000 have now been observed. We then move on to discuss thin amorphous spherical shells with a uniform nonzero curvature, accessible for example with soft matter experi- ments on diblock copolymers. This curvature couples the in-plane stretching modes with the out-of-plane undulation modes, giving rise to qualitative differences in the fluctuations of thermal spherical shells compared to flat membranes. Interesting effects arise because a shell can support a pressure difference between its interior and exterior. Thermal corrections to the pre- dictions of classical shell theory for microscale shells diverge as the shell radius tends to infinity.