Kavli Affiliate: Mark J. Bowick
| First 5 Authors: Roberto Abril Valenzuela, Paul Z. Hanakata, Mark J. Bowick, ,
| Summary:
We study the finite-temperature dynamics of thin elastic sheets in a
single-clamped cantilever configuration. This system is known to exhibit a tilt
transition at which the preferred mean plane of the sheet shifts from
horizontal to a plane above or below the horizontal. The resultant thermally
roughened two-state (up/down) system possesses rich dynamics on multiple time
scales. In the tilted regime, a finite energy barrier separates the
spontaneously chosen up state from the inversion-symmetric down state.
Molecular dynamics simulations confirm that over a sufficiently long time, such
thermalized elastic sheets transition between the two states, residing in each
for a finite dwell time. One might expect that temperature is the primary
driver for tilt inversion. We find, instead, that the primary control
parameter, at fixed tilt order parameter, is the dimensionless and purely
geometrical aspect ratio of the clamped width to the total length of the
otherwise-free sheet. Using a combination of an effective mean-field theory and
Kramers’ theory, we derive the transition rate and examine its asymptotic
behavior. At length scales beyond a material-dependent thermal length scale,
renormalization of the elastic constants qualitatively modifies the temperature
response. In particular, the transition is suppressed by thermal fluctuations,
enhancing the robustness of the tilted state. We check and supplement these
findings with further molecular dynamics simulations for a range of aspect
ratios and temperatures.
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