Statistical mechanics of thin spherical shells

Abstract

We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes and the local out-of-plane undulations, leads to novel phenomena. In spherical shells thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure". Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows non-linearly with increasing outward pressure, with the same universal power law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

16 pages, 6 figures

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Cited by in corpus (28)

• Non-Hookean statistical mechanics of clamped graphene ribbons
• Buckling of thermalized elastic sheets
• Thermalized buckling of isotropically compressed thin sheets
• Scaling behavior of crystalline membranes: an $\epsilon$-expansion approach
• Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface
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• Shallow shell theory of the buckling energy barrier: from the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure
• Thermal buckling transition of crystalline membranes in a field
• The nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature
• Three-loop order approach to flat polymerized membranes
• Rolled up or crumpled: phases of asymmetric tethered membranes
• Anomalous thermal expansion in Ising-like puckered sheets
• Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing
• Statistical modeling of equilibrium phase transition in confined fluids
• Active buckling of pressurized spherical shells : Monte Carlo Simulation
• Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells
• Exact Solution for Elastic Networks on Curved Surfaces
• The effect of anomalous elasticity on the bubbles in van der Waals heterostructures
• Emergent continuous symmetry in anisotropic flexible two-dimensional materials
• Curvature as an external field in mechanical antiferromagnets
• Localized tension-induced giant folding in unstructured elastic sheets
• Thermally driven elastic membranes are quasi-linear across all scales
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• MeMC: A package for monte-carlo simulations of spherical shells
• Renormalized mechanics and stochastic thermodynamics of growing vesicles
• Geometry and dynamics of spring networks of spherical topology