Harvard School of Engineering and Applied Sciences, Cambridge, MA 02138, USA.
Proc Natl Acad Sci U S A. 2012 Nov 27;109(48):19551-6. doi: 10.1073/pnas.1212268109. Epub 2012 Nov 12.
Thermal fluctuations strongly modify the large length-scale elastic behavior of cross-linked membranes, giving rise to scale-dependent elastic moduli. Whereas thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic shells. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and its exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell, using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness and dominates the response when the product of this ratio and the thermal energy becomes large compared with the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.
热涨落强烈地改变了交联膜的大尺度弹性行为，导致了尺度相关的弹性模量。虽然平面膜中的热效应已经被很好地理解了，但是许多自然和人工的微结构都被建模为薄的弹性壳。壳与平面膜的区别在于其非零的曲率，这为面内拉伸模式和面外起伏之间提供了一种尺寸相关的耦合。此外，壳可以支撑其内部和外部之间的压差。关于热涨落对壳的弹性性质的影响，人们知之甚少。在这里，我们使用微扰理论和蒙特卡罗计算机模拟，研究了受内压的球形壳的形状涨落的统计力学，明确地包括了曲率和向内压力的影响。我们预测了在点压痕和压力诱导变形下，薄壳的波动的新特性。由于热涨落引起的贡献随壳的半径与厚度之比的增加而增加，并且当该比值与壳的弯曲刚度的乘积与热能量相比变得大时，它主导了响应。当一个大的均匀向内压力作用在壳上时，热效应会增强，并且当这个压力接近壳的经典屈曲转变时，它会发散。我们的结果与微胶囊的弹性和渗透崩溃有关。
