(587i) Entropic Pressure on Fluctuating Solid Membranes

Biological and crystalline membranes exhibit noticeable fluctuations at room temperature due to their low bending rigidity. These fluctuations significantly impact their overall mechanical behavior and interactions with external objects. When two membranes come into close proximity, they mutually suppress each other's fluctuations, leading to a repulsive force that plays a crucial role in the mechanical behavior of these membranes. From a mechanical perspective, crystalline membranes are modeled as solid membranes with inherent shear resistance, while biological membranes are commonly described as fluid-like entities without shear resistance. Under this premise, the entropic force between two fluctuating biological membranes is proposed to scale as 1/d^3, where d is the intermembrane distance. However, there are numerous instances where these membranes display shear resistance and behave like solid membranes, e.g. red blood cells membranes, viral capsids, etc. In this paper, we develop a statistical mechanics model within the framework of nonlinear elasticity to study the entropic force acting on a confined, fluctuating solid membrane. We demonstrate that, due to the nonlinear elasticity of solid membranes, the entropic force scales differently compared to that of fluid membranes. Our predictions align well with the results obtained from molecular dynamics simulations involving graphene, a representative of a solid membrane, confined between two rigid walls. We gratefully acknowledge financial support from the New Jersey Institute of Technology and the National Science Foundation, United States through Grants No. CMMI-2237530 and CBET- 2327899.