Session: 12-23-01: Symposium on Multiphysics Simulations and Experiments for Solids

Paper Number: 150378

150378 - Entropic Pressure on Fluctuating Solid Membranes 

Biological and crystalline membranes exhibit notable fluctuations at room temperature due to their low bending stiffness. 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 mechanics perspective, crystalline membranes are modeled as solid membranes, while biological membranes are commonly described as fluid entities. Under this premise, the entropic force between two fluctuating biological membranes is proposed to scale as p ∝ 1/d^3, where d is the intermembrane distance. However, However, instances exist where these membranes display shear resistance and behave like solids. Red blood cells (RBCs) endure mechanical stresses within the bloodstream and substantial deformations when squeezed through capillaries, yet their lifespan surpasses artificial drug delivery vesicles. RBC structural integrity is maintained by a network of flexible spectrin polymers forming a two-dimensional cytoskeleton, imparting shear resistance. The spectrin cytoskeleton is modeled as a solid membrane. Viral capsid shells' mechanical behavior is also of interest for understanding virus morphology and interactions. Apart from biological examples, crystalline membranes such as graphene, boron nitride, and MXenes are also modeled as solid membranes. These membranes may encounter noticeable entropic forces, particularly when placed on a substrate or interacting with another membrane. The elasticity of solid membranes presents a more complex scenario compared to their fluid counterparts. Unlike fluid membranes, solid membranes can feature not only bending and stretching rigidities but also non-trivial in-plane shear deformations that nonlinearly interact with the out-of-plane displacement field. To characterize the elasticity of solid membranes, the von Karman nonlinear plate theory is commonly employed. This nonlinearity introduces significant deviations in the entropic effects of thermal fluctuations compared to fluid membranes. However, the influence of these nonlinearities on the entropic forces exerted on a solid membrane has yet to be investigated. In this paper, we develop a statistical mechanics model within nonlinear elasticity to study the entropic force acting on a confined, fluctuating solid membrane. Coping with nonlinearities in the statistical mechanics of continuum systems is a challenging task, making the derivation of analytical expressions for fluctuations, partition functions, and free energy unattainable. Thus, we rely on approximate solutions, with a specific focus on employing variational perturbation theory (VPT) to establish the scaling law for the entropic force within nonlinear elasticity. 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.

Presenting Author: Rubayet Hassan New Jersey Institute of Technology

Presenting Author Biography: Rubayet Hassan
PhD Student
Department of Mechanical and Industrial Engineering
New Jersey Institute of Technology
New Jersey, USA

Research Interest My research focuses on the Mechanics of Nanomaterials and Biological
Systems, with a particular emphasis on employing theoretical and computational methodologies.
I am intrigued by the mechanical behavior of fluctuating surfaces, particularly in the context of
lipid bilayers and man-made flexible nanostructures such as molybdenum disulfide,
phosphorene, boron nitride, and MXenes. One key aspect of my work is developing a continuum
statistical mechanics model to investigate the entropic pressure near these fluctuating surfaces.
Additionally, I utilize molecular dynamics simulations to gain deeper insights into the behavior
of fluctuating membranes, aiming to bridge the gap between theoretical modeling and
computational observations in biophysics and material sciences.
Previous Education
1. M.Sc. in Mechanical Engineering, Georgia Southern University, Georgia, USA
2. M.Sc. in Mechanical Engineering, Konkuk University, Seoul, South Korea
3. B.Sc. in Mechanical Engineering, Khulna University of Engineering & Technology,
Khulna, Bangladesh

Address
New Jersey Institute of Technology
Mechanical and Industrial Engineering Center
Suite 333C
University Heights
Newark, New Jersey 07102

1. LinkedIn: https://www.linkedin.com/in/rubayet-hassan-906525100/
2. Google Scholar:
https://scholar.google.com/citations?user=KepNnIEAAAAJ&hl=en&authuser=1
3. ResearchGate: https://www.researchgate.net/profile/Rubayet-Hassan

Authors:

Rubayet Hassan New Jersey Institute of Technology
Dr. Samaneh Farokhirad New Jersey Institute of Technology
Dr. Fatemeh Ahmadpoor New Jersey Institute of Technology