Related Experiment Video
Updated: Jul 26, 2026
09:20
Perturbing Endothelial Biomechanics via Connexin 43 Structural Disruption
Published on: October 4, 2019
Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based
J A Santiago1,2, G Chacón-Acosta1, F Monroy2,3
1Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, Vasco de Quiroga 4871, 05348 Ciudad de México, Mexico.
Physical Review. E
|September 11, 2019
Summary
This study models fluid membranes with embedded nematic molecules, revealing how molecular ordering creates anisotropic stresses beyond standard elastic models. These findings advance understanding of membrane mechanics and liquid crystal interactions.
Area of Science:
- Physics
- Materials Science
- Biophysics
Background:
- Fluid membranes exhibit complex behavior influenced by internal molecular ordering.
- Anisotropic fluid membranes with embedded nematic molecules present unique mechanical properties.
- Standard Canham-Helfrich elasticity does not fully capture stresses in ordered membranes.
Purpose of the Study:
- To model an elastic membrane with embedded nematic molecules as an anisotropic fluid membrane.
- To investigate the geometric coupling between the director field and membrane curvature.
- To derive analytical expressions for membrane stress and torque induced by nematic director configurations.
Main Methods:
- Utilized differential geometry to analyze membrane mechanics.
- Incorporated Frank energy of liquid crystals to describe nematic director behavior.
- Developed analytical expressions for stress and torque based on director field deformations (splaying, twisting, bending).
Main Results:
- Nematic ordering induces anisotropic stresses in addition to Canham-Helfrich elasticity.
- Derived analytical formulas for membrane stress and torque.
- Visualized forces from nematic textures on spherical and cylindrical surfaces.
Conclusions:
- Nematic textures significantly influence the mechanical properties of fluid membranes.
- The geometric coupling between director field and curvature is crucial for understanding membrane stress.
- This model provides a framework for predicting the behavior of anisotropic fluid membranes.
Related Concept Videos
01:16Stress on an Oblique Plane
Understanding stress on an oblique plane under axial loading is pivotal in material mechanics. This analysis offers insight into a material's durability and strength, which is crucial for civil engineering and structural design. Axial loading refers to force application along the material's central axis, causing compression or elongation and leading to normal stress. Normal stress occurs when a force acts perpendicularly to the material's area, resulting in compressive or tensile stress. When...
01:15Stress: General Loading Conditions
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
01:23Components of Stress
Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the...
Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the...
01:18Stress Concentrations in Circular Shafts
Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
01:18Transformation of Plane Stress
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
01:21General State of Stress
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...