Thermodynamic Model of Structure and Shape in Rigid Polymer‐Laden Membranes

Abstract

A mechanical formulation for multi‐component rigid‐rod‐like polymer‐laden membranes is integrated with the Gibbs‐Duhem equation to describe the role of temperature and adsorption on membrane shape and on the nematic liquid crystal order of the embedded polymer. The rigid‐rod polymer model incorporates curvo‐philic effects promoting polymer re‐orientation along curvature directions and curvo‐phobic effects promoting polymer re‐orientation away from curvature directions, while the membrane curvature energy is described with the Helfrich formulation. The couplings between thermodynamical variables, polymer liquid crystalline order, and membrane curvature are demonstrated and characterized. The theory provides a road‐map to manipulate shape and structure in membranes containing fibers, proteins, and rod‐like polymers.

Microfibril organization modes in plant cell walls of variable curvature: a model system for two dimensional anisotropic soft matter

“…24 The model when integrated with the Gibbs-Duhem equation can describe the role of temperature and adsorption on membrane shape and fiber order. 25 A viscoelastic model that integrates the statics of anisotropic membranes developed in this model with the planar nematodynamics of fibers and the dynamics of isotropic membranes has been developed to study dynamic remodeling of plant cell wall during growth and morphogenesis. 26 The main issue considered in this paper is self-assembly of rigid fibers representing microfibrils on a soft deformable non-planar 2D membrane.…”

Modeling Textural Processes during Self-Assembly of Plant-Based Chiral-Nematic Liquid Crystals

“…An integrated shape and nematic order equation developed in this work gives a complete model whose solution describes the coupled membrane shape and fiber order state [36]. When integrated with the Gibbs-Duhem equation, the model can describe the role of temperature and adsorption on membrane shape and fiber order [37]. A viscoelastic model that integrates the statics of anisotropic membranes, the planar nematodynamics of fibers and the dynamics of isotropic membranes, has been reported to predict transitions between axial and azimuthal fiber arrangements of interest to cellulose fiber orientation in plant morphogenesis [38].…”

Structure and Pattern Formation in Biological Liquid Crystals: Insights From Theory and Simulation of Self-Assembly and Self-Organization

“…In particular nucleation and growth, defect generation mechanisms, and effect of electromagnetic fields (Selinger, 2016;Rey, 2010). More recently, driven by questions arising from biological material synthesis, such as plant cell walls with a basic fibrous composite architecture, models that capture the interaction between orientational ordering and elastic membrane curvature are being developed and refined (Murugesan and Rey, 2010a;Murugesan and Rey, 2010b;Rey et al, 2016;Rey and Murugesan, 2011;Murugesan et al, 2011;Murugesan and Rey, 2010c). Even with the simplest tubular elastic membranes with zero Gaussian curvature (K = 0) the director field n that emerges from PO can display many possible modes, including helical and ring-like orientation of fibrils, leading to new curvophobic and curvophilic mechanisms in 2D nematic ordering on curved elastic membranes.…”