Statistical Mechanical Analysis of the Electromechanical Coupling in an Electrically-Responsive Polymer Chain

Abstract

Polymeric materials that couple deformation and electrostatics have the potential for use in soft sensors and actuators with potential applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. In contrast to the mechanics of polymers that has been studied using statistical mechanics approaches for decades, the coupled response under deformation and electrical field has largely been modeled only phenomenologically at the continuum scale. In this work, we examine the physics of the coupled deformation and electrical response of an electrically-responsive polymer chain using statistical mechanics. We begin with a simple anisotropic model for the electrostatic dipole response to electric field of a single monomer, and use a separation of energy scales between the electrostatic field energy and the induced dipole field energy to reduce the nonlocal and infinite-dimensional statistical averaging to a simpler local finite-dimensional averaging. In this simplified setting, we derive the equations of the most likely monomer orientation density using the maximum term approximation, and a chain free energy is derived using this approximation. These equations are investigated numerically and the results provide insight into the physics of electro-mechanically coupled elastomer chains. Closed-form approximations are also developed in the limit of small electrical energy with respect to thermal energy; in the limit of small mechanical tension force acting on the chain; and using asymptotic matching for general chain conditions.

arXiv commentTo appear in Soft Matter

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• Statistical mechanics of a dielectric polymer chain in the force ensemble
• Polymer networks which locally rotate to accommodate stresses, torques, and deformation
• Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions
• Statistical Field Theory of Polarizable Polymer Chains with Nonlocal Dipolar Interactions
• Discrete-to-Continuum Limits of Long-Range Electrical Interactions in Nanostructures
• Exploiting Instabilities to Enable Large Shape Transformations in Dielectric Elastomers
• Nonuniqueness in Defining the Polarization: Nonlocal Surface Charges and the Electrostatic, Energetic, and Transport Perspectives
• Soft Electromechanical Elastomers Impervious to Instability
• Nonlocal Electrostatics and Boundary Charges in Continuum Limits of Two-Dimensional Materials
• Two-Scale Analysis of the Electrostatics of Dielectric Crystals: Emergence of Polarization Density and Boundary Charges