Publication 21-CNA-005
Nonlinear Statistical Mechanics Drives Intrinsic Electrostriction and Volumetric Torque in Polymer Networks
Matthew Grasinger
Pittsburgh Quantum Institute, University of Pittsburgh
Department of Civil and Environmental Engineering
Carnegie Mellon University, Pittsburgh, PA
UES Inc.
Materials and Manufacturing Directorate, Air Force Research Laboratory
matthew.grasinger.ctr@afresearchlab.com
Carmel Majidi
Department of Civil and Environmental Engineering
Department of Mechanical Engineering
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik Dayal
Pittsburgh Quantum Institute, University of Pittsburgh
Department of Civil and Environmental Engineering
Department of Materials Science and Engineering
Center for Nonlinear Analysis, Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA
Kaushik.Dayal@cmu.edu
Abstract: Statistical mechanics is an important tool for understanding polymer electroelasticity because the elasticity of polymers is primarily due to entropy. However, a common approach for the statistical mechanics of polymer chains, the Gaussian chain approximation, misses key physics. By considering the nonlinearities of the problem, we show a strong coupling between the deformation of a polymer chain and its dielectric response; that is, its net dipole. When chains with this coupling are cross-linked in an elastomer network and an electric field is applied, the field breaks the symmetry of the elastomer’s elastic properties, and, combined with electrostatic torque and incompressibility, leads to intrinsic electrostriction. Conversely, deformation can break the symmetry of the dielectric response leading to volumetric torque (i.e., a couple stress or torque per unit volume) and asymmetric actuation. Both phenomena have important implications for designing high-efficiency soft actuators and soft electroactive materials; and the presence of mechanisms for volumetric torque, in particular, can be used to develop higher degree of freedom actuators and to achieve bioinspired locomotion.
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