Statistical mechanics of a dielectric polymer chain in the force ensemble

Abstract

Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to a fixed force and fixed electric field using statistical mechanics. We assume that the dipoles induced by the applied electric field at each link do not interact with each other and compute the partition function using standard techniques. We then calculate the stretch and polarization by taking appropriate derivatives of the partition function and obtain analytical results in various limits. We also perform Markov chain Monte Carlo simulations using the Metropolis and umbrella sampling methods, as well as develop a new sampling method which improves convergence by exploiting a symmetry inherent in dielectric polymer chains. The analytical expressions are shown to agree with the Monte Carlo results over a range of forces and electric fields. Our results complement recent work on the statistical mechanics of electro-responsive chains which obtains analytical expressions in a different ensemble.

References in corpus (6)

• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Catastrophic thinning of dielectric elastomers
• Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity
• The interplay between symmetry-breaking and symmetry-preserving bifurcations in soft dielectric films and the emergence of giant electro-actuation
• Architected Elastomer Networks for Optimal Electromechanical Response
• Statistical Mechanical Analysis of the Electromechanical Coupling in an Electrically-Responsive Polymer Chain

Cited by in corpus (7)

• Polymer networks which locally rotate to accommodate stresses, torques, and deformation
• Statistical Field Theory of Polarizable Polymer Chains with Nonlocal Dipolar Interactions
• 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