Discrete-symmetry-adapted Markov chain Monte Carlo for the electro-elasticity of polymers: chain taut, collapse, and order

arXiv:2205.00028v2 Announce Type: replace-cross Abstract: Dielectric elastomers are promising for soft robotics and wearable electronics and sensors, but their use is hindered by the high electric fields required. Maximizing electromechanical coupling through molecular mechanisms is essential. However, progress on the role of dipole-dipole interactions between monomers has been limited, in part because the resulting energy landscapes, characterized by multiple symmetric wells separated by high barriers, are difficult to sample with standard methods. This work develops a symmetry-adapted Markov chain Monte Carlo method that exploits the invariance of dipole-dipole interaction energies under simultaneous reflection of neighboring monomer orientations about the plane orthogonal to the applied electric field. Variable sized clusters of neighboring monomers are constructed and reflected, enabling rapid transitions between symmetric energy wells and rendering feasible simulations that are otherwise intractable. Freely jointed chains with anisotropic monomer polarizability reveals qualitatively distinct phenomena depending on the orientation of the monomer dipole relative to its backbone axis. Field-aligning chains exhibit electrically induced tautness, and an apparent compressive stiffness, while field-disaligning chains exhibit local folding and electrically induced collapse at large enough fields. Monomer orientational order is quantified across the applied field and susceptibility parameter space, revealing sharp transitions suggestive of underlying phase transitions. For field-disaligning chains, these orientational transitions correspond directly with sharp changes in chain polarization, linking microstructural rearrangement to the macroscopic dielectric response. The symmetry-adapted approach generalizes naturally to other multifunctional polymer systems whose energy landscapes possess analogous discrete symmetries.