Statistical mechanical analysis of the electromechanical coupling in an electrically-responsive polymer chain

Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions

The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Effects of electrostriction on the bifurcated electro-mechanical performance of conical dielectric elastomer actuators and sensors

Dielectric elastomers (DEs) find applications in many areas, particularly in the field of soft robotics. When modeling and simulating DE-based actuators and sensors, a substantial portion of the literature assumes the selected DE material to behave in some perfectly hyperelastic manner, and the vast majority have assumed invariant permittivity. However, studies on simple planar DEs have revealed instabilities and hastened breakdowns when a variable permittivity is allowed. This is partly due to the intertwined electromechanical properties of DEs rooted on their labyrinthine polymeric microstructures. This work focuses on studying the effects of a varying (with stretch) permittivity on the out-of-plane deformation of a circular DE, using a model derived from principles of strain-induced polymer birefringence. In addition, we utilize the Edward–Vilgis model, which attempts to account for effects related to crosslinking, and length extension, slippage, and entanglement of polymer chains. Our approach reveals the presence of “stagnation” regions in the electromechanical behavior of the DE actuator material. These stagnation regions are characterized by both electrical and mechanical critical electrostrictive coefficient ratios. Mechanically, certain values of the electrostrictive coefficient ratio predict cases where deformation does not occur in response to a change in voltage. Electrically, certain cases are predicted where changes in capacitance cannot be measured in response to changes in deformation. Thus, some combined conditions of loading and material properties could limit the effectiveness of DE membranes in either actuation or sensing. Therefore, our results reveal mechanisms that could be useful to designers of actuators and sensors and unveil an opportunity for exploring new theoretical materials with potential novel applications. Furthermore, since there are known analogous formulations between electrical and optical properties, criticality principles studied in this article could be extended to optomechanical coupling.

Role of chain architecture in the solution phase assembly and thermoreversibility of aqueous PNIPAM/silyl methacrylate copolymers

Stimuli-responsive polymers functionalized with reactive inorganic groups enable creation of macromolecular structures such as hydrogels, micelles, and coatings that demonstrate smart behavior. Prior studies using poly(N-isopropyl acrylamide-co-3-(trimethoxysilyl)propyl methacrylate) (P(NIPAM-co-TMA)) have stabilized micelles and produced functional nanoscale coatings; however, such systems show limited responsiveness over multiple thermal cycles. Here, polymer architecture and TMA content are connected to the aqueous self-assembly, optical response, and thermo-reversibility of two distinct types of PNIPAM/TMA copolymers: random P(NIPAM-co-TMA), and a 'blocky-functionalized' copolymer where TMA is localized to one portion of the chain, P(NIPAM-b-NIPAM-co-TMA). Aqueous solution behavior characterized via cloud point testing (CPT), dynamic light scattering (DLS), and variable-temperature nuclear magnetic resonance spectroscopy (NMR) demonstrates that thermoresponsiveness and thermoreversibility over multiple cycles is a strong function of polymer configuration and TMA content. Despite low TMA content (≤2% mol), blocky-functionalized copolymers assemble into small, well-ordered structures above the cloud point that lead to distinct transmittance behaviors and stimuli-responsiveness over multiple cycles. Conversely, random copolymers form disordered aggregates at elevated temperatures, and only exhibit thermoreversibility at negligible TMA fractions (0.5% mol); higher TMA content leads to irreversible structure formation. This understanding of the architectural and assembly effects on the thermal cyclability of aqueous PNIPAM-co-TMA can be used to improve the scalability of responsive polymer applications requiring thermoreversible behavior, including sensing, separations, and functional coatings.

Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity

Soft robotics requires materials that are capable of large deformation and amenable to actuation with external stimuli such as electric fields. Energy harvesting, biomedical devices, flexible electronics, and sensors are some other applications enabled by electroactive soft materials. The phenomenon of flexoelectricity is an enticing alternative that refers to the development of electric polarization in dielectrics when subjected to strain gradients. In particular, flexoelectricity offers a direct linear coupling between a highly desirable deformation mode (flexure) and electric stimulus. Unfortunately, barring some exceptions, the flexoelectric effect is quite weak and rather substantial bending curvatures are required for an appreciable electromechanical response. Most experiments in the literature appear to confirm modest flexoelectricity in polymers although perplexingly, a singular work has measured a "giant" effect in elastomers under some specific conditions. Due to the lack of an understanding of the microscopic underpinnings of flexoelectricity in elastomers and a commensurate theory, it is not currently possible to either explain the contradictory experimental results on elastomers or pursue avenues for possible design of large flexoelectricity. In this work, we present a statistical-mechanics theory for the emergent flexoelectricity of elastomers consisting of polar monomers. The theory is shown to be valid in broad generality and leads to key insights regarding both giant flexoelectricity and material design. In particular, the theory shows that, in standard elastomer networks, combining stretching and bending is a mechanism for obtaining giant flexoelectricity, which also explains the aforementioned, surprising experimental discovery.

Nonlinear statistical mechanics drives intrinsic electrostriction and volumetric torque in polymer networks

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 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.