Thin dielectric elastomers with compliant electrodes exhibit various types of instability under the action of electromechanical loading. Guided by the thermodynamically-based formulation of Fosdick and Tang (J. Elasticity 88, 255-297, 2007), here we provide an energetic perspective on the stability of dielectric elastomers and we highlight the fundamental energetic divide between voltage control and charge control. By using the concept of energy relaxation, we describe wrinkling for neo-Hookean ideal elastomers, and we show that in voltage control wrinkling is stable as long as the tension-extension inequality holds, whereas wrinkling is always stable in charge control. We finally illustrate some examples involving both homogeneous and inhomogeneous deformations, showing that the type and hierarchy of instabilities taking place in dielectric membranes can be tuned by suitable choices of the boundary conditions.
The wrinkling transition experimentally identified by Mutz et al. [Phys. Rev. Lett. 67, 923 (1991)] and then thoroughly studied by Chaieb et al. [Phys. Rev. Lett. 96, 078101 (2006)] in partially polymerized lipid membranes is reconsidered. One shows that the features associated with this transition, notably the various scaling behaviors of the height-height correlation functions that have been observed, are qualitatively and quantitatively well described by a recent nonperturbative renormalization group (NPRG) approach to quenched disordered membranes by Coquand et al. [Phys. Rev E 97, 030102 …
Electro-mechanical wrinkling of soft dielectric films bonded to hyperelastic substrates
Zhejiang University（浙江大学）；University of Galway（戈尔韦大学）；Center for Soft Machines and Smart Devices, Huanjiang Laboratory（软机器与智能设备中心，环江实验室）；Ningbo University（宁波大学）；SISSA – International School for Advanced Studies（SISSA-高级研究国际学校）
We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean …
The alteration of the dielectric membrane properties by membrane engineering techniques such as carbon nanotube (CNT) coating opens the way to novel molecular transport strategies for biosensing purposes. In this article, we predict a macromolecular transport mechanism enabling the dielectric manipulation of the polymer translocation dynamics in dielectric membrane pores confining mixed electrolytes. In the giant permittivity regime of these engineered membranes governed by attractive polarization forces, multivalent ions adsorbed by the membrane nanopore trigger a monovalent ion separation an…
We investigate the stability of a circular electrodes-coated dielectric membrane under the combined action of an electric field and all-round in-plane tension. It is known that such a membrane is susceptible to the limiting point instability (also known as pull-in instability) which is widely believed to be a precursor to electric breakdown. However, there is experimental evidence showing that the limiting point instability may not necessarily be responsible for rapid thinning and electric breakdown. We explore the possibility that the latter is due to a new instability mechanism, namely local…
The prolate-to-oblate shape transition of phospholipid vesicles in response to frequency variation of an AC electric field can be explained by the dielectric anisotropy of a phospholipid bilayer
Simplified discrete model for axisymmetric dielectric elastomer membranes with robotic applications
Hohai University（河海大学）；University of Birmingham（伯明翰大学）；Nanyang Technological University（南洋理工大学）；University of Michigan（密歇根大学）；Newcastle University（纽卡斯尔大学）
We examine the stability of a soft dielectric plate deformed by the coupled effects of a mechanical pre-stress applied on its lateral faces and an electric field applied through its thickness under charge control. The electric field is created by spraying charges on the major faces of the plate: although in practice this mode of actuation is harder to achieve than a voltage-driven deformation, here we find that it turns out to be much more stable in theory and in simulations. First we show that the electromechanical instability based on the Hessian criterion associated with the free energy of …
Dielectric permittivity of water confined in stacks of charged lipid layers: extracting profiles from molecular dynamics simulations using a modified Poisson-Boltzmann equation
Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学，法国国家科学研究中心，光物质研究所）；UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心查尔斯·萨德龙研究所）
The electrostatic Schwinger-Dyson equations are derived and solved for an electrolyte mixture composed of mono- and multivalent ions confined to a negatively charged nanoslit. The closure of these equations is based on an asymmetric treatment of the ionic species with respect to their electrostatic coupling strength; the weakly coupled monovalent ions are treated within a gaussian approximation while the multivalent counterions of high coupling strength are incorporated with a strong-coupling approach. The resulting self-consistent formalism includes explicitly the interactions of the multival…
We introduce a strain-energy based nonlinear hyper-elastic formulation to model the material properties of ultrasoft dielectric elastomers over a wide range of elastic properties, prestretch, and thicknesses. We build on the uniaxial Gent formulation, and under the conditions of equi-biaxial strain, derive an expression for the bulge deformation versus pressure. A circular bulge test methodology is developed to experimentally measure the mechanical response of the silicone membranes. The Gent model captures both neo-Hookean and strain-stiffening behaviors, and gives predictions which are in ag…
The Derjaguin-Landau-Verywey-Overbeek (DLVO) theory has been a remarkably accurate framework for the characterization of macromolecular stability in water solvent. In view of its solvent-implicit nature neglecting the electrostatics of water molecules with non-negligible charge structure and concentration, the precision of the DLVO formalism is somewhat puzzling. In order to shed light on this issue, we derive from our earlier explicit solvent formalism [S. Buyukdagli el al., Phys. Rev. E, 2013, 87, 063201] a solvent-augmented contact value theorem and assess the contribution of solvent molecu…
