Effective zero-thickness model for a conductive membrane driven by an electric field

Nonlinear ion transport mediated by induced charge in ultrathin nanoporous membranes

Ultrathin membranes with nanoporous conduits show promise for ionic separations and desalination applications, but the mechanisms underlying the nonlinear ionic transport observed in these systems are not well understood. Here, we demonstrate how induced charge at membrane interfaces can lead to nonlinear ionic transport and voltage-dependent conductance through such channels. The application of an electric field on a polarizable membrane leads to induced charges at the membrane interfaces. The induced charges in turn are screened by diffuse charges in the electrolyte, which are acted upon by the electric field. For extremely thin membranes, the induced charge effect can be significant even for moderate applied voltages commonly used in experiments. We apply a continuum Poisson-Nernst-Planck model to characterize the current-voltage behavior of ultrathin membranes over a wide parameter space. The predictions of the model are compared to recent experiments on graphene and MoS_{2} membranes in an electric field. We expect the role of induced charge to be especially pronounced in the limit of atomically thin membranes.

Modification of lipid membrane compressibility induced by an electric field

Changes in membrane deformation and compressibility, induced by an external electric field, are investigated using coarse-grained martini force field simulations in a salt-free environment. We observe changes in the area of the membrane above a critical electric field. Below this value, the membrane compressibility modulus is found to decrease monotonically. For higher electric fields, the membrane projected area remains constant while the net interfacial area increases, with the corresponding compressibility moduli, show the opposite behavior. We find that the mechanical parameters, surface tension and bending modulus, of a freely floating membrane in the absence of explicit ions, are unaffected by the presence of the electric field. We believe these results have a bearing on our understanding of the electroformation of uncharged lipids in a salt-free environment.

Lipid vesicles in pulsed electric fields: Fundamental principles of the membrane response and its biomedical applications

The present review focuses on the effects of pulsed electric fields on lipid vesicles ranging from giant unilamellar vesicles (GUVs) to small unilamellar vesicles (SUVs), from both fundamental and applicative perspectives. Lipid vesicles are the most popular model membrane systems for studying biophysical and biological processes in living cells. Furthermore, as vesicles are made from biocompatible and biodegradable materials, they provide a strategy to create safe and functionalized drug delivery systems in health-care applications. Exposure of lipid vesicles to pulsed electric fields is a common physical method to transiently increase the permeability of the lipid membrane. This method, termed electroporation, has shown many advantages for delivering exogenous molecules including drugs and genetic material into vesicles and living cells. In addition, electroporation can be applied to induce fusion between vesicles and/or cells. First, we discuss in detail how research on cell-size GUVs as model cell systems has provided novel insight into the basic mechanisms of cell electroporation and associated phenomena. Afterwards, we continue with a thorough overview how electroporation and electrofusion have been used as versatile methods to manipulate vesicles of all sizes in different biomedical applications. We conclude by summarizing the open questions in the field of electroporation and possible future directions for vesicles in the biomedical field.

Reduction in Tension and Stiffening of Lipid Membranes in an Electric Field Revealed by X-Ray Scattering

The effect of ac electric fields on the elasticity of supported lipid bilayers is investigated at the microscopic level using grazing incidence synchrotron x-ray scattering. A strong decrease in the membrane tension up to 1  mN/m and a dramatic increase of its effective rigidity up to 300  k_{B}T are observed for local electric potentials seen by the membrane ≲1  V. The experimental results are analyzed using detailed electrokinetic modeling and nonlinear Poisson-Boltzmann theory. Based on a modeling of the electromagnetic stress, which provides an accurate description of the bilayer separation versus pressure curves, we show that the decrease in tension results from the amplification of charge fluctuations on the membrane surface whereas the increase in bending rigidity results from the direct interaction between charges in the electric double layer. These effects eventually lead to a destabilization of the bilayer and vesicle formation. Similar effects are expected at the tens of nanometers length scale in cell membranes with lower tension, and could explain a number of electrically driven processes.

Modelling the Bioelectronic Interface in Engineered Tethered Membranes: From Biosensing to Electroporation

This paper studies the construction and predictive models of three novel measurement platforms: (i) a Pore Formation Measurement Platform (PFMP) for detecting the presence of pore forming proteins and peptides, (ii) the Ion Channel Switch (ICS) biosensor for detecting the presence of analyte molecules in a fluid chamber, and (iii) an Electroporation Measurement Platform (EMP) that provides reliable measurements of the electroporation phenomenon. Common to all three measurement platforms is that they are comprised of an engineered tethered membrane that is formed via a rapid solvent exchange technique allowing the platform to have a lifetime of several months. The membrane is tethered to a gold electrode bioelectronic interface that includes an ionic reservoir separating the membrane and gold surface, allowing the membrane to mimic the physiological response of natural cell membranes. The electrical response of the PFMP, ICS, and EMP are predicted using continuum theories for electrodiffusive flow coupled with boundary conditions for modelling chemical reactions and electrical double layers present at the bioelectronic interface. Experimental measurements are used to validate the predictive accuracy of the dynamic models. These include using the PFMP for measuring the pore formation dynamics of the antimicrobial peptide PGLa and the protein toxin Staphylococcal α-Hemolysin; the ICS biosensor for measuring nano-molar concentrations of streptavidin, ferritin, thyroid stimulating hormone (TSH), and human chorionic gonadotropin (pregnancy hormone hCG); and the EMP for measuring electroporation of membranes with different tethering densities, and membrane compositions.

An engineered membrane to measure electroporation: effect of tethers and bioelectronic interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.

Electrokinetic model for electric-field-induced interfacial instabilities

Technology based on electric-field-induced instabilities on thin polymer film surfaces has emerged as a promising candidate for soft lithography. Typically, the instability is modeled using the perfect dielectric (PD) or the leaky dielectric (LD) model. These assume the electric diffuse layer to be infinitesimally large or small, respectively. In the present work we conduct stability analysis assuming a PD-electrolyte solution interface. The concentration of ions and, hence, the diffuse layer thickness is in general assumed to be of the same order as the electrolyte film thickness. The PD-LD models are then realized as limiting cases of the ratio of the double layer thickness to the film thickness.

Electromechanics of a membrane with spatially distributed fixed charges: flexoelectricity and elastic parameters

We investigate the electrostatic contribution to the lipid membrane mechanical parameters: tension, bending rigidity, spontaneous curvature, and flexocoefficient, using an approach where stress in the membrane is explicitly balanced. Our model includes an applied electrostatic potential as well as a charge distribution in the membrane. We apply our theory to membranes having surface charges and electric dipoles at the surface.

Instability of a fluctuating membrane driven by an ac electric field

Shape fluctuations of a planar lipid membrane in an ac electric field are investigated using a zero-thickness electromechanical model, which accounts for membrane conductivity and capacitance, and asymmetry in the properties of the fluids separated by the membrane. A linear stability analysis shows that unlike in the case of a dc electric field, a purely capacitive membrane can be destabilized in an ac electric field. The theory highlights that the instability originates from electric pressure exerted on the membrane.

Electric-field-induced interfacial instabilities of a soft elastic membrane confined between viscous layers

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.

Diffuse charge and Faradaic reactions in porous electrodes

Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage.