Space Charge Regions in Fixed Charge Membranes and the Associated Property of Capacitance

Influence of the Dielectric Constant on the Ionic Current Rectification of Bipolar Nanopores

In this paper, we investigate how the dielectric constant, ϵ, of an electrolyte solvent influences the current rectification characteristics of bipolar nanopores. It is well recognized that bipolar nanopores with two oppositely charged regions rectify current when exposed to an alternating electric potential difference. Here, we consider dilute electrolytes with NaCl only and with a mixture of NaCl and charged nanoparticles. These systems are studied using two levels of description, all-atom explicit water molecular dynamics (MD) simulations and coarse-grained implicit solvent MD simulations. The charge density and electric potential profiles and current-voltage relationship predicted by the implicit solvent simulations with ϵ = 11.3 show good agreement with the predictions from the explicit water simulations. Under nonequilibrium conditions, the predictions of the implicit solvent simulations with a dielectric constant closer to the one of bulk water are significantly different from the predictions obtained with the explicit water model. These findings are closely aligned with experimental data on the dielectric constant of water when confined to nanometric spaces, which suggests that ϵ decreases significantly compared to its value in the bulk. Moreover, the largest electric current rectification is observed in systems containing nanoparticles when ϵ = 78.8. Using enhanced sampling, we have shown that this larger rectification arises from the presence of a significantly deeper minimum in the free energy of the system with a larger ϵ, and when a negative voltage bias is applied. Since implicit solvent models and mean-field continuum theories are often used to design Janus membranes based on bipolar nanopores, this work highlights the importance of properly accounting for the effects of confinement on the dielectric constant of the electrolyte solvent. The results presented here indicate that the dielectric constant in implicit solvent simulations may be used as an adjustable parameter to approximately account for the effects of nanometric confinement on aqueous electrolyte solvents.

Energy optimisation predicts the capacity of ion buffering in the brain

Neurons store energy in the ionic concentration gradients they build across their cell membrane. The amount of energy stored, and hence the work the ions can do by mixing, can be enhanced by the presence of ion buffers in extra- and intracellular space. Buffers act as sources and sinks of ions, however, and unless the buffering capacities for different ion species obey certain relationships, a complete mixing of the ions may be impeded by the physical conditions of charge neutrality and isotonicity. From these conditions, buffering capacities were calculated that enabled each ion species to mix completely. In all valid buffer distributions, the [Formula: see text] ions were buffered most, with a capacity exceeding that of [Formula: see text] and [Formula: see text] buffering by at least an order of magnitude. The similar magnitude of the (oppositely directed) [Formula: see text] and [Formula: see text] gradients made extracellular space behave as a [Formula: see text]-[Formula: see text] exchanger. Anions such as [Formula: see text] were buffered least. The great capacity of the extra- and intracellular [Formula: see text] buffers caused a large influx of [Formula: see text] ions as is typically observed during energy deprivation. These results explain many characteristics of the physiological buffer distributions but raise the question how the brain controls the capacity of its ion buffers. It is suggested that neurons and glial cells, by their great sensitivity to gradients of charge and osmolarity, respectively, sense deviations from electro-neutral and isotonic mixing, and use these signals to tune the chemical composition, and buffering capacity, of the extra- and intracellular matrices.

Ion Transport and Process of Water Dissociation in Electromembrane System with Bipolar Membrane: Modelling of Symmetrical Case

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation-hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL^® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length, which shows the possibility of an ion that appeared because of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

Effect of Dielectric Saturation on Ion Activity Coefficients in Ion Exchange Membranes

Polymeric ion exchange membranes are used in water purification processes to separate ions from water. The distribution and transport of ionic species through these membranes depend on a variety of factors, including membrane charge density, morphology, chemical structure, and the specific ionic species present in the fluid. The electrical potential distribution between membranes and solutions is typically described using models based on Donnan theory. An extension of the original theory is proposed to account for the nonideal behavior of ions both in the fluid and in the membrane as well to provide a more robust description of interactions of solutes with fixed charge groups on the polymer backbone. In this study, the variation in dielectric permittivity in the membrane medium with electric field strength is taken into account in a model based on Gouy-Chapman double-layer theory to provide a more accurate description of ion activity coefficients in an ion exchange membrane. A semianalytical model is presented that accounts for the variation in dielectric permittivity of water in a charged polymer membrane. A comparison of this model with Manning's counterion condensation model clearly demonstrates that by incorporating changes in water dielectric permittivity with electric field strength, much better agreement with experiments can be obtained over a range of salt concentrations for different ions.

Electrophoresis of Liquid-Layer Coated Particles: Impact of Ion Partitioning and Ion Steric Effects

The biomimetic core-shell nanoparticles coated with membranes of various biological cells have attracted significant research interest, because of their extensive applications in targeted drug delivery systems. The cell membrane consists of a lipid bilayer, which can be regarded as a two-dimensional oriented viscous liquid with low dielectric permittivity, compared to a bulk aqueous medium. Such a liquid layer comprised of cell membrane may bear additional mobile charges, because of the presence of free lipid molecules or charged surfactant molecules, which further results in nonzero charge along the surface of the peripheral layer. In this article, we present an analytical theory for electrophoresis of such cell membrane coated functionalized nanoparticles in the extent of electrolyte solution, considering the combined effects of finite ion size and of ion partitioning. Going beyond the Debye-Huckel approximations, we propose an analytical theory for Donnan potential and electrophoretic mobility. The derived expressions are applicable for moderate to highly charged undertaken core-shell particles when the thickness of the peripheral liquid layer greatly exceeds the electric double layer thickness. The impact of pertinent parameters on the electrophoretic response of such a particle is further discussed.

Electrophoresis of dielectric and immiscible-liquid-layer-encapsulated colloids in aqueous media

In this paper we consider the electrophoresis of a functionalized nanoparticle in electrolyte solution. The undertaken particle is comprised of a rigid inner core encapsulated with a layer of dielectric liquid (e.g., oil or lipid layer), which is immiscible to the bulk aqueous medium. The peripheral liquid layer of the undertaken nanoparticle contains mobile charges due to presence of solubilized surfactants. The mobile electrolyte ions can penetrate across the peripheral layer depending on the difference in the Born energy of the both phases. Such types of nanoparticles have received substantial attention due to their widespread applications in biomedical research. The electric double layer (EDL) is governed by the linearized Poisson-Boltzmann equation under a low potential limit and the electroosmotic flow field is governed by modified Stokes equation. We adopt the flat-plate formalism to obtain the closed analytical expression for the electrophoretic mobility of the undertaken particle under a thin EDL approximation. The dependence of electrophoretic mobility on the pertinent parameters is also illustrated.

Exclusion-Enrichment Effect in Ionic Transistors

A simple model of a nanofluidic transistor consisting of a uniformly charged central section between a pair of plane parallel walls is considered. The linearized Poisson-Boltzmann equation corresponding to weak surface charge is solved exactly, and the solution is presented as an infinite series. The problem is characterized by three dimensionless parameters, namely the normalized surface charge, the ratio of the channel width to the Debye length, and the length-to-width aspect ratio of the charged section. The first of these parameters is presumed small, but the other two are arbitrary. The dependence of the exclusion-enrichment effect on these three parameters is discussed.

Electrochemical impedance of electrodiffusion in charged medium under dc bias

An immobile charged species provides a charged medium for transport of charge carriers that is exploited in many applications, such as permselective membranes, doped semiconductors, biological ion channels, as well as porous media and microchannels with surface charges. In this paper, we theoretically study the electrochemical impedance of electrodiffusion in a charged medium by employing the Nernst-Planck equation and the electroneutrality condition with a background charge density. The impedance response is obtained under different dc bias conditions extending above the diffusion-limiting bias. We find a transition in the impedance behavior around the diffusion-limiting bias and present an analytical approximation for a weakly charged medium under an overlimiting bias.

Recent Progress in Electrochemical pH-Sensing Materials and Configurations for Biomedical Applications

pH-sensing materials and configurations are rapidly evolving toward exciting new applications, especially those in biomedical applications. In this review, we highlight rapid progress in electrochemical pH sensors over the past decade (2008-2018) with an emphasis on key considerations, such as materials selection, system configurations, and testing protocols. In addition to recent progress in optical pH sensors, our main focus in this review is on electromechanical pH sensors due to their significant advances, especially in biomedical applications. We summarize developments of electrochemical pH sensors that by virtue of their optimized material chemistries (from metal oxides to polymers) and geometrical features (from thin films to quantum dots) enable their adoption in biomedical applications. We further present an overview of necessary sensing standards and protocols. Standards ensure the establishment of consistent protocols, facilitating collective understanding of results and building on the current state. Furthermore, they enable objective benchmarking of various pH-sensing reports, materials, and systems, which is critical for the overall progression and development of the field. Additionally, we list critical issues in recent literary reporting and suggest various methods for objective benchmarking. pH regulation in the human body and state-of-the-art pH sensors (from ex vivo to in vivo) are compared for suitability in biomedical applications. We conclude our review by (i) identifying challenges that need to be overcome in electrochemical pH sensing and (ii) providing an outlook on future research along with insights, in which the integration of various pH sensors with advanced electronics can provide a new platform for the development of novel technologies for disease diagnostics and prevention.

Asymmetry-induced electric current rectification in permselective systems

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order 10^{2}-10^{3}.

The electrostatic behavior of the bacterial cell wall using a smoothing function to describe the charge-regulated volume charge density profile

The Donnan potential can be observed in many biological systems due to the presence of polyelectrolytes as proteins and nucleic acids. The aim of this work was to present a useful tool to describe the fixed and charge-regulated volume charge density profile through the use of a smoothing function and to obtain the electrostatic potential profile as well as the Donnan potential of this system by solving Poisson-Boltzmann (PB) equation. When we use the smoothing function, the Donnan potential arises automatically from the solution of only one Poisson-Boltzmann equation and it is not necessary to impose this potential for treating charged system in the presence of a membrane. The electrostatic behavior across the Bacillus brevis wall considering the dependence on the ionization of the cell wall functional groups as a function of the solution pH was analyzed. An important issue was to show that potentiometric titration data could be used together with the Poisson-Boltzmann equation to predict the electrostatic behavior (e.g., zeta potential) of the bacterial cell surface.

Effects of monovalent ions on membrane potential and permselectivity: evaluation of fixed charge density of polymer based zirconium aluminophosphate composite membrane

The composite of poly(vinyl chloride) (PVC) with zirconium aluminophosphate (ZrAlP) employed as additive was prepared by sol–gel method.

Hemichannel composition and electrical synaptic transmission: molecular diversity and its implications for electrical rectification

Unapposed hemichannels (HCs) formed by hexamers of gap junction proteins are now known to be involved in various cellular processes under both physiological and pathological conditions. On the other hand, less is known regarding how differences in the molecular composition of HCs impact electrical synaptic transmission between neurons when they form intercellular heterotypic gap junctions (GJs). Here we review data indicating that molecular differences between apposed HCs at electrical synapses are generally associated with rectification of electrical transmission. Furthermore, this association has been observed at both innexin and connexin (Cx) based electrical synapses. We discuss the possible molecular mechanisms underlying electrical rectification, as well as the potential contribution of intracellular soluble factors to this phenomenon. We conclude that asymmetries in molecular composition and sensitivity to cellular factors of each contributing hemichannel can profoundly influence the transmission of electrical signals, endowing electrical synapses with more complex functional properties.

Stimuli sensitive polymers and self regulated drug delivery systems: a very partial review

Since the early days of the Journal of Controlled Release, there has been considerable interest in materials that can release drug on an "on-demand" basis. So called "stimuli-responsive" and "intelligent" systems have been designed to deliver drug at various times or at various sites in the body, according to a stimulus that is either endogenous or externally applied. In the past three decades, research along these lines has taken numerous directions, and each new generation of investigators has discovered new physicochemical principles and chemical schemes by which the release properties of materials can be altered. No single review could possibly do justice to all of these approaches. In this article, some general observations are made, and a partial history of the field is presented. Both open loop and closed loop systems are discussed. Special emphasis is placed on stimuli-responsive hydrogels, and on systems that can respond repeatedly. It is argued that the most success at present and in the foreseeable future is with systems in which biosensing and actuation (i.e. drug delivery) are separated, with a human and/or cybernetic operator linking the two.

Theoretical voltammetric response of electrodes coated by solid polymer electrolyte membranes

A model for the differential capacitance of metal electrodes coated by solid polymer electrolyte membranes, with acid/base groups attached to the membrane backbone, and in contact with an electrolyte solution is developed. With proper model parameters, the model is able to predict a limit response, given by Mott-Schottky or Gouy-Chapman-Stern theories depending on the dissociation degree and the density of ionizable acid/base groups. The model is also valid for other ionic membranes with proton donor/acceptor molecules as membrane counterions. Results are discussed in light of the electron transfer rate at membrane-coated electrodes for electrochemical reactions that strongly depend on the double layer structure. In this sense, the model provides a tool towards the understanding of the electro-catalytic activity on modified electrodes. It is shown that local maxima and minima in the differential capacitance as a function of the electrode potential may occur as consequence of the dissociation of acid/base molecular species, in absence of specific adsorption of immobile polymer anions on the electrode surface. Although the model extends the conceptual framework for the interpretation of cyclic voltammograms for these systems and the general theory about electrified interfaces, structural features of real systems are more complex and so, presented results only are qualitatively compared with experiments.

Ion effects at electrode/solid polymer electrolyte membrane interfaces

The differential capacity and the potential distribution at electrode/solid polymer electrolyte membrane/solution interfaces are calculated through an analytical approach. The model considers coions' and counterions' permeation through the membrane from the solvent phase and the ions' partitioning equilibrium at the SPEM/solution interface. The latter effects are included by incorporating the Donnan equilibrium, the steric hindrance, the solvation energy change when ions move from water to membrane pores and ion electrostatic interactions. It is shown that capacitance maxima in capacitance-potential curves may appear because of the acid-base dissociation process inside the membrane and the change in the ions' total interaction energy with the applied potential. For low dielectric constants inside membrane pores, εp, sharp peaks can be obtained. These peaks broaden, decrease in magnitude and shift to positive potentials once εp is increased. Finally, model predictions are discussed in light of recent experimental data obtained on Nafion® covered Pt(111) electrodes, providing a theoretical framework for the qualitative electroanalysis of these systems.

Membrane excitability and dissipative instabilities

Electrical excitation is interpreted in terms of a cooperative structural transition of membrane protomers coupled with the translocation of a permeant molecule in a non-equilibrium environment. Equations for flow of permeant and for membrane conformation are derived for the simple case of a single non-charged permeant. On the basis of a few simple physical assumptions, the theory predicts several important properties of electrically excitable membranes: the steepness of the relation between membrane conductance and potential, the presence of a negative conductance, and the occurrence of instabilities following rapid perturbations of membrane environment, giving rise to some simple cases of action potentials. Several experimental tests of the membrane with its changes of electrical properties are proposed. From a thermodynamic point of view, an electrically excitable membrane, in its resting state, lies beyond a dissipative instability and consequently is in a non-equilibrium state but with stable organization, a "dissipative structure" of Prigogine. Membrane excitation following a small perturbation of the environment would correspond to a jump from such an organization to another stable organization but close to thermodynamic equilibrium. It is shown how the cooperative molecular properties of the membrane are amplified by energy dissipation at the macroscopic level.

Electrical characteristics of the ionic psn-junction as a model of the resting axon membrane

As a model for the resting axon membrane, we propose the ionic psn-junction. Its electrical characteristics can be determined in close analogy to the corresponding electronic semiconductor junction. Using the "semianalytic approximation", we calculated the electrical capacity and the ionic currents. In contrast to the abrupt pn-junction, the electrical capacity of the psn-junction turns out to be practically voltage-independent, as it is observed for the squid axon membrane. The passive ionic fluxes for K(+), Na(+) and Cl(-), as the main contributions to the total charge flux, are calculated and compared with literature data on the ion fluxes through the resting squid axon membrane as measured by use of radioactive tracers. From this comparison, the ionic permeabilities can be evaluated and used to compute the resting membrane conductivity, which is found to be close to the experimental value. Further evidence in favor of the proposed asymmetrical membrane structure and possible ways of its test by the methods of protein chemistry are discussed.

Measurement of axonal membrane conductances and capacity by means of a varying potential control voltage clamp

A new mode of voltage clamping in the squid giant axon is introduced and its advantages are analyzed, tested, and utilized to investigate membrane conductances and capacity. This method replaces the constant command potentials of the standard voltage clamp with potentials which vary with time. Some of the advantages in using the varying potential clamp are: (1) slowly varying potentials generate practically pureI K ; (2) rapidly varying potentials generate practically pureI Na; (3) triangular waves generate, under proper conditions, pure capacity currents and easy-to-analyze leakage currents; (4) the method gives direct, on-line display of sodium or potassium I-V characteristics within milliseconds; (5) it enables rapid and accurateE Na andE K determinations; and (6) it enables simple and accurate determination ofC m. The method was utilized to study the effects of various ions on membrane conductances and the effects of ionic composition, ionic strength, and temperature on membrane capacity. Membrane capacity was found to be practically independent of frequency in the 200 to 2,000 Hz range. Replacement of external sodium by Ca(++), by impermeable Tris(+), or even by dextrose or sucrose (low ionic-strength solutions) had negligible effects onC m.C m showed a small, positive temperature coefficient of 1.39% per °C in the 3 to 21°C range, and little change with temperature in the 20 to 40°C range. Above 40°C, bothC m andg L increased considerably with temperature.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

The electrical conductance of semipermeable membranes III. bipolar flow-symmetric electrolytes

The first paper of this series presented a general formulation of the problem of stationary ion flow through membranes. The second treated in detail the special case of unipolar flow across membranes separating symmetric electrolytes. In this, the third paper of the series, we deal with another special case, that of bipolar flow between symmetric electrolytes. Here it is assumed that the total current is carried by both positive and negative permeant ions. The restriction to symmetric electrolytes implies that all ions present in the membrane and surrounding solutions have valences of identical absolute magnitude. After extracting from the general development a set of equations appropriate to the special case being considered, we outline a procedure for the numerical solution of the conductance problem for this case. Numerical results, presented as part of a discussion of approximate analytic methods of solution, establish the utility of these methods. A discussion of the significance of this work for membrane studies is presented in conclusion.