Influence of steric, electric, and dielectric effects on membrane potential

The membrane potential arising through nanofiltration membranes separating two aqueous solutions of the same electrolyte at identical hydrostatic pressures but different concentrations is investigated within the scope of the steric, electric, and dielectric exclusion model. The influence of the ion size and the so-called dielectric exclusion on the membrane potential arising through both neutral and electrically charged membranes is investigated. Dielectric phenomena have no influence on the membrane potential through neutral membranes, unlike ion size effects which increase the membrane potential value. For charged membranes, both steric and dielectric effects increase the membrane potential at a given concentration but the diffusion potential (that is the high-concentration limit of the membrane potential) is affected only by steric effects. It is therefore proposed that membrane potential measurements carried out at high salt concentrations could be used to determine the mean pore size of nanofiltration membranes. In practical cases, the membrane volume charge density and the dielectric constant inside pores depend on the physicochemical properties of both the membrane and the surrounding solutions (pH, concentration, and chemical nature of ions). It is shown that the Donnan and dielectric exclusions affect the membrane potential of charged membranes similarly; namely, a higher salt concentration is needed to screen the membrane fixed charge. The membrane volume charge density and the pore dielectric constant cannot then be determined unambiguously by means of membrane potential experiments, and additional independent measurements are in need. It is suggested to carry out rejection rate measurements (together with membrane potential measurements).     

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (～0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.     

Note on nonaqueous electrokinetic transport in charged porous media

A model for electrokinetic transport in charged capillaries is compared with experiments using nonaqueous lithium chloride solutions. The electrokinetic parameters considered are the pore fluid conductivity and the concentration potential. Methanol/water mixtures were the solvent, and track-etched mica membranes with a well-characterized pore structure were the porous medium. The electrolyte concentrations used were such that the Debye lengths of solutions in pores ranged from much smaller to much larger than the radius of pores. The space-charge model is found to be capable of qualitatively describing the trend of the electrokinetic data, but as expected, at higher concentrations the model fails, probably because the assumption that ion—ion interactions are negligible no longer holds. The experimental results show that the pore fluid conductivity depends strongly on the dielectric constant of the solvent, that the absolute value of the pore wall charge tends to decrease with the lowering of the solvent dielectric constant, and that the wall charge tends to increase with the concentration of the chloride ion.     

Solvent effect on analyte charge state,signal intensity,and stability in negative ion electrospray mass spectrometry; implications for the mechanism of negative ion formation

Department of Chemistry, University of New Orleans, New Orleans, Louisiana, USA The effect of solvent composition on negative ion electrospray ionization (ESI) mass spectrometry was examined. The onset potentials for ES1 of a series of chlorinated solvents and methanol were found to be within the range predicted by D. P. H. Smith, based on differences in the surface tension of the solvents used. The tendency toward electric discharge decreased with increasing percent weight of chlorine in the solvent. This effect has been attributed to an increasing propensity for electron capture for more highly chlorinated solvents. Addition of the electron scavenger gas SF, was even more effective at suppressing corona discharge phenomena. In a comparison of ultimate signal intensity obtainable for a test analyte in 10% methanol, the highest signal, which was stable over the widest range of temperatures, was exhibited by chloroform compared to dichloromethane, 1,2-dichloroethane, carbon tetrachloride, and methanol (100%). Chloroform, thus, is a recommended solvent for negative ion electrospray mass spectrometry (ES/MS) when solubility is not a limiting issue. Solvent polarity was shown to exhibit a profound influence on the distribution of charge states in negative ion ES/MS. For both chlorinated and nonchlorinated organic solvents, the higher the solution dielectric constant, the more the charge-state distribution is shifted toward higher charge states. These observations build on the “electrophoretic” mechanism of droplet charging. Solvents with high solution dielectric constants are considered to be most effective at stabilizing multiply charged ions (where charge separation is greatest), and they are likely to increase the level of droplet charging. Solvents with high basicities (gas phase and solution phase) and high proton affinities, yet low dielectric constants, favor lower charge states in ES mass spectra of lipid A and cardiolipin from Escherichia coli. This indicates that gas-phase processes and solvent basicity contribute much less toward ion formation than solution-phase solvation via preferred orientation of the solvent dipole.     

Electric-field-controlled water and ion permeation of a hydrophobic nanopore

The permeation of hydrophobic, cylindrical nanopores by water molecules and ions is investigated under equilibrium and out-of-equilibrium conditions by extensive molecular-dynamics simulations. Neglecting the chemical structure of the confining pore surface, we focus on the effects of pore radius and electric field on permeation. The simulations confirm the intermittent filling of the pore by water, reported earlier under equilibrium conditions for pore radii larger than a critical radius R(c). Below this radius, water can still permeate the pore under the action of a strong electric field generated by an ion concentration imbalance at both ends of the pore embedded in a structureless membrane. The water driven into the channel undergoes considerable electrostriction characterized by a mean density up to twice the bulk density and by a dramatic drop in dielectric permittivity which can be traced back to a considerable distortion of the hydrogen-bond network inside the pore. The free-energy barrier to ion permeation is estimated by a variant of umbrella sampling for Na(+), K(+), Ca(2+), and Cl(-) ions, and correlates well with known solvation free energies in bulk water. Starting from an initial imbalance in ion concentration, equilibrium is gradually restored by successive ion passages through the water-filled pore. At each passage the electric field across the pore drops, reducing the initial electrostriction, until the pore, of radius less than R(c), closes to water and hence to ion transport, thus providing a possible mechanism for voltage-dependent gating of hydrophobic pores.     

535—The surface compartment model (SCM): Role of surface charge in membrane permeability changes

Small shifts in the surface charge of excitable membranes precede the ion permeability changes that are the basis of the action potential. If we assume that an increase in ion permeability is due to the opening of a molecular pore, we can model this process like subunit dissociation in oligomeric proteins. (The dissociation of hemoglobin tetramers into dimers is sensitive to changes in charge and occurs when the surface charge is approximately the same as on the inner face of the squid axon membrane.) Using the relation between the hemoglobin dissociation constant and charge, together with the estimated number of pores in the axon membrane, we have derived a relation between the fraction of pores open and the surface charge density. When this latter relation is incorporated into the surface compartment model (SCM), the gating currents give rise to voltage (polarization) dependent changes in ion permeability.     

Pore formation coupled to ion transport through lipid membranes as induced by transmembrane ionic charge imbalance: atomistic molecular dynamics study

We have employed atomic-scale molecular dynamics simulations to address ion transport through transient water pores in phospholipid membranes. The formation of a water pore is induced by a transmembrane ionic charge imbalance, which gives rise to a significant potential difference across the membrane. The subsequent transport of ions through the pore discharges the transmembrane potential and makes the water pore metastable, leading eventually to its sealing. The findings highlight the importance of ionic charge fluctuations in spontaneous pore formation and their role in ion leakage through protein-free lipid membranes.     

Electroviscous Effects in Ceramic Nanofiltration Membranes

Membrane permeability and salt rejection of a γ‐alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan‐steric pore model, in which the extended Nernst–Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen–Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ‐Alumina particles were used for ζ‐potential measurements. The ζ‐potential measurements show that monovalent ions did not adsorb on the γ‐alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ‐potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ‐potential higher than 20 mV, and an ionic strength lower than 0.01 m . The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m , there is an optimum ζ‐potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm‐selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.     

Ion current rectification at nanopores in glass membranes

The origin of ion current rectification observed at conical-shaped nanopores in glass membranes immersed in KCl solutions has been investigated using finite-element simulations. The ion concentrations and fluxes (due to diffusion, migration, and electroosmotic convection) were determined by the simultaneous solution of the Nernst-Planck, Poisson, and Navier-Stokes equations for the two-ion (K+ and Cl-) system. Fixed surface charge on both the internal and external glass surfaces that define the pore structure was included to account for electric fields and nonuniform ion conductivity within the nanopores and electric fields in the external solution near the pore mouth. We demonstrate that previous observations of ion current rectification in conical-shaped glass nanopores are a consequence of the voltage-dependent solution conductivity in the vicinity of the pore mouth, both inside and outside of the pore. The simulations also demonstrate that current rectification is maximized at intermediate bulk ion concentrations, a combination of (i) the electrical screening of surface charge at high concentrations and (ii) a fixed number of charge-carrying ions in the pore at lower concentration, which are physical conditions where the voltage dependence of the conductivity disappears. In addition, we have quantitatively shown that electroosmotic flow gives rise to a significant but small contribution to current rectification.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Membrane potential in charged porous membranes

For charged porous membranes, the separation efficiency to charged particles and ions is affected by the electrical properties of the membrane surface. Such properties are most commonly quantified in terms of zeta-potential. In this paper, it is shown that the zeta-potential can be calculated numerically from the membrane potential. The membrane potential expression for charged capillary membranes in contact with electrolyte solutions at different concentrations is established by applying the theory of non-equilibrium thermodynamic to the membrane process and considering the space-charge model. This model uses the Nernst–Planck and Navier–Stokes equations for transport through pores, and the non-linear Poisson–Boltzmann equation, which is numerically solved, for the electrostatic condition of the fluid inside pores. The integral expressions of the phenomenological coefficients coupling the differential flow (solute relative to solvent) and the electrical current with the osmotic pressure and the electrical potential gradients are established and calculated numerically. The mobilities of anions and cations are individually specified. The variations of the membrane potential (or the apparent transport number of ions in the membrane pores) are studied as a function of different parameters: zeta-potential, pore radius, mean concentration in the membrane, ratio of external concentrations and type of ions.     

Mathematical modeling of solution deionization by sorption on aerogel electrodes

The mathematical modeling is used to study the dynamics of solution deionization by sorption on aerogel electrodes. The matter transport by solution flow, diffusion, and sorption in pores are simulated. Several models are proposed to describe the phenomenon with different degree of approximation. Problems arising in numerical computing and ways to solve them are described. It is shown that at low solution concentrations and a small pore size the effect of electro-sorption is not reduced to the formation of a double electric layer on the pore surface, which uptakes ions from the solution. In addition to the formation of this layer distributed ionic charge is accumulated all over the pore space. The dependence of the effective diffusion coefficient inside the porous electrode on the ion concentration is found. Examples of calculating the deionization process at one-cycle and multi-cycle sorption are given.     

Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.     

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).