Charge Inversion Phenomena Research Articles

Electrical conductance of conical nanopores: Symmetric and asymmetric salts and their mixtures.

We have studied experimentally the electrical conductance-voltage curves of negatively and positively charged conical nanopores bathed in ionic solutions with monovalent, divalent, and trivalent cations at electrochemically and biologically relevant ionic concentrations. To better understand the interaction between the pore surface charge and the mobile ions, both single salts and salt mixtures have been considered. We have paid attention to the effects on the conductance of the cation valency, the pore charge asymmetry, and the pore charge inversion phenomena due to trivalent ions, both in single salts and salt mixtures. In addition, we have described how small concentrations of multivalent ions can tune the nanopore conductance due to monovalent majority ions, together with the effect of these charges on the additivity of ionic conductance and fluoride-induced negative differential conductance phenomena. This compilation and discussion of previously presented experimental data offers significant insights on the interaction between fixed and mobile charges confined in nanoscale volumes and should be useful in establishing and checking new models for describing ionic transport in the vicinity of charged surfaces.

Local inversion of the mean electrostatic potential, maximum charge reversal, and capacitive compactness of concentrated 1:1 salts: The crucial role of the ionic excluded volume and ion correlations

• A local inversion of the electrostatic potential in one and three ionic radii from the macroions’s surface is observed. • If the zeta potential is in the above region, an inversion of the macroion’s mobility could be driven by 1:1 electrolytes. • The capacitive compactness around a macroion immersed in very concentrated indiferent 1:1 salts is studied. Recent restricted primitive model Monte Carlo simulations (Takamichi Terao, Mol. Phys. 119 , e1831634, 2020) have suggested the possibility of observing the phenomenon of charge inversion in highly concentrated monovalent salts, in which ionic specific adsorption is absent. By using the non-linear Poisson-Boltzmann equation supplemented by a hard-spheres contribution, integral equations theory, and Monte Carlo simulations, the associated mean electrostatic potential, maximum charge reversal and capacitive compactness are studied here. The main finding of this study is the observation of a local inversion of the mean electrostatic potential in a region bounded by one and three ionic radii measured from the macroions’s surface. If the zeta potential is located in this region, the above result suggests the possibility of observing an inversion of the macroion’s electrophoretic mobility, driven by 1:1 aqueous electrolytes in the absence of ionic specific adsorption . On the other hand, the maximum charge reversal and the capacitive compactness increases and decreases montonically, respectively, as a function of the ionic volume fraction when the salt concentration and/or the ionic size of the aqueous electrolytes increase.

Shift of charge inversion point of a trivalent ion solution in a nanofluidic channel

Understanding the surface properties and related liquid properties in 102 nm spaces (extended nanospaces) is critical for future device engineering. To this end, we used trivalent ions to investigate the charge inversion phenomenon in extended nanospaces. The charge inversion points in bulk didn't substantially differ between a La(NO3)3 solution and a Lu(NO3)3 solution. However, the charge inversion point of a La(NO3)3 solution in extended nanochannels shifted toward the higher-concentration region. The conductivity measurement results suggested a negatively charged surface in the extended nanospaces in the La(NO3)3 solution, consistent with the zeta-potential results. In addition, a much increase in the 1/T1 of the La(NO3)3 solution was shown compared with that of the bulk. We report a new finding that different trivalent ions exhibit different adsorption properties but only in extended nanospaces, not in bulk. We expect our results to contribute to the basic science to understand the liquid properties in nanospaces.

Interfacial structure and differential capacitance of ionic liquid/graphite interface: A perturbed-chain SAFT density functional theory study

The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was combined with the electrostatic free energy from the mean spherical approximation (MSA) theory, and applied to represent densities of pure imidazolium ionic liquids (ILs) with anion [BF4]−. The PC-SAFT parameters of cations were linearized with their molar mass and obtained by simultaneously fitting the model predictions to experimental densities of some ILs. The PC-SAFT-MSA model provides accurate correlations and predictions of densities comparing with experimental data. Then a classical density functional theory (DFT) was developed based on PC-SAFT-MSA. The DFT model was applied to explore the structure and differential capacitance of the electrical double layer (EDL) in ILs on graphite. The model predicts similar density profiles for both cation and anion on a neutral surface, and layered structure with alternating layers of cations and anions on a charged surface. The charge inversion phenomena were also studied based on ion distributions. We further studied the effects of the alkyl chain length, temperature and non-electrostatic solid-fluid interactions on the differential capacitance of the EDL. The model provides bell-shaped differential capacitance curves. The peak positions of differential capacitance curves shift toward positive potentials as ions size asymmetry increases in agreement with previous experiments and simulations studies. The maximum capacitance decreases with increasing alkyl chain length as well as increasing temperature.

A multiscale model for charge inversion in electric double layers.

Charge inversion is a widely observed phenomenon. It is a result of the rich statistical mechanics of the molecular interactions between ions, solvent, and charged surfaces near electric double layers (EDLs). Electrostatic correlations between ions and hydration interactions between ions and water molecules play a dominant role in determining the distribution of ions in EDLs. Due to highly polar nature of water, near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Classical continuum theories fail to accurately describe electrostatic correlations and molecular effects of water in EDLs. In this work, we present an empirical potential based quasi-continuum theory (EQT) to accurately predict the molecular-level properties of aqueous electrolytes. In EQT, we employ rigorous statistical mechanics tools to incorporate interatomic interactions, long-range electrostatics, correlations, and orientation polarization effects at a continuum-level. Explicit consideration of atomic interactions of water molecules is both theoretically and numerically challenging. We develop a systematic coarse-graining approach to coarse-grain interactions of water molecules and electrolyte ions from a high-resolution atomistic scale to the continuum scale. To demonstrate the ability of EQT to incorporate the water orientation polarization, ion hydration, and electrostatic correlations effects, we simulate confined KCl aqueous electrolyte and show that EQT can accurately predict the distribution of ions in a thin EDL and also predict the complex phenomenon of charge inversion.

Molecular dynamics study of an electro-kinetic fluid transport in a charged nanochannel based on the role of the stern layer

Electro-osmotic flow of an aqueous solution of NaCl has been studied using the molecular dynamics simulation. The main objective of this work is to investigate the effects of the electric field and temperature on the flow properties considering the role of the stern layer. By increasing any of the mentioned parameters, the electro-osmotic velocity grows. It is found that the electro-osmotic velocity is a fourth order function of the electric field, while it changes linearly with temperature. Similar trends of change are found for the EDL thickness. By an increase in the studied parameters, a reduction in the stern layer capacity is observed. In this situation, more moving ions are located in the diffuse layer, which are dragging other particles. This is one of the causes that increase the electro-osmotic velocity, a matter which was not predicted by previous researches. A consequence of the stern layer capacity reduction is that in the systems under the influence of higher temperatures or stronger electric fields, charge inversion phenomenon occurs at higher wall charges.

The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study

The electro-osmotic flow of an aqueous solution of NaCl between two parallel silicon walls is studied through a molecular dynamics simulation. The objective here is to examine the dependency of the electro-osmotic flow on the surface charge density by considering the changes made in the structural properties of the electric double layer (EDL). The ion concentration, velocity profiles, and electric charge density of the electrolyte solution are investigated. Due to the partially charged atoms of the water molecules, water concentration is of a layered type near the wall. The obtained profiles revealed that an increase in the surface charge density, at low surface charges where the governing electrostatic coupling regime is Debye–Huckel, increases both the electro-osmotic velocity and the EDL thickness; whereas, a decreasing trend is observed in these two parameters in the intermediate regime. For high values of surface charge density, due to the charge inversion phenomenon, the reversed electro-osmotic flow will be generated in the channel. Results indicate that the absolute value of the reversed electro-osmotic velocity rises with an increase in the surface charge density.

Experimental demonstration of charge inversion in a protein channel in the presence of monovalent cations

Charge inversion takes place when interfacial charges attract counterions in excess of their own nominal charge. To date, this phenomenon has been reported in a variety of membrane channel systems in the presence of multivalent cations. Here, we investigate the charge inversion phenomenon in a protein channel in solutions of monovalent cations. To this end, we perform selectivity experiments in salts of different cations, changing both the electrolyte concentration and the solution acidity. We show that charge inversion can be produced by two different mechanisms, namely specific adsorption and competitive binding.

An ion-exchange nanomembrane sensor for detection of nucleic acids using a surface charge inversion phenomenon

We present a novel low-cost biosensor for rapid, sensitive and selective detection of nucleic acids based on an ionic diode feature of an anion exchange nanoporous membrane under DC bias. The ionic diode feature is associated with external surface charge inversion on the positively charged anion exchange nanomembrane upon hybridization of negatively charged nucleic acid molecules to single-stranded oligoprobes functionalized on the membrane surface resulting in the formation of a cation selective monolayer. The resulting bipolar membrane causes a transition from electroconvection-controlled to water-splitting controlled ion conductance, with a large ion current signature that can be used to accurately quantify the hybridized nucleic acids. The platform is capable of distinguishing two base-pair mismatches in a 22-base pairing segment of microRNAs associated with oral cancer, as well as serotype-specific detection of dengue virus. We also show the sensor׳s capability to selectively capture target nucleic acids from a heterogeneous mixture. The limit of detection is 1pM for short 27 base target molecules in a 15-min assay. Similar hybridization results are shown for short DNA molecules as well as RNAs from Brucella and Escherichia coli. The versatility and simplicity of this low-cost biosensor should enable point-of-care diagnostics in food, medical and environmental safety markets.

Electrostatic correlations on the ionic selectivity of cylindrical membrane nanopores

We characterize the role of electrostatic fluctuations on the charge selectivity of cylindrical nanopores confining electrolyte mixtures. To this end, we develop an extended one-loop theory that can account for correlation effects induced by the surface charge, nanoconfinement of the electrolyte, and interfacial polarization charges associated with the low permittivity membrane. We validate the quantitative accuracy of the theory by comparisons with previously obtained Monte-Carlo simulation data from the literature, and scrutinize in detail the underlying forces driving the ionic selectivity of the nanopore. In the biologically relevant case of electrolytes with divalent cations such as CaCl2 in negatively charged nanopores, electrostatic correlations associated with the dense counterion layer in the channel result in an increase of the pore coion density with the surface charge. This peculiarity analogous to the charge inversion phenomenon remains intact for dielectrically inhomogeneous pores, which indicates that the effect should be observable in nanofiltration membranes or DNA-blocked nanopores characterized by a low membrane permittivity. Our results show that a quantitatively accurate consideration of correlation effects is necessary to determine the ionic selectivity of nanopores in the presence of electrolytes with multivalent counterions.

Ionic density distributions near the charged colloids: Spherical electric double layers

We have studied the structure of the spherical electric double layers on charged colloids by a density functional perturbation theory, which is based both on the modified fundamental-measure theory for the hard spheres and on the one-particle direct correlation functional (DCF) for the electronic residual contribution. The contribution of one-particle DCF has been approximated as the functional integration of the second-order correlation function of the ionic fluids in a bulk phase. The calculated result is in very good agreement with the computer simulations for the ionic density distributions and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations, and compares with the results of Yu et al. [J. Chem. Phys. 120, 7223 (2004)] and modified Poisson-Boltzmann approximation [L. B. Bhuiyan and C. W. Outhwaite, Condens. Matter Phys. 8, 287 (2005)]. The present theory is able to provide interesting insights about the charge inversion phenomena occurring at the interface.

Quantum Analytical Model for Inversion Charge and Threshold Voltage of Short-Channel Dual-Material Double-Gate SON MOSFET

Our previous work analytically establishes that silicon-on-nothing (SON) is superior to silicon-on-insulator MOSFET because of its higher immunity to different short-channel effects and increased current driving capability. Moreover, it has also been shown that our analytical model agrees with various simulation results obtained from MEDICI, ATLAS 2-D, and so on. Because of the ultrathin device structure, classical models are not sufficient to determine accurately potential profile, threshold voltage, or charge inversion phenomena for dual-material double-gate (DMDG) SON MOSFET. Hence, in this paper, for the first time, carrier quantization arising due to the ultrathin body has been included to develop an analytical model for ultrathin low-dimensional DMDG SON structure. The 2-D Poisson and 1-D Schrodinger equations have been solved under the dual-material front gate to find the overall potential and inversion charge profile. The deviation of the quantum threshold voltage from the classical one has been calculated and added to the classical threshold voltage to get its quantum counterpart. The proposed model has also been validated against the numerical device simulator ATLAS 2-D.

The weighted correlation approach for density functional theory: a study on the structureof the electric double layer

Within the framework of density functional theory, a weighted correlation approach isdeveloped in order to obtain the density distributions of an inhomogeneous fluid. It resultsin a formally exact expression, by means of the concept of a weighted pair correlationfunction, used to evaluate the change of the single-particle direct correlation function of thesystem relative to that of a reference state. When applying the approach for practical use,however, an approximation of the pair correlation function has to be made, along with anappropriate definition of a weight function. Noticeably, combining this approach withfundamental measure theory gives rise to a new method, which we call the FMT/WCA-k2 approach, for studying the structural and thermodynamic properties of a charged hard-spherefluid subjected to a spatially varying external potential. Application of the FMT/WCA-k2 approach in a range of electrolyte concentrations and surface charge densities, against theMonte Carlo simulations, shows that it is superior to the typical approaches of densityfunctional theory in predicting the ionic density profiles of both counter-ions and co-ionsnear a highly charged surface. It is capable of capturing the fine features of thestructural properties of the electric double layers, to well reproduce the layeringeffect and the charge inversion phenomenon, also in strongly coupled cases wheredivalent counter-ions are involved. In addition, it is found that the FMT/WCA-k2 approach even has an advantage over the anisotropic, hyper-netted chain approaches ingiving better agreement with the Monte Carlo results.

Efficiently accounting for ion correlations in electrokinetic nanofluidic devices using density functional theory

The electrokinetic behavior of nanofluidic devices is dominated by the electrical double layers at the device walls. Therefore, accurate, predictive models of double layers are essential for device design and optimization. In this paper, we demonstrate that density functional theory (DFT) of electrolytes is an accurate and computationally efficient method for computing finite ion size effects and the resulting ion–ion correlations that are neglected in classical double layer theories such as Poisson–Boltzmann. Because DFT is derived from liquid-theory thermodynamic principles, it is ideal for nanofluidic systems with small spatial dimensions, high surface charge densities, high ion concentrations, and/or large ions. Ion–ion correlations are expected to be important in these regimes, leading to nonlinear phenomena such as charge inversion, wherein more counterions adsorb at the wall than is necessary to neutralize its surface charge, leading to a second layer of co-ions. We show that DFT, unlike other theories that do not include ion–ion correlations, can predict charge inversion and other nonlinear phenomena that lead to qualitatively different current densities and ion velocities for both pressure-driven and electro-osmotic flows. We therefore propose that DFT can be a valuable modeling and design tool for nanofluidic devices as they become smaller and more highly charged.

Insights from Monte Carlo simulations on charge inversion of planar electric double layers in mixtures of asymmetric electrolytes

Monte Carlo simulations of a planar negatively charged dielectric interface in contact with a mixture of 1:1 and 3:1 electrolytes are carried out using the unrestricted primitive model under more realistic hydrated ion sizes. Two typical surface charge densities are chosen to represent the systems from the weak to strong coupling regimes. Our goal is to determine the dependence of the degree of charge inversion on increasing concentration of both mono- and trivalent salts and to provide a systematic study on this peculiar effect between short-range and electrostatic correlations. The numerical results show that addition of monovalent salt diminishes the condensation of trivalent counterions due to either the favorable solvation energy or the available space constraints. As the concentration of trivalent salt increases, on the other hand, the inclusion of the ionic size and size asymmetry results in a damped oscillatory charge inversion at low enough surface charge and another counterintuitive surface charge amplification. It is proposed that both of the anomalous events in the weak coupling regime are thought to be entropic in origin which is completely different from the electrostatic driven charge inversion in the strong coupling regime. In addition, the electrostatic images arising from the dielectric mismatch lead to a decaying depletion effect on the structure of double layer with growing salt concentration in the case of low charged interface but have no effect at high surface charge values. The microscopic information obtained here points to the need for a more quantitative theoretical treatment in describing the charge inversion phenomenon of real colloidal systems.

Charge Inversion by Flexible Polyelectrolytes Adsorbed onto Charged Cylindric Surfaces within Self-Consistent-Field Theory

Self-consistent-field theory (SCFT) is presented to study the charge inversion phenomena by flexible polyelectrolytes (PE) adsorbed onto oppositely charged cylindric surfaces. We focus on the effec...

Molecular Simulation of Ompf Channel in Salts of Divalent Cations: Molecular Insight on Charge Inversion

Extensive recent experimental and theoretical work has shown that the interaction of biologically relevant divalent cations (such as Mg2+, Ca2+) has surprising properties. One of the most fascinating and unexpected effect is the so-called charge inversion or charge reversal phenomenon: cations accumulate at the interface in excess of its own bare charge, thus inverting the effective charge of the interface. Recently, charge inversion has been reported in the bacterial channel OmpF, in the presence of salts of divalent cations [Alcaraz et al. Biophys. J. 96 (2009) 56]. Aiming to get an insight on the atomistic mechanism of the cation interaction with the protein, we have performed extensive MD simulations of a realistic model of the OmpF WT protein in a POPC membrane in MgCl2 and explicit water. The simulations were computationally highly demanding, with half million atoms in a simulation box and production runs around 25 nsec.The simulations were performed employing the NAMD simulation package running in 128 processor at the CESGA Supercomputing Center. Our main result is that we have observed charge inversion of certain important acidic groups. The observed charge inversion is accompanied by a change in the transport mechanism of ions inside the channel and a reversal in the selectivity of the channel. Overall, our simulations give an accurate microscopic image of this unexpected effect with potentially important biological and nanotechnological implications.

Charge inversion of dendrimers in complexes with linear polyelectrolytes in the solutions with low pH

Complexes of fully ionized third-generation dendrimers with oppositely charged linear polyelectrolyte chains are studied by the Brownian dynamics method. A freely jointed model of a dendrimer and a linear chain is used. Electrostatic interactions are considered within the Debye-Huckel approximation with the Debye radius exceeding the dimensions of a dendrimer. In these systems, the phenomenon of charge inversion is observed, and the degree of “overcharging” is higher as compared with that taking place in analogous complexes formed by dendrimers in which only terminal groups are charged. The dependence of the amount of chain units adsorbed on a dendrimer on the polyelectrolyte chain length is nonmonotnic and agrees qualitatively with the predictions of the theory proposed by Nguyen and Shklovskii for a complex composed of a spherical macroion with an oppositely charged linear chain. This nonmonotonic character also manifests itself for certain other structural characteristics of the complexes. Upon the formation of a complex, a chain is shown to penetrate deeply into a dendrimer.

Electroosmotic Flow in Nanotubes with High Surface Charge Densities

The ion distribution and electroosmotic flow of sodium chlorine solutions confined in cylindrical nanotubes with high surface charge densities are studied with molecular dynamics (MD). To obtain a more practical physical model for electroosmotic driven flow in a nanoscale tube, the MD simulation process consists of two steps. The first step is used to equilibrate the system and to obtain a more realistic ion distribution in the solution under different surface charge densities. Then, an external electric field is acted to drive the liquids. The simulation results indicate that with the increase of the surface charge density, both the thickness of the electric double layer and the peak height of the counterion density increase. However, the phenomenon of charge inversion does not occur even as the surface charge density increases to -0.34 C/m2, which is rather difficult to reach for real materials in practical situations. This simulation result confirms the recent experimental observation that monovalent ions of sufficiently high concentrations can reduce or even cancel the charge inversion occurred in the case of multivalent ions [F. H. J. van der Heyden et al. Phys. Rev. Lett. 2006, 96, 224502].

Structure of spherical electric double layers: A density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.