Electrostatic Potential Gradient Research Articles

Laterally controlled ultra-low energy ion implantation using electrostatic masking

We describe the ongoing development of an ultra-low energy (ULE) ion implantation system for the implementation of a laterally controlled ion incorporation into 2D materials like graphene or transition metal dichalcogenides (TMDs). For this purpose, we use ion optics simulations to demonstrate how the generation of an electrostatic potential gradient laterally along the sample surface can be used to control the size of the implanted sample area. The simulations are complemented by experiments on the incorporation of 25eV Mn ions into thin tetrahedral amorphous carbon (ta-C) films on Si substrates. With the help of RBS measurements, it is shown how potential gradients of different strengths influence the amount of introduced Mn.

Evaluation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model in an infinite crystal

Evaluation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model in an infinite crystal

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal.

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400-408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision-performance balance.

Investigation of highly efficient adsorbent based on Ni-MOF-74 in the separation of CO2 from natural gas

Ni-MOF-74 is used in the separation of CO2 from natural gas. However, its low selectivity coefficient for CO2 limits its application. To address this limitation, –CH3, –NH2, -F, and -O-Li groups were introduced to modify Ni-MOF-74. First, the adsorption of pure CO2 on metal–organic frameworks (MOFs) was simulated using the grand canonical Monte Carlo (GCMC) method. The CO2 adsorption capacities of adsorbents modified with -F and -O-Li were respectively 36.5% and 26.95% higher than that of unmodified Ni-MOF-74. The adsorption of a CH4/CO2 mixture on the MOFs was also studied. Ni-MOF-74 modified with -O-Li, denoted as Li-O-Ni-MOF-74, had the highest selectivity coefficient among the modified adsorbents. This was explained based on the analysis of the isosteric heat of adsorption and the electrostatic potential distribution gradient. The specific surface area and pore volume of Li-O-Ni-MOF-74 were respectively 162.03% and 86.42% higher than those of Ni-MOF-74, according to microstructure analysis. This also proved that the modified adsorbent has a higher adsorption capacity. Penetration experiments involving a CO2/CH4 mixture at different flow rates were carried out by an adsorption experiment device. The penetration time and separation factor of Li-O-Ni-MOF-74 were higher than those of Ni-MOF-74. Therefore, an efficient adsorbent based on Ni-MOF-74 for the separation of CO2 from natural gas was identified through GCMC simulation and experimental analysis. This study will help improve the efficiency of natural gas deacidification.

Spontaneous Mosaics of Charge Formed by Liquid Evaporation

AbstractCommonly used liquids have a powerful effect on producing electrostatic patterns in dielectric surfaces. During evaporation, charges are built‐up on dielectric surfaces that support liquids but with an important difference: negative charges appear where the liquid evaporates while positive ones are formed within the residual liquid. After complete evaporation, the result is a mosaic of stable and fixed surface charges resulting in electrostatic potential gradients as large as 20 kV m−1, but charge partitioning can be suppressed with common surfactants. The results can be understood considering the Maxwell–Wagner effect where charge accumulation takes place during current flowing across the interface. All these findings help to explain the hitherto challenging problem of static electricity and the appearance of the ubiquitous electrostatic patterns in dielectrics, what it must be helpful for the controlling of electrostatic charges in industry or in common laboratory activities.

Non-Faradaic Electric Currents in the Nernst-Planck Equations and Nonlocal Diffusiophoresis of Suspended Colloids in Crossed Salt Gradients.

In the Nernst-Planck equations in two or more dimensions, a non-Faradaic solenoidal current can arise as a consequence of connecting patches with different liquid junction potentials. Whereas this current vanishes for binary electrolytes or in one-dimensional problems, it is in general nonvanishing, for example, in crossed salt gradients. For a suspended colloidal particle, chemiphoresis in the concentration gradients is generally vectorially misaligned with electrophoresis in the electrostatic potential gradient, and there is a nonlocal contribution to the latter deriving from the Ohmic electric field associated with the current; in a case study this contributes up to 20%-30% of the total effect.

Laser ionization ion mobility spectrometric interrogation of acoustically levitated droplets.

Acoustically levitated droplets have been suggested as compartmentalized, yet wall-less microreactors for high-throughput reaction optimization purposes. The absence of walls is envisioned to simplify up-scaling of the optimized reaction conditions found in the microliter volumes. A consequent pursuance of high-throughput chemistry calls for a fast, robust and sensitive analysis suited for online interrogation. For reaction optimization, targeted analysis with relatively low sensitivity suffices, while a fast, robust and automated sampling is paramount. To follow this approach, in this contribution, a direct coupling of levitated droplets to a homebuilt ion mobility spectrometer (IMS) is presented. The sampling, transfer to the gas phase, as well as the ionization are all performed by a single exposure of the sampling volume to the resonant output of a mid-IR laser. Once formed, the nascent spatially and temporally evolving analyte ion cloud needs to be guided out of the acoustically confined trap into the inlet of the ion mobility spectrometer. Since the IMS is operated at ambient pressure, no fluid dynamic along a pressure gradient can be employed. Instead, the transfer is achieved by the electrostatic potential gradient inside a dual ring electrode ion optics, guiding the analyte ion cloud into the first stage of the IMS linear drift tube accelerator. The design of the appropriate atmospheric pressure ion optics is based on the original vacuum ion optics design of Wiley and McLaren. The obtained experimental results nicely coincide with ion trajectory calculations based on a collisional model. Graphical Abstract.

Analytic QM/MM atomic charge derivatives avoiding the scaling of coupled perturbed equations with the MM subsystem size.

In electrostatic embedding mixed quantum and molecular mechanics (QM/MM) approaches, the QM charge distribution is polarized by the electrostatic interaction with the MM environment. Analytic derivatives of expectation values of operators are required to extract properties such as vibrational spectra. These derivatives usually require solving a set of coupled perturbed equations for each nucleus/atom in the system, thus becoming prohibitive when the MM subsystem contains thousands of atoms. In the context of Electrostatic Potential Fitting (ESPF) QM/MM, we can easily overcome this bottleneck by defining a set of auxiliary coupled perturbed equations called the Q-vector equations. The Q-vector method scales only with the size of the QM subsystem, producing an effective charge tensor that leads to the atomic charge derivative after contraction with the MM electrostatic potential gradient. As an example, we use the charge derivatives as an analysis tool to identify the most important chromophore-polarizing amino-acids in plant cryptochrome. This finding opens up the route of defining polarizable force fields and simulating vibrational spectroscopy using ESPF QM/MM electrostatic embedding at an affordable computational cost.

Three-Dimensional Imaging of Beam-Induced Biasing of InP/GaInP Tunnel Diodes.

Electron holographic tomography was used to obtain three-dimensional reconstructions of the morphology and electrostatic potential gradient of axial GaInP/InP nanowire tunnel diodes. Crystal growth was carried out in two opposite directions: GaInP-Zn/InP-S and InP-Sn/GaInP-Zn, using Zn as the p-type dopant in the GaInP but with changes to the n-type dopant (S or Sn) in the InP. Secondary electron and electron beam-induced current images obtained using scanning electron microscopy indicated the presence of p-n junctions in both cases and current-voltage characteristics measured via lithographic contacts showed the negative differential resistance, characteristic of band-to-band tunneling, for both diodes. Electron holographic tomography measurements confirmed a short depletion width in both cases (21 ± 3 nm) but different built-in potentials, Vbi, of 1.0 V for the p-type (Zn) to n-type (S) transition, and 0.4 V for both were lower than the expected 1.5 V for these junctions if degenerately doped. Charging induced by the electron beam was evident in phase images which showed nonlinearity in the surrounding vacuum, most severe in the case of the nanowire grounded at the p-type Au contact. We attribute their lower Vbi to asymmetric secondary electron emission, beam-induced current biasing, and poor grounding contacts.

The Importance of the Water Molecular Quadrupole for Estimating Interfacial Potential Shifts Acting on Ions Near the Liquid-Vapor Interface.

Interfacial electrostatic potential gradients arise from nonuniform charge distributions encountered crossing the interface. The charges involved can include the molecular charges predominantly bound to each neutral solvent molecule and distributions of ions (or electrons) free to move in the interfacial region. This paper focuses on the solvent contribution to the interfacial potential. Quasichemical theory (QCT) provides a physical framework for the analysis of near-local (chemical) and far-field contributions to ion solvation free energies. Here, we utilize QCT to analyze cavity net potentials that contribute to the single-ion real solvation free energy. In particular, we discuss the results of molecular dynamics simulations of water droplets large enough to exhibit bulklike behavior in the droplet interior. A multipolar analysis of the cavity potential illustrates the importance of the solvent molecular quadrupole due to the near-cancellation of the dipolar contributions from the cavity-liquid and liquid-vapor interfaces. The results reveal the physical origin of the previously observed strong classical model dependence of the cavity potential.

Charged particle nonlinear resonance with localized electrostatic wave-packets

A resonant wave-particle interaction, in particular a nonlinear resonance characterized by particle phase trapping, is an important process determining charged particle energization in many space and laboratory plasma systems. Although an individual charged particle motion in the nonlinear resonance is well described theoretically, the kinetic equation modeling the long-term evolution of the resonant particle ensemble has been developed only recently. This study is devoted to generalization of this equation for systems with localized wave packets propagating with the wave group velocity different from the wave phase velocity. We limit our consideration to the Landau resonance of electrons and waves propagating in an inhomogeneous magnetic field. Electrons resonate with the wave field-aligned electric fields associated with gradients of wave electrostatic potential or variations of the field-aligned component of the wave vector potential. We demonstrate how wave-packet properties determine the efficiency of resonant particle acceleration and derive the nonlocal integral operator acting on the resonant particle distribution. This operator describes particle distribution variations due to interaction with one wave-packet. We solve kinetic equation with this operator for many wave-packets and show that solutions coincide with the results of the numerical integration of test particle trajectories. To demonstrate the range of possible applications of the proposed approach, we consider the electron evolution induced by the Landau resonances with packets of kinetic Alfven waves, electron acoustic waves, and very oblique whistler waves in the near-Earth space plasma.

Solving the enigma of weak fluorine contacts in the solid state: a periodic DFT study of fluorinated organic crystals.

The nature and strength of weak interactions with organic fluorine in the solid state are revealed by periodic density functional theory (periodic DFT) calculations coupled with experimental data on the structure and sublimation thermodynamics of crystalline organofluorine compounds. To minimize other intermolecular interactions, several sets of crystals of perfluorinated and partially fluorinated organic molecules are considered. This allows us to establish the theoretical levels providing an adequate description of the metric and electron-density parameters of the C–F⋯F–C interactions and the sublimation enthalpy of crystalline perfluorinated compounds. A detailed comparison of the C–F⋯F–C and C–H⋯F–C interactions is performed using the relaxed molecular geometry in the studied crystals. The change in the crystalline packing of aromatic compounds during their partial fluorination points to the structure-directing role of C–H⋯F–C interactions due to the dominant electrostatic contribution to these contacts. C–H⋯F–C and C–H⋯O interactions are found to be identical in nature and comparable in energy. The factors that determine the contribution of these interactions to the crystal packing are revealed. The reliability of the results is confirmed by considering the superposition of the electrostatic potential and electron density gradient fields in the area of the investigated intermolecular interactions.

(Industrial Electrochemistry and Electrochemical Engineering Division Student Achievement Award Address) Mitigating Ionic and Water Transport through Polymeric Membranes in All-Vanadium Redox Flow Batteries Via Design, Engineering, and Prototyping Novel Asymmetric Cell Topologies

Redox flow batteries (RFBs) are open batteries offering scalable architecture and a promising technology for large-scale energy storage. The unique capability of decoupling energy storage capacity from power generation provides RFBs with flexibility for delivering desired capacity or output power. Among many chemistries developed for RFBs, all-vanadium redox flow batteries (VRFBs) currently show great potential for widespread commercialization [1, 2]. A unique attribute among all the chemistries developed for RFBs is that VRFBs utilize vanadium (in four different oxidation states) in the negative and positive electrolytes; this characteristic frees them from irreversible capacity decay as a function of electroactive species transport through the membrane (i.e. crossover). However, crossover of vanadium ions and water through the ion-exchange membrane is inevitable during the charge/discharge cycling. This undesired ionic and water crossover not only results in a lost discharge capacity (long-term impact) during cycling, but also has real-time influence on the cell performance (instantaneous impact). Current efforts to mitigate crossover are largely directed towards developing more highly selective membranes; however, an alternative approach can be pursued with deeper knowledge of the forces that drive crossover. Numerous parameters affect solute (vanadium ions) and solvent (water) transport through the membrane; these include: membrane properties (polymer type, thickness, equivalent weight, and reinforcement), battery configuration (electrode morphology, flow field design), electrolyte composition and operating conditions (flow rate, temperature, and charge/discharge current) [3]. The concentration gradient and the electric field (via migration and electro-osmosis, respectively) are dominant driving forces for vanadium ion transport across the membrane [4, 5]. Water transport is due to multiple driving forces including electro-osmotic drag, thermo-osmosis, and osmotic and hydraulic pressure gradients [6, 7]. Therefore, it is necessary to understand these coincident forces affecting the transport of vanadium ions and water through the membrane. In this talk, we will present extensive experimental data tailored to quantify the contributions to capacity decay stemming from ion-exchange membrane properties (thickness, equivalent weight, and degree of reinforcement), flow field design, electrode configuration and electrolyte properties. A major focus has been to understand the effect of the electrode/membrane interface on the overall capacity decay and contact resistance. Novel ex-situ conductivity cells have been prototyped to assess ionic conductivity of the ion-exchange membranes along with electrolytes leading to details on the impact of interfacial phenomena on ionic conductivity and crossover. To quantify the long-term influence of crossover, a unique set-up has been designed and built that enables real-time measurement of ionic transport across the polymeric membrane using ultraviolet-visible (UV/Vis) spectroscopy. The set-up enables separation of contributions to crossover emerging from concentration and electrostatic potential gradients. Also, to investigate the instantaneous impact of crossover on the VRFB performance, a real-time current density distribution diagnostic has been implemented for measuring the in-plane current density distribution. The insights gained from this suite of experimental diagnostics have enabled identification and quantification of major contributors to capacity decay originating from the membrane, cell configuration, electrolyte composition, and operating conditions. These findings have instigated design of VRFBs with asymmetric configuration of the negative and positive sides. Such asymmetry in the reactor and external electrolytes passively mitigates vanadium ion and water crossover during long-term cycling, improving the energy storage efficiency of VRFBs. The novel cell configurations designed and engineered for this work are under invention disclosures at the University of Tennessee and provide an inexpensive and passive solution for further adopting the VRFBs as a safe and robust technology for grid-scale storage.

Nano- and Mesoscale Ion and Water Transport in Perfluorosulfonic-Acid Membranes

High performance of polymer-electrolyte fuel cells requires rapid cation conduction through perflurosulfonic-acid (PFSA) membranes. Consequently, understanding water and aqueous cation transport in aqueous nanoscale domains (nano length scale) and connectivity and tortuosity of the microscale domains (meso length scales) is critical to optimizing PFSA membrane design. Due to transport coupling, membrane ionic conduction depends not only on electrostatic potential gradients but also on water content gradients (i.e. electro-osmosis). In this work, we model coupled cation and water transport in PFSA membranes at the nano- and mesoscale and predict macroscopic properties. We adopt a mean-field local-density theory for cation and water chemical potentials to predict transport in the nanoscale PFSA aqueous domains. Cation-polymer electrostatic interactions and solvation energy are included. Concentrated solution transport theory (Stefan-Maxwell formulation) models diffusion and specifically accounts for dielectric friction induced by the strong electrostatic fields of charged polymer groups. To model the mesoscale, a resistor network that includes Stefan-Maxwell coupling quantifies transport along the segments of the collection of aqueous domains in PFSA membranes. The nanoscale model parameterizes the properties of each segment of the resistor network. With this methodology, we decouple the influences of nano- and mesoscale resistances on macroscopic water and cation transport and electro-osmosis. At the nanoscale there is coupling between water and cation transport from both diffusional drag and electrostatic-driven convection. Electrostatic and pressure forces on the membrane are countered by immobilization of the polymer matrix. The models show the nature of electro-osmosis depends on water content and the vapor and electrostatic potential boundary conditions of the membrane. This work provides a compelling approach to elucidate the multiscale resistances to water and cation transport in PFSA membranes.

(Invited) Modeling Transport Processes in Perovskite-Based Mixed Ionic-Electronic Conducting Membranes

Although many mixed ionic-electronic conductors (MIEC) share crystallographically similar doped perovskite structures, wide ranges of particular materials offer a diverse range of practically useful applications. Broadly speaking, the MIEC materials may be dominantly oxygen-ion conductors or proton conductors. The present paper is primarily concerned with transport processes that are relevant for membrane applications. Such applications include fuel cells, electrolyzers, gas separations, membrane reactors, and electrochemical compressors. The presentation uses illustrative examples. In practice gases must react at the membrane surfaces to incorporate or release ions or other charge-carrying defects. The mobile charge carrying defects can include oxygen vacancies, protons, and a variety of small polarons. The defect transport may be represented in terms of Nernst-Planck fluxes. An internal electrostatic-potential field must be developed maintain charge-neutrality within the membrane. The Nernst-Planck flux depends on gradients of defect concentrations, electrostatic potential, and hydrostatic stress. Depending on the material and the application, the membrane may be polarized by applying an electric potential from an external circuit. Ideally, for most membrane applications, the defect transport is entirely ionic. However, electronic defects (typically small polarons) can effectively result in electrical “leakage” that frustrates polarization. Applications such fuel cells, electrolyzers, and electrochemical compressors require membrane polarization. Depending on the material’s effective electrical conductivity polarization may not be practical. Local defect concentrations cause crystal-lattice-scale strain, which results in macroscopic stress through the membrane and its mechanical support structure. Such chemo-mechanical coupling can cause membrane distortion and potentially damaging high stresses. Modeling membrane performance requires incorporating the Nernst-Planck fluxes into conservation equations. The rate of change in defect concentrations is balanced by the divergence of the Nernst-Planck fluxes. The local electrostatic fields may be determined in the context of a Poisson equation that effectively produces local electroneutrality. The resulting nonlinear, coupled, system of partial differential equations, generally called the Nernst-Planck-Poisson equations, may be solved computationally.

Imaging of potential gradient on platinum induced by hydrogen adsorption

The local gradient of electrostatic potential in the Pt gate of a Si-metal oxide semiconductor field effect transistor has been visualized using a phase reconstruction method with through-focus images of transmission electron microscopy based on the transport-of-intensity equation, which was quantitatively corrected by electron holography. The potential change by hydrogen adsorption in a specimen was detected by taking the difference between H2-adsorbed and H2-not-adsorbed phase images. We found that the potential gradient was localized at Pt interfaces and that the direction of the polarization was Pt inward. The direct visualization suggests that the potential gradient originated from hydrogen dipoles generated and located at the Pt interfaces.

CDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale.

We develop a "charged" dissipative particle dynamics (cDPD) model for simulating mesoscopic electrokinetic phenomena governed by the stochastic Poisson-Nernst-Planck and the Navier-Stokes equations. Specifically, the transport equations of ionic species are incorporated into the DPD framework by introducing extra degrees of freedom and corresponding evolution equations associated with each DPD particle. Diffusion of ionic species driven by the ionic concentration gradient, electrostatic potential gradient, and thermal fluctuations is captured accurately via pairwise fluxes between DPD particles. The electrostatic potential is obtained by solving the Poisson equation on the moving DPD particles iteratively at each time step. For charged surfaces in bounded systems, an effective boundary treatment methodology is developed for imposing both the correct hydrodynamic and electrokinetics boundary conditions in cDPD simulations. To validate the proposed cDPD model and the corresponding boundary conditions, we first study the electrostatic structure in the vicinity of a charged solid surface, i.e., we perform cDPD simulations of the electrostatic double layer and show that our results are in good agreement with the well-known mean-field theoretical solutions. We also simulate the electrostatic structure and capacity densities between charged parallel plates in salt solutions with different salt concentrations. Moreover, we employ the proposed methodology to study the electro-osmotic and electro-osmotic/pressure-driven flows in a micro-channel. In the latter case, we simulate the dilute poly-electrolyte solution drifting by electro-osmotic flow in a micro-channel, hence demonstrating the flexibility and capability of this method in studying complex fluids with electrostatic interactions at the micro- and nano-scales.

How walls affect the dynamics of self-phoretic microswimmers

We study the effect of a nearby planar wall on the propulsion of a spherical phoretic micro-swimmer driven by reactions on its surface. An asymmetric coverage of catalysts on its surface which absorb reactants and generate products gives rise to an anisotropic interfacial flow that propels the swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a function of the asymmetric catalytic coverage of the surface. By an analysis of the fundamental singularities of the flow and concentration or electrostatic potential gradients generated we are able to obtain and rationalise a phase diagram of behaviours as a function of the characteristics of the swimmer surface. We find a variety of possible behaviours, from "bound states" where the swimmer remains near the wall to "scattering" or repulsive trajectories in which the swimmer ends far from the wall. The formation of some of the bound states is a purely wall-phoretic effect and cannot be obtained by simply mapping a phoretic swimmer to a hydrodynamic one.

Coupled Membrane Transport Parameters for Ionic Species in All-Vanadium Redox Flow Batteries

One of the major sources of capacity loss in all-vanadium redox flow batteries (VRFBs) is the undesired transport of active vanadium species across the ion-exchange membrane, generically termed crossover. In this work, a novel system has been designed and built to investigate the concentration- and electrostatic potential gradient-driven crossover for all vanadium species through the membrane in real-time. For this study, a perfluorosulphonic acid membrane separator (Nafion® 117) was used. The test system utilizes ultraviolet/visible (UV/Vis) spectroscopy to differentiate vanadium ion species and separates contributions to crossover stemming from concentration and electrostatic potential gradients. It is shown that the rate of species transport through the ion-exchange membrane is state of charge dependent and, as a result, interaction coefficients have been deduced which can be used to better estimate expected crossover over a range of operating conditions. The electric field was shown to increase the negative-to-positive transport of V(II)/V(III) and suppress the positive-to-negative transport of V(IV)/V(V) during discharge, with an inverse trend during charging conditions. Electric-field-induced transport coefficients were deduced directly from experimental data.

Highlighting coupling effects in ionic diffusion

The proper description of ion diffusion fluxes is important in the design and development of separation processes such as ion exchange, electrodialysis, metals extraction and fuel cells. The primary objective of this article is to highlight the several distinguishing characteristics of ionic diffusion. Due to the requirements of electro-neutrality and the no-current prescription, an electrostatic potential gradient is induced that tends to accelerate or decelerate ions depending on the sign of their charges. Furthermore, for mixed ion systems the diffusion fluxes are strongly coupled to one another. Diffusional coupling effects result in overshoots and uphill ion diffusion in bulk electrolytes and within charged ion-exchange particles. The induced electrostatic potential also cause forward and reverse ion exchange processes to proceed at significantly different rates, i.e. these are asymmetric. For exchange of three counter-ions, the transient adsorption/desorption trajectories follow completely different equilibration trajectories in composition space. The Nernst–Planck equation is found to be of sufficient accuracy to capture all of the essential features of mixed ion diffusion in the variety of systems examined.