Onsager's Wien effect on a lattice

Two-Dimensional Material-Based Nanofluidic Devices and Their Applications

Nanofluidics is an interdisciplinary field of study that bridges hydrodynamics, statistical physics, chemistry, materials science, biology, and other fields to investigate the transport of fluids and ions on the nanometric scale. The progress in this field, however, has been constrained by challenges in fabricating nanofluidic devices suitable for systematic investigations. Recent advances in two-dimensional (2D) materials have revolutionized the development of nanofluids. Their ultrathin structure and photothermoelectric response make it possible to achieve the scale control, friction limitation, and regulatory response, all of which are challenging to achieve with traditional solid materials. In this review, we provide a comprehensive overview of the preparation methods and corresponding structures of three types of 2D material-based nanofluidic devices, including nanopores, nanochannels, and membranes. We highlight their applications and recent advances in exploring physical mechanisms, detecting biomolecules (DNA, protein), developing iontronics devices, improving ion/gas selectivity, and generating osmotic energy. We discuss the challenges facing 2D material-based nanofluidic devices and the prospects for future advancements in this field.

Ions and dipoles in electric field: nonlinear polarization and field-dependent chemical reaction

We investigate electric-field effects in dilute electrolytes with nonlinear polarization. As a first example of such systems, we add a dipolar component with a relatively large dipole moment [Formula: see text] to an aqueous electrolyte. As a second example, the solvent itself exhibits nonlinear polarization near charged objects. For such systems, we present a Ginzburg-Landau free energy and introduce field-dependent chemical potentials, entropy density, and stress tensor, which satisfy general thermodynamic relations. In the first example, the dipoles accumulate in high-field regions, as predicted by Abrashikin et al.[Phys.Rev.Lett. 99, 077801 (2007)]. Finally, we consider the case, where Bjerrum ion pairs form a dipolar component with nonlinear polarization. The Bjerrum dipoles accumulate in high-field regions, while field-induced dissociation was predicted by Onsager [J. Chem. Phys.2, 599 (1934)]. We present an expression for the field-dependent association constant K(E), which depends on the field strength nonmonotonically.

Photoaccelerated Water Dissociation Across One-Atom-Thick Electrodes

Recent experiments demonstrated that interfacial water dissociation (H₂O ⇆ H⁺ + OH^-) could be accelerated exponentially by an electric field applied to graphene electrodes, a phenomenon related to the Wien effect. Here we report an order-of-magnitude acceleration of the interfacial water dissociation reaction under visible-light illumination. This process is accompanied by spatial separation of protons and hydroxide ions across one-atom-thick graphene and enhanced by strong interfacial electric fields. The found photoeffect is attributed to the combination of graphene's perfect selectivity with respect to protons, which prevents proton-hydroxide recombination, and to proton transport acceleration by the Wien effect, which occurs in synchrony with the water dissociation reaction. Our findings provide fundamental insights into ion dynamics near atomically thin proton-selective interfaces and suggest that strong interfacial fields can enhance and tune very fast ionic processes, which is of relevance for applications in photocatalysis and designing reconfigurable materials.

Conductance of concentrated electrolytes: Multivalency and the Wien effect

The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.

Wien effect in interfacial water dissociation through proton-permeable graphene electrodes

Strong electric fields can accelerate molecular dissociation reactions. The phenomenon known as the Wien effect was previously observed using high-voltage electrolysis cells that produced fields of about 107 V m-1, sufficient to accelerate the dissociation of weakly bound molecules (e.g., organics and weak electrolytes). The observation of the Wien effect for the common case of water dissociation (H2O [Formula: see text] H+ + OH-) has remained elusive. Here we study the dissociation of interfacial water adjacent to proton-permeable graphene electrodes and observe strong acceleration of the reaction in fields reaching above 108 V m-1. The use of graphene electrodes allows measuring the proton currents arising exclusively from the dissociation of interfacial water, while the electric field driving the reaction is monitored through the carrier density induced in graphene by the same field. The observed exponential increase in proton currents is in quantitative agreement with Onsager's theory. Our results also demonstrate that graphene electrodes can be valuable for the investigation of various interfacial phenomena involving proton transport.

Continuum Modeling of Porous Electrodes for Electrochemical Synthesis

Electrochemical synthesis possesses substantial promise to utilize renewable energy sources to power the conversion of abundant feedstocks to value-added commodity chemicals and fuels. Of the potential system architectures for these processes, only systems employing 3-D structured porous electrodes have the capacity to achieve the high rates of conversion necessary for industrial scale. However, the phenomena and environments in these systems are not well understood and are challenging to probe experimentally. Fortunately, continuum modeling is well-suited to rationalize the observed behavior in electrochemical synthesis, as well as to ultimately provide recommendations for guiding the design of next-generation devices and components. In this review, we begin by presenting an historical review of modeling of porous electrode systems, with the aim of showing how past knowledge of macroscale modeling can contribute to the rising challenge of electrochemical synthesis. We then present a detailed overview of the governing physics and assumptions required to simulate porous electrode systems for electrochemical synthesis. Leveraging the developed understanding of porous-electrode theory, we survey and discuss the present literature reports on simulating multiscale phenomena in porous electrodes in order to demonstrate their relevance to understanding and improving the performance of devices for electrochemical synthesis. Lastly, we provide our perspectives regarding future directions in the development of models that can most accurately describe and predict the performance of such devices and discuss the best potential applications of future models.

Magnetic monopole density and antiferromagnetic domain control in spin-ice iridates

Magnetically frustrated systems provide fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles is yet to be found. Using measurements on single crystals of Ho2Ir2O7 combined with dipolar Monte Carlo simulations, we show that the isothermal magnetoresistance is highly sensitive to the monopole density. Moreover, we uncover an unexpected and strong coupling between the monopoles on the holmium sublattice and the antiferromagnetically ordered iridium ions. These results pave the way towards a quantitative experimental measure of monopole density and demonstrate the ability to control antiferromagnetic domain walls using a uniform external magnetic field, a key goal in the design of next-generation spintronic devices.

Prospects of Observing Ionic Coulomb Blockade in Artificial Ion Confinements

Nanofluidics encompasses a wide range of advanced approaches to study charge and mass transport at the nanoscale. Modern technologies allow us to develop and improve artificial nanofluidic platforms that confine ions in a way similar to single-ion channels in living cells. Therefore, nanofluidic platforms show great potential to act as a test field for theoretical models. This review aims to highlight ionic Coulomb blockade (ICB)-an effect that is proposed to be the key player of ion channel selectivity, which is based upon electrostatic exclusion limiting ion transport. Thus, in this perspective, we focus on the most promising approaches that have been reported on the subject. We consider ion confinements of various dimensionalities and highlight the most recent advancements in the field. Furthermore, we concentrate on the most critical obstacles associated with these studies and suggest possible solutions to advance the field further.

Understanding Multi-Ion Transport Mechanisms in Bipolar Membranes

Bipolar membranes (BPMs) have the potential to become critical components in electrochemical devices for a variety of electrolysis and electrosynthesis applications. Because they can operate under large pH gradients, BPMs enable favorable environments for electrocatalysis at the individual electrodes. Critical to the implementation of BPMs in these devices is understanding the kinetics of water dissociation that occurs within the BPM as well as the co- and counter-ion crossover through the BPM, which both present significant obstacles to developing efficient and stable BPM-electrolyzers. In this study, a continuum model of multi-ion transport in a BPM is developed and fit to experimental data. Specifically, concentration profiles are determined for all ionic species, and the importance of a water-dissociation catalyst is demonstrated. The model describes internal concentration polarization and co- and counter-ion crossover in BPMs, determining the mode of transport for ions within the BPM and revealing the significance of salt-ion crossover when operated with pH gradients relevant to electrolysis and electrosynthesis. Finally, a sensitivity analysis reveals that the performance and lifetime of BPMs can be improved substantially by using of thinner dissociation catalysts, managing water transport, modulating the thickness of the individual layers in the BPM to control salt-ion crossover, and increasing the ion-exchange capacity of the ion-exchange layers in order to amplify the water-dissociation kinetics at the interface.

Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi-quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near-surface region, for example if a substrate is solid like aforementioned cellulose.

Anomalous out-of-equilibrium dynamics in the spin-ice material Dy2Ti2O7under moderate magnetic fields

We study experimentally and numerically the dynamics of the spin ice material Dy2Ti2O7in the low temperature (T) and moderate magnetic field (B) regime (T∈ [0.1, 1.7]  K,B∈ [0, 0.3]  T). Our objective is to understand the main physics shaping the out-of-equilibrium magnetisation vs temperature curves in two different regimes. Very far from equilibrium, turning on the magnetic field after having cooled the system in zero field (ZFC) can increase the concentration of magnetic monopoles (localised thermal excitations present in these systems); this accelerates the dynamics. Similarly to electrolytes, this occurs through dissociation of bound monopole pairs. However, for spin ices the polarisation of the vacuum out of which the monopole pairs are created is a key factor shaping the magnetisation curves, with no analog. We observe a threshold field near 0.2 T for this fast dynamics to take place, linked to the maximum magnetic force between the attracting pairs. Surprisingly, within a regime of low temperatures and moderate fields, an extended Ohm's law can be used to describe the ZFC magnetisation curve obtained with the dipolar spin-ice model. However, in real samples the acceleration of the dynamics appears even sharper than in simulations, possibly due to the presence of avalanches. On the other hand, the effect of the field nearer equilibrium can be just the opposite to that at very low temperatures. Single crystals, as noted before for powders, abandon equilibrium at a blocking temperatureTBwhich increases with field. Curiously, this behaviour is present in numerical simulations even within the nearest-neighbours interactions model. Simulations and experiments show that the increasing trend inTBis stronger forB‖[100]. This suggests that the field plays a part in the dynamical arrest through monopole suppression, which is quite manifest for this field orientation.

The history of spin ice

This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.

Ionic Coulomb blockade as a fractional Wien effect

Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet artificial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport that is tunable by an external gate-the ionic analogue of electronic Coulomb blockade-would open new avenues in this quest. However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agreement with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely charged ions form 'Bjerrum pairs', and the conduction proceeds through a mechanism reminiscent of Onsager's Wien effect. Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired by its electronic counterpart.

Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice

Magnetic monopoles, proposed as elementary particles that act as isolated magnetic south and north poles, have long attracted research interest as magnetic analogs to electric charge. In solid-state physics, a classical analog to these elusive particles has emerged as topological excitations within pyrochlore spin ice systems. We present the first real-time imaging of emergent magnetic monopole motion in a macroscopically degenerate artificial spin ice system consisting of thermally activated Ising-type nanomagnets lithographically arranged onto a pre-etched silicon substrate. A real-space characterization of emergent magnetic monopoles within the framework of Debye-Hückel theory is performed, providing visual evidence that these topological defects act like a plasma of Coulomb-type magnetic charges. In contrast to vertex defects in a purely two-dimensional artificial square ice, magnetic monopoles are free to evolve within a divergence-free vacuum, a magnetic Coulomb phase, for which features in the form of pinch-point singularities in magnetic structure factors are observed.

Two fluid model in low energy excited states within spin-ice systems

Excitations in magnetic structures of the so-called spin-ice materials generate two different peaks in the specific heat and anomalies in entropy in the temperature interval between 0 and 1 K. These points are due to the existence of two low-energy excited global states which seem to transit from a bosonic condensate towards a magnetic neutral plasma in a narrow temperature interval between 0.05 ≤ T ≤ 1 K. In this paper, we determine the characteristic features of two states and we analyze the possibilities of existence of a BEC state and its phase transition to the magnetic plasma state from a model of two magnetic charge fluids. From the structural analysis of the many-body excitation states, we obtain theoretical results about entropy and specific heat since these two key physical magnitudes announce the phase transitions. We give criteria for distinguishing if some of these phase transitions is of either first or second order.

Nanoscale Resolution of Electric-field Induced Motion in Ionic Diblock Copolymer Thin Films

Understanding the responses of ionic block copolymers to applied electric fields is crucial when targeting applications in areas such as energy storage, microelectronics, and transducers. This work shows that the identity of counterions in ionic diblock copolymers substantially affects their responses to electric fields, demonstrating the importance of ionic species for materials design. In situ neutron reflectometry measurements revealed that thin films containing imidazolium based cationic diblock copolymers, tetrafluoroborate counteranions led to film contraction under applied electric fields, while bromide counteranions drove expansion under similar field strengths. Coarse-grained molecular dynamics simulations were used to develop a fundamental understanding of these responses, uncovering a nonmonotonic trend in thickness change as a function of field strength. This behavior was attributed to elastic responses of microphase separated diblock copolymer chains resulting from variations in interfacial tension of polymer-polymer interfaces due to the redistribution of counteranions in the presence of electric fields.

Underscreening in concentrated electrolytes

Screening of a surface charge by an electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.

Anomalous Wien Effects in Supercooled Ionic Liquids

We have measured conductivity spectra of several supercooled monocationic and dicationic ionic liquids in the nonlinear regime by applying ac electric fields with large amplitudes up to about 180  kV/cm. Thereby, higher harmonic ac currents up to the 7th order were detected. Our results point to the existence of anomalous Wien effects in supercooled ionic liquids. Most ionic liquids studied here exhibit a conductivity-viscosity relation, which is close to the predictions of the Nernst-Einstein and Stokes-Einstein equations, as observed for classical strong electrolytes like KCl. These "strong" ionic liquids show a much stronger nonlinearity of the conductivity than classical strong electrolytes. On the other hand, the conductivity-viscosity relation of the ionic liquid [P_{6,6,6,14}][Cl] points to ion association effects. This "weak" ionic liquid shows a strength of the nonlinear effect, which is comparable to classical weak electrolytes. However, the nonlinearity increases quadratically with the field. We suggest that a theory for explaining these anomalies will have to go beyond the level of Coulomb lattice gas models.

ac Wien Effect in Spin Ice, Manifest in Nonlinear, Nonequilibrium Susceptibility

The Wien effect is a model process for field-induced charge creation. Here it is derived for a nonelectrical system: the spin ice "magnetolyte"-a unique system showing perfect charge symmetry. An entropic reaction field, analogous to the Jaccard field in ice, opposes direct current, but a frequency window exists in which the Wien effect for magnetolyte and electrolyte are indistinguishable. The universal enhancement of monopole density speeds up the magnetization dynamics, which manifests in the nonlinear, nonequilibrium ac susceptibility. This is a rare instance where such effects may be calculated, providing new insights for electrolytes. Experimental predictions are made for Dy2Ti2O7 spin ice.

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare-earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Spin ices provide one of very few experimentally realized examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterized by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges with a mutual Coulomb interaction, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focusing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

Frequency dependence of dielectric saturation

Dielectric saturation originates from the upper bound to dipole orientation, reached when all dipoles are aligned "perfectly" with respect to the electric field. For Debye-type dynamics, it is well established that the saturation effect is diminished at high frequencies relative to its steady-state value. Here, it is argued that a similar frequency dependence of this nonlinear dielectric effect is expected also for dispersive dynamics, provided that the system is dynamically homogeneous. By contrast, more realistic relaxation time dispersions based upon heterogeneous dynamics display a strongly reduced frequency dependence of dielectric saturation. Calculations demonstrate this effect in terms of both the fundamental and the third harmonic frequency susceptibilities. The relations of signatures of nonlinearity in different Fourier components of the response are briefly discussed.