A Universal Approximation for Conductance Blockade in Thin Nanopore Membranes

Nanopore-based sensing platforms have transformed single-molecule detection and analysis. The foundation of nanopore translocation experiments lies in conductance measurements, yet existing models, which are largely phenomenological, are inaccurate in critical experimental conditions such as thin and tightly fitting pores. Of the two components of the conductance blockade, channel and access resistance, the access resistance is poorly modeled. We present a comprehensive investigation of the access resistance and associated conductance blockade in thin nanopore membranes. By combining a first-principles approach, multiscale modeling, and experimental validation, we propose a unified theoretical modeling framework. The analytical model derived as a result surpasses current approaches across a broad parameter range. Beyond advancing our theoretical understanding, our framework's versatility enables analyte size inference and predictive insights into conductance blockade behavior. Our results will facilitate the design and optimization of nanopore devices for diverse applications, including nanopore base calling and data storage.

Beyond Constant Current: Origin of Pulse-Induced Activation in Phase-Transforming Battery Electrodes

Mechanistic understanding of phase transformation dynamics during battery charging and discharging is crucial toward rationally improving intercalation electrodes. Most studies focus on constant-current conditions. However, in real battery operation, such as in electric vehicles during discharge, the current is rarely constant. In this work we study current pulsing in LiXFePO4 (LFP), a model and technologically important phase-transforming electrode. A current-pulse activation effect has been observed in LFP, which decreases the overpotential by up to ∼70% after a short, high-rate pulse. This effect persists for hours or even days. Using scanning transmission X-ray microscopy and operando X-ray diffraction, we link this long-lived activation effect to a pulse-induced electrode homogenization on both the intra- and interparticle length scales, i.e., within and between particles. Many-particle phase-field simulations explain how such pulse-induced homogeneity contributes to the decreased electrode overpotential. Specifically, we correlate the extent and duration of this activation to lithium surface diffusivity and the magnitude of the current pulse. This work directly links the transient electrode-level electrochemistry to the underlying phase transformation and explains the critical effect of current pulses on phase separation, with significant implication on both battery round-trip efficiency and cycle life. More broadly, the mechanisms revealed here likely extend to other phase-separating electrodes, such as graphite.

Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer

A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3-6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Multiscale dynamics of charging and plating in graphite electrodes coupling operando microscopy and phase-field modelling

The phase separation dynamics in graphitic anodes significantly affects lithium plating propensity, which is the major degradation mechanism that impairs the safety and fast charge capabilities of automotive lithium-ion batteries. In this study, we present comprehensive investigation employing operando high-resolution optical microscopy combined with non-equilibrium thermodynamics implemented in a multi-dimensional (1D+1D to 3D) phase-field modeling framework to reveal the rate-dependent spatial dynamics of phase separation and plating in graphite electrodes. Here we visualize and provide mechanistic understanding of the multistage phase separation, plating, inter/intra-particle lithium exchange and plated lithium back-intercalation phenomena. A strong dependence of intra-particle lithiation heterogeneity on the particle size, shape, orientation, surface condition and C-rate at the particle level is observed, which leads to early onset of plating spatially resolved by a 3D image-based phase-field model. Moreover, we highlight the distinct relaxation processes at different state-of-charges (SOCs), wherein thermodynamically unstable graphite particles undergo a drastic intra-particle lithium redistribution and inter-particle lithium exchange at intermediate SOCs, whereas the electrode equilibrates much slower at low and high SOCs. These physics-based insights into the distinct SOC-dependent relaxation efficiency provide new perspective towards developing advanced fast charge protocols to suppress plating and shorten the constant voltage regime.

Proton-coupled electron transfer at SOFC electrodes

Understanding the charge transfer processes at solid oxide fuel cell (SOFC) electrodes is critical to designing more efficient and robust materials. Activation losses at SOFC electrodes have been widely attributed to the ambipolar migration of charges at the mixed ionic-electronic conductor-gas interface. Empirical Butler-Volmer kinetics based on the transition state theory is often used to model the current-voltage relationship, where charged particles transfer classically over an energy barrier. However, the hydrogen oxidation/water electrolysis reaction H2(g) + O2- ⇌ H2O(g) + 2e- must be modeled through concerted electron and proton tunneling events, where we unify the theory of the electrostatic surface potential with proton-coupled electron transfer kinetics. We derive a framework for the reaction rate that depends on the electrostatic surface potential, adsorbate dipole moment, the electronic structure of the electron donor/acceptor, and vibronic states of the hydrogen species. This theory was used to study the current-voltage characteristics of the Ni/gadolinium-doped ceria electrode in H2/H2O(g), where we find excellent validation of this novel model. These results yield the first reported quantification of the solvent reorganization energy for an SOFC material and suggest that the three-phase boundary mechanism is the dominant pathway for charge transfer at cermet electrodes.

Orientational Ordering in Nano-confined Polar Liquids

Water and other polar liquids exhibit nanoscale structuring near charged interfaces. When a polar liquid is confined between two charged surfaces, the interfacial solvent layers begin to overlap, resulting in solvation forces. Here, we perform molecular dynamics simulations of polar liquids with different dielectric constants and molecular shapes and sizes confined between charged surfaces, demonstrating strong orientational ordering in the nanoconfined liquids. To rationalize the observed structures, we apply a coarse-grained continuum theory that captures the orientational ordering and solvation forces of those liquids. Our findings reveal the subtle behavior of different nanoconfined polar liquids and establish a simple law for the decay length of the interfacial orientations of the solvents, which depends on their molecular size and polarity. These insights shed light on the nature of solvation forces, which are important in colloid and membrane science, scanning probe microscopy, and nano-electrochemistry.

Population effects driving active material degradation in intercalation electrodes

In battery modeling, the electrode is discretized at the macroscopic scale with a single representative particle in each volume. This lacks the accurate physics to describe interparticle interactions in electrodes. To remedy this, we formulate a model that describes the evolution of degradation of a population of battery active material particles using ideas in population genetics of fitness evolution, where the state of a system depends on the health of each particle that contributes to the system. With the fitness formulation, the model incorporates effects of particle size and heterogeneous degradation effects which accumulate in the particles as the battery is cycled, accounting for different active material degradation mechanisms. At the particle scale, degradation progresses nonuniformly across the population of active particles, observed from the autocatalytic relationship between fitness and degradation. Electrode-level degradation is formed from various contributions of the particle-level degradation, especially from smaller particles. It is shown that specific mechanisms of particle-level degradation can be associated with characteristic signatures in the capacity-loss and voltage profiles. Conversely, certain features in the electrode-level phenomena can also provide insight into the relative importance of different particle-level degradation mechanisms.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Selective and Chemical-Free Removal of Toxic Heavy Metal Cations from Water Using Shock Ion Extraction

Electrochemical methods are known to have attractive features and capabilities when used for ion separations and water purification. In this study, we developed a new process called shock ion extraction (shock IX) for selective and chemical-free removal of toxic heavy metals from water. Shock IX is a hybrid process that combines shock electrodialysis (shock ED) and ion exchange using an ion exchange resin wafer (IERW), and this method can be thought of functionally as an electrochemically assisted variation of traditional ion exchange. In particular, shock IX exhibits greater ion removal and selectivity for longer periods of time, compared to the use of ion exchange alone. The use of an IERW in shock ED also increases multivalent ion selectivity, reduces energy consumption, and improves the hydrodynamics and scalability of the system.

Thermodynamics of Charge Regulation during Ion Transport through Silica Nanochannels

Ion-surface interactions can alter the properties of nanopores and dictate nanofluidic transport in engineered and biological systems central to the water-energy nexus. The ion adsorption process, known as "charge regulation", is ion-specific and is dependent on the extent of confinement when the electric double layers (EDLs) between two charged surfaces overlap. A fundamental understanding of the mechanisms behind charge regulation remains lacking. Herein, we study the thermodynamics of charge regulation reactions in 20 nm SiO₂ channels via conductance measurements at various concentrations and temperatures. The effective activation energies (E_a) for ion conductance at low concentrations (strong EDL overlap) are ∼2-fold higher than at high concentrations (no EDL overlap) for the electrolytes studied here: LiCl, NaCl, KCl, and CsCl. We find that E_a values measured at high concentrations result from the temperature dependence of viscosity and its influence on ion mobility, whereas E_a values measured at low concentrations result from the combined effects of ion mobility and the enthalpy of cation adsorption to the charged surface. Notably, the E_a for surface reactions increases from 7.03 kJ mol^-1 for NaCl to 16.72 ± 0.48 kJ mol^-1 for KCl, corresponding to a difference in surface charge of -8.2 to -0.8 mC m^-2, respectively. We construct a charge regulation model to rationalize the cation-specific charge regulation behavior based on an adsorption equilibrium. Our findings show that temperature- and concentration-dependent conductance measurements can help indirectly probe the ion-surface interactions that govern transport and colloidal interactions at the nanoscale─representing a critical step forward in our understanding of charge regulation and adsorption phenomena under nanoconfinement.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

Interfacial Resistive Switching by Multiphase Polarization in Ion-Intercalation Nanofilms

Nonvolatile resistive-switching (RS) memories promise to revolutionize hardware architectures with in-memory computing. Recently, ion-interclation materials have attracted increasing attention as potential RS materials for their ion-modulated electronic conductivity. In this Letter, we propose RS by multiphase polarization (MP) of ion-intercalated thin films between ion-blocking electrodes, in which interfacial phase separation triggered by an applied voltage switches the electron-transfer resistance. We develop an electrochemical phase-field model for simulations of coupled ion-electron transport and ion-modulated electron-transfer rates and use it to analyze the MP switching current and time, resistance ratio, and current-voltage response. The model is able to reproduce the complex cyclic voltammograms of lithium titanate (LTO) memristors, which cannot be explained by existing models based on bulk dielectric breakdown. The theory predicts the achievable switching speeds for multiphase ion-intercalation materials and could be used to guide the design of high-performance MP-based RS memories.

Polar liquids at charged interfaces: A dipolar shell theory

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

Rectified and Salt Concentration Dependent Wetting of Hydrophobic Nanopores

Nanopores lined with hydrophobic groups function as switches for water and all dissolved species, such that transport is allowed only when applying a sufficiently high transmembrane pressure difference or voltage. Here we show a hydrophobic nanopore system whose wetting and ability to transport water and ions is rectified and can be controlled with salt concentration. The nanopore we study contains a junction between a hydrophobic zone and a positively charged hydrophilic zone. The nanopore is closed for transport at low salt concentrations and exhibits finite current only when the concentration reaches a threshold value that is dependent on the pore opening diameter, voltage polarity and magnitude, and type of electrolyte. The smallest nanopore studied here had a 4 nm diameter and did not open for transport in any concentration of KCl or KI examined. A 12 nm nanopore was closed for all KCl solutions but conducted current in KI at concentrations above 100 mM for negative voltages and opened for both voltage polarities at 500 mM KI. Nanopores with a hydrophobic/hydrophilic junction can thus function as diodes, such that one can identify a range of salt concentrations where the pores transport water and ions for only one voltage polarity. Molecular dynamics simulations together with continuum models provided a multiscale explanation of the observed phenomena and linked the salt concentration dependence of wetting with an electrowetting model. Results presented are crucial for designing next-generation chemical and ionic separation devices as well as understanding fundamental properties of hydrophobic interfaces under nanoconfinement.

Water electrolysis: from textbook knowledge to the latest scientific strategies and industrial developments

Replacing fossil fuels with energy sources and carriers that are sustainable, environmentally benign, and affordable is amongst the most pressing challenges for future socio-economic development. To that goal, hydrogen is presumed to be the most promising energy carrier. Electrocatalytic water splitting, if driven by green electricity, would provide hydrogen with minimal CO2 footprint. The viability of water electrolysis still hinges on the availability of durable earth-abundant electrocatalyst materials and the overall process efficiency. This review spans from the fundamentals of electrocatalytically initiated water splitting to the very latest scientific findings from university and institutional research, also covering specifications and special features of the current industrial processes and those processes currently being tested in large-scale applications. Recently developed strategies are described for the optimisation and discovery of active and durable materials for electrodes that ever-increasingly harness first-principles calculations and machine learning. In addition, a technoeconomic analysis of water electrolysis is included that allows an assessment of the extent to which a large-scale implementation of water splitting can help to combat climate change. This review article is intended to cross-pollinate and strengthen efforts from fundamental understanding to technical implementation and to improve the 'junctions' between the field's physical chemists, materials scientists and engineers, as well as stimulate much-needed exchange among these groups on challenges encountered in the different domains.

Correlative image learning of chemo-mechanics in phase-transforming solids

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li_XFePO₄, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Structural Forces in Ionic Liquids: The Role of Ionic Size Asymmetry

Ionic liquids (ILs) are charged fluids composed of anions and cations of different size and shape. The ordering of charge and density in ILs confined between charged interfaces underlies numerous applications of IL electrolytes. Here, we analyze the screening behavior and the resulting structural forces of a representative IL confined between two charge-varied plates. Using both molecular dynamics simulations and a continuum theory, we contrast the screening features of a more-realistic asymmetric system and a less-realistic symmetric one. The ionic size asymmetry plays a nontrivial role in charge screening, affecting both the ionic density profiles and the disjoining pressure distance dependence. Ionic systems with size asymmetry are stronger coupled systems, and this manifests itself both in their response to the electrode polarization and spontaneous structure formation at the interface. Analytical expressions for decay lengths of the disjoining pressure are obtained in agreement with the pressure profiles computed from molecular dynamics simulations.

Advances and challenges in the development of nanosheet membranes

The development of highly efficient separation membranes utilizing emerging materials with controllable pore size and minimized thickness could greatly enhance the broad applications of membrane-based technologies. Having this perspective, many studies on the incorporation of nanosheets in membrane fabrication have been conducted, and strong interest in this area has grown over the past decade. This article reviews the development of nanosheet membranes focusing on two-dimensional materials as a continuous phase, due to their promising properties, such as atomic or nanoscale thickness and large lateral dimensions, to achieve improved performance compared to their discontinuous counterparts. Material characteristics and strategies to process nanosheet materials into separation membranes are reviewed, followed by discussions on the membrane performances in diverse applications. The review concludes with a discussion of remaining challenges and future outlook for nanosheet membrane technologies.

Salt-in-Ionic-Liquid Electrolytes: Ion Network Formation and Negative Effective Charges of Alkali Metal Cations

Salt-in-ionic liquid electrolytes have attracted significant attention as potential electrolytes for next generation batteries largely due to their safety enhancements over typical organic electrolytes. However, recent experimental and computational studies have shown that under certain conditions alkali cations can migrate in electric fields as if they carried a net negative effective charge. In particular, alkali cations were observed to have negative transference numbers at small mole fractions of alkali-metal salt that revert to the expected net positive transference numbers at large mole fractions. Simulations have provided some insights into these observations, where the formation of asymmetric ionic clusters, as well as a percolating ion network, could largely explain the anomalous transport of alkali cations. However, a thermodynamic theory that captures such phenomena has not been developed, as ionic associations were typically treated via the formation of ion pairs. The theory presented herein, based on the classical polymer theories, describes thermoreversible associations between alkali cations and anions, where the formation of large, asymmetric ionic clusters and a percolating ionic network are a natural result of the theory. Furthermore, we present several general methods to calculate the effective charge of alkali cations in ionic liquids. We note that the negative effective charge is a robust prediction with respect to the parameters of the theory and that the formation of a percolating ionic network leads to the restoration of net positive charges of the cations at large mole fractions of alkali metal salt. Overall, we find excellent qualitative agreement between our theory and molecular simulations in terms of ionic cluster statistics and the effective charges of the alkali cations.

Modeling and multiobjective optimization of indoor airborne disease transmission risk and associated energy consumption for building HVAC systems

The COVID-19 pandemic has renewed interest in assessing how the operation of HVAC systems influences the risk of airborne disease transmission in buildings. Various processes, such as ventilation and filtration, have been shown to reduce the probability of disease spread by removing or deactivating exhaled aerosols that potentially contain infectious material. However, such qualitative recommendations fail to specify how much of these or other disinfection techniques are needed to achieve acceptable risk levels in a particular space. An additional complication is that application of these techniques inevitably increases energy costs, the magnitude of which can vary significantly based on local weather. Moreover, the operational flexibility available to the HVAC system may be inherently limited by equipment capacities and occupant comfort requirements. Given this knowledge gap, we propose a set of dynamical models that can be used to estimate airborne transmission risk and energy consumption for building HVAC systems based on controller setpoints and a forecast of weather conditions. By combining physics-based material balances with phenomenological models of the HVAC control system, it is possible to predict time-varying airflows and other HVAC variables, which are then used to calculate key metrics. Through a variety of examples involving real and simulated commercial buildings, we show that our models can be used for monitoring purposes by applying them directly to transient building data as operated, or they may be embedded within a multi-objective optimization framework to evaluate the tradeoff between infection risk and energy consumption. By combining these applications, building managers can determine which spaces are in need of infection risk reduction and how to provide that reduction at the lowest energy cost. The key finding is that both the baseline infection risk and the most energy-efficient disinfection strategy can vary significantly from space to space and depend sensitively on the weather, thus underscoring the importance of the quantitative predictions provided by the models.

Theory of freezing point depression in charged porous media

Freezing in charged porous media can induce significant pressure and cause damage to tissues and functional materials. We formulate a thermodynamically consistent theory to model freezing phenomena inside charged heterogeneous porous space. Two regimes are distinguished: free ions in open pore space lead to negligible effects of freezing point depression and pressure. On the other hand, if nanofluidic salt trapping happens, subsequent ice formation is suppressed due to the high concentration of ions in the electrolyte. In this case our theory predicts that freezing starts at a significantly lower temperature compared to pure water. In one dimension, as the temperature goes even lower, ice continuously grows until the salt concentration reaches saturation, all ions precipitate to form salt crystals, and freezing completes. Enormous pressure can be generated if initial salt concentration is high before salt entrapment. We show modifications to the classical nucleation theory due to the trapped salt ions. Interestingly, although the freezing process is enormously changed by trapped salts, our analysis shows that the Gibbs-Thompson equation on confined melting point shift is not affected by the presence of the electrolyte.

Nonlinear ion transport mediated by induced charge in ultrathin nanoporous membranes

Ultrathin membranes with nanoporous conduits show promise for ionic separations and desalination applications, but the mechanisms underlying the nonlinear ionic transport observed in these systems are not well understood. Here, we demonstrate how induced charge at membrane interfaces can lead to nonlinear ionic transport and voltage-dependent conductance through such channels. The application of an electric field on a polarizable membrane leads to induced charges at the membrane interfaces. The induced charges in turn are screened by diffuse charges in the electrolyte, which are acted upon by the electric field. For extremely thin membranes, the induced charge effect can be significant even for moderate applied voltages commonly used in experiments. We apply a continuum Poisson-Nernst-Planck model to characterize the current-voltage behavior of ultrathin membranes over a wide parameter space. The predictions of the model are compared to recent experiments on graphene and MoS_{2} membranes in an electric field. We expect the role of induced charge to be especially pronounced in the limit of atomically thin membranes.

Electroneutrality breakdown in nanopore arrays

The electrostatic screening of charge in one-dimensional confinement leads to long-range breakdown in electroneutrality within a nanopore. Through a series of continuum simulations, we demonstrate the principles of electroneutrality breakdown for electrolytes in one-dimensional confinement. We show how interacting pores in a membrane can counteract the phenomenon of electroneutrality breakdown, eventually returning to electroneutrality. Emphasis is placed on applying simplifying formulas to reduce the multidimensional partial differential equations into a single ordinary differential equation for the electrostatic potential. Dielectric mismatch between the electrolyte and membrane, pore aspect ratio, and confinement dimensionality are studied independently, outlining the relevance of electroneutrality breakdown in nanoporous membranes for selective ion transport and separations.

Blistering failure of elastic coatings with applications to corrosion resistance

A variety of polymeric surfaces, such as anti-corrosion coatings and polymer-modified asphalts, are prone to blistering when exposed to moisture and air. As water and oxygen diffuse through the material, dissolved species are produced, which generate osmotic pressure that deforms and debonds the coating. These mechanisms are experimentally well-supported; however, comprehensive macroscopic models capable of predicting the formation osmotic blisters, without extensive data-fitting, is scant. Here, we develop a general mathematical theory of blistering and apply it to the failure of anti-corrosion coatings on carbon steel. The model is able to predict the irreversible, nonlinear blister growth dynamics, which eventually reaches a stable state, ruptures, or undergoes runaway delamination, depending on the mechanical and adhesion properties of the coating. For runaway delamination, the theory predicts a critical delamination length, beyond which unstable corrosion-driven growth occurs. The model is able to fit multiple sets of blister growth data with no fitting parameters. Corrosion experiments are also performed to observe undercoat rusting on carbon steel, which yielded trends comparable with model predictions. The theory is used to define three dimensionless numbers which can be used for engineering design of elastic coatings capable of resisting visible deformation, rupture, and delamination.

Fictitious phase separation in Li layered oxides driven by electro-autocatalysis

Layered oxides widely used as lithium-ion battery electrodes are designed to be cycled under conditions that avoid phase transitions. Although the desired single-phase composition ranges are well established near equilibrium, operando diffraction studies on many-particle porous electrodes have suggested phase separation during delithiation. Notably, the separation is not always observed, and never during lithiation. These anomalies have been attributed to irreversible processes during the first delithiation or reversible concentration-dependent diffusion. However, these explanations are not consistent with all experimental observations such as rate and path dependencies and particle-by-particle lithium concentration changes. Here, we show that the apparent phase separation is a dynamical artefact occurring in a many-particle system driven by autocatalytic electrochemical reactions, that is, an interfacial exchange current that increases with the extent of delithiation. We experimentally validate this population-dynamics model using the single-phase material Li_x(Ni_1/3Mn_1/3Co_1/3)O₂ (0.5 < x < 1) and demonstrate generality with other transition-metal compositions. Operando diffraction and nanoscale oxidation-state mapping unambiguously prove that this fictitious phase separation is a repeatable non-equilibrium effect. We quantitatively confirm the theory with multiple-datastream-driven model extraction. More generally, our study experimentally demonstrates the control of ensemble stability by electro-autocatalysis, highlighting the importance of population dynamics in battery electrodes (even non-phase-separating ones).

A guideline to limit indoor airborne transmission of COVID-19

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the "cumulative exposure time," the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

A guideline to limit indoor airborne transmission of COVID-19

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the "cumulative exposure time," the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

Correlated Ion Transport and the Gel Phase in Room Temperature Ionic Liquids

Here we present a theory of ion aggregation and gelation of room temperature ionic liquids (RTILs). Based on it, we investigate the effect of ion aggregation on correlated ion transport-ionic conductivity and transference numbers-obtaining closed-form expressions for these quantities. The theory depends on the maximum number of associations a cation and anion can form and the strength of their association. To validate the presented theory, we perform molecular dynamics simulations on several RTILs and a range of temperatures for one RTIL. The simulations indicate the formation of large clusters, even percolating through the system under certain circumstances, thus forming a gel, with the theory accurately describing the obtained cluster distributions in all cases. However, based on the strength and lifetime of associations in the simulated RTILs, we expect free ions to dominate ionic conductivity despite the presence of clusters, and we do not expect the percolating cluster to trigger structural arrest in the RTIL.

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments

The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated tip-splitting of evolving fingers. When anisotropy is present in the interfacial dynamics, the growth morphology changes to dendritic growth characterized by regular structures. We introduce anisotropy by engraving a six-fold symmetric lattice of channels on a Hele-Shaw cell. We show that the morphology transition in miscible fluids depends not only on the previously reported degree of anisotropy set by the lattice topography, but also on the viscosity ratio between the two fluids, ηin/ηout. Remarkably, ηin/ηout and the degree of anisotropy also govern the global features of the dendritic patterns, inducing a systematic change from six-fold towards twelve-fold symmetric dendrites. Varying either control parameter provides a new method to tune the symmetry of complex patterns, which may also have relevance for analogous phenomena of gradient-driven interfacial dynamics, such as directional solidification or electrodeposition.

Theory of shock electrodialysis I: Water dissociation and electrosmotic vortices

Shock electrodialysis (shock ED), an emerging electrokinetic process for water purification, leverages the new physics of deionization shock waves in porous media. In previous work, a simple leaky membrane model with surface conduction can explain the propagation of deionization shocks in a shock ED system, but it cannot quantitatively predict the deionization and conductance (which determines the energy consumption), and it cannot explain the selective removal of ions in experiments. This two-part series of work establishes a more comprehensive model for shock ED, which applies to multicomponent electrolytes and any electrical double layer thickness, captures the phenomena of electroosmosis, diffusioosmosis, and water dissociation, and incorporates more realistic boundary conditions. In this paper, we will present the model details and show that hydronium transport and electroosmotic vortices (at the inlet and outlet) play important roles in determining the deionization and conductance in shock ED. We also find that the results are quantitatively consistent with experimental data in the literature. Finally, the model is used to investigate design strategies for scale up and optimization.

Theory of shock electrodialysis II: Mechanisms of selective ion removal

Shock electrodialysis (shock ED), an emerging nonlinear electrokinetic process for water treatment, has recently showed its capability to selectively remove multivalent cations from electrolyte mixtures. However, the mechanisms have not been understood yet. Based on the depth-averaged model developed in the first-part of the series paper for planer shock ED system, this work focuses on the mechanisms of selective ion removal. We first assume plug feed flow and do scaling analysis, and identify three possible mechanisms of selective removal of multivalent cations: smaller concentration left behind deionization zone, affinity to the charged surface where non-slip boundary slows down the velocity, and stronger push-back by streaming potential. Then we use numerical simulations to prove our hypothesis and show additional contribution from electroosmotic flow. Simulation results show that Mg is more removed from Na-Mg-Cl mixture at overlimiting current, which is qualitatively consistent with experiment results in literature.

Imaging Arrangements of Discrete Ions at Liquid-Solid Interfaces

The individual and collective behavior of ions near electrically charged interfaces is foundational to a variety of electrochemical phenomena encountered in biology, energy, and the environment. While many theories have been developed to predict the interfacial arrangements of counterions, direct experimental observations and validations have remained elusive. Utilizing cryo-electron microscopy, here we directly visualize individual counterions and reveal their discrete interfacial layering. Comparison with simulations suggests the strong effects of finite ionic size and electrostatic interactions. We also uncover correlated ionic structures under extreme confinement, with the channel widths approaching the ionic diameter (∼1 nm). Our work reveals the roles of ionic size, valency, and confinement in determining the structures of liquid-solid interfaces and opens up new opportunities to study such systems at the single-ion level.

Breakdown of electroneutrality in nanopores

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. We show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

Novel ionic separation mechanisms in electrically driven membrane processes

Electromembrane processes including electrodialysis (ED) and related processes are usually limited by diffusion transport of ions from a bulk solution to ion exchange membranes. The diffusion limited current (DLC) occurs when the concentration at membrane surfaces vanishes and approaches zero. Increasing the applied potential difference above this point has no substantial effect on ion transport and causes operational problems such as low current efficiency, high energy consumption, and mineral scaling. However, it is evident from numerous studies that operating at overlimiting current (OLC) is possible and allows one to enhance the mass transfer of an electromembrane process. While OLC is sometimes possible by electrochemical means, such as water splitting or current induced membrane discharge, it has been found that exotic ion transport mechanisms, such as ion concentration polarization in micro/nanofluidic system, deionization shock waves, and ionic bridges, can provide novel electrokinetic means of achieving OLC. In this paper, these novel ionic separation mechanisms and their role in enhanced current transfer are reviewed in the context of emerging electromembrane processes, such as shock ED and electrodeionization (EDI).

Interfacial Layering in the Electric Double Layer of Ionic Liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.

Selective adsorption of organic anions in a flow cell with asymmetric redox active electrodes

Electrochemically mediated adsorption is an emerging technology that utilizes redox active (or Faradaic) materials and has exhibited high salt adsorption capacity and superb ion selectivity. Here, we use a redox polymer polyvinylferrocene (PVFc) as the anode and a conducting polymer polypyrrole doped with a large anionic surfactant (pPy-DBS) as the cathode for selective electrochemical removal of inorganic and organic components. We fabricated a flow system with alternating adsorption/desorption steps incorporating an electrosorption cell and inline probes (ultraviolet-visible spectroscopy, conductivity and pH sensors) to demonstrate on-the-fly quantification of the ion adsorption performance. The flow system provides a more realistic evaluation of dynamic selectivity for the active materials during cyclic operation than that based on a single equilibrium adsorption step in batch. Our results show a three-fold (cycle) selectivity toward the removal of benzoate, as a representative organic anion, against a 50-fold abundance of perchlorate supporting anion, indicating that electrochemically mediated adsorption is a promising technology for waste water remediation applications.

Heat of nervous conduction: A thermodynamic framework

Early recordings of nervous conduction revealed a notable thermal signature associated with the electrical signal. The observed production and subsequent absorption of heat arise from physicochemical processes that occur at the cell membrane level during the conduction of the action potential. In particular, the reversible release of electrostatic energy stored as a difference of potential across the cell membrane appears as a simple yet consistent explanation for the heat production, as proposed in the "Condenser Theory." However, the Condenser Theory has not been analyzed beyond the analogy between the cell membrane and a parallel-plate capacitor, i.e., a condenser, and cannot account for the magnitude of the heat signature. In this work, we use a detailed electrostatic model of the cell membrane to revisit the Condenser Theory. We derive expressions for free energy and entropy changes associated with the depolarization of the membrane by the action potential, which give a direct measure of the heat produced and absorbed by neurons. We show how the density of surface charges on both sides of the membrane impacts the energy changes. Finally, considering a typical action potential, we show that if the membrane holds a bias of surface charges, such that the internal side of the membrane is 0.05Cm^{-2} more negative than the external side, the size of the heat predicted by the model reaches the range of experimental values. Based on our study, we identify the release of electrostatic energy by the membrane as the primary mechanism of heat production and absorption by neurons during nervous conduction.

Lithium-Battery Anode Gains Additional Functionality for Neuromorphic Computing through Metal-Insulator Phase Separation

Specialized hardware for neural networks requires materials with tunable symmetry, retention, and speed at low power consumption. The study proposes lithium titanates, originally developed as Li-ion battery anode materials, as promising candidates for memristive-based neuromorphic computing hardware. By using ex- and in operando spectroscopy to monitor the lithium filling and emptying of structural positions during electrochemical measurements, the study also investigates the controlled formation of a metallic phase (Li₇ Ti₅ O₁₂ ) percolating through an insulating medium (Li₄ Ti₅ O₁₂ ) with no volume changes under voltage bias, thereby controlling the spatially averaged conductivity of the film device. A theoretical model to explain the observed hysteretic switching behavior based on electrochemical nonequilibrium thermodynamics is presented, in which the metal-insulator transition results from electrically driven phase separation of Li₄ Ti₅ O₁₂ and Li₇ Ti₅ O₁₂ . Ability of highly lithiated phase of Li₇ Ti₅ O₁₂ for Deep Neural Network applications is reported, given the large retentions and symmetry, and opportunity for the low lithiated phase of Li₄ Ti₅ O₁₂ toward Spiking Neural Network applications, due to the shorter retention and large resistance changes. The findings pave the way for lithium oxides to enable thin-film memristive devices with adjustable symmetry and retention.