arXiv subjects

Martin Z. Bazant

Publications and source records attributed to Martin Z. Bazant.

At least 109 records · Page 6Linked to original sources

arXiv2017

Intercalation kinetics in multiphase layered materials

Many intercalation compounds possess layered structures or inter-penetrating lattices that enable phase separation into three or more stable phases, or "stages," driven by competing intra-layer and inter-layer forces. While these structures are often well characterized in equilibrium, their effects on intercalation kinetics and transport far from equilibrium are typically neglected or approximated by empirical solid solution models. Here, we formulate a general phase-field model with thermodynamically consistent reaction kinetics and cooperative transport to capture the dynamics of intercalation in layered materials. As an important case for Li-ion batteries, we model single particles of lithium intercalated graphite as having a periodic two-layer structure with three stable phases, corresponding to zero, one, or two layers full of lithium. The electrochemical intercalation reaction is described by a generalized Butler-Volmer equation with thermodynamic factors to account for the flexible structure of the graphene planes. The model naturally captures the "voltage staircase" discharge curves as a result of staging dynamics with internal "checkerboard" domains, which cannot be described by solid-solution models based on Fickian diffusion. On the other hand, the two-layer model is computationally expensive and excludes low-density stable phases with longer-range periodicity, so we also present a reduced model for graphite, which captures the high-density stages while fitting the low-density voltage profile as an effective solid solution. The two models illustrate the general tradeoff between the explicit modeling of periodic layers or lattices and the needs for computational efficiency and accurate fitting of experimental data.

physics.chem-ph↗

arXiv2017

Theory of linear sweep voltammetry with diffuse charge: unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck (PNP) equations with generalized Frumkin-Butler-Volmer (FBV) boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated currentvoltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times) and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers (EDL) is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

physics.chem-ph↗

arXiv2016

Membraneless flow battery leveraging flow-through heterogeneous porous media for improved power density and reduced crossover

A key factor preventing the market penetration of renewable, intermittent energy sources, such as solar, wind and wave, is the lack of cost-effective energy storage options to counteract intermittency. Here, we propose and demonstrate a novel flow battery architecture that replaces traditional ion-exchange membranes with less expensive heterogeneous flow-through porous media. We present an experimentally-validated model which demonstrates that our architecture promises reduced crossover of reactive species compared to typical membraneless systems employing co-laminar flows in open channels. In addition, our prototype battery exhibits significantly improved power density (0.925 W/cm2) and maximum current density (3 A/cm2) compared to previous membraneless systems.

physics.chem-ph↗

arXiv2016

Resistive Switching in Aqueous Nanopores by Shock Electrodeposition

Solid-state programmable metallization cells have attracted considerable attention as memristive elements for Redox-based Resistive Random Access Memory (ReRAM) for low-power and low-voltage applications. In principle, liquid-state metallization cells could offer the same advantages for aqueous systems, such as biomedical lab-on-a-chip devices, but robust resistive switching has not yet been achieved in liquid electrolytes, where electrodeposition is notoriously unstable to the formation of fractal dendrites. Here, the recently discovered physics of shock electrodeposition are harnessed to stabilize aqueous copper growth in polycarbonate nanopores, whose surfaces are modified with charged polymers. Stable bipolar resistive switching is demonstrated for 500 cycles with <10s retention times, prior to any optimization of the geometry or materials.

physics.chem-ph↗

arXiv2016

Exact solutions and physical analogies for unidirectional flows

Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here, the literature is unified and extended by identifying seventeen physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with non-constant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.

physics.flu-dyn↗

arXiv2016

Dendrite Suppression by Shock Electrodeposition in Charged Porous Media

It is shown that surface conduction can stabilize electrodeposition in random, charged porous media at high rates, above the diffusion-limited current. After linear sweep voltammetry and impedance spectroscopy, copper electrodeposits are visualized by scanning electron microscopy and energy dispersive spectroscopy in two different porous separators (cellulose nitrate, polyethylene), whose surfaces are modified by layer-by-layer deposition of positive or negative charged polyelectrolytes. Above the limiting current, surface conduction inhibits growth in the positive separators and produces irregular dendrites, while it enhances growth and suppresses dendrites behind a deionization shock in the negative separators, also leading to improved cycle life. The discovery of stable uniform growth in the random media differs from the non-uniform growth observed in parallel nanopores and cannot be explained by classical quasi-steady leaky membrane models, which always predict instability and dendritic growth. Instead, the experimental results suggest that transient electro-diffusion in random porous media imparts the stability of a deionization shock to the growing metal interface behind it. Shock electrodeposition could be exploited to enhance the cycle life and recharging rate of metal batteries or to accelerate the fabrication of metal matrix composite coatings.

physics.chem-ph↗

arXiv2016

Performance and Degradation of A Lithium-Bromine Rechargeable Fuel Cell Using Highly Concentrated Catholytes

Lithium-air batteries have been considered as ultimate solutions for the power source of long-range electrified transportation, but state-of-the-art prototypes still suffer from short cycle life, low efficiency and poor power output. Here, a lithium-bromine rechargeable fuel cell using highly concentrated bromine catholytes is demonstrated with comparable specific energy, improved power density, and higher efficiency. The cell is similar in structure to a hybrid-electrolyte Li-air battery, where a lithium metal anode in nonaqueous electrolyte is separated from aqueous bromine catholytes by a lithium-ion conducting ceramic plate. The cell with a flat graphite electrode can discharge at a peak power density around 9mW cm-2 and in principle could provide a specific energy of 791.8 Wh kg-1, superior to most existing cathode materials and catholytes. It can also run in regenerative mode to recover the lithium metal anode and free bromine with 80-90% voltage efficiency, without any catalysts. Degradation of the solid electrolyte and the evaporation of bromine during deep charging are challenges that should be addressed in improved designs to fully exploit the high specific energy of liquid bromine. The proposed system offers a potential power source for long-range electric vehicles, beyond current Li-ion batteries yet close to envisioned Li-air batteries.

physics.chem-ph↗

arXiv2015

Asymmetric collapse by dissolution or melting in a uniform flow

An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and then collapse to a single point in finite time. The simulations reveal a surprising exact relationship whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton--Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In summary, the model raises fundamental mathematical questions about broken symmetries in finite-time singularities of both continuous and stochastic dynamical systems.

physics.flu-dyn↗

arXiv2014

Multicomponent Gas Diffusion in Porous Electrodes

Multicomponent gas transport is investigated with unprecedented precision by AC impedance analysis of porous YSZ anode-supported solid oxide fuel cells. A fuel gas mixture of H2-H2O-N2 is fed to the anode, and impedance data are measured across the range of hydrogen partial pressure (10-100%) for open circuit conditions at three temperatures (800C, 850C and 900C) and for 300mA applied current at 800C. For the first time, analytical formulae for the diffusion resistance (Rb) of three standard models of multicomponent gas transport (Fick, Stefan-Maxwell, and Dusty Gas) are derived and tested against the impedance data. The tortuosity is the only fitting parameter since all the diffusion coefficients are known. Only the Dusty Gas model leads to a remarkable data collapse for over twenty experimental conditions, using a constant tortuosity consistent with permeability measurements and the Bruggeman relation. These results establish the accuracy of the Dusty Gas model for multicomponent gas diffusion in porous media and confirm the efficacy of electrochemical impedance analysis to precisely determine transport mechanisms.

physics.chem-ph↗

arXiv2014

Experimental Verification of Overlimiting Current by Surface Conduction and Electro-osmotic Flow in Microchannels

Possible mechanisms of overlimiting current in unsupported electrolytes, exceeding diffusion limitation, have been intensely studied for their fundamental significance and applications to desalination, separations, sensing, and energy storage. In bulk membrane systems, the primary physical mechanism is electro-convection, driven by electro-osmotic instability on the membrane surface. It has recently been predicted that confinement by charged surfaces in microchannels or porous media favors two new mechanisms, electro-osmotic flow (EOF) and surface conduction (SC), driven by large electric fields in the depleted region acting on the electric double layers on the sidewalls. Here, we provide the first direct evidence for the transition from SC to EOF above a critical channel height, using in situ particle tracking and current-voltage measurements in a micro/nanofluidic device. The dependence of the over-limiting conductance on channel depth (d) is consistent with theoretical predictions, scaling as d^-1 for SC and d^4/5 for EOF with a transition around d=8um. This complete picture of surface-driven over-limiting current can guide engineering applications of ion concentration polarization phenomena in microfluidics and porous media.

physics.flu-dyn↗

arXiv2014

Over-limiting Current and Control of Dendritic Growth by Surface Conduction in Nanopores

Understanding over-limiting current (faster than diffusion) is a long-standing challenge in electrochemistry with applications in desalination and energy storage. Known mechanisms involve either chemical or hydrodynamic instabilities in unconfined electrolytes. Here, it is shown that over-limiting current can be sustained by surface conduction in nano pores, without any such instabilities, and used to control dendritic growth during electrodeposition. Copper electrode posits are grown in anodized aluminum oxide membranes with polyelectrolyte coatings to modify the surface charge. At low currents, uniform electroplating occurs, unaffected by surface modification due to thin electric double layers, but the morphology changes dramatically above the limiting current. With negative surface charge, growth is enhanced along the nanopore surfaces, forming surface dendrites and nanotubes behind a deionization shock. With positive surface charge, dendrites avoid the surfaces and are either guided along the nanopore centers or blocked from penetrating the membrane.

physics.chem-ph↗

arXiv2014

Simple Formula for Marcus-Hush-Chidsey Kinetics

The Marcus-Hush-Chidsey (MHC) model is well known in electro-analytical chemistry as a successful microscopic theory of outer-sphere electron transfer at metal electrodes, but it is unfamiliar and rarely used in electrochemical engineering. One reason may be the difficulty of evaluating the MHC reaction rate, which is defined as an improper integral of the Marcus rate over the Fermi distribution of electron energies. Here, we report a simple analytical approximation of the MHC integral that interpolates between exact asymptotic limits for large overpotentials, as well as for large or small reorganization energies, and exhibits less than 5\% relative error for all reasonable parameter values. This result enables the MHC model to be considered as a practical alternative to the ubiquitous Butler-Volmer equation for improved understanding and engineering of electrochemical systems.

physics.chem-ph↗

arXiv2014

Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Four new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to the macroscopic length of the porous medium; (iii) the microscopic fluidic convection is replaced by a diffusion-dispersion correction in the effective diffusion tensor; and (iv) the surface charge per volume appears as a continuous "background charge density", as in classical membrane models. The coefficient tensors in the upscaled PNP equations can be calculated from periodic reference cell problems. For an insulating solid matrix, all gradients are corrected by the same tensor, and the Einstein relation holds at the macroscopic scale, which is not generally the case for a polarizable matrix, unless the permittivity and electric field are suitably defined. In the limit of thin double layers, Poisson's equation is replaced by macroscopic electroneutrality (balancing ionic and surface charges). The general form of the macroscopic PNP equations may also hold for concentrated solution theories, based on the local-density and mean-field approximations. These results have broad applicability to ion transport in porous electrodes, separators, membranes, ion-exchange resins, soils, porous rocks, and biological tissues.

math-ph↗

arXiv2014

Charge Transfer Kinetics at the Solid-Solid Interface in Porous Electrodes

Interfacial charge transfer is widely assumed to obey Butler-Volmer kinetics. For certain liquid-solid interfaces, Marcus-Hush-Chidsey theory is more accurate and predictive, but it has not been applied to porous electrodes. Here we report a simple method to extract the charge transfer rates in carbon-coated LiFePO4 porous electrodes from chronoamperometry experiments, obtaining curved Tafel plots that contradict the Butler-Volmer equation but fit the Marcus-Hush-Chidsey prediction over a range of temperatures. The fitted reorganization energy matches the Born solvation energy for electron transfer from carbon to the iron redox site. The kinetics are thus limited by electron transfer at the solid-solid (carbon-LixFePO4) interface, rather than by ion transfer at the liquid-solid interface, as previously assumed. The proposed experimental method generalizes Chidsey's method for phase-transforming particles and porous electrodes, and the results show the need to incorporate Marcus kinetics in modeling batteries and other electrochemical systems.

cond-mat.mtrl-sci↗

arXiv2014

Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of diffusional chemical potentials, and the model consistently links the evolving concentration profile to the battery voltage. We examine sources of charge/discharge asymmetry, such as asymmetric charge transfer and surface "wetting" by ions within the solid, which can lead to three distinct phase regions. In order to solve the fourth-order nonlinear CHR initial-boundary-value problem, a control-volume discretization is developed in spherical coordinates. The basic physics are illustrated by simulating many representative cases, including a simple model of the popular cathode material, lithium iron phosphate (neglecting crystal anisotropy and coherency strain). Analytical approximations are also derived for the voltage plateau as a function of the applied current.

physics.chem-ph↗

arXiv2014

Phase Transformation Dynamics in Porous Battery Electrodes

Porous electrodes composed of multiphase active materials are widely used in Li-ion batteries, but their dynamics are poorly understood. Two-phase models are largely empirical, and no models exist for three or more phases. Using a modified porous electrode theory based on non-equilibrium thermodynamics, we show that experimental phase behavior can be accurately predicted from free energy models, without artificially placing phase boundaries or fitting the open circuit voltage. First, we simulate lithium intercalation in porous iron phosphate, a popular two-phase cathode, and show that the zero-current voltage gap, sloping voltage plateau and under-estimated exchange currents all result from size-dependent nucleation and mosaic instability. Next, we simulate porous graphite, the standard anode with three stable phases, and reproduce experimentally observed fronts of color-changing phase transformations. These results provide a framework for physics-based design and control for electrochemical systems with complex thermodynamics.

physics.chem-ph↗

arXiv2014

Water Purification by Shock Electrodialysis: Deionization, Filtration, Separation, and Disinfection

The development of energy and infrastructure efficient water purification systems are among the most critical engineering challenges facing our society. Water purification is often a multi-step process involving filtration, desalination, and disinfection of a feedstream. Shock electrodialysis (shock ED) is a newly developed technique for water desalination, leveraging the formation of ion concentration polarization (ICP) zones and deionization shock waves in microscale pores near to an ion selective element. While shock ED has been demonstrated as an effective water desalination tool, we here present evidence of other simultaneous functionalities. We show that, unlike electrodialysis, shock ED can thoroughly filter micron-scale particles and aggregates of nanoparticles present in the feedwater. We also demonstrate that shock ED can enable disinfection of feedwaters, as approximately $99\%$ of viable bacteria (here \textit{E. coli}) in the inflow were killed or removed by our prototype. Shock ED also separates positive from negative particles, contrary to claims that ICP acts as a virtual barrier for all charged particles. By combining these functionalities (filtration, separation and disinfection) with deionization, shock ED has the potential to enable more compact and efficient water purification systems.

physics.chem-ph↗

arXiv2013

Overlimiting Current and Shock Electrodialysis in Porous Media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electro-osmotic flow also contribute to ionic fluxes. In this paper, we report experimental evidence for surface-driven over-limiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with 500 nm mean pore size) in an aqueous electrolyte (CuSO$_4$ or AgNO$_3$) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electro-osmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM - 1.0 M), after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water ($\approx 10 μ$ $M$) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5mm across the outlet. The results suggest the feasibility of "shock electrodialysis" as a new approach to water desalination and other electrochemical separations.

physics.chem-ph↗