Advances in the fields of catalysis and electrochemical energy conversion often involve nanoparticles, which can have kinetics surprisingly different from the bulk material. Classical theories of ...chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create variations that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend not only on the order parameter but also on its gradients at phase boundaries. Reaction-driven phase transformations are common in electrochemistry, when charge transfer is accompanied by ion intercalation or deposition in a solid phase. Examples abound in Li-ion, metal–air, and lead–acid batteries, as well as metal electrodeposition–dissolution. Despite complex thermodynamics, however, the standard kinetic model is the Butler–Volmer equation, based on a dilute solution approximation. The Marcus theory of charge transfer likewise considers isolated reactants and neglects elastic stress, configurational entropy, and other nonidealities in condensed phases. The limitations of existing theories recently became apparent for the Li-ion battery material Li x FePO4 (LFP). It has a strong tendency to separate into Li-rich and Li-poor solid phases, which scientists believe limits its performance. Chemists first modeled phase separation in LFP as an isotropic “shrinking core” within each particle, but experiments later revealed striped phase boundaries on the active crystal facet. This raised the question: What is the reaction rate at a surface undergoing a phase transformation? Meanwhile, dramatic rate enhancement was attained with LFP nanoparticles, and classical battery models could not predict the roles of phase separation and surface modification. In this Account, I present a general theory of chemical kinetics, developed over the past 7 years, which is capable of answering these questions. The reaction rate is a nonlinear function of the thermodynamic driving force, the free energy of reaction, expressed in terms of variational chemical potentials. The theory unifies and extends the Cahn–Hilliard and Allen–Cahn equations through a master equation for nonequilibrium chemical thermodynamics. For electrochemistry, I have also generalized both Marcus and Butler–Volmer kinetics for concentrated solutions and ionic solids. This new theory provides a quantitative description of LFP phase behavior. Concentration gradients and elastic coherency strain enhance the intercalation rate. At low currents, the charge-transfer rate is focused on exposed phase boundaries, which propagate as “intercalation waves”, nucleated by surface wetting. Unexpectedly, homogeneous reactions are favored above a critical current and below a critical size, which helps to explain the rate capability of LFP nanoparticles. Contrary to other mechanisms, elevated temperatures and currents may enhance battery performance and lifetime by suppressing phase separation. The theory has also been extended to porous electrodes and could be used for battery engineering with multiphase active materials. More broadly, the theory describes nonequilibrium chemical systems at mesoscopic length and time scales, beyond the reach of molecular simulations and bulk continuum models. The reaction rate is consistently defined for inhomogeneous, nonequilibrium states, for example, with phase separation, large electric fields, or mechanical stresses. This research is also potentially applicable to fluid extraction from nanoporous solids, pattern formation in electrophoretic deposition, and electrochemical dynamics in biological cells.
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.
One of the obstacles hindering the scaling-up of the initial successes of machine learning in practical engineering applications is the dependence of the accuracy on the size and quality of the ...database that “drives” the algorithms. Incorporating the already-known physical laws into the training process can significantly reduce the request for data. In this study, we establish a neural network-based computational framework to characterize the finite deformation of elastic plates, which in classic theories is described by the Föppl–von Kármán (FvK) equations with a set of boundary conditions (BCs). A neural network is constructed by taking the spatial coordinates as the input and the displacement field as the output to approximate the exact solution of the FvK equations. The physical information (PDEs, BCs, and potential energy) is then incorporated into the loss function, and a pseudo dataset is sampled without knowing the exact solution to finally train the neural network. The accuracy of the modeling framework is carefully examined by applying it to four different loading cases: in-plane tension with non-uniformly distributed stretching forces, in-plane central-hole tension, out-of-plane deflection, and buckling under compression. Three ways of formulating the loss function are compared: (1) purely data-driven, (2) PDE-based, and (3) energy-based. Through the comparison with the finite element simulations, it is found that all the three approaches can characterize the elastic deformation of plates with a satisfactory accuracy if trained with a proper strategy in terms of sampling size and resolution. Compared with incorporating the PDEs and BCs in the loss, using the total potential energy shows certain advantage in terms of the simplicity of hyperparameter tuning and the computational efficiency.
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•A neural network framework with options of purely data-driven, PDE-based, and energy-based loss functions is developed for elastic plates.•All the three options could achieve a sufficiently high accuracy if trained properly.•The energy-based approach has an advantage since it has less hyperparameters and a higher efficiency.•The advantage of the PDE-based is that it is less dependent on sampling size and resolution.•The purely data-driven approach should be trained with data in both displacement and force fields.
Interfacial charge transfer is widely assumed to obey the Butler-Volmer kinetics. For certain liquid-solid interfaces, the 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-Li(x)FePO4) 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 modelling batteries and other electrochemical systems.
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 CO
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.
The standard model for diffuse charge phenomena in colloid science, electrokinetics, and biology is the Poisson–Boltzmann mean-field theory, which breaks down for multivalent ions and large surface ...charge densities because of electrostatic correlations. In this paper, we formulate a predictive continuum theory of correlated electrolytes based on two extensions of the Bazant–Storey–Kornyshev (BSK) framework: (i) a physical boundary condition enforcing continuity of the Maxwell stress at a charged interface, which upholds the contact theorem for dilute primitive-model electrolytes, and (ii) scaling relationships for the correlation length, for a one-component plasma at a charged plane and around a cylinder, as well as a dilute z:1 electrolyte screening a planar surface. In these cases, the theory accurately reproduces Monte Carlo simulation results from weak to strong coupling, and extensions are possible for more complex models of electrolytes and ionic liquids.
A theoretical investigation of the effects of elastic coherency strain on the thermodynamics, kinetics, and morphology of intercalation in single LiFePO4 nanoparticles yields new insights into this ...important battery material. Anisotropic elastic stiffness and misfit strains lead to the unexpected prediction that low-energy phase boundaries occur along {101} planes, while conflicting reports of phase boundary orientations are resolved by a partial loss of coherency in the 001 direction. Elastic relaxation near surfaces leads to the formation of a striped morphology with a characteristic length scale predicted by the model, yielding an estimate of the interfacial energy. The effects of coherency strain on solubility and galvanostatic discharge are studied with a reaction-limited phase-field model that quantitatively captures the influence of misfit strain, particle size, and temperature on solubility seen in experiments. Coherency strain strongly suppresses phase separation during discharge, which enhances rate capability and extends cycle life. The effects of elevated temperature and the feasibility of nucleation are considered in the context of multiparticle cathodes.
We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) ...or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.
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