Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors

Supercapacitors are promising electrochemical energy storage devices due to their prominent performance in rapid charging/discharging rates, long cycle life, stability, etc. Experimental measurement and theoretical prediction on charging timescale for supercapacitors often have large difference. This work develops a matched asymptotic expansion method to derive the charging dynamics of supercapacitors with porous electrodes, in which the supercapacitors are described by the stack-electrode model. Coupling leading-order solutions between every two stacks by continuity of ionic concentration and fluxes leads to an ODE system, which is a generalized equivalent circuit model for zeta potentials, with the potential-dependent nonlinear capacitance and resistance determined by physical parameters of electrolytes, e.g., specific counterion valences for asymmetric electrolytes. Linearized stability analysis on the ODE system after projection is developed to theoretically characterize the charging timescale. The derived asymptotic solutions are numerically verified. Further numerical investigations on the biexponential charging timescales demonstrate that the proposed generalized equivalent circuit model, as well as companion linearized stability analysis, can faithfully capture the charging dynamics of symmetric/asymmetric electrolytes in supercapacitors with porous electrodes.Comment: 26 pages, 6 figure

How Thermal Effect Regulates Cyclic Voltammetry of Supercapacitors

Cyclic voltammetry (CV) is a powerful technique for characterizing electrochemical properties of electrochemical devices. During charging-discharging cycles, thermal effect has profound impact on its performance, but existing theoretical models cannot clarify such intrinsic mechanism and often give poor prediction. Herein, we propose an interfacial model for the electro-thermal coupling, based on fundamentals in non-equilibrium statistical mechanics. By incorporating molecular interactions, our model shows a quantitative agreement with experimental measurements. The integral capacitance shows a first enhanced then decayed trend against the applied heat bath temperature. Such a relation is attributed to the competition between electrical attraction and Born repulsion via dielectric inhomogeneity, which is rarely understood in previous models. In addition, as evidenced in recent experimental CV tests, our model predicts the non-monotonic dependence of the capacitance on the bulk electrolyte density, further demonstrating its high accuracy. This work demonstrates a potential pathway towards next-generation thermal regulation of electrochemical devices

A Maxwell-Amp\`{e}re Nernst-Planck Framework for Modeling Charge Dynamics

Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. This work proposes a Maxwell-Amp\`{e}re Nernst-Planck (MANP) framework for the description of charge dynamics. The MANP model is shown to be a gradient flow of a convex free-energy functional, and demonstrated to be equivalent to the Poisson-Nernst-Planck model. By the energy dissipation law, the steady state of the MANP model reproduces the charge conserving Poisson-Boltzmann (PB) theory, providing an alternative energy stable approach to study the PB theory from the perspective of a gradient flow. In order to achieve the curl-free condition, the MANP model is equipped with a local curl-free relaxation algorithm, which is shown to naturally preserve the Gauss's law and have robust convergence and linear computational complexity. One of the main advantages of our work is that the model can efficiently deal with space-dependent permittivity instead of solving the variable-coefficient Poisson's equation. Many-body effects such as ionic steric effects and Coulomb correlations can be incorporated within the MANP framework to derive modified MANP models for problems in which the mean-field approximation fails. Numerical results on the charge dynamics with such beyond mean-field effects in inhomogeneous dielectric environments are presented to demonstrate the performance of the MANP models in the description of charge dynamics, illustrating that the proposed MANP model provides a general framework for modeling charge dynamics

Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ('dry' and 'wet') hydration states. The resulting dry-wet transition rates are then used in a spatially-dependent multi-state continuous-time Markov chain Brownian dynamics simulations, and the related Fokker-Planck equation calculations, of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semi-quantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of non-equilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding versus unbinding. Our study thus provides a significant step forward towards efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.Comment: 6 pages, 5 figures, accepted for publication in Proc. Natl. Acad. Sci. (PNAS