Analytical solution to the Poisson–Nernst–Planck equations for the charging of a long electrolyte-filled slit pore

Molecular Understanding of Charging Dynamics in Supercapacitors with Porous Electrodes and Ionic Liquids

Porous electrodes and ionic liquids could significantly enhance the energy storage of supercapacitors. However, they may reduce the charging dynamics and power density due to the nanoconfinement of porous electrodes and the high viscosity of ionic liquids. A comprehensive understanding of the charging mechanism in porous supercapacitors with ionic liquids provides a crucial theoretical foundation for their design optimization. Here, we review the progress of molecular simulations of the charging dynamics in supercapacitors consisting of porous electrodes and ionic liquids. We highlight and delve into the breakthroughs in the ion transport and charging mechanism for electrodes with subnanometer pores and realistic porous structures. We also discuss future directions for the charging dynamics of supercapacitors.

Nonlinear dependence (on ionic strength, pH) of surface charge density and zeta potential in microchannel electrokinetic flow

In this work, a numerical method is proposed to predict the electrokinetic phenomena and combined with an experimental study of the surface charge density (ρ s ) and zeta potential (ζ ) behavior is investigated for borosilicate immersed in KCl and NaCl electrolytes, and for imogolite immersed in KCl, CaCl2, and MgCl2 electrolytes. Simulations and experiments of the electrokinetic flows with electrolyte solutions were performed to accurately determine the electric double layer (EDL), ζ , and ρ s at various electrolyte concentrations and pH. The zeta potential was experimentally determined and numerically predicted by solving the coupled governing equations of mass, species, momentum, and electrical field iteratively. Our numerical prediction shows that ζ for borosilicate develops strong nonlinear behavior with the ion concentration following a power-law. Likewise, the ρ s obeys a nonlinear behavior, decreasing as the concentration increases. Moreover, for imogolite, both ζ and the ρ s behave nonlinearly with the pH. The EDL for borosilicate and imogolite becomes thinner as the electrolyte concentration and pH increase; this behavior is caused by increased ρ s , resulting in the higher attraction of the free charges. The reported nonlinear behavior describes more accurately the interaction of the nanoparticle surface charge with the electrolytes and its effect on the electrolyte transport properties.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

Resonant Nanopumps: ac Gate Voltages in Conical Nanopores Induce Directed Electrolyte Flow

Inducing transport in electrolyte-filled nanopores with dc fields has led to influential applications ranging from nanosensors to DNA sequencing. Here we use the Poisson-Nernst-Planck and Navier-Stokes equations to show that unbiased ac fields can induce comparable directional flows in gated conical nanopores. This flow exclusively occurs at intermediate driving frequencies and hinges on the resonance of two competing timescales, representing space charge development at the ends and in the interior of the pore. We summarize the physics of resonant nanopumping in an analytical model that reproduces the results of numerical simulations. Our findings provide a generic route toward real-time controllable flow patterns, which might find applications in controlling the translocation of small molecules or nanocolloids.

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference $2\Phi$ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements.We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers.Next to the dimensionless applied potential $\Phi$, we consider the ratio $R/R_b$ of the pore's resistance $R$ to the bulk reservoir resistance $R_b$ and the ratio $r_{p}/\ld$ of the pore radius $r_p$ to the Debye length $\ld$.We compare our data to theoretical predictions by Aslyamov and Janssen ($\Phi$), Posey and Morozumi ($R/R_b$), and Henrique, Zuk, and Gupta ($r_{p}/\ld$).Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.