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

Single-Particle Imaging Reveals the Electrical Double-Layer Modulated Ion Dynamics at Crowded Interface

The dynamics of ion transport at the interface is the critical factor for determining the performance of an electrochemical energy storage device. While practical applications are realized in concentrated electrolytes and nanopores, there is a limited understanding of their ion dynamic features. Herein, we studied the interfacial ion dynamics in room-temperature ionic liquids by transient single-particle imaging with microsecond-scale resolution. We observed slowed-down dynamics at lower potential while acceleration was observed at higher potential. Combined with simulation, we found that the microstructure evolution of the electric double layer (EDL) results in potential-dependent kinetics. Then, we established a correspondence between the ion dynamics and interfacial ion composition. Besides, the ordered ion orientation within EDL is also an essential factor for accelerating interfacial ion transport. These results inspire us with a new possibility to optimize electrochemical energy storage through the good control of the rational design of the interfacial ion structures.

A meshless stochastic method for Poisson-Nernst-Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson-Nernst-Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift-diffusion process with time- and space-varying drift. We leverage Green's functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method's convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.

Tracking Ion Transport in Nanochannels via Transient Single-Particle Imaging

The transport behavior of ions in the nanopores has an important impact on the performance of the electrochemical devices. Although the classical Transmission-Line (TL) model has long been used to describe ion transport in pores, the boundary conditions for the applicability of the TL model remain controversial. Here, we investigated the transport kinetics of different ions, within nanochannels of different lengths, by using transient single-particle imaging with temporal resolution up to microseconds. We found that the ion transport kinetics within short nanochannels may deviate significantly from the TL model. The reason is that the ion transport under nanoconfinement is composed of multi basic stages, and the kinetics differ much under different stage domination. With the shortening of nanochannels, the electrical double layer (EDL) formation would become the "rate-determining step" and dominate the apparent ion kinetics. Our results imply that using the TL model directly and treating the in-pore mobility as an unchanged parameter to estimate the ion transport kinetics in short nanopores/nanochannels may lead to orders of magnitude bias. These findings may advance the understanding of the nanoconfined ion transport and promote the related applications.

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.

Iontronic microscopy of a tungsten microelectrode: "seeing" ionic currents under an optical microscope

Optical methods for monitoring electrochemical reactions at an interface are advantageous because of their table-top setup and ease of integration into reactors. Here we apply EDL-modulation microscopy to one of the main components of amperometric measurement devices: a microelectrode. We present experimental measurements of the EDL-modulation contrast from the tip of a tungsten microelectrode at various electrochemical potentials inside a ferrocene-dimethanol Fe(MeOH)2 solution. Using the combination of the dark-field scattering microscope and the lock-in detection technique, we measure the phase and amplitude of local ion-concentration oscillations in response to an AC potential as the electrode potential is scanned through the redox-activity window of the dissolved species. We present the amplitude and phase map of this response, as such this method can be used to study the spatial and temporal variations of the ion-flux due to an electrochemical reaction close to metallic and semiconducting objects of general geometry. We discuss the advantages and possible extensions of using this microscopy method for wide-field imaging of ionic currents.

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.

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.