Transient finite element analysis of electric double layer using Nernst–Planck–Poisson equations with a modified Stern layer

Lim, Jongil; Whitcomb, John D.; Boyd, James G.; Varghese, Julian

doi:10.1016/j.jcis.2006.08.049

Cited by 49 publications

(47 citation statements)

References 28 publications

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“…1,4 It includes the correction of the potential at the closest approach of the redox species, which may be varied with the concentration of the supporting electrolyte; well-known examples are cadmium ions, 5 zinc ions, 6 and some aromatic compounds. 7 However, there are some ambiguities in the participation of the specically adsorbed species, [8][9][10][11][12] in charge interactions, 13,14 in modication by nite ionic size, [15][16][17][18] in the geometrical effects [19][20][21][22][23] of the Poisson-Nernst-Planck equation, in simplication of the plane of the closest approach, 24 in complications by ions [25][26][27][28] and by the orientation of the solvent molecules, 29 in charge distribution within a redox species, 30 and in coupling of the charged redox species and supporting electrolyte. 31,32 The Frumkin's correction has recently been reviewed from a theoretical point of view.…”

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confidence: 99%

Decrease in the double layer capacitance by faradaic current

Aoki¹,

Chen

Zeng

et al. 2017

RSC Adv.

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This study describes the reverse of the well-known double layer effects on charge transfer kinetics in the relationship between a cause and an effect. The reversible redox reaction of a ferrocenyl derivative decreased the capacitive values of the double layer impedance up to negative values, corresponding to an inductive component. This observation was disclosed by the subtraction of the real admittance from the imaginary admittance, which can extract the net double layer capacitance from the Warburg impedance. The inductance-like behavior is caused due to two reasons: (i) the double layer capacitance in the polarized potential domain is determined by the low concentrations of the fieldoriented solvent dipoles that are considered as the conventionally employed redox concentrations and (ii) the double layer capacitance is caused by the orientation of the dipoles in the same direction as that of the electric field, whereas the redox reaction generates charge in the direction opposite to the field. The faradaic effect was demonstrated via the ac-impedance data obtained for the ferrocenyl compound in a KCl solution in the unpolarized potential domain between 1 Hz and 3 kHz frequency. The negative admittance was proportional to the frequency. The theory of negative capacitance was presented by combining the mirror-image surface charge with the Nernst equation.

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mentioning

confidence: 99%

Decrease in the double layer capacitance by faradaic current

Aoki¹,

Chen

Zeng

et al. 2017

RSC Adv.

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“…For example, the model predicts large changes in the gradients of the dependent variables in the EDL, which is a source of numerical error in the solution. 34 Because the surface flux boundary conditions are intimately linked to the solution at the surface, this error interacts with the boundary conditions contributing to instability in the model. However, these numerical difficulties can be managed through suitable choice of the mesh and solver, as opposed to requiring a brute force approach to determine a suitable initial state.…”

Section: Resultsmentioning

confidence: 99%

A Non-Electroneutral Model for Complex Reaction-Diffusion Systems Incorporating Species Interactions

Minton

Purkayastha

Lue³

2017

J. Electrochem. Soc.

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In this study we develop a general framework for describing reaction-diffusion processes in a multi-component electrolyte in which multiple reactions of different types may occur. Our motivation for this is the need to understand how the interactions between species and processes occurring in a complex electrochemical system. We use the framework to develop a modified Poisson-Nernst-Planck model which accounts for the excluded volume interaction (EVI) and incorporates both electrochemical and chemical reactions. Using this model, we investigate how the EVI influences the reactions and how the reactions influence each other in the contexts of the equilibrium state of a system and of a simple electrochemical device under load. Complex behavior quickly emerges even in relatively simple systems, and deviations from the predictions of ideal solution theory, together with how they may influence the behavior of more complex system, are discussed. Electrochemical energy storage devices play a crucial role in the modern world, having enabled the development of a wide range of portable and mobile devices in a vast range of applications. They also have significant future potential in facilitating a shift away from environmentally damaging fossil fuels as our primary source of energy, through the electrification of transport and as load balancing for the variability suffered by most forms of renewable energy. However, modeling these systems can be challenging because the overall behavior is typically the emergent result of a large number of processes and interactions at the microscopic scale, making linking the microscopic behavior to the macroscopic performance complicated. Furthermore, individual processes may themselves be complex, so simplifications have to be made if we wish to understand the device behavior at macroscopic length and time-scales.By way of example, the particular system in which we are interested is that of a lithium-sulfur (LiS) cell, a promising post-lithium-ion technology with both an expected practical energy density of 500-600 Wh kg −1 and a lower raw materials cost. 1,2 The overall discharge process of a LiS cell involves the reduction of solid phase S 8 to solid phase Li 2 S, according to the reactionWhile the overall process is bound by the dissolution of S 8 and the precipitation of Li 2 S, the intermediate steps occur between species in the solvent/electrolyte phase, involving the electrodissolution of lithium from the anode and a range of electrochemical and chemical reactions involving a number of ionic sulfur species at the cathode. While these types of process are not uncommon in traditional (i.e. non-intercalation) battery chemistries, the sheer number of species and intermediate elementary reaction steps involved, together with the integral role played by chemical reaction processes, make understanding the LiS mechanism complex. 3The common approach to modeling LiS cells is similar to that taken for many electrochemical devices, with the reduction of the cell structure to a one-dimension...

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“…Bieniasz [18] extended his numerical technique based on the finite-difference patch-adaptive strategy to time-dependent models involving electrodiffusion transport described by NPP equation systems in one-dimensional space geometry. Lim et al [19] presented a finite element implementation of the NPP and modified NPP models for a transient analysis of electric double layer. Examples of recent applications of the 67 NPP theory to time-dependent problems concern translocation of DNA through nanopores and nanochannels [20], or electrochemical methods like cyclic voltammetry [21] and electrochemical impedance spectroscopy [22].…”

Section: Numerical Solutions Of the Full Set Of The Time-dependent Nementioning

confidence: 99%

“…The second group is represented by techniques based on the finite element method. Although implementations of this method for time-dependent electrodiffusion problems were rare a decade ago [23], recent work [19,24,25,21] indicates advancements. A special class among the numerical methods used to solve the NPP equations in space and time represents the "network thermodynamic method" introduced by Horno et al [26].…”

Section: Numerical Solutions Of the Full Set Of The Time-dependent Nementioning

confidence: 99%

Numerical simulations of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion on a simple ion channel.

Valent¹

2012

JCIS

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The concept of electrodiffusion based on the Nernst-Planck equations for ionic fluxes coupled with the Poisson equation expressing relation between gradient of the electric field and the charge density is widely used in many areas of natural sciences and engineering. In contrast to the steady-state solutions of the Nernst-Planck-Poisson (abbreviated as NPP or PNP) equations, little is known about the time-dependent behavior of electrodiffusion systems. We present numerical solutions of an NPP system modeling dynamics in the interior of a membrane channel containing an electrolyte after a potential jump at one side of the membrane (voltage-clamp). The NPP equations were solved using the VLUGR2 solver based on an adaptive-grid finite-difference method with an implicit timestepping. The used approach allows for solving the full set of the NPP equations without approximations such as the electroneutrality or constant-field assumptions. Calculations reveal interesting nonlinear time evolution of the ionic concentrations and potential.

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Transient finite element analysis of electric double layer using Nernst–Planck–Poisson equations with a modified Stern layer

Cited by 49 publications

References 28 publications

Decrease in the double layer capacitance by faradaic current

Decrease in the double layer capacitance by faradaic current

A Non-Electroneutral Model for Complex Reaction-Diffusion Systems Incorporating Species Interactions

Numerical simulations of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion on a simple ion channel.

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