Charging dynamics of the electric double layer in porous media

Sakaguchi, Hidetsugu; Baba, Ryuji

doi:10.1103/physreve.76.011501

Cited by 29 publications

(39 citation statements)

References 23 publications

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“…Still, comparing the fitted time constants τ 1 = 200 s and τ 2 = 9000 s to τ n = 2.9 × 10 2 s and τ ad = 4.8 × 10 2 s as stated in the main text, respectively, we see that our model predicts both timescales within approximately one order of magnitude. Even though we seem to predict τ 1 better than τ 2 , using a smaller diffusion constant D = 2 × 10 −10 m 2 s −1 , to account for slow diffusion in pores [31,39], leads to τ n = 2.3 × 10 3 s and τ ad = 3.6 × 10 3 s and predictions for τ 2 are better than for τ 1 .…”

Section: Appendix C: Comparison To Experimental Surface Charge Build Upcontrasting

confidence: 56%

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

et al. 2020

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The development of novel electrolytes and electrodes for supercapacitors is hindered by a gap of several orders of magnitude between experimentally measured and theoretically predicted charging time scales. Here, we propose an electrode model, containing many parallel stacked electrodes, that explains the slow charging dynamics of supercapacitors. At low applied potentials, the charging behavior of this model is described well by an equivalent circuit model. Conversely, at high potentials, charging dynamics slow down and evolve on two relaxation time scales: a generalized RC time and a diffusion time, which, interestingly, become similar for porous electrodes. The charging behavior of the stack-electrode model presented here helps to understand the charging dynamics of porous electrodes and agrees qualitatively with experimental time scales measured with porous electrodes.

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Section: Appendix C: Comparison To Experimental Surface Charge Build Upcontrasting

confidence: 56%

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

et al. 2020

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“…Direct tests of the TL and BB models require numerical solutions of the full PNP equations, which becomes challenging at high potentials due to the extremely sharp gradients within thin EDLs. The TL model has been validated with the linearized PNP equations for straight pores [20], whereas nonlinear PNP studies of charging kinetics [21] were limited to low electrode potentials.…”

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confidence: 99%

Enhanced Charging Kinetics of Porous Electrodes: Surface Conduction as a Short-Circuit Mechanism

2014

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We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the highresistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.

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“…The capacitance β is typically unity for gas transport in large pores, but it may take much larger values in nanopores to account for surface capacitance in electrochemical capacitors or surface adsorption and condensation in gas storage materials. In these applications, fluid or ion densities in molecular layers adjacent to pore walls may be several orders of magnitude greater than those in pore centers [24,25,30]. Transport coefficients are fairly well known for a number of important applications.…”

Section: Introductionmentioning

confidence: 98%

“…Here, the flux of ions results mainly from electromigration driven by gradients of the electric potential [10,30,35]. Thus, the ionic conductivity (1/ohm-cm) of the electrolyte is the operative diffusion coefficient, D. The surface charge density is proportional to the electric potential Cf /a, where C is the surface capacitance (F/cm 2 ) and f /a is the ratio of pore surface area to pore volume with f = 2 for planar and f = 4 for circular channels.…”

Section: Introductionmentioning

confidence: 99%

Optimization Algorithms for Hierarchical Problems with Application to Nanoporous Materials

Boggs¹,

Griffiths²,

Lewis³

et al. 2012

SIAM J. Optim.

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We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas storage and filtration, electrical energy storage in batteries and capacitors, and catalysis. The design of such materials involves modeling of the material over many length scales, leading to a hierarchy of mathematical models. Our algorithms are also hierarchical in structure with the goal of exploiting the model hierarchy to obtain solutions more rapidly. We discuss the choice of optimization models, initialization schemes, the hierarchical optimization algorithm, software design, and computational results. Introduction.We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas storage and filtration, electrical energy storage in batteries and capacitors, and catalysis [1,18,36,8,29,21]. Because the design of such materials involves modeling of the material over many length scales, the underlying mathematical models can be considered as a hierarchy of models. Our algorithms are also hierarchical in structure with the goal of exploiting the model hierarchy to obtain solutions more rapidly.An important feature of nanoporous materials is that within the nanopores, a gas can be stored at a much higher density than is possible with equal pressure in an open tank. The problem for applications is that the diffusion of gas into and out of the storage material is very slow. To speed this process, engineers have considered putting channels of various widths into the material; this can be thought of as adding a "vascular" system. The trade-off is, of course, between speeding up the filling or emptying of the material and storing as much as possible. One version of the optimization problem, then, is to maximize the amount of gas that can be stored and extracted in a timely manner subject to sacrificing a fixed amount of volume that is made available for transport channels. Beyond storage of gas, nanoporous materials afford analogous benefits in the storage of electric charge in electrochemical capacitors and batteries.

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Charging dynamics of the electric double layer in porous media

Cited by 29 publications

References 23 publications

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

Enhanced Charging Kinetics of Porous Electrodes: Surface Conduction as a Short-Circuit Mechanism

Optimization Algorithms for Hierarchical Problems with Application to Nanoporous Materials

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