Charging dynamics of electrical double layers inside a cylindrical pore: predicting the effects of arbitrary pore size

Henrique, Filipe; Żuk, Paweł J.; Gupta, Ankur

doi:10.1039/d1sm01239h

Cited by 37 publications

(93 citation statements)

References 54 publications

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“…[17], and for PNP equations in ref. [49]. Then, the time-dependent potential can be accounted for in boundary condition (8), assuming that U(t) varies slowly then the diffusion time scale in z-direction H 2 /D.…”

Section: Resultsmentioning

confidence: 99%

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

2022

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An optimal combination of power and energy characteristics is beneficial for the further progress of supercapacitors-based technologies. We develop a nanoscale dynamic electrolyte model, which describes both static capacitance and the time-dependent charging process, including the initial square-root dependency and two subsequent exponential trends. The observed charging time corresponds to one of the relaxation times of the exponential regimes and significantly depends on the pore size. Additionally, we find analytical expressions providing relations of the time scales to the electrode’s parameters, applied potential, and the final state of the confined electrolyte. Our numerical results for the charging regimes agree with published computer simulations, and estimations of the charging times coincide with the experimental values.

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Section: Resultsmentioning

confidence: 99%

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

2022

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“…Likewise, TL model's transient response fitted MD data [11] and accurately reproduced data from numerical solutions of the PNP equations [17,18]. Reinforcing the TL model's basis, Henrique, Zuk, and Gupta recently analytically derived the TL equation from the PNP equations [18]. As they restricted to small applied potentials, however, their model did not capture Biesheuvel and Bazant's late-time slow down.…”

Section: Introductionmentioning

confidence: 90%

“…Comparison to Henrique, Zuk, and Gupta [18] and Alizadeh and Mani [30] In Ref. [18], Henrique, Zuk, and Gupta studied the charging of a narrow cylindrical pore for arbitrary double layer overlap. For thin double layers, their Eq.…”

Section: B Comparison To Biesheuvel and Bazantmentioning

confidence: 99%

“…The TL impedance found in this way [26] has been widely used to fit experimental data [1,2]. Likewise, TL model's transient response fitted MD data [11] and accurately reproduced data from numerical solutions of the PNP equations [17,18]. Reinforcing the TL model's basis, Henrique, Zuk, and Gupta recently analytically derived the TL equation from the PNP equations [18].…”

Section: Introductionmentioning

confidence: 99%

“…As such simulations cannot model the ion transport over millimeters in the quasineutral pores of porous electrodes, they vastly underestimate the charging times of real devices [13]. Other articles numerically solve the Poisson-Nernst-Plank (PNP) equations [14][15][16][17][18] and dynamical density functional theory (DDFT) [19,20] to study the charging of cylindrical and slit pores. As larger length scales could be studied than in MD, the predicted charging times are larger, accordingly.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Aslyamov¹,

Janssen²

2022

Preprint

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We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson-Nernst-Planck (PNP) equations for a pore for which λD H L, with λD the Debye length and H and L the pore's width and length. For small applied potentials, we find the time-dependent potential drop between the pore's surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.

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Intercalation Engineering of 2D Materials at Macroscale for Smart Human–Machine Interface and Double‐Layer to Faradaic Charge Storage for Ions Separation

Patil

Dutta

2023

Adv Materials Inter

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2D materials have attracted considerable attention in the past decade for their superlative physical properties. Lightweight foam from 2D materials can reduce the use of raw materials, save energy in processing the material and downregulate the carbon emission. Self‐assembling of graphene nanosheets results in 3D porous lightweight foam resembling hydrogels, aerogels, and xerogels. Hierarchical graphene architecture provides an uninterrupted path to electrons and phonon transport conforms to eligibility for developing sensor, energy storage, and energy conversion devices. Artificial intelligence (AI) originates from human–machine interaction and physiological signal reception which requires a large sensing range that illustrates to healthcare surveillance with wearable devices. Spongy architectures with flexibility and reversible compressibility act as a good candidate for pressure sensing for a wide range of real‐time human health monitoring systems by using artificial intelligence. In this review, the new perspective of emerging 2D materials (such as MXene, and borophene) along with the investigation of the graphene foam structure is demonstrated. Electrosorption of salt‐ions under foam electrode are reviewed in the context of electrochemical stability recycling ability, and efficiency of adsorption‐desorption. Beyond these, remaining challenges are depicted for emerging 2D‐materials of interest for health monitoring sensors and flexible supercapacitors for promising research directions.

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Charging dynamics of electrical double layers inside a cylindrical pore: predicting the effects of arbitrary pore size

Abstract: The effect of arbitrary pore size and Debye length on the charging dynamics of electrical double layers inside a cylindrical pore is computed, and its impact on capacitance, charging timescale, and transmission line circuit is highlighted.

Cited by 37 publications

References 54 publications

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

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

Intercalation Engineering of 2D Materials at Macroscale for Smart Human–Machine Interface and Double‐Layer to Faradaic Charge Storage for Ions Separation

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