Recent Advances in Continuum Modeling of Interfacial and Transport Phenomena in Electric Double Layer Capacitors

Abstract

This paper reviews recent advances in physical modeling of interfacial and transport phenomena in electric double layer capacitors (EDLCs) under both equilibrium and dynamic cycling. The models are based on continuum theory and account for (i) the Stern layer at the electrode/electrolyte interface, (ii) finite ion sizes, (iii) steric repulsions, (iv) asymmetric electrolytes featuring ions with different valencies, effective diameters, or diffusion coefficients, (v) electric-field-dependent dielectric permittivity of the electrolyte, and/or (vi) porous three-dimensional morphology of the electrodes. Typical characterization methods such as electrochemical impedance spectroscopy, cyclic voltammetry, and galvanostatic cycling were reproduced numerically to identify the dominant physical phenomena and to gain insight into experimental observations. In addition, recent thermal models derived from first principles for EDLCs under constant-current cycling accounting for irreversible Joule heating and reversible heat generation rates due to ion diffusion, steric effects, and changes in entropy are discussed. Scaling analyses of both equilibrium and dynamic models are also presented as a way to identify self-similar and asymptotic behaviors as well as to develop design rules for electrodes and electrolytes of next generation EDLCs. Electrical double layer capacitors (EDLCs) store energy by ion adsorption in the electrical double layer (EDL) forming at the electrode/electrolyte interfaces.1,2 This process is highly reversible and the cycle life of EDLCs exceeds 100,000 cycles.2,3 EDLCs can operate in a wide range of specific energy and power densities. This versatility is a key feature for electrical energy storage, energy harvesting, and energy regeneration applications. 2The performance of EDLCs is determined by the combination of the electrode material and morphology and of the electrolyte. In general, the key attributes of a good electrode include 1,3-7 (i) large surface area accessible to ions to maximize charge storage, (ii) optimum pore size, short pore length, and good pore connectivity to facilitate ion transport, (iii) large electrical conductivity to enable fast charging and discharging and low ohmic resistance, (iv) thin electrodes and current collectors to reduce the total resistance of the device, (v) small leakage current, (vi) small self-discharge, (vii) environmentally friendly materials, and (viii) low price. However, satisfying all these criteria simultaneously is challenging. For example, increasing surface area often results in larger electrode electrical resistivity.1 Micropores with diameter less than 2 nm contribute greatly to EDLCs capacitance.2 But pores smaller than the ion size are typically inactive and do not contribute to charge storage. 1,8 Porous electrodes must also be electrochemically accessible to ions. Then, interconnected mesopores with diameter ranging from 2 to 50 nm are necessary for fast charging thanks to their easier accessibility to ions. 1,6,[9][10][11] In practice, electrode...

Recent advancements in metal organic framework based electrodes for supercapacitors

“…The improved EDLC of Ni-MOFs is due to the appropriate pore diameter and good electrical conductivity. Evidently, the columnar voids and the electrolyte ions were consistent with the appropriate pore sizes (1.5 nm) of the Ni-MOFs [58]. In addition, the presence of conjugated π bonds is also a key aspect that increases the charge mobility and further enhances the electrical conductivity of the as-prepared Ni-MOFs [31].…”

The Composite Supercapacitor

“…However, if higher currents are required, the ions “jammed” in the small, slightly swollen pores of the active electrode are unable to move quickly, and such high‐energy‐density supercapacitors are unable to deliver high current densities and do not have very high power densities. This is critical for organic and ionic‐liquid electrolytes, which are generally used in supercapacitors for medium‐ and high‐voltage applications, as such electrolytes have large cations of approximately 0.4 to 1.3 nm in their unsolvated or solvated forms . In general, granular activated carbon (AC) coatings have a larger proportion of macro‐ and micropores compared to AC fabrics, which generally have only micropores of approximately 1 nm .…”

“…and ionic-liquid electrolytes,w hich are generally used in supercapacitors for medium-and high-voltagea pplications,a s such electrolytes have large cations of approximately0 .4 to 1.3 nm in their unsolvatedo rs olvated forms. [10] In general, granular activated carbon (AC) coatings have al arger proportion of macro-and micropores compared to AC fabrics, which generally have only micropores of approximately 1nm. [11] As such, AC coatings would allow for faster ion mobility and, thus,h igh power.…”

Modelling of Supercapacitors: Factors Influencing Performance

“…11,12 Verbrugge and Liu (2005) used a model based on the porous electrode theory to calculate the Ragone plot, which relates the energy density and power density. 13 This was however done only z E-mail: gregory.offer@imperial.ac.uk; Juraj.Kosek@vscht.cz for one set of parameters.…”

“…8 The separator does not contribute to the capacitance and acts as an additional ionic resistance in the system. 9,10 Models on the scale of the whole cell are generally based either on the equivalent-circuit (EC) approach or porous electrode theory, and the existing models were recently reviewed by Ike (2015) and Pilon et al (2015). 11,12 Verbrugge and Liu (2005) used a model based on the porous electrode theory to calculate the Ragone plot, which relates the energy density and power density.…”