J. Phys. Chem. C 2009, 113, 19335–19343
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Empirical Analysis of the Contributions of Mesopores and Micropores to the Double-Layer Capacitance of Carbons Thomas E. Rufford,* Denisa Hulicova-Jurcakova, Zhonghua Zhu, and Gao Qing Lu ARC Centre of Excellence for Functional Nanomaterials, School of Chemical Engineering and Australian Institute for Bioengineering and Nanotechnology, The UniVersity of Queensland, 4072 Queensland, Australia ReceiVed: June 25, 2009; ReVised Manuscript ReceiVed: September 1, 2009
Activated carbons with large mesopore volumes were prepared from waste coffee grounds by chemical activation with ZnCl2. These carbons exhibited excellent electrochemical double-layer capacitance of up to 368 F g-1 in 1 M H2SO4. The effect of carbonization temperature and ZnCl2 ratio on carbon pore development and consequently electrochemical double-layer capacitance in 1 M H2SO4 is discussed. Cyclic voltammetry, electrochemical impedance spectroscopy, and galvanic charge-discharge cycles were used to study the effects of mesopores on capacitance at fast charge rates. Activated carbons with greater mesopore content retained higher specific capacitance at fast charge-discharge rates as the mesopores acts as channels or reservoirs for electrolyte transport. An improved model for evaluation of contributions to capacitance from micropore surfaces and mesopore surfaces is proposed. Using this model, the contribution of the mesopores to double-layer capacitance was determined to be 17 µF cm-2. The contribution of micropores to capacitance decreased at fast discharge rates and was found to be dependent on the number of mesopores, which influence the transport of ions through the carbon pore network. 1. Introduction Electrochemical double-layer capacitors (EDLCs) store energy by electrostatic accumulation of charge at electrode surfaces. No charge-transfer reactions are involved in chargedischarge cycles of EDLCs, unlike in the operation of conventional batteries; therefore, EDLCs can achieve stable and reversible charge cycling at fast charge rates. However, the energy density of an EDLC is a fraction of a conventional lead acid battery. To realize the benefits of EDLCs in high-powerdemand applications, such as electric fuel cell vehicles, electrode materials with high energy density, approaching that of conventional batteries, are required. The energy density of an EDLC is proportional to the cell’s specific capacitance, and capacitance depends on the electrodeelectrolyte interfacial area. Therefore, high surface area activated carbons are a popular electrode material for EDLCs. Specific capacitance generally increases with micropore surface area (pores up to 2 nm wide).1,2 However, not all of the micropores in a high surface area activated carbon may be effective for double-layer formation. In H2SO4, 0.7-1 nm wide carbon pores produce optimum specific capacitance,1,3,4 but pores less than 0.5 nm wide are generally considered too narrow for forming a double layer.2,5 Although mesopores (2-50 nm) may not accommodate as great a volumetric density of double layers as micropores, several studies report that mesopores can improve EDLC performance at fast charge rates by facilitating electrolyte diffusion through the carbon network to micropore adsorption sites.3,6,7 However, in a recent study of phenolic-resin-derived carbons, Ferna´ndez and coauthors challenge whether the influence of mesopores on capacitance retention is significant in H2SO4.8 In the same study, they do acknowledge the benefit of mesopores in capacitance retention in tetraethyl ammonium * To whom correspondence should be addressed. Tel: +61 7 33466201. Fax: + 61 7 33654199. E-mail:
[email protected].
tetrafluoroborate (TEABF4)/acetonitrile, in which the ions are much larger than the ions of H2SO4.8 This paper explores the effect of carbon mesopores on doublelayer capacitance in 1 M H2SO4 at fast charge-discharge rates. Theoretical and empirical models for the prediction of capacitance for different size pores are reviewed, and a modified method to calculate the contributions of micropore and mesopore surface areas to double-layer capacitance is proposed. The objective of the model is to investigate the importance of mesopores on capacitance for high-power EDLC applications. A series of activated carbons with varying degrees of mesoporosity were prepared from waste coffee grounds by controlling the amount of ZnCl2 in the activation process. 1.1. Background Models for Contribution of Mesopores to Capacitance. To account for the effect of pore curvature on electrochemical double-layer capacitance, Huang, Sumpter, and Meunier proposed a model for double-layer capacitance with three categories of carbon pores defined,9,10 in accordance with the IUPAC classifications,11 micropores (50 nm). For macropores, the parallel-plate capacitor model described by eq 1 may still be a good approximation of the electrolyte-electrode interface9
Cmacro )
εr,macroε0Smacro d
(1)
in which εr,macro is the dielectric constant of the electrolyte, ε0 is the vacuum permittivity, Smacro is the surface area of the electrolyte-electrode interface, and d is the thickness of the double layer. The nonlinear relationship between capacitance and surface area for high surface area carbon electrodes shows that the parallel-plate model does not provide a sufficient description of double-layer capacitance for all pore shapes and sizes. Huang et al. describe an electric double-cylinder capacitor (EDCC) for
10.1021/jp905975q CCC: $40.75 2009 American Chemical Society Published on Web 10/09/2009
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Rufford et al.
double-layer formation in cylindrical mesopores and an electric wire-in-cylinder capacitor (EWCC) for double-layer formation in micropores.9,10 In the EDCC mesopore model, a double layer of thickness d forms at the pore wall, and the interior pore volume accommodates a reservoir of electrolyte ions (both cations and anions). The capacitance in mesopores is given by9
Cmeso
εr,mesoε0Smeso ) b ln[b/(b - d)]
(2)
in which Cmeso is the capacitance (in F or F g-1) of the mesopores, Smeso is the surface area of the mesopores, and b is the pore radius. Narrow micropores cannot accommodate the reservoir of electrolyte ions, and only the counterions (solvated or desolvated) will enter the pore, forming the wire-in-cylinder capacitor. The capacitance of micropores with the EWCC is then given by eq 3, where a0 is the radius of the ion.9
Cmicro )
εr,microε0Smicro b ln[b/a0]
(3)
Huang et al. reported9 a good fit for eqs 2 and 3 to several sets of published data for carbons with narrow pore size distributions (including mesoporous-templated carbons and carbide-derived carbons). For application to typical activated carbons with nonuniform pore size distributions, Huang et al. commented that the capacitance could be calculated by summation of contributions from different pore size groups, as shown in eq 4 for i groups of micropores and j groups of mesopores. In this case, the surface area of pores wider than 50 nm and the external particle surface area are assumed to be much less than the area of micropores and mesopores; therefore, the capacitance contributed by macropores can be neglected.9
C)
∑ i
εr,microε0Smicro + bi ln[bi /a0]
ε
εS
r,meso 0 meso ∑ bj ln[b j /(bj - d)]
(4)
j
This heuristic model helps us explain the mechanism of double-layer formation within narrow pores. However, the application of eq 4 to the heterogeneous carbon pore structures typically found in commercial EDLC electrodes is not straightforward. A capacitance could be calculated using the heuristic model and pore size distribution, obtained by nonlocal density functional theory,12 but a simpler approach based on appropriate grouping of pore sizes is more practical for real supercapacitor carbon electrodes. Furthermore, the heuristic model does not describe the effect of mesopore channels on the accessibility of electrolyte ions to micropores. A simplified model to account for the different contributions of micropores and mesopores to double-layer capacitance was described by Shi,13 and this model has been adopted in several other studies.14-16 Shi’s method groups pores as micropores (
