Effect of diffuse layer and pore shapes in mesoporous carbon supercapacitors
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Rui Qiao Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634-0921
Bobby G. Sumpter and Vincent Meuniera) Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6367 (Received 14 December 2009; accepted 23 April 2010)
In the spirit of the theoretical evolution from the Helmholtz model to the Gouy– Chapman–Stern model for electric double-layer capacitors, we explored the effect of a diffuse layer on the capacitance of mesoporous carbon supercapacitors by solving the Poisson–Boltzmann (PB) equation in mesopores of diameters ranging from 2 to 20 nm. To evaluate the effect of pore shape, both slit and cylindrical pores were considered. We found that the diffuse layer does not affect the capacitance significantly. For slit pores, the area-normalized capacitance is nearly independent of pore size, which is not experimentally observed for template carbons. In comparison, for cylindrical pores, PB simulations indicate a trend of slightly increasing area-normalized capacitance with pore size, similar to that depicted by the electric double-cylinder capacitor model proposed earlier. These results indicate that it is appropriate to approximate the pore shape of mesoporous carbons as being cylindrical and the electric double-cylinder capacitor model should be used for mesoporous carbons as a replacement of the traditional Helmholtz model.
I. INTRODUCTION
Electrochemical capacitors, or supercapacitors, are electrochemical energy-storage devices characterized by high power densities and exceptional cycle lifetime.1 Supercapacitors are often termed electric double-layer capacitors (EDLCs), because they store energy physically using the charge separation in the electric double layers (EDLs) formed at electrode/electrolyte interfaces.1–5 Mesoporous carbon materials (pore size from 2 to 50 nm) are widely used for EDLCs, partly because mesoporous carbons are excellent conductors and are inexpensive.6–9 The high specific surface area of carbon materials originates primarily from the internal surface of mesopores and is responsible for considerably higher energy densities of EDLCs compared to conventional dielectric capacitors. This feature makes mesoporous carbon-based EDLCs ideal to complement or even substitute batteries in many energy storage applications. Developing an accurate capacitance model for EDLCs is important for the performance optimization of EDLCs. The simplest EDLC capacitance model is based on von a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0188 J. Mater. Res., Vol. 25, No. 8, Aug 2010
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Helmholtz’s description of the EDL,10 as depicted in Fig. 1(a) and Eq. (1): er e0 A er e0 or C=A ¼ ; ð1Þ d d where er is the dielectric constant in the EDL, e0 the vacuum permittivity, A the electrode-specific surface area, and d the EDL thickness. However, the actual EDL structure is far more complicated for low concentration electrolytes: in addition to the compact Helmholtz layer, a di
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