Correlation of Double‐Layer Capacitance with the Pore Structure of Sol‐Gel Derived Carbon Xerogels

Research on carbon-based electrochemical double-layer capacitors (EDLCs) has focused on developing new and improved carbon materials with high surface areas and suitable pore structures. 1-5 Both of these characteristics have been shown to control the energy and power densities of EDLCs. 6 However, the role of microporosity, i.e., pores having diameters less than 20 A, in the performance of an EDLC is still not very clear. In other words, what pore size is too small for the electrolyte to access, hence preventing it from forming a double layer? Most of the studies in the literature have attempted to correlate the double-layer capacitance (DLC) simply in terms of the total Brunauer-Emmett-Teller (BET) surface area of a carbon material, with limited success. 7-9 Some other studies have had better success by correlating the DLC in terms of the micropore and mesopore surface areas. 10-12 However, none of these studies has been able to identify the pore sizes that may not contribute to the DLC. Yet this information is crucial to understanding the performance of an ELDC from a molecular level and to designing better carbon-based EDLCs by tailoring the pore structure for optimum performance. The main reason for this lack of quantification lies in the techniques that have been employed to determine the surface areas of carbon materials. 7-9 The commonly used techniques are global in that they only provide information on the total surface area, which is sometimes divided into the total micropore and mesopore surface areas. These techniques are incapable of providing information on the pore size distributions (PSDs) and corresponding surface area distributions. However, a very promising technique, which has not been explored much in the characterization of EDLCs, is the use of density function theory (DFT) to determine the mesopore size distribution and the corresponding cumulative surface area of carbon materials. 10 Therefore, the objectives here are to demonstrate the use of DFT in determining the PSD and cumulative surface area of carbon materials that are being evaluated as EDLCs, and to show how this information can be used to identify the pore sizes that are contributing to the DLC. The carbon material chosen for this purpose is a carbonized resorcinol-formaldehyde (R-F) resin derived from a sol-gel process. This material has been receiving considerable attention in the recent literature, 1,6,11-17 In this study, the DLCs of a series of carbon xerogels fabricated from R-F resins, carbonized at different temperatures and CO2-activated to different extents, are correlated with their corresponding PSDs and cumulative surface areas determined from DFT. The contribution to the DLC of various pore sizes is revealed, including the pore size range that does not contribute to the DLC of these carbon materials. Qualitative explanations for the inactivity of these small pores are offered and contrasted with the correlation proposed by Shi. 10