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Electrosorption of Ions from Aqueous Solutions by Carbon Aerogel: An Electrical Double-Layer Model Kun-Lin Yang,† Tung-Yu Ying,† Sotira Yiacoumi,*,† Costas Tsouris,‡ and E. Steven Vittoratos§ Georgia Institute of Technology, 200 Bobby Dodd Way, Atlanta, Georgia 30332-0512, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37381-6224, and Chevron Research and Technology Company, 100 Chevron Way, Richmond, California 94802-0627 Received October 31, 2000. In Final Form: January 11, 2001 An electrical double-layer model is developed to predict electrosorption of ions from aqueous solutions by carbon aerogel electrodes. The carbon aerogel electrodes are treated as electrical double-layer capacitors, and electrosorption is modeled using classical electrical double-layer theory. Because of the porous characteristics of the electrodes, the total capacity of the system is obtained by summing the contributions of the individual pores. The pore size distribution of the carbon aerogel is measured by the physical adsorption of N2 and CO2 as well as by mercury intrusion porosimetry. When a pore has a width smaller than a specific value (cutoff pore width), it does not contribute to the total capacity because of the electrical double-layer overlapping effect. This effect greatly reduces the electrosorption capacity for electrodes with significant numbers of micropores, such as carbon aerogel; thus, it is considered in the electrical doublelayer model. The model in this study focuses on the electrosorption of sodium fluoride, which exhibits minimal specific adsorption. Several equilibrium electrosorption experiments are performed under various conditions of ion solution concentration and applied voltage. When the overlapping effect is considered, modeling results agree well with experimental data obtained at voltages up to 1.2 V. Without the doublelayer overlapping correction, the model greatly overestimates the electrosorption capacity. The cutoff pore width is found to decrease with increasing ion solution concentration and applied voltage. An approximate modeling approach is also presented in this work, which is more efficient than the exact solution in terms of numerical computations.
Introduction The electrostatic force has long been used to enhance separation processes.1-7 The basic concept of electrosorption is forcing charged ions to move toward electrodes of opposite charge by imposing an electric field. For electrodes of good electrical conductivity and high surface area, such as activated carbon and carbon aerogel, a strong electrical double layer is formed on their surfaces when an electric field is applied. Charged ions and the applied energy are therefore held in the double layer. Once the electric field is removed, the ions are quickly released back to the bulk solution and the energy can be utilized as in an electrical capacitor.8,9 Carbon aerogel is an excellent electrode material for electrosorption. According to characterization studies,10-12 * Corresponding author. E-mail:
[email protected]. Fax: (404) 894-8266. Phone: (404) 894-2639. † Georgia Institute of Technology. ‡ Oak Ridge National Laboratory. § Chevron Research and Technology Company. (1) Arnold, B. B.; Murphy, G. W. J. Phys. Chem. 1961, 65, 135. (2) Johnson, A. M.; Newman, J. J. Electrochem. Soc. 1971, 118, 510. (3) Oren, Y.; Soffer, A. J. Electrochem. Soc. 1978, 125, 869. (4) Oren, Y.; Soffer, A. J. Appl. Electrochem. 1983, 13, 473. (5) Trainham, J. A.; Newman, J. J. Electrochem. Soc. 1977, 124, 1528. (6) Matlosz, M.; Newman, J. J. Electrochem. Soc. 1986, 133, 1850. (7) Farrell, J.; Bostick, W. D.; Jarabek, R. J.; Fiedor, J. N. Environ. Sci. Technol. 1999, 33, 1244. (8) Mayer, S. T.; Pekala, R. W.; Kaschmitter, J. L. J. Electrochem. Soc. 1993, 140, 446. (9) Bispo-Fonseca, I.; Aggar, J.; Sarrazin, C.; Simon, P.; Fauvarque, J. F. J. Power Sources 1999, 79, 238. (10) Wang, J.; Angnes, L.; Tobias, H. Anal. Chem. 1993, 65, 2300. (11) Pekala, R. W.; Farmer, J. C.; Alviso, C. T.; Tran, T. D.; Mayer, S. T.; Miller, J. M.; Dunn, B. J. Non-Cryst. Solids 1998, 225, 74. (12) Zhang, S. Q.; Wang, J.; Shen, J.; Deng, Z. S.; Lai, Z. Q.; Zhou, B.; Attia, S. M.; Chen, L. Y. Nonstructured Mater. 1999, 11, 375.
carbon aerogel is highly porous and monolithic and has a high surface area (∼400-1000 m2/g), low electrical resistivity (e40 mΩ cm), and controllable pore size distribution (e50 nm). Farmer et al.13-15 have shown that electrosorption by using carbon aerogel electrodes can effectively remove ions such as sodium, chloride, chromium, ammonium, and perchlorate from aqueous solutions. Two factors contribute to the total capacity for electrosorption. The first is the electrical double-layer capacity due to the electrostatic attraction force between the ions and the electrode. This capacity is affected primary by the ion solution concentration and applied voltage, as demonstrated in some experimental studies.13-15 The second contributing factor is the pseudocapacity due to faradaic reactions, which depends on the chemical characteristics of the solute and the functional groups on the electrode surface. Functional groups such as carbonyl and phenolic groups on the carbon electrode are able to react with cations and form chemical bonds. Therefore, the pseudocapacity can be determined by the functional group density on the electrode surface, which can be increased by surface oxidation processes. Oren et al.16,17 and Golub et al.18 have conducted experiments to explore the electrical double-layer formation and faradaic reactions on the carbon surface. Their results have shown that during the (13) Farmer, J. C.; Fix, D. V.; Mack, G. V.; Pekala, R. W.; Poco, J. F. J. Electrochem. Soc. 1996, 143, 159. (14) Farmer, J. C.; Bahowick, S. M.; Harrar, J. E.; Fix, D. V.; Martinelli, R. E.; Vu, A. K.; Carroll, K. L. Energy Fuels 1997, 11, 337. (15) Farmer, J. C.; Fix, D. V.; Mack, G. V.; Pekala, R. W.; Poco, J. F. J. Appl. Electrochem. 1996, 26, 1007. (16) Oren, Y.; Soffer, A. J. Electroanal. Chem. 1986, 206, 101. (17) Oren, Y.; Glatt, I.; Livnat, A.; Kafri, O.; Soffer, A. J. Electroanal. Chem. 1985, 187, 59. (18) Golub, D.; Oren, Y.; Soffer, A. Carbon 1987, 25, 109.
10.1021/la001527s CCC: $20.00 © 2001 American Chemical Society Published on Web 02/16/2001
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charging process on a carbon or graphite electrode, the faradaic or electrochemical charge that crosses the interface becomes significant at high voltage. As pointed out by Wang et al.,10 however, faradaic reactions on carbon aerogel occur to a lesser extent than on carbon or graphite. This advantage enables us to use the electrical doublelayer capacity, without considering faradaic reactions, to account for the total capacity on carbon aerogel. Although several researchers have investigated the electrical double-layer capacity by using carbon or carbon aerogel electrodes, most of these studies are experimental. Among the few theoretical studies in the literature is a comprehensive model for ion adsorption on porous carbon electrodes developed by Johnson and Newman.2 Their analysis basically simulates the electrosorption process from a macroscopic view and demonstrates a good agreement with experimental data. Farmer et al.13,15 have attempted to use the Gouy-Chapman theory, which was developed for simple planar electrodes, to explain their experimental data. The experimental data show that the surface charge density fails to meet a square root dependence on electrolyte concentration as predicted by the classical Gouy-Chapman theory. This discrepancy is explained by the self-shielding effect observed in the porous carbon electrodes. In porous electrodes, the electrical double layers are formed inside the pores instead of adjacent to the electrode surface. The pores can greatly increase the effective area of the porous electrodes as well as the electrical capacity. However, when the pore size is of the same order of magnitude as the electrical doublelayer thickness, the electrical double layers inside the pore overlap and lose their electrical capacities. Because this overlapping effect exists only in microporous (
