New General Pore Size Distribution Model by Classical Thermodynamics Application: Activated Carbon
Publication: Journal of Environmental Engineering
Volume 127, Issue 4
Abstract
A model is developed using classical thermodynamics to characterize pore size distributions (PSDs) of materials containing micropores and mesopores. The thermal equation of equilibrium adsorption (TEEA) is used to provide thermodynamic properties and relate the relative pore filling pressure of vapors to the characteristic pore energies of the adsorbent/adsorbate system for micropore sizes. Pore characteristic energies are calculated by averaging of interaction energies between adsorbate molecules and adsorbent pore walls as well as considering adsorbate-adsorbate interactions. A modified Kelvin equation is used to characterize mesopore sizes by considering variation of the adsorbate surface tension and by excluding the adsorbed film layer for the pore size. The modified-Kelvin equation provides similar pore filling pressures as predicted by density functional theory. Combination of these models provides a complete PSD of the adsorbent for the micropores and mesopores. The resulting PSD is compared with the PSDs from Jaroniec and Choma and Horvath and Kawazoe models as well as a first-order approximation model using Polanyi theory. The major importance of this model is its basis on classical thermodynamic properties, less simplifying assumptions in its derivation compared to other methods, and ease of use.
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References
1.
Ambrose, D., and Patel, N. C. ( 1984). “The correlation and estimation of vapour pressures IV. Extrapolation of vapour pressures.” J. Chem. Thermodynamics, 16, 549.
2.
Avgul, N. N., and Kiselev, A. V. ( 1970). “Physical adsorption of gases and vapors of graphitized carbon blacks.”Chem. and Physics of Carbon, Vol. 6, Marcel Dekker, New York.
3.
Bansal, R. C., Donnet, J.-B., and Stoeckli, F. ( 1988). Active carbon, Marcel Dekker, New York.
4.
Cal, M. P. ( 1995). “Characterization of gas phase adsorption of untreated and chemically treated activated carbon cloths.” PhD dissertation, University of Illinois at Urbana-Champaign, Urbana, Ill.
5.
Choma, J., and Jaroniec, M. ( 1997). “Influence of the pore geometry on the micropore size distribution function of active carbons.” Adsorption Sci. & Technol., 15(8), 571–581.
6.
Cohan, L. H. ( 1938). “Sorption hysteresis and the vapor pressure of concave surfaces.” J. Am. Chem. Soc., 60, 433.
7.
Daley, M. ( 1996). “The development and characterization of tailored, high surface area adsorbents for enhanced adsorption.” PhD dissertation, University of Illinois at Urbana-Champaign, Urbana, Ill.
8.
Derjaguin, B. V., and Churaev, N. V. ( 1976). “Polymolecular adsorption and capillary condensation in narrow slit pores.” J. Colloid Interface Sci., 54, 157–175.
9.
Derjaguin, B. V. ( 1940). “Theory of capillary condensation in the pores of sorbents.” Acta Physicochim, Moscow, 12, 181.
10.
Donnet, J.-B., and Bansal, R. C. ( 1998). Carbon fibers, Marcel Dekker, New York.
11.
Dubinin, M. M. ( 1975). “Physical adsorption of gases and vapors in micropores.” Progress in Surface and Membrane Sci., 9, 1–70.
12.
Dubinin, M. M., and Stoeckli, H. F. ( 1980). “Homogeneous and heterogeneous micropore structures in carbonaceous adsorbents.” J. Colloid Interface Sci., 75, 34–42.
13.
Dubinin, M. M., Polyakov, N. S., and Kataeva, L. I. ( 1991). “Basic properties of equations for physical vapor adsorption in micropores of carbon adsorbents assuming a normal micropore distribution.” Carbon, 29(4/5), 481–488.
14.
Everett, D. H., and Powl, J. C. ( 1976). “Adsorption in slit-like and cylindrical micropores in the Henry's law region.” J. Chem. Soc., Faraday Trans., 1, 72, 619–636.
15.
Gregg, S. J., and Sing, K. S. W. ( 1982). Adsorption, surface area and porosity, 2nd Ed., Academic, New York.
16.
Horvath, G., and Kawazoe, K. ( 1983). “Method for calculation of effective pore size distribution in molecular sieve carbon.” J. Chem. Engrg. Japan, 16, 470–475.
17.
Jacoby, M. ( 1999). “Planning for the future of DOE labs.” Chem. & Engrg. News, March 29, 25.
18.
Jaroniec, M., and Choma, J. ( 1986). “Characterization of heterogeneity of activated carbons by utilizing the benzene adsorption data.” Mat. Chem. Phys., 15, 521.
19.
Kaviany, M. ( 1995). Principles of heat transfer in porous media, 2nd Ed., Springer, New York.
20.
Lastoskie, C., Gubbins, K. E., and Quirke, N. ( 1993). “Pore size distribution analysis of microporous carbons: A density functional theory approach.” J. Physical Chem., 97, 4786–4796.
21.
Lordgooei, M. ( 1999). “Adsorption thermodynamic and mass transfer of toxic volatile organic compounds in activated-carbon fiber-cloth for air pollution control.” PhD dissertation, University of Illinois at Urbana-Champaign, Urbana, Ill.
22.
Lordgooei, M., Sagen, J., Rood, M. J., and Rostam-Abadi, M. ( 1998). “Sorption and modeling of mass transfer of toxic chemical vapors in activated-carbon fiber-cloth adsorbers.” Energy & Fuels, 12, 1079–1088.
23.
Maier, W. F. ( 1998). “Amorphous microporous mixed oxides, new selective catalysts with chemo- and shape-selective properties.” ACS Div. of Fuel Chem., 216th ACS Nat. Meeting, 43(3), 534–537.
24.
Muller, A. ( 1936). “The van der Waals potential and the lattice energy of a n-CH2 chain molecule in a paraffin crystal.” Proc. Royal Soc. London, A154, 624–639.
25.
Olivier, J. P. ( 1995). “Modeling physical adsorption on porous and nonporous solids using density functional theory.” J. Porous Mat., 2, 9.
26.
Polanyi, M. ( 1932). “Theories of the adsorption of gases. A general survey and some additional remarks.” Trans. Faraday Soc., 28, 316–333.
27.
Reid, R. C., Prausnitz, J. M., and Poling, B. E. ( 1987). The properties of gases and liquids, 4th Ed., McGraw-Hill, New York.
28.
Saito, A., and Foley, H. C. ( 1991). “Curvature and parametric sensitivity in models for adsorption in micropores.” AIChE J., 37, 429–436.
29.
Somorjai, G. A. ( 1994). Introduction to surface chemistry and catalysis, Wiley, New York.
30.
Stoeckli, H. F., Lavanchy, A., and Kraehenbuehl, F. ( 1982). Adsorption at the gas-solid and liquid-solid interface, Elsevier Scientific, Amsterdam, 201–209.
31.
Sun, J. ( 1999). “Preparation, evaluation and structural modeling of carbon-based adsorbents used on natural gas vehicles.” PhD dissertation, University of Illinois at Urbana-Champaign, Urbana, Ill.
32.
Tolman, R. C. ( 1949). “The effect of droplet size on surface tension.” J. Chem. Physics, 17, 333.
33.
Valladares, D., and Zgrablich, G. ( 1997). “A test of the Horvath-Kawazoe method by Monte Carlo simulations.” Adsorption Sci. & Technol., 15(1), 15–24.
34.
Wagner, W., Evers, J., and Pentermann, W. ( 1976). “New vapour-pressure measurements and a new rational vapour-pressure equation for oxygen.” J. Chem. Thermodyn., 8, 1049.
Information & Authors
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Published In
Journal of Environmental Engineering
Volume 127 • Issue 4 • April 2001
Pages: 281 - 287
History
Received: Nov 23, 1999
Published online: Apr 1, 2001
Published in print: Apr 2001
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