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Comment on “Estimating Equilibrium Adsorption of Organic Compounds in Activated Carbon from Aqueous Solution’’ SIR: In his recent article entitled “Estimating Equilibrium Adsorption of Organic Compounds in Activated Carbon from Aqueous Solution” (ES&T 1981,15,812),Dr. Arbuckle compared three methods for predicting relative adsorbability: solvophobic theory, Polanyi theory, and the net adsorption energy approach. We direct the attention of your readers to recent significant developments and applications of the solvophobic (c@J)theory that render Dr. Arbuckle’s evaluation obsolete. We would also like to reiterate certain fundamental problems with both the Polanyi theory and the net adsorption energy approach that one of us (G.B.) discussed in a recent interview in ES&T ( 1 , 2). The c@Jtheory, like most theories, has developed through several stages. From its early stages, when Taft, Hammett, and steric parameters were used to correlate adsorption (3),the theory has now jelled into a comprehensive theory incorporating all known thermodynamic interactions (4, 5 ) . Details on how to calculate each interaction from physical-chemical parameters found in handbooks are outlined in the literature (4-6). Unfortunately, Dr. Arbuckle used the first version of the c@Jtheory for the comparison in his paper. This is in spite of the fact that a comprehensive analysis of the most recent version was published in summary 10 months prior to the publication of his paper (2). Several comments are necessary in answer to Dr. Arbuckle’s criticisms of the c@Jtheory. With the exception of the solute accentric factor and cavity surface area, all of the required physical properties may be found in standard references such as the CRC Handbook of Chemistry and Physics (7). A listing of accentric factors may be found in ref 8 or other sources. Molecular surface area may be estimated from liquid density and molecular weight or obtained from a computer program available from the Indiana University chemistry-computer library (9). Thus, in principle, the c@Jtheory does not require inaccessible parameters. As of now, it is true that separate correlations have only been developed for each family of compounds or homologous series. This does not, of course, preclude later incorporation of correction factors directly related to functional polarity for the development of universal correlations. The c@Jtheory is not restricted to small compounds, as Dr. Arbuckle suggests. It has been applied externally to macromolecules such as DNA and proteins ( 10-1 2). In regard to the two other theories that are discussed in Dr. Arbuckle’s paper, your readers would be interested in the following fundamental problems with each. The basic problem with the “thick compressed film theory” (or “Polanyi adsorption potential theory”, as it is often called) is that the original physical model of a three-dimensional film has been questioned and rejected by many scientists, including none other than Polanyi himself (13). Associated with this is the problem of defining or measuring the adsorbate density, which is needed for plotting the characteristic curves ( 1 ) . Quoting Dr. M. Manes, “Thus far no good predictive method has been found for estimating the adsorbate densities” (14). Belfort has shown recently that the Polanyi and ideal adsorption theory based on Gibb’s adsorption isotherm have similar thermodynamic structure (15). One of us (G.B.) has recently presented a detailed 374
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analysis and criticism of the quasi-theoretical net adsorption energy approach (2). Suffice it to mention that the arbitrary choice of the relative values for the acid and base solubility hydrogen bonding parameters is without theoretical justification. See Table IV in Dr. Arbuckle’s paper in which these arbitrary values are assigned and then used for calculating the net adsorption energy. The usefulness of the c@Jtheory extends beyond that of a purely predictive tool. It can provide a comprehensive framework for considering specific contributions to aqueous phase adsorption, leading to an improved understanding of the entire process. Literature Cited (1) (2) (3) (4)
Belfort, G. Environ. Sci. Technol. 1980, 14, 910. Belfort, G. Environ. Sci. Technol. 1980, 14, 1037. Belfort, G. Environ. Sci. Technol. 1979, 13, 939. Belfort, G. In “Chemistry in Water Reuse”; Cooper, W. J., Ed.; Ann Arbor Science: Ann Arbor, MI, 1981; Vol. 2, Chapter 11, pp 207-241. ( 5 ) Belfort, G.; Altshuler, G. “Selective Adsorption of Organic Homologs onto Activated Carbon from Dilute Aqueous Solutions: III-Branching and Predictions”; presented before The Division for Environmental Chemistry at the 181st National Meeting of the American Chemical Society, Atlanta, GA, March 28-April 3, 1981. (6) Horvhth, C.; Melander, W.; Molnir, I. J. Chromatogr. 1976, 125, 129. (7) “Handbook of Chemistry and Physics”, 57th ed.; CRC Press, Cleveland, OH, 1966. (8) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. “The Properties of Gases and Liquids”, 3rd ed.; McGraw-Hill: New York, 1977. (9) Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, IN 47405. (10) Sinanoglu, 0.;Abdulnur, S. Photochem. Photobiol. 1964, 3, 333. (11) Sinanoglu, 0.;Abdulnur, S. Fed. Proc., Fed. Am. SOC.Exp. Biol. 1965, 24 (2) part 111, S-12. (12) Sinanoglu, 0. Znt. J. Quant. Chem. 1980, 18, 381. (13) McBain, J. W. “The Sorption of Gases and Vapors by Solids”; George Routledge & Sons, Ltd.: London, 1932. (14) Manes, M. “The Polanyi Adsorption Potential Theory and Its Applications to Adsorption from Water Solution onto Activated Carbon” Chapter 2, pp 43-64 in “Activated Carbon Adsorption of Organics from Aqueous Phase I”; Suffett, I. H., McGuire, M. J.,Eds.; Ann Arbor Science: Ann Arbor, Michigan, 1980; Chapter 2, pp 43-64. (15) Belfort, G. AZChE J. 1981, 27, 1021. Gordon Altshuler, Georges Belfort
Department of Chemical and Environmental Engineering Rensselaer Polytechnic Institute Troy, New York 12181
SIR: The purpose of my article was not to determine which model gives the greatest insight into adsorption but to determine which could be most readily used by engineers to estimate equilibrium loadings on activated carbon. An empirical model would have been acceptable if the parameters needed were readily available; of course I would rather use a theoretically based model, and therefore I evaluated the three models selected without regard to their validity. As for the solvophobic method, I did state that it may give insight into adsorption phenomena (insight we may be not be able to obtain from other methods). Also,
0013-936X/82/0916-0374$01.25/0
0 1982 American Chemical Society
as indicated by the square of the difference between actual and predicted values (2):
47
method solvophobic Polanyi net adsorption energy m
W
-I
‘Y
.2-
2z -
- I-
Y
,OS:
.OB.04.03-
.OZ-
10
Figure 1. Solvophoblc curve with actual data.
I did use the first version as noted, but my article was submitted before publication of the most recent solvophobic version-this is indicated by the received date published with the article. I have reevaluated the solvophobic theory by correlating the total solute cavity surface &ea (TSA) with loading in a manner similar to Altshuler and Belfort (I),and since the TSA calculation procedure was not readily available, Altshuler and Belfort gracisouly provided TSA’s for the 22 compounds of interest. So that their approach could be made more widely applicable, two changes were made (2): (1)the alcohol data were used to generate a predictive curve for the other four families of compounds (rather than obtaining a separate curve for each family, which would require too much data); (2) two straight lines were used to fit the data (rather than using a single line, which indicates a compound’s size may be limiting its access to part of the adsorbent’s surface). The predictive line from the alcohol data and the loadings for the 13 additional compounds indicate that the solvophobic method can be used to predict loadings (Figure 1) and that larger compounds can be handled, which was not the case for the first version. This method does not predict loadings -.well as the Polanyi and net adsorption energy methods,
(actual - predicted)?, (mmol/g)* 0.6721 0.4665 0.1803
(Note: the improvement in the net adsorption energy method’s value over my ES&T article is due to the use of a log-log plot rather than the arithmetic plot.) In spite of the arbitrariness of the net adsorption energy approach, it still predicts single-point equilibrium loadings best for this data, even though from a theoretical standpoint it is least satisfactory. The Polanyi method (or A. L. Meyers and 9. Sircar’s theory of correspondence (3)) would seem to offer the most potential for use in column modeling, since a complete isotherm is obtained. Others have reported on the successful application of the Polanyi method, particularly to bisolute systems (4). A better understanding of adsorption phenomena is needed and studies should continue in this area, but we must not sit back and wait for an acceptable theory and model. As engineers we must try to use what is presently available and try to provide information for others to use as an aid to design and as a screening process to save valuable laboratory time. Literature Cited Altshuler, G. and G. Belfort, “Selective Adsorption of Organic Homologues onto Activated Carbon from Dilute Aqueous. Solvophobic Interaction Approach. 111. Branching and Predictions” paper submitted to ACS Advances in Chemistry Series book. Arbuckle, W. B. “Predicting Freundlich K Constants for Organic Compounds on Activated Carbon,” ibid. Meyers, A. L. and S. Sircar, “Theory of Correspondence for Adsorption from Dilute Solutions on Heterogeneous Adsorbents,” ibid. Hogan, P. and F. A. DiGiano, “Application of Polanyi Adsorption Potential Theory to Single Solute and Bisolute Adsorption from Aqueous Solution on Activated Carbon,” paper presented at ACS Meeting, Washington, D.C., Sept. 1979.
Wm. Brlan Arbuckle Department of Environmental Engineering University of Florida Gainesviile, Florida 3261 1
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