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Response to ‘Pignatello and Xing’s Comment on “Evaluation of the Glassy/Rubbery Model for Soil Organic Matter”’ SIR: The critique by Pignatello and Xing (1) of our paper demonstrates their continued misapprehension of a number of important concepts. We hope this Rebuttal may prove more enlightening than previous discussions. Glassy Polymers. Pignatello and Xing claim that we ignored polymer literature demonstrating nonlinear sorption in glassy polymers and linear sorption in rubbery polymers. Certainly we cited papers where such examples are found (e.g., refs 22, 24, 25, and 53 in ref 2) such that referring to literature in the subject was not relevant. What we desired to show was that sorption in a glassy phase may be linear, and we used data from the protagonists of the glassy/rubbery concept themselves as befitting this goal (see also response to LeBoeuf (3)). Pignatello and Xing have correctly indicated the trivial fact that uptake in the low concentration (Henry’s law) region may be linear on a glassy phase, denoting yet another reason for linear sorption behavior in a glassy polymer. Linear behavior cannot, however, be explained as a result of plasticization at high concentrations, which would demonstrate sigmoidal (not dual mode model) behavior. Fractional Uptake Analysis. When Pignatello and Xing claim that virtually all experiments show “log (St/Se) to increase progressing from low to high values along the log C axis”, they mistakenly compare sorption at different times for a specific solution concentration. This is not the correct definition for fractional uptake (St/Se). Fractional uptake is determined by following sorbed phase concentration at different times t for the same initial solution concentration and the same solid-to-liquid ratio (4). As we showed in Figures 2 and 4 of our paper (2), there is no trend of fractional uptake as solution concentration increases, and there is no justification for Pignatello and Xing’s assertion that our reanalysis of their data should be dismissed. Their claim that we make a direct correspondence between “fractional uptake (e.g., Xt ) 0.67) and fractional equilibrium (i.e., 0.67 of the time it takes to reach final uptake)” is their own invention; we made no such correspondence. To correctly quote the example from our paper: “Solution and sorbed concentrations can be calculated for fractional uptakes of 30% and 67% (approximately representing 1 min and 1 h uptake data respectively...” out of a total of 14 days to achieve apparent equilibrium (p 3288 (2)). Thus the “flaw” they identified in our analysis is, in fact, a mistake on their part. They and the readers are directed to our response to Weber and Huang (5) for additional discussion of fractional uptake which should lay to rest this erroneous use of trends in Freundlich n values. When Pignatello and Xing repeat the mathematical exercise from our Appendix (2) to show that fractional uptake must be concentration dependent if sorption is nonlinear, they neglect the assumption explicit in this development. The assumption is that the Freundlich model provides an adequate description of both equilibrium and nonequilibrium isotherms. This assumption is examined in our next section. Freundlich Model Fits. Pignatello and Xing do not agree that log-log plots mask poor fits of the Freundlich model to their data and claim that the adequacy of the Freundlich model for their data sets is proved by high R2 values. However, R2 is not a test of model lack of fit. In fact, a significant linear regression can be obtained for a model which demonstrates 10.1021/es992013m CCC: $18.00 Published on Web 07/02/1999
1999 American Chemical Society
FIGURE 1. Residuals (observed log sorption values minus Freundlich model predicted log values) for 24 h sorption data of 2,4dichlorophenol on peat plotted against log equilibrium solution concentration (data from ref 7, provided by Pignatello and Xing). The bell-shaped trend of residuals demonstrates that the Freundlich model does not provide a good fit to the data, despite the R 2 of 0.999.
FIGURE 2. Experimental and computed curves for fractional uptake (St/Se) plotted against equilibrium solution concentration for (A) 2,4-dichlorophenol on peat (1 day/180 days) and (B) 1,3-dichlorobenzene on peat (1 day/30 days). Data provided by Pignatello and Xing, from ref 7. Note the lack of correspondence between the fractional uptake curves for experimental data and the fractional uptake curves computed by using the Freundlich model fits to the data. a significant lack of fit ((6) p 32). Lack of fit is revealed when the ratio between the mean square value for the residuals to the pure error (experimental error) exceeds the tabulated F value. Details of this methodology can be found in ref 6 (pp 26-32). We tested Freundlich model descriptions for 24-h and 180-day 2,4-dichlorophenol sorption on peat (7) for lack of fit (data kindly provided by Pignatello and Xing). The F ratio for the 24-h data was found to be 75 as compared with a tabulated value of 3.07 (95% significance level). The F ratio for 180-day data was 3.15 compared with the same tabulated value of 3.07. In other words, the Freundlich model for both VOL. 33, NO. 16, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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isotherms demonstrated statistically significant lack of fit, despite the impressive R2 values of 0.999! In addition to the lack of fit test, it is strongly recommended to examine residuals. A plot of residuals versus the independent variable for 24-h 2,4-dichlorophenol sorption on peat is shown in Figure 1. The bell-shaped trend in residuals demonstrates clearly the inadequacy of the Freundlich model for describing this data. A third way to examine the adequacy of Freundlich fits is to use reported Freundlich parameters to calculate fractional uptake using eq 8 (Appendix, 2) (rewritten as eq 1 in Pignatello and Xing’s comment). If Freundlich model fits are adequate, fractional uptake using Freundlich parameters should be the same as experimentally determined fractional uptake. Calculated and experimental fractional uptake curves for 2,4-dichlorophenol and 1,3-dichlorobenzene in peat (ref 7, data provided by Pignatello and Xing) are plotted in Figure 2. It is clear that calculated fractional uptake curves do not replicate experimental fractional uptake curves, demonstrating yet a third way that the Freundlich fits do not adequately describe these data sets. Importantly, calculated fractional uptake curves display minimums, with faster approach to equilibrium both at lower and higher concentrations around the minimums. Further discussion of this point is found in ref 5. Thus we conclude that despite the fact that the Freundlich equation has enjoyed long use in soil and environmental science, it may not be used indiscriminately to evaluate sorption kinetics. We close this section by noting that we do not understand why Pignatello and Xing consider the linear isotherm model (plotted with a nonzero intercept?) as the alternative to the Freundlich model in their comment, as we never claimed that such data may be described by a linear model. Mechanisms for Nonlinear Sorption. Pignatello and Xing incorrectly assert that the DOM extracts in (8) were not purified beyond a centrifugation step. In fact, the DOM extracts were filtered twice after centrifugation ((8) p 195). Other observations of nonlinear binding of nonpolar or low polar compounds to DOM include pentachlorobenzene to dissolved humic acid (9) and lindane to fulvic acid (10). Rigid structures in dissolved humic acid (11) should not be considered glassy because glassiness is a characteristic of a phase and not of an individual humic macromolecule or some portion thereof (see also response to LeBoeuf (3)). Concerning their analogy to host-guest complexes, our point in the paper was (and still is) that it is important to distinguish between the complexation ability of an individual macromolecule and sites in a rigid network of a glassy phase. It is not clear to us why Pignatello and Xing believe that the surface of humic substances is strongly reduced when hydrated at room temperature as compared with a dry surface at 77 K. The hydrated warm surface certainly may be more diffuse and labile, but it still exists at the interface, and such a flexible surface may provide a greater capacity for adsorp-
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tion in the interface region than a rigid surface. The debate about surface area not withstanding, Pignatello and Xing misunderstand our point (made previously in refs 12 and 13) concerning penetration of molecules, large and small, into the interior of humic macromolecules. We concur that molecules, large and small, may penetrate into the OM interior (2, 12, 13). We commented simply that on the basis of comparable N2 BET surface areas and Langmuir capacities for large molecules, the exterior surface area cannot be eliminated as the locus of nonlinear sorption for large molecules. Pignatello and Xing contend that a diminution in n(t) is fully consistent with different diffusivities of a compound in rubbery and glassy domains in SOM. However, a diminution in apparent n(t) is also fully consistent with a nonlinear sorption component in a single domain. By definition, a nonlinear sorption component results in a nonproportional shift of the isotherm along the X-axis, resulting in a diminution in apparent n(t). Formally, this diminution in apparent n(t) cannot give direct insights into the effect of concentration on attainment of equilibrium (Figure 2; Figures 2 and 4, (2); Figure 1, (5)).
Literature Cited (1) Pignatello, J. J.; Xing, B. Environ. Sci. Technol. 1999, 33, xxxxxxxx. (2) Graber, E. R.; Borisover, M. D. Environ. Sci. Technol. 1998, 32, 3286-3292. (3) Borisover, M.; Graber, E. R. Environ. Sci. Technol. 1999, 33, xxxx-xxxx. (4) Crank, J. The Mathematics of Diffusion 2nd ed.; Clarendon Press: Oxford, 1975. (5) Graber, E. R.; Borisover, M. Environ. Sci. Technol. 1999, 33, xxxx-xxxx. (6) Draper, N. R.; Smith, H. Applied Regression Analysis; John Wiley & Sons, Inc.: New York, 1968. (7) Xing, B.; Pignatello, J. J. Environ. Toxicol. Chem. 1996, 15, 12821288. (8) Maxin, C. R.; Kogel-Knabner, I. Eur. J. Soil Sci. 1995, 46, 193204. (9) Schlebaum, W.; Badora, A.; Schraa, G.; van Riemsdijk, W. H. Environ. Sci. Technol. 1998, 32, 2273-2277. (10) Tramonti, V.; Zienius, R. H.; Gamble, D. S. Intern. J. Environ. Anal. Chem. 1986, 24, 203-212. (11) Chien, Y.-Y.; Bleam, W. F. Environ. Sci. Technol. 1998, 32, 36533658. (12) Borisover, M.; Graber, E. R. Environ. Sci. Technol. 1997, 31, 1577. (13) Graber, E. R.; Borisover, M. D. Environ. Sci. Technol. 1998, 32, 258-263.
Mikhail Borisover and Ellen R. Graber* Institute of Soil, Water, and Environmental Sciences The Volcani Center, A.R.O. P.O.B. 6, Bet Dagan 50250, Israel ES992013M
