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Response to ‘Weber and Huang’s Comments on “Evaluation of the Glassy/Rubbery Model for Soil Organic Matter”’ SIR: The comments of Weber and Huang (1) contain no concrete criticisms, rather they consist mainly of deplorable insults which can serve only to detract seriously from enlightened scientific discourse. Nevertheless, we invite them to consider the following: 1. Fractional uptake, defined as the ratio of sorbed concentration at any time (St) to equilibrium sorbed concentration (Se) for a given initial solution concentration, can be used to examine rate of attainment of equilibrium in the solid phase. This approach is suitable for finite and infinite bath systems and for systems exhibiting nonlinear sorption uptake isotherms (e.g., sections 10.6.5 and 14.2.1 in ref 2), assuming that all rate limiting processes occur only inside the solid phase. As the system is at fixed temperature, external pressure and water activity (dilute solution), solid-phase concentration shows the deviation of the system from equilibrium. Hence, kinetics of attainment of equilibrium in the solid phase gives kinetics of attainment of equilibrium in the overall system. Weber and Huang (1) were unable to demonstrate any flaws in this fractional uptake analysis. From our plots of fractional uptake against time in Figures 2 and 4 of ref 3, it is clear that rate of attainment of sorbed phase equilibrium was not concentration-dependent. What then may be concluded from the fact that experimentally determined attainment of equilibrium did not show any concentration dependence, on one hand, and that sorption is nonlinear, on the other? This apparent contradiction is the crux of this particular conflict. The solution to this conundrum may be found in different mechanisms. First, a nonzero diffusivity for immobilized sorbate molecules may reduce the effect of concentration on the effective diffusion coefficient (Deff) (4). Second, noninstantaneous achievement of local equilibrium may not have a straightforward effect on concentration dependence of Deff. Third, quality and reproducibility of experimental data may mask concentrationdependent Deff. Crank himself noted that experimental sorption data frequently do not demonstrate a concentration effect on rate of sorption uptake, despite the fact that D is concentration dependent: “If D increases as concentration increases, the shape of the sorption curve when plotted against time is not very sensitive to the form of the diffusion coefficient. It is often not significantly different from the corresponding curve for constant diffusion coefficient.” ((2), pp 182-183). We can calculate maximal possible concentration effects on Deff for a solute sorbed in partitioning and Langmuir modes in a nonswelling sorbent according to the dual mode model equation (4)
DD e Deff e DD 1+K
(1)
where DD is the diffusion coefficient for partitioning mode species and K is capacity of Langmuir holes multiplied by affinity, divided by partitioning mode distribution coefficient. As an example, we compute the full range of possible concentration effect on Deff using dual mode model parameters for 1,3-dichlorobenzene and atrazine in peat and for * Corresponding author email:
[email protected]. 10.1021/es9920056 CCC: $18.00 Published on Web 07/02/1999
1999 American Chemical Society
atrazine in soil (5). Values for (1 + K) are found to be 3.16, 2.18, and 2.02 for these systems, respectively. We suggest that a concentration effect of this order may be masked by experimental error, as is apparently the case for the data of Weber and Huang (6) and Xing and Pignatello (5). 2. Weber and Huang do not agree that log-log plots mask poor fits of the Freundlich model to their data and claim that adequacy of the Freundlich model for their data sets is proved by high R 2 values. They apparently fail to realize that R 2 is not a test of model lack of fit and that a significant linear regression can be obtained for a model which demonstrates a significant lack of fit ((7), p 32). Weber and Huang are advised to consult Draper and Smith (7) for a statistical lack of fit methodology they may use to evaluate their 500+ isotherms. The statistical method is based on comparing experimental error with the difference between predicted and observed values. Weber and Huang are also referred to our response to Pignatello and Xing (8) where they will find examples of Freundlich model fits to actual data sets from ref 5 which have R 2 values of 0.999 and yet demonstrate significant lack of model fit. To demonstrate the fundamental mistake in using the Freundlich exponent n for concluding that apparent equilibrium is achieved faster in higher concentration solutions (6), we solve numerically the mass balance equation for fractional uptake (eq 8, Appendix; ref 3), for reported Freundlich parameters for EPA-23 sediment (1 h, 1 day, 14 days, 368 days) (6, 9) and the reported solid:liquid ratio (6). Curves of fractional uptake as a function of initial solution phase concentration (Figure 1A) and of sorbed phase concentration (Figure 1B) exhibit minimums, with greater fractional uptake (greater approach to apparent equilibrium) both at lower and higher (initial or sorbed) concentrations around the minimums. This result, based on reported Freundlich parameters, thus contradicts Huang and Weber’s conclusions that (i) they observed faster approach to equilibrium from higher initial concentration solutions (6, 9); (ii) they observed an increase in overall apparent rate of sorption as solid-phase concentration increased (9); and (iii) decreasing trends in Freundlich n with increasing time reflect a faster approach to equilibrium in higher concentration solutions (6, 9). Thus the methodology of Weber and Huang is internally inconsistent, and such naive considerations of trends in exponent n cannot be used to conclude anything about concentration effect on attainment of equilibrium. Other examples of fractional uptake curves with minimums generated from Freundlich model fits can be found in our response to Pignatello and Xing (8). The correction (10) to some errors in ref 11 by Weber and Huang was published nearly 5 months after our paper (3). Readers may draw their own conclusions concerning who has crossed “the bounds of intellectual probity and professional propriety”. For Weber and Huang’s future reference, we draw their attention to the fact that there are additional mistakes in tabulated Koc values for Norwood kerogen at all designated Ce values (or errors in tabulated elemental composition). If we simply accept the published values for hysteresis index and log Koc, assuming that a log analysis will render such errors relatively unimportant, then we must point out that the inverse correlation of phenathrene log Koc with O/C atomic ratio (11) can in no way be considered definitive. The data easily may be interpreted to show distinct log Koc values for old and young organic matter, with a sharp discontinuity between them (Figure 7, ref 11). As the “hysteresis index” merely demonstrates that kinetics of phenanthrene uptake by geologic material was slower than VOL. 33, NO. 16, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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to Weber and Huang’s own work with phenanthrene, any such underestimation will be no more than a factor of 2-10 (9), and almost certainly less for the smaller trichloroethylene molecule, which will have little effect on Figure 3 of ref 3. To conclude, Weber and Huang would have served their cause much better had they responded intelligently to our arguments rather than hurl baseless insults in a manner unbecoming to members of the scientific community.
Literature Cited
FIGURE 1. Fractional uptake (St/Se) for Freundlich parameters reported for phenanthrene sorption on EPA-23 sediment (data for time t ) 1 h, 1 day, and 14 days) (6, 9) as a function of (A) initial solution phase concentration and (B) sorbed phase concentration. Sorbed amount at equilibrium (Se) is taken to be sorbed amount at 368 days (9). by young material, its particular merit beyond the kinetic study itself is unproved. 3. Weber and Huang are apparently unaware that trichloroethylene is only very weakly polar with a dipole moment of 0.95 D (12). Perhaps they would also consider such compounds as chlorobenzene (1.69 D), m-dichlorobenzene (1.72 D), and dichloromethane (1.6 D) to be polar (dipole moments from ref 13). They may refer to previous work where we demonstrated that trichloroethylene does not undergo specific hydrogen bonding interactions with soil organic matter (14). The possible effect of using 1 day sorption data (reported as apparent equilibrium (15)) for trichloroethylene is that Koc for old geologic materials may be underestimated if slow sorption kinetics exists for trichloroethylene. According
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(1) Weber, W. J., Jr.; Huang, W. Environ. Sci. Technol. 1999, 33, xxxx-xxxx. (2) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, 1975. (3) Graber, E. R.; Borisover, M. D. Environ. Sci. Technol. 1998, 32, 3286-3292. (4) van Krevelen, D. W. Properties of Polymers; Elsevier: Amsterdam, 1990. (5) Xing, B.; Pignatello, J. J. Environ. Toxicol. Chem. 1996, 15, 12821288. (6) Weber, W. J., Jr.; Huang, W. Environ. Sci. Technol. 1996, 30, 881-888. (7) Draper, N. R.; Smith, H. Applied Regression Analysis; John Wiley & Sons: New York, 1968. (8) Borisover, M. D.; Graber E. R. Environ. Sci. Technol. 1999, 33, xxxx-xxxx. (9) Huang, W.; Weber, W. J., Jr. Environ. Sci. Technol. 1998, 32, 3549-3555. (10) Huang, W.; Weber, W. J., Jr. Environ. Sci. Technol. 1999, 33, 972. (11) Huang, W.; Weber, W. J., Jr. Environ. Sci. Technol. 1997, 31, 2562-2569. (12) Djerassi C.; Schneider R. A.; Vorbrueggen, H.; Allinger, N. L. J. Org. Chem. 1963, 28, 1632. (13) CRC Handbook of Chemistry and Physics, 58th ed.; CRC Press: 1977-1978. (14) Borisover, M. D.; Graber, E. R. Chemosphere 1997, 34, 17611776. (15) Grathwhol, P. Environ. Sci. Technol. 1990, 24, 1687-1692.
Ellen R. Graber* and Mikhail Borisover Institute of Soil, Water, and Environmental Sciences The Volcani Center, A.R.O. P.O.B. 6, Bet Dagan 50250, Israel ES9920056
