Environ. Sci. Technol. 1996, 30, 3130-3131
Response to Comment on “A Distributed Reactivity Model for Sorption by Soils and Sediments. 4. Intraparticle Heterogeneity and Phase-Distribution Relationships under Nonequilibrium Conditions” SIR: We thank Pedit and Miller for their comments and model simulations. Their work confirms that simplistic first-order mass transfer models and pore/surface diffusion models cannot adequately describe the experimental timedependent phase distribution relationships (PDRs) we observed, thus directly supporting our conclusions. To briefly recap those aspects of our work (1) discussed by Pedit and Miller, a Freundlich-type equation was used to fit sets of rate data for sorption of phenanthrene from solutions of varied initial concentration by several soils and sediments. The resulting PDRs were observed to become increasingly more nonlinear as sorption progressed. As we illustrated in our Figures 3-6 in ref 1, three characteristic stages in the patterns of change of KF(t) and n(t) were distinguishable as functions of time on log-time plots: (i) an initial stage in which n(t) changes only slightly as KF(t) increases; (ii) an exponential stage in which both n(t) and KF(t) change significantly; and (iii) an apparent equilibrium stage that is reached sooner by n(t) than by KF(t). On the basis of our experimental observations, we proposed a three-domain particle-scale model for conceptually describing the distributed sorption reactivities of heterogeneous soils and sediments. The proposed domains are comprised by (i) an exposed mineral domain that includes external surfaces, internal micro and mesoporous surfaces, and the interlayer surfaces of swelling clays; (ii) a highly amorphous, swollen soil organic matter (SOM) domain; and (iii) a condensed, tightly cross-linked SOM domain. We suggested that the exposed mineral and swollen SOM domains are likely to exhibit linear and relatively fast sorption, while the condensed SOM domain will exhibit nonlinear and much slower sorption. We suggested that the observed patterns of change in n(t) and KF(t) were inconsistent with simple first-order rate or porediffusion models; such models would generate at best relatively simple X-type patterns of change having no relatively steady initial stage for n(t) as KF(t) increased, with both parameters attaining their respective apparent equilibrium values at approximately the same time. Figure 1 of the comment by Pedit and Miller presents their simulation using a simple first-order mass transfer model calibrated with the Freundlich parameters we measured for sorption of phenanthrene by the EPA-23 sediment. As observed, the first-order model begins to generate a distinct and nearly symmetric X-shape pattern once sorption is initiated; that is, as soon as KF(t) > 0, which does not occur in the simulation until 20 min or so after the beginning of the hypothetical experiment. Figures 1 and 3 of our original paper (1) illustrate that KF(t) had a value greater than zero as little as 1 min after initiation of the actual experiment. It should be noted further that the constant “predicted” value of n(t) ) 0.727, the equilibrium
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value we reported, is apparently stipulated as an initial condition (i.e., for t ) 0 and KF(t) ) 0) in the Pedit and Miller first order-model simulation. The simulation given in Figure 1 of the Pedit and Miller comment thus demonstrates that a first-order model generates no initial period during which n(t) is relatively constant, at least if one interprets an initial period as one that occurs after sorption begins. These results thus support rather than contradict our remarks. Further, as Pedit and Miller note, the first-order model simulation significantly exaggerates the degree of initial and intermediate stage nonlinearity we observed; in the actual experiment, n(t) attained a value of approximately 0.727 only after about 1000 min had elapsed. Lastly, the model simulation given in Figure 1 of the comment by Pedit and Miller continues to generate an increasingly nonsymmetric X-shape after the trend lines for n(t) and KF(t) cross, but then n(t) abruptly reverses its trend and returns to an apparent equilibrium value at the same time as does KF(t). It is clear that the Pedit and Miller first-order model simulation differs remarkably from what we observed and reported in our paper for the sorbents studied. They state that a surface-diffusion model simulation gave results similar to their first-order model simulation. Pedit and Miller then present a pore-diffusion model simulation in Figure 2 of their comment, asserting that this model also predicts n(t) to be near-constant at 0.86 during an initiation period. Inspection of Figure 2 reveals that n(t) actually begins to decrease immediately as soon as KF(t) > 0. Not only is there again no constancy in n(t) as KF(t) begins to take on values other than the initial condition specified in the model (i.e., KF(t) ) 0 at t ) 0), but the patterns of change in n(t) and KF(t) with time are nearly symmetric. It is to be noted that in this simulation, as in that given by the first-order model, both n(t) and KF(t) reach their respective apparent equilibrium values at precisely the same time. This model simulation thus also fails to capture the patterns of time-dependent change in PDR parameters we reported in our paper. Moreover, as acknowledged by Pedit and Miller, the pore-diffusion simulation, like the first-order simulation, is unable to capture the degree of initial linearity we observed and reported. In concluding our paper, we noted that a pore-diffusion model should be capable of adequate simulations of the sorption behavior of porous sorbents having homogeneous sorption sites of relatively constant sorption energy (1). That argument has since been supported by data from investigations of rates of phenanthrene sorption by bentonite, porous silica gels, and other inorganic nonporous sorbents (2). For example, as noted in Figure 1 of this response, a simple X-type pattern of change in n(t) and KF(t) is observed for bentonite. Not surprisingly, the simple X-type change pattern shown in Figure 2 of the comment by Pedit and Miller mimics the experimental observations shown in Figure 1 of this response. In this case, the rate of sorption of phenanthrene by the interlayer surfaces of the swelling clay is controlled mechanistically by pore transport phenomena and is thus consistent phenomenologically with a pore-diffusion model. This differs distinctly from the behavior of the four soils and sediments we reported in the paper (1) commented on by Pedit and Miller.
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1996 American Chemical Society
FIGURE 1. Changes in PDR coefficients for sorption of phenanthrene by bentonite as a function of log time. Error bars represent (σ. Units for KF(t) are (µg/m2)/(µg/L)n. [After Huang et al. (2)].
FIGURE 2. Changes in PDR coefficients for sorption of phenanthrene by base-extracted EPA-20 soil as a function of log time. Error bars represent (σ. Units for KF(t) are (µg/g)/(µg/L)n.
To further confirm our validity of the three-domain hypothesis, we subsequently base-extracted the highly amorphous swollen SOM from the EPA-20 soil for which we earlier reported PDR results (1). The post-extraction results, shown in Figure 2 of this response, illustrate that removal of the swollen SOM eliminates the initially steady behavior of n(t) as KF(t) increases from its initial value. In other words, we extracted domain II from the EPA-20 soil, allowing the solute to have immediate access to the energetically more heterogeneous domain III. It is likely that soils and sediments that do not manifest initially steady values for n(t) as KF(t) increases from zero (e.g., EPA-15 and EPA-23) already have some exposed domain III SOM near or at their particle surfaces and in direct contact with the solution phase. In summary, the simulations by Pedit and Miller add to the increasing body of evidence suggesting that intraorganic matrix diffusion rather than diffusion within rigid porous mineral structures is primarily responsible for the overall slow rates of sorption commonly observed for heterogeneous soils and sediments. It is our further contention that the even slower rates and frequent apparent hysteresis associated with the desorption of contaminants from soils
and sediments are similarly controlled. This is consistent with the common observation that the longer a contaminant resides (ages) on a soil or sediment, the slower it is to desorb and the more difficult it is to extract. Intraorganic matrix diffusion into increasingly “glassy” regions of domain IIItype SOMs might continue for years or decades after the initial uptake of a contaminant by a soil or sediment. The deeper into domain III diffusion proceeds, the more difficult it is to reverse.
Literature Cited (1) Weber, W. J., Jr.; Huang, W. Environ Sci. Technol. 1996, 30, 881-888. (2) Huang, W.; Schlautman, M. A.; Weber, W. J., Jr. Environ Sci. Technol. 1996, 30 (10), 2933-3000.
Walter J. Weber, Jr.* and Weilin Huang Environmental and Water Resources Engineering Program Department of Civil and Environmental Engineering The University of Michigan Ann Arbor, Michigan 48109-2125 ES962007F
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