Correspondence Comment on “A Distributed Reactivity Model for Sorption by Soils and Sediments. 4. Intraparticle Heterogeneity and Phase-Distribution Relationships under Nonequilibrium Conditions” SIR: In a recent paper, Weber and Huang (1) reported on the sorption of phenanthrene by soils and sediments in well-mixed systems. This contribution is valuable to the literature because it documents the time evolution of the solute phase distribution relationship (PDR) between phenanthrene in solution and that sorbed to natural solid materials. Freundlich model parameters, KF and n, were estimated for each PDR, and the temporal evolution of these parameters was used to support mechanistic interpretations. These data sets provide significantly more information upon which to evaluate rate models than is typically available. We agree with most aspects of this paper, including the importance of the heterogeneity of natural solid materials on the sorption process and the inability of simplistic first-order mass transfer models and diffusion models to describe many experimental observations. The purpose of this comment is to show the expected temporal evolution of estimated Freundlich model parameters for a first-order mass transfer model and a pore diffusion model, assuming a sorption isotherm corresponding to a system similar to one investigated by Weber and Huang. Our intent is to clarify further the limitations of common sorption rate models. One of the four systems that Weber and Huang investigated exhibited an initiation period during which n remained constant. All of the systems had extended periods during which KF and n varied rapidly in time. They suggested that these variations might have occurred because solute accessed a new domain on or within the solid phase. They speculated that the new domain was energetically more heterogeneous and had higher sorption capacities for phenanthrene, as evidenced respectively by a rapidly decreasing n and a rapidly increasing KF. They concluded that their results were fundamentally different from the predictions of any first-order mass transfer model. They also stated that models incorporating a nonlinear equilibrium relationship and one or more first-order reaction rate or diffusion relationships would generate a simple X-type pattern of change in n and KF without the initiation stages they observed for n and KF. We used three common sorption rate models (first-order mass transfer, surface diffusion, and pore diffusion) to determine how these models would predict Freundlich model parameters (i.e., KF and n) to vary in time. Each model assumes homogeneous sorptive properties for the solid phase. The Freundlich model parameters for the sorption of phenanthrene by the EPA-23 sediment reported in Table 2 of Weber and Huang’s paper were used for the
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FIGURE 1. Changes in PDR coefficients for sorption of phenanthrene by EPA-23 sediment as a function of log time predicted by a firstorder mass transfer model.
FIGURE 2. Changes in PDR coefficients for Sorption of phenanthrene by EPA-23 sediment as a function of log time predicted by a pore diffusion model.
simulations. Rate model parameters were selected such that the rate models predicted equilibrium to occur at approximately 14 days, the same time found in Weber and Huang’s experiments. The solids concentration was 0.1 g of sorbent to 30 mL of aqueous solution. We varied initial solute concentrations to yield equilibrium concentrations that covered the same range as shown in Figure 1 of Weber and Huang’s paper. Figures 1 and 2 show the PDR coefficients as functions of log time predicted by these models. The results for the first-order mass transfer model are shown in Figure 1. This approach predicts that n maintains a constant value of 0.727 during the initiation period, varies slightly as KF increases rapidly, and finally reaches a constant value of 0.727 as equilibrium is approached. This modeling exercise demonstrates that a first-order mass transfer rate model does generate an initiation period during which n is constant, although the model predicts much greater initial nonlinearity than was observed experimentally. The model does not generate a simple X-type pattern of change in n and KF. Both of these observations contradict the remarks of Weber and Huang. The results for the surface diffusion model (not shown) are similar to those for the first-order mass transfer model, the only notable difference being that
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1996 American Chemical Society
the variation in n is smaller than that observed for the firstorder mass transfer model. The results for the pore diffusion model are shown in Figure 2. This approach does predict a pattern of PDR coefficients similar to those observed by Weber and Huang. The pore diffusion model predicts that n maintains a nearconstant value of 0.86 during the initiation period, decreases rapidly as KF increases rapidly, and finally reaches a constant value of 0.727 as equilibrium is approached. There are some major differences between the pattern of PDR coefficients predicted by the pore diffusion model and the patterns experimentally observed by Weber and Huang (see Figures 3-6 in their paper). The model predicts a constant n value during the initiation phase. A constant n value during the initiation phase is clearly observed in only one of four data sets of Weber and Huang (see Figure 5 of their paper). Weber and Huang might have observed a constant n value during the initiation phase in the other three systems if it were possible to collect data accurately prior to 1 min. Significant experimental uncertainty would be expected for such data. The other notable difference between the modeling and experimental results is that the experimental data suggest that the PDRs are initially more linear than the pore diffusion model predicts. Additional shortcomings of the pore diffusion modeling approach have been discussed elsewhere (e.g., refs 2 and 3). The simple pore diffusion model predicts that Freundlich model parameters approach their ultimate equilibrium values at about the same time, which is consistent with the results shown in Figure 5 of Weber and Huang. However, Figure 3 of Weber and Huang suggests that n reaches its ultimate value before KF. All of the models predict a rapid increase in KF after an initiation period even though the models assume the
sorbent to be homogeneous with respect to sorption capacity (i.e., KF). These model predictions contradict Weber and Huang’s remark that a rapidly increasing KF indicates that solute is accessing domains with higher sorption capacities. The pore diffusion model predicts a rapid decrease in n after an initiation period even though the model assumes the sorbent to be homogeneous with respect to sorption energy (i.e., n). This model prediction contradicts Weber and Huang’s remark that a rapidly decreasing n indicates that solute is accessing domains that are energetically more heterogeneous. These observations aside, we agree with Weber and Huang’s comments that soils and sediments are best viewed as having multiple domains with different sorptive properties and mass transfer processes. Such diversity makes it difficult to model sorption processes accurately at the laboratory scale with the simple models discussed above.
Literature Cited (1) Weber, W. J., Jr.; Huang, W. Environ. Sci. Technol. 1996, 30, 881-888. (2) Ball, W. P.; Roberts, P. V. Environ. Sci. Technol. 1991, 25, 12371249. (3) Pedit, J. A.; Miller, C. T. Environ. Sci. Technol. 1994, 28, 20942104.
Joseph A. Pedit* and Cass T. Miller Department of Environmental Sciences and Engineering University of North Carolina Chapel Hill, North Carolina 27599-7400 ES960440J
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