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Comment on ‘‘Application of PermeantlPolymer Dhsional Model to the Desorption of Polychlorinated Biphenyls from- Hudson River SIR The paper by Carroll et al. (1)modeled desorption of PCBs from historically contaminated sediments by radial diffusion where the labile phase was conceptualized as a swollen polymer and the nonlabile phase as a condensed polymer. While previous researchers have rationalized similar experimental data by invoking either particle size distributions, variable partition coefficients, variation in tortuosity of particle pores, and/or disaggregation/ aggregation of particles, this work succeeds in adding to this list variable diffusivities (amongorganic phases). This paper should stimulate much interest in how modelers through calculation or experimentation arrive upon diffusion coefficients (D) and diffusional lengths. We wish to comment on three issues that either support their conclusions or shed some light on their results. First, Carroll et al. utilize several equations proposed by Salame (2) to estimate the diffusion coefficients for PCBs in swollen and condensed humic polymers using an estimated Permachor value of 50 cal/mL (note that Table 2 in ref 1has a typographical error for the value of Y for the condensed phase; however, all subsequent calculations are correct, Y = 337 cclmol). This value of 50 cal/mLwas arrived at by showing that the Permachor value is quite invariant over the range of solubility parameters calculated for humic materials by various researchers. The scatter of experimental data around this value suggests the Permachor value may range anywhere from 30 to 60 cal/mL. Although the extremes within this range remain within a factor of 2, the diffusion coefficients calculated with these extremes differ by over 3 orders of magnitude because of exponential terms in Salame’sequations. For example, a Permachor value of 30 cal/mL results in values for D of 2.5 x and 5.64 x 10-l8 cm2/s for the swollen and condensed phases, respectively, as opposed to values of 2.6 x and 7.3 x cm2/sused by the authors. From these values, they calculated sphere equivalent diameters (dlon the order of 30 nm (about the length of 200 carbon-carbon bonds). The lower values of D result in more reasonable estimates of d, equal to about 1pm. As the covariance between these parameters (D and d) within their model is unambiguous, another estimation approach must be used. One such approach may be to estimate d directly from an approximation of the surface area and volume for the organic material. The volume is easily estimated from the density and mass, whereas the surface area, again, is difficult to characterize under environmentally relevant conditions (3, 4 ) . Chiou etal. (3)have measured the surface area of natural organic materials at the temperature of liquid nitrogen; however, such extreme conditions may vastly alter the structural character of the polymeric material. Removing the water from around spherical rubbery polystyrene/ butadiene latex beads, for example, results in their deformation and compaction into a film, and as we will discuss, temperature directly affects the form of polymeric material.
0013-936x/95/0929-0283$09.00/0
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In the end, the heterogeneity of sediment and soil particles makes any such geometric description an empirical modeling tool, yet one we are obligated to define if we assume a diffusive process. Second, eq 3 in the paper by Carroll et al. describes Fickian diffusion in spherical geometry assuming a constant boundary condition at the particle surface of zero concentration (analogous to diffusion to an infinite bath). Berens (5) states that a prerequisite for the use of his equation is “the demonstration that the chosen experimental conditions produce Fickian behavior with a sample known to have a uniform particle size;without this evidence, it might be impossible to distinguish particle-size distribution effects from a contribution of non-Fickian sorption”. Carroll et al. have characterized the nonlabile portion of the sediment organic matter as a condensed polymer, which further calls into question the appropriateness of always assuming only Fickian diffusion occurs in sediment or soil organic matter. It is well-established that diffusion in glassy polymers can be a function of time, concentration, or both, with high solute concentrations effectively swelling the polymer to a rubbery state. Similarly, glassy to rubbery transitions may result from temperature shifts. Hence, this begs the question: Do changes in conditions of temperature and solute concentration result in “glassy” to “rubbery” transitions of diageneticsediment and soil organic materials resulting in variation in the proportion of (organic) mass to which “labile”versus “nonlabile”sorption is associated (i.e.,this size of each compartment)? Such changes possibly may occur even during extended experiments where large changes in solute concentration occur, such as in the author’s desorption experiments for the sediments containing initially 205 mg/kg PCBs (see Figure 6 in ref 1).In such experiments, an unrestricted division of material as either “condensed” and “swollen” may be not totally appropriate. As noted in the paper, these transitions are also consistent with the more rapid release of PCBs from the heated (and subsequently cooled) sediments. Third, Carrol et al. observed that a disproportionate amount of ortho-chlorinated congeners appear to reside in the “labile”phase, as evidenced by the more rapid rate of desorption compared to other congeners. A n analogous observation was noted by Vogt and Jafvert (unpublished data), who conducted gas purge experiments with sediments historically contaminated with DDT. When comparing their results to a unidirectional diffusion model (diffusionfrom a finite plane), they found that model results utilizing data obtained over a 50-day period resulted in underestimating the removal of the degradation products DDE and DDD at short time periods and overestimating the removal of DDT at short time periods. These observations are very significant as they suggest, for field samples, that very hydrophobic compounds are not uniformly distributed even within the same particle due to reaction and/or transport. In the box model utilized by Carrol et al., the initial concentration of chemical in each portion (condensed and swollen) is easily adjusted. In models where a single diffusion coefficient is assumed, this phenomenon similarly may be accounted for by assuming an initial concentration profile within the particles and would require solution by numerical methods. The as-
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sumption of an initially uniform solute concentration prolile 1 (2) Salame, M. Polym. Eng. Sci. 1986, 26, 1543-1546. (3) Chiou, T.C.; Lee, J.-F.;Boyd, S. A. Environ. Sci. Technol. 1990, often has resulted in lower than expected calculated 24, 1164-1166. diffusion coefficients when modeling experimental data. (4) Bower, C. A.; Gschwend, F. B. Soil Sci. Proc. 1952, 16, 342. The same may be said of weakly sorbed compounds that (5) Berens, A. R.; Huvard, G. S.J. Disp. Sci. Technol. 1981,2,359387. are more highly reactive. In conclusion, these comments are made to corroborate some of the merits of the authors’ modeling approach and Lorin W.Phillips and Chad T. Jafvert* the significance of their results. Department of Civil Engineering Purdue University literature Cited West Lafayette, Indiana 47907 (1) Carroll, K. M.; Harkness M.R.; Bracco, A. A.; Balcarcel, R. R. Environ. Sci. Technol. 1994, 28, 253-258.
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