Environ. Sci. Technol. 1999, 33, 2204-2212
Determining PCB Sorption/ Desorption Behavior on Sediments Using Selective Supercritical Fluid Extraction. 2. Describing PCB Extraction with Simple Diffusion Models K A R O L P I L O R Z , * ,† E R L A N D B J O ¨ RKLUND,† SØREN BØWADT,‡ LENNART MATHIASSON,† AND STEVEN B. HAWTHORNE§ Department of Analytical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden, VKI, Agern Alle´ 11, DK-2970 Hørsholm, Denmark, and Energy and Environmental Research Center, University of North Dakota, Grand Forks, North Dakota 58202-9018
A simple diffusion model is fitted to selective SFE profiles obtained in Part 1 for native (not spiked) PCBs in historically contaminated sediments and soils. The model takes two types of geometry into consideration, a spherical one (Hot Ball, HB) and a planar one (Finite Slab, FS) and is extended to describe the influence of increasing temperature during the extraction. In this work, soil/ sediment organic matter (SOM) is treated as a polymerlike organic material (POM). Consequently, diffusion is considered to be an activated process where the diffusion coefficients depend on the temperature according to the Arrhenius equation. When using one type of POM in the model, the characteristic “temperature humps” obtained in the extraction profiles are simulated relatively well, but at least three types of POM are needed for excellent fits to experimental data. The final model, consisting of three different POMs with spherical geometry, was fitted to all matrixes to estimate diffusion coefficients and activation energies. These data correlated with relevant literature values obtained from long-term water desorption experiments, indicating that it might be possible to replace these experiments with rapid SFE to characterize soils and sediments and to predict the rate of release of pollutants under field conditions.
Introduction In part 1 of this series of papers (1), a new method using supercritical fluid extraction (SFE) with a temperature step gradient is utilized to characterize the relative ability of soils and sediments to bind organic pollutants. Extraction profiles for between five and nine native (not spiked) PCBs in four * Corresponding author on leave from Physical Chemistry Department, MCS University, 20 031 Lublin, Poland; e-mail address:
[email protected]; fax: +48 81 5333348; tel: +48 81 5375671. † Lund University. ‡ VKI. § University of North Dakota. 2204
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historically contaminated sediments and one soil were obtained. From these data, it seems as if water desorption experiments normally extending over time periods of several months (2, 3) can now be performed in only a few hours using SFE. The ultimate goal of this type of investigation is to predict the release of organic contaminants from soils and sediments at given natural conditions. The problem of connecting model parameters obtained in SFE experiments with desorption processes occurring under natural conditions is left open for further investigations. To describe the slow release and uptake of hydrophobic organic contaminants (HOC), many processes could be taken into consideration (4-6). Several independent researchers suggest that diffusion might be the slowest of these processes, thus having a profound influence on the extraction behavior of soils and sediments (3, 7-9). Recent studies propose that there exists at least two different types of polymer-like organic material (POM), the “soft or rubbery” and the “hard or glassy”, within soil/sediment organic matter (SOM) (5, 6, 10). It is interesting to note the similarity between the physical background proposed to describe the different extraction kinetics for spiked vs aged contaminants in SFE (11-13) and the processes suggested to cause the slow sorption of HOC to natural soils and sediments as discussed above. Despite these similarities, very few papers have been devoted to linking supercritical fluid behavior to sorption/desorption of HOC under natural conditions. Some initial investigations have been presented by Hawthorne (14), Bjo¨rklund (15), and Bøwadt (16), laying the groundwork for utilizing supercritical carbon dioxide as a test medium for environmentally relevant desorption reactions. This discussion has recently been continued in two SFE papers (17, 18) that were part of a long series of publications. In the first paper from 1992 (19), a “distributed reactivity model” including instantaneous partitioning (linear part) and Freundlich isotherms (nonlinear part) was presented. Later, the polymer nature of SOM was realized and a “dual reactive” (20) and “treble reactive domain model” (21) was introduced, taking into consideration the partitioning into “condensed” SOM. They also suspected slow diffusion in “condensed glassy” SOM to cause sorption/ desorption hysteresis (22). Transport of molecules in polymers is strongly influenced by the physical state of the polymer, i.e. whether it is glassy or rubbery. This depends on both temperature and uptake of solvents that can cause swelling. The glass transition temperature can be substantially decreased by swelling as demonstrated by Weber, where water decreased the transition temperature by 19 °C down to 43 °C for SOM (20). High solubility of subcritical carbon dioxide in PVC at 25 °C and 64 bar (8 wt %) has been demonstrated (23), and since carbon dioxide is very effective in lowering glass transition temperature, it was shown to lower this temperature for PVC from 85 to 30 °C. The influence in supercritical conditions should be even more pronounced as higher pressures are involved. An important effect of polymer swelling is an increase in diffusion coefficients for both solvent molecules and other substances present in the matrix. Carbon dioxide, for example, caused an increase in the diffusion coefficient for plasticizers such as dimethyl phthalate in PVC by several orders of magnitude (24). Since diffusion seems to be important in the interpretation of results obtained from sorption/desorption experiments, we are encouraged to use a model including only the diffusion process in organic matter to describe the release of contaminants from sediments during selective SFE. Other processes involved in the molecular transport are considered 10.1021/es981075u CCC: $18.00
1999 American Chemical Society Published on Web 05/20/1999
to be much faster and are neglected. The concentration of PCBs in supercritical CO2 is assumed to be low enough to allow the usage of a very simple formula for the diffusion calculations. In this paper, an extended version of such a simple diffusion model, applied on SFE profiles by Bartle et al. in 1990 (25), is presented. The main difference as compared to the original model is that the temperature step gradient during the course of the extraction is taken into consideration. It has been proposed that up to three different compartments (domains) might govern the sorption/desorption of HOC on soil/sediment particles (8, 9). To check if an increasing number of compartments in the model improves the fitting to experimental data, up to three different types of POM have been used in this paper. A model consisting of several types of HB has previously been used to determine particle size distribution of polymer powders by analysis of their sorption/desorption kinetics of organic vapors (26). This model was later used to describe desorption of PCBs from soil into water (3) over time periods up to 12 months. This is in great contrast to the 4 h of supercritical fluid extraction needed to obtain the profiles presented here. It may seem strange to imagine all organic matter in soil in the form of balls, as in the hot ball model. However, this model also describes diffusion from any conical cut of a sphere, provided the walls are converging to the center and are impenetrable for diffusing molecules. Pores in the mineral skeleton of soil filled with SOM might be described in this way. Another possible type of pore structure is a channel with parallel, impenetrable walls that is described by the finite slab model. If the channel is open at both ends, only half of its length is taken as the slab thickness. The hot ball and the finite slab models are two extremes; the “easy” and the “hard” one, when considering the influence of the geometry of the system on the speed of extraction. It is possible to imagine a system with a still more “difficultto-extract” geometry like a hollow sphere. However, such a model involves an additional parameter, i.e., the ratio of POM layer thickness and the sphere radius. A basis for the choice of a particular value of this ratio can hardly be found. Moreover, this model becomes very similar to the finite slab when the above-mentioned ratio is small. In the model proposed in this paper to describe the extraction profiles, the organic matter is considered to be a polymer-like substance, and the diffusion is expected to be an activated process obeying the Arrhenius equation (3). The above assumptions are necessary for the description of the influence of temperature on the extraction process.
Materials and Methods Sample. In this paper, extraction profiles obtained for between five and nine native (not spiked) PCB congeners in four sediments and one soil were used. These profiles were presented in detail in part 1 (1) for river sediment SRM 1939 (National Institute of Standards and Technology, [NIST], Gaithersburg, MD), marine sediment SRM 1944 [NIST], harbor sediment CRM 536 (Community Bureau of References (BCR), Brussels, Belgium), freshwater sediment Ja¨rnsjo¨n (Sweden), and industrial soil CRM 481 (BCR). The materials can be divided into two groups in terms of PCB contamination level; low and highly contaminated samples (Table 1 of ref 1). The first contains SRM 1944, CRM 536, and Ja¨rnsjo¨n with congener concentration ranges of 25-80, 13-50, and 2-50 ng/g, respectively. The second group contains SRM 1939 and CRM 481 with congener concentration ranges of 100-4000 and 3000-137 000 ng/g, respectively. Extraction Conditions. The kinetic profiles were obtained using four sequentially stronger SFE conditions, each 1 h for a total of 4 h, as described earlier (1). SFE conditions were 120 bar, 40 °C (first hour); 400 bar, 40 °C (second hour); 400 bar, 100 °C (third hour); and 400 bar, 150 °C (fourth hour).
Eight fractions were collected every hour after 5, 10, 15, 20, 30, 40, 50, and 60 min. Nomenclature. The model is called the single, double, or triple POM model depending on the number of polymerlike organic material compartments involved. Two types of geometry of POM have been compared: the spherical ones the hot ballsand the planar onesthe finite slab. When necessary, the geometry of POM was specified in the model name by replacing POM by a particular geometry abbreviation, e.g., the triple HB model. Calculations. All calculations and graph plotting were performed in Excel97 for Windows95 (Microsoft Corporation, Redmond, WA). The Solver option (Frontline Systems Inc., Incline Village, NV) available with this software was used to minimize the sum of the squared deviations. The quality of the fit is presented as a relative standard deviation (RSD) calculated as a ratio of the square root of the minimized sum divided by the number of degrees of freedom (number of points minus number of parameters fitted) and the mean value of the recovery. The number of parameters fitted depends on how many types of POM are included in the model used. Every type of POM needs three parameters: the initial amount of a pollutant in the particular POM, the diffusion coefficient at 40 °C divided by the squared diffusion path length (D/a2 (s-1)), and the diffusion activation energy (E (kJ/mol)). For a more convenient presentation of the results, the contribution of a certain pollutant from a single POM to its total recovery (m0 (ng/g)) is expressed as a ratio x. Obviously, multiplication of x with m0 will give the initial amount of a pollutant present in a specific POM. Two additional parameters, tsh and f1 (which are discussed in detail below) are necessary. This means that the single POM model only needs 5 parameters, while the double and triple POM models need 8 and 11 parameters, respectively. Mathematical details of the model are given in the Appendix.
Results and Discussion Solubility Considerations and the Hot Ball Model. The basis for this paper is the hot ball model (25), which assumes that the analytes reaching the bulk supercritical fluid never reach the solubility limitations. None of the profiles presented here seem to be limited by solubility. The PCBs in CRM 481 (the most highly contaminated matrix used) most closely match Arochlor 1260. PCB-153 is a major component of Arochlor 1260 and constitutes nearly 10% of this PCB mixture (27). If all PCB-153 present in CRM 481 were completely dissolved in 2 mL of carbon dioxide (estimated volume of fluid inside the extraction cell) at 40 °C and 120 bar, the concentration would be about 50 ppm. This is below the solubility limit of another hexachlorobiphenylsPCB-128 (90 ppm at the same conditions) (28). Although the solubility of PCB-153 could differ from that of PCB-128, the estimated concentration of 50 ppm is never reached since PCB-153 is extracted for 4 h with an estimated total volume of carbon dioxide of 400 mL (measured at the pump). The maximum concentration reached in the effluent was below 2 ppm (7 µg eluted in the 15-20-min fraction during the first hour in the profile). Of course, the local concentration close to the surface of POM is important for the diffusion process, but there is no way to directly measure this concentration. It should be stressed that CRM 481 is extremely contaminated, and for all other sediments the maximum effluent concentration reached is several times lower. Another argument supporting that there are no solubility limitations is the similar shapes of the extraction profiles obtained for the most polluted material, CRM 481, and the relatively low contaminated sediment, CRM 536, which contains 103 times less PCB. Reduced Time and Concentration Profiles. Sketches of the POM according to the hot ball and the finite slab models are presented in Figure 1. VOL. 33, NO. 13, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Time Needed for 50% Extraction of a Target Compound from POMs with Different D/a2 Ratio for Two Different Models, the Hot Ball (HB) and the Finite Slab (FS) D/a2 (s-1) 10-2
FIGURE 1. Schematic pictures of the POM according to the hot ball (a) and the finite slab (b). The radius of the ball and the thickness of the slab are marked by the letter “a”. The gray color depicts organic matter while the black in panel b represents the impenetrable bottom. The diffusion proceeds in the direction indicated by the arrow.
FIGURE 2. Concentration profiles, i.e., concentration of a pollutant vs distance from center of the ball or bottom of the slab for two different times. Concentration and distance are expressed as dimensionless variables. The diffusion process is governed by a dimensionless quantity, reduced time (tr), defined as follows:
tr )
D t a2
(1)
where D is the diffusion coefficient, t is time, and a is the diffusion path length in the system, i.e., radius of the ball or the thickness of the slab. In Figure 2, concentration profiles calculated for different values of the reduced time for both the hot ball and the finite slab models are presented. It is assumed that the molecules diffusing out of the POM are removed very fast from the POM surface, whereby the PCB concentration at the surface can be set to zero. For a short time period (tr ) 0.01), the two models do not differ to any great extent. This can be expected, since the slab geometry is suitable for description of diffusion in any system for very short times, considering that only molecules close to the surface manage to leave the organic matter. However, already at this early stage it is visible that the extraction rate from a ball is large. Assuming the same surface area of the balls and the slab, the total flux of PCB is almost the same for short time periods. However, the recovery is three times higher for the balls because the volume of the balls, and consequently the initial amount of PCB, is three times smaller. The longer time period (tr ≈ 0.20) is chosen to give 50% recovery for the FS model. The same time period gives a 92% recovery for the HB model. When comparing the time necessary to obtain equal recovery, the two models give results that are even more different. For very short time periods, the extraction from the balls is 9 times faster than from the slab, while very long time spans give an extraction rate that is only 4 times faster. These results follow from eqs A.5 and A.6 in the short and long time limit, respectively. A recovery of 50% is obtained for times between these two 2206
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1.0 × 1.0 × 10-3 1.0 × 10-4 1.0 × 10-5 1.0 × 10-6
HB
D/a2 (s-1)
FS
HB
FS
10-7
3.1 s 19.7 s 1.0 × 3.5 day 22.8 day 0.5 min 3.3 min 1.0 × 10-8 35.4 day 0.6 yr 5.1 min 0.5 h 1.0 × 10-9 1.0 yr 6.2 yr 0.8 h 5.5 h 1.0 × 10-10 9.7 yr 62.4 yr 8.5 h 2.3 day
TABLE 2. Temperature Dependence of the Diffusion Coefficient D/D40 (D40 for 40 °C) at temp (°C) Ea (kJ/mol)
10
25
40
100
150
10 20 30 40 50 60 70 80 90 100 110 120 130
0.67 0.44 0.30 0.20 0.13 0.09 0.06 0.04 0.026 0.017 0.011 0.008 0.005
0.82 0.68 0.56 0.46 0.38 0.31 0.26 0.21 0.18 0.14 0.12 0.10 0.08
1 1 1 1 1 1 1 1 1 1 1 1 1
1.9 3.4 6.4 11.8 21.9 40.7 75.4 139.8 259.3 480.9 891.7 1653.6 3066.4
3 7 20 54 147 400 1085 2943 7988 21679 58836 159680 433366
extremes, where the extraction from a ball is about 6.4 times faster than from a slab (see Table 1). The D/a2 ratio has a large influence on the extraction rate. This is illustrated in Table 1, where the times needed to extract 50% of a pollutant from a sediment are given for both the ball and the slab geometry. The range of these ratios corresponds to extraction times extending from seconds to decades. The calculations are based on numerically found reduced times for 50% recovery equal to 0.03055 and 0.1967 for HB and FS, respectively. Influence of Temperature on the Diffusion Coefficient. Once the impact of D/a2 ratio on the extraction time has been shown, the effect of temperature should be considered. In accordance with the assumptions discussed above (polymer-like nature of SOM), the temperature will influence the diffusion process in SOM according to Arrhenius equation:
D ) D0 exp(-Ea/RT)
(2)
where Ea is activation energy, R is the gaseous constant, T is the absolute temperature, and D0 is the diffusion coefficient obtained when extrapolating to very high temperatures. Table 2 illustrates the large changes in the diffusion coefficient with temperature. Even with an activation energy as low as 80 kJ/mol, the diffusion constant changes with more than a factor of 100 from 40 to 100 °C. This will of course dramatically change the extraction rate. For example an increase in the D/a2 ratio in Table 1 from 10-6 to 10-4 s-1, due to this change of temperature, would alter the extraction time according to the FS model from 2.3 day to 0.5 h. The activation energies in Table 2 have been chosen not to be extreme; however, it should be noted that in the paper by Carroll et al. (3) even higher activation energies are postulated for PCB diffusion in swollen (221 kJ/mol) and condensed (192 kJ/mol) organic matter. Obviously, with these values of activation energy, the impact of the temperature on the extraction process would be even more pronounced. It should be mentioned here that Carroll’s results are obtained at 25 °C for sorption from water, where condensed organic matter probably exists in a glassy state. During supercritical
FIGURE 3. Temperature “hump” for one HB modelsrecovery vs time. Parameters: m0 ) 3000 ng/g, D/a2 ) 6 × 10-6 s-1, E ) 35 kJ/mol, temperature rise from 40 to 100 °C. fluid extraction, it is more likely that the POM is in a rubbery state. Obviously, the glass transition is not taken into consideration in the calculations made for Table 2. Origin of Temperature Humps. The next thing to consider is the effect of an increase in temperature during the time of an extraction. If the rise in temperature is fast, the concentration profile does not change markedly. Therefore, the reduced time is not affected, while the diffusion coefficient is increased. This means that an extraction at an elevated temperature will take a much shorter time to reach the same yield of extracted analytes that has been reported for SFE of PCBs (29). In Figure 3, an example of such a situation is presented for the HB model. The parameters needed for the calculations are chosen to produce an extraction profile comparable to the experimental profiles presented below. At a certain time, ts ) 120 min, the temperature is suddenly increased from 40 to 100 °C. The broken line shows the course of the extraction if it were performed at the elevated temperature (100 °C) and was started about 106 min later, i.e., the recovery values obtained after 120 min of extraction at 40 °C would be obtained with 120 - 106 ) 14 min of extraction at 100 °C. The dotted line shows a continued extraction at the lower temperature (40 °C). The postulated lack of influence of a fast temperature rise, on the actual stage of diffusion, can be mathematically expressed as follows:
Dts ) Detes
(3)
where D denotes the diffusion coefficient at the lower temperature, superscript e denotes an elevated temperature, and tes denotes the temperature step time in the new elevated time scale. After the temperature step, the time for the diffusion process can be calculated according to
D te ) t - ts + ts e D
(4)
The actual origin of humps in the extraction profiles is the change of the diffusion time scale caused by the increase in temperature-dependent diffusion coefficients. If more than one temperature rise is generated during the extraction, the procedure of changing the time scale has to be repeated. Fitting of Single and Double SOM Models to Experimental Data. The extraction profiles presented in part 1 (1) show two features that cannot be explained by the simple diffusion model presented by Bartle et al. (25). The features are (i) slow extraction at the beginning of the profile ( 60 kJ) for PCBs in one material only, namely, SRM 1939. The obtained values for the diffusion activation energies for low contaminated materials (SRM 1944, CRM 536, and Ja¨rnsjo¨n) and for highly contaminated materials (SRM 1939 and CRM 481) are plotted in Figure 7, panels a and b, respectively. The most striking feature is the clear difference between the two types of materials, differing several orders of magnitude in PCB concentration. To clearly show this difference, the mean values of energies for a particular POM in each material are connected by lines. For highly contaminated materials, the diffusion activation energy in POM3 is higher than in POM2, whereas for the other materials usually VOL. 33, NO. 13, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 4. Fitted Parameters and Calculated x3 (x3 ) 1 - x1 - x2) for the Triple HB Model Including Three Types of Polymer-Like Organic Material Marked by the Subscripts 1-3a
SRM 1939
SRM 1944
CRM 481m
CRM 536
Ja¨ rnsjo¨ n
PCB
m0 (ng/g)
x1
x2
x3
Ddens/a2 (× 10-6/s)
D2/a2 (×10-6/s)
D3/a2 (×10-6/s)
E2 (kJ/mol)
E3 (kJ/mol)
tsh (min)
RSD %
52 101 149 153 138 28 52 101 118 149 153 105 138 52 101 118 149 153 138 180 28 52 101 118 149 153 138 180 170 28 52 118 105 138
3100 580 450 270 310 82c 54c 61 32c 34c 32 22 44 2.8c 34 12 74 130 89 110 61c 36c 64 32c 41c 56c 42c 35c 20c 52 14c 2.9 2.7 1.8c
0.35 0.35 0.44 0.50 0.52 0.71 0.89 0.80 0.84 0.86 0.89 0.73 0.78 0.81 0.81 0.76 0.83 0.84 0.80 0.79 0.68 0.70 0.54 0.69 0.69 0.64 0.64 0.63 0.58 0.19 0.42 0.46 0.47 0.53
0.35 0.37 0.30 0.25 0.27 0.15 0.07 0.10 0.10 0.08 0.06 0.11 0.09 0.08 0.09 0.13 0.08 0.08 0.10 0.11 0.19 0.16 0.20 0.19 0.19 0.19 0.21 0.24 0.26 0.36 0.32 0.26 0.29 0.15
0.30 0.28 0.26 0.25 0.21 0.14 0.05 0.10 0.06 0.06 0.05 0.16 0.13 0.10 0.09 0.11 0.09 0.08 0.09 0.10 0.13 0.14 0.26 0.12 0.12 0.17 0.15 0.13 0.16 0.45 0.26 0.27 0.24 0.31
71 86 62 56 56 1900 1800 580 3500 2200 2200 670 2200 230 480 340 460 530 390 440 1900 1200 1000 1600 1600 1500 2000 1400 1300 220 430 710 320 250
3.1 3.9 1.7 2.1 1.7 0.16 0.28 0.96 0.19 0.42 0.51 1.0 0.25 1.8 1.1 1.2 0.98 0.99 1.2 1.4 0.19 0.36 0.63 0.46 0.24 0.44 0.50 0.46 0.51 1.2 1.4 0.59 1.3 2.5
0.050 0.026 0.030 0.026 0.023 0.016 0.0097 0.035 0.039 0.036 0.034 0.014 0.038 0.024 0.0070 0.010 0.0041 0.0097 0.0056 0.011 0.011 0.011 0.038 0.023 0.0049 0.024 0.024 0.018 0.0070 0.22 0.35 0.14 0.15 3.1
60 55 64 63 64 75 72 64 74 64 69 64 65 68 60 56 56 60 51 53 72 77 57 68 76 68 63 60 54 70 69 72 60 68
71 74 74 74 77 59 60 56 43 46 67 52 43 77 81 75 82 76 77 72 63 66 46 58 74 54 55 59 66 53 43 42 43 17
-8.4 -9.7 -11 -11 -13 5.0 20 0.42 -18 -3.6 3.6 -29 -21 -16 -22 -23 -24 -24 -25 -26 -9.3 2.1 -3.4 -26 -16 -15 -28 -23 -37 -20 -18 -21 -20 -15
0.24 0.28 0.28 0.51 0.35 0.26 0.19 0.16 0.16 0.16 0.09 0.26 0.28 0.13 0.09 0.09 0.09 0.08 0.10 0.12 0.15 0.21 0.31 0.12 0.19 0.24 0.22 0.26 0.31 0.50 0.18 0.34 0.30 0.26
a Experimental data for four sediments and one soil (1). All numbers are presented with two significant digits. Congeners according to GC retention time. Superscripts c and m denote parameter hit constraint and m0 in µg/g, respectively.
FIGURE 7. Comparison of activation energies obtained from fitting of the triple HB model to all materials for low contaminated materials (a) and highly contaminated materials (b). Data points corresponding to a particular material are shifted to improve the readability. The mean values of the activation energies for different congeners in POM2 and POM3 extracted from the individual materials are connected by lines. For Ja1 rnsjo1 n, one energy for POM3 is excluded from the mean value. the opposite is true. This tendency is not so visible for individual congeners (the ranges for POM3 and POM2 overlap), but it is quite clear for the mean values. In a similar way, the obtained diffusion coefficients for the different POMs in low and highly contaminated materials are plotted in Figure 8, panels a and b, respectively. An analogous tendency to that observed for activation energies is visible here. For highly contaminated materials, the 2210
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FIGURE 8. Comparison of the D/a2 values obtained from the fitting procedure, applying the triple HB model on all materials; low contaminated materials (a) and highly contaminated materials (b). Data points corresponding to a particular material are shifted to improve the readability. Geometric means of the obtained D/a2 values for the congeners in the various POMs in a particular material are connected by lines. For Ja1 rnsjo1 n, PCB-138 is excluded from the mean value for POM3. Ranges of the D/a2 values obtained by Carroll et al (3), recalculated to 40 °C, are presented as horizontal segments. distance (in logarithmic scale) between POM2 and POM3 is the same or even bigger than between POM1 and POM2. The opposite takes place for low contaminated materials, especially visible for Ja¨rnsjo¨n sediment. The results in Figures 7 and 8 are somewhat surprising since the level of contamina-
tion is the only obvious way to classify the samples; however, partitioning into POM should not be influenced by the concentration. It must be stressed though that the number of samples investigated is too limited to draw any certain conclusions and that other properties (30) of the matrixes could be the major factors governing the observed differences between the investigated materials. The best support for the model was achieved when the ranges of diffusion coefficients of PCBs in swollen and condensed matter for water desorption experiments of a highly contaminated sediment presented in a paper by Carroll et al. (3) were plotted together with the same type of values obtained in this investigation (Figure 8). To clarify that Carroll’s parameters are obtained by using the double HB model, they are plotted at half-height, between the other POMs. The values estimated from Carroll’s paper (3) (Figure 8 in the cited paper) were recalculated to 40 °C with the parameters given in Table 2 in the same reference, and surprisingly, the recalculated ranges fit very well with our results. It must be stressed that Carroll performed his water desorption experiments at 25 °C and that applicability of the activation energies from his work up to 40 °C can hardly be expected. Even so, this gives hope for establishing a relation between the parameters obtained by SFE and those obtained in water desorption experiments. An important feature of the materials visible in Table 4 is the contribution patterns of the different POMs (x1, x2, and x3). During the fitting procedure, it was observed that these parameters were the most robust. The contribution patterns reflect the combination of the partition coefficients and POM mass distribution (not distinguishable with the present model), e.g., x1 is equal to 0.5 for PCB-52, which means that half of the molecules of this congener reside in POM1. However, it does not imply that half of the organic matter has properties of POM1. This might suggest the usage of these contribution patterns to characterize sediments and soils. For SRM 1939, the contribution from POM1 increases with the retention time of the congeners in the GC analysis. This cannot be explained by any analytical error, but it is a real trend observed also for the Ja¨rnsjo¨n sediment. The trend can, however, not be seen for any of the other materials where the contribution is more constant. Another similarity between these two materials is the relatively low contribution from POM1 (usually below 50%) as compared to the other materials (above 60%). The only common feature for SRM 1939 and Ja¨rnsjo¨n sediments is their freshwater origin as compared to the marine sediments SRM 1944 and CRM 536. None of the sample characteristics listed in part 3 (30), including elemental analysis, conductivity, pH, and thermal gravimetric analysis, could explain the observed differences. Surprisingly, SRM 1944 and CRM 481 show very similar contribution patterns. The average contribution from POM1, for all congeners, is equal for the two materials (81%). The average contributions from POM2 and POM3 for SRM 1944 are equal (9%). The same is seen for CRM 481 where both POM2 and POM3 contribute to the same extent (10% each). It is necessary to stress that the PCB content for these materials differs by 3 orders of magnitude and their origin is quite different (marine sediment and soil, respectively). Regarding CRM 536, it is a material somewhere between the other matrixes with average contributions of 64%, 20%, and 16% for POM1, POM2 and POM3, respectively. The final striking feature visible in Table 4 is the similar contribution from POM2 and POM3. The average of the x2/x3 ratio for all congeners and all sediments (excluding PCB-138 in Ja¨rnsjo¨n) is 1.2 (RSD ) 24%, n ) 33). This might suggest that there are actually only two kinds of POM, but the second one (modeled in our calculation as POM2 and POM3) has a wide range of diffusion properties. This picture is in agreement with current literature (6); therefore, at least a semi-
quantitative description of sediments and soils can be obtained with our fitting procedure. Although surprisingly good fits were obtained for the triple HB model, this does not prove that three types of POM exist in reality. Neither does it prove that the diffusion from the POM is the only important factor. It could instead be expected that any parameter (in this case the D/a2 ratio and the activation energy) describing SOM is represented by a continuous distribution not only by a few discrete values. However, approximation of this complex reality by only three kinds of homogeneous POMs seems to be a sufficient way of describing the obtained supercritical fluid extraction profiles. Consequently, it might be possible to use supercritical fluid extraction profiles to characterize soils and sediments and from these data to estimate the rate of release of organic pollutant under natural field conditions. This was supported by comparing to literature data obtained from water desorption experiments extending over time periods up to 1 year (3). The physical meaning of the obtained parameters should, however, be verified in further experiments, and the model has to be extended to include a description of the slow initial rate. In addition, the nature of the density hump needs an explanation. An attempt to realize these objectives will be presented in the next paper of this series.
Appendix Solutions to differential equations describing diffusion from a ball or a slab are in principle given in the book by Carslaw and Jeager (31). It is only necessary to “translate” from heat conduction language to diffusion language, which is made by replacing temperature with concentration and both heat conductivity and diffusivity with diffusion coefficient (32). The chosen initial and boundary conditions, namely, even initial distribution of PCBs in the POM and its fast removal from the surface, correspond to the case of constant initial temperature and zero surface temperature. The solutions are presented in the form of two series that are mathematically equivalent but numerically different. One nicely converges for long times, while the second one converges for short times. In the papers by Bartle et al. (25, 33), only the long time solutions were presented. Formulas for the concentration profile as well as the extraction profile are given. Hot ball concentration profiles for long and short time, respectively, based on eqs 9.3(4) and 9.3(5) in ref 31 are given by
c
∞
(-1)n
nxπ
(
)
Dt 2 2 nπ ) c0 a n)1 n a2 a ∞ 2n + 1 - r/a 2n + 1 + r/a 1erfc - erfc r n)0 4Dt 4Dt )-
2a
∑ rπ ∑
{
sin
x
exp -
x
a2
a2
}
(A.1)
where erfc ) 1 - erf is the error function complement and erf is the error function. It is necessary to have separate formulas for calculation of the concentration in the center of a ball. Based on eqs 9.3(6) and 9.3(7) in ref 31 we get:
c c0
∞
) -2
∑(-1)
n
n)1
(
)
Dt 2 2 nπ ) a2 (2n + 1)2a2 2a ∞ 1exp (A.2) 4Dt xDtπ n)0
exp -
∑
(
)
VOL. 33, NO. 13, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
2211
A small correction is made to the eq 9.3(7) in ref 31 where a factor 2 is missing. For slab geometry, for long and short times, respectively, based on eqs 3.3(8) and 3.3(9) in ref 31 we get:
c
)
c0
∞
4
(-1)n
(2n + 1)xπ
∑ 2n + 1 cos π
2a
(
n)0
exp -
∞
1-
∑(-1)
n
n)0
{
×
Dt (2n + 1)
π2 )
4
2
)
2
}
a 2n + 1 - x/a 2n + 1 + x/a erfc + erfc 4Dt 4Dt
x
x
a2
a2
(A.3)
For the extraction curve calculations, we can use the formulas derived for average temperature. Average temperature corresponds to the ratio of amount of pollutant left in SOM m to its initial amount m0, and recovery, as a function of time is obtained as follows:
recovery m )1m0 m0
(A.4)
The ratio m/m0 for the ball geometry is given for long and short times, respectively (9.3(8) and 9.3(9) in ref 31):
m
)
m0
6
∞
∑
1
π2 n)1 n2
(
x
1-6
)
n2π2Dt
exp -
a2
)
Dt + 3 - 12 a2π a2 Dt
x
Dt a2
∞
∑ ierfc
na
xDt
n)1
(A.5)
where ierfc is the integral from the function erfc. For the slab geometry, we have (3.3(10) and 3.3(11) in ref 31):
m
)
m0
8
∞
1
∑ (2n + 1)
π2 n)0
2
x{
1-2
(
exp -
Dt 2
a
1
xπ
)
(2n + 1)2π2Dt 4a2 ∞
+2
∑(-1)
n)1
n
)
ierfc
na
xDt
}
(A.6)
Note the difference for the long time form as compared to eq 15 in ref 33, which erroneously produces values grater than 1. Fortunately, it is not necessary to calculate the function ierfc. One can neglect summation in the short time forms of eqs A.5 and A.6 for the reduced time shorter than 0.075. This causes a relative error of about 3.4 × 10-7 for a ball and 5 × 10-8 for a slab. Retaining only the four first elements in summation in the long time forms in these equations causes a relative error of about 7.5 × 10-10 for a ball and 5 × 10-9 for slab. These errors diminish for reduced times longer or shorter than the chosen boundary value of 0.075.
Acknowledgments K.P. acknowledges the Wenner-Gren Foundation for making these investigations possible by granting a research scholarship. Financial support from the Swedish Environmental Protection Agency is also gratefully acknowledged.
Literature Cited (1) Bjo¨rklund, E.; Bøwadt, S.; Mathiasson, L.; Hawthorne, S. B. Environ. Sci. Technol. 1999, 33, 2193-2203. 2212
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(2) Pignatello, J. J.; Ferrandino, F. J.; Huang, L. Q. Environ. Sci. Technol. 1993, 27, 1563-1571. (3) Carroll, K. M.; Harkness, M. R.; Bracco, A. A.; Balcarcel, R. R. Environ. Sci. Technol. 1994, 28, 253-258. (4) Alexander, M. Environ. Sci. Technol. 1995, 29, 2713-2717. (5) Pignatello, J. J.; Xing, B. Environ. Sci. Technol. 1996, 30, 1-11. (6) Luthy, R. G.; Aiken, G. R.; Brusseau, M. L.; Cunningham, S. D.; Gshwend, P. M.; Pignatello, J. J.; Reinhard, M.; Traina, S. J.; Weber, W. J., Jr.; Westall, J. C. Environ. Sci. Technol. 1997, 31, 3341-3347. (7) Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Environ. Sci. Technol. 1991, 25, 134-142. (8) Weber, W. J., Jr.; Huang, W. Environ. Sci. Technol. 1996, 30, 881-888. (9) Cornelissen, G.; Van Noort, P. C. M.; Parsons, J. R.; Govers, H. A. J. Environ. Sci. Technol. 1997, 31, 454-460. (10) Xing, B.; Pignatello, J. J. Environ. Sci. Technol. 1998, 32, 614619. (11) Pawliszyn, J. J. Chromatogr. Sci. 1993, 31, 31-37. (12) Langenfeld, J. J.; Hawthorne, S. B.; Miller, D. J.; Pawliszyn J. Anal. Chem. 1995, 67, 1727-1736. (13) Clifford, A. A.; Burford, M. D.; Hawthorne, S. B.; Langenfeld, J. J.; Miller, D. J. J. Chem. Soc., Faraday Trans. 1995, 91, 13331338. (14) Hawthorne, S. B.; Bjo¨rklund, E.; Langenfeld, J. J.; Bøwadt, S.; Miller, D. J. Discrete Behavior of Organic Pollutants During Supercritical Fluid Extraction. Presented at the Ecotoxicology Workshop, Winnipeg, Canada, June 16-19th, 1996. (15) Bjo¨rklund E.; Hawthorne, S. B.; Bøwadt, S.; Mathiasson, L. In Investigation of PCB Sorption/Desorption Behavior on Sediments and Soils Using Supercritical Fluid Extraction; Vartiainen, T., Komulainen, H., Eds.; 7th Nordic Symposium on Organic Pollutants, Kuopio University Publications C, Natural and Environmental Sciences 68; Kuopio University: Kuopio, Finland, 1997. (16) Bøwadt, S. Application of SFE for the Extraction of PCBs in Certification and Intercomparison Exercises on Different Matrices with Special Focus on Reference Materials; EC JRC: Geel, Belgium, 1996. (17) Weber, W. J., Jr.; Young, T. M. Environ. Sci. Technol. 1997, 31, 1686-1691. (18) Young, T. M.; Weber, W. J., Jr. Environ. Sci. Technol. 1997, 31, 1692-1696. (19) Weber, W. J., Jr.; McGinley, P. M.; Katz, L. E. Environ. Sci. Technol. 1992, 26, 1955-1962. (20) Leboeuf, E. J.; Weber, W. J., Jr. Environ. Sci. Technol. 1997, 31, 1697-1702. (21) Huang, W.; Young, T. M.; Schlautman, M. A.; Yu, H.; Weber, W. J., Jr. Environ. Sci. Technol. 1997, 31, 1703-1710. (22) Huang, W.; Weber W. J., Jr. Environ. Sci. Technol. 1997, 31, 25622569. (23) Berens, A. R. Makromol. Chem., Macromol. Symp. 1989, 29, 95-108. (24) Berens, A. R.; Huvard, G. S.; Korsmeyer, R. W., Kunig, F. W. J. Appl. Polym. Sci. 1992, 46, 231-242. (25) Bartle, K. D.; Clifford, A. A.; Hawthorne, S. B.; Langenfeld, J. J.; Miller, D. J.; Robinson, R. J. Supercrit. Fluids 1990, 3, 143-149. (26) Berens, A. R.; Huvard, G. S. J. Dispersion Sci. Technol. 1981, 2, 359-378. (27) Frame, G. M.; Cochran, J. W.; Bøwadt, S. J. High Resolut. Chromatogr. 1996, 19, 657-668. (28) Miller, D. J.; Hawthorne, S. B.; Clifford, A. A. J. Supercrit. Fluids 1997, 10, 57-63. (29) Langenfeld, J. J.; Hawthorne, S. B.; Miller, D. J.; Pawliszyn, J. Anal. Chem. 1993, 65, 338-344. (30) Hawthorne, S. B.; Bjo¨rklund, E.; Bøwadt, S.; Mathiasson; L. Environ. Sci. Technol. Submitted for publication. (31) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Oxford University Press: London, 1959. (32) Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford University Press: London, 1975. (33) Bartle, K. D.; Boddington, T.; Clifford, A. A.; Hawthorne, S. B. J. Supercrit. Fluids 1992, 5, 207-212.
Received for review October 19, 1998. Revised manuscript received April 5, 1999. Accepted April 14, 1999. ES981075U
