Environ. Sci. Technol. 2004, 38, 3305-3309
Modeling Maximum Adsorption Capacities of Soot and Soot-like Materials for PAHs and PCBs P A U L C . M . V A N N O O R T , * ,† M I C H I E L T . O . J O N K E R , ‡,§ A N D ALBERT A. KOELMANS§ Institute for Inland Water Management and Wastewater Treatment (RIZA), P.O. Box 17, 8200 AA Lelystad, The Netherlands, Toxicology Division, Institute for Risk Assessment Sciences, Utrecht University, Utrecht, The Netherlands, and Aquatic Ecology and Water Quality Management Group, Department of Environmental Sciences, Wageningen University, Wageningen, The Netherlands
Recent studies have shown that not partitioning but adsorption is the main mechanism for sorption of hydrophobic organic compounds to soot and soot-like materials. For compounds that adsorb by van der Waals forces only, variation in soot-water distribution coefficients will result from differences in these forces for adsorption, as well as the maximum number of accessible sites. This maximum number of accessible sites may a priori be expected to vary due to differences in both sorbent characteristics and sorbate dimensions. In this modeling study, variation in maximum adsorption capacities is explained from sorbent and sorbate properties. Maximum adsorption capacities were calculated using (a) literature values for soot-water distribution coefficients for polycyclic aromatic hydrocarbons and polychlorobiphenyls on 10 different soot and soot-like materials and (b) Langmuir affinities for adsorption at a carbonaceous surface estimated using a recently reported method. The variation in maximum adsorption capacities could be explained by the variation in sorbent specific surface area, sorbent organic carbon content, and the sorbentsorbate contact area. Furthermore, increasing sorbate thickness was related to a decrease in maximum adsorption capacities, which points to adsorption in micropores. Maximum adsorption capacities decreased by 1-2 orders of magnitude as the contact area increased by 50%. This points to adsorption sites being hardly larger than sorbates.
Introduction Quantitative insight into sorption of organic compounds by geosorbents is fundamental to the assessment of the environmental risk of water, air, and soil pollution by these compounds. Sorption by these sorbents limits the extent to which organic compounds may be taken up by humans and biota. Over the past few years, a substantial body of indirect evidence has grown to show that the presence of soot or * Corresponding author phone: +31 320 298884; fax: +31 320 298303; e-mail:
[email protected]. † Institute for Inland Water Management and Wastewater Treatment (RIZA). ‡ Utrecht University. § Wageningen University. 10.1021/es035120w CCC: $27.50 Published on Web 05/01/2004
2004 American Chemical Society
soot-like materials in geosorbents may lead to enhanced sorption compared to predictions based on dissolution of organic compounds in organic matter in geosorbents (1-4). Enhanced sorption seriously limits bioavailability of organic compounds associated with geosorbents. This has prompted investigations on soot-water distribution coefficients for polycyclic aromatic hydrocarbons (PAHs) (5, 6), polychlorobiphenyls (PCBs) (7, 8), and polychlorinated dibenzo-pdioxins, polychlorinated dibenzofurans, and polybrominated diphenyl ethers (9). These studies confirmed that adsorption by soot is enhanced compared to absorption by dissolution in natural organic matter and that the enhancement is highest for the compounds with a planar molecular configuration. Recently, for five different types of soot and five soot-like materials, soot-water distribution coefficients (KS) for 17 PAHs and 11 PCBs were reported (8). In this report, statistical data analysis revealed that the sorbent average pore diameter (APD) and sorbate 1-octanol-water partition coefficients (log Kow; for PCBs) or sorbate total surface area (TSA; for PAHs) could explain about 75% of the variation in log KS values. The remaining variation was due to differences in sorbent total pore volume (TPV), sorbate molar volume (Vmol), and other sorbent characteristics. The KS values were obtained for very low aqueous concentrations (pg/L to ng/L range) (8). While that study and most others in this area remain merely empirical in nature, it is of great importance to link these observations as much as possible to underlying physicochemical mechanisms, which is the aim of the present study. At low concentrations, as used in ref 8, monolayer adsorption at a small percentage of the available adsorption sites can be expected. This monolayer adsorption can be described by a Langmuir isotherm:
q)
bCQmax 1 + bC
(1)
in which q is the sorbed concentration in equilibrium with a concentration C in solution. Qmax and b are the maximum adsorption capacity of the sorbent and the sorption affinity, respectively. In the case of bC , 1 (i.e., at very low concentrations), eq 1 reduces to
KS ) q/C ) bQmax
(2)
Very recently, the nonlinear sorption isotherm for phenanthrene in a sediment was found to be virtually linear for the concentration in water range of 0-10 ng/L (10). Therefore, KS values from ref 8 can be taken to represent the product of Langmuir affinity and maximum adsorption capacity. The observed variation of log KS with, for example, APD, log Kow, TSA, TPV, and Vmol may reflect the influence of these variables on the product of Langmuir affinity and maximum adsorption capacity. The remaining questions, however, are (a) how to separate the variation in b from the variation in Qmax and (b) how the latter can be related to sorbent and sorbate properties. Variation of b with the type of carbonaceous soot or soot-like material can be taken to be absent as described below. Very recently, on the basis of thermodynamic data for sorption of organic compounds to a graphitized carbon, it was shown that Langmuir affinity for adsorption (b) on sootlike materials from water can be estimated by (11)
b)
1 exp(∆Sm - 15 J/(mol‚K))/R SS
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TABLE 1. Values for Sorbate-Sorbent CAs Relative to That of Naphthalene and Estimated Langmuir Sorption Affinities (b) along with Dataa Used To Estimate b (Subcooled Liquid Solubilities (SL), Solid Aqueous Solubilities (SS), Fusion Enthalpy (∆Hfus), and Fusion Entropy (∆Sfus)) compoundb
CA
b, m3/µmol
phenanthrene fluoranthene benz[a]anthracene benzo[k]fluoranthene PCB-18 PCB-28 PCB-52 PCB-72 PCB-77 PCB-101 PCB-118 PCB-126 PCB-138 PCB-156 PCB-169
1.340 1.506 1.719 1.896 1.333 1.459 1.402 1.561 1.573 1.470 1.663 1.689 1.538 1.756 1.806
0.00823 0.0501 1.410 23.6 0.0407 0.827 0.417 9.95 15.6 3.55 250 136 10.9 1010 1670
∆Hfus, kJ/mol
∆Sfus, J/(mol‚K)
SS, mmol/m3
47.6 48.9 50 50.8 49.4c 66.8c 46.2
6.17 1.186 0.0482 0.00317 1.55d 0.621d 0.103d
56.3 53.9 76.1c 67.5c
0.0093d 0.0306d 0.0063d 0.0041d
81.5c 68.1b
0.0030d 0.00036d
25.7c
SL, mmol/m3
0.537c
20.1c
0.0508c
a From ref 21 unless indicated otherwise. b Substitution patterns of PCBs: PCB-18, 2,2′,5-B; PCB-28, 2,4,4′-B; PCB-52, 2,2′,5,5′-B; PCB-72, 2,3′,5,5′B; PCB-77, 3,3′,4,4′-B; PCB-101, 2,2′,4,5,5′-B; PCB-118, 2,3′,4,4′,5-B; PCB-126, 3,3′,4,4′,5-B; PCB-138, 2,2′,3,4,4′,5′-B; PCB-156, 2,3,3′,4,4′,5-B; PCB-169, 3,3′,4,4′,5,5′-B. c Estimated from regression equations in ref 13. d From ref 22.
where SS and ∆Sm (J/(mol‚K)) are the solid solubility in water and the sorbate entropy of melting, respectively. Equation 3 was validated using literature Langmuir affinity data for adsorption of neutral aromatic compounds on various carbonaceous materials. It was able to predict that b for the least planar PCBs was lower than for more planar PCB congeners. From eq 3 it can be derived that bCw , 1 for Cw < 0.01SS. This condition is fulfilled since the soot-water distribution coefficients in ref 7 were obtained at concentrations of 0.03-200 ng/L for PAHs and 0.01-20 ng/L for PCBs (M. T. O. Jonker, unpublished results), with the lowest concentrations for the least water soluble compounds, which is more than a factor of 100 below the solid solubilities. Because measured KS values at low concentrations equal bQmax, estimation of b values subsequently allows calculation of Qmax. In the current study, maximum adsorption capacities (Qmax) for the sorbents used in ref 8 were calculated from KS data in ref 8 and estimates for b. The resulting values were related to sorbent properties and estimates of sorbatesorbent molecular contact areas.
Methods Calculation of Maximum Sorption Capacities. Maximum adsorption capacities for the 10 sorbents studied in ref 8 were calculated by dividing KS values for added PAHs and PCBs from ref 8 by Langmuir affinities estimated using eq 3. Maximum adsorption capacities for native PAHs were not calculated, because KS data for the native compounds are controlled by other mechanisms than Langmuir adsorption only (8, 12). The estimated Langmuir affinities are listed in Table 1 along with sorbate solubility data and fusion thermodynamics data needed to estimate the sorption affinities. For two PCBs studied in ref 8 (PCB-72 and PCB-138), no experimental solubility and fusion data could be found in the literature. For these PCBs, fusion enthalpies and liquid solubilities therefore were estimated using regression equations from ref 13. In ref 8, KS values for six added PAHs are presented, including anthracene and benzo[ghi]perylene. However, these two PAHs were omitted from the present study since we suspected their estimated Langmuir affinities to be erroneous for the following reasons. For benzo[ghi]perylene, the entropy of fusion listed in ref 14 is unusually low compared to those of other PAHs. Also, the liquid solubility of this PAH, 3306
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calculated from the solid solubility reported in ref 15 and the entropy of fusion from ref 14, did not fit the regression of PAH liquid solubilities versus PAH total surface area (data not shown). This suggests that either the value of the entropy of fusion for benzo[ghi]perylene or the selected value of the solid solubility is biased. For anthracene, both the entropy and enthalpy of fusion are very high compared to those of other PAHs. We speculate that a relatively high fusion enthalpy may indicate intermolecular interactions in the solid other than van der Waals forces, whereas eq 1 was derived on the assumption that sorbent-sorbate interactions for adsorption by carbonaceous materials are van der Waals forces only. In the case of other than van der Waals forces, the use of eq 3 would be inappropriate. Estimation of Sorbate-Sorbent Contact Areas. The carbonaceous surface of soot and soot-like materials may be envisaged as being built from planar PAH-like moieties (16). The surface area occupied by a sorbate will depend on the size of the sorbate; large sorbates will cover a relatively large area. These areas, the sorbate-sorbent contact areas, were taken to be equal to the maximum value of the area of the hypothetical shadow produced by the sorbate on a planar surface. The areas were determined by cutting and weighing prints of 3D representations of molecular structures made in ACD/Chemsketch (Advanced Chemistry Development Inc., Toronto, Ontario, Canada). For PCBs, the software was allowed to rotate molecular structures to visually maximize the planar surface area displayed on-screen. PCB dihedral angles were set to 40°, 60°, and 90° for non-, mono-, and di-o-PCBs, respectively, on the basis of data in ref 17. Although these angles are for the gas phase, we assumed that they also apply to the adsorbed state, as the dihedral angles for solid 4,4′-dichlorobiphenyl, 2,2′,4,4′,6,6′-hexachlorobiphenyl, and decachlorobiphenyl were reported to be 39.4° (18), 87.3° (19), and 86.7° (20), respectively, which are very close to the values given for the gas phase. Contact areas (CAs) relative to that of arbitrarily chosen naphthalene are given in Table 1.
Results and Discussion The maximum adsorption capacities (Qmax) calculated from eqs 2 and 3 are given in Table 2. From this table, it appears that Qmax values strongly depend on both the sorbate and sorbent. The variation in log Qmax values among both sorbates and sorbents spans 3-4 log units. The variation among sorbents, however, can significantly be reduced by normal-
TABLE 2. Logarithmic Maximum Sorption Capacities (log Qmax, nmol/(g of Sorbent)) for Added (Deuterated) PAHs and Added PCBs on Various Types of Soot and Soot-like Sorbents and Sorbent SSAs (m2/g) from Ref 8 compound phenanthrene fluoranthene benz[a]anthracene benzo[k]fluoranthene PCB-18 PCB-28 PCB-52 PCB-72 PCB-77 PCB-101 PCB-118 PCB-126 PCB-138 PCB-156 PCB-169
diesel soot activated (SRM 1650), traffic soot, oil soot, coal soot, fly ash, wood soot, carbon, charcoal, graphite, coal, SSA ) 62.7 SSA ) 59.4 SSA ) 38.1 SSA ) 8.2 SSA ) 3.7 SSA ) 3.6 SSA ) 761 SSA ) 153 SSA ) 12.4 SSA ) 3.5 4.50 4.60 4.42 3.81
5.02 4.69 4.29 3.45
4.09 4.03 3.60 2.98
3.42 3.17 2.44 1.80
3.84 3.77 3.13 2.27
3.99 3.63 2.92 2.07
7.85 7.37 6.46 5.35
6.53 6.12 5.21 4.06
5.25 5.70 5.50 4.79
5.33 4.65 4.10 3.06
3.95 3.51 3.35 2.66 3.30 2.97 1.73 2.51 2.92 1.38 1.41
3.34 2.51 2.80 1.81 2.23 2.44 0.93 1.59 2.45 0.71 0.65
2.87 2.04 2.37 1.39 1.64 2.03 0.45 1.06 2.02 0.29 0.23
2.54 2.46 1.93 1.53 2.24 1.87 0.54 1.43 1.87 0.26 0.33
3.34 2.57 2.64 1.62 2.06 2.13 0.67 1.26 1.98 0.30 0.17
6.55 5.52 5.74 5.51 5.45 5.63 4.05 4.73 5.51 3.70 3.53
5.86 4.90 5.01 4.05 4.22 4.35 2.72 3.25 3.92 2.11 1.98
4.27 4.29 4.02 3.64 4.60 3.85 2.65 3.89 3.73 2.29 2.73
4.49 4.17 3.82 3.13 3.59 3.41 2.12 2.66 3.23 1.58 1.41
TABLE 3. Slopes and Intercepts (with Standard Errors) from Regression of Log Qmax* (nmol/m2) vs Contact Area Relative to That of Naphthalene di- and mono-o-PCBs
PAH
non-o-PCBs
sorbent
slope
intercept
radj2
slope
intercept
radj2
slope
intercept
radj2
traffic soot oil soot wood soot coal soot NIST 1650 diesel soot coal charcoal activated carbon graphite fly ash
-2.7 ( 0.5 -2.0 ( 0.4 -3.4 ( 0.4 -3.0 ( 0.3 -1.2 ( 0.6 -3.9 ( 0.4 -4.4 ( 0.6 -4.5 ( 0.5 -0.9 ( 1.0 -2.9 ( 0.6
7.0 ( 0.8 5.3 ( 0.7 8.2 ( 0.6 6.6 ( 0.5 4.5 ( 1.0 10.1 ( 0.7 10.5 ( 0.9 11.1 ( 0.8 5.6 ( 1.6 7.3 ( 1.0
0.92 0.86 0.96 0.97 0.51 0.96 0.95 0.96 -0.1 0.86
-6.1 ( 0.6 -6.3 ( 0.6 -7.2 ( 0.5 -6.3 ( 0.6
10.3 ( 0.9 10.2 ( 0.9 12.3 ( 0.7 10.4 ( 1.0
0.94 0.94 0.97 0.93
-8.1 ( 0.8 -6.8 ( 0.7 -8.1 ( 0.7 -6.0 ( 0.6
14.4 ( 1.3 11.4 ( 1.3 14.3 ( 1.3 10.3 ( 1.1
0.98 0.97 0.98 0.98
-6.8 ( 0.7 -8.6 ( 0.5 -6.3 ( 0.8 -5.0 ( 0.7 -5.5 ( 0.8
13.1 ( 1.1 15.1 ( 0.8 12.1 ( 1.3 10.1 ( 1.1 9.5 ( 1.3
0.93 0.97 0.89 0.87 0.85
-9.4 ( 0.8 -9.6 ( 0.7 -8.2 ( 1.2 -8.0 ( 1.1 -8.2 ( 0.7
17.9 ( 1.4 17.2 ( 1.3 15.6 ( 2.1 16.2 ( 1.9 14.7 ( 1.2
0.99 0.99 0.96 0.96 0.98
izing to the sorbent specific surface area (SSA) with SSA data given in ref 8. Normalization to SSA reduces standard deviations for a given sorbate by up to a factor of 4 for the group of sorbents comprising the soots and fly ash and for the group of sorbents comprising active carbon, charcoal, graphite, and coal. This indicates that the maximum amount of a given compound that can be adsorbed is proportional to the specific surface area of the carbonaceous material. However, after this normalization still some variation is present. In the following discussion, we will first address the variation among sorbates. After that, we will further examine the remaining variation after normalization to SSA. Variation in Qmax values among sorbates seems to be systematic. In general, Qmax values strongly decrease with increasing molecular size: Qmax values for PCB-169 are 3-4 orders of magnitude less than for phenanthrene. This suggests a strong dependence of Qmax on sorbate dimensions. This suggestion is in line with the results of Walters and Luthy (23), who found that the experimental maximum capacities of PAH sorption to Filtrasorb 400 activated carbon decreased by almost 2 orders of magnitude on going from naphthalene to chrysene. Therefore, the logs of SSA-normalized Qmax values (log Qmax*, nmol/m2) were regressed against relative sorbatesorbent CAs. The results of this regression are presented in Table 3. Also, typical examples are plotted in Figure 1 for wood soot and fly ash. Note that data for mono- and di-oPCBs were pooled. This was done as there were no significant differences in log Qmax* data between these groups. Generally, log Qmax* correlated well with CA: in many cases adjusted r2 values were between 0.93 and 0.99. Only in two cases, PAHs sorbed by NIST diesel soot and PAHs sorbed to graphite, unexplained substantial data scatter resulted in a poor correlation.
FIGURE 1. Log Qmax* vs sorbate relative contact area for wood soot (A) and fly ash (B): solid squares, PAHs; open squares, non-ochloro-PCBs; open triangles: mono- and di-o-chloro-PCBs. Lines represent linear regressions. From the data in Table 3, and from Figure 1, it can be derived that, at a given value of CA, the order of log Qmax* is PAHs > non-o-PCBs > mono- and di-o-PCBs. This is the same order as that for the extent of planarity of the compound classes investigated. The dihedral angle between the benzene rings in di-o-PCBs, for instance, is close to 90°. Hence, these PCBs are thicker than PAHs, which are planar. The order given above suggests that, besides CA, also sorbate thickness affects the occupation of the available surface. Apparently, for nonplanar “thick” sorbates, less surface is available than for planar sorbates. For a freely accessible surface, this phenomenon would be difficult to understand. However, if the sorption sites are located in narrow micropores, rather than on a freely accessible surface, thinner molecules may penetrate more easily and access a larger number of sites in the end. Therefore, the present data suggest that adsorption sites are located in narrow micropores. Previously, a similar suggestion was made to explain the variation in (1) PAH and VOL. 38, NO. 12, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Relation between intercepts from log Qmax*-CA plots and sorbent total organic carbon fraction (foc) for PAHs (solid squares), non-o-PCBs (open squares), and mono- and di-o-PCBs (open triangles). PCB soot log KS values with the average pore diameter (8) and (2) soot-gas-phase distribution of low molecular weight PAHs (24). Values for intercepts for different groups of compounds vary substantially among sorbents (see Table 3). The variation in these intercepts reflects, for a given sorbate, the differences in Qmax* among sorbents. These sorbents can roughly be divided into two types of carbonaceous sorbents: materials resulting from combustion (the soots and fly ash) on one hand, having the lower four intercepts, and carbonized materials (coal, charcoal, activated carbon, and graphite) on the other, with higher intercepts. These two groups of sorbents differ in the environment in which they were created. Clague et al. (25) observed that oxygen contents of engine soots were higher than those of carbon black and that the oxygen content of the surface of an engine soot, as measured by X-ray photoelectron spectroscopy, was higher than that of bulk oxygen. The relatively high oxygen content of engine and exhaust soots was explained by the presence of hot oxidative environments for these soots as compared to carbon black. Oxidation of a carbonaceous surface may result in oxygen-containing functional groups protruding from the surface so that they may limit accessibility of the surface. In other words, with increasing oxygen content the number of possible adsorption sites may be reduced, which may qualitatively explain the trend in intercepts in Table 3. Note that, although the oxygen contents of the presently studied sorbents are not known, increasing oxygen content will be coupled to a concomitantly decreasing carbon content. A plot of the intercepts from Table 3 against the total organic carbon content (foc) of the sorbents (taken from ref 8) indeed shows the expected trend, which supports the hypothesis (Figure 2). Note that data for NIST diesel soot and for PAHs on graphite were not included in Figure 2 because of the low adjusted r2 values for these data sets (see Table 3). Furthermore, values for fly ash were also excluded because this sorbent mainly consists of minerals (>96%; M. T. O. Jonker, unpublished results). On the basis of the stepwise approach described above, CA and foc can be identified as quantitative descriptors for Qmax*. Sorbate thickness appeared to be a qualitative descriptor for Qmax*. Although a relationship with sorbate thickness is consistent with findings in ref 8, the variation in log values for soot-water distribution coefficients observed in ref 8 could not be explained by the variation in SSA and foc. Probably, the use of relative contact areas and of log SSA, instead of SSA, as variables resulted in this apparent discrepancy. In the present study, for the four sorbate groups, separate multiple regression analyses of log Qmax (nmol/m2) versus the quantitative descriptors CA and foc were performed using the statistical software package SPP 10.1 for Windows (SPSS, Inc., Chicago, IL; settings were identical to those described in ref 8). As opposed to the data analysis for Table 3, log Qmax* data for di-o-PCBs were regressed separately 3308
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FIGURE 3. Log Qmax* estimated from eqs 4-7 vs values calculated from distribution coefficients for PAHs (solid circles), di-o-chloroPCBs (open circles), mono-o-chloro-PCBs (triangles), and non-ochloro-PCBs (crosses). The line represents y ) x. from those for mono-o-PCBs in order not to obscure possible small differences between these two groups of compounds. As explained before, data for fly ash were not used because of this sorbent’s deviating composition. For the four sorbate groups, the multiple regression analyses resulted in
PAHs:
log Qmax* (nmol/m2) ) 5.43 + 3.34foc 2.89(CA)radj2 ) 0.75 (4)
non-o-PCBs:
log Qmax* (nmol/m2) ) 12.22 + 3.77foc - 8.05(CA)radj2 ) 0.85 (5)
mono-o-PCBs: log Qmax* (nmol/m2) ) 10.57 + 3.65foc - 7.35(CA)radj2 ) 0.89 (6) di-o-PCBs:
log Qmax* (nmol/m2) ) 7.99 + 3.14foc 5.44(CA)radj2 ) 0.80 (7)
The independent variables (i.e., CA and foc) explained 4060% and 60-40% of the total variance of log Qmax* values, respectively. Equations 4-7 show that for the four sorbate groups substantially different equations are needed to estimate Qmax*. Note, however, that the coefficient for foc in eqs 4-7 hardly varies among compound classes. This suggests that foc can be considered as a general correction factor for SSA. Also note, however, that adsorption to soot will be absent when foc ) 0. Therefore, eqs 4-7 will not be valid beyond the foc range of 0.3-1 for which they were derived. In Figure 3, log Qmax* values estimated from eqs 4-7 are plotted against values calculated from eqs 2 and 3 (i.e., values from Table 2 normalized to SSA). Average deviations for Qmax* were within a factor of 2. For 95% of the data, the difference was less than a factor of 7. At this stage, it is interesting to compare eq 4 with the regression of experimental log Qmax* values for PAHs on an activated carbon from the study of Walters and Luthy (23) versus CA. Their Qmax values, after normalization to the active carbon specific surface area, fit
log Qmax* (nmol/m2) ) 6.19 - 2.52(CA)radj2 ) 0.73 (8) Note that foc is not included in eq 8 because it was not a variable in the study by Walters and Luthy. The coefficient for CA in eq 8 is almost equal to that in eq 4. This further supports the general applicability of eq 4. However, the intercept in eq 8 is much less than expected from eq 4 taking foc ) 1. Here, we follow the explanation provided by Jonker and Koelmans that differences of up to 2.5 log units between their log KS values for an activated carbon and data reported
in ref 23 are caused by different types of activated carbon, by different partitioning methods, and/or by different aqueous concentrations (8). If sorption sites were much larger than sorbate sizes, an increase of CA would not, or hardly, affect the adsorption capacity. Consequently, the strong decrease of log Qmax* with increasing CA deduced in the present study strongly suggests that the dimensions of the adsorption sites closely resemble those of the sorbates. This notion is supported by the observed change in entropy upon sorption by carbonaceous materials (which formed part of the basis for the derivation of eq 1 (11)), which can be explained as follows. Equation 1 was based on a difference in entropy between the liquid state and the sorbed state of about 15 J/(mol‚K), which was deduced from literature data (11). As discussed in ref 11, a sorbed state that is comparable to a rotationally and translationally restricted 2-dimensional liquid would be expected to be about 33 J/(mol‚K) lower in entropy than the liquid state. Hence, the entropy of the sorbed state is about 18 J/(mol‚K) higher than that of a rotationally and translationally restricted 2-dimensional liquid. Consequently, the sorbed state is rather a rotationally and translationally restricted 2-dimensional (2D-RRS) gas (11). Trouton’s rule states that the entropy of vaporization from the liquid state is about 87 J/(mol‚K) (26). Upon vaporization, the change in entropy is predominantly caused by a change in translational degrees of freedom. Therefore, the entropy of vaporization of a 2-dimensional liquid to a 2-dimensional gas state can be estimated to be 2/3 × 87 J/(mol‚K) ) 59 J/(mol‚K). Consequently, a sorbed state that is less than 59 J/(mol‚K) (in fact about 18 J/(mol‚K)) higher in entropy than a 2-dimensional liquid suggests that the sorbate is not in a free 2D-RRS gas state, but that it has additional translational limitations presumably imposed by the confinements of the sorption site. Such would be the case for sorption sites with dimensions that closely resemble sorbate dimensions as suggested above. In other words, the above-mentioned suggestion that the sorption sites are hardly larger than the sorbates is in line with expectations based on the entropy of adsorption. The present data analysis demonstrates that maximum adsorption capacities of a wide range of soot-like materials for adsorption of PAHs and different types of PCBs can be estimated from sorbent specific surface area, sorbent organic carbon content, and sorbate-sorbent contact area. We expect that, as confirmed by comparison with limited literature data, the relations derived in the present study may also apply to other carbonaceous materials. Additional studies, especially focusing on experimentally determined maximum capacities of a wider range of carbonaceous materials and geosorbents for adsorption of PAHs, PCBs, and other organic compound classes are however needed to further verify the relations and equations presented in this paper.
M.T.O.J. and A.A.K. acknowledge funding by TNO, The Netherlands.
Acknowledgments
Received for review October 9, 2003. Revised manuscript received March 30, 2004. Accepted March 31, 2004.
This study was financially supported in part by the European Union, Project ABACUS (Grant EVK1-CT-2001-00101).
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