Environ. Sei. Technol.
1999, 33, 2390-2394
Estimating the Organic Carbon Partition Coefficient and Its Variability for Hydrophobic Chemicals
RAJESH SETH,* DONALD MACKAY,** AND JANE MUNCKE*
Environmental Modelling Centre, Trent University, Peterborough, Ontario K9J 7B8, and Swiss Federal Institute of Technology, Zurich, Switzerland
Numerous correlations have been developed between the organic carbon/water partition coefficient Koc and various molecular properties and descriptors, but most notably the octanol/water partition coefficient /C0w and water solubility. From an analysis of the theory underlying in this partitioning and an examination of the existing database, it is suggested that the preferred approach is to correlate the quantity log(/<bc/Kbw), which is essentially the ratio of activity coefficients in octanol and organic carbon, with a molecular property or with log Kau rather than log Koc with log Kcm- Such an approach is presented for estimating Koc for hydrophobic chemicals, including an expression of uncertainty limits, based on a correlation derived between log(/(bc//<bw) and log /Cow- In its simplest form the correlation is that Koc = 0.35/<bw subject to variation by a factor of 2.5 in either direction. It is suggested that new experimental data be assessed for consistency and achievement of true equilibrium by comparison with this correlation.
Introduction
Since most sorption ofhydrophobic organic substances is to the natural organic matter present in these media, the usual approach is to assume that all sorption is to that matter and to invoke a partition coefficient between organic carbon (Koc) or organic matter (Kom) and water. Koc is then Kr/<j>, where ifp (L/kg) is the ratio of concentrations in the solid phase (mg/kg)and in water (mg/L)and 0 is the mass fraction organic carbon. Numerous measurements of ifocand Kom have been reported in the literature, and many correlations have been derived between them and various molecular descriptors. Gawlik et al. (1) reviewed 24 correlations of Koc with water solubility, 76 with the octanol/water partition coefficient Kow, 35 with RP-HPLC retention time, and 38 with topological indices or other molecular properties. They concluded that it was not possible to recommend any single correlation as being preferred universally for all compounds. Major difficulties thus face the environmental scientist when selecting amongthese correlations and even when assessing conflicting experimental data for the same substance.
Part of this difficulty lies in the expected variability in Koc resulting from the complex and variable nature of organic
* Corresponding author phone: (705) 748-1489; fax: (705) 748-1569; e-mail: dmackay@trentu.ca.
*" Trent University.
* Swiss Federal Institute of Technology.
matter. There has been considerable research into the chemical nature, structure, and properties of sediments and soil organic matter (2—4). It is viewed as a combination of fulvic and humic acids and humin, with an average carbon content of approximately 58% (5). Organic matter is variable in properties and consists of aggregates of material that may be in a continuous state of degradation, rearrangement, and replenishment. Hydrophobic solutes appear to bind readily and rapidly with the outer surface region in a few hours to a few days and then diffuse slowly into (and out of) the hydrophobic interior region and narrow cavities in the organic matter during time periods of weeks (6). The measured concentration in the solid phase is thus expected to vary with time explaining much ofthe variability in reported data. Chiou et al. (4) have also shown differences between the sorptive behavior of soils and sediments, with sediment Koc values being about twice those of soils. Additionally PAHs exhibit higher partitioning to soil/sediment organic matter than other nonpolar solutes such as PCBs apparentlybecause of more favorable PAH—organic matter interactions (4). It should also be noted that material other than organic carbon has sorptive capacity; thus even when the organic carbon content is zero, a finite value of ifp is expected. Finally, the water associated with the solids after filtering or centrifuging will contain dissolved solute. The quantity of this solute can become appreciable when Koc is low, i.e., log Koc less than about 2.5, especially when the organic carbon content ofthe sorbent is low.
Studies by Chiou et al. (4) and others indicate that for any given chemical, an inherent variability in Koc values is expected as a result of different environmental conditions and equilibration times. Thus it is unlikely that a highly accurate, generally applicable correlation for K0c or Kom can be established. In this study we review and criticize existing correlation approaches, set out a theoretical basis for correlations, and suggest an approach that includes a measure of variability. Amethod is recommended by which new experimental data can be assessed for consistency, taking in account equilibration time.
Theory Underlying Partitioning
The most reliable correlation equations for Koc are likely to be those which have a sound basis in the thermodynamic theory underlying the partitioning phenomenon. The two most commonly used correlations are with the octanol/water partition coefficient (Kow) and water solubility (Sw)-
When a chemical achieves equilibrium in a two-phase system such as organic carbon and water, it will have equal chemical potentials or fugacities (f) in both phases. The fugacity in the aqueous phase can be expressed approximately on a Raoult's law basis as
(1)
where jrw is the mole fraction of the chemical dissolved in water and P^ is the reference fugacity or approximately the vapor pressure ofthe pure chemical in the liquid state. Pls is measurable for liquids, whereas for solids and gases it must be estimated, yw is the activity coefficient of the dissolved chemical which varies with chemical structure and is dependent on concentration, but for small mole fractions y is assumed to be constant. The activity coefficient is an expression of the chemical's hydrophobicity and describes the tendency ofthe chemicalto partition from water into the gas phase, the activity a being the product of xw and yw-
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The concentration C (mol/m3) of a chemical in water is *w/vw, where vwis the molar volume ofwater (approximately 18 x 10~6 m3/mol). Other common units for concentration are mg/L or g/m3, both of which are MjCor M^w/vw or Af// (vw7w-Pls), where M[ is the molecular mass of the chemical (g/mol). By analogy, the fugacity in the organic carbon phase can be expressed as
f=xcycPL
(2)
where xc denotes the mole fraction and yc the activity coefficient. Values of xc and yc are difficult to measure individually, but their product can be measured readily.
The concentration of the chemical (g/m3) in the organic carbon phase is M\xdvc, where vcis the molar volume of the wet organic carbon phase (which is also uncertain), but more commonly concentration is expressed in the more readily measurable units of mg/kg OC which is M\xd(vqoc) or Mfl (vcpcycPLS), where pc is the density of organic carbon (g carbon/cm3 wet phase or kg/L). The organic carbon/water partition coefficient Koc (L/kg) expressed as the ratio of concentrations in the OC phase (mg/kg) to that in water (mg/L) is thus
VcPcYc
(3)
The group vqoc is also the molecular mass Mc (g/mol) of the OC phase, and since vwisMw/pw, where Mwis the molecular mass of water and pw its density, Koc is also given by
MwYw McYcPw
(4)
The commonest correlation for Koc is with the octanol/ water coefficient Kow, for which extensive databases and reliable estimation methods exist. The fugacity ofa chemical in the octanol phase of an octanol/ water two-phase system, by analogy with water, is
/=x0Yopl
The octanol/water partition coefficient is thus vwYw MwYwPo
v0Yo moYoPw
(5)
(6)
where the subscript O refers to the octanol phase.
Also used in Koc correlations is the solubility of pure chemical in water, which is reached when its fugacity equals that of the pure liquid saturated with water, and is approximately the pure liquid vapor pressure if water is sparingly soluble in the liquid. In such cases
/ = Pl xwYv/Pl
(7)
which implies that xwis approximately 1/ywand the solubility Sw in g/m3 (or mg/L) is M[Xw/ vw or Mj/(vwyw)- For solids the fugacity is that of the solid phase Pss; thus xw is (Pss/ Pls)/ yw or F/ yw, where Fis the fugacity ratio which can be estimated from the melting point and the entropy of fusion. In units of g/m3 (or mg/L), the solubility is FMJ(vwyw). For liquids F can be regarded as 1.0.
Existing Correlations. Most of the reported correlations are between log Koc and log Kow or log Sw- Unfortunately, the low water solubilities and high Kow values of highly hydrophobic compounds are difficult to measure accurately, and this may contribute to a loss of correlation. A major problem with the solubility correlations is the need to include
an estimate for F for solid substances. This "correction" is frequently and wrongly ignored. The most attractive approach is to use Kow for correlation purposes, largely because it avoids the necessity of estimating Fand also because of the availability of an extensive database (MedChem Master file) fornearly 10 OOOchemicals (7).Forotherchemicals,ifowcan be estimated from structural properties (8). An additional advantage of using Kow is that it contains the quantity yo, activity coefficient of the chemical in octanol. As molar volume increases, it is likely that yo increases reflecting growing molecular dissimilarity or nonideality. It is possible that yc, the corresponding coefficient in organic carbon, also increases, and thus any increasingly nonideal behavior in organic carbon may be compensated for in part by the increase in yo-
In a systematic study, Sab ljic et al. (9) examined Koc versus Kow relationships for different chemicals, and general and class-specific models for predicting Koc from Kow data were derived. For the predominantly hydrophobic chemicals, however, Sabljic et al. (9) noted that the Koc data had large uncertainties, particularly in the log ifowrange from 4 to 7.5. They derived a model based on first-order molecular connectivity indices. Such correlations may give an apparently superior fit to those with ifowas a result of inclusion of some erroneous experimentaldata in the ifowcorrelations. As more accurate and critically reviewed if0wdata become available, it is likely that Kow will become the favored molecular descriptor.
Because of the wide variation in Koc, the correlation is usually of the form
log Koc = A log K0
B
(8)
For example, Karickhoff (10) obtained values of A of 1.0 and B of — 0.35 for PAHs from benzene to pyrene. For most of the other proposed correlations (1), A is less than 1.0, typically 0.8. The factors which control A are examined below.
Discussion
Development of Estimation Methodology. As eqs 3 and 6
show, both Koc and K0w contain the term yw. This quantity varies from less than 1.0, for highly polar substances, to values of 106 or more for nonpolar hydrophobic substances. A relationship between Koc and Kow is thus highly autocor-related, being strongly influenced by the variable yw which is present in both quantities. Subtle contributions of, or changes to, the other terms such as yo or yc tend to be obscured. This problem can be avoided by correlating Kod Kow which, from eqs 3 and 6, is voyo/(vcpcyc)or voyol (Mcyc)-The key quantities in these ratios that vary from chemical to chemical are yc, which expresses (inversely) the affinity of the chemical for the OC phase, and yo, which is similar but applies to the octanol phase. Two situations may arise:
First is the special case in which yolyc (and hence Kod Kow) is constant for chemicals with different molecular properties (or Kow)- Then, from eqs 3, 6, and 8, A is 1.0 and B is log(v0y0/vqocyc).
Second, yolyc may vary with molecular properties (or with Kow)' e.g., yd yo may increase with increased molecular mass or K0w, and a relationship may exist of the form
YolYc =YK0nw where Y and n are constants or
YqVq
Y'Kow - Woe1 W
YcVcPc
where Y' is Yvo/vcpc- This leads to the correlation
VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY ■ 2391
log Koc = (1 - n) log Kow + log Y'
If ydyo is weakly dependent on Kow, for example, to the power n of 0.2, we obtain
log Koc = 0.8 log Kow + log Y
(9)
The preponderance of correlations with A in the range 0.6—0.8 suggests that this second situation applies. The implication is that with increasing molecular size or Kow, yc increases more than yo, or at least the ratio yd yo increases. Chiou et al. (4) have shown that yc is lower for PAHs than other nonpolar solutes such as PCBs, i.e., PAHs behave more ideally in organic matter. It is therefore likely that the ratio yd yo and its dependence on molecular size also depend on chemical class. Thus, general correlations covering a wide range of chemicals are likely to be less accurate than class-specific correlations.
Data Analysis. Most of the data treated here for hydrophobic chemicals were obtained from the set compiled by Sabljic et al. (9) (81 data points). Data were also obtained from Karickhoff (10) (5 data points), Chin et al. (11) (4 data points), Chiou et al. (12) (11 data points), Pussemier et al. (13) (11 data points), and Schwarzenbach and Westall (14) (6 data points). When the organic matter partition coefficient Kom was reported, it was adjusted to Koc as 1.724ifoM (5).
Aeon ventional plot of log Koc versus log Kow for the data yielded the correlation (n = number of data points; r2 = coefficient of determination; s = standard error of estimate):
log Koc = 0.81 log Kow + 0.09
118; r = 0.89; s = 0.42
(10)
Figure 1 is a plot of log(ifoc/^ow) as a function oflogifowfor the same data. Plots of log(ifoc/^ow) versus molecular weight, molecular volume, and molecular area were generally similar (since Kow is related to these molecular descriptors) and are not included here. Figure 1 shows that 78% of the data (92 data points) lie in the range of KodKow of 0.1 — 1.0 with 3% (4 data points) exceeding 1.0 and 19% (22 data points) less than 0.1. Linear regression yielded
-0.19 log K0
0.09
(11)
118; r = 0.31;
■■ 0.42
Although eqs 10 and 11 are algebraically similar, the high r2 value of 0.89 for eq 10 is largely a result of the strong autocorrelating influence of ywon both Koc and Kow values. This autocorrelation masks the variability in Koc shown in Figure 1.
The primary reason for the negative slope in eq 11 and the slope of 0.81 in eq 10 is a group of 15 data points, with Koc/ Kow < 0.1, to the lower right of Figure 1. They are PCBs (8 data points), chlorobenzenes (tri, tetra, penta, and hexa), DDT, DDE, and aldrin. The only data point with Kod Kow significantly above 1.0 was mirex. As shown in Table 1, which summarizes data from a handbook by Mackay et al. (15), for chemicals such as DDT, DDE, aldrin, and mirex, there is a wide range in the reported Koc values. Clearly, any correlation is readily distorted if an erroneously low value ofifoc is used. This has the effect of reducing the slope A in eq 8.
Koc data (275 points) for 48 congeners of PCBs compiled by Mackay et al. (16) are plotted in Figure 2. The eight most studied congeners account for more than 50% of these data. The scatter in the data is impressive with 12% exceeding Kod Kow of 1.0, 36% lying between 1.0 and 0.1, 39% lying between 0.1 and 0.01, and 13% lying below 0.01. It seems inconceivable that organic matter varies so greatly in
0.5 0
1.
■£ -0.5
o
^ -1
V)
o
-1.5 -2 -2.5
♦ Chiouetal. (1983) -Karickhoff (1981)
OChin et al. (1988) ■ Pussemier et al. (1990)
ASchwarzenbach and Westall (1981)   OSabljic et al. (1995)
log Kow
FIGURE 1. Plot of \og(KoclKovi) vs log Kbw for hydrophobic chemicals for the Initial data set compiled (regression eq 11).
TABLE 1. Variability In the Reported Kow and Koc for Selected Chemicals from Mackay et al. (15)a
log Koc
chemical
DDT DDE aldrin mirex
range
4.09-6.81
3.7- 6.64 2.6-4.7
3.08- 6.42
data (numbers)
25
4
a Including both measured and estimated values, obvious outliers were ignored.
5.5 6.5 7.5 8.5
log Kow
FIGURE 2. Scatter In log(Kbc/Kbw) as a function of log Kan for PCBs, using data from ref 16.
properties; thus we believe that many of these data points are erroneous. The principal cause is believed to be non-attainment of equilibrium: i.e., the equilibration times used in these estimations were insufficient. In a critical review of research over the past decade, Pignatello and Xing (6) have shown that the solid-phase to solution-phase partition coefficients are routinely measured and reported at non-equilibrium conditions. In most cases, the uptake or release of organics by natural particles is bimodal in that it occurs in fast and slow stages. Many reported Koc values for soil represent principally the fast component rather than overall sorption (17). This has the effect of reducing these values, especially for hydrophobic chemicals which require longer equilibrium times.
Support for attributing the variability in Koc values to nonattainment of equilibrium, for predominantly hydrophobic chemicals with high Kow values, can also be found
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15
0 5 0
* -0.5
£ -1 o
-1.5 -2 -2.5
7
Eq. 14
\ X. - - v " '
° a- •y0 _....... ■•»• "i* x    * *
^'' o'         o° . 9          »   ■■* * ■
n -°p  J, -5—* * I-'
............
0
♦Chiou et ai. (1983)	-Ka rickhoff (1981)
OChin etai. (198B)	■ Pussemleret al. (1990)
A Schwarzenbach and Westall (198	)   OSabljicetal. (1995)
JCHippelein and McLachlan (1998)	• Cousins et al. (1998)
log Kow
RGURE3. Plot of log(Kbc/Kbw) vs log Kan for hydrophobic chemicals for the modified data set as explained in the text (regression eq 12).
in some recent experimental studies (18,19). For 10 different congeners of PCBs with log Kow > 5.5, the KodKow data derived based on Ks\ measurements of Cousins et al. (19) showed that on increasing the equilibration time from 3 to 83 days, the Kod Kow values increased from between 0.005 and 0.43 to between 0.08 and 0.6. Further increase in equilibration time had little effect. The Koc values were derived from the measured Ks\ (soil—air) values and K\w (air—water) partition coefficients for which also accurate estimates are available.
Of the 24 data points with log Kow > 5.5 in Figure 1, a majority (14 data points) were PCBs. These data points were replaced by 23 data points for various congeners of PCBs with log Kow > 5.5 obtained using Ks\ measurements by Cousins et al. (19) and Hippelein and McLachlan (18). An equilibration time of approximately 3 months was used in both cases. Alinear regression on this modified data (Figure 3) yielded
\og(Koc/Kow) = 0.03 log Kow - 0.61
(12)
n = 117; r = 0.02; s = 0.38
or equivalently
logÄoc = 1.03 logZ0
0.61
(13)
The low correlation coefficient for eq 12 is the result of the random variability in Koc values, as also shown by the residuals plot in Figure 4. This variability is masked in the conventional log Koc versus log Kow plot which, for the modified data set, also yielded eq 13 but with an r2 value of 0.95 and gives a false impression of predictability.
The residuals are uniformly distributed and are independent of Kow for log Kow values greater than about 2.5 (Figure 4). The residuals for the new data introduced (log Kow > 5.5), though random, are seen to be predominantly positive. This is due to the influence of the large number of data points between log Kow values of 3 and 5 for which we have no basis for reexamination. The residuals for K0w values less than 2.5 are less scattered but mainly positive with a tendency to increase with reducing Kow values, denoting underestimation of the predicted Koc values. However, as mentioned earlier, the measured Koc values for such chemicals are susceptible to overestimation due to the inclusion of dissolved solute in the water associated with the organic matter and the presence of sorption to nonorganic matter.
♦ V X
****** ♦
log Kow
FIGURE 4. Plot of residuals between experimental and predicted values of log Koc using eq 12.
Recommended Approach. The large variability in reported Koc values requires that the estimates derived based on correlations should include a measure of the associated uncertainty, and we have used 95% confidence boundaries for the purpose. Alinear regression analysis was conducted on the modified data set used to obtain eq 12, and 95% confidence limits were obtained for the slope and intercept. The boundaries obtained using these limits are plotted in Figure 3 and correspond to the following equations:
upper limit
log(Koc/Kow) = 0.08 log Kow - 0.41 or equivalently
log Koc = 1.08 log Kow- 0.41
lower limit
log(Koc/Kow) = -0.01 log Kow - 0.81 or equivalently
log Koc = 0.99 log K0
0.81
(14)
(15)
(16)
(17)
Equations 14 and 16 show that the slope of the regressed line on the modified data (eq 12) is not significantly different from zero, which, when substituted in eq 12, justifies the frequently used approximation of Koc = 0.4ifow-
As noted by Cousins et al. (19), although their data set was obtained for the same group of chemicals (PCBs) and using exactly the same technique as Hippelein and McLachlan (18), the slopes of the regressions obtained using the two data sets independently were distinctly different (as can also be seen from their data plotted in Figure 3). This difference was attributed to the variability in the organic matter of the soils used. Both these data sets are however within the confidence boundaries defined by eqs 14 and 16. We thus recommend that in environmental and/or risk assessments, Koc values for hydrophobic chemicals should be considered as a distribution bounded by eqs 14 (or 15) and 16 (or 17), rather than as discrete numbers derived from one of the numerous correlations in the literature. These equations should be applicable to all situations where partitioning into organic matter is expected to be the dominant process for chemical sorption. If the results are found to be sensitive to Koc then, if needed, a more accurate estimate of its value should be sought for the specific environmental situation under consideration.
Because the coefficient on log Kow is not significantly different from zero, we suggest a simpler correlation that log(ifoc/^ow) is —0.48 with an upper limit of —0.05 and a
VOL. 33, NO. 14, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY ■ 2393
lower limit of —0.86. This is equivalent to asserting that Koc is 0.33ifow with an upper limit of 0.89ifow and a lower limit of 0.14ifow- A useful rule of thumb may thus be that Koc is 0.35ifow with variation by a factor of 2.5 in either direction. If this rule ofthumb is applied to the data used in developing the correlation equations above, about 80%ofthe data points in Figure 3 lie within these limits.
In conclusion, the variability in the composition of organic matter present in soils and sediments and the experimental difficulties and constraints in ifocmeasurements are believed to explain the wide variability in the reported values. Therefore, considerable uncertainties are expected in Koc values estimated from correlations. Koc estimations based on Kow values are preferable to those based on solubility. The suggested approach is to correlate KodKow with a molecular property or Kow, rather than log Koc with log Kow-This, in our opinion, gives a better indication of uncertainty in Koc- It is suggested that Koc estimates using correlations be viewed as a distribution, which includes this uncertainty, rather than a single value. When gathering and reporting experimental data for hydrophobic chemicals, it is desirable to calculate ifoc//?owand examine and report its magnitude. Values exceeding 1.0 and below 0.1 should be subjected to special scrutiny. Finally, when measuring Koc, care must be taken to ensure that equilibrium is achieved. The time required could be severalmonths and can be estimated using the correlation for the "slow" sorption rate constant as a function of molecular volume suggested by Cornelissen et al. (20).
Acknowledgments
The authors are grateful for financial support provided by NSERC and the consortium of chemical companies which support the Environmental Modelling Centre.
Literature Cited
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(5) Lyman, W. J. In Handbook of Chemical Property Estimation Methods; Lyman, W. J., Reehl, W. F., Rosenblatt, D. FL, Eds.; American Chemical Society: Washington, DC, 1990; Chapter 4.
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(11) Chin, Y.-P.;Peven, C. S.; Weber, W. J. Water Res. 1988,22 (7), 873.
(12) Chiou, C. T.; Porter, P. E.; Schmedding, D. W. Environ. Sei. Technol. 1983, 17 (4), 227.
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(15) Mackay, D.; Shiu, W. Y.; Ma, K. C. Illustrated Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals; Lewis Publishers: Chelsea, MI, 1997; Vol. 5.
(16) Mackay, D.; Shiu, W. Y.; Ma, K. C. Illustrated Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals; Lewis Publishers: Chelsea, ML, 1992; Vol. 1.
(17) Pignatello, J. J.; Ferrandino, F. J.; Huang. L. Q. Environ. Sei. Technol. 1993, 27, 1563.
(18) Hippelein, M.; McLachlan, M. S. Environ. Sei. Technol. 1998, 32, 310.
(19) Cousins, LT.;McLachlan,M. S.; Jones, K C.Environ. Sei. Technol. 1998, 32, 2734.
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Received for review August 31, 1998. Revised manuscript received April 12, 1999. Accepted April 19, 1999.
ES980893J
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