Environ. Sci. Technol. 1990, 2 4 , 575-580
sampled, since relatively long time series were observed within each system. It shows promise for use in other longitudinal studies of health effects of environmental contaminants . This is the longest time series of coliform measurements reported in the literature to date, and as such, it has provided a unique opportunity to perform a longitudinal study of the relationship between rainfall and coliform contamination. The relationships we have reported were averages, obtained over the observed systems. The actual relationships probably vary according to other system characteristics, such as depth of the source, type of water treatment, and nearby sources of contamination; geographical factors, such as depth of the water table and type of material through which the well casing passed; and environmental factors, such as season and ground permeability. The number of systems studied was too small to permit these analyses. A larger study including more systems with different combinations of characteristics and more information on each system would be needed in order to study these questions further. Acknowledgments
We thank E. Rice for assistance with the study, R. Neff for statistical advice, W. Zeigler for technical assistance, E. Fuller for sample collection, and V. Bergen for manuscript preparation. L i t e r a t u r e Cited (1) Craun, G. F.; McCabe, L. J. J. Am. Water Works Assoc. 1973, 65, 74-83. (2) Craun, G. F.; McCabe, J. L.; Hughes, J. M. J. Am. Water Works Assoc. 1976, 68, 420-424. (3) Craun, G. F. Groundwater 1979, 17, 183. (4) National Interim Primary Drinking Water Regulations. U.S.Environmental Protection Agency, Washington, DC, 1976; EPS-57019-76-003. (5) Fed. Regist. US.Environmental Protection Agency, 40 CFR Parts 141 and 142, Washington, DC, 1989,54,No. 124, 27544-27568.
(6) Sandhu, S. S.; et al. Appl. Environ. Microbiol. 1979,37,744. (7) Geldreich, E. E.; Best, L. C.; Kenner, B. A,; van Donsel, D. J. J. Water Pollut. Control Fed. 1968, 40, 1861-1872. (8) Sartor, J. D.; Boyd, G. B.; Agardy, F. J. J. Water Pollut. Control Fed. 1974,46, 458-467. (9) van Donsel, D. J.; Geldreich, E. E.; Clarke, N. A. Appl. Microbiol. 1967, 15, 1362-1370. (10) Qureshi, A. A.; Dutka, B. J. Water Res. 1979,13,977-985. (11) Kelch, W. J.; Lee, J. S. J. Water Pollut. Control Fed. 1978, 50, 862-868. (12) Barrell, R. A.; Rowland, M. G. J. Hyg. 1979, 83, 143. (13) Lamka, K. G.; LeChevallier, M. W.; Seidler, R. J. A p p . Environ. Microbiol. 1980, 39, 734-738. (14) McDonald, A.; Kay, D. Water Res. 1981, 15, 961-968. (15) Kay, D.; McDonald, A. Appl. Environ. Microbiol. 1983,46, 611-618. (16) Stukel, T. A.; Reed, F. C.; Greenberg, E. R.; Jacobs, N. J. J . A m . Water Works Assoc. 1987, 79, 50-54. (17) Climatological Data-New England; National Oceanic and Atmospheric Administration: Washington, DC, 1983 and 1984. (18) Geldreich, E. E. Handbook for Evaluating Water Bacteriological Laboratories, 2nd ed.; U.S.Environmental Protection Agency: Cincinnati, OH 1975. (19) Standard Methods for the Examination of Water and Wastewater, 16th ed.; A.P.H.A., A.W.W.A., and W.P.C.F.: Washington, DC, 1985. (20) Jacobs, N. J.; Zeigler, W. L.; Reed, F. C.; Stukel, T. A,; Rice, E. W. Appl. Environ. Microbiol. 1986, 51, 1007-1012. (21) Bordner, R., Winter, J., Eds. Microbiological methods for monitoring the environment-water and wastes; U.S. Environmental Protection Agency: Cincinnati, OH, 1978. (22) Kom, E. L.; Whittemore, A. S. Biometrics 1979,35,795-802. (23) SUGI Supplemental Library User’s Guide, Version 5 ed.; SAS Institute, Inc.: Cary, NC, 1986.
Received for review March 14,1989. Revised manuscript received September 25, 1989. Accepted December 6,1989. This project was supported by the U.S. Environmental Protection Agency through cooperative agreement CR-810805 with the Connecticut River Watershed Council and by the Hitchcock Foundation. This paper was presented at the Environmetrics 87 conference in Washington, DC, in November 1987.
Adsorption from Aqueous Phase by Activated Carbon: A Simplified Application of the Solvophobic Theory Nagamany Nirmalakhandan and Richard E. Speecet
New Mexico State University, Las Cruces, New Mexico 88001, and Vanderbilt University, Nashville, Tennessee 37235
A simple approach to predict adsorption capacity of activated carbon is presented. Developed from the solvophobic theory of adsorption, this simplified approach uses molecular descriptors that are easy to calculate from the molecular structure of the adsorbates. A distinctive feature of this approach is that a single generalized model could predict the adsorbability of different classes of compounds. The predictive abilities of this general model and the different class-specific models derived by using the regular solvophobic approach are compared to demonstrate better quality of prediction possible by this general model. Introduction
Use of activated carbon in water, wastewater, and hazardous wastes treatment has been growing rapidly over the
* New Mexico State University. t Vanderbilt
University.
0013-936X190/0924-0575$02.50/0
past decade due to increasing awareness of the potential hazards of manmade chemicals, and the stringent regulatory standards enacted by regulatory agencies. Today’s treatment goals are focused on individual chemicals, rather than gross parameters such as BOD, TOC, etc. Thus, treatment technologies have also to be developed and designed toward meeting those chemical-specificstandards and goals. Adsorption of chemicals from aqueous solutions by activated carbon has been identified as one of the feasible technologies for meeting such chemical-specificstandards. Because activated carbon can adsorb chemicals preferentially, for proper selection and design of a treatment system, a knowledge of the adsorbability of different chemicals on different carbons is desirable. Adsorbability data are routinely generated in the laboratory using isotherm studies on batch systems. These data are used only as a screening tool in evaluating the suitability of the adsorption process for the chemical(s) of interest. If suitable then,
0 1990 American Chemical Society
Environ. Sci. Technol., Vol. 24, No. 4, 1990 575
continuous-flow pilot studies are run to obtain engineering data for design and scaleup. Since continuous-flow pilot studies are time consuming and expensive to run, often batch data are used instead with an appropriate safety factor. Batch studies can also indicate the preferential adsorbability in multisolute systems. However, considering the large number of chemicals identified as pollutants, and the availability of a range of carbons, experimental determination of the adsorbability becomes a laborious and sometimes risky undertaking. In addition, considering the overall treatment process costs, other process parameters may be of more importance than the adsorption capacity itself [Harbold (@I. Due to these practical considerations there is a growing interest in developing methods of predicting adsorbability with the minimum of experimental inputs. Such predictive methods can also be used in choosing the best parameters to test at pilot scale, to classify compounds according to adsorbability, and to corroborate and rationalize contradictory laboratory data. Many theories have been proposed to explain the adsorption phenomenon. Developed from fundamental thermodynamic and physical chemical concepts, these theories have been able to model the process with varying degrees of complexity and success. Three major models that have been discussed in detail in the literature are as follows: (1)the Polanyi adsorption potential theory developed by Manes and co-workers (9),(2) the net adsorption energy concept formalized by Suffet and McGuire ( I 4 ) ,and (3) the solvophobic approach adapted by Belfort and co-workers (I, 2). These theories were developed primarily to understand the mechanisms of adsorption of solutes from aqueous phase, rather than to predict ultimate design parameters. Applications of these models, in general, demand considerable insights, and numerous parameter inputs, which are either not readily available or questionable. Thus, at this point of development, the utility of these theories is of limited value to the process designer. In conjunction with these rigorous approaches, semitheoretical models too have been proposed to predict adsorption parameters. These models are also developed from the above well-founded theoretical concepts, but use empirical parameters as inputs. Thus, they are easier to use and are often sufficiently accurate for engineering purposes. One such method, reported by Kamlet et al. (61, uses the linear solvation energy relationship (LSER) approach to predict adsorption capacity, using three solvatochromic parameters. Another, reported by Chitra and Govind ( 4 ) , applies a group contribution technique to model the Freundlich isotherm constants, using nine parameters applicable to alcohols, aldehydes, ketones, and esters. Scope In this study, yet another simple, semitheoretical approach is presented, which can be used to predict adsorbability purely from the molecular structure of a chemical, without any experimental inputs. This approach follows the solvophobic theory and uses the molecular connectivity indexes and a modified polarizability factor to derive surrogate parameters to represent the solvophobic terms. The specific objective of this paper is to demonstrate the utility of this approach and its validity by analyzing the same three data sets used by Belfort et al. (I, 2) in validating their own model and comparing our results against theirs. A brief description of the solvophobic theory is outlined below, and the development of our x-9 model is detailed thereafter, followed by a comparison of 576
Environ. Sci. Technol., Vol. 24, No. 4, 1990
the results of our model against those of Belfort et al. Solvophobic Theory The solvophobictheory (C0 theory) has been developed by Belfort and co-workers from the generalized solution interaction theory originally proposed by Sinanoglu (13). Using a rather complex but elegant line of reasoning, Belfort et al. adapted this solution interaction theory to model the solvent role in the solute-solid adsorption phenomenon. Detailed description and derivation of the solvophobic theory have been presented elsewhere (I, 2). Here, only a very brief overview is given to lay the foundation for our approach. In the solvophobic analysis, the adsorption of solutes by activated carbon from the aqueous phase is modeled as a reversible association reaction given by s, + c = sic (1) where S, is the adsorbing solute, C is the activated carbon, and S,C is the adsorbed solute-carbon complex. The equilibrium constant for this reaction in the presence of a solvent, Ksols,is related to the overall free energy change, AGsol, under saturation conditions by the equation (2) AGsol = -RT In Kso1,, To model the effect of the solvent, two conceptual steps are proposed in the C 0 theory. First, a cavity in the solvent must be created to contain the solute. Second, the solute interacts with the surrounding solvent. The latter results from van der Waals and electrostatic effects. Considering all these j effects and summing them up, and substituting in (2) for dilute solute-solvent systems, In Ksol,r= (1/R79AGsol = ( l / R T ) ~ W s o l l l (3) The summation term in the above equation, which represents a series of solvophobic terms, could be expanded by using simple notations: UAGsoll, = Const + {AGcav{+{AGvd,J + (AG,,J - R T In ( R T / P , V ) (4) where, cav relates to the cavity term, vdw relates to the van der Waals term, and est relates to the electrostatic effects. The last term (cratic term) is a measure of the reduction in entropy associated with the free volume reduction involved in transferring of the solute molecule from the gas phase into the solvent. Rigorous determination of the appropriate numerical values for the above terms has been made possible with certain assumptions, but involves considerable data input such as solute molecular surface area (total surface area, TSA), surface tension corrected for TSA, ionization potential, molar volume of solute, molecular volume of solute, dipole moment, dielectric constant of the solvent, ionic charge, ionic strength, etc. Recognizing this as a major limitation to the utility of their comprehensive analysis, Belfort et al. suggested a simplified approach to make it more manageable. Instead of using the whole array of solvophobic terms, they proposed surrogate molecular properties to relate to adsorbability. Since the solvophobic terms are more related to the surface area and volume, their logical choice has been the total surface area of the solute, TSA. They also found that, in some homologous series, simply the molecular weight alone could correlate well with adsorbability. From a predictive point of view, this analysis leads to a linear relationship between the log of adsorbability and the solvophobic parameters in the comprehensive analysis, in the simplified approach, between log of adsorbability and total surface area. In their model validation studies,
Belfort et al. used [QOb]as the measure of adsorbability where, Qo and b are the Langmuirian isotherm model parameters. Thus, the comprehensive solvophobic model takes the form [QObI = A[(AGaV\ -k IAGvdw)-k {AGJ - R T In (RT/PoV)I + (5) and, the simplified solvophobic model takes the form (6) In [QOb] = A’[TSA] + B’ where, A, B, A’, and B’ are the model coefficients in the respective equations.
Connectivity-Polarizability (x-9) Model The x-9 model developed here follows the solvophobic concept and attempts to derive surrogate parameters that could be obtained directly from the molecular structure for all classes of compounds. The major objective of our study is to address one of the disturbing results of Belfort’s simplified approach even though TSA fits the adsorption data, different models are needed for different classes of compounds. This leads to a possible conclusion that TSA does not adequately encode all the adsorption-related information contained by the solvophobic terms in tandem. From the solvophobic analysis it is clear that the adsorption of solutes from aqueous phase on a given carbon is related directly and indirectly to a host of shape- and size-related properties, as well as polarizability related properties. A series of molecular topological parameters proposed by Kier and Hall (7,8)as molecular connectivity indexes have been shown to be rich in such information content. They have been successfully correlated with many similar molecular properties, as well as phenomenological properties such as aqueous solubility and octanol-water partitioning. We also use a modified form of Ketelaars polarizability model to derive a parameter to represent the electronic interactions. In this study, the third-order cluster type connectivity index, 3xc,and the modified polarizability parameter, 9, are correlated against adsorbability data, In [Q%] , of three congeneric data sets generated and reported on by Belfort et al. The first set contains 12 alcohols, the next one 21 ketones, and the last one 19 phenols. The first two sets were obtained from ref 1, and the third, from ref 2. Even though the chemicals in these data sets are not as diverse as one would like to test, they are internally consistent, in that the same carbon was used under identical conditions in all the isotherm studies. (In the original study, these compounds were selected by Belfort et al. primarily to examine the effects of branching among congeneric sets.) In deriving our model, a multiple regression analysis procedure was used to derive the best model for all 52 compounds together. The algorithm used in calculating the third-order cluster type connectivity index, 3xc, is shown in the Appendix. The d term is formulated as an atomic contribution term as in Ketelaars model for polarizability, but the coefficients of the atomic terms were optimized statistically to obtain the best model, as described elsewhere (10-12). Results of Connectivity Model The regression procedure resulted in the following model: In [QOb] = -0.78 + 1.009 - 0 . 7 8 3 ~ c (7)
n = 52; r = 0.95; r2 = 0.90; SE = 0.61 where 9 = -1.00 X (number of C) - 0.137 X (number of H). The overall quality of the fit of this model is shown in Figure 1. In evaluating the quality of this model as a
n = 52; r = 0.95; std error = 0.616
0
12Alcohols
A 21Ketonw --
I
-2
.~ , 0
A
.
Q
;
.
1
4
‘
$
19Phenols
’
I
i .
Calculated Adsorbability Flgure 1. Comparison between observed and calculated adsorbability-connectivity model using eq 7.
general predictive tool, it has to be borne in mind that the @I values used in deriving the model were calculated from the Langmuirian isotherm constants Qo and b, which in turn were obtained by fitting the “best straight line” through the experimental data points. In general, the regression coefficients of these best straight lines ranged from 0.95 to 0.98. Thus, considerable uncertainty are associated with the Qob values. Given such uncertainty, the precision of the model can be seen to be as good as that of the experimental determinations. Table I lists the chemicals considered, their observed and calculated In [ Qob] values, and the error, obtained as the difference between the observed and calculated values. On analyzing these differences, nine chemicals showed errors more than a factor of 2 (In = 0.69). An unduly high error of a factor of 7.2 (In = -1.98) was noted for 2propanone. Compared to the standard error of 0.609 (In unit) of the model, such a high error indicates positive outlying tendency, either due to experimental errors in vb, or due to abnormal mechanistic behavior of this compound. This suspicion was further strengthened when deletion of this compound increased the r from 0.95 to 0.97, yielding a more precise fit to the rest of the data. As can be seen later, this compound showed similar high errors in the studies by Belfort et al. Scrutiny of the parent data set revealed that, for this compound, the linear isotherm did not fit the experimental data satisfactorily-the r value was 0.61, confirming the possibility of some experimental errors. The ability to highlight such abnormal data points adds further credence to our model. The most significant point to note is that the same model is able to fit all 52 compounds. This clearly shows that the x - 9 combination is more efficient than TSA in predicting adsorption data of mixed classes of compounds. This result is highly significant in that TSA requires different models for each class of chemicals. Also, as will be shown later, the quality of fit of the x - 9 model to the entire data set is superior to that of the TSA models and the comprehensive models, even though the latter two are applicable only to the congeneric sub sets. The statistical robustness of our approach is demonstrated by examining the independent variables for any collinearity effects. As a preliminary test, intercorrelation between x and ip was checked and was found to be 0.132, indicating negligible collinearity effects. The question of collinearity is further addressed by use of several collinearity indicators. First, the percentage of total variance in data matrix accounted by the first principal component was used as an indicator. For completely orthogonal data, this indicator is normally less than lo%, while a value greater than 90% indicates severe collinearity. The calculated value of 56.690 showed minimal effects of collinearity. Second, the number of principal components needed to account for 99% of the variance was calculated Environ. Sci. Technol., Vol. 24, No. 4, 1990 577
Table I. Comparison of Adsorbability: Observed vs Calculated Using Equation 7
IP 1 2
3 4
5 6 7
8 9 10 11 12
1-butanol 2-methyl- 1-butanol I-pentanol 2,3-dimethyl-2-butanol 3,3-dimethyl-l-butanol 2-ethyl-1-butanol 2-methyl-3-pentanol 4-methyl-I-pentanol 1-hexanol 2,4-dimethyl-3-pentanol 3-ethyl-3-pentanol 1-heptanol
2.79 3.52 3.52 4.26 4.26 4.26 4.26 4.26 4.26 4.99 4.99 4.99
2-propanone 2- butanone 2-pentanone 3-pentanone 3-methyl-2-butanone 2-hexanone 4-methyl-Z-pentanone 2-methyl-3-pentanone 3,3-dimethyl-2-butanone 2-heptanone 3-heptanone 4-heptanone 4-methyl-2-hexanone 5-methyl-2-hexanone 2,4-dimethyl-3-pentanone 2-octanone 3-methyl-2-heptanone 5-methyl-3-heptanone 2-nonanone 5-nonanone 2,6-dimethyl-4-heptanone
2.20 2.93 3.66 3.66 3.66 4.39 4.39 4.39 4.39 5.12 5.12 5.12 5.12 5.12 5.12 5.86 5.86 5.86 6.59 6.59 6.59
phenol 2-methylphenol 4-ethylphenol 2,6-dimethylphenol 2,3-dimethylphenol 3,4-dimethylphenol 3,5-dimethylphenol 2,5-dimethylphenol 4-propylphenol 4-isopropylphenol 2,3,5-trimethylphenol 2,3$-trimethylphenol 2-butylphenol 4-butylphenol 4-tert-butylphenol 2-pentylphenol 4-pentylphenol 4-tert-pentylphenol 2-hexylphenol
5.35 6.08 6.82 6.82 6.82 6.82 6.82 6.82 7.55 7.55 7.55 7.55 8.28 8.28 8.28 9.01 9.01 9.01 9.74
3Xc
12 Alcohols 0.00
0.29 0.00
1.65 1.56 0.20 0.57 0.41 0.00
0.86 0.93 0.00
adsorbability, In lQobl obsd calcd
error
1.29 2.54 2.14 1.78 2.07 3.33 3.16 3.52 4.12 3.45 3.30 4.72
2.01 2.51 2.74 2.17 2.24 3.31 3.02 3.15 3.47 3.53 3.47 4.21
-0.72" 0.03 -0.60 -0.39 -0.17 0.02 0.14 0.37 0.65 -0.08 -0.17 0.52
-0.84 1.17 3.14 2.67 1.67 3.64 3.27 2.84 2.59 4.81 5.18 5.51 4.42 4.45 3.88 4.98 4.97 4.79 4.99
1.14 1.95 2.68 2.74 2.49 3.41 3.09 3.27 2.49 4.15 4.20 4.20 3.92 3.82 3.79 4.88 4.75 4.71 5.61 5.67 5.02
-1.98"~~ -0.78" 0.46 -0.07 -0.82" 0.23 0.18 -0.43 0.10 0.67 0.98" 1.31° 0.50 0.63 0.09
4.44 5.07 5.81 5.71 5.71 5.67 5.64 5.67 6.54 6.33 6.31 6.34 7.30 7.27 6.31 8.04 8.01 6.77 8.74
0.26 0.33 0.09 0.79" 0.49 0.43 0.46 0.43 -0.24 -0.53 0.19 0.36
21 Ketones
13 14 15 16 17 18 19 20 21 22
23 24
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
43 44 45 46 47 48 49 50 51 52
0.35 0.25 0.25 0.18 0.49 0.25 0.66 0.43 1.42 0.25 0.18 0.18 0.54 0.66 0.70
0.25 0.41 0.47 0.25 0.18 0.99 19 Phenols 0.17 0.29 0.28 0.41 0.41 0.46 0.50 0.46 0.28 0.55 0.58 0.54 0.25 0.29 1.50 0.25 0.29 1.85 0.29
5.05
5.27 4.70 5.40 5.90
6.50 6.20 6.10 6.10 6.10 6.30 5.80 6.50 6.70 7.20 7.23 6.50 7.20 7.40 6.70 7.10
0.10
0.22 0.08
-0.62 -0.62 0.25
-0.10
-0.04 0.19 -0.84" -0.61
-0.07 -1.64"
"Error greater than factor of 2. bExperimental error possible.
as 2, which being equal to the number of variables in the model confirmed the absence of any collinearity problems. Finally, the condition number, 1.14, calculated as the square root of the ratio of the largest eigenvalue (=1.132) to the smallest eigenvalue (=0.868), also confirmed negligible collinearity, compared to the threshold value of 30 suggested by Belsley et al. (3).
Comparison between Connectivity Model and the Solvophobic Models Results of our model are now compared against those of Belfort et al. Even though the objective of their studies 578
Environ. Sci. Technol., Voi. 24, No. 4, 1990
was primarily to validate the solvophobic theory, their results enable us to evaluate the predictive ability of the solvophobic approach. We fully appreciate that the implications of the solvophobic theory (and the other theories of adsorption) extend beyond just predictive ability. However, from an engineering point of view, there is a pressing need for a general and simple predictive technique for rapid estimation of adsorption parameters. The emphasis of our study is in meeting this need, and the comparisons below are made only in that context. As indicated earlier, the first point to note is that, in both their comprehensive and the simplified solvophobic
-2
0
2
4
6
S
-2
2
0
Calculated Adsorbability Flgure 2. Comparison between observed and calculated adsorbability-comprehensive solvophobic model using eqs 8- 10.
6
4
Figure 3. Comparison between observed and calculated adsorbabili-simplified solvophobic model using eqs 11-13.
models, separate eauations are needed to model the three classes .of compounds considered here. Comprehensive Models: Alcohols
s
8
o
A A
In [QOb]= 0.793 - 0.204(1/RT)AGSoI
12Alcohols
n = 12; r = 0.946; SE = 0.402
A 21 Ketones
A
Ketones In [QOb] = 1.784 - 0.149(1/RT)AGSo1 n = 21; r = 0.852; SE = 0.873
Phenols In [QOb] = 4.675 - 0.033(1/RT)AGs0,
n = 19; r = 0.888; SE = 0.325 Simplified Models: Alcohols
In [QOb] = -8.592 - O.04OTSA
n = 12; r = 0.926; SE = 0.398 Ketones In [QOb] = -5.715 - 0.030TSA
n = 21; r = 0.905; SE = 0.708 Phenols In [QOb]= 1.996 + O.Ol3TSA n = 19; r = 0.874; SE = 0.343
In contrast, in the x-9 approach, the same equation fits all three classes with the same degree of fit as shown in Figure 1. Considering the amount of data inputs and the computational aspects in the solvophobic models, this is a desirable feature when a large number of different classes of compounds are to be evaluated. Comparing Figure 1 with Figures 2 and 3, the overall quality of fit is seen to be almost the same in all the three approaches. However, compared on the basis of the regression coefficient, r, that in the x-@ model (=0.95) is more than the r of any of the smaller subsets modeled by the solvophobic approaches (=0.92,0.85, and 0.89). Rather than using r for comparing the quality of fits of the different sized models, the adjusted r2 is used as a more appropriate parameter. Calculated as
KN - Ur2 -PI ( N - P - 1) the adjusted r2 is the coefficient of variation, adjusted for effects of number of cases and number of variables. This allows two or more data sets of different cases and variaadj r2 =
S
Calculated Adsorbabfity
-2 ! 100
19Phenols
0
I
I
I
4
200
300
400
500
TSA (A2) Flgure 4. Correlation between observed adsorbability and TSA-simplified solvophobic model based on eq 6.
bles to be compared on an equitable basis. On this basis, the x-9 model can be clearly seen to be better than the two solvophobic models (0.88 vs 0.84, 0.81. and 0.75). The above results suggest that the x-@ parameters have a greater utility value and could be more efficient than TSA in encoding the adsorption-related molecular information that is conceptualized by the solvophobic energy terms. To test this hypothesis further, we attempted to correlate the adsorbability of the entire data set of 52 chemicals with TSA, and as shown in Figure 4, the result was found to be very unsatisfactory. Suitability of TSA in other structure-activity studies also has shown similar results: they fit the data reasonably well within congeneric sets, but not so well when diverse classes of chemicals are tested. In contrast, the connectivity indexes appear to work well among diverse classes of chemicals as well (10-1 2).
Conclusions In this study of prediction of adsorbability of activated carbon, simple surrogate parameters are proposed to represent the solvophobic terms derived from the solvophobic theory. The proposed parameters can be calculated from the molecular structure of solutes, without any experimental inputs. In correlating with the experimental data, they are shown to be more suitable than the commonly used total surface area parameter. The quality of fit of the proposed model using two simple molecular descriptors is even better than the comprehensive solvophobic model, which requires over 10 parametric inputs. While the comprehensive solvophobic model is conceded as a significant advance in understanding the adsorption of solutes from aqueous phase by activated carbon, its practical applicability has remained a difficult task. The proposed approach is expected to be a simple alternative for the process engineer. However, the limitations of the agplicability of the reported results have to be appreciated the correlations are valid only within the range of the experimental conditions under which the parent data were gathered-e.g., the effect of pH on ionization and the Environ. Sci. Technol., Voi. 24, No. 4, 1990 579
dependency of Langmuirian parameters on concentrations. Appendix
Sample Calculation of 3xc for 2,4-Dimethyl-3-pentanol. Step 1. Draw hydrogen-suppressed molecular skeleton and number nodes:
1
Step 2. Identify subgraphs containing three bonds connected together as a cluster: subgraph 1
1
A
subgraph 2
subgraph 3
2Y4 A S
3
3
5
Step 3. Allocate nodal values equal t o number of bonds at t h e node: nodeIDno.:
1
2
3
4
5
6
7
8
node value:
1
3
3
3
1
1
1
1
Step 4. For each subgroup, find
l/n (nodal value):
subgroup:
1
l/n (nodal value):
1/(1*3*3*1) 1/(3*3*3*1) 1/(3*3*1*1) = 0.11
2
= 0.04
3 = 0.11
Step 5. F i n d square root of contributions from each subgroup and sum up t o get 3xc: 3XC
= = 0.86
+ qizi +- fi
Glossary A, A’ regression model coefficients Langmuir model constant b regression model coefficients B, B’ activated carbon equilibrium constant for solute-carbon complex Kso1.i formation n number of chemicals used in model N number of cases in multiple regression analysis number of independent parameters used in mulP tiple regression analysis pressure Langmuir model constant r multiple regression correlation coefficient universal gas constant R adsorbing solute Si SiC adsorbed solute-carbon complex T absolute temperature total surface area TSA V molar volume free energy of cavity formation AGCW free energy of solute-solvent electrostatic interacAGwt tion overall free energy change AGSO1 free energy of solute-solvent van der Waals interAGvdw action third-order cluster type connectivity index 3xc
c
580
Environ. Sci. Technol., Vol. 24, No. 4, 1990
modified polarizability parameter Registry No. 1-Butanol,71-36-3; 2-methyl-1-butanol, 137-32-6; 1-pentanol, 71-41-0; 2,3-dimethyl-2-butanol, 594-60-5; 3,3-dimethyl-1-butanol, 624-95-3; 2-ethyl-1-butanol, 97-95-0; 2methyl-3-pentanol, 565-67-3; 4+methyl-l-pentanol,626-89-1; 1hexanol, 111-27-3; 2,4-dimethyl-3-pentanol, 600-36-2; 3-ethyl-3pentanol, 597-49-9; 1-heptanol, 111-70-6; 2-propanone, 67-64-1; 2-butanone, 78-93-3; 2-pentanone, 107-87-9;3-pentanone,96-22-0; 3-methyl-2-butanone, 563-80-4; 2-hexanone, 591-78-6; 4methyl-2-pentanone, 108-10-1; 2-methyl-3-pentanone, 565-69-5; 3,3-dimethyl-2-butanone, 75-97-8; 2-heptanone, 110-43-0;3-heptanone, 106-35-4; 4-heptanone, 123-19-3; 4-methyl-2-hexanone, 105-42-0;5-methyl-2-hexanone, 110-12-3; 2,4-dimethyl-&pentanone, 565-80-0; 2-octanone, 111-13-7; 3-methyl-2-heptanone, 2371-19-9; 5methyl-3-heptanone, 541-85-5; 2-nonanone, 821-55-6; 108-83-8; phenol, 5-nonanone, 502-56-7;2,6-dimethyl-4-heptanone, 108-95-2;2-methylphenol, 95-48-7; 4-ethylphenol, 123-07-9; 2,6dimethylphenol, 576-26-1; 2,3-dimethylphenol, 526-75-0; 3,4-dimethylphenol, 95-65-8; 3,5-dimethylphenol, 108-68-9; 2,5-dimethylphenol, 95-87-4; 4-propylphenol, 645-56-7; 4-isopropylphenol, 99-89-8; 2,3,5-trimethylphenol, 697-82-5; 2,3,6-trimethylphenol, 2416-94-6; 2-butylphenol, 3180-09-4; Cbutylphenol, 1638-22-8;4-tert-butylphenol, 98-54-4; 2-pentylphenol, 136-81-2; 4-pentylphenol, 14938-35-3; 4-tert-pentylphenol, 80-46-6; 2hexylphenol, 3226-32-2.
9
L i t e r a t u r e Cited Belfort, G.; Altshuler, G. L.; Thallam, K. K.; Feerick, C. P.; Woodfield, K. L. AIChEJ. 1984, 30, 197-207. Belfort, G.; Altshuler, G. L.; Thallam, K. K.; Feerick, C. P.; Woodfield, K. L. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Proceedings of Engineering Foundation Conference, Bavaria, West Germany, 1984; Chapter 6, pp 77-93. Belsley, D. A.; Kuh, E.; Welsh, R. E. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity; Wiley: New York, 1980. Chitra, S. P.; Govind, R. AZChE J. 1986, 32, 167-169. Harbold, H. J . Environ. Eng. (N.Y.) 1984, 110, 849-853. Kamlet, M. J.; Doherty, M. R.; Abraham, M. H.; Taft, R. W. Carbon 1985,23, 549-554. Kier, L. B.; Hall, L. H. Molecular Connectivity in Chemistry and Drug Design; Academic Press: New York, 1976. Kier, L. B.; Hall, K. H. Molecular Connectivity in Structure Activity Analysis; Research Studies Press Ltd.: Hertfordshire, England, 1986. Manes, M. In Activated Carbon Adsorption of Organics from Aqueous Phase; Suffet, I. H., McGuire, M. J., Eds.; Ann Arbor Science Publishers: Ann Arbor, MI, 1980; Vol. 1, Chapter 2, pp 43-64. Nirmalakhandan, N.; Speece, R. E. Environ. Sci. Technol. 1988,22, 328-338. Nirmalakhandan, N.; Speece, R. E. Environ. Sci. Technol. 1988,22, 1349-1357. Nirmalakhandan, N.; Speece, R. E. Environ. Sci. Technol. 1989,23, 708-713. Sinanoglu, 0. In Molecular Associations in Biology; Pullman, B., Ed.; Academic Press: New York, 1968; pp 427-439. Suffet, I. H.; McGuire, M. J. In Activated Carbon Adsorption of Organics from Aqueous Phase; Suffet, I. H., McGuire, M. J., Eds.;Ann Arbor Science Publishers: Ann Arbor, MI, 1980; Vol. 1, Chapter 4, pp 91-115. Received for review March 28,1989.Accepted November 15,1989.
