Environ. Sci. Technol. 1900, 24, 1013-1020
(43) Nazaroff, W. W.; Cass, G. R. Environ. Sci. Technol. 1989, 23, 157-166.
Received for review November 14,1989. Accepted March 12,1990. This publication is based upon research that was supported (in
part) by a Research Agreement from the Getty Conservation Institute. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Getty Conservation Institute of the J.Paul Getty Trust.
A Model for Anionic Surfactant Sorption Domlnic M. Di Toro,*otpt Laura J. Dodge,+ and Vincent C.
HydroQual Inc., 1 Lethbridge Plaza, Mahwah, New Jersey 07430, Environmental Engineering and Science Program, Manhattan College, Bronx, New York, 10471, and Human and Environmental Safety Division, Procter and Gamble Company, Cincinnati, Ohio 452 17
A model for anionic surfactant sorption to soils, sediments, and sludges is proposed. It relates the partition coefficient that characterizes the linear, low-concentration, portion of the isotherm to the surfactant critical micelle concentration as a measure of hydrophobicity, to either the organic carbon fraction or the cation-exchange capacity of the particles, and to the particle concentration itself. The particle interaction model is used as the framework for the latter effect. The available data span the low particle concentration region as well as the asymptotic region where only particle concentration controls the extent of sorption. Introduction The extent of the sorption of chemicals to particles significantly influences their fate, bioavailability, and toxicity. All modern environmental fate models require a specification of the partition coefficient in the water column and sediment compartments (1-3). The bioavailability and toxicity of chemicals in sediments is also influenced by the extent of sorption. For sedimentdwelling animals the interstitial water concentration has been found to correlate to bioaccumulation (4) and toxicity (5). That concentration is determined by the total quantity of chemical in the sediment and the extent of sorption. Hence the partition coefficient is directly involved in determining both the chemical and biological fate of chemicals. A model that can predict partition coefficients for a class of chemicals and particle types would be of considerable utility. A class of problems for which a model is available is the sorption of nonionic hydrophobic organic chemicals to soils and sediments [see Karickhoff (6)for an excellent review]. The characteristic that indexes the hydrophobicity of the chemical is the octanol-water partition coefficient, KOw. The important particle property is the mass fraction of organic carbon, f,. For particles with f, > 0.5%, the organic carbon appears to be the predominant sorption phase. The only other important environmental variable appears to be the particle concentration itself (7). For the reversible (or labile) component of sorption, a model has been proposed (the particle interaction model) that predicts the partition coefficient of nonionic hydrophobic chemicals over a range of nearly 7 orders of magnitude with a log,, standard error of 0.38 (8). Review of Previous Models for Surfactant Sorption. The sorption of surfactants to clay and mineral + HydroQual
Inc.
* Manhattan College.
'Procter and Gamble Co. Presently at the Institute of Environmental Sciences, Miami University, Oxford, OH 45056. 0013-936X/90/0924-1013$02.50/0
particles has been extensively studied and a number of reviews are available (9-11). A description of surfactant sorption has been proposed that identifies three distinct regions of the isotherm (12,13). The sorption at low solution concentrations conforms to a linear isotherm. At higher concentrations a Langmuir isotherm fits the data. Generally, this corresponds to the concentration range of surfactants in the environment of micrograms per liter to low milligrams per liter. The experimental data base for sorption of surfactants to inorganic adsorbents is quite extensive. The effect of chain length (14-16),position of the hydrophilic group (13, pH, and ionic strength (13,18,19)have all been investigated. The effect of particle concentration has also been observed (20,21). The focus of the surfactant sorption models proposed to date has been on the form of the isotherm (21-27). The sorption of surfactants to sediments has been less extensively examined. Data have been fit with linear (28, 29), Langmuir (30),and Freundlich (31-33) isotherms. The use of fraction organic carbon and octanol-water partition coefficient has been suggested as correlating parameters (28,29). The purpose of this paper is to present a model for the sorption of anionic surfactants that is constructed in the same spirit as the models for nonionic hydrophobic organic chemicals, including the particle interaction effect. Sorption Model Scope. The purpose of the data analysis presented below is to identify the correlating parameters for the partition coefficient. The scope of the investigation is limited in a number of ways. First, the investigation is restricted to soils, sediments, and sludges that are directly relevant to environmental fate and effects. Although the clay literature is large, it is unclear how to apply these results to natural sediments and soils. Second, only the linear portion of the isotherm is considered. It is possible that environmentally relevant concentrations could exceed the linear range. However, a model of the linear portion of the isotherm, which is characterized by the partition coefficient, is a necessary first step. Finally, the data are limited to anionic surfactants. Although some data for cationic (34-36) and nonionic (28) surfactants have been reported, the number of observations are too few to establish statistically valid model parameters for these classes of chemicals. The approach taken to the model building is as follows. First, data from diverse sources are evaluated for the presence of a minimum number of necessary parameters. The model is patterned after the model for nonionic hydrophobic organic chemicals (6, 8). The critical micelle concentration (CMC) of the surfactant is the analogue of KO, in the models for nonionic hydrophobic organic
0 1990 American Chemical Society
Environ. Sci. Technol., Vol. 24, No. 7, 1990
1013
Table I. Sorption Data
chemicals
Table 111. Statistical Summary-Sorption
adsorbent
humic acid river sediments activated sludge C12LAS Cl,&AS-Cl4LAS soils river sediments C8SO4-Cl4SO4 humic acids C12LAS,CllAOS soils C12LAS river sediments Cl1.BLAS
isotherm
no. of data points
Langmuir
8
30
1
ref
linear linear
50
28 29
Freundlich
15
31, 33
Freundlich
6
chemical
river sediment 5 river sediment 6 river sediment 2 river sediment 3 river sediment 1 river sediment 7 river sediment 4 humic acid activated sludge soil, EPA B1 Rapid Ck. 4 Beaver Ck., EPA 5 Rapid Ck. 3 humic acid A humic acid B soil A soil B soil B soil C soil D river sediment B river sediment D river sediment C river sediment G river sediment F river sediment E
LAS LAS LAS LAS LAS LAS LAS LAS LAS LAS LAS LAS LAS SO4 LAS LAS LAS AOS LAS AOS LAS LAS LAS LAS LAS LAS
a
fm,
%
0.34 0.67 1.00 1.00 1.13 1.34 3.41 4O.Oa 4O.Oa 0.90 0.99 2.28 3.50 4O.Oa 40.0a
1.30 1.40 1.70 2.50 3.80 6.00
CEC, mequiv/100 g ref 4.15 7.00 10.1 4.65 5.10 8.70 14.4 3.00 15.4 19.0 15.7 650 580 10.9 15.1 15.1 9.30 16.1 31.0 13.0 27.0 7.00 7.00 13.0
30 30 30 30 30 30 30 30 28 29 29 29 29 31 31 33 33 33 33 33 57 57 57 57 57 57
Assumed value for humic acids and sludges (68).
chemical sorption. In order to use CMC effectively, a method for its calculation is required as a function of surfactant properties, temperature, and ionic strength. Next the applicability of reduced isotherms is developed. Two important particle properties are considered: the f , and the cation-exchange capacity (CEC). The parameter estimates are made by using multiple linear regression. In the last step, the particle interaction model (8) is incorporated and the parameters are estimated by using nonlinear regression. Data Reduction. The data sets employed below are summarized in Tables I and 11. This represents the only data in the literature that meets the criteria set forth in the previous section. For the linear isotherm the partition coefficients are used directly. For the Langmuir isotherms the limiting low-concentration partition coefficients are calculated from the Langmuir parameters. Since the Freundlich isotherms have no low-concentration limit, these data are reanalyzed by a Langmuir isotherm from which the linear partition coefficient can be calculated. The reanalysis was done with the reported Freundlich parameters. Ten evenly spaced points were generated from the Freundlich isotherm that spanned the reported data range for that experiment. A nonlinear regression was employed to fit a Langmuir isotherm to these points. The Langmuir isotherm curves that resulted 1014
Environ. Sci. Technol., Vol. 24, No. 7, 1990
=, L/g 0.00316 0.982 26.0
C,S04 (No. of Cases = 5)
min mean max
20.0 60.0 100.
min mean max
Others (No. of Cases = 6) 20.0 0.00102 60.0 0.0307 100. 0.172
57
Table 11. Properties of t h e Adsorbents adsorbent
min mean max
m, g/L CMC, M LAS (No. of Cases = 69) 0.10 O.oooO427 14.5 0.00176 100.0 0.00792
Data
0.00152 0.0307 0.172
0.00823 0.0270 0.0640 0.00600 0.0270 0.0640
from the fitting procedure are virtually indistinguishable from the Freundlich curve used by the authors. Hence, there is no reason to prefer the authors’ original analysis using the Freundlich isotherm over the Langmuir isotherm from which the linear partition coefficient can be calculated. Table I11 presents a statistical summary of the data set parameters: partition coefficient (T);the critical micelle concentration (CMC), which is either reported or calculated by use of the equation presented below; and particle concentration (m). The partition coefficient varies over almost 3 orders of magnitude, as do the chemical and particle properties (Table 11). Critical Micelle Concentration. An important observation has been made for the sorption of a homologous series of surfactants to a mineral adsorbent (37). If the isotherms for the homologous series are plotted vs the “reduced” concentration, which is defined as the ratio of dissolved concentration to the CMC, then the sorption isotherms of the different homologues (9, 38,39), for at least the linear Langmuir region (40) superimpose on a single curve. The use of the reduced concentration to superimpose isotherms for a homologous series of surfactants into a single curve suggests that normalization by CMC may be useful in establishing a model for the partition coefficient. An extensive tabulation of CMC data for surfactants is available ( 4 1 ) to which has been added more recent data (31,33,42-52).Table IV presents a statistical summary. There is a preponderance of high-temperature CMC data. Also, most of the CMC data are for linear alkyl sulfates whereas most of the sorption data are for the linear alkylbenzenesulfonates. Hence, a method for calculating CMC from the surfactant structural properties is required. CMC Model. The model is based on a previously proposed model for CMC (53,54)to which has been added additional temperature-dependent terms to increase the applicable temperature range. In addition the parameters of the model are estimated jointly with a much larger data set. The derivation of the CMC model equation is presented in the Appendix. The result is In [CMC] = B o +
n(1 -M)& RT
+--RT
MI0
Acp0(1- +iij
In T - KgIn I (1) R where n is the length of the alkyl chain, 4 is the position of the head group on the chain, Tis temperature in K, and I is the ionic strength of the solution. There are seven model parameters, which are defined in the Appendix, for which estimates are needed: Bo,Ag, p, AHIo,Acpo, y, and Kg-
Table IV. Statistical Summary-Critical Micelle Concentration
Table V. Entropy of Micellization Statistical Summary
temp, ionic str, chain "C M length, n
position, @
CMC, M
Linear Alkyl Sulfates (C,S04) (No. of Cases = 220) min 0.00 0.00 8.00 1.00 0.000110 mean 40.0 0.0190 13.1 2.32 0.0212 max 90.0 1.00 19.0 9.00 0.180 Linear Alkylsulfonates (C,S03) (No. of Cases = 49) min 22.50 0.00 8.00 1.00 0.000450 mean 40.3 0.00408 11.4 1.00 0.0429 max 80.0 0.10 16.0 1.00 0.177 Linear Alkylbenzenesulfonates (LAS) (No. of Cases = 35) min 19.0 0.00 8.00 1.00 0.0000904 mean 34.8 0.0484 10.9 1.94 0.00376 max 60.0 0.348 17.0 4.00 0.0163
min mean max
temp, "C
chain length, n
kcal/mol
5.00 38.2 70.0
8.00 11.5 14.0
-5.50 -1.14 2.50
" 9
Regression Equation variableb
coefficient
constant
27.8 -0,0850 -7.55 x 10-4
T nT
SE 2.09 0.00805 2.78 X 10''
ONumber of cases, 22. bunits: T,K; n, number of carbons in the alkyl chain.
Linear Alkylbenzenesulfonates (LAS)' (No. of Cases = 17) min 20.0 0.00 6.00 0.0000890 mean 49.8 0.00941 11.1 0.00526 max 75.0 0.0400 16.0 0.0371
c,sog
-
Branched Alkslbenzenesulfonates (ABS) (No. of Cases = 18) min 25.0 0.00 9.00 0.000440 0.00 mean 45.9 11.8 0.00631 75.0 0.00 15.0 0.0230 max N-Alkyl Trimethylammonium Bromides (C,TAB) (No. of Cases = 91) min mean max
1.00 32.4 70.0
0.00 0.0877 0.800
8.00 11.6 16.0
E
I
0.000630 0.0476 0.282
'
-4.00-
-6.00
0.0
N-Alkyl Trimethylammonium Chlorides (C,TAC) (No. of Cases = 23) min mean max a
23.0 26.7 40.0
0.00 0.0183 0.10
10.0 13.5 18.0
20.0
40.0
TEMPERATURE
0.000300 0.0127 0.0650
No position information.
Although some of the parameters in this equation have been estimated by others for individual groups of surfactants, no comprehensive regression formula is available. The regression analysis presented below is performed for each of three classes of chemicals. The linear alkyl and alkylbenzene sulfates and sulfonates for which the head position is reported are the largest group and they are used to estimate all the parameters. The data for linear alkylbenzenesulfonates with no reported head position, together with the branched alkylbenzenesulfonates,are then analyzed. The quaternary ammonium surfactants (QACs) are the third group. The parameters Acp0 and y are obtained separately from a tabulation of the enthalpy of micellization, AHm, for linear alkyl sulfates and sulfonates (53). I t is related to the CMC via d In [CMC] AHm= -RT = AHr' + AcpoT(l- yn) (2) dT Table V gives the statistical summary of the data, which are shown in Figure 1 together with the regression line with respect to temperature. A multiple linear regression, Table V, that includes the effect of chain length, n, as well as temperature suggests that a regression with both variables is appropriate. All coefficients are significant at a >95% level of confidence. The full surfactant data sets are analyzed by using indicator variables that differentiate the various subclasses of surfactants. In particular, BENZ denotes the presence (BENZ = 1) or absence (BENZ = 0) of a benzene ring in the surfactant; HEAD distinguishes between the sulfates (HEAD = 0) and sulfonates (HEAD = 1). BRANCH
60.0
00.0
(OC)
Figure 1. Enthalpy of micellization for C,SO, and C,SO, as a function of temperature.
distinguishes between a linear (BRANCH = 0) or branched alkyl chain (BRANCH = 1). For the n-alkyl trimethylammonium chlorides and bromides (QACs), HEAD distinguishes the chloride (HEAD = 0) and bromide (HEAD = 1)counterion. The final regression equation using these indicator variables is In [CMC] = Bo + C1(HEAD) + C,(BENZ) +
where is obtained from eq 1 by expanding terms. Table VI lists the regression coefficients and their coefficients of variation for the prediction equation and an example calculation. All coefficients are significant at a >95% level of confidence. The regression equations can predict In [CMC] for the sulfates, sulfonates, and QACs with a standard deviation of -0.4 (0.78 for alkylbenzenesulfonates (ABS) and linear alkyl sulfates (LAS) without 4) (Table VI). This is approximately equivalent to a coefficient of variation, CV, for CMC of -40% (78%). Figures 2 and 3 compare the estimated and observed CMCs. Residual analysis reveals no trends with respect to the dependent or any of the independent variables. The regression coefficients themselves can be compared to estimated thermodynamic properties obtained by others. The free energy change per unit methylene group, CH2, added to the alkyl chain is a In [CMC] = &(I - 04) + Tr In T (4) RT an The values obtained from the regression analysis follow from this equation: RT[-2.02 (1-0.0184) + 0.38 In ( T ) ] = -0.720 kcal/mol (for T = 25 "C, RT = 0.593 kcal/mol, Environ. Sci. Technol., Vol. 24, No. 7, 1990
1015
Table
VI. Critical Micelle Concentration Regression Equation Parameters (CV% ) C,LAS C,ABS BO' C,d CZd
C,d c4
C6 C8
c7
CB C9
RZ SE est
C,TAC C,TAB
C,SO,, C,S03, C,LAS
($J not specified)
-3.2295 X loz (0.18) 2.1355 X lo-' (31.18) -3.5291 (2.80)
-3.2099 X 10' (0.60) 2.1355 X lo-' (31.18)b -3.5291 (2.80)b 1.5581 (17.13) 4.9218 X 10' (2.78) -1.9335 (2.02)
-3.2517 -4.2381
4.2780 X 10' (9.44)' 3.7990 X lo-' (36.85)' -5.4959 x 10-1 (5.59)b 0.988 0.779
4.2780 X 10' (9.44)' 3.7990 X lo-' (36.85)' -5.0335 X lo-' (7.13) 0.997 0.398
5.1104 X 10' (0.72) -2.0244 (0.73) 1.8254 X 10-z (3.86) 4.2780 X 10' (9.44)' 3.7990 X lo-' (36.85)' -5.4959 x lo-' (5.59) 0.998 0.411
X X
lo2 (0.33) lo-' (24.06)
5.2677 X 10' (1.23) -1.9462 (0.87)
a Units: CMC, mol/L; T , K; R = 0.001 987 kcal/mol K; n, number of carbons in alkyl chain; 4, position of head group (4 = 1 for end position), I , mol/L. *From C,S04, C,S03, C,LAS regression. 'Estimated from AHmregression. d(HEAD,BENZ, BRANCH): C,SO, (0, 0, 0); C,S03 (1,0, 0); C,LAS (1, 1,O); C,ABS (1,1, 1);C,TAC (0, 0, 0); C,TAB (1,0, 0). Example: For Clo (24) LAS, T = 24 "C, I,, = 0.005 M, HEAD = 1, BENZ = 1, BRANCH = 0; n = l o , $ = 2,1/RT = 1.6937, In T = 5.6942, In Z = (I, + CMC) = In (0.005 + 0.003877) = -4.7243, and eq 19 is In [CMC] = -322.95 + 0.21355 - 3.5291 86.553 - 34.286 + 0.618 + 243.6 21.632 + 2.596 = -5.553.
+
-
1.00
N-220
0.00
0.00
E/ J
+
0.00
-J
0 -1.0
z
Y
ANCHED ABS (AI -4.00
-3.00
-9.00
-1.00
1
0.00
OBSERVED L O G 1 0 CMC (MOLE/LI
Figure 2. Estimated vs observed CMCs for the iinear and branched alkyl and alkylbenzene sulfates and sulfonates from the regressions in Table VI. Lines of perfect agreement are shown. The individual groups of data are displaced for clarity.
and 4 = 1) for C,S04, C,S03, and C,LAS and -0.683 kcal/mol for the QACs. The reported range is -0.604 to -0.805 kcal/mol (54). Similarly, the ionic strength coefficients, Kg= -0.550 and -0.503, are within the reported range of -0.43 to -0.71 (54). The effect of the addition of a benzene ring is estimated to be equivalent to about 3.5 methylene groups (64) or -2.11 to -2.82 kcal/mol. The regression coefficient is equivalent to RT(-3.53) = -2.09 kcal/mol. Hence these regression equation coefficients are reasonable, despite the large number that are estimated simultaneously. The most significant variables that affect the CMC are chain length and ionic strength. In order to compute the CMC it is necessary to specify the background ionic strength, I,,. However, the surfactant itself contributes to the ionic strength. Therefore, in order to compute the CMC an iterative technique is used. An initial guess is made for the CMC. This is used in the regression eq 3 to compute CMC, which is used to compute a new ionic strength, and so on. This procedure has been found to converge quite quickly. The example in Table VI is for the final iteration of the procedure. CMC Normalization. The proper CMC normalization for partition coefficients can be deduced as follows. The partition coefficient is defined as the ratio of particulate concentration, r (pg of chemical/g of solid), to dissolved 1016
Environ. Sci. Technol., Vol. 24, No. 7, 1990
-5.0 -B%
-4.00
-3.00
-2.00
O B S E R V E D L O G 1 0 CMC
-1.00
I
0.00
(MOLE/L)
Figure 3. Estimated vs observed CMCs for n-akyltrimethylammonium chlorides and bromides from the regressions in Table VI. Lines of perfect agreement are shown. The individual groups of data are displaced for clarity.
concentration, cd (pg of chemical/L) at equilibrium, that is P = r/cd (5) If an isotherm is normalized by using r w cd/CMC, then multiplying eq 5 by [CMC] yields
so that P[CMC] should be constant for a homologous group
of surfactants sorbing to a particular solid. Figure 4 illustrates the results using two data sets (33,35,37). Note that a[CMC] is essentially constant for each particle type-which are distinguished by the different plotting symbols. This suggests that CMC normalization can be applied to soil, sediment, and sludge partitioning. Particle Properties: f, and CEC. The relative hydrophobicity of surfactants seems to be well indexed by the CMC. However, particle properties also influence the magnitude of the partition coefficient. Whereas the use of CMC eliminates some of the variability of ?r in Figure 4, there is still substantial variability due to the differing soil and sediment types. The appropriate parameters that are most frequently reported are fraction organic carbon (foe) and cation-exchange capacity (CEC). These will be employed as the particle parameters in the analysis presented below.
2.00
-
3 4
0)
1
I
3 4
0.00-g
3
2.00
I
I
3
4 4
4
-
3
Y
I
I
1
I
I
-
0.00-
c 0 4
cl
-2.00-
-2.00,
+-
+
0 -I
-4.00
I
I
I
I
I
1
1
I
-4.00
c .
0 -2.00
\
W -I
0 -3.00-
I
3
Y
u I
4 -4.00-
z
*
U
-5.00-b
3
3 3
4 3 3-
4
3 4 4
4
4
3
8
S I
b
b
E
bb b
-
I
I
1
I
I
I
I
I
I
-3.00-4.00,
[i:g6+ bb
b
-2.00
I
e
u+
+-
+
-
-5.00-
0 d
a 0
-6.00
I
I
1
I
-6.00
1.50 1.00-
1
0.50-
3 a
E
0.00
m W
-0.50-
1
I
I
I
I
.. . .... .'Am.&# ..: ... d! I
1
m m
I
-
3.
'
2.
% .; a
I
L
J
I
-
-1.00-
-1.50A 2.00
I
I
I
3.00
4.00
5.00
sujfonates, closed symbols are sulfates. Line of perfect agreement sh6wn. Residuals (logloa* (right).
Multiple Linear Regression Analysis. The results of a multiple linear regression analysis of log a versus log [CMC] and log f, or log (CEC) are listed in Table VII. Note that the exponent of CMC is minus 1 within the errors of estimation, confirming the linear CMC normalization. The estimate and observed log,, a using f, as the particle property are compared in Figure 5. An analysis of the residuals, Figure 5 right, suggests a strong inverse correlation between log,, a and log,, m, indicting that lower partition coefficients are associated with higher particle concentrations (7). The reason for the particle concentration normalization used in Figure 5 is given below. Including log m in the multiple regression results in a significant increase in the R2from 0.546 (0.698) to 0.808 (0.823) for the CMC-f, (CMC-CEC) regressions, Table VII. Hence an explicit consideration of the particle effect is warranted.
Particle Interaction Model The particle interaction model (8,55) is based on the premise that in addition to the conventional adsorption-
6.00
- lo&, aa) vs normalized particle concentration
desorption reactions, a third reaction induced by particle interactions exists that causes an additional desorption as particle concentrations increase. It has been suggested that actual collisions are responsible for the desorption (56). The model yields the following equation for the partition coefficient: a = a,/(l mac/u,) (7) where a, is the classical partition coefficient (the ratio of the adsorption to the desorption rate constants); m is the particle concentration; and u, is the ratio of the adsorption to the particle interaction desorpion reaction rate constants. At low particle concentrations where the particle interaction reaction is not important, a = n,: In view of the success of the CMC normalization and the multiple linear regression results, it seems reasonable to relate the classical partition, coefficient, a,, to f, or CEC as follows: a, = ci(f,)'2/[CMCI (8)
+
A, = c~(CEC)'~/[CMC] (9) The linear inverse dependency of a, on CMC is just a
Environ. Sci. Technol., Vol. 24, No. 7, 1990
1017
I
I
Figure 6. Estimated vs observed partition coefficients using the particle interaction model with .~r, given by the CMC-I, equation, Table VI11 (left). Open symbok are sulfonates, closed symbols are sulfates. "aked observed partition coefficient, A/A, vs normalized particle concentratkn, mn,lu,. The line is the particle interaction model, eq 7. Data are grouped in half decades. Means and standard deviations are shown (right).
Table VII. Multiple Linear Regression variable"
coefficient
SE
loglo A vs log,, [CMCI and log,, f, ( N = 75) -3.79 0.314 constant loglo [CMCI -0.934 0.095 0.338 0.121 log10 f, R2 = 0.573 SE est = 0.545 log,, A vs log,, [CMC] and log,, CEC ( N = 80) constant -4.66 0.385 log10 [CMCI -0.979 0.093 log,, (CEC) 0.694 0.161 R2 = 0.593 SE est = 0.546 vs log,, [CMC], log,, f,, and log,, m ( N = 75) constant -1.89 0.294 loglo [CMCI -0.440 0.083 log,, fw 0.284 0.082 -0.664 0.071 log10 m R2 = 0.808 SE est = 0.368 log,,
log,,
A
vs log,, [CMC], log,, CEC, and log,, m ( N = 80) constant -2.23 0.353 loglo [CMCI -0.451 0.081 log,, (CEC) 0.367 0.112 log,, m -0.646 0.065 R2 = 0.823 SE est = 0.362
"Units: g/L.
P
A,
L/g; CMC, mol/L; CEC, mequiv/100 g; fw, %; m,
restatement of the normalization presented in eq 6. Table VI11 presents the results of a logarithmic nonlinear regression estimate of cl, c2, and v, using eq 7 and either eq 8 or eq 9 and the data summarized in Tables 1-111. The results are most interesting. The particle interaction coefficient, ux, is 1.06 or 1.18, which is very close to the value found for neutral hydrophobic chemicals sorption to soils and sediments (8)and nickel and cobalt sorption to clay (55). Figure 6 displays the estimated vs observed partition coefficient using eqs 7 and 8. The normalized plot in Figure 6 compares the normalized partition coefficient to the normalized particle concentration. The line is eqs 7 and 8. The consistent effect of increasing particle concentration is evident.
Discussion The particle interaction model with the classical partition coefficient correlated to CMC and f, provides a reasonable fit to the available sorption data for soils, sediments, and sludges. The use of CMC as an index of hydrophobicity raises an interesting question. Would 1018
Environ. Sci. Technol., Vol. 24, No. 7, 1990
Table VIII. Particle Interaction Model. Nonlinear Regression Equation 7 with reGiven by variable" C1 C2
ux
= clCfoe)c2/(CMC)
coefficient
SE
4.22 X lo4 0.405 1.06
1.44 X IO" 0.221 0.178
RZ = 0.900 Equation 7 with reGiven by rC = c,(CEC)c2/(CMC) C1 3.93 x 10-5 2.84 x 10-5 C2 0.909 0.290 1.18 0.209 R2 = 0.909 "Units: A, L/g; CMC, mol/L; CEC, mequiv/100 g; f, g/L; uX, unitless.
%; m,
external chemical changes-e.g., high background ionic strength that lowers the CMC-affect the partition coefficient via the CMC change. To investigate this phenomenon it would be necessary to perform the experiments at low particle concentrations so that ma, < u, and a = a,. Otherwise, if mac >> v,, then only the particle effect is seen, i.e., a = u,/m. In fact a substantial fraction of the available data are in the asymptotic region of the particle concentration where mr, >> u,, as can be seen in Figure 6. The last two data groups at the highest normalized particle concentrations are such that T = v,/m. Since u, is a constant, the partition coefficient is only a function of the particle concentration and not the chemical or particle properties. The mechanism by which particle interactions cause a desorption is still unresolved. If the mechanism is an actual collision (50),then an interesting consquence of this hypothesis is that u, should be essentially constant and independent of particle and chemical properties. Since Y, for anionic surfactants is essentially the same as that found for neutral hydrophobic organics and metal sorption, this offers support for this type of mechanism. In any case, the fact that surfactants ft the same particle interaction model as neutral hydrophobic organic chemicals and metals argues that whatever the mechanism is, it must be ubiquitous. Some speculation on the nonlinear relationship of a, to f , is in order. It seems clear that hydrophobic interactions play some role in surfactant sorption, as has been suggested in other studies (24-16,28-30). The nonlinear relationship may be due to the electrostatic repulsion between the negatively charged surfactant and the soil or sediment
particle. As f, increases CEC increases and the surface becomes more negative. Thus, the increase in hydrophobic bonding is diminished by the increased repulsion. The result is a more gradual increase of .rr, with respect to f,. It is interesting to note that CEC and f, covary as well. It has been suggested that CEC varies approximately in (64). This relationship is used to esproportion to fW1l2 timate the CEC for the high organic content humic acids and sludges in the data base. Thus, the linearity of .rrc to CEC may be coincidental since no direct measurement of CEC is available for these experiments. It has been shown previously that pH affects the extent of sorption to clays (9-11), so it should be significant for sediments and soils as well. The residual variation in the model may well be do to the (unreported) variations in pH at which the experiments were conducted. This anionic surfactant sorption model can be applied to a number of environmental questions. In particular it can provide the partition coefficient for use in environmental fate calculations (e.g., ref 3). The partition coefficient can also be used to evaluate the environmental effect of surfactants in sediments (65).
An empirical constant, Kg,has been added to the ionic strength term in order to conform to the experimentally determined relationship between CMC and ionic strength. Because the micelles comprise many individual surfactant molecules when fully formed at equilibrium, it appears reasonable to assume that the surface charge, uo, is constant. The logarithmic temperature dependence in the second term in eq 14 is included below. The temperature dependency of AG,O is assumed to be of the form (67)
AS; Acp0 AG,"(T) = -AHr0 ---In T (16) RT R R RT where AH;, ASP, and Acpo are the reaction enthalpy, entropy, and specific heat at constant pressure at the reference temperature (25 "C). Thus eq 14 becomes AHro Acp0 In [CMC] = Bo + -- -In T - K, In I (17) RT R where
Acknowledgments
We are pleased to acknowledge the contributions of Richard Sedlak and Keith Booman of the Soap and Detergent Association, and of William Leo and James Halden of HydroQual. Appendix Critical Micelle Concentration Model. The formation of micelles is a distinctive feature of surfactant chemistry and a number of models of the phenomenon have been proposed (53,54,66). The pseudophase model of micelle formation assumes that micelles are a separate thermodynamic phase. At equilibrium the chemical potential, p, of each phase is equal: PSOLUTE= PMICELLE
(10)
so that for an ideal solute and unit activity for the micelle phase AGOSOLUTE+ RT In [CMC] = AGOMICELLE + ZF$, (11) where AGO is the Gibbs free energy of formation, R is the universal gas constant, and T i s the temperature in K. The electrostatic term, ZF$o, where Z is the charge, F is the Faraday, and $ois the surface potential of the micelle, is included since the micelle is charged for ionic surfactants. Applying the Gouy-Chapman double-layer theory and assuming the surface potential is sufficiently large so that
ZF$o/RT
>> 1
(12)
yields the following expression for the surface potential term (53):
where uo is the surface charge density, to is the permittivity of free space, D is the dielectric constant, and Z is the ionic strength of the medium. Substituting this equation into eq 11 yields AGr0 + In In [CMC] = RT
where
(L - K ,) In I (14) 2@RT
The In (1/T) = -In T term from the surface charge expression is included in the Acpoterm. Finally, the effect of alkyl chain length, n, adds a term of the form AgIRT (53),where Ag is the free energy contribution per methylene group, CH2,in the alkyl chain. If the position of the head group, 4, is not at the end of the chain (4 = 1) but at interior positions (4 > l),then the effective chain length is shortened to n(1 - 04) with 0a constant to be determined empirically. Hence the leading term becomes
As shown in Table VI, the chain length also affects the heat
capacity term, which is modified as follows: Acpo(l- yn) with y a constant to be determined empirically. The final form of the model is 4 1 -P&& AHr' In [CMC] = Bo +
+--RT
RT
ACpo(l - yn)
R
In T - K, In I (20)
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Received for review April 29,1988. Revised manuscript received October 2,1989. Accepted March 10,1990. This researchproject was sponsored by the Soap and Detergent Association and performed at HydroQual Inc.
