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Application of Octanol/Water Partition Coefficients in Surfactant Science: A Quantitative Structure-Property Relationship for Micellization of Anionic Surfactants David W. Roberts* Unilever Research Port Sunlight, Wirral, United Kingdom Received June 1, 2001. In Final Form: October 21, 2001 The octanol/water partition coefficient, usually as its logarithm, log P, is widely used as a hydrophobicity parameter in modeling pharmacological and toxicological properties. Since log P values can be calculated from molecular structure by summation of fragment values, they are very useful in predicting various biological properties of chemicals. Although hydrophobicity is a key concept in surfactant science, to date log P has not found much application in this field. In this paper, a log P based quantitative structureproperty relationship (QSPR) is derived for anionic surfactant micellization potential, quantified as pCMC, the negative logarithm of the critical micelle concentration. The micellization potential of anionic surfactants covering a diverse range of structures is found to be well modeled by a combination of two parameters, πh and L, the former being the log P fragment value for the hydrophobe (simply defined as the whole molecule minus the negatively charged fundamental fragment) and the latter being the length, in C-C single bond units, of the hydrophobe. These parameters are simple to calculate, providing a rapid and accurate “back of envelope” method for estimation of CMC values. For surfactants with branching in their alkyl chains, the best agreement between calculated and observed pCMC values is obtained when the position-dependent branching factor, normally used in the log P calculation to quantify the effect of alkyl chain branching on solvation energy in the aqueous phase, is not applied. This is interpreted in terms of alkyl chain branching reducing the free energy of the micelle by reducing the amount of water in the interior of the micelle. Some of the log P fragment values and factors used in the calculation of the πh values used here have been derived inferentially, in previously published work, from fitting aquatic toxicity data for surfactants to quantitative structure-activity relationship equations. These are now validated by their successful application in the QSPR for micellization.
Introduction The octanol/water partition coefficient, usually as its logarithm, log P, is widely used as a hydrophobicity parameter in modeling pharmacological and toxicological properties. Since log P values can be calculated from molecular structure by summation of fragment values, they are very useful in predicting various biological properties of chemicals. Although hydrophobicity is a key concept in surfactant science, to date log P has not found much application in this field. The work presented here forms part of a wider program on the application of log P to modeling environmental and physicochemical properties of surfactants. An earlier paper1 presented a QSPR (quantitative structure-property relationship) for micellization of simple anionic surfactants. The surfactant molecular structure can be considered to be divided into hydrophobe and hydrophile portions. The division can in principle be assigned by consideration of which parts of the molecule would reside in the micelle interior and which would be exposed to water molecules in the outer layer of the micelle (vide infra). It was argued that the micellization potential (i.e., tendency to form micelles), quantified by pCMC (negative logarithm of the molar critical micelle concentration), should be a function of the hydrophobicity of the hydrophobe portion of the surfactant, which can be * Address: Unilever Research Port Sunlight, DP-PTECH, Quarry Road East, Bebington, Wirral, CH63 3JW, U.K. Tel: +44 (0)151 641 3092. Fax: +44 (0)151 641 1827. E-mail: david.w.roberts@ unilever.com. (1) Roberts, D. W. Quantitative Correlations for the Effects of Chain Branching on Aquatic Toxicity and Micellisation of Anionic Surfactants. Jorn. Com. Esp. Deterg. 1992, 23, 81-92.
modeled by the log P fragment value, and the micellar radius, which can be expressed as the length of the hydrophobe in units of C-C bond lengths. The effect of increasing micellar radius is to increase the spacing between the charged headgroups at the outer layer of the micelle. This reduces the repulsion forces between the headgroups, making micellization energetically more favorable. CMC data for a set of LAS (linear alkyl benzene sulfonate) isomers and homologues and a set of primary alcohol sulfates PAS (some linear and some β-branched) were found to fit a QSPR covering both sets of surfactants:
pCMC ) 0.32πh + 0.09L - 0.82
(1)
where πh is the derived log P fragment value for the hydrophobe portion of the surfactant and L is the length of the hydrophobe. In the calculation of πh by the Leo and Hansch method,2 no branching factor was applied, but for the surfactants considered the L parameter varies according to branching (e.g., for primary alcohol sulfates L is the difference between total carbon number and length of the β-branch) and was found sufficient to model the effect of branching on the pCMC value. When these studies were carried out in the mid 1980s, the position-dependent branching factor (PDBF) for log P and πh calculation3 had not yet been developed; using the standard Leo and Hansch branch factor, for example, the 2-sulfophenyl and the 6-sulfophenyl isomers of C12 LAS would be calculated to (2) Leo, A. J.; Hansch, C. Substituent Constants for Correlation Analysis in Chemistry and Biology; Wiley: New York, 1979. (3) Roberts, D. W. Aquatic Toxicity of Linear Alkyl Benzene Sulphonates (LAS) - A QSAR Analysis. Jorn. Com. Esp. Deterg. 1989, 20, 35-43.
10.1021/la0108050 CCC: $22.00 © 2002 American Chemical Society Published on Web 12/27/2001
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have the same log P values. Thus, the role of L in eq 1 could be twofold: to quantify the micellar radius and to compensate for the neglect of branching in πh. For both LAS and PAS, if πh is calculated using the PDBF where applicable, L is quite strongly correlated with πh, that is, any increase in L leads to an increase in πh. Because of this correlation, it is not possible to establish by regression analysis to what extent L plays these two roles. Here, the QSPR approach is extended to more complex surfactant types, the ether sulfates and the ester sulfonates. For these surfactants, L and πh can be varied independently; for example, starting from a given alcohol ethoxy sulfate, if L is increased by increasing the carbon number of the alkyl group, then πh will be increased, but if L is increased by adding ethyleneoxy (EO) groups, then πh will be decreased. By analyzing CMC data for these surfactants, the relative importance of hydrophobicity and micellar radius can be quantified. Calculation of πh Values In the earlier paper,1 the division of the surfactant molecular structure into hydrophobe and hydrophile portions was made by consideration of which parts of the molecule would reside in the micelle interior and which would be exposed to water molecules in the outer layer of the micelle. The πh value was calculated by applying the Leo and Hansch log P calculation method to the portion of the molecule which had been defined as the hydrophobe. However, it is not always obvious which parts of the molecule should be assigned to the hydrophobe and which to the hydrophile. Here, a simpler and unambiguous method is adopted as follows. Log P is calculated for the complete structure, using the Leo and Hansch method2 and applying where appropriate recent modifications4,5 to the calculation of proximity factors and contributions of ethyleneoxy units. From this log P value, the fragment value for the ionic group (SO3- or OSO3-) is subtracted to give the πh value. Log P values for the various surfactants discussed here are calculated as follows. Note that πh values for alcohol propoxy and butoxy sulfates are substantially affected by whether the PDBF is applied. Linear primary alcohol sulfates Parent structure n-C12H25OSO3Na, log P ) 1.60 For ROSO3Na, log P ) 1.60 + 0.54(C - 12) where C is the carbon number of R πh ) log P + 5.23 Secondary alcohol sulfates R1R2CHOSO3Na and βbranched primary alcohol sulfates R1R2CHCH2OSO3Na As for linear primary alcohol sulfates with the same total carbon number. If the PDBF is applied, 1.44 log(Cs+1), where Cs is the carbon number of R1 or R2, whichever is the shorter, is subtracted from πh. Alcohol ethoxy sulfates Parent structure n-C12H25OCH2CH2OSO3Na, log P ) 2.22 For R(OCH2CH2)nOSO3Na, log P ) 2.22 + 0.54(C - 12) - 0.25(n - 1) πh ) log P + 5.23 (4) Roberts, D. W. Aquatic Toxicity - Are Surfactant Properties Relevant? J. Surfactants Deterg. 2000, 3 (3), 309-315. (5) Roberts, D. W. Use of Octanol/Water Partition Coefficients as Hydrophobicity Parameters in Surfactant Science. Proceedings of CESIO World Surfactants Congress, 5th, Florence, Italy, May 29-June 2, 2000; pp 1517-1524.
Roberts
Alcohol propoxy sulfates Parent structure n-C12H25OCH2CHMeOSO3Na, log P ) 2.33 For R(OCH2CHMe)nOSO3Na, log P ) 2.33 + 0.54(C - 12) - 0.14(n - 1) [if branching is neglected, log P ) 2.76 + 0.54(C - 12) + 0.29(n - 1)] πh ) log P + 5.23 Alcohol butoxy sulfates Parent structure n-C12H25OCH2CHEtOSO3Na, log P ) 2.47 For R(OCH2CHEt)nOSO3Na, log P ) 2.61 + 0.54(C - 12) + 0.14(n - 1) [if branching is neglected, log P ) 3.30 + 0.54(C - 12) + 0.83(n - 1)] πh ) log P + 5.23 Ester sulfonates Parent structure MeCH(SO3Na)CO2Me, log P ) -4.02 For R1CH(SO3Na)CO2R2, log P ) -4.02 + 0.54(C - 2) where C is the combined carbon number of R1and R2 πh ) log P + 5.87 Linear alkylbenzene sulfonates Parent structure n-C12H25C6H4SO3Na (para), log P ) 3.97 For R1R2CHC6H4OSO3Na, log P ) 3.97 + 0.54(C - 11) 1.44 log(Cs+1) where C is the combined carbon number of R1 and R2 and Cs is the carbon number of the shorter of R1 and R2 If branching is neglected, log P ) 3.97 + 0.54(C - 11) πh ) log P + 4.53 Primary Alcohol Sulfates and Primary Alcohol Ether Sulfates at 50 °C Weil et al.6 report CMC values for ethoxylated, propoxylated, and butoxylated alcohol sulfates at 50 °C. In an earlier paper,7 they give CMC values for C12 and C16 alcohol sulfates, determined by the same method (pinacyanole chloride dye titration) at the same temperature. Data for stearyl (C18) surfactants were also reported by Weil et al. but are not included here: it has previously been noted that for homologous series of linear surfactants plots of pCMC against chain length are linear up to about C16 but then begin to level out toward a limiting value. This may reflect the ability of longer chains to fold in a strain-free configuration so as to reduce the overall contact of the hydrophobe with water. The effect can be incorporated into QSPR models by use of more complex mathematical functions, but in this paper the approach taken is to ignore data for stearyl surfactants and to recognize that their pCMC values will be somewhat overpredicted by the QSPR equations. The data, excluding stearyl surfactants, are shown in Table 1. Using the πh values calculated without the PDBF regression analysis of pCMC against πh and L gives the QSPR:
pCMC ) 0.32((0.13)πh + 0.08((0.05)L 1.02((0.71) (2) n ) 16
R2 ) 0.927
s ) 0.17
F ) 83
(6) Weil, J. K.; Stirton, A. J.; Nun˜ez-Ponzoa, M. V. Ether Alcohol Sulfates. The Effect of Oxypropylation and Oxybutylation on Surface Active Properties. J. Am. Oil Chem. Soc. 1966, 43, 603-606. (7) Weil, J. K.; Stirton, A. J.; Bistline, R. G., Jr.; Maurer, E. W. Tallow Alcohol Sulfates. Properties in Relation to Chemical Modification. J. Am. Oil Chem. Soc. 1959, 36, 241-244.
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Table 1. Primary Alcohol Sulfatesa and Ether Sulfatesb at 50 °C surfactant
log P
πh
L
pCMC (calcd)
pCMC (obsd)
C12P1S C12P2S C12Bu1S C12Bu2S C14P1S C14P2S C14Bu1S C14Bu2S C16E1S C16E2S C16P1S C16P2S C16Bu1S C16Bu2S C12PAS C16PAS
2.33 2.19 2.61 2.75 3.41 3.27 3.69 3.83 4.38 4.13 4.49 4.35 4.77 4.91 1.60 3.76
7.56 7.42 7.84 7.98 8.64 8.50 8.92 9.06 9.61 9.36 9.72 9.58 10.00 10.14 6.83 8.99
15 18 15 18 17 20 17 20 19 22 19 22 19 22 12 16
2.65 2.84 2.74 3.06 3.23 3.42 3.34 3.64 3.77 3.92 3.81 4.00 3.93 4.22 2.12 3.29
2.57 2.81 2.74 3.10 3.24 3.44 3.37 3.70 3.66 3.85 3.80 4.12 3.92 4.21 2.17 3.38
a
Table 2. Primary Alcohol Sulfates and Ether Sulfates at 20-40 °C CnH2n+1(OCH2CHMe)mOSO3Na at 20 °Ca pCMC
pCMC
n
m
calcd
obsd
n
m
calcd
obsd
8 8 8 8 8 8 10 10 10 10 10
1 2 3 4 5 6 1 2 3 4 5
1.49 1.67 1.86 2.05 2.24 2.42 2.07 2.26 2.44 2.63 2.82
1.35 1.56 1.78 2.02 2.22 2.48 1.96 2.13 2.37 2.59 2.78
12 12 12 12 14 14 14 14 16 16 16 16
1 2 3 4 1 2 3 4 1 2 3 4
2.65 2.84 3.02 3.21 3.23 3.42 3.61 3.79 3.81 4.00 4.19 4.37
2.58 2.78 2.96 3.12 3.10 3.30 3.52 3.74 3.60 3.82 4.00 4.20
CnH2n+1(OCH2CH2)mOSO3Na at 25 °Cb
CnH2n+1OSO3Nac
pCMC
Reference 7. b Reference 6. n
m
calcd
obsd
n
10 12 12 14 16
2 1 2 2 2
2.17 2.61 2.75 3.33 3.91
1.91 2.35 2.55 3.07 3.66
6 7 8 9 10 11 12 13 14 15 16
a
Figure 1. QSPR for primary alcohol sulfates and ether sulfates at 50 °C. No branching factors were applied.
pCMC T (°C) calcd obsd 25 25 40 25 40 25 40 40 40 40 40
0.38 0.67 0.96 1.25 1.54 1.83 2.12 2.41 2.71 3.00 3.29
0.38 0.66 0.85 1.22 1.48 1.80 2.07 2.37 2.66 2.92 3.24
Reference 8. b Reference 9. c Reference 10.
Using eq 3, pCMC (calcd) values can now be calculated and compared against experimental pCMC values for other data sets. Primary Alcohol Sulfates and Primary Alcohol Ether Sulfates at 20-40 °C Chlebicki and Slipko8 report CMC values at 20 °C for a range of single component linear alcohol propoxy sulfates with alkyl groups ranging from C8 to C18 and with 1-6 PO groups. The pCMC values for the C8 to C16 compounds are shown in Table 2. Barry and Wilson9 give CMC values for five linear alcohol ethoxy sulfates (C10C16, E1, and E2) at 25 °C, and a review by Domingo10 gives CMC values at 25 and 40 °C for linear primary alcohol sulfates from C6 to C16 (including odd carbon numbers). pCMC values taken from these sources are shown in Table 2. Regression analysis of these experimental pCMC values against pCMC (calcd) values calculated using eq 3 gives
Figure 2. QSPR for primary alcohol sulfates and ether sulfates at 50 °C. Branching factors were applied for propyleneoxy and butyleneoxy ether sulfates.
This QSPR is shown as a graphical plot in Figure 1. There is substantial scatter of points from the best straight line. With the PDBF incorporated into the πh calculation, the QSPR becomes
pCMC ) 0.39((0.05)πH + 0.08((0.02)L 1.50((0.30) (3) n ) 16
R2 ) 0.989
s ) 0.07
F ) 582
This QSPR, shown as a graphical plot in Figure 2, fits the data much better than the QSPR of eq 2 and Figure 1.
pCMC ) 0.96((0.02) pCMC (calcd) ( 0.06 n ) 39
R2 ) 0.994
s ) 0.07
(4)
F ) 6362
This good agreement between calculated and experimental pCMC values is not surprising, since the surfactants are of the same general structures in both data sets. (8) Chlebicki, J.; Slipko, K. Synthesis and Surface Activity of Polyoxypropylated Higher Alcohol Sulphates. Tenside 1980, 17, 130134. (9) Barry, B. W.; Wilson, R. CMC, counterion binding and thermodynamics of ethoxylated anionic and cationic surfactants. Colloid Polym. Sci. 1978, 256, 251-260. (10) Domingo, X. In Anionic Surfactants. Organic Chemistry; Stache, H. W., Ed.; Surfactant Science Series, Vol. 56; Marcel Dekker: New York, 1996; p 251.
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Table 3. Ester Sulfonates,a R1CH(SO3Na)CO2R2 pCMC R1
R2
calcd
2 7 10 1 7 10 12 2 7 10 12 1 7 10 12
10 5 2 12 6 3 1 12 7 4 2 14 8 5 3
2.13 1.96 2.21 2.50 2.17 2.42 2.58 2.71 2.38 2.63 2.79 3.08 2.59 2.84 3.00
a
pCMC
obsd
R1
R2
calcd
obsd
2.02 1.81 2.11 2.49 2.16 2.28 2.55 2.72 2.35 2.55 2.72 3.11 2.68 2.77 2.96
14 2 7 10 14 7 10 12 14 16 14 16 14 16
1 14 9 6 2 10 7 5 3 1 4 2 5 3
3.16 3.29 2.89 3.05 3.37 3.18 3.26 3.42 3.58 3.74 3.80 3.95 4.00 4.16
3.40 3.35 2.92 3.06 3.47 3.31 3.30 3.47 3.59 3.80 3.80 3.89 3.89 4.15
References 11-14.
Figure 3. QSPR for alcohol sulfates, ether sulfates, and ester sulfonates.
values are very well predicted by the QSPR derived from the latter set of surfactants.
Ester Sulfonates Schwuger and Lewandowski11 quote CMC values originally determined by Stirton et al.12-14 for 31 ester sulfonates. These are shown in Table 3. The temperature is not quoted. The general formula of these surfactants is
R1CH(SO3Na)CO2R2 In all cases, the R groups are both linear. For these surfactants, the πh values are calculated by subtraction of -5.87 (the fragment value for the aliphatic sulfonate group) from the log P values, which are in turn calculated by the Leo and Hansch method using the proximity factor modification of Roberts, Marshall, and Hodges.15 In some of these ester sulfonates, the longest alkyl chain is in the alcohol-derived portion of the molecule (i.e., R2), and in others it is in the fatty acid derived portion (i.e., R1). The L parameter is taken as the carbon number of R1CH or R2, whichever is the larger. Regression analysis of the experimental pCMC values against those calculated from πh and L using eq 3 gives
pCMC ) 1.05((0.05) pCMC (calcd) -0.15((0.16) (5) n ) 29
R2 ) 0.984
s ) 0.08
F ) 1743
Two pCMC values, corresponding to the two compounds with the highest πh and L values, are omitted from Table 3 and from the regression analysis. The slope and intercept are, within the 95% confidence limits, not significantly different from 1 and 0, respectively. Although the ester sulfonates are very different in chemical structure from the primary alcohol sulfates and ether sulfates, their CMC (11) Schwuger, M. J.; Lewandowski, H. In Anionic Surfactants. Organic Chemistry; Stache, H. W., Ed.; Surfactant Science Series, Vol. 56; Marcel Dekker: New York, 1996; p 472. (12) Stirton, A. J.; Bistline, R. G., Jr.; Weil, J. K.; Ault, W. C.; Maurer, E. W. Sodium Salts of Alkyl Esters of R-Sulpho Fatty Acids. Wetting, Lime Soap Dispersion and Related Properties. J. Am. Oil Chem. Soc. 1962, 39, 128-131. (13) Stirton, A. J.; Bistline, R. G., Jr.; Barr, E. A.; Nun˜ez-Ponzoa, M. V. Salts of Alkyl Esters of R-Sulfopalmitic and R-Sulfostearic acids. J. Am. Oil Chem. Soc. 1965, 42, 1078-1081. (14) Bistline, R. G., Jr.; Stirton, A. J. Benzyl, Cyclohexyl and Phenyl Esters of Alpha-Sulfo Fatty Acids. J. Am. Oil Chem. Soc. 1968, 45, 78-79. (15) Roberts, D. W.; Marshall, S. J.; Hodges, G. Quantitative structure-activity relationships for acute aquatic toxicity of surfactants. Fourth World Surfactants Congress Proceedings, Barcelona, Spain, 1996; A. E. P. S. A. T.: Barcelona, 1996; Vol. 4, pp 340-351.
Alcohol Sulfates, Ether Sulfates, and Ester Sulfonates Together Combining the data sets used to generate eqs 4 and 5 gives a data set covering 68 surfactants. A plot of pCMC against pCMC (calcd) is shown in Figure 3. Regression analysis gives the composite QSPR:
pCMC ) 1.00((0.03) pCMC (calcd) -0.05((0.08) (6) n ) 68
R2 ) 0.988
s ) 0.09
F ) 5286
In this equation, pCMC (calcd) is as defined in eq 3, that is,
pCMC (calcd) ) 0.39πh + 0.08L - 1.50 This expression quantifies the relative contributions of hydrophobicity and micellar radius to the micellization potential of these surfactants. It can be used, for example, to compare the effects of a methylene group and an ethyleneoxy group on micellization potential, as follows. Each methylene group increases πh by 0.54 and L by 1, so it increases pCMC by
0.39 × 0.54 + 0.08 × 1 ) 0.29 Each ethyleneoxy unit (after the first) decreases πh by 0.25 and increases L by 3, so it increases pCMC by
0.39 × (-0.25) + 0.08 × 3 ) 0.14 The increase in L outweighs the decrease in πh, so that overall the ethyleneoxy unit contributes positively (about half as much as a methylene group) to the micellization potential of anionic surfactants when it is included in the hydrophobe. Anionic Surfactants with Branched Alkyl Groups Tables 4 and 5 show experimental 40 °C CMC data for 26 linear alkyl benzene sulfonates (LAS) with alkyl carbon numbers ranging from C10 to C143 and 26 secondary alcohol sulfates (SALS) with carbon numbers ranging from C8 to C19 plus one C29 homologue (taken from Domingo’s review,10 originally reported by Evans16). Two sets of pCMC (calcd) figures are given; both sets are calculated from eq (16) Evans, H. C. Alkyl Sulphates. Part I. Critical Micelle Concentration of the Sodium Salts. J. Chem. Soc. 1956, 579-586.
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Table 4. Linear Alkylbenzene Sulfonates, RC6H4SO3Na (para)a carbon number of R
C6H4SO3Na position
pCMC calcd (with BF)
pCMC calcd (no BF)
pCMC obsdb
10 10 10 10 11 11 11 11 11 12 12 12 12 12 13 13 13 13 13 13 14 14 14 14 14 14
2 3 4 5 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7
2.24 2.06 1.91 1.78 2.54 2.35 2.20 2.07 1.94 2.83 2.64 2.49 2.36 2.24 3.12 2.94 2.78 2.65 2.53 2.41 3.41 3.23 3.08 2.94 2.82 2.70
2.41 2.33 2.25 2.17 2.70 2.62 2.54 2.46 2.38 3.00 2.91 2.83 2.75 2.67 3.29 3.20 3.12 3.04 2.96 2.88 3.58 3.49 3.41 3.33 3.25 3.17
2.27 2.23 2.18 2.09 2.55 2.50 2.40 2.30 2.25 2.83 2.78 2.65 2.57 2.46 3.11 3.00 2.90 2.78 2.70 2.60 3.39 3.28 3.15 3.05 2.90 2.80
Table 5. Secondary Alcohol Sulfates carbon number
substitution position
pCMC calcd (with BF)
pCMC calcd (no BF)
pCMC obsda
8 10 11 11 13 13 14 14 14 14 14 15 15 15 15 16 16 16 17 17 18 18 18 19 19 29
2 2 3 6 2 7 2 3 4 5 7 2 3 5 8 4 6 8 2 9 2 4 6 5 10 15
0.71 1.29 1.41 1.00 2.17 1.46 2.46 2.28 2.13 1.99 1.75 2.75 2.57 2.28 1.93 2.71 2.45 2.22 3.33 2.40 3.62 3.29 3.03 3.45 2.87 5.28
0.88 1.46 1.67 1.43 2.33 1.93 2.63 2.54 2.46 2.38 2.22 2.92 2.84 2.67 2.43 3.05 2.88 2.72 3.50 2.93 3.79 3.63 3.47 3.84 3.43 5.94
0.74 1.31 1.54 1.08 2.19 1.71 2.48 2.37 2.29 2.17 2.01 2.77 2.66 2.47 2.18 2.76 2.63 2.37 3.31 2.63 3.59 3.35 3.14 3.48 3.03 4.10
a
References 10-16.
a
For LAS, the L parameter used in the pCMC calculation is obtained as follows. If C is the carbon number of the alkyl chain and P is the number corresponding to substitution position of the sulfophenyl group, L ) C - P + 4.67. The length of the -C6H4unit is 5.88 Å, i.e., 4.67 C-C single bond units (the length of the C-C bond, projected along the line of the extended alkyl chain, is 1.26 Å). b Reference 3.
3, but in one set the PDBF is applied in the πh calculation and in the other it is not. Regression analyses (leaving out the C29 SALS homologue, vide infra) give the equations
pCMC ) 0.93((0.04) pCMC (calcd, with PDBF) +0.28((0.09) (7) n ) 51
R2 ) 0.981
s ) 0.08
F ) 2468
pCMC ) 0.94((0.03) pCMC (calcd, no PDBF) -0.06((0.10) (8) n ) 51
2
R ) 0.984
s ) 0.07
F ) 3110
Both regression equations are of similarly high statistical quality, but eq 8, having an intercept much closer to zero and a slope similarly close to unity as compared with eq 7, shows a closer agreement between experimental and predicted values. In other words, eq 3 predicts the CMC values of LAS and SALS better when the PDBF is not applied. Two sets of data on β-branched primary alcohol sulfates provide further evidence regarding the applicabilty of the PDBF. Greiner and Herbst17 report CMC values for 13 primary alcohol sulfates (4 linear and 9 β-branched) with carbon numbers ranging from C12 to C15. Go¨tte and Schwuger18 report CMC values for the 7 linear primary alcohol sulfates ranging from C10 to C16 and the 7 β-branched C16 isomers. (17) Greiner, A.; Herbst, M. Strukturabha¨ngige Eigenschaften von Tensiden, untersucht an Reihen von 2-Alkyl sulfaten, Phosphinoxiden und ω-H-Perfluorverbindungen. J. Prakt. Chem. 1987, 329, 29-38. (18) Go¨tte, E.; Schwuger, M. J. U ¨ berlegungen und Experimente zum Mechanismus des Waschprozesses mit prima¨ren Alkyl sulfaten. Tenside 1969, 6, 131-135.
Table 6. Primary Alcohol Sulfates, R1R2CHCH2OSO3Naa pCMC values carbon numbers R1
R2
8 9 10 9 8 5 11 10 12 11 10 8 6 13 11 14 13 12 11 10 9 8 7
0 0 0 1 2 5 0 1 0 1 2 4 6 0 2 0 1 2 3 4 5 6 7
a
observed ref 17
2.22 2.02 1.92 1.74 2.59 2.40 2.85 2.74 2.52 2.51 2.15 3.24 3.00
calculated
ref 18
with PDBF
no PDBF
1.52 1.80 2.09
1.54 1.83 2.12 1.87 1.70 1.29 2.41 2.17 2.71 2.46 2.28 1.99 1.75 3.00 2.49 3.29 3.04 2.86 2.71 2.57 2.45 2.33 2.22
1.54 1.83 2.12 2.04 1.96 1.72 2.41 2.33 2.71 2.62 2.54 2.38 2.22 3.00 2.75 3.29 3.21 3.13 3.04 2.96 2.88 2.80 2.72
2.37 2.66
2.95 3.23 3.13 3.02 2.92 2.81 2.71 2.60 2.50
L ) 2 + carbon number of longer of R1 and R2.
The two sets of data are shown in Table 6. pCMC (calcd) values are given based on eq 3, with and without application of the PDBF in calculation of πh. It can be seen from Table 6 that for the four linear alcohol sulfates which are common to both data sets, agreement between the two sets of data is not very good, the pCMC values from Greiner and Herbst being larger than those from Go¨tte and Schwuger by an amount ranging from 0.13 to 0.29. It seems likely that there is a systematic difference between the experimental conditions used in the two studies. Therefore, rather than combining the data, it is best to analyze the two data sets separately. The Go¨tte and Schwuger linear PAS data agree closely with other
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Figure 4. pCMC vs pCMC (calcd, branching factors applied) for linear and β-branched primary alcohol sulfates.
values quoted in Domingo, and it therefore seems reasonable to use only the Go¨tte and Schwuger data in testing the predictive capability of eq 3 but to use both sets of data to explore the applicability or nonapplicability of the PDBF. Figure 4 shows plots of both sets of experimental pCMC data against the pCMC (calcd) values obtained from eq 3 with the PDBF, and Figure 5 shows the corresponding plots with pCMC (calcd) values obtained from eq 3 without the PDBF. Comparing the two figures, it is clear that for both sets of experimental data, the branched isomers are collinear with the unbranched isomers when the PDBF is not applied. When the PDBF is applied in calculation of pCMC (calcd), the deviations from linearity become very obvious. The regression equations are as follows:
Greiner and Herbst data, PDBF applied pCMC ) 0.91((0.16) pCMC (calcd, with PDBF) +0.48((0.36) (9) n ) 13
R2 ) 0.917
s ) 0.13
F ) 121.8
Go¨tte and Schwuger data, PDBF applied pCMC ) 1.00((0.17) pCMC (calcd, with PDBF) +0.08((0.43) (10) n ) 14
R2 ) 0.920
s ) 0.15
F ) 138.4
Greiner and Herbst data, PDBF not applied pCMC ) 1.19((0.11) pCMC (calcd, no PDBF) -0.38((0.27) (11) n ) 13
R2 ) 0.975
s ) 0.07
F ) 434.6
Go¨tte and Schwuger data, PDBF not applied pCMC ) 0.94((0.07) pCMC (calcd, no PDBF) +0.05((0.19) (12) n ) 14
R2 ) 0.985
s ) 0.06
F ) 776.4
Note that eq 12, for the Go¨tte and Schwuger data and derived without use of the PDBF, has slope and intercept very close to 1 and 0, respectively. Overall, it is evident that for modeling micellization potential no branching factor is required for πh when the branching is in the “pure hydrophobe” part of the molecule. This can be rationalized as follows. The branching factor models the water sharing effect, which reduces the number of water molecules required to
Figure 5. pCMC vs pCMC (calcd, branching factors not applied) for linear and β-branched primary alcohol sulfates.
Figure 6. Effect of branching on micelle free energy. (A) An idealized representation of a micelle of a linear surfactant. Wide spaces between hydrocarbon chains need to be filled by water molecules. (B) Micelle of a branched surfactant. Spaces between main chains are partly filled by hydrocarbon branches, reducing the degree of water/hydrophobe contact.
hydrate the hydrocarbon chain in aqueous solution when the hydrocarbon chain is branched.2,3 As a result of this water sharing effect, the free energy of the branched hydrocarbon chain in water is lower than the free energy of its linear isomer. There is no comparable effect in the octanol solvent. Thus, branching displaces the octanol/ water partitioning equilibrium in favor of the aqueous phase. It appears that in the case of micellization this effect must be counteracted by some effect whereby branching reduces the free energy of the hydrocarbon chain in the micelle interior. This can be rationalized in terms of the curvature of micelles. Consider an idealized symmetrical micelle of a linear surfactant. The further the distance from the center of the micelle, the greater the spacing between the alkyl chains (Figure 6). If these spaces are filled by water, the consequent contact between water and hydrophobe will be energetically unfavorable to micellization. If the alkyl chain is branched, these spaces can be packed more efficiently with the alkyl chains, reducing the extent of water/hydrophobe contact within the micelle. Thus, branching in the alkyl chain reduces the free energy both in the aqueous phase and in the micelle, and the micelle/water partitioning equilibrium is not substantially affected overall. The symmetrical C29 SALS homologue which was omitted from the regression analysis used to derive eqs 7 and 8 has a much higher CMC than might be expected on the basis of extrapolation from the C8-C19 SALS data. Its calculated pCMC value (using eq 3) is 5.94, whereas the experimental value is 4.10. Symmetrical C29 SALS may be regarded as a di-C14 double-chain surfactant, (nC14H29)2CHOSO3Na. Surfactants of this type tend to form lamellar phase bilayers rather than spherical micelles.19 For the lamellar phase, there is no equivalent of the
Octanol/Water Partition Coefficients
Langmuir, Vol. 18, No. 2, 2002 351
micellar radius effect which is modeled by the L parameter, and the effect of branching in reducing the free energy of the surfactant in the aqueous medium is not balanced by a similar effect in the lamellar bilayer. Thus, for modeling the CMC of a surfactant which forms lamellar phase aggregates rather than spherical micelles, the PDBF should be applied, if there is branching, in the calculation of πh, and the L parameter should be omitted in the calculation of pCMC. On this basis, the modified calculation for the symmetrical C29 SALS homologue proceeds as follows: Starting from parent structure n-C12H25OSO3Na, log P ) 1.60,
and apply the PDBF ) -1.44 log(14+1) ) -1.69 log P ) 1.60 + 9.18 - 1.69 ) 9.09 πh ) log P - f(OSO3-) ) 9.09 + 5.23 ) 14.32 Applying eq 3 but without the L term,
pCMC ) 0.39πh - 1.50 ) 0.39 × 14.32 - 1.50 ) 4.08 which agrees well with the observed value of 4.10. Overall Regression Equations The approach adopted here was to use a subset of a larger data set on pCMC values as a training set to develop a QSPR (in this case eq 3), whose predictive value can then be tested against the remaining data. This approach is often although not always adopted in development of quantitative structure-activity relationships (QSARs) and QSPRs from a large data set. To get an overall picture of the statistics, it is useful at this stage to examine the predictive ability of eq 3 against the full data set together. After eliminating duplicated data (where the same compound appears in Tables 1 and 2, the data in Table 2 is used), there remains a data set of 133 compounds and their CMC values, excluding C29 SALS (vide supra). Regression analysis of pCMC (observed) against values calculated from eq 3 gives
All anionics pCMC ) 0.99((0.03) pCMC (calcd) - 0.09((0.08) (13) R2 ) 0.976
s ) 0.12
pCMC ) 1.00((0.03) pCMC (calcd) - 0.05((0.08) (14) n ) 75
R2 ) 0.988
s ) 0.09
F ) 6122
SALS, LAS and β-branched PAS pCMC ) 0.95((0.03) pCMC (calcd) - 0.07((0.10) (15) n ) 58
R2 ) 0.982
s ) 0.08
F ) 3074
Conclusions
add 17 CH2 groups: 17 × 0.54 ) 9.18
n ) 133
All anionics except SALS, LAS, and β-branched PAS
F ) 5360
Not all of the deviations from perfect linearity are random. Thus, it can be seen from Tables 4, 5, and 6 that although the differences are not much greater than might be expected from experimental error, every pCMC value for SALS, LAS, and β-branched PAS is overpredicted by eq 3. The origin of these systematic deviations is not clear and, because the deviations are small, cannot be determined unequivocally by statistical analysis. Possibly steric repulsion forces, arising from the relatively large effective diameter of the hydrophobe near the point of attachment of the ionic group, are stronger for these surfactants and play a role in determining the pCMC values. Treating this group of surfactants separately leads to the equations (19) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed; Academic Press: London, 1992; p 375.
The micellization potential of anionic surfactants covering a diverse range of structures is well modeled by a combination of two parameters, πh and L, the former being the log P fragment value for the hydrophobe (simply defined as the whole molecule minus the negatively charged fundamental fragment) and the latter being the length, in C-C single bond units, of the hydrophobe. These parameters are simple to calculate, providing a rapid and accurate “back of envelope” method for estimation of CMC values. Some of the log P fragment values and factors used in the calculation of the πh values used here have been derived inferentially from fitting aquatic toxicity data for surfactants to QSAR equations. These are as follows: The position-dependent branch factor, PDBF, derived originally from goldfish toxicity data for LAS homologues and isomers,3 subsequently found to be applicable in aquatic toxicity of nonionic surfactants20-22 and skin sensitization potential of 3-alkyl catechols.23 This is now validated by its successful application to quantify the effects on CMC of methyl and ethyl branches in alkyleneoxy units of ether sulfates. The log P increment of -0.25 for ethyleneoxy groups (from which the increments of -0.14 and +0.14 are derived for propyleneoxy and butyleneoxy groups, respectively) in ether sulfates, derived4 from rotifer chronic aquatic toxicity data.24 This is now validated by its use in calculating πh and hence pCMC values for ether sulfates and the finding that the same high-quality linear correlation between pCMC (obsd) and pCMC (calcd) includes both ether sulfates and surfactants without alkyleneoxy groups. The modified proximity factors for situations when one of two neighboring hydrophilic groups is much more hydrophilic than the other: for the ester sulfonates4,25 the proximity factor for the geminal -CO2- and SO3- entities is +1.49 as compared with +3.09 by the original Leo and Hansch method, and for ether sulfates4 the proximity (20) Roberts, D. W. QSAR issues in aquatic toxicity of surfactants. Sci. Total Environ. 1991, 109/110, 557-568. (21) Roberts, D. W.; Marshall, S. J. Applications of hydrophobicity parameters to prediction of the acute aquatic toxicity of commercial surfactant mixtures. SAR QSAR Environ. Res. 1995, 4, 167-176. (22) Roberts, D. W.; Garcı´a, M. T.; Ribosa, I.; Hreczuch, W. QSAR Analysis of Aquatic Toxicity of Ethoxylated Alcohols. Jorn. Com. Esp. Deterg. 1997, 27, 53-63. (23) Roberts, D. W.; Benezra, C. Quantitative structure-activity relationships for skin sensitisation potential of urushiol analogues. Contact Dermatitis 1993, 29, 78-83. (24) Rosen, M. J.; Zhu, Y. P.; Morrall, S. W.; Versteeg, D. J.; Dyer, S. D. Estimation of Surfactant Environmental Behaviour from Physical Chemical Parameters. Fourth World Surfactants Congress Proceedings, Barcelona, Spain, 1996; A. E. P. S. A. T.: Barcelona, 1996; Vol. 3, pp 304-313. (25) Roberts, D. W.; Marshall, S. J.; Hodges, G. Quantitative Structure-Activity Relationships for Acute Aquatic Toxicity of Surfactants. Fourth World Surfactants Congress Proceedings, Barcelona, Spain, 1996; A. E. P. S. A. T.: Barcelona, 1996; Vol. 4, pp 340-351.
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factor for the vicinal -O- and OSO3- entities is +1.48 as compared with +1.83 by the original Leo and Hansch method. These modified values are validated by their use in calculating πh and hence pCMC values and the finding that the same high-quality linear correlation between pCMC (obsd) and pCMC (calcd) includes both ether sulfates and ester sulfonates together with other surfactants for which proximity factors are not required. Two other reports on development of QSPRs for anionic surfactant CMCs have been published. Huibers et al.26 developed a three-parameter QSPR for a set of 119 anionic surfactants, with an R2 value of 0.940, based on zerothorder connectivity indices, dipole moments, and the sum of carbon atoms incorporated in hydrophilic headgroups (in their treatment, units such as ethyleneoxy groups are assumed to be part of the headgroup). For a subset of 68 compounds excluding ether sulfates and other surfactants which they classify as having complex headgroups, they obtained a QSPR with an R2 value of 0.988 based on firstorder connectivity indices, third-order shape indices, and headgroup position on the longest linear chain. There is some overlap between their CMC data set and that used here. Jalili-Heravi and Konouz27 developed two-parameter and three-parameter QSPRs, based on topological (Wiener numbers and Randic indices) and electronic (dipole moment) indices for a set of 31 surfactants, these being
the linear primary alcohol sulfates from C10 to C16 excluding the C11 homologue, 21 secondary alcohol sulfates, and four linear alkane sulfonates RSO3Na. The two-parameter QSPR, based on Wiener number and reciprocal of dipole moment, has an R2 value of 0.964, and the addition of a further parameter, reciprocal of the Randic index, improves the R2 to 0.982. Although these QSPR approaches appear very different from that adopted here, they are based on the same mechanistic principles. As the authors make clear, the connectivity and topological indices are correlated with hydrophobe surface area, and this together with polarity (represented by dipole moment) is well recognized as determining the log P value.2 The use of two topological/ connectivity indices together in the same QSPR equation is analogous to using separate L and πh (without alkyl chain branching factors) in the approach adopted here. A major practical difference is that the QSPR parameters used here can be calculated manually, and trends in the values of the parameters are immediately obvious from inspection of molecular structure. Further work is currently in progress to test the QSPR developed here against CMC data on further anionic surfactants and to extend the approach to cationic surfactants.
(26) Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Prediction of Critical Micelle Concentration Using a Structure-Property Relationship Approach. 2. Anionic Surfactants. J. Colloid Interface Sci. 1997, 187, 113-120.
(27) Jalali-Heravi, M.; Konouz, E. Prediction of Critical Micelle Concentration of some Anionic Surfactants Using Multiple Regression Techniques: A Quantitative Structure-Activity Relationship Study. J. Surfactants Deterg. 2000, 3, 47-52.
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