A Simple Method To Estimate the Surfactant Micelle−Water

Langmuir 2000, 16, 3595-3605

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A Simple Method To Estimate the Surfactant Micelle-Water Distribution Coefficients of Aromatic Hydrocarbons George Guohua Liu* and Dipak Roy Department of Civil and Environmental Engineering, Polytechnic University, Six MetroTech Center, Brooklyn, New York 11201-3840

Milton J. Rosen Surfactant Research Institute, Brooklyn College of the City University of New York, Brooklyn, New York 11210 Received July 2, 1999. In Final Form: January 3, 2000 To predict surfactant micellar solubilization of aromatic hydrocarbons (arenes), a simple model is tried with the geometric mean, (π20πcmc)1/2, of the surface tension reductions, and the total molecular surface area of the arene, TSA, to estimate micelle-water distribution coefficients, KXM, in the dilute solution range. The solubilization experiment was conducted by the generator-column method. The structures of the arenes used vary from one ring to five rings and include both homopolycyclic aromatic hydrocarbons (PAH) and some hetero-PAH. The surfactant solutions are five typical surfactants. An acceptable congruence between the predicted log KXM vs log KOW correlation and the experimental log KXM vs log KOW correlation, previously published, is found. Therefore, this model may be used as an alternative tool to estimate KXM for the soil flushing/washing process.

Introduction Aromatic hydrocarbons (arenes) are typical nonpolar hydrophobic organic molecules that contain one or more benzene rings arranged in various configurations. Because most arenes are sparingly water-soluble and some are carcinogens, the surfactant-enhanced soil flushing/washing process, as an alternative in situ remediation technology to remove arenes from a groundwater/soil system, has been studied intensively.1-20 In this process, the * To whom all correspondence should be addressed. Email: [email protected]. (1) Roy, D.; Liu, M. W. Ecological Issues and Environmental Impact Assessment, 1993, Chapter 11. (2) Sanseverino, J.; Graves, D. A.; Leavitt, M. E.; Gupta, S. K. Remediation of Hazardous Waste Contaminated Soils; Marcel Dekker: New York, 1994; pp 345-371. (3) Mihelcic, J. R.; McNally, D. L.; Lueking, D. R. Surfactant-enhanced Subsurface Remediation: Emerging Technologies; American Chemical Society: Washington, DC, 1995; pp 113-123. (4) Guha, S.; Jaffe, P. R. Environ. Sci. Technol. 1996, 30, 13821391. (5) Rose, J. D.; Sabatini, D. A.; Deeds, N. E.; Brown, R. E.; Harwell, J. H. Environ. Sci. Technol. 1995, 29, 2484-2489. (6) Edwards, D. A.; Luthy, R. G.; Liu, Z. B. Environ. Sci. Technol. 1991, 25, 127-133. (7) Wayt, H. J.; Wilson, D. J. Sep. Sci. Technol. 1989, 24 (12 & 13), 905-937. (8) Sun, S.; Inskeep, W. P. Environ. Sci. Technol. 1995, 29, 903-913. (9) Rouse, J. D.; Sabatini, D. A.; Harwell, J. H. Environ. Sci. Technol. 1993, 27, 2072-2078. (10) Liu, G.-H.; Chen, C. F.; Roy, D.; Maillercheruve, K. Y. 69th Annual Meeting of NYWEA, New York, Jan 27-29, 1997. (11) Hayworth, J. S.; Burris, D. R. Environ. Sci. Technol. 1997, 31, 1277-1283. (12) Yeom, I. T.; Ghosh, M. M.; Cox, C. D.; Robinson, K. G. Environ. Sci. Technol. 1995, 29, 3015-3021. (13) Klle, D. E.; Chiou, C. T. Environ. Sci. Technol. 1990, 24, 205208. (14) Klle, D. E.; Chiou, C. T. Environ. Sci. Technol. 1989, 23, 832838. (15) Chiou, C. T.; Porter, P. E.; Schmedding, D. W. Environ. Sci. Technol. 1983, 17, 227-231. (16) Jafvert, C. T.; Vanhoof, P. L.; Heath, J. C. Water Res. 1994, 28, 1009-1017.

enhanced solubilization of arenes results mainly from the “hydrophobic interactions”,18,21 which is the major driving force for the transfer of the arenes from water to the micellar phase. The solubilization of arenes occurs mostly in the micelle hydrophobic interior,22-25 though some polarizable arenes, like benzene, may also be solubilized in the micelle outer layer through hydrogen bonding26 or by the formation of an electron donor-acceptor complex.19,20 Thus, in the solubilization process, the micelle acts as a nonpolar solvent23-25 and enhances the solubilization of arenes, even though weak monomer-enhanced solubilization of other nonpolar hydrophobic organic compounds,14 other than arenes, has been reported at surfactant concentrations less than the critical micelle concentration (cmc). For the purpose of the soil flushing process, the solubilization of nonpolar hydrophobic arenes in surfactant micellar solution can be considered as occurring separately in two pseudophases,22,23 i.e., the water phase and the micelle phase. Many researchers have developed methods to evaluate and/or predict surfactant-enhanced solubilization of hydrocarbons. Molar solubilization ratios (MSRs)6,22 were used to illustrate the solubilization capacity of a particular surfactant micelle solution for a specific solute at sur(17) Jafvert, C. T. Environ. Sci. Technol. 1991, 25, 1039-1045. (18) Valsaraj, K. T.; Thibodeaux, L. J. Water Res. 1989, 23, 183-189. (19) Pennell, K. D.; Adinolfi, A. M.; Abriola, L. M.; Diallo, M. S. Environ. Sci. Technol. 1997, 31, 1382-1389. (20) Diallo, M. S.; Abriola, L. M.; Weber, W. J., Jr. Environ. Sci. Technol. 1994, 28, 1829-1837. (21) Frank, H. S.; Evans, J. Chem. Phys. 1945, 13, 507-532. (22) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley & Sons: New York, 1989; pp 171-202. (23) Shinoda, K. Principles of Solution and Solubility; Marcel Dekker: New York, 1978; pp 181-199. (24) Hutchinson, E.; Shinoda, K. Surfactant Solutions: New Methods of Investigation; Marcel Dekker: New York, 1987; pp 4-15. (25) Saito, H.; Shinoda, K. J. Colloid Interface Sci. 1967, 24, 10-15. (26) Mukerjee, P.; Cardinal, J. R. J. Phys. Chem. 1978, 82 (14), 16201626.

10.1021/la990866m CCC: $19.00 © 2000 American Chemical Society Published on Web 03/18/2000

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factant concentrations above the cmc. A computational method7 was developed with the assumption of stepwise equilibrium between the number of micelles and solute. The group contribution model27 was explored for the prediction of the solubilization of chemicals in a specific surfactant micelle solution using the structural formula of the solute and its Henry’s law constant. Using linear free-energy relationships (LFERs),28,29 the micelle-water distribution coefficients, KXM, of a set of nonpolar hydrophobic organic compounds often can be correlated with their octanol-water partition coefficients, KOW.12-18 The micelle-water distribution coefficient, KXM, has been widely used not only for predicting surfactantenhanced solubilization but also for evaluating the liquidsolid-phase partition coefficient of nonpolar hydrophobic hydrocarbons.1,12-18 Nevertheless, it should be noted that there is appreciable scatter between the reported values of KXM of arenes, which has been attributed to both the experimental methods and the purity and/or the concentration of the surfactant used.17 The experimental procedure using “flask shaking” method, even for the measurement of KOW, has been questioned in its ability to produce reliable and reproducible values.29 At different surfactant concentration ranges, the surfactant micelle may have various asymmetric shapes and different sizes30-37 with a Gaussian distribution.31 Although the different nonideal entropy of mixing at different micellized surfactant concentrations will influence the measurement of KXM, the value of KXM can be assumed constant17 in the dilute solution range for its application in the soil flushing process. On this assumption, the objective of our work is to develop a simple method, using both the characteristics of solubilizate and the properties of the surfactant micellar solution, to predict the KXM of arenes for use in the soil flushing process. Previously, it had been found that the solubility of arenes in potassium laurate micellar solutions decreases with their molecular length or molecular volume.38 Also, it was reported that the molecular surface areas of some hydrophobic organic solutes correlate well with their sodium dodecyl sulfate (SDS) micelle-water distribution coefficients.10,18 Other investigations have shown that the KXM of nonpolar additives correlates with chain length of sodium alkyl sulfate39 and that the KXM of arenes increases with a decrease of the hydrophilelipophile balance value (HLB) of dodecyl alcohol ethoxylate.20 More recently, a semiempirical model16 was constructed that relates KXM to KOW and nonionic surfactant structure properties defined by two arbitrary numerical parameters. Our work starts with the application of lattice theory40 to interpret the partial mole excess free energy change of

arenes in two phases, the micelle pseudophase and pure water. The increase in chemical potential of arenes in the micelle interior is assumed to be related to the energy barrier, produced by water penetration/hydration of the micelle, to the transfer of arenes into the micelle interior. The molecule interchange energy in each phase is determined from the intermolecular force operating on the total molecular surface of the arenes. This approach was first conceptualized by Langmuir and successfully applied to predict the solubility of nonpolar organic compounds in mixtures of water and pure organic solvents of over 10% volume.29,41 The microscopic intermolecular force between the micelle phase and pure water is further expressed by the macroscopic interfacial/surface tension reduction at the interface. Finally, log KXM is approximately expressed as the product of the molecular surface area of the arenes and the geometric mean of two interfacial/surface tension reductions, π20 and πcmc, by the surfactant solution. The developed equation is supported by the measured KXM values of four PAH compounds in SDS micellar solutions obtained by the generator-column method.42,43 The generalization of the developed equation is evaluated by previously published KXM values of the arenes in five types of surfactant micellar solutions, including one anionic surfactant, one cationic surfactant, and three nonionic surfactants. The developed equation is further tested by the congruence of the predicted log KXM vs log KOW correlation and the reported log KXM vs log KOW correlation.

(27) Smith, G. A.; Christian, S. D.; Tucher, E. E.; Scamehore, J. F. Langmuir 1987, 3, 598-599. (28) Leo, A.; Hansch, C. J. Org. Chem. 1971, 36, 1539-1544. (29) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M. Environmental Organic Chemistry; John Wiley & Sons: New York, 1993; pp 124-156. (30) Tanford, C. J. Phys. Chem. 1972, 76, 3020-3024. (31) Tanford, C. J. Phys. Chem. 1974, 78, 2469-2479. (32) Reiss-Husson, F.; Luzzati, V. J. Phys. Chem. 1964, 68, 35043511. (33) Mazer, N. A.; Benedek G. B.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075-1085. (34) Forrest, B. J.; Reeves, L. W. Chem. Rev. 1981, 81, 1-14. (35) Young, C. Y.; Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1978, 82, 1375-1378. (36) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Martic, C. C. J. Phys. Chem. 1980, 84, 1044-1057. (37) Mukerjee, P. J. Phys. Chem. 1972, 76, 565-570. (38) Klevens, H. B. J. Phys. Chem. 1950, 54, 283-297. (39) Abu-Hamdiyyah, M.; Rahman, I. A. J. Phys. Chem. 1987, 91, 1530-1537.

XAT ) nAT/nW; XS ) nST/nW; Xcmc ) nscmc/nW; XAW ) nAW/nW; XM ) nM/nW ) (XS - Xcmc); XAM ) nAM/nM ) (XAT - XAW)/(XS - Xcmc)

Framework Phase Distribution of Arenes. At constant volume, pressure, and temperature, if the distribution of arenes in two pseudophases, intrinsic (pure) water and surfactant micelle, reaches equilibrium, the mass balance of arenes in the dilute solution range, expressed by mole fraction, is

nAT nAW nAM nM nAW nAT - nAW nST - nscmc ) + ≈ + nT nT nM nT nW nST - nscmc nW (1) nT ≈ nW where n ) mole number and the subscripts are Aj ) arenes solubilized/dissolved in the j phase, with j ) T, M, and W (T ) total solution; W ) pure water; M ) micellized surfactant), ST ) total surfactant, and Scmc ) surfactant at critical micelle concentration. For convenience, the mole fractions of arenes and surfactant are defined by the symbols,

Clearly, solubilization occurs only when the total surfactant mole fraction XS g Xcmc; here, Xcmc is the critical micelle (40) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986; Chapters 7 and 9. (41) Yalkowsky, S. B.; Samuel, H. Aqueous Solubility: Methods of Estimation for Organic Compounds; Marcel Dekker: New York, 1992; pp 75-97. (42) May, W. E.; Wasik, S. P.; Freeman, D. H. Anal. Chem. 1978, 50, 175-179, 997-1000. (43) Hurter, P. N.; Hatton, T. A. Langmuir 1992, 8, 1291-1299.

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mole fraction above which the micelles form, and the arene is solubilized in the micellar interior as the mole fraction, XAM. Selecting the mole fraction of arenes in pure water, XAW, as a reference to evaluate the micelle-enhanced solubilization of arenes and dividing eq 1 by XAW give the same results as those obtained by other researchers6,13-18

XAT XAM ) (X - Xcmc) + 1 ) KXMXM + 1 XAW XAW S

)

(2)

where XAM/XAW ) the ratio of micelle-water mole fractions and KXM ) micelle-water phase distribution coefficient of arenes. By the thermodynamic relationship that at constant volume, pressure, and temperature the chemical potentials of arenes in pure water and in the micelle phase at equilibrium are equal to each other

RT(ln XAM + ln γAM) + µ°AM ) RT(ln XAW + ln γAW) + µ°AW where R ) universal constant [8.3145 J/(mol K)], T ) temperature (K), γAj ) activity coefficient of arenes in the j phase, W or M, µ°Aj ) standard potential energy of arenes in the j phase, W or M, and KXM will be given as the following expression:

(3)

∆µAMW ) µ°AW - µ°AM ) -µ°AMW µ°AW ) 0 The difference between the standard chemical potential of arenes in the micelle interior phase and that of arenes in pure water, ∆µAMW, is related to the energy barrier to its transfer into the micellar interior, mostly produced by the tension at the interface between the water and the hydrated/water penetrated outer layer of the micelle operating on the molecular surface of the arene. Estimation with Surface Tension and Molecular Surface. Because the presence of arenes in micelles obeys a Poisson distribution44 and the solubilization of the arenes occurs mainly in the micellar interior, the two liquid mixtures, arenes with water and arenes with micelle, can be thought of as a typical quasicrystalline state (lattice array). Moreover, the van der Waals-London dispersion force and induction forces operating on nonpolar hydrophobic arenes are of short effective range because these intermolecular forces vary inversely with the sixth power of the separation distance between the molecules.40 This means that only the pairwise potential energy from nearest-neighbor molecules needs to be considered in summation, the basic assumption of lattice theory. In the dilute solution range, the mole fraction of solvent, Xj ) (1 - XAj) f 1, when XAj f 0. Therefore, it is possible to apply lattice theory (Appendix I) to describe the partial mole excess free energy of the arene in each phase, RT ln(γAj), (44) Almgren, M.; Grieser, F.; Thomas, J. K. J. Am. Chem. Soc. 1979, 101, 279-291.

µAMW γAW γAM RT

zN {[ΓAW - 0.5(ΓWW + ΓAA)] RT [ΓAM - 0.5(ΓMM + ΓAA)]} -

)

KXM ) XAM/XAW

RT ln KXM ) RT ln(γAW/γAM) + ∆µAMW

( )

ln KXM ) ln

µAMW RT

zN {[0.5(ΓMM - ΓWW) - (ΓAM - ΓAW)]} RT µAMW (4) RT

where z ) coordination number, N ) Avogadro’s constant (6.022 × 1023 molecules/mol), Γij ) potential energy between molecules i and j, with i or j ) A, W, or M. In eq 4, ΓMM is the potential energy of the surfactant hydrocarbon chain in the micellar interior, and ΓAM is that between the arene molecule and the surfactant hydrocarbon chain in the micelle interior. The cancellation of the potential energy, ΓAA, of the arene means that the arene is either solubilized in the micellar interior or dissolved in pure water. Also, because the intermolecular forces operating on the arene are of short effective range and some part of the arene’s molecular volume may not be exposed to the molecular interaction, the potential energy, Γij, is better expressed as the work done by the intermolecular force operating on the microscopic molecular surface area,29,41 a,

Γij ) -fija ) -[f hij(TSA)h + f pij(TSA)p]/z ≈ f hij(TSA/z) (5) where a ) TSA/z ) microscopic molecular surface area of the arenes, responding to 1-1 molecule interaction (cm2), fij ) intermolecular force (erg/cm2), f hij ) hydrophobic intermolecular force (erg/cm2), f pij ) polar intermolecular force (erg/cm2), TSA ) total molecular surface area of arenes (cm2), (TSA)h ) hydrophobic molecular surface area of arenes (cm2), (TSA)p ) polar molecular surface area of arenes (cm2). In eq 5, (TSA)h is approximated to TSA because the polar surface area, (TSA)p, of most arenes is small and, correspondingly, the polar force, f pij, is negligible. As proved by London,40 the polar force is not important when the dipole moment is less than 1 D, and the induction force always tends to be much smaller than the dispersion force. From eq 5 it is obvious that for a binary mixture of arene-solvent the magnitude of Γij depends on the TSA of the arene. This dependence is reasonable because the number of occupied π orbitals on the “closed shell” of the arene, which determine their properties in the ground state, increases with the growing geometric size of the arene.45 Expressing the microscopic intermolecular force (energy), fij, in eq 5 by the macroscopic interfacial/surface tension, Ψij, of the liquid phase according to Girifalco’s equation46,47 (see Appendix II) and further substituting it for Γij in eq 4 give (45) Zander, M. Polycyclische Aromatische Kohlenwasserstoffe; VDIBericht No. 358; VDI-Verlag: Dusseldorf, Germany, 1980; p 11. (46) Girifalco, L. A.; Good, R. J. J. Phys. Chem. 1957, 61, 904-909. (47) Good, R. J.; Girifalco, L. A. J. Phys. Chem. 1960, 64, 561-565.

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log KXM )

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N [2(ΨW - ΨM) 2.3RT (ΨAW - ΨAM)](TSA) -

µAMW 2.3RT

or

log KXM )

N {(ΨW - ΨM) + 2[ΦAW(ΨAΨW)1/2 2.3RT µAMW (6) ΦAM(ΨAΨM)1/2]}(TSA) 2.3RT

where Ψij ) interfacial/surface tension of the liquid phase, with i or j ) A, W, or M, and Φij ) interaction factor describing the interaction extent between i and j. µAMW is the most difficult to express accurately. Here, we consider the contribution of the water hydration/penetration into the micelle, which occurs in both ionic surfactants48 and nonionic surfactants.20,22,48 With higher water core concentration, the micellar interior is less hydrophobic22 and the standard state chemical potential would increase because of more unfavorable arene-water interaction in the micelle, which will decrease the partition coefficient.43 On the other hand, the water hydration in the micellar outer layer and water penetration in the micellar core reduce the available micellar volume,49 VM, or lyophobic sites, NM, for the solubilization of arenes. Statistically, the probability of the reduced volume, ∆VM, or the reduced lyophobic sites, ∆NM, in the lattice array is proportional to the Boltzmann distribution,50

µAMW ) -RT ln(∆NM/NM) ) -RT ln(∆VM/VM) ) N∆WAMW where k ) Boltzmann’s constant, k ) R/N. If the interchange energy, ∆WAM, can be expressed as the interfacial tension at the interface between water and the outer layer of the micelle, σMW, acting on the arene molecular surface,

∆WAMW ) σMW(TSA)

(7)

where σMW ) interfacial tension at the micelle outer layerwater interface (erg/cm2) and subscript MW ) micelle/ water interface. Substitution of NσMW(TSA) for µAMW in eq 6 yields

log KXM )

N [2(ΨW - ΨM) 2.3RT (ΨAW - ΨAM) - σMW](TSA)

or its equivalent form log KXM )

(8)

N {(ΨW - ΨM) + 2[ΦAW(ΨAΨW)1/2 2.3RT ΦAM(ΨAΨM)1/2] - σMW}(TSA)

The physical meaning of eq 8 is that the driving force for the distribution of the arene to two liquid phases, the water and the micellar interior, depends on the difference between their surface tensions before solubilization (ΨW (48) Birdi, K. S. Progress in Colloid and Polymer Science; Kilian, H.-G. (Ulm), Weiss, A. (Munich), Eds.; Steinkopff Verlag: Darmstadt, Germany, 1985; Vol. 70, pp 23-29. (49) Simon, R. V. M.; McIntosh, T. J. J. Phys. Chem. 1982, 86, 14491456. (50) Alberty, R. A. Physical Chemistry, 7th ed.; John Wiley & Sons: New York, 1987; Chapter 3.

- ΨM) and that between their interfacial tension at solubilization equilibrium (ΨAW - ΨAM). The resistance to the transfer of the arene to the micellar interior comes from the interfacial tension at the interface between water and the outer layer of the micelle, σMW. The rationality of eq 8 is that the interfacial/surface tension is also the measure of the hydrophobic incompatibility (interaction) of the arene with the pure water phase and the micellar pseudophase.22 Approximation for Application. However, there are three obstacles to the application (8) to estimate the KXM value of most arenes. The first one is that the calculation of the interaction factor, Φij, with molar volume cannot be generalized for liquid-solid systems47 (see Appendix II). The second is the reliability of the surface tensions of the solid arenes in the subcooled liquid state, as extrapolated from the surface tension of their liquid state at higher temperature. The third is that the surface tension of the micelle interior phase is not easily obtained and its estimation by comparison of its structure with other similar organic solvents is not accurate. Realizing these difficulties, we treat the summation of the interfacial/ surface tensions in eq 8 as the total interfacial/surface tension reduction, πASW, by the total solution of surfactant monomer, micelle, and arene,

[2(ΨW - ΨM) - (ΨAW - ΨAM) - σMW] ) πASW (9) Therefore, eq 8 changes to

log KXM )

N π (TSA) 2.3RT ASW

(8′)

This πASW can be thought of as the contributions from the interfacial/surface tension reduction by the two pseudophases in solution, the interfacial tension reduction, πAmoW, by the mixture of the arene, surfactant monomer, and water, and the interfacial tension reduction, πAMW, by the mixture of the arene, surfactant micelle, and water. According to the Berthelot theory51 (see Appendix III), these interfacial/surface tension reductions have the relation

πASW ) (πAmoWπAMW)1/2

(10)

where π ) interfacial/surface tension reduction (erg/cm2) and subscripts are ASW ) total solution of arenes, surfactant, and water at XS ) Xcmc + XM, AmoW ) phase of arenes, monomer, and water at X20 e XS < Xcmc, and AMW ) phase of arenes, micelle, and water at XM ) (XS - Xcmc). It is noted that when a nonpolar organic liquid is dissolved in water, the surface tension reduction of water is about 20 erg/cm2 for most nonpolar organic liquids,29 the same as the value of πAmoW ) π20 at X20 e XS < Xcmc for any surfactant solution. Also, πAMW can be approximated to πcmc at Xcmc, which can be calculated from the Gibbs equation (22)

πcmc ) π20 + 2.3nRTΩMax log(Xcmc/X20)

(11)

n ) number of species at the surface that changes with surfactant concentration and ΩMax ) (excess) interfacial concentration of the surfactant (the effectiveness of surfactant adsorption at the interface of liquid-air or liquid-hydrocarbon). This approximation is not arbitrary because when the arene is solubilized in the surfactant solution, although (51) Hildeband, J. H.; Scott, R. L. Solubility of Nonelectrolytes, 3rd ed.; Reinhold Publ. Corp.: New York, 1950.

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ΩMax in the Gibbs equation decreases in the range of 99% to 84%, the ratio of Xcmc/X20 changes little,22 which means the πcmc decreases slightly. Thus, with eq 10 to express the summation of interfacial/surface tension, πASW, in eq 8′ and by further substitution of π20 and πcmc for πAmoW and πAmoW, a geometric mean equation for predicting KXM of arenes is established as

log KXM )

N (π π )1/2(TSA) 2.3RT 20 cmc

(12)

Prediction of KXM of arenes by eq 12 is accomplished using the literature-available parameters, π20 and πcmc for the surfactant solutions and the TSA of arenes. It will be tested by the results of our experiment and literature data published previously. Materials and Method Chemicals and Materials. Three parent arene compounds (homo-PAH), naphthalene (two benzene rings, purity > 99%), phenanthrene (three benzene rings with angularity 1, purity > 96%), and pyrene (symmetric four benzene rings, purity > 99%), were from Sigma Chemicals, St. Louis, MO. Sodium dodecyl sulfate, SDS (purity > 99%), a typical anionic surfactant, was from Fisher Scientific, Fairlawn, NJ. These chemicals were not further purified before use. The optima-grade solvents, methanol, methylene chloride, and acetonitrile, were from Fisher Scientific, Fairlawn, NJ. The hydrophilic Teflon filters of 0.50-mm pore size (HPLC certification) were obtained from Millipore, Bedford, MA, and the C18 Maxi-SPE (maximum solid-phase extraction) cartridges were obtained from Alltech, Deerfield, IL. The standardization of the SDS solution was done by potentiometric titration with Hyamine 1622 (Phoenix Co., Houston, TX). The acid-washed silica glass beads (bioanalytical grade) of diameter from 150 to 212 µm were from Sigma Chemicals, St. Louis, MO. Solubilization Experiment. A 1.0-cm i.d. Pyrex glass column (Ace Glass Inc., Vineland, NJ), with an adjustable length of 8-16 cm and Teflon top and bottom fittings, was first filled with a methanol solution of PAH (about 500 mg/L). Then, the column was packed with glass beads and during packing time the column was vibrated periodically with a surface-touching vibrator to distribute the glass beads uniformly and eliminate bubbles from the glass-methanol matrix. After the packing length reached the desired length of 14.0 cm and the weight of glass beads packed was about 18.5 g, all fittings were carefully attached and the same methanol solution of PAH was recirculated through the column from a reservoir for 4 h. Then, the column was dried with high-purity nitrogen gas at a flow rate as slow as possible for 24 h or more. To make sure that the methanol had all evaporated, a sample of the gas flowing through the column was monitored with GC. To confirm that the PAH had coated the glass bead to over 1 mg/g of glass bead, a sample of the glass beads was extracted with methylene chloride and the extract was analyzed with HPLC. A series of fresh SDS solutions running in concentration up to 8.00 times the cmc were prepared volumetrically and then standardized by potentiometric titration. For each PAH, the surfactant solution of 15-mL volume was continuously recirculated at a flow rate of 0.20-0.45 mL/min through the column to ensure that the aqueous phase was completely saturated. At temperature 25.0 ( 1.5 °C the saturation generally was reached after 3 h because of the large contact area between the small glass beads and the solution. An additional circulation time of 2 h may be required to make sure that the amounts of PAH adsorbed to the PTFE tubing wall and other inside faces of fittings are in equilibrium with the aqueous phase. When equilibrium was positively confirmed (constant concentration of PAH by monitoring a sample of 2 mL with UV), the effluent line was connected to a set of Teflon filters and a C18 cartridge in sequence. A 2-8mL sample of the effluent solution was passed through the cartridge, and enough PAH was accumulated in the cartridge to allow quantification of solution load. The cartridge was then removed and washed with deionized water mixed with 2.5%

methanol and the PAH eluted with methylene chloride of optimal volume determined in a preliminary study. The eluate was collected in a brown glass vial of 2.0-mL volume with zero headspace and immediately analyzed, according to EPA method 8100/8310, by HPLC equipped with a Spherisorb PAH 5-µm C18 column of 250 × 4.6 mm (Alltech, Deerfield, IL) and a UV detector (Waters, Millford, MA) at 254 nm. The mobile phase run first was 30/70 water-acetonitrile for 2 min and then 100% acetonitrile at a flow rate of 1.0 mL/min for 15 min. Each sample was triply analyzed, and the chromatography was processed by a software package of WINer on Windows (Thermo Separation Products, San Jose, CA). With this method, a relatively high reproducibility of the PAH solubility was obtained at the controlled temperature, but much time was required because the column had to be repacked for each concentration of surfactant solution.

Results and Discussion The solubilizations of naphthalene, phenanthrene, and pyrene in SDS micellar solutions, together with the value for anthracene published previously,1 are plotted in Figure 1a-d. In these figures, the SDS concentration, XS, and the solubility of PAH, XAT, are reported in mole fractions as defined in the section Phase Distribution of Arenes. It is obvious that the solubilization of each PAH compound has two regions separated by Xcmc of 1.44 × 10-4 at 298 K, a literature value.22 In region I, 0 e XS e 1.44 × 10-4, the solubilities of naphthalene, phenanthrene, pyrene, and anthracene, XAT, are less than their reported solubilities in pure water, XAW. These results agree with other research44 and indicate that the monomer of SDS does not contribute to the solubilization of PAH22 and that a “salting out” phenomenon exists, even though the concentration of SDS is small. In region II of 1.44 × 10-4 e XS e 1.15 × 10-3, the XAT of all four PAH compounds increases linearly with XS, as described by other researchers.6,22,23 From these linear relations shown in Figure 1a-d and using the literature values of XAW for the four PAH compounds,52,53 the solubilization extent of the four PAH compounds is respectively expressed by eq 2 as

(XAT/XAW)Naphthalene ) 17100(XS - Xcmc) + 0.93 (XAT/XAW)Phenanthrene ) 205800(XS - Xcmc) + 0.86 (XAT/XAW)Pyrene ) 858900(XS - Xcmc) + 0.93 (XAT/XAW)Anthracene ) 181300(XS - Xcmc) + 0.92 (13) A difference of only 0.12 log unit exists between log KXM values obtained from eq 13 and the published values of four PAH compounds (Table 1). These log KXM values are correlated to the TSA of the corresponding PAH compounds,54 and as shown in Figure 2 the correlation line, log KXM vs TSA, with a confidence level over 95%, is

log KXM ) 0.0272(TSA) - 0.0546

(14)

Using its slope, 0.0272, to calculate πASM of the SDS micelle solution from eq 8′

πASM ) [0.0272(2.303RT)]/N ) 25.75 (erg/cm2) (52) Mackay, D.; Shiu, W. Y. J. Phys. Chem. Ref. Data 1981, 10, 1175-1199. (53) Miller, M. M.; Waslk, S. P. Environ. Sci. Technol. 1985, 19, 522529. (54) Karcher, W.; Ellison, S.; Ewald, M.; Garrigues, P.; Gevers, E.; Jacob, J. Spectral Atlas of Polycyclic Aromatic Compounds; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988; Vol. 2, Chapters 2 and 4.

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Table 1. SDS Micelle-Water Distribution Coeffcients, KXM, of Four PAH Compounds at 298 K surface tension reductions (erg/cm2) PAH compounds

TSAa (Å)2

naphthalene phenanthrene pyrene anthracene

155.8 198.0 213.5 202.2

a

Spectral Atlas of PAC Vol. 2.54

π20 20.0 b

πcmc 32.5b

predicted distribution coefficient

experimental distribution coefficient

πASW

KXM

log KXM

KXM

log KXM

log KXM

4.24 5.39 5.81 5.50

1.71 × 104 2.06 × 105 8.08 × 105 1.81 × 105

4.23c 5.31c 5.91c 5.26d

4.31e

25.5

1.73 × 104 2.43 × 105 6.42 × 105 3.16 × 105

Compiled by Rosen.22

c

This work.

d

Roy and Liu.1

e

6.18e 5.55e

Javfert’s calculation.17

Figure 2. Correlation of log KXM with TSA of four PAH compounds in a SDS micellar solution.

In eq 14, there exists a residual of -0.0546. This residual may be produced by approximating the hydrophobic surface area of the arene to the TSA of the arene as described in the section Estimation with Surface Tension and Molecular Surface. However, this residual is probably mostly attributable to the experiment error and the precision of the analytical method. Considering it as an error, the predicted log KXM values deviate only about 0.68-1.8% from the published values (see Table 1)17,18,44 of the four PAH compounds in the SDS micellar solution. Moreover, because an average error over 0.1 log unit exists between the published values, this residual is small enough to be neglected. This indicates that the log KXM values of the four PAH compounds in the dilute SDS micellar solution can be predicted by eq 12. It is also expected that eq 12 can be used generally to predict the log KXM values of both liquid and solid arenes in the surfactant micellar solution. The generality of this equation is verified below, using previously published log KXM values of arenes in both ionic and nonionic surfactant micellar solutions. Generalization

Figure 1. SDS-enhanced solubilization of (a) naphthalene (pH ) 6.4; T ) 295.5 K), (b) phenanthrene (pH ) 6.4; T ) 295.5 K), (c) pyrene (pH ) 6.4; T ) 295.5 K), and (d) anthracene (tem > 298 K).

Surprisingly, this experimental value is close to the geometric mean value, πASM ) 25.5 erg/cm2, calculated from eq 12 with two surface tension reductions by the SDS solution at 298 K, π20 ) 20 erg/cm2 and πCMC ) 32.5 erg/cm2. The difference between two πASM values is less than 1%.

KXM of 13 Chemicals in the SDS Micelle Solution. The previously published log KXM values of 13 chemicals, which include three liquid arenes, seven solid arenes, and three other nonarene hydrophobic liquids (polyhalogenated organics), in the SDS micellar solution, are listed in Table 2. These values are classified into two series based on the solubilization experimental conditions. One series is the log KXM values calculated from the enhanced solubility obtained at gas-phase equilibrium,18 and another series is the log KXM values calculated from the solubility in the saturated solution.17,44 In both series of log KXM, listed in Table 2, KXM is the ratio of mole fractions referenced to the pure water solubility. The log KXM values of these chemicals are predicted with the geometric mean equation (12), and they are listed in Table 2. For three liquid arenes and three polyhalogenated liquid chemicals, their log KXM values are also predicted with eq 8. In this prediction, the surface tension

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Table 2. SDS Micelle-Water Distribution Coeffcient of 13 Chemicals, KXM, at 298 K interaction factor

surface tension Ψa (erg/cm2) ΦAW

chemical methylene chloride chloroform carbon tetrachloride toluene m-dichlorobenzene benzene 1-methylnaphthalene biphenyl naphthalene phenanthrene anthracene pyrene perylene 1-octanol surface tension reductions (erg/cm2)

26.5 26.7 26.9 27.93 35.43 28.22

0.80 0.76 0.61 0.71 0.70 0.72

ΦAM 0.99 0.99 0.99 0.99 0.99 0.99

TSA (Å)2

experimental log KXM

predicted log KXM

log KcOW, log KOW, gas-phase log(CAO/CAW) log(XAO/XAW) eq 8 eq 12 equilibrium saturated

82.0b 99.0b 119.0b 127.9b 144.7b 110.0c 172.5b 182.0b 155.8d 198.0d 202.2d 213.5d 251.5d

1.25e 1.96e 2.83e 2.69c 3.48e 2.13f 3.87f 4.09c 3.36f 4.57f 4.54f 5.18f 6.12g

2.07 2.78 3.65 3.51 4.30 2.94 4.69 4.91 4.17 5.39 5.36 6.00 6.94

2.84 3.06 2.03 3.39 3.86 3.03

2.21 2.67 3.21 3.45 3.90 2.97 4.65 4.91 4.20 5.34 5.46 5.76 6.79

2.29h 2.83h 3.44h 3.22h 3.88h 3.04h 4.35i 4.36i 3.79h 5.09i 5.72j

this work

3.48k 2.96k 4.71k 4.79k 4.31k 5.55k 6.18k 7.18k

4.23 5.31 5.26l 5.91 7.09m

27.1

π20 ) 20.0

πcmc ) 32.5 n

σMW ) 29.0o

πASW ) (π20πcmc)1/2 ) 25.5

a CRC, 79th ed.55 b Mackay et al.52 c Schwarzenbach et al.29 d Spectral Atlas of PAC, Vol. 2.54 e Chiou.62 f Miller et al.53 g Javfert.17 Valsaraj et al.18 i Valsaraj’s calculation18 of Almgren’s data.44 j Hinze.63 k Javfert’s calculation17 of Almgren’s data.44 l Roy and Liu.1 c m Recalculated with Almgren’s data.44 n Compiled value by Rosen.22 o Bolden et al.56 Note: log K OW ) log K OW + log(0.12/0.018), log KcOW ) log(CAO/CAW), log KOW ) log(XAO/XAW), C (mol/L), X (mol/mol), octanol mole volume ) 0.12 L/mol, water mole volume ) 0.018 L/mol. h

of 1-octanol (C8H17OH),55 27.1 erg/cm2, is selected as the ΨM of the SDS micelle interior phase. This selection is based on the assumption that the hydrocarbon chain of SDS extending into the micelle interior is about eight methylene groups, -CH2-. This will be discussed later. The interfacial tension at the interface between water and the outer layer of the SDS micelle, σMW, is chosen as 29 erg/cm2, which has been used to calculate the Laplace pressure acting across the curvature of the outer layer of the SDS micelle.18,56 The interaction factors, ΦAW, and ΦAM, are calculated from Girifalco’s equation46,47 (see Appendix II). All cited parameters, together with the TSA of the 13 chemicals, are shown in Table 2. From Table 2, it is seen that the predicted log KXM values of the 13 chemicals with eq 12 are almost the same as the published values. The average absolute difference between the predicted log KXM values by eq 12 and the published log KXM values obtained at gas-phase equilibrium18 is less than 0.22 log unit. The average absolute difference between the predicted log KXM values by eq 12 and the published log KXM values obtained in saturated solution17,44 is less than 0.15 log unit. This means that the predicted log KXM values of 10 arenes are much closer to these published values in the saturated-solution series and our experimental results. As to the three liquid polyhalogenated organics, methylene chloride, chloroform, and carbon tetrachloride, a significant difference exists between the predicted log KXM values by eq 8 and the published values. The possible reason is that the halogen, Cl, straddling between the polar and the nonpolar positions, may contribute to the interfacial tension between water and the outer layer of the SDS micelle and produce a different value of σMW, rather than 29 (erg/cm2), to be put into eq 8. Also, because the contribution of the electronic intramolecular interaction of these polyhalogenated liquid organics to the intermolecular interaction28,29 in two pseudophases is complex, the validity of eq (55) CRC Handbook of Chemistry & Physics, 79th ed.; CRC Press: Boca Raton, FL, 1998-1999; pp 6-135 to 6-138. (56) Bolden P. L.; Hoskins J. C.; King, A. D., Jr. J. Colloid Interface Sci. 1983, 91, 454-463.

8 for predicting log KXM of the polyhalogenated chemicals is questionable. The predicted log KXM values of the 13 chemicals by the geometric mean eq 12 and the published log KXM values are further respectively correlated to the logarithm of their corresponding octanol-water partition coefficient, log KOW or log KcOW, according to LFERs,28,29

log KXM ) a log KOW + b

(15-1)

log KXM ) a log KcOW + b′

(15-2)

or

where a, b, or b′ ) correlation constants, relying on the lipophilicity of the solvent, KOW ) octanol-water partition coefficient, mole fractions ratio XAO/XAW, KcOW ) octanolwater partition coefficient, mole concentrations ratio CAO/ CAW, CAj ) mole concentration of arenes, A, in the j phase, with j ) O or W, superscript c ) mole concentration, and subscript O ) octanol phase. The correlation of the predicted log KXM values to the log KOW values is

log KXM ) 0.975 log KOW + 0.018

(16)

This correlation line is shown in Figure 3, in which the two other correlation lines are also presented. The lowest one responds to the correlation of the log KXM values obtained from gas-phase equilibrium to log KOW,

log KXM ) 0.846 log KOW + 0.405

(17)

and the upper one is the correlation of the log KXM values obtained from the saturation solution to log KOW,

log KXM ) 1.061 log KOW - 0.214

(18)

The position of these correlation lines reflects the fact that the method of gas-phase equilibrium may underinterpret the solubilization of solid arenes, which have low Henry’s constants,16 and the saturation method may

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Figure 3. Correlation of log KXM to log KOW of 13 chemicals for a SDS micelle solution. Table 3. CTAB Micelle-Water Distribution Coeffcient, KXM, at 298 K log KXM chemical

TSA (Å)2

log KcOW, log(CAO/CAW)

benzene biphenyl naphthalene anthracene pyrene perylene

110.0a 182.0b 155.8c 202.2c 213.5c 251.5c

2.13d 4.09a 3.36d 4.54d 5.18d 6.12e

surface tension reduction (erg/cm2)

log(XAO/XAW) log KOW,

predicted by eq 12

2.94 4.91 4.17 5.36 6.00 6.94

3.29 5.45 4.66 6.05 6.39 7.53

πcmc ) 40.5g or πcmc ) 38.0h

experimental 3.27 5.49 4.80 6.18 6.89 7.40

calculated from the KM (L/mol) valuesf KXM ) 55.5KM/(60 + n), n ) number of solute molecular in micelle interior

πASW ) (π20πcmc)1/2 ) 28.6

a Schwarzenbach et al.29 b Mackay et al.52 c Spectral Atlas of PAC, Vol. 2.54 d Miller et al.53 e Javfert.17 f Almgren et al.44 g Klle et al.14 h Fang Li et al.59 Note: log KOW ) log KcOW + log(0.12/0.018), log KcOW ) log(CAO/CAW), log KOW ) log(XAO/XAW), C (mol/L), X (mol/mol), octanol mole volume ) 0.12 L/mol, water mole volume ) 0.018 L/mol.

overinterpret the enhanced solubilization of arenes because unfiltered PAH particles or supersaturation may exist at nonequilibrium.44 In the correlation of log KXM vs log KOW, the slope, a (a > 1 or a < 1), in one sense, and the intercept, b (b > 0 or b < 0), in a slightly different way, indicate the relative lipophilicity of the solvent system referring to the octanolwater system.28,29 The slope a is a measure of the solvent system’s sensitivity to the changes in lipophilicity of solutes. The slope a less than unity means less energy to transfer a hydrophobic solute from the aqueous phase to the nonaqueous (solvent) phase than in the octanol-water system. The intercept b larger than zero means that the relative lipophilicity of the solvent system is less than that of the octanol-water system. In this view, in the correlation of the predicted log KXM vs log KOW of eq 16, a ) 0.975 < 1 and b ) 0.018 > 0 indicate that the sensitivity to the hydrophobicity of the 13 chemicals and the relative lipophilicity of the SDS micelle-water system are less than those of the octanol-water system. For the surfactant sodium n-alkyl sulfate series, the contribution to micelle formation (or lipophilicity) of 4.55.0 methylene units of hydrocarbon chain may be offset by the hydrophilic head of SDS, -SO4-, which is estimated by setting log cmc equal to zero in the empirical equation (22)

log cmc ) 1.51 - 0.30n where n ) number of methylene units or carbon atoms in the hydrophobic chain.

That is, only about 7 of the 12 methylene units in the SDS hydrocarbon chain can really account for the lipophilicity of the SDS micelle interior phase. Compared to 8 methylene units in the octanol molecule, the sensitivity of the micellar interior phase to the lipophilicity change of the arene should be less than that of octanol. The smaller lipophilicity of the SDS micelle-water system is also supported by the water hydration/penetration extending to five and six carbon atoms adjacent to the hydrophilic head.57,58 Therefore, a strong hydrogen-bonding force and an electron attractive force exist between the hydrophilic head in the SDS micellar outer layer and water. This intermolecular force reduces the solvent system’s sensitivity to the relative changes in the lipophilicity of arenes or, in another words, it renders the SDS micellar phase more incompatible with the nonpolar hydrophobic arenes than octanol. Thus, the slope, a, in the correlation line, log KXM vs log KOW, should be less than 1, and the intercept, b, is positive. The congruence of the predicted log KXM vs log KOW correlation leads to the conclusion that the micelle-water distribution coefficient, log KXM, of arenes in the SDS micellar solution can generally be predicted by eq 12. KXM of Six PAH Compounds in CTAB Micelle Solution. Table 3 lists the published log KXM values of six PAH compounds in cetyltrimethylammonium bromide (CTAB) micellar solution under the condition of supersaturation,44 yielding slightly higher values of log KXM. (57) Benjamin, L. J. Phys. Chem. 1961, 64, 1221. (58) Walker, T. J. Colloid Interface Sci. 1971, 45, 372.

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Table 4. Micelle-Water Distribution Coefficients of Four PAH Compounds in Three Nonionic Surfactant Solutions, KXM, at 298 K nonionic surfactant solutions surface tension reduction

micelle-water phase distribution coeffcient, log KXM naphthalene

phenanthrene

pyrene

trade name

cmc (mmol/L)a

πcmc (erg/cm2)a-c

πASW (erg/cm2)

experimentd

predicted by eq 12

experimentd

predicted by eq 12

experimentd

predicted by eq 12

Brij 30 Tergitol NP-10 Triton X-100

0.02-0.023 0.05-0.054 0.02-0.17

43.4 41.0 38.5

29.5 28.6 27.8

4.74 4.79 4.76

4.88 4.72 4.60

6.02 6.04 5.96

6.20 6.00 5.84

6.75 6.67 6.49

6.68 6.47 6.30

log KOW ) 4.17f

1-octanol a

Edwards et al.6 b

Rosen.22 c

log KOW ) 5.36f

log KOW ) 6.00f

benzo(a)pyrene experimente

predicted by eq 12

7.74

8.00 7.74 7.54

log KOW ) 7.32f

Referring to pure water solubility, recalculated from the KXMa of the samples containing sample. f Calculated from the log KcOW values of Miller et al.53 Note: log KOW ) log KcOW

Klle and Chiou.17 d

1% methanol. e Yeom et al.,12 super saturation + log(0.12/0.018), log KcOW ) log(CAO/CAW), log KOW ) log(XAO/XAW), C (mol/L), X (mol/mol), octanol mole volume ) 0.12 L/mol, water mole volume ) 0.018 L/mol.

Figure 4. Correlation log KXM of six PAH compounds to log KOW for a CTAB micelle solution.

There is a positive difference of an average of 0.13 log units between those values and the predicted values of log KXM using eq 12, which are also listed in Table 3. In the prediction, a cmc value of 0.0009 M22 and a surface tension reduction, πcmc, of 38.0 erg/cm2 59 or 40.5 erg/cm2 14 at 25 °C are employed to yield the expression

log KXM ) 0.029∼0.030(TSA)

(19)

Both the published log KXM values (see Table 3) and the predicted log KXM values are correlated with the corresponding log KOW values, shown in Figure 4, and the predicted correlation line is

log KXM ) 1.047 log KOW + 0.273

(20)

and the published correlation line is

log KXM ) 1.064 log KOW + 0.297

(21)

It is seen that both linear slopes, a, are larger than 1, but their intercept, b, is positive. The reason for a >1 is that the length of hydrocarbon chain, C16H33-, of CTAB is 2 times longer than that of the octanol molecule, C8H17-. Even though the hydrophilic head -N+-(CH3)3 of CTAB can offset 6.5 units of -CH2approximated from the empirical equation,60

log cmc ) 2.01 - 0.32n where n ) number of methylene units or carbon atoms in the hydrophobic chain, the rest of its hydrocarbon chain (59) Li, F.; Li, C.-Z.; Wang, H.-Q.; Xue, Q.-J. Colloids Surf., A 1997, 127, 89-86. (60) Zana, R. J. Colloid Interface Sci. 1980, 78, 330.

is still longer than that of the octanol molecule which renders the micellar interior more sensitive to the changes in hydrophobicity of the arene than octanol phase. The b > 0 in both correlations (20) and (21), can be explained by the contribution of the hydrophilic fraction in the CTAB to the CTAB-water system. For the congruence of the two correlation lines in Figure 4, the confidence level of the predicted correlation line is 0.994 and that of the published correlation line is 0.985. It is obvious that the geometric mean equation (12) can give reliable log KXM values for these six PAH compounds in the CTAB micelle solution. KXM of Four PAH Compounds in Three Nonionic Surfactant Micelle Solutions. Three nonionic surfactants used to evaluate the generality of eq 12 are all of the poly(oxyethylene) (POE) type of nonionic surfactant, including one alkyl POE type (Brij 30), one octylphenol POE type (Triton X-100), and one nonylphenol POE type (Tergitol NP-10). These three groups of nonionic surfactants represent more than 70% of the 1.72 billion lbs. of U.S. nonionic surfactant production in 198661 and are widely applied in the surfactant-enhanced solubilization of nonpolar hydrophobic organic compounds. Therefore, if the geometric mean equation (12) can predict the value of log KXM of arenes, the applicability of this equation may have more meaning that is general. In a previous study,6 the phase distribution coefficients, KXM, of three PAH compounds, naphthalene, phenanthrene, and pyrene, in the three nonionic surfactants micellar solutions, Brij 30, Tergitol NP-10, and Triton X-100, were calculated based on their apparent water solubility. Because the samples were prepared with 1% volume of methanol, the reported apparent water solubilities of the three PAH compounds are slightly higher than their pure water solubilities. Referring to pure water solubility, the phase distribution coefficients, KXM, have been recalculated as mole fraction ratios. The recalculated values are listed in Table 4. The experimental KXM value of benzo[a]pyrene in Triton X-100 micellar solution12 is also listed in this table. In Table 4, the surface tension reductions of these nonionic micelle solutions, πcmc, are from two sources,6,14 and they are almost the same as the values compiled by Rosen22 with an average difference of less than 0.5 erg/ cm2 at 25 °C. With these three surface tension reductions, the KXM values of the three PAH compounds in three (61) Geek, B. F. Chem. Eng. News 1988, 66, 21. (62) Chiou, C. T. Hazard Assessment of Chemicals; Academic Press: New York, 1981; pp 117-153. (63) Hinze, W. L. ACS Symp. Ser. 1987, 342, 2-82.

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Figure 5. Correlation of log KXM to log KOW of four PAH compounds for a three nonionic surfactants micelle solution.

nonionic surfactant micellar solutions are predicted by eq 12 as respectively

log(KXM)Brij30 ) 0.0313(TSA) log(KXM)Tergitol NP-10 ) 0.0303(TSA)

(22)

log(KXM)Triton X-100 ) 0.0296(TSA) All of these predicted values are listed in Table 4. It can be seen that the average absolute difference of log KXM between the predicted values and the experimental values is less than 0.1 log unit, and the relative percentage deviation of these values is only 1.5%. For comparison, the plots of log KXM vs log KOW for the three PAH compounds in the three nonionic surfactant micellar solutions are shown in Figure 5. Line 1 is the correlation of log KOW vs log KOW as a reference. The correlation lines of the predicted log KXM vs log KOW in three micellar solutions, marked as 2, 3, and 4, are

line 2. Brij30 log KXM ) 0.984 log KOW + 0.810 line 3. Tergitol NP-10 log KXM ) 0.953 log KOW + 0.784 (23) line 4. Triton X-100

log KXM ) 0.928 log KOW + 0.764 R2 ) 0.998

and the correlation lines of the experimental log KXM vs log KOW, marked 5, 6, and 7, are

line 5. Brij30 log KXM ) 1.091 log KOW + 0.176 line 6. Tergitol NP-10 log KXM ) 1.027 log KOW + 0.507 (24) line 7. Triton X-100

log KXM ) 0.943 log KOW + 0.843 R2 ) 0.999

It had been found20 that for the solubilization of the PAH compounds in nonionic surfactant micellar solutions

the higher the surfactant HLB number, the lower the phase distribution coefficients, KXM. Based on this finding, it can be further reasoned that if a set of nonpolar hydrophobic solutes experiences the same types of intermolecular interaction in different solvent systems, the magnitude of a and b in the correlation line of log KXM vs log KOW can be described by the HLB. This has been proved by a semiempirical method.16 According to this method, the experimental distribution coefficients, KCM(M-1), of the three PAH compounds can be correlated to the responded octanol-water distribution coefficients, KOW (M/M), and nonionic surfactant structural properties (the number of hydrocarbons in the hydrophobic chain, Cn, and the number, n, of the oxyethylene (EO) hydrophilic groups) as

KCM ) KOW[0.031Cn - 0.0058(EO)n] Changing KCM and KOW above to mole fraction ratios and taking the logarithm on both sides,

log KXM ) log KOW + log{[0.031Cn - 0.0058(EO)n]/0.12} (25) Equation 25 gives the same slope, a ) 1.0, for the three nonionic surfactants and three intercepts, bBrij30 ) 0.463, bTergitolNP-10 ) 0.527, and bTritonX-100 ) 0.499, respectively. It is seen that there is not much difference, comparing either the values of slope a or the values of intercept b, between that predicted by eq 12 and that obtained by the semiempirical equation. It is concluded that the geometric mean equation (12) can be generalized for its application to predict the log KXM values of the arenes in the nonionic surfactant micellar solution. Summary and Conclusion On the assumption that the two liquid mixtures, arenes with water and arenes with micelle, are in a typical quasicrystalline state (lattice array) and the intermolecular force effectively acts only on the surface area of nearestneighbor molecules, eq 12 is developed to predict the surfactant-enhanced solubilization of arenes. In this equation the micelle-water distribution coefficients, KXM,

Surfactant Micelle-Water Distribution Coefficients

of arenes in the dilute solution range are estimated from the product of the geometric mean, (π20πcmc)1/2, of the two surface tension reductions by the surfactant and the total molecular surface area of the arene, TSA. The rationality is that interfacial tension reduction, a macroproperty of the solution, is the reflection of a microproperty of the surfactant solution and the total molecular surface area of the arene, TSA, is a measure of the hydrophobicity of arenes. Our experimental results, obtained by the generator-column method, together with previously published values, prove that the developed equation (12) predicts the KXM values of arenes well. The structures of arenes used vary from one ring to five rings and include both homo-PAH and some hetero-PAH, and the surfactants used are SDS, CTAB, and three nonionic surfactants of POE type. For KXM of 10 arenes in the SDS micellar solution, an average difference of less than 0.15 log unit exists between the predicted values and the published values obtained by the saturated-solution method. For KXM of six arenes in the CTAB micellar solution, there is an average difference of less than 0.13 log unit between the predicted values and the published values. For the three nonionic surfactant micellar solutions, KXM of four arenes predicted have an average difference of less than 0.1 log unit from the published values. The congruence of the correlation lines of log KXM vs log KOW gives the conclusion that eq 12 can be used as an alternative estimation tool to predict the micelle-water distribution coefficient, KXM, of arenes for the surfactant micellar solution enhanced-soil flushing process. Considering that the measurement of surface tension reduction, πcmc, is much easier than the analysis of the solubility of the arene in a surfactant micellar solution, the developed equation (12) may be more applicable in practice. However, because this is the first time that eq 12 has been used to predict micelle-water distribution coefficients, KXM, more research is needed to validate its use, especially for predicting the KXM of hetero-arenes and other nonarene hydrophobic organics.

Langmuir, Vol. 16, No. 8, 2000 3605

the molecules are confined to lattice positions. The potential energy of a liquid, pure or mixed, is further assumed a pairwise additive for all molecular pairs, and only the nearest neighbors need to be considered in summation. For a binary system, the intermolecular forces operating on three types of pairwise nearest neighbors are Γ11, Γ22, and Γ12, respectively. The partial mole excess free energy, ∂GE/∂n1, of a nonpolar solute, 1, is

∂GE ) RT ln γ1 ) zN [Γ12 - 0.5(Γ11 + Γ22)](1 - X1)2 ∂n1 Appendix II If the intermolecular force fij (erg/cm2) is the Gibbs free energy at the interface between phases i and j, Girifalco and Good46,47 express the cohesion and the adhesion as

fii ) 2Ψi at i ) j fij ) Ψij - Ψi - Ψj ) -2Φij(ΨiΨj)1/2 at i * j Φij ) 4(ViVj)1/3/(Vi1/3 + Vj1/3)2 where Φij ) interaction extent between phases i and j, Ψi or Ψj ) surface tension of phase i or phase j refering to air (erg/cm2), Ψij ) interfacial tension between phases i and j (erg/cm2), Vi or Vj ) molar volume of i or j (cm3/mol), and subscript i ) j means such as molecule species and i * j means unlike molecule species. Appendix III The Berthelot relation51 for the attractive constants between like molecules, Ψii and Ψjj, and that between unlike molecules, Ψij, is

Acknowledgment. G.G.L. acknowledges the financial support to him during this research from Brooklyn Navy Yard. Appendix I The basic approach of lattice theory40 is that a liquid mixture is assumed to be in a quasi-crystalline state and

Ψij (ΨiiΨjj)1/2

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