Effects of High Salt Concentrations on the Micellization of Octyl

Jun 17, 2002 - Tori, K.; Nakagawa, T. Kolloid-Z. 1963, 189, 50. [Crossref], [CAS]. (7) . ..... Kelly, E. J.; Robinson, R. A.; Stokes, R. H. J. Phys. C...
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Langmuir 2002, 18, 5375-5381

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Effects of High Salt Concentrations on the Micellization of Octyl Glucoside: Salting-Out of Monomers and Electrolyte Effects on the Micelle-Water Interfacial Tension1 Pasupati Mukerjee* and Chun C. Chan School of Pharmacy, University of Wisconsin, Madison, Wisconsin 53705 Received January 18, 2002. In Final Form: April 24, 2002 The effects of two added electrolytes up to high concentrations, 0-4 M NaCl and 0-6.6 M LiCl, on the critical micellization concentration (cmc) of octyl glucoside (OG), a nonionic surfactant, in aqueous solution have been measured. The fluorescence probe 6-p-toluidino-2-naphthalene sulfonate was used to determine the cmc values. Log cmc values were found to vary linearly with the molar electrolyte concentration, CS, up to the highest concentrations. A theoretical approach based on the salting-out of the monomeric chain, presented in 1965, has been expanded by incorporating an additional effect of added electrolytes on the interfacial tension of the micelle-water interface. A group additivity relationship for the salting-out of hydrocarbon chains, also proposed in 1965, has been shown to give a good account of the salting-out coefficients of some hydrocarbons, primary alcohols, and methyl esters of carboxylic acids of different chain lengths obtained from literature data. Salting-out coefficients for the octyl group of OG in NaCl and LiCl, calculated on this basis, significantly overestimated the effects of electrolytes on the cmc of OG. Electrolyte effects on the interfacial tension of the estimated surface areas of OG micelles where hydrocarbons are exposed to water were calculated based on literature data on the effects of NaCl and LiCl on the dodecanewater interfacial tension. When these latter effects were combined with the estimated salting-out of the chains, the electrolyte effects on the cmc of OG could be explained nearly quantitatively up to the highest CS. The results of some earlier studies in the literature have been shown to be compatible with the approaches presented. For long-chain surfactants in concentrated brine associated with some petroleum-oil recovery operations, the salting-out effects may have pronounced influences on their activities and how they change with salt concentration.

Introduction Inorganic electrolytes can have pronounced effects on the formation of micelles by uncharged surfactants, nonionic and zwitterionic, in aqueous solution2-12 resulting in significant reduction of their critical micellization concentrations (cmc). In 1965, a theoretical treatment was developed based on the application of the principles of salting-out of nonelectrolytes by electrolytes.13 This approach was shown to be superior to some earlier explanations.3,4,13 The activity coefficient, f, of a nonelectrolyte in electrolyte solutions can be represented by the Setchenow relationship,14,15

log f ) ksCs

(1)

where Cs is the molar electrolyte concentration and ks is * To whom correspondence should be addressed. (1) Mukerjee, P.; Chan, C. C. Abstracts of Papers of the American Chemical Society 1993, 206, 164-COLL. (2) Hsiao, L.; Dunning, H. N.; Lorenz, P. B. J. Phys. Chem. 1956, 60, 657. (3) Shinoda, K.; Yamaguchi, T.; Hori, R. Bull. Chem. Soc. Jpn. 1961, 34, 237. (4) Becher, P. J. Colloid Sci. 1962, 17, 325. (5) Becher, P. J. Colloid Sci. 1963, 18, 196. (6) Schick, M. J.; Atlas, S. M.; Eirich, F. R. J. Phys. Chem. 1962, 66, 1326. (7) Tori, K.; Nakagawa, T. Kolloid-Z. 1963, 189, 50. (8) Ray, A.; Ne´methy, G. J. Am. Chem. Soc. 1971, 93, 6787. (9) Tausk, R. J. M.; Karmiggelt, J.; Oudshoorn, C.; Overbeek, J. Th. G. Biophys. Chem. 1974, 1, 175. (10) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems, NSRDS-NBS36; U.S. Government Printing Office: Washington, DC, 1971. (11) Nishikido, N.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 169. (12) Zhang, Li; Somasundaran, P.; Maltesch, C. Langmuir 1996, 12, 2371.

the salting-out coefficient.14,15 For monomer-micelle equilibria, it was suggested that the salting-out of the hydrocarbon chain of the surfactant monomer is of primary importance and that the salt effects on the hydrophilic headgroups of both the monomeric and micellized surfactants exposed to water were likely to cancel to a great extent.8,13,16 The equation derived from this model,13

log cmc ) log cmc(0) - kCs

(2)

where cmc(0) is the cmc value in the absence of electrolytes and k is a constant, has been found to be moderately successful in describing the cmc values of many nonionic and zwitterionic systems.8,13 The experimental values of k were in reasonable accord with some calculated estimates of the salting-out coefficients, ks, for many electrolytes.8,9,13 For some zwitterionic systems, there seems to be an imperfect cancellation of the expected salting-in of the zwitterionic headgroups of the surfactants in the monomeric and micellized states.13 Salting-out of monomers has also been shown to be important for ionic surfactants.13,17,18 No effect of added electrolytes on the exposed hydrocarbon portions of the micelles was considered in the above model used in 1965.13 Later, in 1970, a proposal was made that the micelle-water interfacial tension is substantial and that this tension leads to a high Laplace pressure inside the micelles.19 The interfacial tension of the micelle(13) Mukerjee, P. J. Phys. Chem. 1965, 69, 4038. (14) McDevitt, W. F.; Long, F. A. J. Am. Chem. Soc. 1952, 74, 1773. (15) Long, F. A.; McDevitt, W. F. Chem. Rev. 1952, 51, 119. (16) Mukerjee, P. J. Phys. Chem. 1970, 74, 3824. (17) Mukerjee, P. Adv. Colloid Interface Sci. 1967, 1, 241. (18) Franchini, M. K.; Carstensen, J. T. J. Pharm. Sci. 1996, 85, 220. (19) Mukerjee, P. Kolloid Z. Z. Polym. 1970, 236, 76.

10.1021/la020059e CCC: $22.00 © 2002 American Chemical Society Published on Web 06/17/2002

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water interface has been used in many subsequent theories,20,21 and some calculated Laplace pressures have been shown to provide a reasonable explanation of the relative solubilities of hydrocarbon gases in liquid hydrocarbons and micelles of ionic surfactants.22 Since inorganic electrolytes are known to increase hydrocarbon-water interfacial tensions and micelles have exposed hydrocarbon-water interfaces, these electrolytes are expected to influence the free energies of micelles and, therefore, the cmc. The present study was conducted to evaluate the importance of this factor and to extend the studies of electrolyte effects on the cmc to high electrolyte concentrations. We report data on the cmc of octyl glucoside (OG) up to 4 M NaCl and 6.6 M LiCl. We have compared these data with expectations from the previous theory based on salting-out13 and a more complete theory in which the effects of electrolytes on the micelle-water interfacial tension are included. Experimental Section OG was purchased from Calbiochem. It was dried under vacuum before use. LiCl (Johnson Matthey Inc., Puratronic, 99.996%) and NaCl (Mallinckrodt, Analytical Reagent) were dried at 250 °C before use. The water used was double distilled. The fluorescent probe, potassium 6-p-toluidino-2-naphthalene sulfonate (TNS), purchased from Sigma Co., was purified. TNS (0.5 g) was dissolved in about 30 mL of water at 65 °C. The hot solution was filtered. The filtrate was left overnight in a refrigerator at 0 °C. The collected crystals were first air-dried and then dried under a vacuum. The procedure was repeated three times. Purified TNS crystals were stored in a dark vacuum desiccator over phosphorus pentoxide in a refrigerator at 0 °C. Two stock solutions containing the same TNS and electrolyte concentration, one containing dissolved OG, were mixed by weight. Densities of the stock solutions were measured and used to calculate molar concentrations. The fluorescence intensity was measured in a Perkin-Elmer MPF-4 fluorescence spectrometer with a cell holder maintained at 25 ( 0.1 °C with circulating water. The excitation wavelength was 370 nm, and the intensities were measured at 435 nm. Different relative sensitivity settings at constant slit widths and dynode voltages allowed precise relative intensity measurements over the required wide range. In 0.1 M OG, the fluorescence intensity varied linearly over the TNS concentration range of 5.25 × 10-6 to 2.7 × 10-5 M.

Results Figure 1 shows a typical variation of fluorescence intensity (I) of TNS (5.25 × 10-6 M) with increasing concentration (C) of OG. The value of I is close to zero at low OG concentrations. Around the cmc region, I increases rapidly with C, the I-C relationship showing a strong upward curvature. Above this region, I increases roughly linearly over a range of C and then levels off toward an asymptotic maximum, Imax, representing complete solubilization of TNS. Although reasonable cmc values can be obtained in many cases by locating the intersection of two linear portions of the I-C curves below and above the cmc region, the curvature of the I-C curve at high C values makes it somewhat difficult to define the linear variation of I above the cmc. As described before,23 this uncertainty can be reduced substantially by the following treatment. The solubilization of TNS can be treated to a reasonable approximation as a distribution or partition of TNS ions (20) Nagarajan, R. Adv. Colloid Interface Sci. 1986, 26, 205. (21) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934. (22) Mukerjee, P. Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; p 153. (23) Mukerjee, P.; Moroi, Y.; Murata, M.; Yang, A. Y. S. Hepatology 1984, 4, No. 5, Suppl., 61S.

Figure 1. Variation of fluorescence intensity, I, of TNS, in relative units, with molar concentration, C, of OG in water.

between micelles and the aqueous medium.24 At constant instrument settings, I can be expressed as

I ) Ea[Da] + Es[Ds]

(3)

where [Da] and [Ds] are the molarities of TNS in the aqueous phase and in the solubilized state, respectively, and Ea and Es are constants representing the relative efficiency of fluorescence of TNS in the two states. Es is much higher than Ea, by a factor of about 500. In terms of the total TNS concentration [Dt], [Dt] ) [Da] + [Ds], and representing the intensity, I0, without added surfactant, as Ea[Dt] and Imax as Es[Dt], we obtain the ratio of the concentrations of the solubilized and free TNS, Q, as

Q)

[Ds] [Da]

)

I - I0 IM - I

(4)

The partition coefficient, Kp*, between micelles and the aqueous phase24 can be written as

K p* )

[Ds]φa [Da]φm

(5)

where φa and φm are the volume fractions of the aqueous phase and the micelles, respectively.

h φm ) (C - cmc)V

(6)

where V h ) the partial molal volume of the micellized surfactant expressed as liter/mole, φa equaling 1 - φm. φa is close to unity in our studies. Using the approximation φa ) 1, we obtain a new partition coefficient, Kp.

Kp )

[Ds] [Da](C - cmc)

(7)

From the theoretical considerations presented in detail,25 the usual approximation that the monomer concentration can be represented above the cmc by the cmc itself10,26 is (24) Mukerjee, P. J. Pharm. Sci. 1971, 60, 1531. (25) Mukerjee, P. J. Pharm. Sci. 1974, 63, 972. (26) Mittal, K. L.; Mukerjee, P. Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; p 1.

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Figure 2. 1/(I - I0) plotted against 1/(C - cmc) for OG in water.

expected to be satisfactory because OG is a nonionic surfactant and it has a high micellar aggregation number of about 80.27-29 Combining eqs 4 and 7, we obtain the relationship

Q ) (I - I0)/(Im - I) ) Kp(C - cmc)

(8)

Q is thus proportional to the micellar concentration, C cmc. A rearrangement gives

1 1 ) I - I0 Kp(C - cmc)(Im - I)

(9)

Multiplying both sides by (Im - I)/(Im - I0) and adding 1/(Im - I0) to both sides, eq 10 is obtained.

1 1 1 ) + (I - I0) [Kp(Im - I0)(C - cmc)] (Im - I0)

(10)

Using the experimentally determined I and I0 values, Im can be obtained by extrapolation of a plot of 1/(I - I0) against 1/(C - cmc), using more refined cmc values reiteratively. Such a plot for OG solutions in water (Figure 2) shows that eq 10 is obeyed in this system. From the estimated value of Im, Q values can be calculated (eq 4). A plot of Q against C for OG solutions (Figure 3) shows a nearly horizontal pre-cmc portion and a line above the cmc, proportional to the micellar concentration, C - cmc, the slope of which equals Kp (eq 8). Because Q shows linearity above the cmc over a wide range, the cmc can be pinpointed more reliably from the extrapolation of the Q versus C lines below and above the cmc than from the I versus C lines in Figure 1. For reasons explained before,10,22 the data in the curving region within a few percent of the cmc were ignored. Two observations suggested that the above simple model needs some modifications for explaining fully our I versus C data. Somewhat below the cmc, a Q value of the order of 0.1 was noted in all cases. Compared to the range of Q values of 0.2-8 above the cmc (Figure 3), this is small, and a part of it is due to the formation of small amounts of the micelles with aggregation number of about 8027-29 (27) Lasser, von H. R.; Elias, H. G. Kolloid Z. Z. Polym. 1972, 250, 58. (28) Roxby, R. W.; Mills, B. P. J. Phys. Chem. 1990, 94, 456. (29) Kameyama, K.; Takagi, T. J. Colloid Interface Sci. 1990, 137, 1.

Figure 3. Q ) (I - I0)/(Im - I0) plotted against molar concentration, C, of OG in water.

reported for OG in water. A more detailed analysis30 suggested that smaller micelles growing rapidly to the above optimal size were probably responsible in part for the small rise in Q slightly below the cmc. To examine the possible importance of this in determining the cmc and Kp values, we estimated the I value at a concentration 3% below the cmc, designated as Icmc, graphically. The increase in I from I0 to Icmc was about 10-15% of Im - I0. Assuming this Icmc gives a conservatively high estimate of any weak interactions of TNS with monomers or small micelles, I0 in eq 10 was replaced by Icmc The change in the estimated Im was small. Using this Im, replacing I0 by Icmc in eq 8, and plotting in the manner of Figure 3, the cmc value was redetermined for OG in water. It agreed with the determinations based on I0 (Figure 3) within about 1%. The Kp values, discussed in the accompanying paper,31 were also similar. The cmc of OG in water, 0.0241 M, is in good agreement with earlier determinations using surface tension,10 light scattering,29 and optical rotatory dispersion.32 The second deviation from the simple model was observed at high electrolyte concentrations. Unlike Figure 2, plots of eq 10 using both I0 or Icmc led to nonlinearity at high C values well above the cmc, suggesting a change in the nature of the micelles leading to some changes in Im and Kp. These changes had minor effects on the cmc but more significant effects on Kp. In electrolyte solutions, Im was determined at micelle concentrations below the concentration where transitions to different micelles occurred by a procedure outlined in the accompanying paper dealing with electrolyte effects on Kp.31 Critical Micellization Concentration Values. The cmc values of OG at different concentrations of added NaCl and LiCl are tabulated in Table 1. Their reliability was estimated to vary from (1% for OG in water to (3% at the highest electrolyte concentrations where the cmc’s were much lower. Figure 4 shows plots of the cmc values of OG against [NaCl] and [LiCl]. The cmc decreases by a factor of 10 as [NaCl] increases to 4.0 M and 17 as [LiCl] increases to 6.6 M. The salt effects on the cmc are substantial even though the micelles are uncharged. (30) Chan, C. C. Dissertation, University of Wisconsin, Madison, WI, 1993. (31) Chan, C. C.; Mukerjee, P. Langmuir 2002, 18, 5382. (32) Mukerjee, P.; Perrin, J.; Witzke, E. J. Pharm. Sci. 1970, 59, 1513.

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Figure 4. Effects of electrolytes on the cmc of OG: NaCl, b; LiCl, 9.

Figure 5. Log cmc data of OG in NaCl solutions compared to calculated lines based on eq 2 (lower, dashed line) and eq 21 (upper, continuous line).

Table 1. Critical Micellization Concentration Values of OG in NaCl and LiCl Solutions concn of NaCl (M)

cmc (M)

concn of LiCl (M)

cmc (M)

0 1.008 3.010 4.003

0.0241 0.0133 0.0041 0.00255

0 0.875 4.870 6.040 6.568

0.0241 0.0148 0.00257 0.00177 0.00136

Figures 5 and 6 show that log cmc varies roughly linearly with Cs up to the highest concentrations. Discussion The effects of inorganic electrolytes on the activity of polar headgroups of surfactant monomers, even when they are expected to be fairly significant as in surfactants containing poly(oxyethylene) groups,8,16 have been shown to largely cancel out in determining the cmc, as proposed,13 because the polar groups are exposed to salt solutions both in the monomeric and micellar states. In view of the observed and expected small effect of added NaCl on the activity of the polar mannitol,33 the salt effect on the polar glucose part of the OG monomer is likely to be of small absolute magnitude and, therefore, cancel out almost completely in the monomer-micelle equilibrium. This makes octyl glucoside a particularly good model system to examine the relative influence of electrolytes in the salting-out of the monomeric chain and in the increase of micelle-water interfacial tension. The interfacial tension, γ, of alkane-water interfaces increases linearly with the electrolyte molality, m.34 Thus

Figure 6. Log cmc data of OG in LiCl solutions compared to calculated lines based on eq 2 (lower, dashed line) and eq 21 (upper, continuous line).

where γ0 is the value of γ when m ) 0, and β is a constant.

For the model interface we consider to be appropriate for our work, dodecane-water, the values of β in erg cm-2 kg mol-1 units are 1.41 for NaCl and 1.56 for LiCl.34 Thus, at the highest LiCl concentration used here, 6.57 M (7.59 m), γ should increase by 11.8 erg cm-2 over γ0, 52 erg

(33) Kelly, E. J.; Robinson, R. A.; Stokes, R. H. J. Phys. Chem. 1961, 65, 1958.

(34) Aveyard, R.; Saleem, S. M. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1609.

γ ) γ0 + βm

(11)

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cm-2. This 23% increase is likely to be significant. For the micellar interface, if A is the area per amphiphile and A0 is the area not in contact with the aqueous medium, the interfacial free energy per monomer is (A - A0)γ or (A A0)(γ0 + βm). If the monomer (L)-micelle (M) equilibrium is represented as

nL h M

(12)

where n is the aggregation number, the chemical potentials of the monomer, µL, and the micelle, µM, can be written as

µL ) µ°L + RT ln[L]f

(13)

and

µM ) µ°M + RT ln[M] + nN(A - A0)(γ0 + βm)

(14)

where µ°L is the standard chemical potential of L, µ°M is the standard chemical potential of M factoring out the micellar interfacial energy, f is the activity coefficient of L due to salt effects (f ) 1 when Cs ) 0), R is the molar gas constant, T is the absolute temperature, and N is Avogadro’s number. The electrolyte effect on µL is in the term RT ln f and that on µM is in the term N(A - A0)βm. For the condition of monomer-micelle equilibrium,

µL ) µM/n

(15)

we obtain

µ°L + RT ln[L] + RT ln f ) µ°M/n + RT ln[M]/n + N(A - A0)(γ0 + βm) (16) Making the usual substitution [L] ) cmc at the cmc,25,26 eq 16 becomes

ln cmc + ln f ) µ°M/n + ln[M]/n - µ°L/RT + N(A - A0)(γ0 + βm)/RT (17) In the absence of added electrolyte, m ) 0 and f ) 1 so that

ln cmc(0) ) µ°M/n + ln[M]0/n - µ°L/RT + N(A - A0)γ0/RT (18) where cmc(0) and [M]0 represent values when no salt is added. The term ln[M]0/n is small in magnitude at the cmc because of the large value of n, about 80 for OG,27-29 and should cancel the similarly small term ln[M]/n in eq 17 when eq 18 is subtracted from eq 17. This leads to the equation

ln cmc + ln f ) ln cmc(0) + N(A - A0)βm/RT

(19)

from which we obtain the working relationship

log cmc ) log cmc(0) - ksCs + N(A - A0)βm/2.303RT (20) by representing f in terms of eq 1, log f ) ksCs. At 25 °C, eq 20 simplifies to

log cmc ) log cmc(0) - ksCs + (A - A0)βm/948

(21)

in which A and A0 are in Å2 units. In this equation, the salting-out term, -ksCs, and the interfacial effect term, (A - A0)βm/948, act as opposing factors for the cmc. If the

latter term is neglected, eq 21 reduces to eq 2 derived in 196513 if the constant k in eq 2 is ascribed entirely to salting-out of the monomeric chain. Equation 21 has three parameters, (A - A0), β, and ks, which can be independently estimated. From the molar volumes of alkanes,35 the molar volume of the octyl group is estimated as 146 mL/mol. The length of the stretchedout octyl chain is calculated to be 10.8 Å from a published formula.36 The aggregation number, 80, of OG27-29 is incompatible with a spherical micelle without an empty center. Using a rigid cylinder model with two hemispherical caps of the same radius, r, as the cylindrical part, the value of A is calculated to be 51 Å2 if r is 10.8 Å. To estimate A0, it was found from Corey-Pauling-Koltun (CPK) precision molecular models that the glucoside headgroup is shaped like a mushroom stalk. The cross-sectional area of the glucosidyl linkage near the micellar interface was estimated to be about 21 Å2. Using this figure for A0, the hydrocarbon interface per amphiphile in contact with the aqueous medium, A - A0, was calculated to be 30 Å2. The β values used were those estimated for the dodecanewater interface, 1.41 and 1.56 erg cm-2 kg mol-1 for NaCl and LiCl, respectively.34 Estimation of ks Values in LiCl and NaCl. Of several theoretical approaches14,15,37-40 for estimating ks values, none appears to be satisfactory for long-chain molecules. The scaled particle theory,40 moderately successful for small solutes but less so for large solutes,40 showed highly inconsistent results for large hydrocarbons, C3H8 to C8H18.30 We have, therefore, used a semiempirical method13 based on the Long and McDevitt theory14,15 which leads to eq 22.

Ks ) V h i(Vs - V h s)/2.303RTβ0

(22)

Here V h i is the partial molal volume of the nonelectrolyte, Vs and V h s are the true and the partial molal volumes of the electrolyte, and β0 is the compressibility of water. This relatively simple treatment is less adequate for ions such as I- or SCN- because it ignores additional effects of polarizability,39 but it gives otherwise a good description of relative ks values in different electrolytes although the absolute values are overestimated.41 In a study of ionsolvent interactions not directed to salting-out effects,42,43 the Vs - V h s was represented as the electrostriction (E) of water caused by added electrolytes in an analysis of the V h s data of electrolytes at infinite dilution. Deno and Spink41 showed that these E values can be used in eq 22 to substitute for Vs - V h s. Some estimated E values,43 which differ somewhat from those used by Deno and Spink,41 are used in Table 2 to correlate ks values of benzene. As E varies from 9.1 mL/mol for CsCl to 51.5 mL/mol for Na2SO4, by more than a factor of 5, the ks/E ratio remains fairly constant, 1.27 ( 0.06 (standard error of the mean (SEM)). Equation 22, supported by some data for aromatic hydrocarbons,41 suggests that ks should be proportional to the molar volume of the nonelectrolyte. To estimate the (35) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; van Nostrand: New York, 1970. (36) Stigter, D. J. Phys. Chem. 1975, 79, 1015. (37) Debye, P.; McAulay, J. Phys. Z. 1925, 26, 22. (38) Conway, B. E.; Desnoyers, J. E.; Smith, A. C. Philos. Trans. R. Soc. London 1964, A256, 389. (39) Bockris, J. O’M.; Bowler-Reed, J.; Kitchener, J. A. Trans. Faraday Soc. 1951, 47, 184. (40) Masterton, W. L.; Lee, T. P. J. Phys. Chem. 1970, 74, 1776. (41) Deno, N. C.; Spink, C. H. J. Phys. Chem. 1963, 67, 1347. (42) Mukerjee, P. J. Phys. Chem. 1961, 65, 740. (43) Mukerjee, P. J. Phys. Chem. 1961, 65, 744.

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Table 2. Relationship of Benzene ks Values and Electrostrictions (E) Caused by Electrolytes electrolyte Na2SO4 NaOH NaF NaCl LiCl KCl RbCl CsCl NaBr KBr

ksa (L mol-1)

Eb (mL/mol)

(ks × 100)/E

0.55 0.26 0.25 0.198 0.141 0.166 0.140 0.088 0.155 0.199

51.5 22.3 18.7 13.9 10.6 10.4 9.8 9.1 13.6 10.1

1.07 1.17 1.34 1.42 1.33 1.60 1.43 0.97 1.14 1.18 average 1.26 ( 0.06 (SEM)

a Salting-out coefficients (refs 15 and 41). b Electrostrictions at infinite dilution (refs 42 and 43).

Table 3. Chain Length Effect on Salting-Out by NaCl and LiCl at 25 °Ca NaCl solute

ks (exp)

CH4 C2H6 C3H8 C4H10 CH3OH C2H5OH C3H7OH C4H9OH C5H11OH C6H13OH CH3OOCCH3 C2H5OOCCH3 C3H7OOCCH3 C4H9OOCCH3 C5H11OOCCH3

0.141b 0.175b 0.207b 0.232b 0.077c 0.130c 0.168c 0.188c 0.202c 0.224c 0.116d 0.167d 0.206d 0.228d 0.239d

LiCl

ks (calcd)

ks (exp)

ks (calcd)

0.144 0.174 0.205 0.235 0.087 0.118 0.148 0.179 0.209 0.240 0.130 0.161 0.191 0.222 0.252

0.112b 0.138b 0.165b 0.186b

0.113 0.138 0.163 0.188

0.086d 0.122d 0.156d 0.176d 0.203d

0.099 0.124 0.149 0.174 0.199

a Calculations are based on the estimated group k values of s 0.087 (-CH3), 0.0305 (-CH2-), 0 (-OH), and 0.043 (-OOCCH3) for NaCl and 0.069 (-CH3), 0.025 (-CH2-), and 0.030 (-OOCCH3) for LiCl solutions. ks(CH4) values were calculated by subtracting ks(CH2) from ks(C2H6). Experimental values were ks values from the literature, recalculated for the molar concentration scale used in eq 1. b Experimental ks values from ref 44. c Experimental ks values are averages of values presented in refs 45, 46, and 47. d Experimental ks values calculated from activity coefficients presented in ref 48. Data up to 3 M were used.

ks values of the -C8H17 group in NaCl and LiCl, we have extended a group additivity principle for ks based on the group additivity of molar volumes.13 The ks values in eq 1 for C2H6, C3H8, and C4H10 for NaCl and LiCl, using the molar concentration scale (eq 1), were estimated for 25 °C from the data presented by Morrison and Billet44 and were used to calculate ks(-CH3) values of 0.087 for NaCl and 0.069 for LiCl and ks(-CH2-) values of 0.0305 for NaCl and 0.025 for LiCl (all in L mol-1 units). For straightchain alkyl groups containing n′ carbon atoms, ks values can be calculated from eqs 23 and 24.

ks(NaCl) ) 0.087 + 0.0305(n′ - 1)

(23)

ks(LiCl) ) 0.069 + 0.025(n′ - 1)

(24)

Table 3 compares some calculated and experimental ks data for some hydrocarbons and alkanols, methanol to hexanol, in NaCl solutions, obtained from different sources45-48 and converted to the molar concentration scale (eq 1). It is assumed that the salt effect on the polar -OH group is negligible. The agreement is reasonable in (44) Morrison, T. J.; Billet, F. J. Chem. Soc. 1952, 3819. (45) Aveyard, R.; Heselden, R. J. Chem. Soc., Faraday Trans. 1 1975, 71, 312.

magnitude and trend suggesting that the group additivity principle for ks is reasonably valid. The calculated ks values for the octyl group from eqs 23 and 24 are 0.301 and 0.244 for NaCl and LiCl, respectively. The ratio of ks(LiCl)/ks(NaCl) is 0.80, in reasonable agreement with the ratio of 0.76 of the estimated electrostrictions42,43 of 10.6 and 13.9 (mL/mol) for LiCl and NaCl (Table 2). Comparison with Experimental Data. The above estimates of (A - A0), β, and ks values can be used to calculate the salt effects on the cmc of OG by using eq 2 (replacing k by ks) or the more complete eq 21. Figures 5 and 6 show that eq 21, which includes salt effects on the interfacial free energy of the micellar interface, gives a much better description of the data up to the highest concentrations of 4.0 M for NaCl and 6.57 M for LiCl. Thus, a combination of the calculated salt effects on the octyl group and the calculated effects of NaCl and LiCl on the micelle-water interfacial tension appears to provide a nearly quantitative explanation of the experimental cmc data up to high concentrations of LiCl and NaCl. Some Implications for Other Systems. (a) The cmc data on n-dodecyl β-D-maltoside at a single salt concentration, 0.75 M, have been published for a number of electrolytes.12 The values for LiCl and NaCl are 1.09 × 10-4 and 0.833 × 10-4 M. From the plot of the surface tension data shown,12 we estimate the cmc in water to be 1.7 × 10-4 M. To assess how our treatment fits the data, we make the reasonable approximation that the interfacial free energy effects for dodecyl maltoside are the same as for OG. When these effects are combined with the ks values calculated from eqs 22 and 23 for the dodecyl group, 0.344 for LiCl and 0.423 for NaCl, the cmc values are calculated from eq 21 to be 1.02 × 10-4 M in 0.75 M LiCl and 0.89 × 10-4 M in 0.75 M NaCl as compared to the experimental values12 of 1.09 × 10-4 and 0.833 × 10-4 M, respectively. The agreement is reasonable and provides some support for the group additivity principles used for eqs 22 and 23. (b) Ray and Ne´methy8 made a systematic study of electrolyte effects on the cmc of two nonionic surfactants, p-t-octylphenoxy (polyethoxy) ethanols. The data were found to be in reasonable accord with the theoretical treatment presented earlier.13 However, when the experimental k values (eq 2) for the cmc data were plotted against ks values of benzene, although a linear relationship expected from eq 22 and a good concordance of the salt order were found, there was a small but puzzling negative intercept at ks ) 0. This suggested a small but systematic reduction of the micellar k values beyond what might be expected from the salting-out of the surfactant chain. This reduction can be qualitatively ascribed to the destabilization of the micelles caused by the increase of the interfacial free energy of the micelle-water interface (eq 21), as proposed in this paper. This explanation is consistent with the results for quaternary ammonium salts for which the authors reported a positive intercept in the plot of micellar k versus ks for benzene at ks ) 0. This opposite effect was explained8 by the expected relative stabilization of the micelles by hydrophobic interactions with the quaternary ammonium ions, based on earlier work on anionic micelles.49 (c) An interesting and theoretically important feature of the relative importance of LiCl and NaCl is the reversal (46) Wilcox, F. L.; Schrier, E. E. J. Phys. Chem. 1971, 75, 3757. (47) Perron, G.; Joly, D.; Desnoyers, J. E.; Ave´dikian, L.; Morel, J.-P. Can. J. Chem. 1978, 56, 552. (48) Cross, R. F.; McTigne, P. T. J. Phys. Chem. 1976, 80, 814. (49) Mukerjee, P.; Mysels, K. J.; Kapauan, P. J. Phys. Chem. 1967, 71, 4166.

Effects of Salt Concentration on Micellization

of the order of electrolyte effects on bulk interfaces, for which LiCl is more potent than NaCl, and on salting-out (eqs 23 and 24, Tables 2 and 3), for which NaCl is more potent than LiCl. Although salting-out coefficients show broad correlations with electrolyte effects on bulk surface tensions of water,50 the above results for LiCl and NaCl underscore the possible pitfalls of extending macroscopic approaches to molecular systems. (d) It has been shown that salting-out effects can affect the behavior of ionic surfactants in electrolyte solutions17,18 over and above the expected charge effects. These effects can be of considerable importance for long-chain surfactants. Brine concentrations as high as 250 g NaCl/L, that is, about 4 M, are encountered in some petroleum-oil recovery operations.51 A typical long-chain surfactant, hexadecyl benzene sulfonate, used in oil recovery opera(50) Melander, W.; Horvath, C. Arch. Biochem. Biophys. 1977, 183, 200. (51) Akstinat, M. H. Enhanced Oil Recovery; Fayers, F. J., Ed.; Developments in Petroleum Science Vol. 13; Elsevier: New York, 1981; p 43.

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tions or related laboratory research, is expected to have a ks value in NaCl of about 0.74 from eq 23 and the ks value of benzene (Table 1). The activity coefficient of the monomeric chain due to salting-out (eq 1) can have the extraordinarily high value of 912 in 4 M NaCl as compared to 0 M NaCl. Moreover, small variations in salt concentration can produce significant effects. Thus, increasing NaCl concentration from 3 to 4 M can increase the saltingout effect by a factor of 5.5, much higher than expected common-ion effects or effects of interionic interactions on the anionic surfactant. This illustrative example suggests a critical role of salting-out of long-chain surfactants in determining their thermodynamic properties and behavior at high salt concentrations. Acknowledgment. This paper is dedicated to the memory of Karol J. Mysels. We acknowledge gratefully the support of the National Science Foundation for part of this research. LA020059E