Solubilization of benzene by aqueous sodium octylsulfate: Effect of added sodium chloride

Solubilization of Benzene by Aqueous Sodium Octylsulfate: Effect of Added Sodium Chloride E D W I N E. T U C K E R AND S H E R R I L D. C H R I S T I A N Department of Chemistry, University of Oklahoma, Norman, Oklahoma 73019 Received August 7, 1984; accepted September 21, 1984 Highly precise vapor pressure-solubility data have been obtained for benzene in aqueous solutions of sodium octylsulfate (SOS) containing approximately 0.4 M sodium chloride, at 15, 25, 35, and 45°C. A mass action model, using a form of the Poisson distribution equation modified to include cooperativebenzene-benzeneinteractions within the micelle, providesan excellent fit of the solubilization data at each temperature. Values are reported of equilibrium constants for the interaction of a single benzene molecule with micellar SOS, the cooperativityparameters in the Poisson model, and activity coefficients for benzene solubilized in the micelle. A comparison of the solubilization results with those obtained for SOS solutions with no added salt indicates the influence of NaC1 on properties of the micelles and micelle solubilizates. As has been reported previously, careful measurements of the dependence of extent of solubilization on the sohibilizate activityindicate that solute-solute interactions within the micelles lead to significant departures from Henry's law. © 1985AcademicPress,Inc. Although there have been many investigations of the solubilization of aromatic and aliphatic hydrocarbons by aqueous surfactant solutions, only a few studies have been made of the dependence of the extent of solubilization on the thermodynamic activity of the hydrocarbon (1-3). Most research on solubilization has been limited to measurements on mixtures prepared by equilibrating surfactant solutions with pure liquid hydrocarbons or hydrocarbon mixtures (4-8). In other studies, although the extent of solubilization has been measured at various solubilizate concentrations, the accuracy of the results has not been sufficient to indicate how the molar solubilization ratio depends on the activity (9). Careful investigations of solubilizate-micelle complexes, at infinite dilution and throughout a range of activities, will be needed to increase our basic understanding of the nature of hydrocarbon-micelle interactions and also to provide information of relevance to practical processes such as ultrafiltration and detergency. Previous reports from this laboratory have

provided extensive and precise information about the solubilization of benzene, cyclohexane, and mixtures of these hydrocarbons by aqueous solutions of sodium octylsulfate (SOS) and sodium deoxycholate (1-3, 8). In every case when measurements have been made of the dependence of the concentration of solubilized hydrocarbon on activity, it has been determined that Henry's law is not adequate to represent the results at varying solubilizate activity; the departure from linearity is particularly pronounced when benzene is the solubilizate. Recent measurements from this laboratory show that solutions of n-butanol, n-pentanol, and benzene with aqueous cetylpyridinium chloride exhibit more than a factor of two decrease in the apparent Henry's law constant as the solubilizate activity varies from near zero to the saturation value (10). To rationalize the sizable increase in relative solubilization ratios that occurs as the concentration of benzene and other solubilizates increases, we have developed a mass action model based on the Poisson distribu-

562 0021-9797/85 $3.00 Copyright © 1985 by Academic Press, Inc. All fights of reproduction in any form reserved.

Journal of Colloid and Interface Science, VoL 104, No. 2, April 1985

SOLUBILIZATION OF BENZENE tion equation, modified to include a cooperativity factor accounting for hydrocarbonhydrocarbon molecular interactions within the micelle (3). Solubilization data are accurately represented by this model, yielding values of equilibrium constants for the reaction micellar SOS + benzene = micellar SOS. benzene

[1]

for ideal dilute solution (unit molarity) standard states for the solute species. Values of the cooperativity parameter, b, representing the free energy of pairwise interaction of benzene molecules (divided by - R T ) , are also inferred. It is well known that added electrolytes affect the properties of surfactant micelles of both the anionic and cationic types. For example, added NaC1 decreases the critical micelle concentration (CMC) and increases the average molecular weight of the micelles (8, 11). We thought it would be useful to obtain extensive solubilization data for benzene in aqueous SOS solutions containing added NaC1, for comparison with results of an earlier study of similar solutions without added electrolyte (3). The present article gives results of the new investigation, including treatment of the data with the modified Poisson solubilization model. A direct indication of the effect of added NaC1 on the solubilization thermodynamics is facilitated by comparing the dependence of the derived values of activity coefficients of benzene in the micelle on its intramicellar mole fraction, for the systems with and without added NaC1.

563

known) is introduced into the thermostatted central reservoir, and the solution is degassed. The initial pressure is recorded, as are equilibrium pressure readings obtained after the addition of successive samples of benzene (0.0002135 + 2 × 10-7 mole per increment). The observed values of pressure and total numbers of moles of water, SOS, NaC1, and benzene constitute the primary measurements at each temperature (15, 25, 35, and 45°C). This information is processed as described previously to yield values of the total concentration of benzene in the condensed phase, [B], at known total concentrations of surfactant and salt, [SOS] and [NaC1], and known concentrations of monomeric benzene, Ca (3). In calculating these results, the assumption is made that the benzene monomer concentration in solution is directly proportional to the fugacity of benzene in the vapor phase, inferred from the pressure-composition data using virial coefficients to correct for the slight extent of vapor phase nonideality. A complete table of the derived solubilization results, comprising 394 sets of cB, [SOS], [NaCI], [B] values at the four temperatures, is available from the authors. Figure 1 includes plots of [B] as a function of [SOS], at chosen values of cB (0.002, 0.004, . . . , 0.014 M) at 25°C. The plotted values have been calculated by a numerical interpolation procedure described previously (3), from solO,OZ4 M 0.00 O. 012 M 0.04

j

.... o,,

O. 03 0.008 M

EXPERIMENTAL

N z m

0.02

0.006 M

The automated vapor pressure apparatus 0.01 0.004 M and its use in studying the solubilization of _ ~ 0.002 M volatile hydrocarbons in aqueous solutions ° 0?05 o.~o o.'~s o.~o .... have been described previously (3, 12). TechSODIUMOCTYLSULFATEMOLARITY niques for purifying and preparing SOS soFIG. 1. Aqueousbenzene solubilityat indicatedfixed lutions have also been described (1). Initially, molarities of benzene monomer, against sodium octyla known volume of aqueous SOS, containing sulfate concentrationat 25°C. Solutionscontain 0.4 M approximately 0.4 M NaC1 (accurately NaCI. Journal of Colloid and Interface Science, Vol. 104, No. 2, April 1985

564

TUCKER

AND CHRISTIAN

ubilization isotherms at nearly constant [SOS]. Deviations of points from the solid curves (drawn empirically) reflect variations in NaC1 concentration for the different SOS solutions, rather than experimental error (vide infra). TREATMENT

Mass

Action

OF DATA

Model

In the absence of interactions between solubilizate molecules in the micelle, it is assumed that the Poisson distribution equations will provide a good description of the partitioning of the solubilizate among the various species (3, 13). Thus, letting CA, represent the molar concentration of micelles of aggregation number n, one predicts that the total concentrations of SOS and benzene in the various micellar species are given by [SOS]mi~ = ncA,[1

and CAn[a + a 2 + a3/2! + a4/3! +

• • .] = acA,exp(a)

[2]

where a = n K ~ c B , and where/£1 equals 1 I n times the equilibrium constant for the reaction An + benzene = An" benzene. The individual terms in a i in Eqs. 2 (where i = 1, 2, 3, • • • ) represent contributions to the mass balance equations of micellar species containing i solubilizate molecules. When net attractive or repulsive interactions occur between solubilizate molecules, it is necessary to modify the Poisson equations to account for these effects (3). Letting - b R T represent the free energy of interaction between pairs of solubilizate molecules within a micelle, we introduce multiplicative factors, exp(b), to modify the terms for the respective species concentrations in Eqs. [2]. Thus, in accounting for the micelle species containing only two benzene molecules, the factor exp[b] Journalof Colloidand InterfaceScience,Vol. 104, No. 2, April 1985

[SOS]mic =

nCA,[1 + +

a + a2eb/2!

+ a3e3b/3!

• . . + aiei(i-1)b/2/i! +

• . .]

and [B]mic =

+

+ a + a2/2!

+ a3/3! + • • • ] = ncA,exp(a)

[B]mic =

appears in the a 2 terms of [SOS]talc and [B]mic of Eqs. [2]. In the expressions representing micelles containing three benzene molecules, the factor exp(3b) is included, because we infer that there should be three times as many pair interactions of solubilizate molecules as in micelles containing two benzenes. For the micelle containing i solubilizate molecules, the factor exp[i(i - 1)b/2] is included to account for the presumed i(i - 1)/2 pair interactions. The resulting modified Poisson equations corresponding to this model are

CAn[a -}- a 2 e b + a 3 e 3 b / 2 !

• • • + aiei"-l)b/2/(i

-- 1)t +

• • • ].

[3]

It is likely that the factors exp[i(i - 1)b/2] in the higher order terms of Eqs. [3] overemphasize the importance of pair interactions in micelles containing large numbers of solubilizate molecules; steric factors and other repulsive terms will probably act to attenuate the terms accounting for the larger species. In any event, Eqs. [3] quite efficiently represent solubilization data for aqueous surfactant systems, in cases where either (net) attractive or repulsive interactions occur. Although Eqs. [3] cannot be reduced to closed forms for representing [SOS]mi~ and [B]mi~ as functions of a and b, they can be evaluated numerically for given values of these variables. It is also possible to express the molar solubilization ratio, [B]mic/[SOS]mie as a general quartic polynomial in a, with coefficients that are analytic functions of b alone. Such expressions are sufficiently accurate to represent most solubilization data to within experimental error. The modified Poisson equations (Eqs. [3], in the form of the quartic polynomial expansion of [B]mic/ [SOS]~i~), have been used in fitting all of the solubilization data corresponding to SOS

SOLUBILIZATION OF BENZENE

concentrations greater than the CMC (approximately 0.068 M). Premicellar Solubilization of Benzene

by SOS Although the tendency of octylsulfate solutions to solubilize benzene increases dramatically as the concentration of SOS is increased beyond the CMC (see Fig. 1), the solubilization data show that significant concentrations of small octylsulfate-benzene complexes form at [SOS] values less than the CMC. Both the present results and the vapor pressure data obtained previously for solutions of benzene in aqueous SOS (3) can be analyzed to obtain a value of K~I, the equilibrium constant for formation of the 1:1 complex between the octylsulfate anion and benzene. At least one other premicellar SOSbenzene aggregate must be included to provide a satisfactory least squares fit of the vapor pressure-composition data at values of [SOS] less than the CMC. As in the previous study, the equilibrium constant at each temperature is inferred for formation of a presumed species A6B2, containing 6 octylsulfate anions and two benzene molecules. Presumably other premicellar aggregates are present as well, but the least squares goodness of fit of all the solubilization data at each temperature is significantly improved if the A6B2 species is assumed to exist along with the 1:1 complex, AB. SOS Micelle Size and Size Distribution When attempts are made to fit all of the solubilization results at each temperature [using as parameters the equilibrium constants for formation of the premicellar aggregates, SOS micelles (An), and the micellar solubilizates in the modified Poisson model], the best fit of data is provided by choosing an n value equal to approximately 30. Previously, in fitting solubilization data for benzene in aqueous SOS solutions without added salt, we found an optimum n value approximately

565

equal to 16 (3). These numbers are somewhat smaller than other estimates of the aggregation numbers for SOS micelles, but they do indicate an increase in micelle size with added salt, in agreement with similar results for other alkylsulfate solutions (11). As in the vapor pressure study of benzeneSOS solutions without added salt, we find that the solubilization data may be much better correlated by assuming that more than one micellar aggregate is present. In the previous study, we noted that a distribution of micellar sizes probably exists; however, to simplify the modeling of solubilization results, we assumed that micelles of only two sizes, n = 16 and n = 22, are present. By analogy with the earlier procedure, we have modeled the new solubilization results by assuming that micelles of only two sizes (n = 26 and n = 32) exist in the aqueous SOS-NaC1 solutions, and that these species individually form all of the solubilizates, in amounts calculated from the separate b and/£1 values of the modified Poisson equations (Eqs. [3]). At the highest concentration of SOS at each temperature (ca. 0.20 M), we assume that the anion concentration is 0.060 M, somewhat less than the molarity of SOS at the CMC (ca. 0.068 M). [This choice of the surfactant monomer concentration is based on consideration of results of anion activity measurements for similar solutions (14) and our own mass action modelling of alkylsulfate surfactant systems.] We also assume that the amount of SOS in the A26 micelles equals the amount of SOS in the A32 micelles in these most concentrated solutions (before benzene is added). Mass action equations analogous to those given previously may be formulated (3); these involve separate values of the micellar formation constant for each micelle (A26 and A32) at each total concentration of SOS, as well as the unknown constant b and Kl required in Eqs. [3] for each micelle, and equilibrium constants for formation of the premicellar solubilizates. Nonlinear least squares methods described previously (3, 15) are used to infer all of the Journal of Colloid and Interface Science, Vol. 104, No. 2, April 1985

566

TUCKER AND CHRISTIAN

variable parameters required in the solubilization model.

than expected, although the premicellar solubilization constants are in general less reliable than those reported previously. This owes primarily to the fact that the CMC is DERIVED SOLUBILIZATION RESULTS considerably smaller in the SOS solutions The constants used in modeling the vapor containing 0.4 M NaC1, making it more pressure data for the aqueous SOS-benzene- difficult to obtain formation constants for NaC1 solutions are given in Table I. The the smaller solubilizate species. The constant variable parameters which have been deter(K62) for formation of A6B2 is considerably mined from the least squares analysis are larger than that reported for the unsalted listed with their standard errors, along with solutions. This reflects the "salting-out" effect the fixed constants chosen as described above. of NaCI on benzene and it may indicate that Results are discussed with reference to (a) the Na ÷ ions neutralize the charge of premithe formation ofpremicellar solubilizates; (b) cellar complexes containing benzene bound specific constants for the A26 and A32 micelles; to several octylsulfate anions. A Setchenow and (c) values of the parameters in the modconstant is included in the analysis to account ified Poisson equations (Eqs. [3]). for the decrease in concentration of monoValues of Kll, the formation constant for the 1:1 adduct between the octylsulfate anion meric benzene, at a given benzene activity, (OS-) and benzene, are comparable to those caused by increasing the concentration of obtained for the SOS solutions containing electrolyte (17). Table II reports equilibrium constants for no added NaC1 (3). /£11 increases with information of the A26 and A32 micelles, and creasing temperature below about 35°C, as the concentration of octylsulfate anion, [OS-], is typical of complexes forming primarily by for solutions at the indicated molarities of hydrophobic association (12, 16), and the constant apparently reaches a maximum SOS. K26 and K32 are fixed for the most value in the vicinity of 35 or 45°C. The concentrated solution at each temperature value of K~I at 15°C is somewhat smaller by the assumption that the surfactant mono-

TABLE I Mass Action Parameters for Sodium Octylsulfate-Benzene Complexes in Aqueous 0.4 M NaC1 Solutions

Ki1/dm 3 mole-i a K62/107 dm 2~ mole -Tb KI for Az6 mieelles/ dm 3 mole -~ c K~ for A32 micelles/ dm 3 mole-~ d b for A26 micellese b for A32 micelles y rmsd/mole dm -3g

15°C

250C

35°C

0.265 + 0.036 8.1 +_ 0.6

0.78 _+ 0.02 6.8 + 0.5

1.28 _+ 0.03 5.5 + 0.5

1.28 + 0.02 4.8 _+ 0.4

11.10 _+ 0.07

11.89 _+ 0.09

11.49 _+ 0.18

9.88 _+ 0.15

12.09 0.017 0.055 1.92

11.67 0,036 0,062 1.13

11.28 0.036 0.060 1.57

+ 0.10 +__0.005 + 0.001 × 10-5

+ 0.12 _+ 0.001 _+ 0.002 × 10-3

+ + + ×

0.23 0.001 0.003 10-3

45°C

11.49 0.038 0.047 1.37

_+ 0.18 _+ 0.007 _+ 0.002 × 10-5

a Equilibrium constant for A + B = AB (where A denotes octylsulfate and B denotes benzene). b Equilibrium constant for 6A + 2B = A6B2. c Equilibrium constant for A26 + B = A26 • B, divided by 26. d Equilibrium constant for A32 + B = A32" B, divided by 32. e Cooperativity parameter in modified Poisson equations for B. • • B interaction in A26 micelle (see text). fCooperativity parameter in modified Poisson equations for B • • • B interaction in A32 micelle. g Root mean square deviation in total benzene molarity from least-squares analysis. Journal of Colloid and Interface Science, Vol. 104, No. 2, April 1985

567

SOLUBILIZATION OF BENZENE TABLE II Micelle Formation Constants and Monomer Concentrations

15°C

[SOS]"

K26~

K32¢

cosd

0.206 0.146

(13.29) e 12.36 ___0.12

(13.78) f 12.74 + 0.10

(0.060)g 0.0635

0.104 11.34+0.10

11.67+0.07

0.0673

0.206 (13.30)e (13.78)I (0.060)g 25°C 0.147 12.28 + 0.04 12.70 _+0.03 0.0638 0.104 11.51+0.04 11.92 +0.02 0.0662 0.200 (13.27)e (13.76)f (0.060)g 35°C 0.141 11.96+0.04 12.41_+0.03 0.0652 0.099 11.05 _+0.06 11.53 + 0.04 0.0682 45°C

0.203 0.155 0.103

(13.29) e 12.81 _+ 0.25 11.16_+0.11

(13.77) f 13.44 _+ 0.20 11.61 _+0.07

(0.060)g 0.0612 0.0678

a Molarity of sodium octylsulfate, in aqueous 0.4 M NaCI. bFormation constant for 26 OS- = (OS-)26 to the 1/ 26th power (unit molarity, ideal dilute solution standard states). CFormation constant for 32 OS- = (OS-)32 to the 1/ 32nd power (unit molarity, ideal dilute solution standard states). d Molarity of OS . e/(2 6 value chosen to give equal amounts of SOS in A26 and A32 micelles (see text). IK32 value chosen to give equal amounts of SOS in A26 and A32 micelles. g Monomer molarity of OS- chosen for most concentrated solution at each temperature.

mer concentration is exactly 0.060 M and that the A26 and A32 micelles contain equal amounts of SOS (in the absence of added benzene). The octylsulfate m o n o m e r concentration and the micelle formation constants at the other SOS molarities are inferred by the least squares analysis. The mass action model thus yields values of the surfactant m o n o m e r concentration for each aqueous solution of SOS, and these concentrations tend toward the value of [OS-] at the CMC (approximately 0.068 M ) as [SOS] decreases to this value. The analysis also indicates that the average micelle size increases as more and more benzene is solubilized, owing to the effect of the larger cooperativity factor for the larger micelles (see Table I).

In comparing the properties of micellebenzene complexes in the presence and in the absence of NaC1, the most important parameters are values of K1 and b for the micellar species. The average values of/£1 for the A26 and A32 micelles at the four temperatures are 11.1 and 11,5, respectively, compared with average values of K1 equal to 9.8 a n d 11.4 for the A16 and A22 micelles of the previous study (3). T h e b values are on average 0.032 and 0.056 for the A26 and A32 micelles in the NaCl-containing solutions, compared with 0.031 and 0.049 for the A16 and A22 micelles in the unsalted solutions. Thus, addition of 0.4 M NaC1 to aqueous SOS solutions causes relatively small changes in the thermodynamic properties of the micellar aggregates, based on the ideal dilute solution (unit molarity) standard states used in both investigations. The addition of salt does substantially decrease the CMC and increase the micelle size, but the tendency of the micelles to take up benzene and the deviation of the solubilization isotherms from Henry's law is almost the same with or without added NaC1. A final comparison of results of the two studies can be made by calculating values of the activity coefficient of benzene in the micelles (TB,mic), using the pure component standard state basis for benzene. The analysis described above yields values of the total amounts of benzene and octylsulfate in the micelles as a function of benzene fugacity; this information can be translated into values of the activity coefficient by the equation "YB,mic = f B / ( X B , m i c f

O)

where fB and f o are the fugacity of benzene in equilibrium with the micellar solution and the fugacity of pure benzene at the given temperature, and XB,mic is the mole fraction of benzene in the micelle solubilizates. Figure 2 shows plots of the activity coefficient of benzene vs the intramicellar mole fraction of benzene, for the most concentrated SOS solutions at each temperature. These results pertain to solutions containing apJournal of Colloid and Interface Science. Vol. 104, No. 2, April 1985

568

TUCKER AND CHRISTIAN

*

~ 4.8 -x x ~o

o

Energy, BartlesviUeEnergy Technology Center (Contract DE-AT 1981BC10476), and the University of Oklahoma Energy Resources.Institute.

+

* .15oc XXx

~ozxZo ~ []

A

o

x

* x

.

REFERENCES

4soczxzxa ~ .

.

4.0 3.8

o8ocff i 0.05

i

i

0.10

0.15

0.20

INTRAMICELLAR MOLE FRACTION OF BENZENE

FIG. 2. Activity coctticient of intramiccllar benzene, plotted against mole fraction of benzene in sodium octylsulfate miceUes. proximately 0.20 M SOS a n d 0.4 M added NaC1, whereas those from the previous study are for solutions containing approximately 0.30 M SOS, but no added NaC1. The activity coefficient plots [Fig. 2 o f this paper a n d Fig. 4 o f the previous report (3)] are quite similar, although the limiting activity coefficients are about 10% higher for the solutions containing 0.4 M NaC1, a n d the decrease in activity coefficient with increasing benzene concentration is greater for the salted solutions. In other words, added NaC1 decreases the tendency o f the SDS micelles to take up a single molecule o f benzene, but the cooperativity effect (measured by b in the modified Poisson model) is enough greater in the solutions containing NaC1 to cause t h e m to solubilize m o r e benzene at the higher benzene activities (than do the unsalted solutions). W e m a y note that measurements o f activity coefficients o f intramicellar solubilizate species, as a function o f solubilizate concentration, are practically nonexistent in the literature (3). ACKNOWLEDGMENTS The research described here has been supported by the National Science Foundation (Grants CHE-8103084 and CHE-8402866), the United States Department of

Journal of Colloid and Interface Science, V o l .

1 0 4 , N o . 2, A p r i l 1 9 8 5

1. Christian, S. D., Tucker, E. E., and Lane, E. H., J. Colloid Interface Sci. 84, 423 (1981). 2. Christian, S. D., Smith, L. S., Bushon~, D. S., and Tucker, E. E., J. Colloid Interface Sci. 89, 514 (1982). 3. Tucker, E. E., and Christian, S. D., Faraday Syrup. Chem. Soc. 17, 11 (1982). 4. McBain, M. E. L., and Hutchinson, E., "Solubilization and Related Phenomena." Academic Press, New York, 1955. 5. Elworthy, P. H., Florence, A. T., and McFarlane, C. B., "Solubilization by Surface-ActiveAgents." Chapman & Hall, London, 1968. 6. Mukerjee, P., in "Solution Chemistry of Surfactants" (K. L. Mittal, Ed.), Vol. 1, p. 153. Plenum, New York, 1978. 7. Nagarajan, R., Chaiko, M. A., and Ruckenstein, E., J. Phys. Chem. 88, 2916 (1984). 8. Thomas, D. C., and Christian, S. D., J. Colloid Interface Sci. 82, 430 (1981); Thomas, D. C., Ph.D. dissertation, University of Oklahoma, 1978. 9. Wishnia, A., J. Phys. Chem. 67, 2079 (1963); Matheson, I. B. C., and King, A. D., J. Colloid Interface Sci. 66, 464 (1978); Hoskins, J. C., and King, A. D., J. Colloid Interface Sci. 82, 264 (1981); Simon, S. A., McDaniel, R. V., and McIntosh, T. J., J. Phys. Chem. 86, 1449 (1982). 10. Smith, G. A., unpublished research, University of Oklahoma. 1I. Llanos, P., and Zana, R., J. Phys. Chem. 84, 3339 (1980); Doughty, D. A., J. Phys. Chem. 83, 2621 (1979). 12. Tucker, E. E., and Christian, S. D., J. Chem. Thermodyn. 11, 1137 0979); Tucker, E. E., Lane, E. H., and Christian, S. D., J. Solution Chem. 10, 1 (1981). 13. Atik, S. S., Nam, M, and Singer, L. A., Chem. Phys. Left. 67, 75 (1979). 14. Kale, K. M., Cussler, E. L., and Evans, D. F., J. Solution Chem. 11, 581 (1982); Kale, K. M., private communication. 15. Christian, S. D., and Tucker, E. E., Amer. Lab. 14(9), 31 (1982). 16. Christian, S. D., and Tucker, E. E., J. Solution Chem. 11, 749 (1982). 17. King, M. B., "Phase Equilibrium in Mixtures," p. 260. Pergamon, Oxford, 1969.