Anal. Chem. 1995, 67, 1459-1464
This Research Contribution is in Commemoration of the Life and Science of 1. M. Kolthoff (1894- 1993).
General Method for the Study of Solute-Surfactant Association Equilibria of Volatile Solutes by Headspace Gas Chromatography Abul Hussam,* Subhash C. Basu, Mark Hixon, and Zohra Olumee
Chemistry Department, George Mason University, Fairfax, Virginia 22030
A general methodology for measurement of solutesurfactant associations for volatile solutes based on headspace gas chromatographyhas been developed. A general theoretical model is also developed to treat the experimental data that requires no analytical solute standard. The model is applicable to any volatile solutes, especially very hydrophobic solutes such as n-alkylbenzenes, for which accurate aqueous standard solutions cannot be prepared. Parameters such as solute-surfactant association constant, solute-micelles association constant and partition coefficient, critical micelles concentration, intramicellar mole fraction, and intramicellar activity coefficient of n-alkylbenzenes are obtained as a function of aqueous surfactant concentrations. The physicochemical interaction of a lipophilic solute and surfactant molecules has been studied with a wide variety of techniques over many years. The understanding of such interactions is crucial to the design and development of surfactants important in areas ranging from tertiary oil recovery to targeted drug delivery.'-: Systematic studies on the solubilization of very hydrophobic solutes at concentrations low enough to obtain reliable thermodynamic information are limited.6 Only the solubilization of benzene and cyclohexane in aqueous sodium octyl sulfate solution was studied thoroughly by a precise vapor pressure measurement at solute concentrations below the saturation limit in order to obtain detailed mass action parameter^.^-^ The primary problem of studying hydrocarbon solubilization is the measurement of accurate hydrocarbon concentrations in the aqueous phase and in the micellar solution. (1) Miller. C. A; Qutubuddin. S. Enhanced Oil Recovery Using Microemulsions. In Interfacial Phenomena in Nonaqueous Media; Elicke, H. F., Pratitt, G., Eds.; Marcel Dekker: New York, 1986. (2) Mittal, K. L.; Fendler, E. J.; Eds.; Solution Behavion ofSulfactants; Plenum Press: New York, 1982; Vol. 1. (3) Fendler, J. H.; Fendler, E. J. Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975. (4) Bunton. C. A. Prog. Solid State Chem. 1973,8, 239. (5) Cordes, E. H.; Gitler, C. Prog. Bioorg. Chem. 1973,2, 1. (6)Ownby, D. W.; King, A. D., Jr. J. Colloid Intelface Sci. 1984,101, 271 and references therein. (7) Christian, S. D.; Tucker, E. E.; Lane, E. H. J. Colloid Inte$ace Sci. 1981, 84, 423. (8)Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. Soc. 1982,17, 11. (9) Tucker, E. E.; Christian. S. D. J. Colloid IntetjCace Sci. 1985,104, 562.
0003-2700/95/0367-1459$9.00/0 0 1995 American Chemical Society
Therefore, the need for a technique that does not require accurate standards but is sensitive enough to detect very low concentrations is obvious. Gas chromatography (GC) has been used quite extensively to study various solute-solvent interactions, and it was recognized as a valuable technique to study solutesurfactant systems.lO"l GC was used to measure the headspace concentration of alcohols after gas stripping of the aqueous surfactant solution or direct measurement of solute concentration in vapor and in the liquid phases after appropriate calibrati~n.'~J~ Benzene was the only sparingly soluble hydrocarbon studied by a GC technique in various aqueous micellar solution^.'^ Headspace gas chromatography (HSGC) was also used to measure the vapor-phase composition of hexanol partitioning in microemul~ i o n s . ' ~ JSince ~ the goal of most previous studies was to determine the distribution coefficient of solute between aqueous phase and micelles, measurements were made at surfactant concentrations much higher than the critical micelles concentration (cmc). The purpose of this study is to develop an automated HSGC and the methodology to study interactions between hydrophobic solutes at very low concentration and aqueous surfactants over a wide range of concentrations. A simple mass balance equation is developed to obtain the cmc and association constants for solute-surfactant and solute-micelles equilibria. The partitioning of solute between micelles and the aqueous phase is also obtained. Furthermore, it is shown that the intramicellar mole fraction and the intramicellar activity coefficient of the solute can be calculated. The latter is possible only if a reliable activity coefficient of solute in surfactant-free aqueous solution is available. The unique advantage of the present methodology is that solute concentration is not needed to calculate any of the above parameters. To test this methodology, we have selected n-alkylbenzenes such as benzene, toluene, ethylbenzene, and n-butylbenzene, all of which are hydrophobic. Among the selected solutes, benzene is the one most studied by other techniques, and therefore a critical comparison could be made. Also, the needed infinite dilution (10) Conder, J. R.; Young, C. L. Physicochemical Measurements by Gas Chromatography; Wiley: New York, 1979. (11) h u b , R J.; Pecsok, R L Physicochemical Applications of Gas Chromatography; Wiley: New York, 1978. (12) Hayase, IC;Hayano, S. Bull. Chem. Soc. Jpn. 1977,50 (11, 83. (13) Spink, H. C.; Colgan, S. J. Phys. Chem. 1983,87, 888. (14) Nagarajan, R; Chaiko, M. A; Ruckenstein, E.]. Phys. Chem. 1984,88,2916. (15) Camali, J. 0.;Fowkes, F. M. Longmuir 1985,1, 576. (16) Biais, J.; Odberg, L.; Stenius, P. J. Colloid Intelface Sci. 1982,86, 350.
Analytical Chemisfy, Vol. 67, No. 8,April 75, 7995 1459
activity coefficients (y") of solutes in water are available." The data show that y" of n-butylbenzene is one of the largest ever known (5.33 x 1@),which thereby constitutes a stringent test for the proposed methodology. Finally, the use of GC to separate, detect, and measure a large number of volatile solutes simultaneously with a very high sensitivity and selectivity makes this methodology general. THEORY
We consider the following equilibria in solution while the surfactant, S, is added to a very dilute aqueous solution of the solute, P
S, = (S, - cmc)/n
(3)
where SP is the surfactant-solute complex which is present before the micelles formation, S,P is the predominant micelles-solute complex in the postmicellar region, and S, is the total concentration of surfactant. For simplicity we assume that only one type of complex, SP, is present in the premicellar region. We also assume that micelles are monodisperse with an aggregation number n and the solute is monomeric. For a very dilute solution these assumptions are valid. Equation 3 relates micellar concentration, S,, with the total concentration of the surfactant, the critical micelles concentration, cmc, and n. Combining eqs 1-3, the total concentration of solute, Pt,,, is obtained:
In HSGC, the peak area due to the monomeric solute in the gas phase in equilibrium with the aqueous phase is measured. The solute peak area is proportional to the gas-phase concentration of the solute, [PI,; therefore,
A = *[PI,
(5)
where II, is the gas chromatographic response factor of the solute. The solute concentration in the gas phase is also related to the concentration of the free solute in the aqueous phase by the distribution constant,
is constant,17then eqs 4 and 7 yield
A,/A, = 1 + K,,ISl
+ (K,,/n)[S, - cmcl
where A0 and Af ?e the peak areas due to the solute in the absence and in the presence of the surfactant, respectively. The first two terms of eq 8 shows 1:l interaction between the monomer solute and the monomer surfactant primarily in the premicellar region. After the onset of micelles formation, if the premicellar complex becomes very weak compared to the micelles-solute complex, the second term can be neglected. Therefore, a plot of Ao/Ar vs S, is linear with a slope of KII in the premicellar region and yields another straight line with a slope of &/n in the postmicellar region. The intersection point of the straight limes corresponds to the cmc. Equation 8 shows that solute concentration is not needed to obtain K11, K,l/n, and cmc. It is applicable to all solutes for which A0 and Af can be reliably measured. However, if a reliable measurement of A0 is not possible due to the limited solubility of solute in neat aqueous solution, then the experiment can be done with micelles solubilized in solute of known S,. In this case, a series of Af values are measured d e r successive dilution of the micellar solution with the solvent. If the solution remains in the postmicellar region throughout the dilution and if K11, then eq 8 can be rewritten as
l/Af = [ l - (K,,/n)cmcI/A,
+ (1/AJ (K,,/n)S,
Assuming (i) a negligibie amount of solute partition in the gas phase, (ii) that K, is independent of the presence of surfactant, and (i) that the gas chromatographic response factor of the solute (17) Li,J.; Cam, P.W. Anal. Chi" 1903,65, 1443.
1460 Analytical Chemistry, Vol. 67, No. 8, April 75, 7995
@a>
Equation 8a shows that the plot of 1/Af vs S, is a straight l i e with (l/Ao) ( K d n ) as the slope and [l - (K,l/n)cmcl/Ao as the intercept. If the cmc is known, then K,l/n can be calculated from the ratio of the intercept and the slope. Thus the value of A0 can be calculated from the slope. For many surfactants for which S, >> cmc, eq 8a can be further simplified:
1/A, = 1/Ao
+ (1/AJ (K,,/n)St
(8b)
Once Af and A0 are obtained, the fraction of solute in the aqueous phase, F,, and in the micellar phase, F,, can also be calculated:
Given the total moles of solute, t, the mole fractions of solute in the aqueous and micellar phases are x, = (F,t)/55.555
Combining eqs 5 and 6, the free solute concentration can be related to the peak area due to the solute by the following equation,
(8)
x, = (Fmt) / [ (S, - cmc)
(11)
+ F,tl
(12)
respectively. If the total concentration of solute is negligible in comparison to the micelles concentration, then the mole fractionbased solute partition coefficient between micelles and the aqueous phase is given by
K, = XJX,
= 55.555Fm/[F,(St - cmc)]
(13)
It can be shown that the molar concentration-based partition
I 1
CT
I
I I
PC
WB
GC
Figure 1. Block diagram of the headspace gas chromatograph. PC, personal computer; IC, interface controller; WB, water bath; GC, gas chromatograph; I, integrator; MS, magnetic stirrer; C, cell; AB, autoburet; HVB, heated valve box (thermostated to 165 "C); CT, cold trap; VP, vacuum pump; L, sampling loop; V1, six-port gas sampling valve; V2 and V3, four-port sample selection valves; and B, ballast. Fused silica vapor transfer line between C and V2 is also thermostated to 165 "C. Solid lines indicate fluid transfer tubing, and dashed lines indicate electrical connections.
coefficient is given by
where M, is the molar volume of water and Mmis the molar volume of micelles. It is clear from eqs 13 and 14 that micelleswater partition coefficients can be calculated without knowing solute concentration. Furthermore, if a pseudophase model of micelles is accepted, then under equilibrium conditions, the thermodynamic activities of the solute are the same in both micellar and water phases, i.e.,
where yw is the activity coefficient of solute in the water phase and y m is the activity coefficient of solute in the micellar phase. Based on pure solute as the standard state, ym is also known as the intramicellar activity coefficient. Combining eqs 13 and 15, we get
If the solute concentration is in the Henry's law region, then yw can be replaced by its infinite dilution activity coefficient. yw can be obtained from the literature, or it can be measured by using the same HSGC technique.17 Equation 16 shows that measurements of ym can be obtained without a standard solute concentration. EXPERIMENTALSECTION Apparatus. A custom-made computer-controlled headspace gas chromatograph was used to precisely sample the vapor phase which was in equilibrium with the solution phase. A block diagram of the HSGC is shown in Figure 1. It is similar to that described elsewhereI8 with some modfications. In the present apparatus, the heated valve box (HVB) is located on the top of (18)Hussam, A; Cam, P. W. Anal. Chem. 1985,57, 793.
the gas chromatograph injector. The three valves (Valco Instruments Co., Houston, TX) in the valve box are V1, a six-port gas sampling valve, and V2 and V3, four-port sample selection valves. In Figure 1the valves are shown in a vapor loading position. The location of the valve box, the tubing interconnections between valves, and the location of the sample cell were optimized to reduce the overall dead volume of the system. For example, the volumes of the ballast (B) and the sampling loop (L) are 130 and 57 pL, respectively. The total volume of equilibrium vapor drawn into sampling valves and tubing manifolds is about 200 pL for each measurement, and exactly 57 pL was injected onto a fused silica capillary column (HP, cross-linked methylsilicone, 25 m, 0.31 mm id., 0.52 pm film) of the GC (HP Model 5890). One end of the capillary column was inserted through the empty GC injector and directly connected to the gas sampling valve (V1) situated right above the injector. The vapor transfer line between the sample cell (C) and V2 is a short piece of fused silica tubing (12 pL in volume). Similar fused silica tubing is also used to transfer liquids from the autoburet. The entire system is controlled by a data-acquisition board (ADALAB, Interactive Microware, State College, PA) and a custom-made control board interfaced to a personal computer (AT&T Model 6300). The computerization allowed a precise control of valve actuation, temperature of the water bath (Haake Model A81), activation of the autoburet (Metrohm Model 655 Dosimat), the GC, and the integrator (HP 3392 A) at all times. The system was thoroughly tested for sampling reproducibility by sampling the vapor phase in equilibrium with a solution containing an equimolar mixture of ethanol, 2-butanone, toluene, octane, and isooctane (present as an octane impurity) at 25.00 i0.02 "C. The sampling reproducibility of 281 replicates was found to be less than 0.50% in relative standard deviation (RSD) for all peaks. This excellent sampling precision is rarely achieved by manual HSGC or commercial HSGC. Chemicals. Electrophoresis grade SDS (Ultrapure brand, Bethesda Research Laboratory, Bethesda, MD) was used throughout the experiment. Solutes listed before and n-alkylbenzenes (benzene, toluene, ethylbenzene, and n-butylbenzene) were either reagent grade or HPLC grade (Aldrich Chemical Co., Milwaukee, WI), used without further purification. Procedure. An aqueous stock solution of n-alkylbenzenes was prepared by mixing 5.0 p L of solutes in 250.0 mL of water in a volumetric flask (ca. mole fractions, 4.0 x benzene, 3.4 x toluene, 2.9 x ethylbenzene, and 2.3 x nbutylbenzene). The solution was allowed to equilibrate overnight at room temperature, and then ca. 20.0 mL of the solution from the top was discarded, and the rest was transferred into another 250.0 mL volumetric flask. In this way, undissolved solute that may remain on top of the solution was discarded, and the maximum concentrations of n-alkylbenzenes were maintained below their aqueous solubilities (in mole fractions, 3.9 x benzene, 1.1 x toluene, 3.0 x W5ethylbenzene, and 1.9 x n-butylbenzene). Although the exact concentrations of n-alkylbenzenes are not necessary in this work, their concentrations should be below saturation limits. To maintain a constant solute concentration during dilution, the stock 50.0 mL of 500 mM SDS solution was prepared in the aqueous stock solution. All stock solutions were stored in the refrigerator when not in use. Before the gas sampling procedure was initiated, the sample cell (C) containing a glass coated magnetic stir bar was filled with Analytical Chemistry, Vol. 67, No. 8, April 15, 1995
1461
Table 1. Values of KII from Linear Least-Squares Regression of Ad& Vs R in the Premicellar Region at 25 "C
4 3 2
\
s
solute
KII (M-9
intercept
?-
benzene toluene ethylbenzene n-butylbenzene
2.5 f 2.6 10.0 2.0 24.7 f 3.1 124.1 f 13.6
0.987 f 0.013 1.001 k 0.010 1.013 k 0.015 1.030 f 0.070
0.7456 0.8895 0.9563 0.9650
*
2 Table 2. Values of Knt from Linear Least-Squares in the Postmicellar Region at Regression of AdAt Vs 25 O c a
1 Pod
0
l
.
1
.
,
.
,
.
10 15 20 25 30
5
0
i
Total SDS, mM Figure 2. Peak area ratio as a function of total SDS concentration for benzene (O),toluene (O), and ethylbenzene (U).
solute benzene to1uene ethylbenzene n-butylbenzene
Knl
@-'Ib
1474 i 11 4171 f 44
*
lit. Knl 1300 f 30oC 3100 f 30oC 530od
10197 64 76117 & 100
intercept 0.837 f 0.003 0.591 f 0.013 -0.026 f 0.019 -6.567 f 0.298
St between 9.803 and 26.81 mM except n-butylbenzene, between
30
and 23.81 mM. The ?-values for all measurements exceed 0.999. r - - 7 9.803 See text for detailed explanation. Reference 20. Reference 21.
25
t
=O
t
i'
2 15 --. 3 10
5 0 0
5
10
15
20
25
30
Total SDS, mM Figure 3. Peak area ratio as a function of total SDS concentration for c-butylbenzene. Compare the AdAf scale difference with that of Figure 2.
15.00 mL of aqueous hydrocarbon stock. The sample was allowed to equilibrate for at least 1h, and then five blank runs were taken. The average peak area, Ao, for each solute was obtained from blank runs with a precision of 1%RSD or better. After this, the fused silica capillary from the precalibrated autoburet was inserted into the thermostated sample cell through an inert Teflon/ aluminum coated septum. The autoburet was preprogrammed to add 50.0 f 0.5 ,uL of the stock SDS solution after each activation by the computer. After each addition, the sample was allowed to equilibrate for 45 min, and two chromatograms were recorded. Thus Ai values were obtained. The process continued until 17 such additions were made. All necessary precautions were taken to ensure sampling precision better than 2%RSD. All experiments were performed at 25.00 f 0.02 "C. RESULTS AND DISCUSSION
Solute-Surfactant Association Constant,KII. Figures 2 and 3 show the peak area ratios as a function of total SDS concentration according to eq 8. They clearly show the pre- and postmicellar linear regions separated by the arrow pointing to the average cmc value. Table 1 shows the results of the linear regression of the data in the premicellar region. The calculated K11 values show increased magnitude as the number of methylene 1462 Analytical Chemistry, Vol. 67, No. 8, April 15, 7995
group increases in the benzene homologues. Except for benzene, other members of the homologue show significant interaction between a monomer solute and a SDS molecule. The intercepts are all unity (within experimental error) as predicted by the theory. Since no experimental values for KII are available in the literature for the system studied, it is difficult to compare our measurement. However, it clearly indicates the potential of the experimental technique to study weak molecular interactions. Solute-Micelles Association Constant,Knl.We estimate that there were about 6 micelles per probe solute molecule (Le., [micelles]/ [ solute]) at 1.0 mM of micelles. Since the probe solute concentration remains unchanged, the addition of more surfactant increases the [micellesl/[solutel to ca. 100 at the highest surfactant concentration. Therefore, solute-solute interaction in the water continuous bulk phase can be neglected, and &I and K, reported here can be regarded as their infinite dilution values. In the postmicellar region, the peak area ratio increases significantly as more solute solubilizes in the micelles, thus decreasing the concentration of free solute. Table 2 lists values of K,I as obtained from the regression of data in this region. According to eq 8, the slope (&I/%) was used to calculate the value of the micelles-solute association constant by assuming the micellar aggregation number, n = 62.19 Our Knlvalues for benzene and toluene are higher than those in the literature.20a21Both literature values were obtained at millimolar and higher concentrations of solute, where solubility measurement near saturation limit may not represent the equilibrium between micelles and solute. Our values also show a much better precision (
