4719
Langmuir 1996,11, 4719-4723
Solubilization of n-Alkylbenzenesinto 1-Dodecanesulfonic Acid Micelles Midori Take'uchi and Yoshikiyo Moroi" Department of Chemistry, Faculty of Science, Kyushu University, Higashi-ku, Fukuoka 812, J a p a n Received April 24, 1995. I n Final Form: September 5, 1995@ The solubilization of benzene, toluene, ethylbenzene, n-propylbenzene, n-butylbenzene, and npentylbenzene into 1-dodecanesulfonic acid was measured. Concentrations of all the substrates in equilibrium were determined spectrophotometrically at 293.15,298.15,303.15,and 308.15 K. The first stepwise association constants (Kd between solubilizate monomer and vacant micelle were evaluated from the equilibrium concentration and were found to increase with hydrophobicity of the solubilizate molecules. They were 1.31 x lo3,3.28 x lo3,9.64x lo3,2.96 x lo4,9.52x lo4,and 3.95 x lo5 mol-l dm3 at 298.15 K for benzene, toluene, ethylbenzene, n-propylbenzene, n-butylbenzene, and n-pentylbenzene, respectively. The standard Gibbs energy, enthalpy, and entropy changes in this system were compared with those for solubilizations of polycyclic aromatic compounds and ofp-n-alkylbenzoic acids to thermodynamically study the solubilized state of the solubilizates.
Introduction Organic substances of slight aqueous solubility become soluble and stably exist in aqueous solution with added surfactants. This phenomenon is well-known as solubilization,lY2 where hydrophobic organic substances are incorporated into the inner part of surfactant aggregates or micelles. Solubilization is quite important industrially as well as biologically3 and is very interesting chemically, e.g., in micelle catalyzed r e a ~ t i o n s in , ~ emulsion polymerizations, and i n protein separation from biomemb r a n e ~ Unfortunately, .~ however, solubilization has been treated in most cases as a partitioning of solubilizate molecules between a micellar phase and the intermicellar bulk p h a ~ e , which ~ - ~ is inconsistent with the phase rule as pointed out by one of the authors.2J0 In this sense, the solubilization results based upon reasonable treatment are more preferable for discussion on the thermodynamical parameters of solubilization, where the treatment regards micelles as a chemical species.11J2 A complex apparatus such as a vacuum line combined with an accurate pressure gauge is commonly employed for solubilization of gaseous solubilizates in surfactant solution.13J4 Fortunately, a very simple glass vessel was devised as an apparatus to determine the solubilization
* To whom correspondence should be addressed.
* Abstract published in Advance ACS Abstracts, November 15, 1995. (1)Elworthy, P.H.; Florence,A. T.; Macfarlence,C.B.Solubilitation by Surface-Active Agents and Its Application in Chemist9 and Biological Sciences; Chapman & Hall: London, 1968. (2)Moroi, Y. Micelles: Theoretical and Applied Aspects; Plenum Press: New York, 1992;Chapter 9. (3)Kroc, R. A.; Kroc, R. L.; Whedon, G. D.; Garey, W. Hepatology, The Chemistry of Bile in Health and Disease; Williams & Wilkins: Baltimore, MD, 1984;Vol. 4(5). 14)Fendler, J. H.; Frendler, E. J. Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975. (5) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley-Interscience: New York, 1973. (6)Larsen, J. W.;Magid, L. J. J. Phys. Chem. 1974,78,834. (7)Bunton, C. A.; Sepulveda, L. J. Phys. Chem. 1979,83,680. (8) Gamboa, C.;Olea, A. F. Langmuir 1993,9,2066. (9)Uchiyama, H.; Tucker, E. E.; Christian, S. D.; Scamehom, J. F. J . Phys. Chem. 1994.98,1714. (10)Moroi, Y. J. Phys. Chem. 1980,84,2186. (11)Moroi, Y.;Sato, K.; Matuura, R. J.Phys. Chem. 1982,86,2463. (12)Moroi, Y.;Noma, H.; Matuura, R. J.Phys. Chem. 1983,87,872. (13)Tucker, E.E.;Christian, S. D. J. Chem. Thermodyn. 1979,11, 1137. (14)Matheson, I.B.C.; King, A. D., Jr. J.Colloid Interface Sci. 1979, 66,464.
of volatile or gaseous substances.15 The apparatus worked well for prod;ction of constant chemical potential of the solubilizate. In this paper, solubilization of volatile n-alkylbenzenes into 1-dodecanesulfonic acid micelles was studied from the stepwise association equilibria between solubilizates and micelles, using the glass apparatus. The thermodynamic parameters on the solubilizations of p-n-alkylbenzoic acids16 and of polycyclic aromatic ~ o m p o u n d s ~ ~ ithe n t osame micelles are available, although the temperature dependence has not been studied as for the former. It can be expected, therefore, that comparison of the present results with the preceding ones leads to more correct information on the thermodynamics of solubilization and on the solubilization site in the solubilized state.
Experimental Section Materials. 1-Dodecanesulfonic acid was synthesized as described in the previous paper,ls and the solution concentration was determined by acid-base titration. Benzene, toluene, and ethylbenzene of guaranteed reagent grade from Nacalai Tesque, Inc. were washed four times with concentrated sulfuric acid at lower temperatures, four times with water and diluted NaOH solution alternately, and finally three times with water. nPropylbenzene,n-butylbenzene,and n-pentylbenzenefrom Tokyo Kasei Co. were distilled once and washed with water 10 times. The water used was distilledtwice from alkaline permanganate. Solubili~ation.~~ Eight surfactant solutions of different concentrationswere separately poured into eight tubes of the special glass apparatus (Figure 1).A minute amount of benzene, ethylbenzene,n-propylbenzene, and n-butylbenzenewas placed on the hollow in the middle of it. As for n-pentylbenzene, approximately 1 mL of the liquid was dropped in, because the aqueous solubility is very small and the absorbance below the critical micelle concentration (cmc)cannot be detected unless its concentration reaches the maximum additiveconcentration.The whole glass vessel with its cover was kept in a thermostatcontrolledenvironmentwithinhO.01 Kat 293.15,298.15,303.15, and 308.15 Kfor 24h, while the surfactant solutionswere agitated with rotors in the tubes. Inside the apparatus, the volatile solubilizates easily evaporate because of the small amount used and their highvolatility,and the chemical potential ofthe gaseous solubilizate molecules becomes constant throughout the phases, or the concentration ofmonomericsolubilizate can be set identical (15) Moroi, Y.; Morisue, T. J. Phys. Chem. 1993,97,12668. (16)Moroi, Y.;Matuura, R. J. Colloid Interface Sci. 1988,125,463. (17)Moroi, Y.;Mitunobu, K.; Morisue, T.; Kadobayashi, Y.; Sakai, M. J.Phys. Chem. 1996,99,2372. (18)Matsuoka, K.;Moroi, Y. J. Phys. Chem. 1993,97,13006.
0743-746319512411-4719$09.0010 0 1995 American Chemical Society
4720 Langmuir, Vol. 11, No. 12, 1995
Take'uchi and Moroi
n U
n
When the concentration of solubilizate is less than a few times the micellar concentration, an incorporation of the solubilizates into micelles can be assumed to be so slight as not to change the intrinsic properties of the micelles. In this case, it is rgasonable to assume that-the value of escaping rate constant kJ isj times as large as the k l value. That is, the probability of a solubilizate molecule escaping from a mother micelle containingj solubilizate molecules is j times the probability of the molecule eeapigg from a micelle containing just one solubilizatemolecule (kl=$I). Moreover,the probability of a solubilizate molecule entering a micelle remains the same regaraess of the number of solubilizate molecules in the micelle (kJ = KO). We, therefore, have the following equation for the stepwise association constant of solubilization:
r;; = Klfi C
Figure 1. Apparatus for solubilization: a = solubilizate, b = surfactant solution, c = disk rotor, and d = magnetic stirrer.
in the eight solutions. After the equilibration, each surfactant solution was separately drawn into each injection tube through the injection needle, which was readily and immediately capped with a silicone rubber. The concentrations of solubilizates in the surfactant solutionswere determined spectrophotometrically from the calibration curves using a capped optical cell. Theory The monodispersity of the micellar aggregation number n is assumed to avoid the difficultiesarising from their polydispersity. Even in the case of the polydispersity the present discussion remains essentially the same.ll The association equilibrium between surfactant monomers (SIand micelles (M) is represented by
where K, is the equilibrium constant of micelle formation. The stepwise association equilibria between micelles and solubilizates (R) can be represented schematically as follows: El
+ R E2 MR,
where MRi fs the micelles associated with i molecules of solubilizate,Kiis the stepwiseassociationconstant between m-1 and monomer molecule of solubilizate, and m is the maximum number of solubilizate molecules per micelle. From eqs 1and 2, we have the followingequations for the total micelle concentration ([MJ), the total equivalent concentration of solubilizate ([RJ), and the average number of solubilizate molecules per micelles (R): m
When eq 6 is introduced into eqs 3 and 4, then [Mtl and [&I become the following equations: [M,l = [MI exp(Kl[R1)
(7)
[Rtl = [Rl + f;r[[RI [MI exp(Kl[Rl)
(8)
Hence, the average number of solubilizate moleculesper micelle, R, is given by
R = ( [Rtl - [RlMMt1 = El[Rl
(9)
Thus, the probability that a micelle is associated with i solubilizates can be written by
P(i) = [MR,I/[M,l = R' exp(-R)/i!
(10)
which is the Poisson distribution. The important point here resides in the condition that both solubilizates and micelles are independent and indistinguishable, which is possible only when the solubilization is so small that the intrinsic properties of micelles do not change.2 The Poisson distribution of solubilizates among micelles has been examined photochemically and confirmed for a small amount of solubilization.19,20 From eq 9, the following useful expression can be derived ([R,] - [RI)/[Rl = Kl(C - cmc)/n
(11)
where [Mt] = (C - cmc)/n,n is the aggregation number, and C is the total surfactant concentration. Finally, the K1 value (the first stepwise association constant between a solubilizate and a vacant micelle)can be evaluated by the slope of the plots of ([RJ - [RI)/[Rl against C - cmc. The important point here is that the whole equations above can be used due to the constancy of [R]throughout the aqueous phases which is manipulated by the devised glass apparatus.
M+R=MR, MR,
(6)
i
(3)
(4)
Results and Discussion The molar extinction coefficients (€1 were determined by measuring the absorbances of the solubilizates of specified concentration in micellar solution. The absorbances were plotted against the solubilizate concentrations, and straight lines were obtained. The E values at 260 nm were determined to be 2.32 x lo2for toluene, 2.16 x 10, for ethylbenzene, 2.01 x 10, for n-propylbenzene, 2.11 x 10, for n-butylbenzene, and 2.22 x 10, mol-l dm3 cm-I for n-pentylbenzene. The E value at 254 n m for benzene is 1.88 x lo2 mol-' dm3 cm-l as taken from the literature.,l Solubilizate concentration changes of ethylbenzene and n-pentylbenzenewith changes in surfactant concentration (19) Tachiya, M.Chem. Phys. Lett. 1976,33,289. (20) Infelta, P.P. Chem. Phys. Lett. 1979,61, 88. (21)Eastman, J. W.; Rehfeld, S. J. J. Phys. Chem. 1970,74, 1438.
Langmuir, Vol. 11, No. 12, 1995 4721
Solubilization of ndlkylbenzenes 20
m
I
/ I
Ethylbenzene
4-
3-
0
308.15K 303.15K 298.15K 293.15K
2. a
b
=
1-
0
10
30
20
40
d
50
0
308.15K 303.15K 298.15K 293.15K
Surfactant Concentration / lO’mol dmJ
Figure 2. Concentration changes of the ethylbenzene with changes in surfactant concentration. a C
n-pentylbenzene
t
10
0
20
30
-
C cmc / 103mol
Figure 4. Plots of ([&I - [R])/[R] of ethylbenzene against micellar concentration(C - cmc). The lines are based upon the linear regression analysis of the plots. 201
d
308.i~~ 303.15K 298.15K 293.15K
30
40
a
b 0
O r
0
n
n
B. h
I00
z
t
10
20
Surfactant C~ncentration/lO~~mol dm’3
Figure 3. Concentration changes of n-pentylbenzene with changes in surfactant concentration. are given in Figures 2 and 3, respectively. The monomeric concentration of n-pentylbenzene below the cmc does not monotonously decrease with temperature. The vapor pressure should increase with increasing temperature, but aqueous solubility of gaseous molecules decreases with increasing temperature. The above two conditions caused the presence of the solubility minimum a t 303.15 K. Plots can be divided into two straight lines whose intersection was employed as the cmc a t each temperature. Solubilizate concentrations below the cmc remain almost constant for all the solubilizates regardless of surfactant concentrations, which indicates the constancy of chemical potential of the solubilizate molecule throughout the phases inside the glass apparatus. The meanvalue ofthe solubilizate concentration below the cmc gives the value of the monomer concentration in aqueous bulk [Rl of solubilizate molecules. A steep increase in solubilizate concentrations above the cmc is brought about by the incorporation of substrates into micelles. The longer the alkyl chain of the substrate, the better the linearity of the variation of solubilizate concentrations. In other words, the solubilizate concentrations of n-pentylbenzene at each temperature were almost on perfect lines both above and below the cmc, while those of benzene and toluene show
(1
0
10
-
20
30
C cmc / lO”m0l dmJ
Figure 6. Plots of ([&I - [R])/[R] of n-pentylbenzene against micellar concentration (C - cmc). The lines are based upon the linear regression analysis of the plots. a small deviation from straight lines, which also causes the deviations in the following analysis based on eq 11. The fair linearities of these volatile solubilizates are attributed to their higher possibility of escaping from the solution due to the small standard Gibbs energy decrease for solubilization. They are not stabilized very much by solubilization. Now we _can determine the first stepwise association constant (ICl)from the values in the figures above and from other plots on the basis of eq 11. The slope of the line obtained by plots of ([&I - [Rl)/[Rl against C - cmc gives K J n . The relationships are shown in Figures 4 and 5 for ethyl- and n-pentylbenzene, respectively. Differences in slope among tempezature may be relatively small, but the differences in the K1 values become evident when they are determined by multiplication of the slope by the aggregation number: 76.3,65.9,55.1,and 51.5 at 293.15, 298.15,303,15,and 308.15 K, respectively.18 Thesevalues
4722 Langmuir, Vol. 11, No. 12, 1995
Take'uchi and Moroi
Table 1. Association Constants (&) and Thermodynamic Parameters of Solubilization solubilizate benzene
toluene
ethylbenzene
n-propylbenzene
n-butylbenzene
n-pentylbenzene
T (K)
R
293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15
1.21 0.726 0.554 0.502 2.29 1.23 1.18 1.08 3.72 2.59 1.80 1.28 3.99 3.30 2.62 2.29 3.55 3.09 2.73 2.94 12.1 10.1 8.40 8.06
Kl
AGO
m
(mol-' dm3)
(kJ mol-')
(kJ mol-')
3.34 x 1.31 x 1.16 x 1.06 x 4.00 x 3.28 x 3.05 x 2.61 x 1.09 x 9.64 x 8.05 x 7.29 x 3.38 x 2.96 x 2.50 x 2.23 x 1.12 x 9.52 x 8.06 x 7.02 x 4.21 x 3.95 x 3.40 x 2.88 x
were measured by static light scattering. The RI values became larger a t lower temperatures for the same solubilizate and increased according to the number of carbons in the alkyl chain a t the same temperature, which reflects the constant increase with increasing hydropht bicity of these substrates. Table 1 shows the KI and 8 values and other thermodynamic parameters. The R values obtained are small enough to confirm that an incorporation of the solubilizates could not change the intrinsic properties of the mother micelles. As for npentylbenzene, R values are rather large due to a large amount of the solubilizate placed inside the apparatus for the convenience of the measurement. The Gibbs energy change of solubilization can be expressed in the following form:
AGO = -RT In Kl
(12)
-17.7 -17.8 -17.8 -17.8 -20.2 -20.1 -20.2 -20.2 -22.7 -22.7 -22.7 -22.8 -25.4 -25.5 -25.5 -25.6 -28.3 -28.4 -28.5 -28.6 -31.9 -31.9 -32.1 -32.2
103
103 103
103 103
103 103 103 104
103 103 103 104 104 104 104 105 104 104 104 105 106 105 105
-TR,AS" (kJ mol-')
-15.8
-1.6
-20.4
-1.5
-20.9
-1.8
-21.2
-4.3
-23.5
-5.0
-24.9
-7.0
Total Number of Carbon Atom 6
8
10
14
12
16
-20
-25
I
\\ '\\
Polycyclic Aromatic Compounds
-30
-35
Furthermore, AGO is made up of three contributions:
(13) where p o ~is ~ thel standard chemical potential of MR1 a t infinite dilution and p o and ~ ,U'R are the corresponding potentials. From the variation of AGO with temperature, the enthalpy and entropy changes, A W and AS",of solubilization can be respectively determined by the following equations:
(14) A S o = -(AGO - AHo)/T The thermodynamic parameters derived from eqs 12, 14, and 15 are also summarized in Table 1. The absolute value of AGO increases as the number of carbons in the alkyl chain increases, which corresponds to a n increase of the K1 values. The enthalpy change3 are estimated from the slope of the linear plots of In K1 vs 1/T. The Gibbs energy changes in the solubilization of n-alkylbenzenes were plotted against the number of carbons in the alkyl chains in Figure 6. I t can be said from the figure that n-alkylbenzenes andp-n-alkylbenzoic acids have a similar location in the micelles because their
-40
I
.
1
.
I
.
s .
I
AGO values are almost identical, suggesting that the hydrophobic interactions between the alkyl groups and micellar interior are the same for the two and that the -COOH group in the benzoic acids tends to keep this part of the molecule in contact with water a t the micellar surface. But the line linking the circles slightly curves and concaves against the abscissa compared with that of the triangles. This difference can be attributed to the fact that p-n-alkylbenzoic acids with a nondissociated carboxyl group are solubilized into the micelle with their benzoic acid residue anchored to the micellar surface due to the strong interaction between the residue and the polar head groups or water molecules around them, while the n-akylbenzenes have only n-electron clouds of the benzene rings for interaction with water molecules o r surfactant head groups. However, the interaction is still weak, and therefore, the present solubilizates may be gradually pulled into the inner micellar core with elongation of their alkyl chains, which can hydrophobically interact with the
Langmuir, Vol. 11, No. 12, 1995 4723
Solubilization of n-Alkylbenzenes micellar core. This inference is supported by spectral change. The spectra of benzene and toluene remain the same both above and below the cmc, while the spectra of n-butylbenzene and n-pentylbenzene are a little different around 250 nm between above and below the cmc, suggesting that their microenvironments in the solubilized state differ from those in the aqueous bulk below the cmc. They also support the above reasoning. The contributions per methylene or methyl group in nalkylbenzenes and p-n-alkylbenzoic acids to the transfer Gibbs energy change from aqueous bulk to micelle are calculated to be -2.81 and -2.59 k J mol-l, respectively, when plots are analyzed by a linear regression. These values should be compared with the incremental Gibbs energy of transfer per methylene group of -1.30 k J mol-l resulting from the solubilization of p-alkylphenols into CTAB micelle^.^ The former are twice the latter. On the other hand, the slope linking the squares is less steep than the others, and the polycyclic aromatic compounds are stabilized by solubilization to a lesser extent. The contribution per one aromatic carbon from aqueous bulk to micelle is -1.77 k J m01-l.l~ This may indicate that they have stronger interactions with water molecules a t the micellar surfaces, because they consist of benzene rings, and that they cannot move deeply into a micellar core without alkyl chains which are capable of strong interactions with the micellar core. The Gibbs energy change or A@ includes two terms, LVI" and -TASo. The two terms for the n-alkylbenzenes were plotted against the number of carbons in their alkyl chains in Figure 7. We can understand that the negative values of both the enthalpy and the entropy terms positively contribute to the negative Gibbs energy changes in the present solubilizations. As we can see, the absolute value of AHo becomes large more rapidly than that of -TASo. Thus we can conclude from the present results t h a t the solubilization of n-alkylbenzenes is enthalpy driven, where the favorable enthalpy term is largely due to London dispersion forces between the solubilizates and surfactants in the micellar state. However, when we compare it with the former result that negative ASo values or positive values of -TASo should negatively contribute to the Gibbs energy change for solubilization of the polycyclic aromatic compounds into the same micelle,17 we can say the entropy is playing a n important role in the present systems.
-10
-
,
i o
-15
L
P
-20
-30
1 -20 0
1 2 3 4 5 Carbon Number of Alkylchain
6
Figure 7. Standard enthalpy and entropy change vs number of carbons in the alkyl chain. The alkyl chain can interact with water molecules, detaining their arrangement around the chain in aqueous bulk. The release of structured water molecules upon solubilization enlarges the entropy of the system,22while the fixation of solubilizates themselves into the micelle results in a decrease in the entropy. This is the reason why the positive entropy changes became rather small in total as compared with the enthalpy changes for the solubilization of n-alkylbenzenes, when a n alkyl chain transfers from the water phase to the hydrophobic inner micelle. On the other hand, the entropy changes were negative for the solubilization of polycyclic aromatic c o m p ~ u n d s ,because ~ ~ , ~ ~ they site on the outer micelle, detaining water molecules around them and fixing themselves on the outer micelles. LA950328J (22) Blokzijl, W.; Engberts, I. B. F. N. Angew. Chem., Int. E d . Engl. 1993,32, 1595. (23)Morisue, T.;Moroi, Y.; Shibata, 0. J. Phys. Chem. 1993,97, 12668.
