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Solubilization of 1-Alkanols in Ionic Micelles Measured by Piezoelectric Gas Sensors Yoshiaki Eda, Noboru Takisawa, and Keishiro Shirahama* Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan Received May 22, 1995. In Final Form: September 11, 1995X The partition coefficients of 1-alkanols (1-butanol to 1-heptanol) between ionic micelles and water, expressed in the mole ratio scale (KN) and in the mole fraction scale (KX), were measured at 25 °C by using polymer-coated piezoelectric gas sensors. While KN is constant over the concentration range measured, KX decreases with increasing mole fraction of the 1-alkanols in micelles. It is demonstrated that KN is equal to the value of KX at infinite dilution. The thermodynamic analysis shows that the micellar palisade supplies the solubilization site for 1-alkanols and is less lipophilic than hydrocarbons and 1-alkanols. The dependence of the partition coefficient on the chain length of the cationic surfactants is explained in terms of the micellar electrostatic potential change on solubilization.
Introduction The solubilization of organic compounds by surfactants is a familiar phenomenon in our daily lives. The solubilization of aliphatic alcohols in micelles has been studied by means of various techniques, such as vapor pressure,1-6 total solubility,7 NMR paramagnetic relaxation,8-10 decrease in cmc,11,12 Krafft point depression,13 fluorescence,14 and calorimetry.15 However, reported partition coefficients in micelles have been reported to vary by a factor of about 5 depending on the method employed.16 The vapor pressure method is thought to be a reliable technique for measuring partition coefficients because few assumptions are required. A previous paper1 reported an application of gas sensors based on piezoelectric quartz oscillators to the vapor pressure method to measure the solubilization of 1-alkanols (1-propanol to 1-pentanol) in ionic and nonionic micelles. The piezoelectric gas sensor has the advantages that it can be constructed at a reasonable expense and that it can avoid the interference of nonvolatile species in solution. In this paper, we measured the solubilization of 1-alkanols (1-butanol to 1-heptanol) in ionic micelles to analyze X Abstract published in Advance ACS Abstracts, December 15, 1995.
(1) Eda, Y.; Takisawa, N.; Shirahama, K. Prog. Anesth. Mech. 1993, 1, 27. (2) Eda, Y.; Takisawa, N.; Shirahama, K. In The Polymeric Materials Encyclopedia: Synthesis, Properties and Application; Salamone, J. C., Ed.; CRC Press: Boca Raton, in press. (3) Hayase, K.; Hayano, S.; Tsubota, H. J. Colloid Interface Sci. 1984, 101, 336. (4) Morgan, M. E.; Uchiyama, H.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1994, 10, 2170. (5) Wan-Badhi, W.; Bloor, D. M.; Wyn-Jones, E. Langmuir 1994, 10, 2219. (6) Treiner, C.; Khodja, A.; Fromon, M.; Chevalet, J. J. Solution Chem. 1989, 18, 217. (7) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1984, 101, 587. (8) Marangoni, D. G.; Kwak, J. C. T. Langmuir 1991, 7, 2083. (9) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Chem. Soc., Faraday Trans. 1991, 87 (7), 947. (10) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1989, 93, 2190. (11) Shirahama, K.; Kashiwabara, T. J. Colloid Interface Sci. 1971, 36, 65. (12) Rao, I. V.; Ruckenstein, E. J. Colloid Interface Sci. 1986, 113, 375. (13) Kaneshina, S.; Kamaya, H.; Ueda, I. J. Colloid Interface Sci. 1981, 83, 589. (14) Abuin, E. B.; Lissi, E. A. J. Colloid Interface Sci. 1983, 95, 198. (15) Makayssi, A.; Bury, R.; Treiner C. Langmuir 1994, 10, 1359. (16) Marangoni, D. G.; Kwak, J. C. T. In Solubilization; Christian, S. D., Scamehom, J. F., Eds.; Surfactant Science Series No. 55; Marcel Dekker: New York, 1995; Chapter 14.
0743-7463/96/2412-0325$12.00/0
the dependence of the solubilization on the 1-alkanol chain length more clearly. The solubilization of 1-alkanols by dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromide (C12TAB, C14TAB, and C16TAB) and sodium dodecyl sulfate (SDS) are discussed thermodynamically by comparing them with the transfers of 1-alkanols from water to n-dodecane and to 1-alkanols themselves. The effects of head groups and of the chain length of the surfactants are also discussed. Experimental Section Materials. 1-Butanol (C4OH), 1-pentanol (C5OH), 1-hexanol (C6OH), and 1-heptanol (C7OH) were used as received from Wako Pure Chemical. Water was purified by deionization and double distillation, once from alkaline KMnO4 solution. Dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromide (C12TAB, C14TAB, and C16TAB) were obtained from Tokyo Kasei and recrystallized from acetone containing a slight amount of water. Sodium dodecyl sulfate (SDS) was obtained from Pierce and used as received. The sensor coating used was Elvaloy HP441, which is a lipophilic polymer obtained from Du Pont. Instrumentation. Figure 1 shows the experimental setup for the piezoelectric sensor system. A piezoelectric crystal (6 MHz, AT cut, 8 mm diameter) was obtained from Kinseki and used after removal of its metal casing. A coated piezoelectric crystal was connected to an oscillator circuit fabricated in our laboratory and powered by a 5 V dc power supply. The frequency of the vibrating crystal was measured by a frequency counter (Hioki 3601) connected to a microcomputer (NEC, PC9801). All the measurements were carried out at room temperature (25 °C). Sorption amounts of vapors to the sensor coating could be calculated with the Sauerbrey equation,17 which describes the mass-frequency relationship at an AT cut quartz surface as follows:
∆F )
2F02
∆m ) Cf∆m AxFqµq
(1)
where ∆F is the measured frequency decrease, ∆m the mass increase on the adsorption of vapor, F0 the intrinsic crystal frequency (6 × 106 Hz), A the electrode area (0.20 cm2), Fq the density of quartz (2.65 g cm-3), µq the shear modulus (2.95 × 1011 dyn cm-2), and Cf the integrated sensitivity (0.42 Hz ng-1). Coating Procedure. As described previously,1,2,18 the dipping method was adopted to coat piezoelectric crystals with polymer films. A naked crystal was wetted well and cleaned by immersion into tetrahydrofuran. The clean crystal was then dipped into a (17) Sauerbrey, G. A. Z. Phys. 1959, 155, 206. (18) Eda, Y.; Takisawa, N.; Shirahama, K. Sens. Mater. 1995, 7, 405.
© 1996 American Chemical Society
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Figure 1. Experimental setup for the piezoelectric sensor system.
Figure 3. Sensor responses for 1-pentanol solutions in water and in 200 mM SDS at 25 °C.
Figure 2. Time course of the frequency of an Elvaloy HP441coated piezoelectric crystal. solution of Elvaloy HP441 in tetrahydrofuran and dried in air. The resulting amount of coating could be roughly controlled by changing concentration of the polymer solution and was determined from the frequency decrease (∆FM) of the crystal in reference to eq 1.
Results and Discussion Figure 2 shows a typical frequency change of an Elvaloy HP441-coated crystal (∆FM ) 7.4 kHz) when the crystal was set in the headspace of a closed vessel (cell) containing an aqueous 1-pentanol solution (mole fraction Xa ) 6.6 × 10-4). As the vapor from the solution was absorbed to the sensor coating, the sensor frequency decreased (∆F ) 82 Hz), which corresponds to the sorption of 195 ng of 1-pentanol and water calculated via eq 1. The frequency immediately reverted to its original value on removing the crystal from the cell to the ambient atmosphere, which means the sorbed vapor was released. This response was repeatable and reproducible. To offset the response to water, the difference between the two frequencies (∆F′) of the sensor in vapors from the solution and from pure water was adopted as the sensor response to the alcohol. The solution was dilute enough to consider the activity of water in the solution to be nearly equal to unity. Thus the response (∆F′ ) 61 Hz) includes only the contribution of the alcohol vapor from the solution. Figure 3 shows the sensor responses (∆F′) for two series of aqueous solutions of 1-pentanol, one is the responses for solutions with no surfactant, namely, the calibration line, and the other is the responses for solutions containing 200 mM SDS. The response ∆F′ was lowered in the presence of SDS, which is due to the solubilization of 1-pentanol in the SDS micelle resulting in the decrease in vapor pressure of the alcohol. It is seen that the calibration line divides the total mole fraction (Xa) of
Figure 4. Solubilization isotherm of 1-pentanol to SDS micelle in the mole ratio scale (Namic vs Naaq) and in the mole fraction scale (Xamic vs Xaaq) at 25 °C.
1-pentanol in the SDS solution into the fraction of “free” alcohol in the aqueous phase (Xaaq) and the fraction of “solubilized” alcohol (Xa - Xaaq). The concentration of SDS is much higher than its critical micelle concentration (cmc ) 8.2 mM19 ), so most of the SDS molecules in the solution aggregate to form micelles. Thus the mole ratio of the solubilized alcohol to the surfactant in the micellar phase (Namic) and the mole fraction of the alcohol in the micellar phase (Xamic) are calculated from
namic
mic
Na
nsmic
namic
mic
Xa
)
Xa - Xaaq ) Xs
)
nsmic + namic
Xa - Xaaq )
Xs - (Xa - Xaaq)
(2)
(3)
where N, X, and n represent the mole ratio, the mole fraction, and the number of molecules, the subscripts “a” and “s” refer to the alcohol and the surfactant, and the superscripts “mic” and “aq” to the micellar phase and the aqueous phase, respectively. Figure 4 shows the plots of Namic against Naaq and of Xamic against Xaaq, where Naaq represents the mole ratio of the alcohol in the aqueous (19) Moroi, Y. In Micelles; Plenum Press: New York, 1992; p 222.
Solubilization of 1-Alkanols in Ionic Micelles
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phase. Because of low concentration,
Naaq ≈ Xaaq
(4)
While Namic is proportional to Naaq, Xamic does not show linearity with Xaaq. The apparent partition coefficients of the alcohol between the micellar and the aqueous phases in the mole ratio scale (KN) and in the mole fraction scale (KX) are defined as
KN )
KX )
Namic
(5)
Naaq Xamic
(6)
Xaaq
The value of KN is obtained from the slope of the straight line of the plot of Namic vs Naaq. On the other hand, KX depends on Xamic, so a unique value of KX cannot be obtained. Some papers have referred to the dependence of KX on the amount of added solubilizate.4,6,14 For example, an empirical equation,4 KX ) K0(1 - BXamic)2, has been used to analyze the solubilization isotherms of 1-pentanol by cationic micelles, where K0 represents the partition coefficient at infinite dilution and B is a parameter related to the number of head groups constituting binding sites. However, the physicochemical interpretation of this equation is not clear, although it represents the experimental data quite well. Thus we propose that the partition coefficient in the mole fraction scale at infinite dilution, or the true partition coefficient (K), is obtained from the following equation.
K ) lim
Xamicf0
( ) Xamic Xaaq
(7)
As the mole fraction is equal to the mole ratio when a 1-alkanol is infinitely diluted, the true partition coefficient in the mole fraction scale corresponds to the partition coefficient in the mole ratio scale.
(8)
K ) KN With K, eqs 2 and 3 are rewritten as
Namic ) KNaaq KNaaq
mic
Xa
)
1 + KNaaq
≈
(9) KXaaq
1 + KXaaq
Figure 5. Apparent partition coefficients of 1-pentanol between SDS micelle and water in the mole ratio scale (KN) and in the mole fraction scale (KX) as a function of the mole fraction in the micelle (Xamic). Table 1. Partition Coefficients of 1-Alkanols between Micellar and Aqueous Phases surfactant SDS
C12TAB
C14TAB
C16TAB
SDSb
[surfactant]/ M 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.040 0.020 0.020 0.020
1-alkanol
Ka
C4OH C5OH C6OH C7OH C4OH C5OH C6OH C7OH C4OH C5OH C6OH C7OH C4OH C5OH C6OH C7OH C4OH C5OH C6OH C7OH
320 ( 10 840 ( 50 2300 ( 200 7200 ( 600 190 ( 50 480 ( 40 1480 ( 30 4400 ( 200 230 ( 30 630 ( 60 1800 ( 100 7100 ( 200 360 ( 60 920 ( 70 3100 ( 300 7900 ( 300 300 722 2250 6020
0.19-0.38 0.18-0.44 0.17-0.42 0.12-0.31 0.14-0.33 0.10-0.31 0.15-0.35 0.11-0.24 0.14-0.32 0.06-0.27 0.10-0.35 0.15-0.32 0.22-0.44 0.20-0.36 0.15-0.32 0.17-0.33
a The error in K was estimated from the standard deviation of apparent KN values from K. b From ref 3.
The standard free energies for transfer (∆Gt°) of 1-alkanols from the bulk phase to micelles were calculated from
∆Gt° ) -RT ln K (10)
range of Xamic
(12)
Equation 10 is now in the form of the Langmuir adsorption isotherm, with the maximum Xamic equal to unity. Therefore Figure 5 is in the form of a Scatchard plot expressed as
and are shown as a function of the carbon number of the 1-alkanols in Figure 6. For comparison, the free energies of transfer of 1-alkanols to n-dodecane20 (a liquid hydrocarbon) and for phase separation of 1-alkanols are also plotted. The phase-separation free energy (∆Gs°) was defined as
KX ) K(1 - Xamic)
∆Gs° ) RT ln Xasat
(11)
The K values obtained from the slope of the plot of Namic vs Naaq are presented in Table 1. The partition coefficients for the 1-alkanols in SDS micelles are in good agreement with the values measured by gas chromatography.3 Therefore, the present technique using piezoelectric sensors appears to provide a reliable measurement of solubilization equilibria in micellar solutions.
(13)
where Xasat represents the solubility of 1-alkanols in water.21 ∆Gs° represents the free energy change for transfer of 1-alkanols from the aqueous phase to 1-alkanols themselves saturated with water. (20) Aveyard, R.; Mitchel, R. W. Trans. Faraday Soc. 1969, 65, 2645. (21) Kinoshita, K.; Ishikawa, H.; Shinoda, K. Bull. Chem. Soc. Jpn. 1958, 31, 1081.
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Figure 6. Free energies for transfers (∆Gt°) of 1-alkanols from the aqueous phase to micelles, n-dodecane, and 1-alkanols themselves as a function of carbon number of 1-alkanols. Table 2. Transfer Free Energies per Methylene Group of 1-Alkanols micelle
∆Gt° (CH2)/ kJ mol-1
SDS C12TAB C14TAB C16TAB
-2.6 -2.6 -2.8 -2.6
a
transfer to other lipophilic fields
∆Gt° (CH2)/ kJ mol-1
n-C12H26a 1-alkanols themselvesb
-3.4 -3.5
From ref 20. b From ref 21.
It is interesting to note that the ∆Gt° values to micelles are more negative than the ∆Gt° values to n-dodecane by more than 10 kJ mol-1. This difference can be explained by considering that the solubilization occurs mainly at the palisade layer near the micelle/water interface. Solubilized 1-alkanol molecules can be oriented with their polar hydroxyl groups exposed to the water and their alkyl groups in the micelle interior, whereas alcohols partitioned to the bulk phase of n-dodecane must undergo an energetically unfavorable dehydration. Therefore the transfer to micelles is more favorable than to hydrocarbons. The value of ∆Gt° to micelles decreased linearly with increasing number of carbon atoms in the 1-alkanols. The ∆Gt° values of 1-alkanols to n-dodecane and the ∆Gs° values exhibit a similar linear dependence. This linearity indicates that the main driving force of solubilization is the hydrophobic interaction. The slopes of these straight lines correspond to the increments of the transfer free energy per methylene group of 1-alkanols (∆Gt°(CH2)), which are good indices of the lipophilicity of solubilization sites in micelles. These values are listed in Table 2. The values of ∆Gt°(CH2) to cationic and anionic micelles are less negative than those to n-dodecane and ∆Gs°(CH2). This signifies that the palisade layers of micelles are less lipophilic than the bulk phases of hydrocarbons and 1-alkanols themselves, which is in agreement with the results of NMR and fluorescence spectroscopy indicating that the micellar surface region has a high polarity roughly comparable to that of methanol.22 The effect of head group charge on the transfer free energies is also shown in Figure 6. The transfer of an alcohol to SDS micelles is more favorable than that to C12TAB micelles. This implies the presence of attractive (22) Zachariasse, K. A.; Kozankiewicz, B.; Ku¨hnle, W. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1, p 565.
Figure 7. Dependence of ∆Gt° of 1-alkanols on chain length of alkyltrimethylammonium bromides.
interactions between solubilized alcohol and the head group of SDS, i.e., the sulfate group of SDS can hydrogen bond to the hydroxyl group of 1-alkanols, while the trimethylammonium group of C12TAB cannot. Figure 7 shows the ∆Gt° of 1-alkanols to micelles of C12TAB, C14TAB, and C16TAB. The solubilization of the alcohols becomes more favorable as the carbon number of the surfactant increases. This tendency can be explained by the free energy for the dilution of micellar surface charge density on solubilization. The micellar charge density decreases on solubilization because 1-alkanols are solubilized near the micellar surfaces, which is also supported by the fact that added alcohols give rise to increases in the degree of ionization of SDS micelles.23 This charge dilution is also a factor in the solubilization of 1-alkanols by ionic micelles in addition to the hydrophobic interaction between the surfactant and alcohol alkyl chains. The following simple geometrical consideration shows that the closer the packing of the head groups at the micellar surface, the larger the contribution of micellar charge dilution. According to Coulomb’s law, the electrostatic potential (µel) is defined as
NAz2e2 1 µel(r) ) ) Kel 4πr r
(14)
where r represents the distance between a pair of adjacent head groups, NA Avogadro’s number (6.02 × 1023 mol-1), z the valence of the head group (+1 for the trimethylammonium group), e the charge of a proton (1.60 × 10-19 C), the dielectric constant in water (6.95 × 10-10 C2 J-1 m-1), and Kel the constant (1.77 kJ mol-1 nm). The free energy change for micellar charge dilution on the solubilization of an alcohol is expressed by
∆Gel° ) µel(d0 + dA) - µel(d0) )
(
-Kel
)
1 1 (15) d0 d0 + dA
where d0 represents the original distance between head groups, and dA the increase in distance occupied by the solubilized alcohol molecule. ∆Gel° is intrinsically included in the ∆Gt° value. In general, a micelle with a longer chain shows a closer packing because the larger molecular (23) Manabe, M.; Koda, M.; Shirahama, K. J. Colloid Interface Sci. 1980, 77, 189.
Solubilization of 1-Alkanols in Ionic Micelles
weight causes a stronger cohesion.24 Assuming that dA is independent of the chain length of the surfactants, eq 12 indicates that the longer surfactant with a smaller d0 gives a more negative ∆Gel° in agreement with the results shown in Figure 7. Moreover the order of Kel is similar to the difference of ∆Gt° between alkyltrimethylammonium bromides. Conclusions The quartz oscillators coated with Elvaloy HP441 function as useful sensors responsive to 1-alkanols. By (24) Leibner, J. E.; Jacobus, J. J. Phys. Chem. 1977, 81, 130.
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using these sensors, the solubilization of 1-alkanols to micelles can be easily measured with fewer assumptions than often are needed in other methods for obtaining similar data. The present measurement gave unambiguous thermodynamic evidence that the micellar palisade supplies the solubilization site for 1-alkanols and is less lipophilic than the bulk phases of hydrocarbons and 1-alkanols themselves. The dependence of solubilization on the chain length of surfactants can be explained in terms of the packing of micelles and the electrostatic potential between ionized head groups. LA9503966
