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Does the Schulman’s Titration of Microemulsions Really Provide Meaningful Parameters? Mauro Giustini,† Sergio Murgia,‡ and Gerardo Palazzo*,§ Consorzio Interuniversitario per lo sviluppo dei Sistemi a Grande Interfase (CSGI), Dipartimento di Chimica, Universita` “La Sapienza”, I-00185 Roma, Italy, Dipartimento di Scienze Chimiche, Universita` Cagliari, I-09042 Monserrato (CA), Italy, and Dipartimento di Chimica, Universita` di Bari, via Orabona 4, I-70126 Bari, Italy Received June 16, 2004. In Final Form: July 23, 2004 In 1955, Bowcott and Schulman coined the term microemulsions and, in passing, proposed a cosurfactant titration of interfaces tailored for water-in-oil systems (Bowcott, J. E.; Schulman, J. H. Z. Elektrochem. 1955, 59, 283). This procedure, elegant and inexpensive, is accomplished by dilution with both oil and cosurfactant up to the onset of microemulsion formation. The rationale they proposed for this method should furnish, with high accuracy, the composition of reverse micelles and continuous bulk in the presence of cosurfactant partition. The present paper demonstrates, by means of pulsed gradient spin-echo NMR, that the Schulman’s titration quantitatively describes the cosurfactant partition and that the titration path really corresponds to a dilution path for reverse micelles (at constant composition) dispersed in a continuous bulk (at constant composition).
Under suitable conditions (T, P, composition) water, apolar compounds, and surfactants give rise to thermodynamically stable mixtures called microemulsions.1 The structure of microemulsions can be idealized as a set of interfaces dividing polar and apolar domains. Characteristic lengths are in the range 1-100 nm, so that they appear optically transparent (sometimes bluish). To attain the thermodynamic stability, the oil/water interfacial tension is very low. Ever since their discovery, microemulsions have been subject to numerous theoretical and experimental investigations. On the applied front, they are of interest in enhanced oil recovery, cutting oils, drug delivery, detergency, lubrication, etc. However, to attain the appropriate packing of amphiphiles at the interface, the addition of other surface-active substances is often required. These cosurfactants (usually medium-chain linear alcohols) partition themselves among the oil, water, and interface domains. Therefore, without a quantitative description of the dependence of the partition equilibria on the system composition, a full understanding of quaternary microemulsions cannot be attained. At the dawn of the microemulsion science, Bowcott and Schulman proposed a cosurfactant titration of the interface.2 This simple and inexpensive method is accomplished by dilution with both oil and cosurfactant up to the onset of microemulsion formation. This procedure was tailored for water-in-oil (w/o) microemulsion (reverse micelles), and when the dilution steps are repeated, it should provide reverse micelles more and more diluted but with constant composition of interface and continuous bulk. Such a path of dilution is of paramount importance in scattering and diffusion studies because it allows the extrapolation to single-particle properties by reducing interparticle interactions. Furthermore, the analysis of titration data should permit an easy evaluation of interface and con* Author to whom correspondence should be addressed. E-mail:
[email protected]. † Universita ` “La Sapienza”. ‡ Universita ` Cagliari. § Universita ` di Bari. (1) For reviews, see: De Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982, 86, 2294. Langevin, D. Acc. Chem. Res. 1988, 21, 255. Gelbart, W. M.; Ben-Shail, A. J. Phys. Chem. 1996, 100, 13169. (2) Bowcott, J. E.; Schulman, J. H. Z. Elektrochem. 1955, 59, 283.
tinuous phase composition. For these reasons, the Schulman’s titration was widely used in experimental investigations of w/o microemulsions.3 Quite surprisingly, its validity was not yet tested by independent experiments, although it was often used as a starting point in the analysis of data obtained by more sophisticated techniques.4,5 Moreover, there is not a general agreement on the thermodynamic ground of this titration method. Several analyses of the results of this procedure have been proposed, leading to different interpretations of the same data.6 The present contribution wishes to elucidate two main points: (i) is it the correct hypothesis that a titration path corresponds to a dilution path, and (ii) do the parameters extracted from the titration (interface and bulk composition, see below) really describe the system? We have focused our investigation on microemulsions made of hexadecyltrimethylammonium bromide (CTAB), water, 1-pentanol, and n-hexane that form reverse micelles in a wide range of compositions and that have been previously characterized.5,7,8 The source of chemicals and their purification is described elsewhere.8 Three parameters are needed in order to define the composition of a four-component system. In this paper, we will use the mole ratios pentanol/CTAB (P0), hexane/CTAB (N0), and water/CTAB (W0), which was fixed at 15. The titration was performed as follows: a stable, transparent microemulsion at W0 ) 15 was placed in a vial within a thermostated sample holder made of a double jacketed beaker connected to a water bath. The hexane (3) See, for example: Gerbacia, W.; Rosano, H. L. J. Colloid Interface Sci. 1973, 44, 242. Bansal, V. K.; Shah, D. O.; O’Connel, J. P. J. Colloid Interface Sci. 1980, 75, 462. Birdi, K. S. Colloid Polym. Sci. 1982, 26, 628. Singh, H. N.; Swarup, S.; Singh, R. P.; Saleem, S. M. Ber. BunsenGes. Phys. Chem. 1983, 87, 1115. Hait, S. K.; Moulik, S. P. Langmuir 2002, 18, 6736. (4) See, for example: Petit, C.; Bommarius, A. S.; Pileni, M. P.; Hatton, T. A. J. Phys. Chem. 1992, 96, 4653. (5) Giustini, M.; Palazzo, G.; Colafemmina, G.; Della Monica, M.; Giomini, M.; Ceglie, A. J. Phys. Chem. 1996, 100, 3190. (6) Gu, G.; Wang, W.; Yan, H. J. Therm. Anal. 1998, 51, 115. Moulik, S. P.; Digout, L. G.; Aylward, W. M., Palepu, R. Langmuir 2000, 16, 3101. (7) Colafemmina, G.; Palazzo, G.; Balestrieri, E.; Giomini, M.; Giustini, M.; Ceglie, A. Prog. Colloid Polym. Sci. 1997, 105, 281. (8) Palazzo, G.; Lopez, F.; Giustini, M.; Colafemmina, G.; Ceglie, A. J. Phys. Chem. B 2003, 107, 1924.
10.1021/la0485125 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/06/2004
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Table 1. Results of Titrations and PGSE-NMR Measurements PGSTE-NMR sample composition P0 4.79 4.83 4.89 4.96 5.00 5.07 5.12 5.17 5.21 5.27
a
N0 51.0 52.1 53.6 54.7 55.8 57.1 58.2 59.3 60.4 61.4
titrationa Pmic 0.50 0.50 0.49 0.49 0.48 0.48 0.47 0.47 0.46 0.46
self-diffusion coefficients (m2s-1) CTAB
pentanol
10-11
7.80 × 8.10 × 10-11 8.18 × 10-11 7.92 × 10-11 8.06 × 10-11 8.00 × 10-11 7.54 × 10-11 8.52 × 10-11 9.82 × 10-11 9.09 × 10-11
10-9
1.14 × 1.22 × 10-9 1.30 × 10-9 1.39 × 10-9 1.26 × 10-9 1.40 × 10-9 1.34 × 10-9 1.37 × 10-9 1.40 × 10-9 1.39 × 10-9
evaluated parameters Pmic 0.58 0.53 0.49 0.43 0.52 0.43 0.47 0.46 0.45 0.45
P0Pmic
(na/no)bulk
2.76 2.58 2.40 2.16 2.59 2.20 2.42 2.37 2.33 2.38
0.040 0.043 0.047 0.051 0.043 0.050 0.046 0.047 0.048 0.047
mean 2.42 ( 0.06
mean 0.046 ( 0.001
P0Pmic ) 2.41 ( 0.03; (na/no)bulk ) (4.63 ( 0.05) × 10-2.
was added under continuous stirring to destabilize the system that phase-separates (becomes turbid); the singlephase microemulsion is then restored by the addition of a requisite amount of pentanol. The hexane was added in a discrete amount (100 µL) with a microsyringe (Hamilton). The pentanol was added continuously by means of a syringe driven by a micrometric screw (previously calibrated); the minimum appreciable amount of n-pentanol results in 1.3 × 10-4 grams. To avoid hexane evaporation, a cotton flock soaked with hexane was placed on the vial opening where the syringe needle was inserted. The transition turbid-to-limpid was recognized with a homebuilt nephelometer: the light from a laser diode (λ ) 680 nm; 5 mW) was focused on the sample holder, and the transmitted light was collected by a photodiode connected to a digital voltmeter. Usually, several steps of oil and pentanol dilution are performed. Strictly, what one obtains with this procedure is a well-defined phase-separation boundary (precision better than 0.2%) between reverse micelles and a multiphase region (reverse micelles plus lamellae).9 It is customary to represent such a phase boundary by plotting P0 vs N0 (Schulman’s plot).2,3 The peculiar feature of the Schulman’s plot is its linearity, as shown in Figure 1. More surprising, this linearity holds independently from the nature of oil, cosurfactant, and surfactant.2,3,5 This striking phase behavior was easily rationalized by assuming that along the phase boundary the system is composed of the same aggregates dispersed in a continuous phase of constant composition. Under this assumption, along the titration path, the mass balance requires that:
P0 ) P0Pmic + (na/no)bulk No
(1)
where (na/no)bulk is the (constant) mole ratio alcohol/oil in the continuous bulk, while Pmic is the fraction of micellized pentanol, so that P0Pmic is the mole ratio cosurfactant/ surfactant within the reverse micelle. According to eq 1, the data in a Schulman’s plot can be easily fitted to a straight line whose slope and intercept give the continuous bulk and reverse micelle composition, respectively. To test such a hypothesis, several samples along the titration path were prepared and transferred into NMR tubes that where flame sealed to avoid solvent evaporation (their composition is show in Figure 1 and listed in Table 1). All the samples have been investigated through pulsed gradient spin-echo NMR experiments10 with a stimulated (9) Palazzo, G.; Carbone, L.; Colafemmina, G.; Angelico, R.; Ceglie, A.; Giustini, M. Phys. Chem. Chem. Phys. 2004, 6, 1423
Figure 1. Schulman’s plot of the samples of Table 1, the straight line represents the linear regression according to eq 1; (2.41 ( 0.03) + (0.0463 ( 0.0005) × N0.
echo sequence (PGSTE-NMR) on a Bruker Avance 300 MHz (7.05 T) spectrometer (equipped with a Bruker field gradient probe) obtaining the self-diffusion coefficient of CTAB and pentanol (Figure 2 and Table 1). In all the cases, the echo decays were strictly monoexponential. In the present system, the translational motion of CTAB coincides with the motion of the reverse micelle, as previously demonstrated.5,7 Since the CTAB diffusion remains constant, we argue that along the titration path the micellar size and shape and the bulk viscosity remain essentially unchanged. This is an indirect indication that the interface and bulk compositions remain steady. Indeed, the amount of alcohol at the interface strongly influences the micellar size, while the viscosity of continuous bulk is strongly affected by the pentanol/hexane ratio.8,9 More quantitative insight comes from the analysis of the pentanol self-diffusion coefficient. The alcohol molecules experience a fast exchange between two sites: the continuous organic bulk, where they diffuse with a selfdiffusion coefficient, Dfree, and the aggregates characterized by a diffusion coefficient, Dmic.8 Under these conditions, the experimentally observed self-diffusion coefficient (Dobs) is a population average of the two diffusion coefficients:11 (10) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1.
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Figure 4. Comparison between the Pmic values coming from the titration and the analysis of PGSTE-NMR data. Figure 2. Self-diffusion coefficients of CTAB (open dots) and pentanol (closed dots) for the samples of Figure 1 (the numerical values are listed in Table 1). The curve represents the prediction of eq 2; Pmic values are obtained from titration (third column in Table 1); the slope of the linear regression in Figure 1 gives an estimate of the continuous phase composition, and Dfree was evaluated according to the second-order polynomial of Figure 3.
Figure 3. Self-diffusion coefficients of pentanol in binary mixtures of pentanol/hexane, the curve is the second-order bestfit polynomial: 3.51 - 28.91N0 + 142.45N02.
Dobs ) PmicDmic + (1 - Pmic)Dfree
(2)
In the present case, Dmic coincides with the CTAB selfdiffusion coefficient.5 The self-diffusion coefficient of pentanol in pentanol/hexane solutions (Dfree) depends on the composition of the mixture itself, as shown in Figure 3. Comparing the experimental self-diffusion coefficients of pentanol with the predictions of eqs 1 and 2, one can obtain a first indication of the quantitative validity of eq 1. Actually, if eq 1 holds, Pmic will be simply the ratio between the intercept (P0Pmic) and the overall alcohol/ CTAB ratio (P0) in the Schulman’s plot. Furthermore, the slope of the linear regression of titration data gives an estimate of the continuous phase composition, (na/no)bulk. According to the second-order polynomial of Figure 3, one can evaluate the corresponding value of Dfree and so (11) Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1983, 87, 4756. Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1984, 88, 5391
evaluate Dobs through eq 2. In Figure 2, the experimental self-diffusion coefficients of pentanol (closed dots) are compared with the prediction of eqs 1 and 2 (continuous curve). The agreement is excellent, taking into account that we are not dealing with a best fit but with the prediction of eq 2, where the values of Dmic, Pmic, and Dfree come from independent experiments. This encouraged us to make a direct comparison between the titration and self-diffusion data (without any crossover). This can be achieved because, knowing Dobs and Dmic, the fraction of pentanol moving with the micelle can be evaluated from eq 2 by an iterative procedure. In the first step, all the alcohol was assumed to be present in the bulk phase and (from the polynomial of Figure 3) a first value for the self-diffusion coefficient of the pentanol diffusing in the bulk, Dfree(1) was calculated. Using Dfree (1), eq 2 allows us to obtain the first value of the fraction of pentanol in the micelle, Pmic(1). From Pmic(1) one can easily determine a second composition of the bulk phase and the corresponding free-pentanol diffusion Dfree(2) and, therefore, of Pmic(2), and so on. The procedure converges within four to five iterations, furnishing, for each sample, a Pmic value evaluated only from PGSE-NMR data (Table 1). In Figure 4, the values of Pmic extracted in this way from PGSENMR experiments are compared with the Pmic values evaluated from titrations (Pmic ) P0Pmic/P0). It is clear that there is a complete agreement between the two sets of data. In conclusion, it is undoubtedly demonstrated that the data treatment of the classic Schulman’s titration successfully describes the microemulsion behavior along a path where the self-assembled aggregates increase their inter-aggregate distance without any change in the aggregate and in the continuous phase composition. Indeed, P0Pmic and (na/no)bulk probed by PGSE-NMR slightly fluctuate around fixed values. Moreover, their mean values coincide with the corresponding values determined by means of the Schulman’s titration. Finally, we note that both PGSE-NMR and the titration do not allow us to discriminate if the alcohol is partitioned preferentially in the water or in the interfacial film. However, the low pentanol solubility in water12 and the high tendency of pentanol to partition into direct micelles13 strongly suggest that in the reverse micelles pentanol is solubilized essentially in the interfacial film. (12) Aveyard, R.; Mitchell, R. W. J. Chem. Soc., Faraday Trans. 1 1969, 65, 2645. (13) The partition constant for the process POH(water) f POH(direct micelles) is ∼36 for DTAB, see: Inglese, A.; De Lisi, R.; Milioto, S. J. Phys. Chem. 1996, 100, 2260.
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Acknowledgment. The authors express their gratitude to Maura Monduzzi, Andrea Ceglie, and Marcello Giomini for their continuous encouragement and scientific support. The financial support of MIUR of Italy (PRIN 2003 NANOSCIENZE PER LO SVILUPPO DI NUOVE
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TECNOLOGIE) and of Consorzio Interuniversitario per lo sviluppo dei Sistemi a Grande Interfase (CSGI-Firenze) is acknowledged. LA0485125
