Langmuir 1997, 13, 4817-4820
4817
Measurement of the Partition Coefficient of Surfactants in Water/Oil Systems F. Ravera,† M. Ferrari,† L. Liggieri,*,† R. Miller,‡ and A. Passerone† Istituto di Chimica Fisica Applicata dei MaterialisCNR, via De Marini 6, 16149 Genova, Italy, and Max-Plank-Institut fu¨ r Kolloid und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin, Germany Received December 10, 1996. In Final Form: June 10, 1997X The partition coefficients between water and hexane of some n-alkyldimethylphosphine oxides (CnDMPO) and octylphenyl poly(ethylene glycol) ethers (Triton X-100 and Triton X-405) and of one poly(oxyethylene) cetyl ether (C16E20) have been determined by using an indirect technique based on the measurement of the surface tension of the aqueous surfactant solution after equilibration with the second liquid phase. Though some of the surfactants studied have been described in the past as insoluble in alkanes, the results show that at monomeric concentrations, most of them have a non-zero value of the partition coefficient. These results are particularly important when dynamics adsorption phenomena at liquid-liquid interfaces are concerned.
1. Introduction In two immiscible liquids with a common solute, the ratio between the equilibrium concentrations is given by the partition or distribution coefficient kp. By writing the equilibrium conditions for these systems, the expression of kp can be derived in terms of thermodynamic parameters. In fact, for a solute in two liquids R and β, under the hypothesis of dilute and ideal solutions, the equality of the chemical potentials in the two phases gives the ratio between the equilibrium concentrations cR and cβ1
(
)
cR vR µ0R - µ0β ) exp ) kp cβ vβ RT
(1)
where vR and vβ are the molar volumes, µ0Rand µ0β the standard chemical potentials, and R and T are the gas constant and the absolute temperature. Though this parameter is essentially linked to the solution bulk properties, its value may play an important role in dynamic transport processes involving a solute with amphiphilic properties and liquid-liquid surfaces. For example, in adsorption and diffusion processes in water-oil systems, the knowledge of the kp value is fundamental in interpreting the experimental data.2-7 For these kinds of systems, the hypothesis of ideal solution is usually satisfied because the solutions are very diluted. Then, at least for monomeric solutions, i.e., below the critical micellar concentration (cmc), the equilibrium concentration ratio is constant at constant temperature. However, because of the very low bulk concentrations of the surfactant solutions, the common experimental †
Istituto di Chimica Fisica Applicata dei MaterialisCNR. Max-Plank-Institut fu¨r Kolloid und Grenzfla¨chenforschung. X Abstract published in Advance ACS Abstracts, August 1, 1997. ‡
(1) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic: London, 1993; Vol. I, p 2.68. (2) Miller, R.; Loglio, G.; Tesei, U. Colloid Polym. Sci. 1992, 270, 598. (3) Ravera, F.; Liggieri, L.; Passerone, A.; Steinchen, A. J. Colloid Interface Sci. 1994, 163, 309. (4) MacLeod, C. A.; Radke, C. J. Colloid Interface Sci. 1994, 166, 73. (5) Fainerman, V. B.; Zholob, S. A.; Miller, R. Langmuir 1997, 13, 283. (6) Ferrari, M.; Liggieri, L.; Ravera, F.; Amodio, C.; Miller, R. J. Colloid Interface Sci. 1997, 186, 40. (7) Liggieri, L.; Ravera, F.; Ferrari, M.; Passerone, A.; Miller, R. J. Colloid Interface Sci. 1997, 186, 46.
S0743-7463(96)02096-3 CCC: $14.00
techniques based on chemical analysis may not be used in evaluating kp. The aim of this paper is to propose a particular experimental procedure to measure the partition coefficient of surfactants. This technique utilizes the surface properties of one of the two phases for estimating its bulk concentrations. This method has been applied to some common surfactants in the water-hexane system, and the experimental results are presented in the following sections. Moreover, the limits of the applicability of this technique are shown and the measurement errors of these experimental data are critically evaluated. 2. Experimental Methods For the sake of simplicity, the treatment is referred to surfactants in water-hexane systems, but it can be generalized to all water-oil systems. Thus, in the present study, kp is assumed to be the ratio between the concentration in hexane, ch; and in water, cw, i.e.,
kp )
ch cw
(2)
Firstly, equilibrium surface tension measurements of the solutions made with water saturated with hexane are taken as a function of the surfactant concentration. These measurements allow the adsorption isotherm of such systems to be determined. Afterwards, a volume Vw of aqueous solution with initial concentration cw0 is brought in contact with a volume Vh of pure hexane for a time long enough to obtain two phases at the partition equilibrium: the surfactant transfer to the initially pure liquid has the effect of depleting the aqueous solution. It has been observed that the time needed for this equilibration, in the experimental conditions of this work, is about 1 day for most of the surfactants used. Then, the equilibrium surface tension γeq of the depleted solution is measured and cw is calculated from its surface tension value using the previously obtained cw-γeq isotherm as a calibration curve. Obviously, this extrapolation of cw is possible only if it is below the cmc; otherwise, the surface tension measurement does not give any information about the solution concentration. Finally, from the surfactant mass balance, kp can be expressed in terms of known quantities, as
kp )
(
)
Vw cw0 -1 V h cw
© 1997 American Chemical Society
(3)
4818 Langmuir, Vol. 13, No. 18, 1997
Figure 1. Dynamic surface tension signals of C12DMPO at hexane-saturated water/air with the aim to obtain the equilibrium values. The bulk concentrations are those reported in Figure 3. The surface tension measurements are performed by the pendant drop method using ASTRA (automatic surface tension real-time acquisition): an automatic apparatus based on the drop shape technique8,9 developed by us. It allows the coordinates of the drop profile to be acquired by using a CCD camera connected to a Frame Grabber board in a 486 PC. At present, the minimum achieved sampling time is 0.5 s in a time scale ranging from minutes to hours. At the end of the whole acquisition, the surface tension value of each drop profile is calculated from the stored coordinates by fitting the Gauss-Laplace equation, which describes the theoretical drop shape. An improved version of the Maze-Burnet algorithm10 is used which requires less than 2 s for the calculation of each data point. The accuracy in the surface tension measurements achieved by ASTRA is of the order of 0.1 mN/m, with a reproducibility of better than 0.05 mN/m. The experimental setup consists of a thermostatic glass cell with a volume of about 30 cm3 in which a drop of the aqueous solution under study is formed at the tip of a capillary tube by a gas-tight syringe (Hamilton). Capillary tubes are made of Teflon in order to avoid the drop spreading. The external diameter of this tube, of about 5 mm, is used as a reference length in calculating the magnification coefficient for each shape acquisition. Because of these unique properties, ASTRA is particularly suitable for dynamic interfacial tension measurements.6,7 In fact, in this study, the evaluation of the equilibrium data is made on the basis of the dynamic behavior of the surface tension. Figures 1 and 2 show some examples of dynamic surface tension signals in which the achievement of the adsorption equilibrium is evident.
3. Accuracy of the Method Since this technique is based on the utilization of the adsorption isotherm curve to evaluate the bulk concentration, the necessary condition for the application of this method is that the solute behaves as a surfactant at least in one of the two liquids. For the same reason, the concentration range in which kp can be determined has an upper limit in the cmc. For very low concentrations, the evaluation of the surface isotherm with suitable accuracy through the equilibrium surface tension measurements presents some difficulties due, principally, to the length of time needed for the equilibration and to the effects of the adsorption onto the solid walls of the container. Thus, an operative lower limit for the accessible concentration range exists, which in the present study is about 10-9 mol/cm3. (8) Liggieri, L.; Passerone, A. High Temp. Technol. 1989, 7, 82. (9) Liggieri, L.; Ravera, F.; Passerone, A. J. Colloid Int. Sci. 1994, 169, 238. (10) Maze, C.; Burnet, G. Surface Sci. 1971, 24, 335.
Ravera et al.
Figure 2. Same as Figure 1 for Triton X-100. The bulk concentrations are those reported in Figure 4.
From eq 3, the error on the partition coefficient can be calculated by taking into account the principal sources of error arising from the direct measurements of quantities like liquid volume, mass of surfactants, and surface tension. This error is ∆kp )
[
(
) (
)]
Vw cw0 - cw ∆Vw ∆Vh cw0 ∆cw0 ∆cw + + + Vh cw Vw Vh cw cw0 cw
(4)
where the error on the extrapolated concentration is ∆cw )
| |
∂cw |∆γeq ∂γeq
(5)
which is calculated from the best-fit γeq-cw isotherm. The errors on the parameters defining this curve have been assumed negligible with respect to that of the equilibrium surface tension. This latter error is actually larger than the accuracy provided by ASTRA because, especially with commercial surfactants, an uncertainty about the achievement of the adsorption equilibrium must be taken into account due to the presence of some impurities. Hence, a realistic estimation of this error is within 0.2-0.5 mN/ m, depending on the surfactant. Moreover, eq 5 means that the measurement is more accurate if the absolute value of the γeq-cw curve slope at the concentration studied is higher: this is usually true in the range of concentrations close to the cmc. Thus, this source of error depends on the specific surfactant and on the concentration range considered, and the resolution of the measurement is then limited by these intrinsic characteristics of the system. The relative error on the initial concentration (∆cw0/ cw0) depends on the technique adopted to measure the surfactant mass and the liquid volumes. In the present study, this error has been calculated to be in the range (1.5-1.7) × 10-2. The relative errors on the volumes of the two liquid phases, Vh and Vw, are also dependent on the specific direct measurement and here are about 5 × 10-3. Since ∆kp strongly depends on the ratio between the water and the hexane volumes used for the equilibration, its value can be adjusted in order to improve the accuracy of the measurement. However, if this ratio is very small, with high kp, the concentration in the depleted aqueous phase becomes too low, causing other disadvantages: for example, the system may go out of the range available by the isotherm or it may be in a range of low isotherm slope with the consequent increasing of the relative errors on cw. Moreover, if the volume of the initially pure phase is
Partition Coefficient of Surfactants in Water/Oil
Langmuir, Vol. 13, No. 18, 1997 4819
Figure 3. Surface isotherm at T ) 20 °C for CnDMPO at hexane-saturated water/air: n ) 10 (b), n ) 12 (9); n ) 13 (2).
large, the achievement of the partition equilibrium may require a very long time. In conclusion, an optimization of the experimental parameters, like the liquid volumes and the concentration range, on the basis of the characteristics of the studied surfactant is useful to minimize the error. 4. Materials The hexane was of spectrophotometric grade purity by Merck-Uvasol and used without further purification. The water used for the surfactant solutions was produced by a Millipore Milli-Q purifier. The surfactants used were as follows: n-alkyldimethylphosphine oxides, CnDMPO, with different alkyl chain lengths, n ) 10, 12, 13; octylphenyl poly(ethylene glycol) ethers with two different ethoxy units, Triton X-100 and Triton X-405; and one poly(oxyethylene) cetyl ether, C16E20 (Brij 58). The high-purity-grade phosphine oxides were purchased from Gamma-Service Berlin. The Triton’s were gas chromatographic grade and were purchased from Merck, while C16E20 was from Sigma. All these surfactants were used as received without further purification. All parts of the experimental cell were cleaned with chromic acid and rinsed several times with distilled water and then with Milli-Q water. 5. Results and Discussion For all phosphine oxides and for Triton X-100, the Langmuir isotherm fits well the experimental data in the concentration range considered (Figures 3 and 4). Thus, in this case, an explicit expression of cw as a function of γeq exists
[
cw ) aL exp
γ0 - γeq Γ∞RT
-1
]
(6)
where γ0 is the surface tension of the pure solvent and aL and Γ∞ are the Langmuir-Szyszkowsky constant and the saturation adsorption, respectively. These two latter parameters are evaluated by the fitting procedure on the equilibrium values. In Table 1, the best-fit values obtained with this procedure are reported. In a range of very low concentrations, evaluating the surface isotherm through the experimental equilibrium data presents some difficulties as explained above, while sometimes an overlapping of different relationships, corresponding to different thermodynamic states, is necessary to describe the correct adsorption isotherm.11 (11) Lunkenheimer, K.; Hirte, R. J. Phys. Chem. 1992, 96, 8683.
Figure 4. Surface isotherm at T ) 20 °C for hexane-saturated water/air, with Triton X-100 (b),Triton X-405 (2), and C16E20 (9). Table 1. Best-Fit Langmuir Parameters, Corresponding to the Theoretical Curves of Figures 3 and 4 (b), for Surfactants in a Hexane-Saturated Water/Air System at T ) 20 °C surfactant
aL, mol/cm3
Γ∞, mol/cm2
C10DMPO C12DMPO C13DMPO Triton X-100
4.15 × 10-8 7.34 × 10-9 1.24 × 10-8 1.40 × 10-9
3.74 × 10-10 4.54 × 10-10 9.83 × 10-10 3.20 × 10-10
Table 2. Measured Partition Coefficient kp for Different Surfactants in Water/Hexane, at T ) 20 °C surfactant
kp
cw, mol/cm3
C10DMPO C12DMPO C13DMPO Triton X-405 Triton X-100 C16E20
1.30 ( 0.05 7.7 ( 0.3 34.7 ( 0.6
