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Association, Partition, and Surface Activity in Biphasic Systems Displaying Relaxation Oscillations Vincent Pradines, Rawad Tadmouri, Dominique Lavabre, Jean-Claude Micheau, and Ve´ronique Pimienta* Laboratoire des IMRCP, UMR au CNRS N° 5623, UniVersite´ Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex, France ReceiVed June 19, 2007. In Final Form: August 3, 2007 Several biphasic systems giving rise to periodical Marangoni instability have been analyzed from the point of view of the physicochemical properties of the involved compounds. In each case, the compound at the origin of the oscillatory behavior has been identified: the reactant cetyltrimethylammonium bromide (CTAB) for the CTAB/picric acid (PH) system and the product of reaction dodecyl sulfate tetraalkylammonium (TAADS) for the sodium dodecyl sulfate/tetraalkylammonium bromide (SDS/TAAB) system. The properties of the latter system have been varied progressively by increasing the chain length of the tetraalkylammonium ion. Oscillations were observed whichever the direction of transfer (from water to dichloromethane and from dichloromethane to water). The comparison of the dynamic interfacial tension, recorded during transfer, to equilibrium measurements shows that the instability is favored when partition is highly in favor of the organic phase. The main criteria for the appearance of the instability are a high surface activity and a low interfacial adsorption.
1. Introduction Surface active solute transfer induces solutal Marangoni instability in biphasic systems. This instability, triggered by surface tension gradients, can give rise to a wide variety of dissipative structures such as regular convective cells,1 interfacial deformation,2 interfacial turbulences,3 or emulsification.4 The development of such instabilities can considerably intensify mass transfer and thus be determining for extraction processes.4 In parallel to numerous experimental observations, theoretical studies were aimed to establish criteria predicting the instability onset. The first study was performed by Sterling and Scriven5 who applied the linear stability analysis to systems where a solute is transferred through a nondeformable interface between two semiinfinite liquid layers. According to these authors, the instability can develop in systems far from partition equilibrium and its appearance depends mainly on the solvent properties, on the surface activity of the solute, and on the formation of critical solute concentration gradients in the normal to the interface direction. Because of the dependence on solvent properties (solute diffusion coefficient and kinematic viscosity), the direction of solute transfer could, in some cases, be determining. However, the criteria proposed by Sterling and Scriven could not cover the numerous experimental observations, and several authors extended the initial model by taking into account additional processes such as limiting adsorption/desorption,6 thermal effects,7 gravity,8 or interfacial reaction.9 In most cases, the addition of supplementary effects led to the prediction of a more extended domain * To whom correspondence should be addressed. E-mail: pimienta@ chimie.ups-tlse.fr. Telephone: +33 5 61 55 62 75. Fax: +33 5 61 55 81 55. (1) Orell, A.; Westwaster, J. W. AIChE J. 1962, 8, 350. (2) Kai, S.; Muller, S. C.; Mori, T.; Miki, M. Physica D 1991, 50, 412. (3) Maroudas, N.; Sawistowski, H. Chem. Eng. Sci. 1996, 51 (15), 3755. (4) Sherwood, T. K.; Wei, J. C. Ind. Eng. Chem. 1957, 49 (6), 1030. (5) Sterling, C. V.; Scriven, L. E. AIChE J. 1959, 5, 514. (6) Hennenberg, M.; Sanfeld, A.; Bish, P. M. AIChE J. 1981, 27, 1002. (7) Perez De Ortiz, E. S.; Sawisrowski, H. Chem. Eng. Sci. 1975, 30, 1527. (8) Sørensen, T. S.; Hennenberg, M.; Sanfeld, A. J. Chem. Soc., Faraday Trans. 2 1980, 76, 1170. (9) Mendes-Tatsis, M. A.; Perez de Ortiz, E. S. Chem. Eng. Sci. 1996, 51, 3755.
of development of the instability. Unfortunately, the proposed stability criteria are difficult to evaluate for actual systems that combine several effects. Among the various experimental observations, a particular behavior has been reported for systems involving surfactant molecules. In these systems, the instability appears only transiently, periodically arising and fading. This phenomenon gives rise to oscillations of the interfacial tension and of the electrical potential. Such oscillations have been recorded in various systems of different geometries. For instance, solubilization from a pointlike source or the local injection of a surfactant solution in a water bulk can give rise to oscillations of the interfacial tension whether the water phase is in contact with air10 or with an organic phase.11,12 Kovalchuck et al.13 have performed a comprehensive study on both experimental and theoretical levels of the periodic development of convective motions observed during the dissolution of a droplet of surfactant formed at the tip of a capillary immersed in an aqueous phase. The oscillations recorded at the water/air (or oil) interface showed a particular asymmetrical shape showing an abrupt decrease of the surface tension followed by a gradual recovery. The drop of the interfacial tension (that means the increase of the concentration of adsorbed surfactant) was correlated to the convective motion, while the relaxing increase corresponded to the diffusive regime. The theoretical model these authors have improved in successive studies gives, for the first time, an explanation for the periodical nature of the instability that would be related to a wall effect. According to them, the interaction of the direct and reflected longitudinal waves could suppress the instability development. A similar behavior has also been reported in liquid/liquid systems involving mass transfer of a surfactant. The most famous one was discovered by Nakache and Dupeyrat.14 These authors (10) Kovalchuk, M. N.; Vollhardt, D. J. Phys. Chem. B 2000, 104, 7987. (11) Yui, H.; Ikezoe, Y.; Takahashi, T.; Sawada, T. J. Phys. Chem. B 2003, 107, 8433. (12) (a) Kovalchuk, M. N.; Vollhardt, D. J. Phys. Chem. B 2005, 109, 22868. (b) Kovalchuk, M. N.; Vollhardt, D. Colloids Surf. A 2006, 291, 101. (13) Kovalchuk, M. N.; Vollhardt, D. AdV. Colloid Interface Sci. 2006, 120, 1. (14) Nakache, E.; Dupeyrat, M. Bielectrochem. Bioenerg. 1978, 5, 134.
10.1021/la7018154 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/10/2007
Properties of Oscillating Biphasic Systems
observed periodic interfacial deformation together with oscillations of the electrical potential and interfacial tension in a system in which the transfer of a surfactant is coupled to a chemical reaction. In their system, an aqueous solution of a cationic surfactant (alkyltrimethylammonium halogenide) overlays an organic solution (nitrobenzene or nitroethane) of picric acid. Although this system was, later on, studied by numerous authors in various situations (three layer system in a U-tube15 or in two concentric tubes,16 or adding supplementary compounds17), no consensus was achieved to explain the origin of the oscillations.13 Meanwhile, other systems involving compounds with similar properties were also proposed18 without, however, bringing new insight. In this work, we have analyzed in detail the physicochemical properties of two systems (cetyltrimethylammonium bromide (CTAB)/picric acid (PH)19 and sodium dodecyl sulfate (SDS)/ tetraalkylammonium bromide (TAAB)) with the purpose to highlight their common features and specify the main processes taking place. In the first part, we will recall our results on the first system, CTAB/PH, and analyze them in regard to the criteria proposed by the theoreticians. We have shown, in particular, that for this system oscillations appear even in the absence of picric acid.20 The analyses of the properties of the SDS/TAAB system have shown, at first insight, great differences from the former one, but we will show that a subsystem with similar properties can also, in this case, be deduced from our findings. Moreover, for the SDS/TAAB system, we progressively varied the properties of the involved compounds by increasing the chain length of the quaternary ammonium salt from tetraethylammonium bromide (TEAB) to tetrabutylammonium bromide (TBAB). We will analyze the recorded oscillations in relation to the variation of the physicochemical properties of the series. 2. Experimental Section All chemical reagents used were of analytical grade. Cetyltrimethylammonium bromide (CTAB, Aldrich, g 99%), CH2Cl2 (Aldrich, HPLC grade), tetraethylammonium bromide (TEAB, Acros Organic, 99+%), tetrapropylammonium bromide (TPAB, Acros Organic, 98+%), tetrabutylammonium bromide (TBAB, Acros Organics, 99+%), and sodium dodecyl sulfate (SDS, Prolabo, 98%) were used as received. All the solutions were prepared with ultrapure water (resistivity > 16 MΩ cm). TAADSs were extracted by CH2Cl2 from an equimolar solution of SDS and TAABs. The organic phase was then washed with water and dried over sodium sulfate. CH2Cl2 was finally evaporated. TEADS (yield 70%) was obtained as a white powder, while TPADS (yield 90%) and TBADS (yield 90%) were obtained as colorless viscous liquids at room temperature. Purity was verified by mass spectroscopy, and sodium and bromide ions could not be detected. Temporal interfacial tension measurements were performed as described in ref 20. The organic phase and aqueous phase (15 mL each) are introduced in a glass beaker of 31 mm inner diameter. (15) (a)Yoshikawa, K.; Matsubara, Y. J. Am. Chem. Soc. 1983, 105, 5967. (b) Szpakowska, M.; Czaplicka, I. B.; Nagy, O. J. Phys. Chem. A 2006, 110, 7286. (16) Takahashi, S.; Tsuyumoto, I.; Kitamori, T.; Sawada, T. Electrochim. Acta 1998, 44, 165. (17) Yoshidome, T.; Higashi, T.; Mitsushio, M.; Kamata, S. Chem. Lett. 1998, 855. (18) (a) Yoshikawa, K.; Masaru, S.; Satoshi, N.; Maeda, S. Langmuir 1988, 4, 759. (b) Arai, K.; Fukuyama, S.; Kusu, F.; Takamura, K. Electrochim. Acta 1995, 40, 2913. (c) Li, H.; Wang, M. Chem. Phys. Lett. 2000, 330, 503. (d) Maeda, K.; Hyogo, W.; Nagami, S.; Kihara, S. Bull. Chem. Soc. Jpn. 1997, 70, 1505. (e) Maeda, K.; Nagami, S.; Yoshida, Y.; Ohde, H.; Kihara, S. J. Electroanal. Chem. 2001, 496, 124. (f) Shioi, A.; Kumagai, H.; Sugiura, Y.; Kitayama, Y. Langmuir 2002, 18, 5516. (g) Suzuki, H.; Tsuchiya, Y. Physica D 1995, 84, 276. (19) Pimienta, V.; Lavabre, D.; Buhse, T.; Micheau, J. C. J. Phys. Chem. B 2004, 108, 7331. (20) Lavabre, D.; Pradines, V.; Micheau, J. C.; Pimienta, V. J. Phys. Chem. B 2005, 109, 7582.
Langmuir, Vol. 23, No. 23, 2007 11665 Surface tension measurements were performed using a small cylinder (2.8 mm diameter; 10 mm high) made of high-density polyethylene and connected to a microbalance. The cylinder was lowered to the liquid/liquid interface and pulled at its maximum before the breakage of the interfacial film. The absolute error was about (1 mN m-1; however, the error involved in the amplitude of the oscillations was estimated to be around (0.1 mN m-1. The potential was measured with two Hg/Hg2Cl2 electrodes placed in beakers containing saturated KCl solution and connected by two salt bridges to the two phases. Data were recorded using a high impedance multimeter (Agilent 34970A, input resistance > 10 GΩ). The microbalance and multimeter were connected to a personal computer. Equilibrium interfacial tension measurements at the water/CH2Cl2 interface were performed with a pendant drop tensiometer (KRUSS GmbH, model DSA 10-MK2, Germany) at room temperature (20 °C). Solutions were pre-equilibrated for 12 h. A drop of the CH2Cl2 solution was formed in the aqueous phase. The size and shape of the drop formed at the tip of a needle (Ø ) 0.5 mm) fixed on a glass syringe were analyzed by the Drop Shape Analysis software. The absolute error was estimated to be about (0.2 mN m-1. During an experiment, the blank was repeated several times with pure solvents to check any contamination of the syringe by the surfactants. The conditions for the quantitative analysis of TAADSs by electrospray ionization liquid chromatography mass spectrometry (ESI-LC-MS) are similar to the ones used for TAABs in ref 23. Analysis by mass spectroscopy in the multiple reaction monitoring (MRM) mode was performed, as in a previous study, on the transition corresponding to the cation TAA+. A supplementary transition corresponding to the dodecyl sulfate anion was also considered: 265 f 96 representing the precursor ion and product ion of SD-.
3. Systems Involving CTAB Transfer 3.1. Nonreactive System. To our knowledge, Bekki et al.21 described the only example, in the literature, in which the transfer of a long chain alkyltrimethylammonium salt gave rise, in a biphasic system, to a periodical instability. These authors have observed a quasi-periodical motion of a nitroethane lens located on the surface of a water solution of dodecyltrimethylammonium bromide (DTAB). The authors pointed out the fact that the instability was observed only when DTAB diffused from the aqueous to the organic phase (for which partition is largely in favor) and for DTAB concentrations below (or close to) the critical micellar concentration (cmc). According to the authors, for higher concentrations, the incompressible condensed monolayer adsorbed at the interface prevents the formation of interfacial tension gradients. In systems in which the two layers entirely overlay (in a beaker or in a U-tube), the authors generally specify that oscillations were not observed in the absence of a second reactant (picric acid) dissolved in the organic phase. In fact, in contradiction with the literature and with our previous observations in the U-tube configuration,19 we have obtained, after an induction period that lasted from 0.5 to 1 h, regular oscillations of the interfacial tension and electrical potential when CTAB is transferred from water to dichloromethane20 in a two phase system (Figure 1). The oscillations lasted for 5 h and were detected for a CTAB initial concentration in the aqueous phase ranging from 10-3 to 2 × 10-2 mol L-1. The oscillations were not completely reproducible, but some qualitative features could be drawn up from our observations: the period became longer with increasing initial concentration (from 150 to 350 s), while the amplitude did not vary significantly with a typical value of about 1 mN m-1. (21) Bekki, S.; Nakache, E.; Vignes-Adler, M.; Adler, P. M. J. Colloid Interface Sci. 1990, 140, 492.
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ABAQ a A+AQ + B-AQ ABAQ a ABORG ABORG a A+ORG + B-ORG
Figure 1. Simultaneous measurement of interfacial tension (γ) and electrical potential (U ) UAQ - UORG) during the transfer of CTAB from water to CH2Cl2. [CTAB]0 ) 5 × 10-3 mol L-1, and diameter of the beaker L ) 31 mm. The period increases with time from 180 to 350 s, and amplitude ≈ 1 mN m-1.
During an experiment, the period also increased with time (Figure 1). During the induction period, the interfacial tension (γ) increased until an upper threshold value at which the oscillations started was reached. This value decreased with initial concentration from 12 mN m-1 for the lower concentration to 8 mN m-1 for the highest concentration. We have also tested the effect of the diameter of the beaker. For a larger interface size (L ) 62 mm), no difference was observed; however, when the diameter was decreased to L ) 21 mm, the period (60 s) and amplitude (0.12 mN m-1) decreased. For a further reduction of the diameter (L ) 15 mm), the oscillations completely disappeared. This observation could explain why we did not observe any oscillations in the U-tube configuration, as the diameter of the contact interface was also of 15 mm. We have taken advantage of a particular property of CTAB, that is, the relatively high value of the temperature at the Krafft point (25 °C), and profited from the presence of crystals to visualize the convective flows.20 Hence, we could correlate the appearance of the movements to the interfacial tension and electrical potential oscillations. The sudden drop corresponded to the convective stage while the movements stopped, that is, the diffusive regime was restored, during the slow increase of the interfacial tension. The shape of the electrical signal was quite different from the one obtained by surface tension measurements. A peak of potential (in the reverse direction to the expected evolution) was correlated to the moving stage of the instability. To account for the electrical potential data, two components needed to be taken into account. In the quiet stage, the signal was comparable to surface tension: the main contribution resulted from the electrical double layer. In the convective stage, a supplementary contribution due to streaming potential22 was at the origin of the observed peaks. Indeed, all the required properties pointed out in the literature were fulfilled in this case. As indicated by the physicochemical properties of the constituents of the system, the appearance of the instability was foreseeable. In ref 23, we have reported a detailed study of the partition of the compounds involved in the present work. The collected equilibrium experimental data were fitted using a three-step model taking into account possible dissociation in the two phases and partition of the molecular species. (22) Davies, J. T.; Rideal, E. K. Interfacial phenomena, 2nd ed.; Academic Press: New York, 1963. (23) Pradines, V.; Despoux, S.; Claparols, C.; Martins, N.; Micheau, J. C.; Lavabre, D.; Pimienta, V. J. Phys. Org. Chem. 2006, 19, 350.
(1; Kd1) (2; KP) (3; Kd2)
where AQ stands for water and ORG stands for CH2Cl2, A and B are the cation (here CTA+) and the anion (here Br-), respectively, Kd1 and Kd2 are the dissociation constants in water and CH2Cl2, respectively, and Kp is the partition coefficient. For CTAB, which was found to undergo dissociation only in the aqueous phase (Kd2 ) 0), partition was highly in favor of the organic phase. In the concentration domain for which the oscillations were detected, 87 to 97% of the CTAB transferred to CH2Cl2 at equilibrium. Interfacial tension at the water/CH2Cl2 interface at partition equilibrium is reported in Figure 2. Interfacial tension decreases from 27 to 1 mN m-1 until a plateau accounting for the formation of aggregates is reached. These aggregates are formed in the aqueous phase, which implies that only the surfactants solubilized in this phase contribute to the reduction of the interfacial tension.25 That is why we plotted the interfacial tension against the concentration of CTAB in the water phase at partition equilibrium.23 The critical concentration (that we will call the critical aggregation concentration, cac, to differentiate it from the cmc determined in pure water (Table 3)) was obtained at 2.3 × 10-4 mol L-1. This value, about 3.5 times lower than the classical cmc (8 × 10-4 mol L-1), accounts for a well-known phenomenon which is the lowering of the critical aggregation concentration observed by the addition of an hydrophobic compound in a surfactant solution.26 This effect is, in our case, due to the solubilization of CH2Cl2 in the water phase. This observation shows that the comparison to the cmc of the initial concentration range of surfactant in the aqueous phase in the domain of development of the instability is, in fact, meaningless, as the cmc is notably modified by the presence of the organic solvent. The threshold γ values at which the instability was triggered (12-8 mN m-1) are indicated in Figure 2 by the striped domain. The conditions for the appearance of the instability arise during the diffusive stage (during the induction period and after each drop of γ). Normal gradients building up in the diffusive regime can be schematized as follows: For simply structured surfactants such as CTAB, the kinetic of adsorption is diffusion controlled.27,28 A local equilibrium can be assumed between the surface layer and the concentration at the subsurface ([CTAB]T,AQ,s in Scheme 1) on the aqueous side.21 The concentration at the subsurface, giving rise to oscillations, can be estimated from the equilibrium plot in Figure 2 by the projection of the limits of the striped domain on the abscissa. The concentration range, indicated by the arrows, gives an evaluation of [CTAB]T,AQ,s. When the oscillations start, if we consider that the bulk concentration ([CTAB]T,AQ) is still close (24) CTAB is almost fully dissociated in water. (25) For CTAB, the formation of reverse micelles in the organic phase implies a cosurfactant. Moreover, the infrared spectra of the organic phases show that the quantity of water solubilized does not vary with the concentration of surfactant, contrary to what is expected in the presence of reverse micelles. Aggregation occurs then in the aqueous phase. The plateau is due to a constant concentration of monomers in this phase. In the organic phase, the concentration of monomers at partition equilibrium increases continuously with initial concentration, and thus, the monomers do not contribute to the interfacial tension. (26) Solubilization in surfactant aggregates; Christian, S. D., Scamehorn, J. E., Eds.; Marcel Dekker, Inc.: New York, 1995. (27) Deshikan, S. D.; Bush, D.; Eschenazi, E.; Papadopoulos, K. D. Colloids Surf. A 1998, 136, 133. (28) Miller, R.; Kretzschmar, G. AdV. Colloid Interface Sci. 1991, 37, 97.
Properties of Oscillating Biphasic Systems
Figure 2. Water/CH2Cl2 interfacial tension versus total concentration in the aqueous phase calculated according to ref 23 at partition equilibrium. The subscript T stands for total concentration, that is, associated plus dissociated form (here [CTAB]T,AQ ≈ [CTA+]AQ).24 The horizontal striped domain corresponds to the threshold interfacial tension at which the oscillations start; the limits of the related aqueous subsurface concentration ([CTAB]T,AQ,s in Scheme 1) are indicated by the arrows. Scheme 1. Sketch of the Diffusion Bulk Concentration Profiles as a Function of the Distance from the Interface (x ) 0) during Transfer of CTAB: (A) from AQ to ORG and (B) from ORG to AQa
a The subscript T stands for total concentration in the bulk aqueous phase, and the subscript s refers to the concentration at the subsurface. Partition is assumed at the interface: [CTAB]ORG,s/[CTAB]T,AQ,s ) Kp. The concentration of adsorbed surfactant (surface excess) is not represented.
to the initial concentration [CTAB]0, the ratio [CTAB]T,AQ/ [CTAB]T,AQ,s between the bulk and the subsurface can be estimated. It ranges from 20 to 200 in the domain giving rise to oscillations. The system does, moreover, fulfill the criteria proposed by Sterling and Scriven5 who predicted the instability for the solute diffusing out of the phase in which its diffusivity is lower
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Figure 3. Oscillations observed during transfer from CH2Cl2 to water. [CTAB]0 ) 5 × 10-3 mol L-1.
(DCTAB,H2O ) 4.2 × 10-6 cm2 s-1 < DCTAB,CH2Cl2 ) 1.2 × 10-5 cm2 s-1)29 and kinematic viscosity is higher (νH2O ) 9.5 × 10-3 cm2 s-1 > νCH2Cl2 ) 3.2 × 10-3 cm2 s-1). To this point, our observations seem to match those of the theoretical studies. However, and although Sterling an Scriven predicted a stable transfer in the reverse direction, we observed small but clear oscillations when CTAB (5 × 10-3 mol L-1) was initially dissolved in the organic phase. These small amplitude (0.3 mN m-1) oscillations showed a shorter period (30 s) and lasted only for some minutes (Figure 3). However, the oscillatory pattern was very similar to the one observed in previous conditions. In this direction of transfer, the other requirements for the instability to appear are also less favorable. Partition is no longer in favor of the receiving phase, and only 6% of CTAB would be transferred to the aqueous phase at equilibrium. The diffusion profile expected for transfer from ORG to AQ is represented in Scheme 1b. The gradients are smaller. In the aqueous phase, the maximum concentration is found at the interface. In Scheme 1, [CTAB]T,AQ,s has the same value whichever the direction of transfer. This is verified in the simplest case when the diffusion coefficients are identical in both phases. In our case, faster diffusion in the organic phase would lead, in fact, to a slightly higher value of [CTAB]T,AQ,s for the transfer from ORG to AQ. This is in agreement with the low interfacial tension (around 4 mN m-1) at which the oscillations were triggered. The interface gets closer to saturation, disfavoring the development of the instability. 3.2. Reactive System: CTAB/Picric Acid. In the same experimental conditions as those for the transfer of CTAB from the aqueous to the organic phase, the addition of picric acid in the organic phase led to similar convective fluxes. However, they were more intense and new regimes appeared. We could observe small rotating waves deforming the interface and, in some cases, permanent turbulences in the aqueous phase (switches to diffusive regimes are not observed anymore). In the U-tube configuration (i.e., for a smaller diameter), picric acid was essential to obtain oscillations but in this case no movement could be detected by eye. In the presence of picric acid, the organic phase became gradually yellow while the aqueous phase remained uncolored. This implies that, at the concentrations used, although its partition is in favor of the aqueous phase,23 picric acid did not enter this phase: it reacted near the interface and was brought back to the (29) Calculated using the Wilke and Chang empirical correlation method; see Reid, R.; Sherwood, T. K. The properties of Gases and Liquids; McGraw-Hill: New York, 1958; p 549.
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organic phase. The yellow compound detected in the organic phase was cetyltrimethylammonium picrate (CTAP).30
CTA+ + P- a CTAP
(4)
When picric acid reaches the aqueous phase, it is quickly hydrolyzed and the resulting picrate anion associates with CTA+ to give CTAP. This compound was found to be very hydrophobic, almost insoluble in water, and slightly surface active.31 If we focus on the modifications induced by the reaction on the diffusive profile of CTAB, the formation of the ion pair would, according to previous remarks on the nonreactive system, favor the appearance of the instability. Partition of the surfactant is increased: it undergoes spontaneous transfer and also extraction by means of the ion pair CTAP. At equilibrium, 100% of the surfactant is expected in the organic phase. The concentration gradient of CTAB in the normal to the interface direction is increased. [CTAB]T,AQ,s is brought to a very low value by the conjugated effects of transfer and chemical reaction. The concentration of adsorbed surfactant is decreased, favoring the formation of interfacial tension gradients. Although the consideration of the concentration profile of CTAB is certainly not sufficient to explain the observed fluid dynamics (all the coupled processes taking place in the system should be taken into account), some features arise from it: long lasting regular oscillations seem to be, for the CTAB systems, favored when the system is initially far from equilibrium, inducing high normal gradients and moderate adsorption at the interface. To relate these observations to wider experimental results, we have decided to study in detail new systems involving, this time, an anionic surfactant.
4. Systems Involving Sodium Dodecyl Sulfate (SDS) Biphasic systems involving SDS and giving rise to such oscillatory instability are rather scarce in the literature. Sawada et al.32 observed sustained oscillations at the water/nitrobenzene interface by a continuous local injection of SDS in the aqueous phase. For systems in which initially homogeneous solutions are put into contact, oscillatory regimes were observed for aqueous SDS in the presence of a nitrobenzene solution of phenanthroline18c or an octanol solution of tetrabutylammonium bromide (TBAB).18b This last compound was used in the present study; however, to get a gradual variation of the physicochemical properties, we extended our investigations to the series of tetraalkylammonium bromides (TAABs) of shorter chain length (tetraethylammonium bromide (TEAB) and tetrapropylammonium bromide (TPAB)). These compounds that are frequently used as phase transfer catalysts are known to form hydrophobic ion pairs with anions in water.33 4.1. Reactive Systems. As in the previous system, we used dichloromethane as the organic solvent. TAAB solutions in CH2Cl2 were then carefully overlaid by an aqueous solution of SDS. The three systems, involving TEAB, TPAB, and TBAB, gave rise to oscillations (Figure 4). The oscillations were not as regular as those observed with CTAB. For the three compounds, irregular noisy oscillations were obtained at the beginning of the experiment, and then they became more regular (reported in Figure 4). The oscillatory pattern (30) Nakache, E.; Dupeyrat, M.; Vignes-Adler, M. J. Colloid Interface Sci. 1983, 94, 189. (31) Pimienta, V.; Etchenique, R.; Buhse, T. J. Phys. Chem. A 2001, 105, 10037. (32) Ikezoe, Y.; Ishizaki, S.; Takahashi, T.; Yui, H.; Fujinami, M.; Sawada, T. J. Colloid Interface Sci. 2004, 275, 298. (33) Portet, F. I.; Treiner, C.; Desbe`ne, P. L. J. Chromatogr., A 2000, 878, 99.
Figure 4. Oscillations of the interfacial tension and electrical potential in biphasic H2O/CH2Cl2 systems: (A) [SDS]0 ) 2 × 10-2 mol L-1 and [TEAB]0 ) 1.5 × 10-2 mol L-1; (B) [SDS]0 ) 10-2 mol L-1 and [TPAB]0 ) 10-2 mol L-1; and (C) [SDS]0 ) 10-2 mol L-1 and [TBAB]0 ) 10-2 mol L-1.
showed, as in previous systems, a fast decrease of the interfacial tension followed by a slower increase. The electrical potential data were perfectly symmetrical to the interfacial tension showing the only contribution of the electrical double layer (no streaming potential was detected). For TEAB, the oscillations (the amplitude of which was about 1 mN m-1) could last for more than 3 h. For TPAB and TBAB, the oscillations were detected for only about 1 h but their amplitude could reach 2-4 mN m-1. In every case, the concentrations used were around 10-2 mol L-1 for SDS and TAAB. These concentrations match with the upper values used in the CTAB/PH system. Whichever the TAAB used, the threshold interfacial tension value at which the oscillations were triggered varied from 6 to 15 mN m-1 without drawing out any clear tendency. One of the reasons could be, as we will see in the
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Table 1. Dissociation in Water (Kd1) and Water/CH2Cl2 Partition (Kp) Equilibrium Constants of the Three TAABs23 and Percentage of [TAAB]ORG in the Organic Phase at Partition Equilibrium for an Initial Aqueous Concentration (C0 ) 10-2 mol L-1) in Contact with the Same Volume of Organic Phasea
TEAB TPAB TBAB
Kd1/mol L-1
Kp
[TAAB]ORG at equilibrium for C0 ) 10-2 mol L-1 (%)
0.11 0.8 1.6
7.2 × 10-4 0.17 28
0 0.2 13
a Values of Kd are not tabulated because dissociation of these 2 compounds in the organic phase is negligible.
following, that two surfactants, whose relative concentrations vary with time, are involved, preventing any intuitive explanation. Moreover, during the oscillations, most of all for TPAB and TBAB, a mistlike emulsion gradually appearing at the interface may contribute to the decrease of the interfacial tension. 4.2. Physicochemical Properties of the Involved Compounds. 4.2.1. The Surfactant: SDS. 4.2.1.1. Partition. SDS is not soluble in dichloromethane, and no spontaneous transfer occurs in the biphasic system. This constitutes the first important difference with CTAB, as no oscillations were observed in the nonreactive system, that is, in the absence of TAAB. 4.2.1.2. Interfacial Activity. SDS is one of the most currently used anionic surfactants. Its surface activity is lower than that of CTAB, and its cmc in water is 10 times higher (8 × 10-3 mol L-1). At the water/CH2Cl2 interface, the interfacial tension varies from 27 to 1 mN m-1 at the cmc. This value is not affected by the presence of CH2Cl2. 4.2.2. Tetraalkylammium Bromides: TAAB. 4.2.2.1. Partition. The TAABs showed a higher affinity for the aqueous phase. Their partition can be modeled by eqs 1-3. Dissociation in the organic phase (Kd2) was found to be extremely low (more than 4 orders of magnitude lower than that in water).23 Dissociation in the aqueous phase is high for the three TAABs. Kd1 increases with chain length, indicating a decrease of the attractive electrostatic interactions between the polar head and Br- due to increasing steric hindrance of the alkyl chains. The partition coefficient greatly increases along the series. For a more concrete evaluation of the partition, we have added in Table 1 the percentage of TAAB at equilibrium in the organic phase for a typical concentration used in the oscillatory experiment. 4.2.2.2. Surface Activity. In the literature, TPAB and TBAB are commonly considered as surface active compounds. However, this activity is detected at a much higher concentration range than the one used in this study. Measurements at the water/air interface have shown that the most surface active TBAB decreases the surface tension by only 3 mN m-1 at 10-2 mol L-1. Qualitatively, the role of TAAB can be compared to the one of picric acid in the previous system. In the concentration range used here, they are not surface active (or very weakly surface active), and they transfer to the aqueous phase where they undergo dissociation and can react with SD- to form TAADS. 4.2.3. Tetraalkylammonium Dodecyl Sulfates: TAADS. For this study, we have extracted and purified the three TAADSs to determine their properties. 4.2.3.1. Partition. As for TAABs, we have performed an assay of TAADSs at partition equilibrium by mass spectroscopy. As the concentrations in the organic phase did not vary sufficiently (especially for TPADS and TBADS), the aqueous phases were analyzed (Figure 5). Partition varied widely from one TAADS to another. Fitting of the experimental data provided the results reported in Table
Figure 5. Total aqueous concentration at partition equilibrium [TAADS]T,AQ ) [TAA+]AQ + [TAADS]AQ versus the initial concentration in the aqueous phase C0 (VAQ ) VORG): (0) TEADS; (O) TPADS, ([) TABDS; and (solid line) fitting using eqs 1 and 2. Table 2. Dissociation in Water (Kd1)34 and Water/CH2Cl2 Partition (Kp) Equilibrium Constants of the Three TAADSs and Percentage of [TAADS]ORG in the Organic Phase at Partition Equilibrium of an Initial Aqueous Solution (C0 ) 10-2 mol L-1) in Contact with the Same Volume of Organic Phase
TEADS TPADS TBADS
Kd1/mol L-1
Kp
[TAADS]ORG at equilibrium for C0 ) 10-2 mol L-1 (%)
5 × 10-2 1.3 × 10-3 6 × 10-5
3.4 1.1 × 103 4.9 × 103
28 98.8 99.98
2. Kd1 was fixed to the values we have determined in a previous study devoted to SDS/TAAB mixtures;34 Kp was obtained from the present measurements. Kd2 could not be determined by titration of the aqueous phase; however, dissociation in the organic phase is certainly negligible. The dissociation constant Kd1 greatly decreases with increasing chain length, showing, in this case, the contribution of increasing hydrophobic attractive interactions between the alkyl chains of TAA+ and the long chains35 of SD-. As expected, the constant Kp increases with chain length, with the partition of TPADS and TBADS being largely in favor of the organic phase. 4.2.3.2. Interfacial Activity. We have measured the water/ CH2Cl2 interfacial tension of the purified TAADSs at partition equilibrium. The interfacial tensions are plotted in Figure 6 versus total TAADS in the aqueous phase ([TAADS]T,AQ ) [TAA+]AQ + [TAADS]AQ) at the partition equilibrium calculated from Table 2. The three compounds are surface active, with TBADS being the most surface active at lower concentrations. The effect of this compound on the interfacial tension is however limited by the formation of aggregates in the aqueous phase. This is again a consequence of the solubilization of CH2Cl2 in water. A comparison of the cmc in pure water and the cac in the biphasic system is given, together with the corresponding values of γ, in Table 3. For TBADS, the aggregation concentration is divided by a factor of 300 in the presence of CH2Cl2. This early aggregation has two consequences: (1) at the cac, the interfacial tension has been lowered only by 4 mN m-1 (γcac ) 24 mN m-1; for pure solvents, γwater/CH2Cl2 ) 28 mN m-1) and (2) the surface concentration, Γcac (Table 3), is from 4 to 5 times lower for TBADS than for TEADS and TPADS. (34) Pradines, V.; Lavabre, D.; Micheau, J. C.; Pimienta, V. Langmuir 2005, 21, 11167. (35) Pradines, V.; Poteau, R.; Pimienta V. ChemPhysChem. 2007, 8, 1524.
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Figure 6. Water/CH2Cl2 interfacial tension versus [TAADS]T,AQ at partition equilibrium (calculated using Kd1 and Kp given in Table 2): (0) TEADS; (O) TPADS; and ([) TBADS. Table 3. cmc and Corresponding γ at the Water/Air Interface and cac and Corresponding γ at the Water/CH2Cl2 Interface for the Three TAADSs and CTABa water/air
TEADS TPADS TBADS CTAB
water/CH2Cl2
cmc/mM
γcmc/ mN m-1
cac/mM
5 4 1.6 0.8
42 40 40 42
1.7 0.12 0.005 0.24
γcac/ mN m-1 1 8 24 0.5
Γcac/mol m-2 4 × 10-6 5 × 10-6 1 × 10-6 3.5 × 10-6
a The interfacial concentration at the cac, Γ , was estimated cac graphically from Gibb’s equation, Γcac ) (1/2.3RT)(δγ/δ log C)cac.
4.3. Nonreactive System: Transfer of TAADSs. The physicochemical analysis of the compounds involved in the present systems showed important differences from the previous one (CTAB/picric acid). As already mentioned, SDS alone did not give rise to the instability; the reaction is now essential to induce transfer and thus the oscillatory regime. A theoretical study on a similar system, for which extraction of a surfactant is induced by an interfacial reaction, was performed by MendesTatsis et al.9 According to the authors, unstable transfer was predicted for diffusion-controlled and fast interfacial reactions. These criteria are verified in our experimental system, as adsorption and the counterion exchange reaction can be considered to be fast compared to diffusive transfer. The determination of the properties of the compounds involved in the SDS/TAAB systems led us to another remark: in this case, the surface active compound undergoing mass transfer is the product of reaction TAADS. As a consequence, we decided to use the purified TAADSs alone in similar conditions as for the transfer of CTAB. 4.3.1. Transfer from AQ to ORG. The three ion pairs, initially solubilized in the aqueous phase, gave rise to unstable transfer. The oscillations that were irregular at the beginning of experiment became more regular (Figure 7) after a while. Globally, the initial concentration domain, duration, and period of the oscillations are comparable to those of CTAB. The mean amplitude is higher and can reach 3 mN m-1. For TEADS, long lasting regular oscillations were observed only for C0 values between 5 × 10-4 and 10-3 mol L-1. The contribution of streaming potential on the electrical potential is very important. TPADS is the ion pair giving rise to the more reproducible results in a concentration domain ranging from 5 × 10-4 to 10-2 mol L-1. In this concentration range, the period increased from 400 to 3000 s. The mean amplitude also increased with concentration
Figure 7. Oscillations of the interfacial tension and electrical potential for TAADS ion pairs transferring from AQ to ORG: (A) [TEADS]0 ) 10-3 mol L-1; (B) [TPADS]0 ) 2 × 10-3 mol L-1; and (C) [TBADS]0 ) 2 × 10-3 mol L-1.
to reach 3 mN m-1. The streaming potential appeared only at the beginning of experiment, with the two signals becoming identical after a while. This effect was similar for TBADS, which showed high amplitude oscillations for C0 ranging from 10-3 to 2 × 10-2 mol L-1. The initial concentrations (C0) at which oscillations were detected were, in the case of TEADS and contrary to the cases of TPADS and TBADS (and CTAB), lower to the cac. TEADS is also the only ion pair for which partition is in favor of the aqueous phase (Table 2). Normal gradients, built in the vicinity of the interface, under diffusive transfer are small. This could be correlated to the interfacial tension level (13-8 mN m-1) reached at the end of the diffusive phases. These values are only slightly superior to the values predicted by the equilibrium isotherm (Figure 6) for the initial concentrations C0 brought in contact with the organic phase. For TPADS and TBADS, partition is largely in favor of the organic phase. Normal gradients are steeper, and the level of the interfacial tension reached when oscillations start is much higher: from 17 to 20 mN m-1 for the
Properties of Oscillating Biphasic Systems
two ion pairs. For TPADS, this value corresponds to a nonsaturated interface (Γ < Γcac). For TBADS, this value is in fact lower to the minimum value reached in the equilibrium isotherm (γcac ) 24 mN m-1). Limited adsorption (Table 3, Γcac) is provided, in this case, by early aggregation. Moreover, the interfacial tension (and this is observed for the three TAADSs) decreased with time. Of course, the interpretation of the recorded curves based only on diffusive dynamics cannot lead to a quantitative evaluation of a biphasic system periodically submitted to convective fluxes. The agitation induced is, for instance, certainly at the origin of the already mentioned mistlike emulsion gradually appearing at the interface, and that may decrease interfacial tension. If we compare the data obtained for the three TAADSs and for CTAB, the compound that gave equivalent results in terms of reproducibility and initial concentration range was TPADS. It is interesting to note that TPADS is also the compound for which the partition and adsorption properties are closest to those of CTAB. Another important feature arising from this study is that a common process appears now for the two systems CTAB/ PH and SDS/TAAB. A surfactant giving rise to unstable transfer is involved in the two cases: the reactant CTAB in the first system and the product of reaction TAADS in the second one. 4.3.2. Transfer from ORG to AQ. A priori, we did not expect to observe oscillations, especially for TPADS and TBADS with their partitions being extremely low in this direction of transfer. However, we recorded long lasting oscillations showing very regular patterns for the three compounds (Figure 8). TEADS, despite a partition equilibrium in favor of the receiving phase, was again the less favorable ion pair to induce the instability. Regular oscillations could be observed for less than 1 h and only for an initial concentration in the organic phase of 5 × 10-4 mol L-1. Except for their duration, the oscillations (amplitude, period, global level of the interfacial tension, and streaming potential) were finally relatively similar to the ones observed for the transfer from AQ to ORG. TPADS and TBADS also showed a similar behavior in both directions of transfer. Long lasting oscillations were obtained for the two compounds for initial concentration ranging, as previously, between 5 × 10-4 and 3 × 10-2 mol L-1. No clear tendency could be determined for the variation of the period with the initial concentrations, but the amplitude (2-3 mN m-1) and level of γ (around 20-16 mN m-1) at the beginning of the oscillations were comparable to those of previous experiments. The diffusion profiles presented in Scheme 1 can qualitatively apply to these two compounds. Because of their partition properties, normal diffusive gradients are completely different for the two directions of transfer. However, the concentration [TAADS]T,AQ,s, which governs the extent of adsorption, is similar in both directions of transfer. From AQ to ORG, low aqueous concentrations at the interface are reached if partition is largely in favor of the organic phase; from ORG to AQ, small normal gradients are formed, but a low concentration of adsorbed surfactants is guaranteed by partition in favor of the organic phase. This leads, as observed, to equivalent values of the interfacial tension. It arises from all the examined systems that the high interfacial activity and low interfacial concentration of adsorbed surfactants (ensuring their mobility at the interface) are the only criteria still holding. The amplitude of the normal gradients, considered as critical in previous theoretical studies,5,36 seems to finally owe its importance only to the level of adsorption induced at the interface.
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Figure 8. Oscillations of the interfacial tension and electrical potential for TAADS ion pairs transferring from ORG to AQ: (A) [TEADS]0 ) 5 × 10-4 mol L-1; (B) [TPADS]0 ) 10-2 mol L-1; and (C) [TBADS]0 ) 2.5 × 10-2 mol L-1.
5. Conclusion We have for this study analyzed several oscillating biphasic systems. The main physicochemical properties (adsorption, partition, and reaction) of the various compounds involved have been obtained. Thanks to this approach, we have determined the main processes taking place during the diffusive regime for the two reactive systems. We have also identified the compound at the origin of the instability in each case: the reactant CTAB for (36) (a) Hennenberg, M.; Sørensen, T. S.; Sanfeld, A. J. Chem. Soc., Faraday Trans. 2 1977, 73, 48. (b) Reichenbach, J.; Linde, H. J. Colloid Interface Sci. 1981, 84, 433.
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the first system and the product TAADS for the second one. When used alone, these surfactants give rise to oscillations whichever the direction of transfer. An interpretation of the dynamic data or, more precisely, of the diffusive stages was attempted with regard to the equilibrium properties of the compounds. Although our approach is qualitative, good coherency arises from the analysis of the global interfacial tension level at which oscillations are triggered in the various experimental situations. Four surfactants have been investigated (CTAB and three TAADS), and oscillations were favored by a high surface activity and a low concentration of adsorbed surfactants. This last property is achieved in both directions of transfer when partition is highly in favor of the organic phase. Thus, the compound showing a lower interfacial activity and partition coefficient, TEADS, was the least efficient to trigger the instability. CTAB gave longer lasting and more regular oscillations when transfer occurred from AQ to ORG. From ORG to AQ, the interfacial tension reached at the end of the diffusive stage is low and the interface gets closer to saturation, disfavoring the creation of interfacial tension gradients. TPADS and TBADS exhibited regular oscillations in both directions of transfer. Their partition coefficients were the highest, resulting in low adsorption. Moreover, the equilibrium adsorption isotherm of TBADS at the
Pradines et al.
water/CH2Cl2 interface showed an interesting feature: adsorption in this case is limited by early aggregation occurring in the aqueous phase in the presence of CH2Cl2. We believe that detailed knowledge of the physicochemical features of the involved compounds brings new insight to the processes and properties needed to induce the instability. However, our observations also raise new questions, in particular, on the origin of amplification of the convective cell when transfer occurs from the organic to the aqueous phase. The qualitative explanation proposed by Sterling and Scriven, based on the formation of high normal concentration gradients, can only apply for the transfer from AQ to ORG. Fluxes induced in the aqueous bulk by the movements initiated by the tangential gradients on the interface may amplify a local excess of surfactant by the supply of concentrated bulk solution to the interface. In the reverse direction, this reasoning does not hold anymore because gradients are smaller and reversed. In this case, the concentration of surfactant is at maximum at the interface, and the diluted solution supplied by the convective cells rather dampens the instability. A detailed study of the velocity fields in the two phases in both directions of transfer could bring new elements. LA7018154
