pubs.acs.org/Langmuir © 2010 American Chemical Society
Auto-Oscillation of Surface Tension: Effect of pH on Fatty Acid Systems N. M. Kovalchuk† and D. Vollhardt*,‡ †
Institute of Biocolloid Chemistry, 03142 Kyiv, Ukraine, and ‡Max-Planck Institute of Colloids and Interfaces, D-14424 Potsdam/Golm, Germany Received June 10, 2010. Revised Manuscript Received August 9, 2010
Spontaneous nonlinear oscillations of surface tension produced by transfer of either octanoic or nonanoic acids from a droplet situated in the bulk water to the air/water interface are studied experimentally. It is shown that the oscillation amplitude decreases significantly with the increase of pH of aqueous phase. At pH > 6.5, detectable oscillations for the two fatty acids studied do not exist. The results are discussed in terms of the mechanism proposed recently for spontaneous oscillations produced by transfer of nonionic surfactants.
Introduction Self-organization in systems far from equilibrium and, in particular, artificial systems producing spontaneous oscillations at liquid interfaces are of great interest currently, as they can be helpful for the explanation of rhythmic processes in living organisms as well as for designing mimetic processes. One of intensively studied systems of such kind is the liquid membrane system (Figure 1) where a surfactant is transferred from a surfactant-containing aqueous phase (donor phase, 2) to another aqueous phase (acceptor phase, 3) through an interposed oil-phase (membrane, 1).1-4 The transfer of an ionic surfactant in this system is often accompanied by spontaneous oscillations of electrical potential across the membrane. The appearance of oscillations and their characteristics depends on the chemical composition of each of the three liquid phases involved, which makes this system promising for applications in biomimetic sensors for taste5 or drug6 molecular recognition, but at the same time, this enormously complicates the analysis of the processes in it. It has been shown that the oscillations of electrical potential across the liquid membrane are accompanied by synchronous oscillations of interfacial tension.7,8 Therefore, in all proposed models the oscillations are ascribed to an abrupt adsorption of the surfactant at the liquid interface followed by its gradual desorption.9-11 However, the physical mechanisms causing this adsorption/desorption interchange have not been clarified so far. It is also not clear why in systems with rather similar composition the oscillations can occur either at donor/membrane12 or at acceptor/membrane13 interface. (1) Yoshikawa, K.; Matsubara, Y. J. Biophys. Chem. 1983, 17, 183. (2) Yoshikawa, K.; Matsubara, Y. J. Am. Chem. Soc. 1984, 106, 4423. (3) Arai, K.; Kusu, F. In Liquid interfaces in chemical, biological and pharmaceutical applications, Volkov, A G., Ed.; Surface Science Series 95; Marcel Dekker, Inc.: New York, 2001. (4) Kovalchuk, N. M.; Vollhardt, D. Adv. Colloid Interface Sci. 2006, 120, 1. (5) Plocharska-Jankowska, E.; Szpakovska, M.; Matefi-Tempfli, S.; Nagy, O. B. Biophys. Chem. 2005, 114, 85. (6) Arai, K.; Fukuyama, S.; Kusu, F.; Takamura, K. Bioelectrochem. Bioenerg. 1994, 33, 159. (7) Pimienta, V.; Lavabre, D.; Buhse, T.; Micheau, J. C. J. Phys. Chem. B 2004, 108, 7331. (8) Takahashi, S.; Tsuyumoto, I.; Kitamori, T.; Sawada, T. Electrochim. Acta 1998, 44, 165. (9) Arai, K.; Fukuyama, S.; Kusu, F.; Takamura, K. Electrochim. Acta 1995, 40, 2913. (10) Ogawa, T.; Shimazaki, H.; Aoyagi, S.; Sakai, K. J. Membr. Sci. 2006, 285, 120. (11) Szpakowska, M.; Magnuszewska, A.; Nagy, O. B. J. Colloid Interface Sci. 2008, 325, 494. (12) Pimienta, V.; Etchenique, R.; Buhse, T. J. Phys. Chem. A 2001, 105, 10037. (13) Arai, K.; Kusu, F.; Takamura, K. Chem. Lett. 1990, 1990, 1517.
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Recently, oscillations of interfacial tension were obtained on the acceptor-membrane14 as well as donor/membrane15,16 interface by transfer of nonionic surfactants. For this case, the oscillation mechanism was explained on the basis of direct numerical simulations.15,17 It has been shown that the oscillations are the result of Marangoni instability periodically terminated due to contraction/expansion in different parts of the surfactant adsorption layer. The induction period before the oscillation and a gradual increase of interfacial tension during each oscillation correspond to the regime of slow surfactant transfer in the system because of diffusion and buoyancy driven convection. The abrupt decrease of interfacial tension is an indication of the development of convective Marangoni instability, when the surfactant transfer to the interface occurs very rapidly, as the velocity of convective motion increases by several orders of magnitude. The oscillation mechanism generated in liquid membrane systems either at the donor/membrane or at the acceptor/membrane interface is shown to be similar to the mechanism underlying spontaneous oscillations at a liquid interface due to surfactant transfer from a point source, for example, a surfactant droplet situated in the bulk phase.18,19 The measuring cell for experiments with droplet dissolution under a liquid interface is presented in Figure 2. The comparison with Figure 1 makes it clear that the conditions for surfactant transfer and adsorption at the acceptor/membrane interface in liquid membrane systems are very similar to the conditions in the system with a droplet. Therefore, the latter system represents a very good model system for elucidation of the oscillation mechanism. One of the advantages of this system is the possibility of completely excluding the effect of surfactant transfer to the acceptor bulk phase by studying oscillations at the air/liquid interface and using a nonvolatile surfactant. That is why we perform our study on the mechanism governing oscillations using this simple system. Recently, it has been shown20 that the properties of oscillations produced by dissolution of various fatty acids droplets in water are in qualitatively good agreement with those predicted on the basis of the model proposed in ref 18. In ref 20, the study was (14) Kovalchuk, N. M.; Vollhardt, D. J. Phys. Chem. B 2006, 110, 9774. (15) Kovalchuk, N. M.; Vollhardt, D. J. Phys. Chem. C 2008, 112, 9016. (16) Tadmouri, R.; Kovalchuk, N. M.; Pimienta, V.; Vollhardt, D.; Micheau, J.-C. Colloids Surf. A 2010, 354, 134. (17) Kovalchuk, N. M.; Vollhardt, D. Colloids Surf. A 2007, 309, 231. (18) Kovalchuk, N. M.; Vollhardt, D. Phys. Rev. E 2002, 66, 026302. (19) Kovalchuk, N. M.; Vollhardt, D. J. Phys. Chem. B 2005, 109, 22868. (20) Kovalchuk, N. M.; Vollhardt, D. Mater. Sci. Eng., C 2002, 22, 147.
Published on Web 08/20/2010
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Article into the aqueous phase to the depth of 14 mm. This depth was chosen as optimal on the basis of previous studies.20 The freshly annealed Wilhelmy plate was brought into contact with the aqueous phase, the vessel was covered to prevent water evaporation and in this way to diminish the thermal convection in the system. After the measuring cell was thermostatted over 2 h, a droplet of diameter 2-3 mm was formed on the tip of the pipet by adding fatty acid with a syringe into the pipet and the measurement was started. Reference measurements performed during thermostatting have detected no changes in the surface tension.
Results and Discussion
Figure 1. Liquid membrane system: 1, membrane phase; 2, donor phase; 3, acceptor phase. The system has cylindrical geometry; the bottom of the inner container is open.
Figure 2. Measuring cell for the study of auto-oscillations of the surface tension: 1, vessel with aqueous solution; 2, cover; 3, Pasteur pipet; 4, fatty acid droplet; 5, Wilhelmy plate; 6, vapor (or a second immiscible liquid).
performed only at low pH, when fatty acids are in nondissociated state. Here, we present the results for higher pH, displaying how the transition from nonionic to ionic surfactant, and, in particular, the degree of dissociation of fatty acid, influences appearance and characteristics of the oscillations.
Experimental Section The surfactants, octanoic (for gas chromatography, purity 99.5þ, Aldrich) and nonanoic (purity >97%, Sigma) acids were used as purchased. The initial pH value was adjusted by 0.1 N aqueous HCl solution (Merck) used as purchased, aqueous NaOH solution (purity 99.99%, Sigma-Aldrich), or 0.01 M phosphate buffer, being the mixture of disodium hydrogen phosphate dihydrate, Na2HPO4 3 2H2O (purity >98%, Fluka) with sodium dihydrogen phosphate dihydrate NaH2PO4 3 2H2O (purity >99%, Fluka). All aqueous solutions were prepared in ultrapure deionized water produced by a Millipore Milli-Q water purification system. Monitoring of the time dependence of surface tension during dissolution of a fatty acid droplet was performed by a homemade tensiometric setup with an electronic balance equipped with a platinum Wilhelmy plate. The values of surface tension were sampled every 2 s, and the readings were stored in a data file. The equilibrium surface tension was measured by Lauda TE 1C tensiometer using the du Nuoy ring technique. The experimental study of oscillations was performed as follows (Figure 2): 40 mL of aqueous solution with desired pH was poured into a glass vessel with a diameter of 44 mm. A cleaned glass Pasteur pipet with the mouth of about 1 mm was immersed Langmuir 2010, 26(18), 14624–14627
Let us briefly reiterate the oscillation mechanism discussed in detail in ref 18. Initially, the distribution of a surfactant dissolving from the droplet occurs by diffusion and, if the solute density depends on the surfactant concentration, by buoyancy-driven convection. This process is rather slow and only after a certain time does a noticeable amount of surfactant reach the interface. From the geometry of the measuring cell presented in Figure 2, it is obvious that the path of surfactant to the capillary region of the interface (point A in Figure 2) is much shorter than that to the wall region of the interface (point B in Figure 2). Therefore, the surfactant concentration near point A is always higher than that near point B, and Marangoni convection develops in the system because of the of surface tension gradient. The convective flow on the interface is directed from the capillary to the wall, and according to the continuity of convective fluxes, it is directed upward in the bulk solution near the capillary. The increase of the convection velocity near the droplet accelerates the surfactant transfer to the capillary region on the interface and, therefore, increases the surface tension gradient, causing further acceleration of convection in this way. This feedback gives rise to Marangoni instability in the considered system. The instability develops very quickly, and the velocity as well as the amount of surfactant, transferred to the interface and spread over it, increases by several orders of magnitude within a few seconds. This results in an abrupt decrease of the surface tension (Figure 3). When the edge of the convective wave spreading the surfactant over the interface reaches the wall region, the adsorbed surfactant layer becomes compressed here, as it cannot move through the wall and cannot instantaneously desorb. Therefore, a reverse concentration gradient appears near the wall which suppresses the convection resulting in termination of the instability and returning the system to the next slow stage in its evolution. During this stage, the surfactant desorbs gradually from the interface causing an increase of the surface tension (Figure 3). After a certain time, the instability develops again giving rise to the next oscillation. It has been shown in ref 21 that surfactant solubility and surface activity are the crucial factors for oscillation appearance and characteristics. It is well-known that the dissociated form of fatty acid is much more soluble in water and much less surface active in aqueous solutions than the nondissociated form.22-25 Our measurements performed for octanoic acid used in the experiments have shown the same tendency (Figure 4). For octanoic acid, pKa = 4.89; i.e., at pH 3.6, it is practically in the nondissociated form, at pH = 4.9, it is half-dissociated, and it is essentially dissociated at pH = 7. (21) Kovalchuk, N. M.; Vollhardt, D. Phys. Rev. E 2004, 69, 016307. (22) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (23) Lord, D. L.; Hayes, K. F.; Demond, A. H.; Salehzaden, A. Environ. Sci. Technol. 1997, 31, 2045. (24) Fainerman, V. B.; Miller, R.; M€ohwald, H. J. Phys. Chem. B 2002, 106, 809. (25) Bahtz, J.; Knorr, D.; Tedeschi, C.; Leser, M. E.; Valles-Pamies, B.; Miller, R. Colloids Surf. B 2009, 74, 492.
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Figure 3. Oscillations produced by dissolution of octanoic acid droplet in 1, pure water; 2, aqueous solution of NaOH with initial pH = 8.4.
Figure 4. Surface tension isotherms of aqueous octanoic acid solutions: 1, pH = 3.6, adjusted with HCl; 2, pH = 4.9, adjusted either with NaOH (open squares) or with phosphate buffer (filled squares); 3, pH = 7, adjusted with phosphate buffer.
To analyze the possible development of auto-oscillations at different pH values, as a first approximation, we are using the data obtained by numerical simulations for the systems containing a nonionic surfactant droplet.21 The model used in ref 21 is based on the Langmuir adsorption isotherm
Table 1. Dependence of the Parameter of Langmuir Isotherm, KL, on Solution pH
Γ ¼ Γm
KLC 1 þ KLC
ð1Þ
where Γ is the surfactant adsorption, Γm is the saturation adsorption, C is the surfactant bulk concentration at the interface, and KL is the Langmuir constant. That is why the Langmuir isotherm was chosen to fit the experimental data presented in Figure 4 assuming it would provide enough information for the qualitative analysis. The fitting was performed by the free software IsoFit.26 The value of Γm for all three curves was kept constant Γm = 8.3 10-6 mol/m2.27 The calculated values of KL are presented in Table 1. The value of KL obtained for pH = 3.6 is in good agreement with that calculated in ref 27 for nondissociated octanoic acid (KL = 1.4 m3/mol). Note that the values of surface tension obtained for pH adjusted either with NaOH or with phosphate buffer fall precisely enough into the same curve (curve 2 in Figure 4). According to ref 23, the solubility limit increases 10 times by the increase of pH value from 3 to 6.5. At the same time, according to Table 1, the parameter of Langmuir isotherm, KL, decreases about 80 times by the increase of pH value from 3.6 to 7.0. Therefore, it can be concluded that with increasing pH the surface activity of octanoic acid decreases more quickly that its solubility increases. According to ref 21, the decrease of surfactant activity and the simultaneous, but slower, increase of the surfactant solubility result in a noticeable decrease of both the oscillation period and the amplitude. When the activity becomes low enough, the amplitude reduces to very small values that cannot be detected in the experiment. Therefore, it can be expected that the increase of pH in the studied system will result in a decrease of oscillations period and amplitude, and above a certain pH value, there will be no oscillations observed at all. The experimental study has shown that the system behavior depends crucially on how the desirable initial pH value is adjusted. By using NaOH, the dissolution of a fatty acid droplet (26) http://www.thomascat.info/thomascat/Scientific/AdSo/AdSo.htm (27) Malysa, K.; Miller, R.; Lunkenheimer, K. Colloids Surf. 1991, 53, 47.
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pH KL, m3/mol
3.6 1.5
4.9 0.75
7.0 0.018
causes a rather rapid decrease of pH in the solution. As a result, the oscillation characteristics are practically independent of the initial pH value (Figure 3) and are similar to those for fatty acids at low pH.20 The situation changes drastically when pH is adjusted with phosphate buffer. Despite the droplet dissolution, the capacity of the buffer allows the pH value to be maintained at a desirable level over the long term. For example, dissolution of octanoic acid droplets in phosphate buffer with initial pH 6.96 causes a decrease of the pH value to 6.94 after 3 h and to 6.9 after 5 h in the absence of Marangoni convection in the system. In the oscillatory regime, pH decreased more quickly but still only by 0.3-0.5 units over 12 h depending on the initial pH value and the intensity of oscillations. The results of the experiments with phosphate buffer are presented in Figure 5. The oscillations are somewhat similar for octanoic and nonanoic acids. In line with theoretical predictions, the amplitude of the oscillations decreases with the increase of pH, and at pH above 6.5, the oscillations become undetectable. However, the period of the oscillations practically does not change with pH, whereas an essential decrease in the period was expected. To clarify this apparent problem, it is important to note that here the surfactant is treated as a single component with some average properties contributed from both the dissociated and nondissociated forms. But in reality, the system consists of a mixture of two surfactants, namely, the ionic and nonionic components with very different properties. With the pKa = 4.89 for octanoic acid taken into account, it is easy to calculate that only ∼1% octanoic acid molecules are in the nondissociated form at pH 7. Therefore, at pH 7 the concentration of the dissociated form of octanoic acid is 2 orders of magnitude larger than the concentration of the nondissociated form, whereas according to ref 24, the surface activity of the dissociated form is expected to be 3-4 orders of magnitude smaller. According to the Langmuir model, the surface pressure owing to surfactant adsorption is determined by the product of its bulk concentration and the Langmuir constant (eq 1). Therefore, as a very rough approximation, it can be inferred that, in the case under consideration, the surface pressure is determined mainly by Langmuir 2010, 26(18), 14624–14627
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Figure 6. Contribution of the nondissociated form of octanoic acid to the surface tension at pH = 7 (compact line) calculated with parameters of the Langmuir isotherm obtained for nondissociated octanoic acid at pH = 3.6 (Table 1). Squares represent the experimental data from Figure 3, curve 3.
This is particularly important for surfactants involved in the traditional liquid membrane systems, as, because of reactions at the interface, they usually include two surfactants with rather different adsorption properties.7,28,29
Conclusions
Figure 5. (a) Oscillations produced by dissolution of an octanoic acid droplet in aqueous phosphate buffer solution with different pH. (b) Oscillations produced by dissolution of a nonanoic acid droplet in aqueous phosphate buffer solution with different pH.
the nondissociated form of the surfactant. Assuming that the surface activity of nondissociated fatty acid is independent of pH, we estimated the contribution to the surface tension from nondissociated octanoic acid at pH = 7. The result is presented as a compact line in Figure 6. The squares in Figure 6 are the experimental data for pH = 7 presented in Figure 4 (curve 3). It is seen from Figure 6 that the agreement between calculated and experimental data is quite good, thus supporting the assumption made above. If we accept now that the development of the oscillations in the system under consideration is determined mainly by the adsorption of the much more surface active nondissociated fatty acid, we will see that with the increase of pH the activity of this surfactant does not change, but the solubility decreases. The increase of pH from 3 to 6.5 causes a 10-fold increase of the total solubility,23 but at pH= 3, 99% of the molecules are in nondissociated form, whereas at pH = 6.5, only 2.5% of the molecules are in the nondissociated state, i.e., the effective solubility for the nondissociated component becomes about 4 times smaller. After application of the results of ref 21, a rather small increase in the oscillation period can be predicted for this system and a strong decrease in the oscillation amplitude with the increase of pH. This conclusion is in good qualitative agreement with the obtained experimental results. The performed qualitative analysis clearly displays the importance of precise accounting for each type of surfactant involved.
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A system containing a surfactant droplet under the liquid interface is a suitable model system for the investigation of selforganization processes at the acceptor/membrane interface in liquid membrane systems. The performed study of spontaneous oscillations caused by dissolution of a droplet of either octanoic or nonanoic acid under water/air interface has shown essential dependence of appearance and characteristics of the oscillations on pH of the aqueous phase. The increase of pH resulted in a decrease of the oscillation amplitude, and for pH above 6.5, the amplitude became so small that oscillations were no longer detectable. Such behavior can be explained according to the oscillations mechanism proposed earlier in ref 18. The increase in pH causes dissociation of fatty acid in the solution. Although the total solubility of acid increases with the increase of pH, the dissolved amount of its nondissociated form decreases. The surface activity of dissociated molecules is several orders of magnitude smaller than that of the nondissociated form. Therefore, the amount of the nondissociated form is more important for the development of Marangoni instability in the considered system. According to the oscillation mechanism proposed for the case of nonionic surfactants18 and the theoretical study of the effect of the surfactant properties on the oscillation characteristics,21 the decrease of the effective solubility of a surfactant should result in an essential decrease of the oscillations amplitude. This is in reasonable agreement with experiments. Acknowledgment. The work was supported by COST D43 Action. N.M.K. thanks the Max Planck Institute of Colloids and Interfaces for the financial support. (28) Nakache, E.; Dupeyrat, M.; Vignes-Adler, M. J. Colloid Interface Sci. 1983, 94, 187. (29) Pradines, V.; Lavabre, D.; Micheau, J. C.; Pimienta, V. Langmuir 2005, 21, 11167.
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