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Surface Tension of Aqueous Amphiphiles Fredric M. Menger,* Ashley L. Galloway, and Mary E. Chlebowski Department of Chemistry, Emory University, Atlanta, Georgia 30322 Received May 23, 2005. In Final Form: July 8, 2005 Surface tension measurements show that at low concentrations a surfactant bearing two ester groups in its chain assembles into small aggregates or else rearranges at the air/water interface to occupy less area per molecule. Only at higher surfactant concentrations do bona fide micelles form. The air/water interface, it is argued, saturates abruptly and cooperatively (as does the aggregation into micelles at the higher concentrations) to give a “critical monolayer concentration”. Yet saturation does not reduce the surface tension a great deal. The bulk of surface tension reduction is imparted by monomeric surfactant in the solution via a mechanism that is obscure but may be related in part to the mechanical perturbation of the saturated film during measurement.
Surface tension has historically provided one of the more popular means for determining critical micelle concentrations (CMC).1 Thus, the surface tension plotted against the log of the surfactant concentration, as in Figure 1,2 typically shows three main regions: (a) an almost horizontal section at very low concentrations; (b) a steep linear decline at intermediate concentrations; and (c) a flat region at high concentrations. The point at which region (b) becomes region (c) is taken as the critical micelle concentration (CMC). According to the Gibbs equation, Γ ) -(1/2RT)(dγ/d ln c) where Γ ) the surface excess; γ ) the surface tension; and c ) the bulk surfactant concentration.3 The 2 refers to DTAB. The surface excess has been defined as the interfacial surfactant concentration over and above the bulk concentration (which implies, of course, an interface of finite thickness in order for the interface and bulk concentrations to have comparable units). Since region (b) in Figure 1 embodies a constant slope (i.e., dγ/d ln c is constant), it follows that the air/water interface possesses a constant surface excess over the entire concentration range of (b). This can happen only if the air/water interface is saturated with surfactant molecules.4,5 The bulk concentration is considered negligible relative to the surface excess; were it otherwise, the reciprocal of Γ in region (b) could not be used to obtain the area-per-molecule at the interface, as is done routinely.6 Now there are certain peculiarities evident with the above analysis: Since the presaturation region (a) in Figure 1 is rather flat, this means that the surface tension changes only slightly as the concentration reaches the saturation point at the beginning of region (b). There are two possible reasons for this behavior: The interface gradually “fills up” until saturation is attained, but this process has only a slight effect upon the surface tension. Alternatively, and seemingly more likely, the interface * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Jo¨nsson, B.; Lindman, B.; Holmberg, K.; Kronberg, B. Surfactants and Polymers in Aqueous Solutions; Wiley: Chichester, U.K., 1998; pp 253-255. (2) Espert, A.; Klitzing, R. v.; Poulin, P.; Colin, A.; Zana, R.; Langevin, D. Langmuir 1998, 14, 4251. (3) Myers, D. Surfactant Science and Technology; VCH: New York, 1988; pp 185-186. (4) Rosen, M. J. Surfactants and Interfacial Phenomena; WileyInterscience: New York, 1978; p 60. (5) Osipow, L. I. Surface Chemistry; Reinhold: New York, 1962; p 129. (6) Kumar, A.; Alami, E.; Holmberg, K.; Seredyuk, V.; Menger, F. M. Colloids Surf. A 2003, 228, 197.
Figure 1. Surface tension vs log concentration plots for gemini surfactant 12-2-12 (left) and DTAB (right). Data taken from ref 2.
Figure 2. Regions (a), (b), and (c) in Figure 1 approximated by imposing three intersecting lines and two critical points.
remains unoccupied in region (a), and the surface tension remains flat, until a sudden and cooperative saturation takes place at region (b) in Figure 1. In other words, the presence of a few molecules at the interface promotes the further adsorption of many neighbors, whereupon the entire interface becomes quickly saturated. Regions (a) and (b) can be defined by two intersecting straight lines seen in Figure 2. The break is not as sharp as that between regions (b) and (c) at the CMC, but nonetheless the transition from unsaturated film at region (a) to saturated film at region (b) is reasonably abrupt. It seems, in summary, that there is a “critical monolayer concentration” below which there is little monolayer
10.1021/la051363l CCC: $30.25 © 2005 American Chemical Society Published on Web 09/01/2005
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Nou¨y, the Wilhelmy plate, the drop weight, and the oscillating jet methods)7 that induces the major surface tension reduction once the interface is saturated. Surface agitations that take place during actual manipulation of a surfactant solution, for whatever purpose, could also serve to lower the apparent surface tension. Recently, we published a paper on the colloidal properties of surfactants possessing two ester or ether groups within their hydrophobic chains such as compound A below.8,9A plot of surface tension vs concentration (γ vs
Figure 3. Surface tension vs [A] at low concentrations of A.
adsorption and above which the monolayer is saturated. Figure 2 is so labeled. Perusal of Figure 1 shows that the major reduction in surface tension occurs in region (b) where, as just stated, the interface is saturated. If this is correct, then monomer added to the bulk solution must be lowering the surface tension without actually affecting the concentration at the air/water interface. Stated in other words, the monomer in solution has a far greater effect on surface tension than does the surfactant that has entered and saturated the interface, a rather surprising conclusion. For example, as seen with DTAB in Figure 1, the surface tension is lowered from 72 dynes/cm in pure water to 66 dynes/cm at saturation, whereas additional monomer in the bulk water lowers the surface tension from 66 dynes/ cm ultimately to 40 dynes/cm.2 In region (c), micelle formation removes added monomer from solution, so that the latter is no longer available to further lower the surface tension, and the plot becomes flat once again. As mentioned, this point is taken as the CMC. One wonders, of course, what molecular processes can be involved in region (b) where monomer in the bulk solution reduces the surface tension precipitously after the interface has been already saturated according to the Gibbs equation. One explanation invokes activity coefficient changes in the bulk solution; interfacial surfactant, being in equilibrium with that in the bulk solution, must be similarly affected. However, this explanation is not satisfying for Figure 1 because, as seen with 12-2-12, region (b) begins below 0.1 mM where activity coefficient effects are negligible. (Furthermore, in any case, thermodynamic models often lack certain mechanistic insights available from analyses at the molecular level.) Nor can one easily attribute the appreciable slope of region (b) to surfactant entry into the interface “in excess of the surface excess at saturation”, which is, as mentioned, considered negligible in the Gibbs analysis. Another possibility relates to the methods of measuring the surface tension. In the du Nou¨y ring method, for example, the force needed to pull a metal ring off the surface of the solution equates with the interfacial tension. However, the act of removing the ring from the air/water interface disrupts the structure of the interface. Additional surfactant from solution must be supplied to this region as the interface expands to accommodate the rising ring. It is here, presumably, where an increased monomer concentration in solution assists the removal of the ring and, as a result, the intrinsic surface tension at saturation is reduced. There is an interesting implication here of an “uncertainty principle”. Since adsorption of surfactant at the air/water interface lowers the surface tension only slightly at saturation, it must be the act of observation (by the du
[A]), using data available at the time of publication, is shown in Figure 3. Two important comments are necessary here. First, since our overall concentration range was small (owing to the scarcity of compound), the plot used [A], rather than log [A], as the X axis. Using [A] rather than its log is a time-honored procedure (e.g., see the study of sodium dodecyl sulfate by Karol Mysels)10 although its theoretical basis is doubtful. The fact remains that one can observe a sharp break at the CMC with either [A] or log [A]. Indeed, over small concentration ranges, γ vs [A] may even be operationally preferable for CMC determinations. Second, it can be seen from Figure 3 that the plot does not level off at the higher concentrations as would be expected for true micelle formation. We therefore concluded that small aggregates were forming. These are less efficient than conventional micelles in totally consuming additional surfactant. When the small aggregates incorporate a portion of the added monomer, less monomer is available in solution to interact with the interface, and a reduction in slope would occur, as observed. A “critical aggregation concentration” of 1.3 mM was estimated for A. It is interesting with regard to Figure 3 that Zana et al.11 observed post-CMC declines in surface tension, as have others,12,13 but they stated that no explanation exists for the lack of horizontal behavior. It seems reasonable that, as in our case, additional monomer in solution is not totally taken up by micelle formation or growth, and thus the surface tension of the saturated interface continues to decline. However, there is another rationale for Figure 3 that had not been previously considered by us. It is possible that there is a conformational change at the air/water interface. Thus, at lower concentrations, the molecules could be forming loops on the water in which the cationic nitrogen and one or both esters reside in the water (Figure 4). At an abrupt concentration (akin to a phase change in a π-A plot with an insoluble monolayer), the molecules rearrange to a more upright position where they occupy a smaller area per molecule. Since the abrupt slope change (7) Although the capillary rise method for determining surface tension is beset with its own difficulties (e.g., an uncertainty is measuring contact angles correctly), it has the advantage of not involving a mechanical disturbance of the water surface. Surface tension and conductivity are preferred over dye-adsorption for CMC determinations because the latter can give dye-induced micellization and thus low CMC values. (8) Menger, F. M.; Chlebowski, M. E. Langmuir 2005, 21, 2689. (9) Menger, F. M.; Galloway, A. L. J. Am. Chem. Soc. 2004, 126 (48), 15883-9. (10) Mysels, K. J. Langmuir 1986, 2, 423. (11) Alami, E.; Beinert, G.; Marie, P.; Zana, R. Langmuir 1993, 9, 1465. (12) Devinsky, F.; Lacko, I.; Bittererova, F.; Tomeckova, L. J. Colloid Interface Sci. 1986, 114, 314. (13) Attwood, D.; Natarajon, R. J. Pharm. Pharmacol. 1979, 32, 460.
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Figure 4. Conformation change of A at air/water interface as a possible explanation for the abrupt slope change in Figure 3.
Figure 5. Surface tension vs [A] including high concentrations of A.
in Figure 3 is obscured in a plot of γ vs log [A], it is not possible to quantitate the area decrease. We have now synthesized larger quantities of A via a multistep pathway described earlier.9 In this manner, we were able to examine the surface tension properties of A up to 0.1 M while taking over 50 points (Figure 5). When the concentration range was extended fully, and the data
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thereby compressed, the break at 1.3 mM becomes indiscernible, whereas a new, more obvious break appears at about 0.03 M. This latter break is also seen in a surface tension vs log [A] plot (not shown). In both plots there exists a small dip near 0.03 M that may be related to an impurity (although the compound had been chromatographed and was spectroscopically and analytically pure). The major break in the surface tension plot occurring at 0.03 M in Figure 5 probably represents true micelle formation, a phenomenon not visible until we had sufficient quantities of our hard-to-synthesize surfactant on hand. Dynamic light scattering confirms the presence of aggregates with an average hydrodynamic radius of about 3-4 nm. A CMC of 0.03 M is about 35 times higher than that of a conventional surfactant without the ester groups but with the same number of chain carbons (i.e. 16). Application of the Gibbs equation using log [A] below the CMC gives a molecular area of 79 Å2 at saturation. In summary, surface tension measurements of A show a break at low concentrations, indicating that it assembles into small aggregates or else rearranges at the air/water interface to occupy less area per molecule. Only at higher surfactant concentrations do bona fide micelles form. The air/water interface, it is argued, saturates abruptly and cooperatively (as does the aggregation into micelles at the higher concentrations) to give a critical monolayer concentration. Yet saturation of the interface does not reduce its surface tension a great deal. The bulk of surface tension reduction is imparted by monomeric surfactant in the solution via a mechanism that is obscure but may be related in part to the mechanical perturbation of the saturated film during measurement. Acknowledgment. This work was supported by the National Institutes of Health. We thank Prof. Eric van der Linden and Hans Lyklema of Wageningen University and Dr. Marc Stuart of Groningen University for valuable input. LA051363L
