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Dependence of Phase Behavior of Some Non-ionic Surfactants at the Air–Water Interface on Micellization in the Bulk
Journal of Colloid and Interface Science 252, 365–372 (2002) doi:10.1006/jcis.2002.8478
Dependence of Phase Behavior of Some Non-ionic Surfactants at the Air–Water Interface on Micellization in the Bulk Md. Nazrul Islam and Teiji Kato1 Department of Applied Chemistry, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya 321-8585, Japan Received November 28, 2001; accepted May 9, 2002
The temperature-dependent surface phase behavior of two sparingly soluble surfactants, namely, ethylene glycol n-dodecyl ether (EGDE) and ethylene glycol n-tetradecyl ether (EGTE), at the air– water interface was investigated by film balance and Brewster angle microscopy (BAM). A cusp point followed by a pronounced plateau region in the surface pressure–time (π–t) adsorption isotherms of the amphiphiles measured by film balance indicates the first-order phase transition. Bright two-dimensional condensed phase domains in a dark background are observed by BAM just after the phase transition. In both cases the critical surface pressure necessary for the phase transition increases with increasing temperature. The domains are found to be circular up to 5 and 27◦ C for EGDE and EGTE, respectively, above which they show a fingering pattern. Condensed domains are observed up to 23 and 37◦ C for EGDE and EGTE, respectively. The surface properties of the amphiphiles are found to be markedly affected by their tendency to aggregate in the bulk as micelles. The CMC values of both the amphiphiles show a maximum at a definite temperature, Tmax , that corresponds well to their respective maximum temperatures of domain formation. An increase in temperature beyond Tmax results in an increasing trend for the formation of micelles. Consequently the system suffers from a shortage of two-dimensional surface concentration of the molecules to attain the surface pressure necessary for phase transition. With increasing temperature, the enthalpy, H◦m , and entropy, S◦m , of micellization change from negative to positive in both cases. An enthalpy–entropy compensation effect is found to hold for both the amphiphiles over the entire temperature range. The thermodynamic quantities reveal that the increase in temperature is favorable for micellization when the temperature exceeds the corresponding Tmax of the amphiphiles. C 2002 Elsevier Science (USA) Key Words: non-ionic surfactant; phase transition; Brewster angle microscopy; adsorbed layers; line tension; critical micelle concentration.
INTRODUCTION
Langmuir monolayers at the air–water interface provide a simple model for understanding the existence of various phases in two-dimensional systems. When the monolayer is compressed 1 To whom correspondence and reprint requests should be addressed. Fax: +81-28-689-6179. E-mail: [email protected].
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isothermally, it undergoes a transition from a two-dimensional (2-D) lower density phase to a higher density condensed phase showing a cusp point followed by a plateau region in the π – A isotherm, provided that the van der Waals interaction between the hydrophobic alkyl chains and the repulsive interaction between the head groups favor the coherence of the molecules. Recent development of Brewster angle microscopy (BAM) (1, 2) allows direct visualization of the change in the surface morphology during the phase transition without using any probe impurity. Moreover, by placing an analyzer in the path of the reflected beam it is possible to detect the internal anisotropy of the molecules in a domain that occurs due to the difference in the surface reflectivity of the p-polarized light (3, 4). Despite extensive work on the adsorption kinetics of watersoluble amphiphiles, the concept of phase transition and structure formation in adsorbed layers has been reported quite recently. H´enon et al. (5–7) first reported such phase transition and structure formation during adsorption from the aqueous solution of sparingly soluble fatty acids. Although they reported the striking influence of surface-active impurities in the formation of condensed domains, now a number of sparingly soluble highly purified amphiphiles are known to form condensed domains in adsorbed layers (8–15). For a clear understanding of the kinetics and the thermodynamic behavior, the π –t adsorption kinetics of Gibbs monolayers has been compared with the π –A isotherm of Langmuir monolayers. It is found that due to the slow and homogeneous growth process in Gibbs monolayers, the condensed phase domains are more ordered than those in Langmuir monolaers (9–12). Recently, it has been reported that at a particular temperature a minimum bulk concentration is necessary for the phase transition in Gibbs monolayers (11, 13, 14) and if the bulk concentration is increased, phase transition can occur at higher temperatures (14). However, each amphiphile has a definite temperature, above which it cannot show any indicative feature of phase transition, no matter whatever the bulk concentration is. In a recent paper we have reported that 2-hydroxyethyllaurate can form a condensed domain maximum up to 25◦ C (14). Similar behavior has also been observed for ethylene glycol n-dodecyl ether (EGDE) and ethylene glycol n-tetradecyl ether (EGTE), which form condensed domains up to 23 and 37◦ C, respectively. Now the question arises why 0021-9797/02 $35.00
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condensed domains are not observed above a particular temperature although the bulk concentration is sufficiently high. To understand what is behind this behavior, the question of a possible dependency of the surface property of molecules on their bulk property should be addressed. Unlike with adsorption at the air/water interface, amphiphile molecules can order themselves in the bulk of a solution. In this process, the amphiphile molecules form a micelle core by the cooperative association of the hydrophobic alkyl chains, while the hydrophilic head groups extend from the core into the aqueous medium. Like the surface properties, the bulk properties of an amphiphile also depend on the length of the alkyl chain, the size and charge of the head group, temperature, and the nature of the solvent medium. Collectively these phenomena govern the bulk properties, such as the size of a micelle, the critical micelle concentration (CMC), and the degree of association of an amphiphile. Micellization is an important phenomenon, because a number of interfacial phenomena, such as detergency and solubilization, depend on the existence of micelles in solution (16). Of late, micelles have become a field of great interest to the organic chemist for their unusual catalytic functions in organic reactions (17, 18). Extensive research work has been reported in the literature concerning the micelle size and shape, the thermodynamics of micellization, and the effect of impurity, some of which are listed for non-ionic (19–26) and ionic (27–32) surfactants. Besides the surface tensiometry, other micelle-induced properties (33), such as electrical conductivity (34), dye-solubilization (35), refractive index (36), nuclear magnetic resonance spectroscopy (37) and spectrofluorometry (38), have also been employed to measure CMC and other related properties. The objective of the present work was twofold. The first was to study the adsorption kinetics and the surface morphology of amphiphiles at different temperatures. The second was to measure the critical micelle concentration by measuring surface tension at different temperatures and to investigate how micellization affects the surface concentration, and thereby the surface morphology, of amphiphiles. We observed that both the amphiphiles show a maximum in the CMC vs temperature curves at a definite temperature, Tmax . These temperatures are 23 and 37◦ C for EGDE and EGTE, respectively, which correspond well to their maximum temperature of domain formation. Above Tmax , the CMC values of both the amphiphiles gradually decrease, showing a preferential tendency to undergo micellization. As a result the system cannot acquire the necessary surface pressure for the phase transition due to the low 2-D surface concentration of the molecules. EXPERIMENTAL
The amphiphiles EGDE and EGTE were supplied by Nikko Chemical Company Ltd. (Tokyo, Japan) with a purity of >99% and were used without further purification. The experimental setup for the adsorption kinetics and surface morphology study
was equipped with a handmade Langmuir trough 2 mm thick, above which a BAM was mounted. Surface pressure was measured by the Wilhelmey method using a small rectangular glass plate. The BAM is composed of a 20-mW semiconductor laser, a Glan-Thompson polarizer, an analyzer, a zooming microscope with a CCD camera of high sensitivity, a TV monitor, and a video recording system. Images recorded were treated with image processing software to maximize the contrast and to correct the distortion of the images caused by oblique glancing of the microscope. Details of the instrumentation were reported elsewhere (39). The experiments were carried out by pouring a definite amount of aqueous solution into the trough. To attain equilibrium with a desired experimental temperature, the solution was allowed to stand about 25 min before the start of the experiment. The molecules already adsorbed at the surface during this span of time were removed by sweeping the surface with the movable Teflon barriers. Under these conditions, the surface concentration of the amphiphile molecules can be considered 0, i.e., π = 0 at t = 0. The increase in surface pressure was then followed with time and simultaneously the surface of the aqueous solution was observed by BAM. For CMC measurement, the surface tensions of the solutions of different concentrations were measured by a surface tensiometer (Kr¨uss K 10) equipped with a platinum plate. The solutions were transferred into a vessel that was thermostated by circulating water of a desired temperature. The surface tension measurements were started with a dilute solution and the subsequent concentrated solutions were made adding a previously prepared stock solution to the vessel. Establishment of equilibrium was checked by taking a series of readings after 15-min intervals until no significant change occurred. In order to eliminate the evaporation losses beyond 25◦ C, the vessel was covered with a lid. The accuracy of the measurements was within ±0.1 mN/m. Ultrapure water with a resistivity of 18 M · cm (Elgastat UHQ-PS) was used throughout the study. RESULTS AND DISCUSSION
Surface Properties of the Surfactants During the continuous adsorption of the molecules from the bulk at the air–water interface, π –t curves of both EGDE and EGTE monolayers show a cusp point followed by a pronounced plateau region, indicating the characteristic feature of the firstorder phase transition. Figure 1 shows the adsorption kinetics of EGDE and EGTE monolayers at the solution surfaces at different temperatures. The π –t curves for EDGE monolayers at 2, 5, and 10◦ C were taken with a 1.3 × 10−5 M solution, whereas those for 15, 20, and 23◦ C were taken with 2.0 × 10−5 , 2.5 × 10−5 , and 3.0 × 10−5 M solutions, respectively. On the other hand, the π–t curves for EGTE monolayers were taken with a 1.0 × 10−5 M solution. For the latter, we chose this concentration just to reduce the time length of the experiments, although the CMC values of the amphiphile range from 1.7 × 10−6 to 3.4 × 10−6 M over
PHASE BEHAVIOR AND MICELLIZATION
FIG. 1. (a) The π –t adsorption kinetics of aqueous solutions of EGDE at different temperatures with different concentrations: 2–10◦ C, 1.3 × 10−5 M; 15◦ C, 2.0 × 10−5 ; 20◦ C, 2.5 × 10−5 M; and 23◦ C, 3.0 × 10−5 M solutions. (b) The π –t adsorption kinetics of a 1.0 × 10−5 M aqueous solution of EGTE at different temperatures. The appearance of the phase transition is indicated by the arrows in each of the isotherms.
the temperatures of the experiments. Although the amphilpiles are structurally similar, their adsorption kinetics at the solution surface respond differently to temperature. For EGDE, the time necessary for the appearance of phase transition increases with increasing temperature (Fig. 1a). This fact becomes evident when we observe the π–t adsorption isotherms at 2, 5, and 10◦ C which were taken with a 1.3 × 10−5 M solution. On the other hand, the EGTE monolayers show a pronounced plateau region in the π–t adsorption isotherms at almost 0 surface pressure (Fig. 1b). Such phase behavior is due to the existence of gas; a (G)–LE phase transition as has been reported previously (40). After the plateau region of the G–LE coexistence state, the surface pressure starts to increase gradually and that leads to a cusp point followed by a plateau region for the LE–LC phase transition. The isotherms at lower temperatures have not attained their equilibrium values within the specified time of the experiments. The dynamic adsorption process takes a prolonged period of time to attain equilibrium at lower temperatures.
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Condensed domains observed by BAM in both cases after the cusp point in the adsorption isotherms is direct evidence of the existence of phase transition. Figure 2 shows the BAM images of EGDE monolayers at different temperatures. At 2◦ C, the condensed domains are found to be circular, with uniform brightness all over the domains. This suggests that the molecules are almost perpendicular with respect to the normal surface. The domains can retain their circular shape up to 5◦ C. However, the structures formed in the initial stage are found to be irregularly shaped (Fig. 2B) at this temperature, and they undergo relaxation to a circular shape (Figs. 2C and 2D) with time. Such a feature is obviously due to the existence of competition between the growth rate instability and the relaxation rate governed by the line tension that favors a circular shape to minimize the perimeter of a domain. Above 5◦ C, the domains are of a fingering pattern (Fig. 2E). The number of fingers in a domain is found to increase with increasing temperature (Fig. 2F). Pollard et al. (40) have reported that adsorbed monolayers of EGTE form circular domains at 22.5◦ C. We studied the surface morphology of the amphiphile over a wide range of temperatures. Figure 3 shows the BAM images of EGTE monolayers at different temperatures. At lower temperatures, EGTE monolayers form condensed circular domains with internal stripes. A maximum of three stripes is observed in a fully developed domain at 15◦ C (Fig. 3A). The internal stripes in a condensed domain are due to the sudden jump of the tilt-azimuthal direction of the molecules (8). The number of stripes in a domain decreases with increasing temperature, which is in accord with our previous reports (13, 14). At 25◦ C, the domains lose their stripe texture, showing uniform brightness all over the domains (Fig. 3C). In the case of EGTE, the domains are found to be circular up to 27◦ C. Since the hydrophobic alkyl chain of EGTE is longer than that of EGDE by two –CH2 – groups, it is expected that the former should have a higher line tension than the latter. Thus, the higher line tension of EGTE monolayers gives circular domains at higher temperatures than those of EGDE. At 30◦ C, the domains are of fingering pattern (Fig. 3D). Comparing the BAM images of Figs. 2 and 3 it can be seen that the images of EGDE at 2 and 10◦ C almost correspond to those of EGTE at 25 and 30◦ C, respectively. Temperature-Dependent Micellization of the Surfactants The CMC of the surfactants at different temperatures are taken from the sharp break in the surface tension vs concentration curves (data are not shown). The CMC values of non-ionic amphiphiles depend on the balance forces between the van der Waals interactions in the alkyl chains and the opposing hydration of the head groups. At a particular temperature, the CMC value of EGTE is much lower than the corresponding value of EGDE. This is because of the increase in the hydrophobic character of the amphiphile chain with increasing alkyl chain length. It is usually observed that the CMC values of non-ionic surfactants gradually decrease with increasing temperature, while those of ionic surfactants pass through a minimum nearly at room
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temperature and then increase with further increases in temperature. Unlike the observed behavior of the non-ionic surfactants, the CMC values of both EGDE and EGTE show a maximum at a definite temperature (Tmax ) and then decrease gradually with further increase in temperature. The maximum value of CMC is observed at 23 and 37◦ C for EGDE and EGTE, respectively (Fig. 4). Below Tmax , the increase in CMC values with increasing temperature could be the result of the thermal solubility and higher degree of hydration of the amphiphiles. Since hydrophobic interaction is endothermic in nature, we expect aggregation of the molecules in the form of micelles to be more favorable
with increasing temperature. So there must be a competition between the hydrophobic interaction and its opposing hydration of the head group during micellization. When the temperature exceeds Tmax , the hydrophobic effect dominates over the solubilizing effect and the CMC values decrease with increasing temperature above Tmax . We have measured the CMC values of the amphiphiles over a wide range of temperature. This may arise a question about the homogeneity of the solution since it is well known that an aqueous solution of a surfactant becomes turbid on heating to a temperature known as the cloud point. It depends on the structure
FIG. 2. BAM images of EGDE monolayers at different temperatures; (A) 2◦ C, (B–D) 5◦ C, (E) 10◦ C, and (F) 15◦ C. The initial growth of images at 5◦ C is irregular (B) and undergo relaxation to a circular shape with time (C and D). The bar in A indicates 100 µm.
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FIG. 3. BAM images of the condensed domains of EGTE monolayers at different temperatures; (A) 15◦ C, (B) 20◦ C, (C) 25◦ C, and (D) 30◦ C. The bar in image A indicates 100 µm.
of a surfactant and its concentration (41, 42). The appearance of turbidity is believed to be due to the sharp increase in aggregation number and the dehydration of the hydrophilic head groups with increasing temperature (43). The concentration of surfactant in the coexisting homogeneous aqueous phase is equal to the CMC of the surfactant at that temperature (16, 41–43). However, we did not observe any visible appearance of cloudiness during the experiments. Since the maximum concentration of the solution used in this study is around the maximum value of CMC, it can be inferred from the above facts that cloudiness will not occur in the solutions corresponding to the maximum CMC value at Tmax of the respective amphiphiles. The thermodynamics of the micelle formation of both ionic and non-ionic surfactants has been studied for a long time by measuring their CMC over a wide range of temperatures. Although these studies allow us to understand the nature of process involved in micelle formation, until now the thermodynamic treatment of micelle formation has not been quite satisfactory. In an attempt to show the temperature-dependent micellization of ionic surfactants, Muller (44) has shown that when CMC∗ is a minimum at temperature T ∗ , the CMC values at other temperatures can be given by
where Cp is the heat capacity change, R is the gas constant, and α the counter ion binding capability of a micelle that is defined as the ratio of number of surfactant ions to its counter ions in a micelle. We observed that Eq. [1] can be fairly applied in the case of non-ionic surfactants which show a maximum CMC over a particular temperature range in the form ln(CMC/CMCmax ) = [Cp /(1 + α)R][(1 − Tmax /T ) + ln(Tmax /T )],
where CMCmax is the maximum value at Tmax . The data treatment was performed similarly to that described by Muller. When ln CMC is plotted against [(1 − T /Tmax ) + ln(Tmax /T )], the slope and intercept gives Cp /R and ln CMCmax , respectively. From the value of Cp /R the enthalpy (Hm◦ ) and entropy (Sm◦ ) changes of micellization were calculated by the following expressions:
and
Hm◦ = Cp (T − Tmax )
[3]
Sm◦
[4]
=
◦ Smax
+ Cp ln T /Tmax ,
◦ where Smax = −G ◦max /Tmax = −R ln CMCmax .
ln(CMC/CMCmax ) = [Cp /(1 + α)R][(1 − Tmax /T + ln(Tmax /T )],
[1]
[2]
[5]
In line with Eq. [3] the values of Hm◦ of both EGDE and EGTE change from negative to positive with increasing
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the amphiphiles which bear a relatively shorter ethylene oxide chain (25). The dehydration of appreciable numbers of water molecules from the head group has been reported to be a major contributing factor for the negative enthalpy of micellization. On the other hand, a positive entropy change occurs due to the destruction of the iceberg around the monomeric units of the hydrophobic alkyl chains during their aggregation into a micelle core. However, at lower temperature the entropy change of micellization is negative, which may occur if the ordering effect of a substantial number of monomeric molecules outweighs the disordering effect of the destruction of the iceberg around the alkyl chain. Formation of Domains and Its Dependence on Micellization
FIG. 4. Dependence of the CMC values of (a) EGDE and (b) EGTE on temperature.
temperature, showing Hm◦ = 0 at Tmax . This behavior is consistent with the CMC values plotted in Fig. 4. Therefore, at Tmax , micellization is entirely an entropy-driven process. On the other hand, the entropy terms are negative at lower temperatures, which become positive and increase monotonically with increasing temperature (Table 1). Negative enthalpy and entropy of micellization have been reported by other investigators for TABLE 1 Thermodynamic Parameters of Micellization for EGDE and EGTE at Different Temperatures EGDE
EGTE
T /◦ C
Hm◦ (KJ mol−1 )
◦ Sm (JK−1 mol−1 )
10 15 20 25 30 35
−39.7 −24.5 −9.2 +6.1 +21.4 +36.7
−50 +3 +56 +107 +158 +208
T /◦ C
Hm◦ (KJ mol−1 )
◦ Sm (JK−1 mol−1 )
15 20 25 30 35 40 45
−39.9 −30.8 −21.7 −12.7 −3.6 +5.4 +14.5
−27 +3 +34 +64 +94 +123 +151
Brewster angle microscopic study reveals that the condensed domains in the monolayers of EGDE and EGTE are observed up to 23 and 37◦ C, respectively. Above these temperatures no cusp point is observed in the π –t adsorption isotherms irrespective of the concentration of the solutions, suggesting that phase transition is not possible above these temperatures. This can be made clear by the following example. The EGDE monolayers cannot show any characteristic feature of phase transition at ≥24◦ C even with a 4.0 × 10−5 M solution of EGDE (data are not shown), while the CMC value of the amphiphile is around 2.75 × 10−5 M (Fig. 4a) at this temperature. Figure 5a shows that the critical surface pressure necessary for the phase transition increases with increasing temperature and attains the highest value at Tmax that is the maximum temperature for the appearance of the phase transition. On the other hand, equilibrium surface pressure at ≥CMC decreases with increasing temperature. The two curves coincide at Tmax , which implies that critical surface pressure and equilibrium surface pressure at ≥CMC are equal at this temperature. Above Tmax the system needs still higher values of critical surface pressure (as shown by arrows in Fig. 5) for phase transition to occur. But the lower surface concentration of the molecules does not allow the system to attain the critical value when the temperature exceeds Tmax . At 24◦ C, the EGDE monolayer should attain a surface pressure of 49 mN/m for the phase transition. On the other hand, the equilibrium surface pressure attainable at and above CMC is around 47 mN/m, which is less than the surface pressure necessary for the phase transition at this temperature. This result suggests that phase transition is not possible in EGDE monolayers at ≥24◦ C. Again, Fig. 4a shows that above Tmax , the CMC values start to decrease gradually with increasing temperature. This suggests that when temperature exceeds Tmax , the stability of the micelles gradually increases. Therefore, the molecules prefer forming micelle in the bulk to adsorbing at the surface. Consequently, the system suffers from a shortage of 2-D surface concentration of the molecules to achieve the surface pressure necessary for the phase transition at and above this temperature. Again, coherence of the molecules in a domain is possible if the energy difference between the condensed and the expanded phases dominates the thermokinetic molecular motion. Increased molecular
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FIG. 5. Dependence of critical surface pressure, πc , necessary for the phase transition (I, II) and equilibrium surface pressure, π (CMC), attainable at and above CMC (I , II ) for EGDE (a) and EGTE (b) on temperature. The arrows in each of the plots indicate the hypothetical surface pressure necessary for the phase transition above Tmax of the respective amphiphiles.
motion and chain flexibility with increasing temperature cause poorer packing in the adsorbed layers and consequently the area per molecule increases. Therefore, a predominance of kinetic energy of the molecules over line tension at and above this temperature does not allow the molecules to cohere in a domain. As a whole, all these effects do not favor the molecules forming condensed domains in EGDE monolayers at ≥24◦ C. Similar phenomena hold in the case of EGTE, as shown in Figs. 4b and 5b, where phase transition and thereby formation of condensed domain is possible up to 37◦ C. Therefore, we expect that condensed domain formation in adsorbed layers is a function of both the surface concentration and the state of molecular arrangement in the bulk. If the experimental condition is more favorable for micellization in the bulk than adsorption at the surface, the system cannot acquire the necessary surface pressure for the phase transition due to the shortage of 2-D surface concentration. CONCLUSIONS
We have provided evidence of a first-order phase transition in adsorbed layers of EGDE and EGTE over a wide range of temperature. In both cases condensed domains are observed by
BAM just after the appearance of the cusp point in π –t curves. From the study of the phase behavior and the micellization of the amphiphiles at different temperatures, we have shown that phase transition in Gibbs monolayers is possible as long as the CMC values of the amphiphiles increase with increasing temperature. In contrast to the usual behavior of non-ionic surfactants, the CMC values of both surfactants increase with increasing temperature up to a maximum value at Tmax and then decrease gradually with further increases in temperature. Interestingly, the Tmax of the amphiphiles corresponds well to their respective maximum temperature of formation of condensed domain. The values of Hm◦ in both cases change from negative to positive, showing Hm◦ = 0, corresponding to the temperature of the maximum value of CMC. The values of Sm◦ also change from negative to positive with increasing temperature. In both cases, an enthalpy–entropy compensation effect is observed; when enthalpy contributes less to free energy, its counterpart entropy term is more effective in contributing to free energy being a negative value and vice versa. When the temperature is increased above Tmax , the CMC values start to decrease and the molecules prefer forming micelle to adsorbing at the surface. This results in a considerable decrease of 2-D surface concentration of the amphiphiles. As a result the system cannot acquire the necessary surface pressure for the phase transition due to the low 2-D surface concentration. In this paper, we emphasize that the amphiphile which forms condensed domain in adsorbed layers shows a maximum CMC at a definite temperature and the phase transition in the adsorbed layers is possible as long as the CMC values increase with increasing temperature. This temperature can be determined by measuring CMC as a function of temperature. Above this temperature, the higher degree of stability of micelles in the bulk would not allow the system to acquire sufficient surface pressure for a phase transition. ACKNOWLEDGMENTS We thank Associate Professor N. Suzuki of this laboratory for helpful discussion. Part of this research was supported by SVBL of Utsunomiya University.
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Tanford, C., J. Phys. Chem. 78, 2469 (1974). Stigter, D., J. Phys. Chem. 78, 2480 (1975). Pethica, B. A., and Arakawa, J., J. Colloid Interface Sci. 75, 441 (1980). Collaghan, A., Doyle, R., Alexander, E., and Papelu, R., Langmuir 9, 3422 (1993). Adamson, A. W., “Physical Chemistry of Surfaces.” Wiley, New York, 1990. Mukerjee, P., and Mysels, K., J. Phys. Chem. 59, 2937 (1955). Rose, S., and Olivier, J. P., J. Phys. Chem. 63, 1673 (1959). Ekwall, P., Mandell, L., and Solyom, P., J. Colloid Interface Sci. 35, 519 (1971). Muller, N., and Birkham, R. H., J. Phys. Chem. 71, 957 (1967). Frindi, M., Michels, B., Levy, H., and Zana, R., Langmuir 10, 1140 (1994). Kato, T., Tatehara, A., Suzuki, N., Iimura, K., Araki, T., and Iriyama, K., Jpn. J. Appl. Phys. 34, L911 (1995). Pollard, M. L., Rennan, P., Steiner, C., and Maldarelli, C., Langmuir 14, 7222 (1998). Cohen, A. W., and Rosen, M. J., J. Am. Oil Chem. Soc. 58, 1062 (1981). Moroi, Y., “Micelles—Theoretical and Applied Aspects.” Plenum, New York, 1992. Paradies, H. H., J. Phys. Chem. 84, 599 (1980). Muller, N., Langmuir 10, 2202 (1994).
Dependence of Phase Behavior of Some Non-ionic Surfactants at the Air–Water Interface on Micellization in the Bulk Md. Nazrul Islam and Teiji Kato1 Department of Applied Chemistry, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya 321-8585, Japan Received November 28, 2001; accepted May 9, 2002
The temperature-dependent surface phase behavior of two sparingly soluble surfactants, namely, ethylene glycol n-dodecyl ether (EGDE) and ethylene glycol n-tetradecyl ether (EGTE), at the air– water interface was investigated by film balance and Brewster angle microscopy (BAM). A cusp point followed by a pronounced plateau region in the surface pressure–time (π–t) adsorption isotherms of the amphiphiles measured by film balance indicates the first-order phase transition. Bright two-dimensional condensed phase domains in a dark background are observed by BAM just after the phase transition. In both cases the critical surface pressure necessary for the phase transition increases with increasing temperature. The domains are found to be circular up to 5 and 27◦ C for EGDE and EGTE, respectively, above which they show a fingering pattern. Condensed domains are observed up to 23 and 37◦ C for EGDE and EGTE, respectively. The surface properties of the amphiphiles are found to be markedly affected by their tendency to aggregate in the bulk as micelles. The CMC values of both the amphiphiles show a maximum at a definite temperature, Tmax , that corresponds well to their respective maximum temperatures of domain formation. An increase in temperature beyond Tmax results in an increasing trend for the formation of micelles. Consequently the system suffers from a shortage of two-dimensional surface concentration of the molecules to attain the surface pressure necessary for phase transition. With increasing temperature, the enthalpy, H◦m , and entropy, S◦m , of micellization change from negative to positive in both cases. An enthalpy–entropy compensation effect is found to hold for both the amphiphiles over the entire temperature range. The thermodynamic quantities reveal that the increase in temperature is favorable for micellization when the temperature exceeds the corresponding Tmax of the amphiphiles. C 2002 Elsevier Science (USA) Key Words: non-ionic surfactant; phase transition; Brewster angle microscopy; adsorbed layers; line tension; critical micelle concentration.
INTRODUCTION
Langmuir monolayers at the air–water interface provide a simple model for understanding the existence of various phases in two-dimensional systems. When the monolayer is compressed 1 To whom correspondence and reprint requests should be addressed. Fax: +81-28-689-6179. E-mail: [email protected].
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isothermally, it undergoes a transition from a two-dimensional (2-D) lower density phase to a higher density condensed phase showing a cusp point followed by a plateau region in the π – A isotherm, provided that the van der Waals interaction between the hydrophobic alkyl chains and the repulsive interaction between the head groups favor the coherence of the molecules. Recent development of Brewster angle microscopy (BAM) (1, 2) allows direct visualization of the change in the surface morphology during the phase transition without using any probe impurity. Moreover, by placing an analyzer in the path of the reflected beam it is possible to detect the internal anisotropy of the molecules in a domain that occurs due to the difference in the surface reflectivity of the p-polarized light (3, 4). Despite extensive work on the adsorption kinetics of watersoluble amphiphiles, the concept of phase transition and structure formation in adsorbed layers has been reported quite recently. H´enon et al. (5–7) first reported such phase transition and structure formation during adsorption from the aqueous solution of sparingly soluble fatty acids. Although they reported the striking influence of surface-active impurities in the formation of condensed domains, now a number of sparingly soluble highly purified amphiphiles are known to form condensed domains in adsorbed layers (8–15). For a clear understanding of the kinetics and the thermodynamic behavior, the π –t adsorption kinetics of Gibbs monolayers has been compared with the π –A isotherm of Langmuir monolayers. It is found that due to the slow and homogeneous growth process in Gibbs monolayers, the condensed phase domains are more ordered than those in Langmuir monolaers (9–12). Recently, it has been reported that at a particular temperature a minimum bulk concentration is necessary for the phase transition in Gibbs monolayers (11, 13, 14) and if the bulk concentration is increased, phase transition can occur at higher temperatures (14). However, each amphiphile has a definite temperature, above which it cannot show any indicative feature of phase transition, no matter whatever the bulk concentration is. In a recent paper we have reported that 2-hydroxyethyllaurate can form a condensed domain maximum up to 25◦ C (14). Similar behavior has also been observed for ethylene glycol n-dodecyl ether (EGDE) and ethylene glycol n-tetradecyl ether (EGTE), which form condensed domains up to 23 and 37◦ C, respectively. Now the question arises why 0021-9797/02 $35.00
C 2002 Elsevier Science (USA)
All rights reserved.
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condensed domains are not observed above a particular temperature although the bulk concentration is sufficiently high. To understand what is behind this behavior, the question of a possible dependency of the surface property of molecules on their bulk property should be addressed. Unlike with adsorption at the air/water interface, amphiphile molecules can order themselves in the bulk of a solution. In this process, the amphiphile molecules form a micelle core by the cooperative association of the hydrophobic alkyl chains, while the hydrophilic head groups extend from the core into the aqueous medium. Like the surface properties, the bulk properties of an amphiphile also depend on the length of the alkyl chain, the size and charge of the head group, temperature, and the nature of the solvent medium. Collectively these phenomena govern the bulk properties, such as the size of a micelle, the critical micelle concentration (CMC), and the degree of association of an amphiphile. Micellization is an important phenomenon, because a number of interfacial phenomena, such as detergency and solubilization, depend on the existence of micelles in solution (16). Of late, micelles have become a field of great interest to the organic chemist for their unusual catalytic functions in organic reactions (17, 18). Extensive research work has been reported in the literature concerning the micelle size and shape, the thermodynamics of micellization, and the effect of impurity, some of which are listed for non-ionic (19–26) and ionic (27–32) surfactants. Besides the surface tensiometry, other micelle-induced properties (33), such as electrical conductivity (34), dye-solubilization (35), refractive index (36), nuclear magnetic resonance spectroscopy (37) and spectrofluorometry (38), have also been employed to measure CMC and other related properties. The objective of the present work was twofold. The first was to study the adsorption kinetics and the surface morphology of amphiphiles at different temperatures. The second was to measure the critical micelle concentration by measuring surface tension at different temperatures and to investigate how micellization affects the surface concentration, and thereby the surface morphology, of amphiphiles. We observed that both the amphiphiles show a maximum in the CMC vs temperature curves at a definite temperature, Tmax . These temperatures are 23 and 37◦ C for EGDE and EGTE, respectively, which correspond well to their maximum temperature of domain formation. Above Tmax , the CMC values of both the amphiphiles gradually decrease, showing a preferential tendency to undergo micellization. As a result the system cannot acquire the necessary surface pressure for the phase transition due to the low 2-D surface concentration of the molecules. EXPERIMENTAL
The amphiphiles EGDE and EGTE were supplied by Nikko Chemical Company Ltd. (Tokyo, Japan) with a purity of >99% and were used without further purification. The experimental setup for the adsorption kinetics and surface morphology study
was equipped with a handmade Langmuir trough 2 mm thick, above which a BAM was mounted. Surface pressure was measured by the Wilhelmey method using a small rectangular glass plate. The BAM is composed of a 20-mW semiconductor laser, a Glan-Thompson polarizer, an analyzer, a zooming microscope with a CCD camera of high sensitivity, a TV monitor, and a video recording system. Images recorded were treated with image processing software to maximize the contrast and to correct the distortion of the images caused by oblique glancing of the microscope. Details of the instrumentation were reported elsewhere (39). The experiments were carried out by pouring a definite amount of aqueous solution into the trough. To attain equilibrium with a desired experimental temperature, the solution was allowed to stand about 25 min before the start of the experiment. The molecules already adsorbed at the surface during this span of time were removed by sweeping the surface with the movable Teflon barriers. Under these conditions, the surface concentration of the amphiphile molecules can be considered 0, i.e., π = 0 at t = 0. The increase in surface pressure was then followed with time and simultaneously the surface of the aqueous solution was observed by BAM. For CMC measurement, the surface tensions of the solutions of different concentrations were measured by a surface tensiometer (Kr¨uss K 10) equipped with a platinum plate. The solutions were transferred into a vessel that was thermostated by circulating water of a desired temperature. The surface tension measurements were started with a dilute solution and the subsequent concentrated solutions were made adding a previously prepared stock solution to the vessel. Establishment of equilibrium was checked by taking a series of readings after 15-min intervals until no significant change occurred. In order to eliminate the evaporation losses beyond 25◦ C, the vessel was covered with a lid. The accuracy of the measurements was within ±0.1 mN/m. Ultrapure water with a resistivity of 18 M · cm (Elgastat UHQ-PS) was used throughout the study. RESULTS AND DISCUSSION
Surface Properties of the Surfactants During the continuous adsorption of the molecules from the bulk at the air–water interface, π –t curves of both EGDE and EGTE monolayers show a cusp point followed by a pronounced plateau region, indicating the characteristic feature of the firstorder phase transition. Figure 1 shows the adsorption kinetics of EGDE and EGTE monolayers at the solution surfaces at different temperatures. The π –t curves for EDGE monolayers at 2, 5, and 10◦ C were taken with a 1.3 × 10−5 M solution, whereas those for 15, 20, and 23◦ C were taken with 2.0 × 10−5 , 2.5 × 10−5 , and 3.0 × 10−5 M solutions, respectively. On the other hand, the π–t curves for EGTE monolayers were taken with a 1.0 × 10−5 M solution. For the latter, we chose this concentration just to reduce the time length of the experiments, although the CMC values of the amphiphile range from 1.7 × 10−6 to 3.4 × 10−6 M over
PHASE BEHAVIOR AND MICELLIZATION
FIG. 1. (a) The π –t adsorption kinetics of aqueous solutions of EGDE at different temperatures with different concentrations: 2–10◦ C, 1.3 × 10−5 M; 15◦ C, 2.0 × 10−5 ; 20◦ C, 2.5 × 10−5 M; and 23◦ C, 3.0 × 10−5 M solutions. (b) The π –t adsorption kinetics of a 1.0 × 10−5 M aqueous solution of EGTE at different temperatures. The appearance of the phase transition is indicated by the arrows in each of the isotherms.
the temperatures of the experiments. Although the amphilpiles are structurally similar, their adsorption kinetics at the solution surface respond differently to temperature. For EGDE, the time necessary for the appearance of phase transition increases with increasing temperature (Fig. 1a). This fact becomes evident when we observe the π–t adsorption isotherms at 2, 5, and 10◦ C which were taken with a 1.3 × 10−5 M solution. On the other hand, the EGTE monolayers show a pronounced plateau region in the π–t adsorption isotherms at almost 0 surface pressure (Fig. 1b). Such phase behavior is due to the existence of gas; a (G)–LE phase transition as has been reported previously (40). After the plateau region of the G–LE coexistence state, the surface pressure starts to increase gradually and that leads to a cusp point followed by a plateau region for the LE–LC phase transition. The isotherms at lower temperatures have not attained their equilibrium values within the specified time of the experiments. The dynamic adsorption process takes a prolonged period of time to attain equilibrium at lower temperatures.
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Condensed domains observed by BAM in both cases after the cusp point in the adsorption isotherms is direct evidence of the existence of phase transition. Figure 2 shows the BAM images of EGDE monolayers at different temperatures. At 2◦ C, the condensed domains are found to be circular, with uniform brightness all over the domains. This suggests that the molecules are almost perpendicular with respect to the normal surface. The domains can retain their circular shape up to 5◦ C. However, the structures formed in the initial stage are found to be irregularly shaped (Fig. 2B) at this temperature, and they undergo relaxation to a circular shape (Figs. 2C and 2D) with time. Such a feature is obviously due to the existence of competition between the growth rate instability and the relaxation rate governed by the line tension that favors a circular shape to minimize the perimeter of a domain. Above 5◦ C, the domains are of a fingering pattern (Fig. 2E). The number of fingers in a domain is found to increase with increasing temperature (Fig. 2F). Pollard et al. (40) have reported that adsorbed monolayers of EGTE form circular domains at 22.5◦ C. We studied the surface morphology of the amphiphile over a wide range of temperatures. Figure 3 shows the BAM images of EGTE monolayers at different temperatures. At lower temperatures, EGTE monolayers form condensed circular domains with internal stripes. A maximum of three stripes is observed in a fully developed domain at 15◦ C (Fig. 3A). The internal stripes in a condensed domain are due to the sudden jump of the tilt-azimuthal direction of the molecules (8). The number of stripes in a domain decreases with increasing temperature, which is in accord with our previous reports (13, 14). At 25◦ C, the domains lose their stripe texture, showing uniform brightness all over the domains (Fig. 3C). In the case of EGTE, the domains are found to be circular up to 27◦ C. Since the hydrophobic alkyl chain of EGTE is longer than that of EGDE by two –CH2 – groups, it is expected that the former should have a higher line tension than the latter. Thus, the higher line tension of EGTE monolayers gives circular domains at higher temperatures than those of EGDE. At 30◦ C, the domains are of fingering pattern (Fig. 3D). Comparing the BAM images of Figs. 2 and 3 it can be seen that the images of EGDE at 2 and 10◦ C almost correspond to those of EGTE at 25 and 30◦ C, respectively. Temperature-Dependent Micellization of the Surfactants The CMC of the surfactants at different temperatures are taken from the sharp break in the surface tension vs concentration curves (data are not shown). The CMC values of non-ionic amphiphiles depend on the balance forces between the van der Waals interactions in the alkyl chains and the opposing hydration of the head groups. At a particular temperature, the CMC value of EGTE is much lower than the corresponding value of EGDE. This is because of the increase in the hydrophobic character of the amphiphile chain with increasing alkyl chain length. It is usually observed that the CMC values of non-ionic surfactants gradually decrease with increasing temperature, while those of ionic surfactants pass through a minimum nearly at room
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temperature and then increase with further increases in temperature. Unlike the observed behavior of the non-ionic surfactants, the CMC values of both EGDE and EGTE show a maximum at a definite temperature (Tmax ) and then decrease gradually with further increase in temperature. The maximum value of CMC is observed at 23 and 37◦ C for EGDE and EGTE, respectively (Fig. 4). Below Tmax , the increase in CMC values with increasing temperature could be the result of the thermal solubility and higher degree of hydration of the amphiphiles. Since hydrophobic interaction is endothermic in nature, we expect aggregation of the molecules in the form of micelles to be more favorable
with increasing temperature. So there must be a competition between the hydrophobic interaction and its opposing hydration of the head group during micellization. When the temperature exceeds Tmax , the hydrophobic effect dominates over the solubilizing effect and the CMC values decrease with increasing temperature above Tmax . We have measured the CMC values of the amphiphiles over a wide range of temperature. This may arise a question about the homogeneity of the solution since it is well known that an aqueous solution of a surfactant becomes turbid on heating to a temperature known as the cloud point. It depends on the structure
FIG. 2. BAM images of EGDE monolayers at different temperatures; (A) 2◦ C, (B–D) 5◦ C, (E) 10◦ C, and (F) 15◦ C. The initial growth of images at 5◦ C is irregular (B) and undergo relaxation to a circular shape with time (C and D). The bar in A indicates 100 µm.
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FIG. 3. BAM images of the condensed domains of EGTE monolayers at different temperatures; (A) 15◦ C, (B) 20◦ C, (C) 25◦ C, and (D) 30◦ C. The bar in image A indicates 100 µm.
of a surfactant and its concentration (41, 42). The appearance of turbidity is believed to be due to the sharp increase in aggregation number and the dehydration of the hydrophilic head groups with increasing temperature (43). The concentration of surfactant in the coexisting homogeneous aqueous phase is equal to the CMC of the surfactant at that temperature (16, 41–43). However, we did not observe any visible appearance of cloudiness during the experiments. Since the maximum concentration of the solution used in this study is around the maximum value of CMC, it can be inferred from the above facts that cloudiness will not occur in the solutions corresponding to the maximum CMC value at Tmax of the respective amphiphiles. The thermodynamics of the micelle formation of both ionic and non-ionic surfactants has been studied for a long time by measuring their CMC over a wide range of temperatures. Although these studies allow us to understand the nature of process involved in micelle formation, until now the thermodynamic treatment of micelle formation has not been quite satisfactory. In an attempt to show the temperature-dependent micellization of ionic surfactants, Muller (44) has shown that when CMC∗ is a minimum at temperature T ∗ , the CMC values at other temperatures can be given by
where Cp is the heat capacity change, R is the gas constant, and α the counter ion binding capability of a micelle that is defined as the ratio of number of surfactant ions to its counter ions in a micelle. We observed that Eq. [1] can be fairly applied in the case of non-ionic surfactants which show a maximum CMC over a particular temperature range in the form ln(CMC/CMCmax ) = [Cp /(1 + α)R][(1 − Tmax /T ) + ln(Tmax /T )],
where CMCmax is the maximum value at Tmax . The data treatment was performed similarly to that described by Muller. When ln CMC is plotted against [(1 − T /Tmax ) + ln(Tmax /T )], the slope and intercept gives Cp /R and ln CMCmax , respectively. From the value of Cp /R the enthalpy (Hm◦ ) and entropy (Sm◦ ) changes of micellization were calculated by the following expressions:
and
Hm◦ = Cp (T − Tmax )
[3]
Sm◦
[4]
=
◦ Smax
+ Cp ln T /Tmax ,
◦ where Smax = −G ◦max /Tmax = −R ln CMCmax .
ln(CMC/CMCmax ) = [Cp /(1 + α)R][(1 − Tmax /T + ln(Tmax /T )],
[1]
[2]
[5]
In line with Eq. [3] the values of Hm◦ of both EGDE and EGTE change from negative to positive with increasing
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the amphiphiles which bear a relatively shorter ethylene oxide chain (25). The dehydration of appreciable numbers of water molecules from the head group has been reported to be a major contributing factor for the negative enthalpy of micellization. On the other hand, a positive entropy change occurs due to the destruction of the iceberg around the monomeric units of the hydrophobic alkyl chains during their aggregation into a micelle core. However, at lower temperature the entropy change of micellization is negative, which may occur if the ordering effect of a substantial number of monomeric molecules outweighs the disordering effect of the destruction of the iceberg around the alkyl chain. Formation of Domains and Its Dependence on Micellization
FIG. 4. Dependence of the CMC values of (a) EGDE and (b) EGTE on temperature.
temperature, showing Hm◦ = 0 at Tmax . This behavior is consistent with the CMC values plotted in Fig. 4. Therefore, at Tmax , micellization is entirely an entropy-driven process. On the other hand, the entropy terms are negative at lower temperatures, which become positive and increase monotonically with increasing temperature (Table 1). Negative enthalpy and entropy of micellization have been reported by other investigators for TABLE 1 Thermodynamic Parameters of Micellization for EGDE and EGTE at Different Temperatures EGDE
EGTE
T /◦ C
Hm◦ (KJ mol−1 )
◦ Sm (JK−1 mol−1 )
10 15 20 25 30 35
−39.7 −24.5 −9.2 +6.1 +21.4 +36.7
−50 +3 +56 +107 +158 +208
T /◦ C
Hm◦ (KJ mol−1 )
◦ Sm (JK−1 mol−1 )
15 20 25 30 35 40 45
−39.9 −30.8 −21.7 −12.7 −3.6 +5.4 +14.5
−27 +3 +34 +64 +94 +123 +151
Brewster angle microscopic study reveals that the condensed domains in the monolayers of EGDE and EGTE are observed up to 23 and 37◦ C, respectively. Above these temperatures no cusp point is observed in the π –t adsorption isotherms irrespective of the concentration of the solutions, suggesting that phase transition is not possible above these temperatures. This can be made clear by the following example. The EGDE monolayers cannot show any characteristic feature of phase transition at ≥24◦ C even with a 4.0 × 10−5 M solution of EGDE (data are not shown), while the CMC value of the amphiphile is around 2.75 × 10−5 M (Fig. 4a) at this temperature. Figure 5a shows that the critical surface pressure necessary for the phase transition increases with increasing temperature and attains the highest value at Tmax that is the maximum temperature for the appearance of the phase transition. On the other hand, equilibrium surface pressure at ≥CMC decreases with increasing temperature. The two curves coincide at Tmax , which implies that critical surface pressure and equilibrium surface pressure at ≥CMC are equal at this temperature. Above Tmax the system needs still higher values of critical surface pressure (as shown by arrows in Fig. 5) for phase transition to occur. But the lower surface concentration of the molecules does not allow the system to attain the critical value when the temperature exceeds Tmax . At 24◦ C, the EGDE monolayer should attain a surface pressure of 49 mN/m for the phase transition. On the other hand, the equilibrium surface pressure attainable at and above CMC is around 47 mN/m, which is less than the surface pressure necessary for the phase transition at this temperature. This result suggests that phase transition is not possible in EGDE monolayers at ≥24◦ C. Again, Fig. 4a shows that above Tmax , the CMC values start to decrease gradually with increasing temperature. This suggests that when temperature exceeds Tmax , the stability of the micelles gradually increases. Therefore, the molecules prefer forming micelle in the bulk to adsorbing at the surface. Consequently, the system suffers from a shortage of 2-D surface concentration of the molecules to achieve the surface pressure necessary for the phase transition at and above this temperature. Again, coherence of the molecules in a domain is possible if the energy difference between the condensed and the expanded phases dominates the thermokinetic molecular motion. Increased molecular
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FIG. 5. Dependence of critical surface pressure, πc , necessary for the phase transition (I, II) and equilibrium surface pressure, π (CMC), attainable at and above CMC (I , II ) for EGDE (a) and EGTE (b) on temperature. The arrows in each of the plots indicate the hypothetical surface pressure necessary for the phase transition above Tmax of the respective amphiphiles.
motion and chain flexibility with increasing temperature cause poorer packing in the adsorbed layers and consequently the area per molecule increases. Therefore, a predominance of kinetic energy of the molecules over line tension at and above this temperature does not allow the molecules to cohere in a domain. As a whole, all these effects do not favor the molecules forming condensed domains in EGDE monolayers at ≥24◦ C. Similar phenomena hold in the case of EGTE, as shown in Figs. 4b and 5b, where phase transition and thereby formation of condensed domain is possible up to 37◦ C. Therefore, we expect that condensed domain formation in adsorbed layers is a function of both the surface concentration and the state of molecular arrangement in the bulk. If the experimental condition is more favorable for micellization in the bulk than adsorption at the surface, the system cannot acquire the necessary surface pressure for the phase transition due to the shortage of 2-D surface concentration. CONCLUSIONS
We have provided evidence of a first-order phase transition in adsorbed layers of EGDE and EGTE over a wide range of temperature. In both cases condensed domains are observed by
BAM just after the appearance of the cusp point in π –t curves. From the study of the phase behavior and the micellization of the amphiphiles at different temperatures, we have shown that phase transition in Gibbs monolayers is possible as long as the CMC values of the amphiphiles increase with increasing temperature. In contrast to the usual behavior of non-ionic surfactants, the CMC values of both surfactants increase with increasing temperature up to a maximum value at Tmax and then decrease gradually with further increases in temperature. Interestingly, the Tmax of the amphiphiles corresponds well to their respective maximum temperature of formation of condensed domain. The values of Hm◦ in both cases change from negative to positive, showing Hm◦ = 0, corresponding to the temperature of the maximum value of CMC. The values of Sm◦ also change from negative to positive with increasing temperature. In both cases, an enthalpy–entropy compensation effect is observed; when enthalpy contributes less to free energy, its counterpart entropy term is more effective in contributing to free energy being a negative value and vice versa. When the temperature is increased above Tmax , the CMC values start to decrease and the molecules prefer forming micelle to adsorbing at the surface. This results in a considerable decrease of 2-D surface concentration of the amphiphiles. As a result the system cannot acquire the necessary surface pressure for the phase transition due to the low 2-D surface concentration. In this paper, we emphasize that the amphiphile which forms condensed domain in adsorbed layers shows a maximum CMC at a definite temperature and the phase transition in the adsorbed layers is possible as long as the CMC values increase with increasing temperature. This temperature can be determined by measuring CMC as a function of temperature. Above this temperature, the higher degree of stability of micelles in the bulk would not allow the system to acquire sufficient surface pressure for a phase transition. ACKNOWLEDGMENTS We thank Associate Professor N. Suzuki of this laboratory for helpful discussion. Part of this research was supported by SVBL of Utsunomiya University.
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