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Line Tension Induced Instability of Condensed Domains Formed in Adsorbed Monolayers at the Air-Water Interface Md. Mufazzal Hossain and Teiji Kato* Department of Applied Chemistry, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya 321-8585, Japan Received December 28, 1999. In Final Form: September 18, 2000 The morphological features and textures in condensed domains formed during first-order phase transition in adsorbed monolayers of 2-hydroxyethyl laurate have been studied at different temperatures. Domains in these monolayers are not observed at g26 °C, indicating that the critical temperature for the phase transition is near this value. Under equilibrium conditions, the shapes of the domains show a transition from circular to fingering pattern near 15 °C. The domains have more branching in their structures with a further increase in the temperature. Increased formation rate by a temperature jump causes fractal domains at g15 °C but does not change the domain shapes at lower temperatures. The fractal structures formed by a high growth rate undergo relaxation to their equilibrium shapes within 25 min. A continuous variation in the textures of the domains with temperature is observed. Similar to the shape transition, above 13 °C the domains show a transition from stripe texture to one of uniform molecular orientation. Below this temperature, the width of the stripes formed reduces with decreasing temperature. At 13 °C, the texture is either absent or present as a special fingering in the stripes.
Introduction Langmuir monolayers are often characterized by measuring π-A isotherms together with some other microscopic and/or spectroscopic results. Fluorescence microscopy (FM)1,2 and Brewster angle microscopy (BAM)3,4 are two such powerful tools for in situ characterization of the monolayer morphologies at the air-water interface. In recent years a large variety of monolayer structures have been visualized by these techniques. The morphological shapes of the condensed phase observed during compression were found to be dependent on a number of factors such as the nature of the amphiphilic molecules, the temperature, the modification of the subphase water, the presence of impurity, and the compression rate. The equilibrium shapes of the domains are governed in part by a competition between the line tension and the dipoledipole repulsion between the molecules.5,6 High line tension favors circular shape domains to reduce the area,7 while dipole-dipole repulsion tends to stabilize noncircular domains. With increasing temperature, branching of the circular shape domains for the same amphiphile in spread monolayers was observed and explained on the basis of diffusion-limited aggregation of molecules in the domains.8 Miller et al.9,10 found fractal-like structures in phospholipid monolayers and stated that constitutional supercooling due to different solubilities of impurities in * To whom correspondence should be addressed. Phone: +81-28-689-6170. Fax: +81-28-689-6179. E-mail: teiji@ cc.utsunomiya-u.ac.jp. (1) Tscharner, V. von; McConnell, Biophys. J. 1981, 36, 36. (2) Losche, M.; Mo¨hwald, H. Rev. Sci. Instrum. 1984, 55, 1968. (3) He´non, S.; Meunier, J. Rev. Sci. Instrum. 1991, 62, 936. (4) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590. (5) Keller, D. J.; McConnell, H. M.; Moy, V. T. J. Phys. Chem. 1986, 90, 2311. (6) Andelman, D.; Brochard, F.; Joanny, J. F.J. Chem. Phys. 1987, 86, 3673. (7) Siegel, S.; Vollhardt, D. Thin Solid Films 1996, 284/285, 424. (8) Suresh, K. A.; Nittmann, J.; Rondelez, F. Europhys. Lett. 1988, 6, 437. (9) Miller, A.; Knoll, W.; Mo¨hwald, H. Phys. Rev. Lett. 1986, 56, 2633. (10) Miller, A.; Mo¨hwald, H. J. Chem. Phys. 1987, 86, 4258.
the two different phases (solid and fluid) governs such structure formation. McConnell et al.11 theoretically showed that a second-order phase transition is also possible in Langmuir monolayers during compression. Thus a circular shape domain can change to an elliptical domain due to the second-order transition.11,12 However, the shapes of the domains formed under nonequilibrium conditions may differ from equilibrium shapes. Thus, fractal domains can be formed by the very rapid compression of the spread monolayers, although the equilibrium shapes are circular.13,14 On the other hand, different textures in the domains such as star,15,16 stripe,16-18 and boojum19,20 in monolayers have also been reported in the literature. Qiu et al.21 examined the variation of domain textures with temperature. At high temperatures, the domains have uniform textures consisting of molecules oriented normal to the surface. When the temperature is lowered, the domains undergo a sharp transition to a tilted phase, causing textures in the domains.21,22 Despite extensive work on morphologies and textures of Langmuir monolayers, it is only recently that investigations of adsorbed monolayers at the air-water interface have begun. Phase transition and therefore condensed domain formation are also allowed in Gibbs (11) Keller, D. J.; Korb, J. P.; McConnell, H. M. J. Phys. Chem. 1987, 91, 6417. (12) Weis, R. M.; McConnell, H. M. J. Phys. Chem. 1985, 89, 4453. (13) Gehlert, U.; Vollhardt, D. Langmuir 1997, 13, 277. (14) Weidemann, G.; Vollhardt, D. Langmuir 1997, 13, 1623. (15) He´non, S.; Meunier, J. J. Chem. Phys. 1993, 98, 9148. (16) Overbeck, G. A.; Ho¨nig, D.; Mo¨bius, D. Thin Solid Films 1994, 242, 213. (17) Ruiz-Garcia, J.; Qui, X.; Tsao, M. W.; Marshall, G.; Knobler, C. M.; Overbeck, G. A.; Mo¨bius, D. J. Phys. Chem. 1993, 97, 6955. (18) Rivie`re, S.; He´non, S.; Meunier, J. Phys. Rev. E 1994, 49, 1375. (19) Schwartz, D. K.; Tsao, M.-W.; Knobler, C. M. J. Chem. Phys. 1994, 101, 8258. (20) Fischer, T. M.; Bruinsma, R. F.; Knobler, C. M. Phys. Rev. E 1994, 50, 413. (21) Qui, X.; Ruiz-Gercia, J.; Stine, K. J.; Knobler, C. M.; Selinger, J. V. Phys. Rev. Lett. 1991, 67, 703. (22) Fischer, B.; Tsao, M.-W.; Ruiz-Garcia, J.; Ficher, T. M.; Schwartz, D. K.; Knobler, C. M. J. Phys. Chem. 1994, 98, 7430.
10.1021/la991710p CCC: $19.00 © 2000 American Chemical Society Published on Web 12/02/2000
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monolayers of specially tailored amphiphiles during adsorption from aqueous solution. Although He´non et al.15,18,23 stated that such condensed domain formation is due to sparingly soluble amphiphiles or the effect of less soluble impurities present in the surfactants, the highly surface active, purified, and slightly water soluble amphiphiles are known to form condensed domains.24-30 In our previous reports, we provided sufficient evidence for the phase transition in the adsorbed monolayers of a highly purified amphiphile, 2-hydroxyethyl laurate (2-HEL), at different temperatures up to 10 °C. We also stated that such a phase transition is a transient or kinetic phenomenon on the way to the global equilibrium.27,28 It has been revealed, however, that both thermodynamic properties such as critical two-dimensional (2-D) surface density for the phase transition and major morphological features of the domains such as shapes and crystal structures are similar for both Gibbs and Langmuir monolayers.25-27 Still, a question remains unanswered as to whether some other experimental variables, which according to previous studies affect the morphology of the domains in spread monolayers, affect the domains in the adsorbed monolayers similarly. The aim of this paper is to answer this question. Condensed domain formation in adsorbed monolayers of purified amphiphiles has extended our understanding about ordering in two-dimensions without any applied external forces. The system appears to be in a pseudoequilibrated state; thus, we can avoid the compression which reportedly affects the domain morphology. By using a highly surface active and purified amphiphile, we can also neglect the effect of impurities. The rate of formation of the domains can be controlled by changing the concentrations or the temperatures. In this report we discuss the formation of domains with a variety of textures and morphological features in Gibbs monolayers under different sets of experimental conditions with the same amphiphile. Nonequilibrium structure formation in these monolayers is reported for the first time. Conditions necessary for the phase transition in these monolayers are also discussed. Experimental Section The amphiphile, 2-hydroxyethyl laurate, was synthesized with a purity g99.5% in our laboratory.31 The high purity requirement for studying interfacial properties was checked by both 400 MHz 1H NMR and tensiometer (KRUSS K10). By the latter method, the equilibrium surface tension vs concentration curve was measured at 26 °C ( 0.2 °C to determine the critical micelle concentration (cmc). The absence of a minimum in this curve indicates that the prepared amphiphile contains negligible or no impurity of higher surface activity (Figure 1).32 The temperature was controlled by circulating water from a low-temperature bath (YAMATO, BU150A). Ultrapure water of resistivity 18 MΩ cm (Elgastat, UHQ-PS) was used throughout the present study. All other experiments were performed in a very shallow type home-built Langmuir trough (2 mm depth), above which a BAM was mounted. Surface pressure was measured by the Wilhelmy (23) He´non, S.; Meunier, J. Thin Solid Films 1993, 234, 471. (24) Melzer, V.; Vollhardt, D.; Phys. Rev. Lett. 1996, 76, 3770. (25) Vollhardt, D.; Melzer, V. J. Phys. Chem. B 1997, 101, 3370. (26) Melzer, V.; Vollhardt, D.; Brezesinski, G.; Mo¨hwald, H. J. Phys. Chem. B 1998, 102, 591. (27) Hossain, M. M.; Yoshida, M.; Iimura, K.; Suzuki, N.; Kato, T. Colloids Surf. A 2000, 171, 105. (28) Hossain M. M.; Yoshida, M.; Kato, T. Langmuir 2000, 16, 3345. (29) Fainerman, V. B.; Vollhardt, D.; V. Melzer, J. Chem. Phys. 1997, 107, 243. (30) Vollhardt, D. Adv. Colloid Interface Sci. 1999, 79, 19. (31) Bevan, T. H.; Malkin, T.; Smith, D. B. J. Chem. Soc. 1955, pt I, 1043. (32) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 21, 331.
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Figure 1. A plot of γ vs log C at 26 °C for determination of cmc.
Figure 2. π-t adsorption kinetics at different temperatures with different concentrations of 2-HEL: (2-10 °C) 1.4 × 10-5 M, (15 °C) 2.2 × 10-5 M, (20 °C) 3.0 × 10-5 M, and (25 °C) 5.0 × 10-5 M solutions. The arrows indicate the position of the cusp points. method using a small glass plate. This plate was cleaned by immersion into 1% HF acid followed by washing with ultrapure water prior to use. Two different types of experiments were performed. For surface pressure (π)-time (t) curve measurement, an aqueous solution of 2-HEL was poured into the trough and maintained for 25 min to attain the temperature of the experiment. The surface pressure was measured just after sweeping the surface with movable Teflon barriers with a constant sweep speed to a predefined area to remove the molecules already adsorbed. The surface of the solution was observed simultaneously with BAM. For the temperature jump experiment, the aqueous solution was maintained in the trough for 2 h to reach equilibrium at a certain higher temperature. The temperature was such that the condensed domains are not formed due to the low 2-D surface concentration.28 The equilibrium is then disturbed by a jump in the temperature at a rate of -5 °C/min to a lower value, at which condensed domain formation is possible. Although, in all the experiments we lowered the temperature by 5 °C, the net decrease was about 4 °C. The special feature of our trough is that it can raise or reduce the temperature of the water surface linearly in a controlled programmable way.33 A 25 mW semiconductor laser was used as a light source for BAM observation. Image processing software was used to optimize the contrast and to correct the distortion of the BAM images. Details of the experimental procedure27 and the experimental set up33 were published elsewhere.
Results 1. Surface Pressure and cmc Measurements. Figure 2 presents adsorption kinetics of aqueous solutions of 2-HEL at different temperatures. The π-t curves up to (33) Kato, T.; Tatehana, A.; Suzuki, N.; Iimura, K.; Araki, T.; Iriyama, K.; Jpn. J. Appl. Phys. 1995, 34, L911.
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Figure 3. A plot of critical surface pressure necessary for the phase transition, πc, against temperature. The line was drawn by linear regression. πc at 25 °C, which is indicated by arrows, is determined from the extrapolation of the line to correct the corresponding π-t curve in Figure 2.
10 °C are measured with solutions of 1.4 × 10-5 M, whereas those for higher temperatures are obtained with higher concentrations. In our previous report, we demonstrated that cusp points for the phase transition are absent with 1.4 × 10-5 M solution at g15 °C due to the low twodimensional surface concentration.28 However, with a 2.2 × 10-5 M solution, the cusp point in the π-t curve is observed at 15 °C. Similarly with 3.0 × 10-5 and 5.0 × 10-5 M, solution cusp points for the phase transition are observed at 20 and 25 °C, respectively. We choose the concentrations at different temperatures arbitrarily, considering the fact that condensed domains are formed during the experiment. The critical times necessary to attain the cusp points are also ≈1000 s, except that for the curve at 10 °C. At 25 °C, the surface pressure increases very rapidly with time, and we are unable to measure the zero surface pressure at this temperature. Therefore, we corrected the data taking into consideration that the critical surface pressure for the cusp point, πc is equal to that obtained from the extrapolation of the πc vs temperature curve (Figure 3). Both higher concentrations and higher temperatures contribute to this accelerated adsorption of the molecules. With increasing temperature the πc increases linearly (Figure 3). For temperatures g26 °C, a cusp point in the π-t curve is not observed even with ≈6.0 × 10-5 M solution of 2-HEL (data are not shown). On the other hand, the cmc at 26 °C is around 4.0 × 10-5 M (Figure 1). From this figure it is clear that surface concentration does not increase above 4.7 × 10-5 M as the surface tension is the same above this bulk concentration. These results suggest that the cusp point at this temperature will be absent even with more concentrated solutions of 2-HEL. Moreover, above the cmc the equilibrium surface tension is 23.7 mN m-1 (Figure 1), which stipulates that the system can acquire a maximum of 48.1 mN m-1 of surface pressure (considering 71.8 mN m-1 the standard surface tension of water). This surface pressure is lower than the expected πc (from the extrapolation of the πc vs temperature curve in Figure 3) at this temperature. All the results presented here lead us to conclude that a phase transition is not possible in the adsorbed monolayers of 2-HEL above 25 °C, regardless of the concentration. 2. Growth of Domains and Their Morphological Features. Brewster angle microscopic observation confirms the existence of the first-order phase transition from the fluidlike phase to condensed phase in adsorbed monolayers up to 25 °C. After the cusp point of each of the π-t curves in Figure 2, condensed phase domains with a variety of morphological shapes are observed. Figure 4
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shows the growth course of the domains with 2.2 × 10-5 M aqueous solution of 2-HEL at 15 °C. Just after the cusp point in the π-t curve, the domains grow initially with a distorted circular or cardioid shape with almost equal brightness all over the domains (image A). These domains then undergo branching to form fingering patterns (image B). Each of the fingers shows a tendency to have more branching in its structure (images C, D), but the lower rate of adsorption at the latter stage compared to the capturing rate of the molecules into the domains inhibits the tendency of further branching. As a result the fingers widen with time at this stage and finally fuse with each other to form a uniform monolayer. The domains preserve their identity and fingering pattern before they touch with other domains (image F). Figure 5 presents typical domain shapes at different temperatures recorded with different solution concentrations whose π-t curves are presented in the Figure 2. Image D at 13 °C is obtained with a 2.2 × 10-5 M aqueous solution of 2-HEL. The domains are circular in shape up to 13 °C, above which they show a fingering pattern. Generally, with an increase in the temperature, the branching of the fingering domains increases. Above 26 °C, condensed domain formation was not observed, although the concentration was increased up to 6.0 × 10-5 M. The growth of the domains with time is affected differently at different temperatures (Figure 6). Below 13 °C, the domains preserve their circular shapes from the very beginning until deformation takes place at the moment of close contact (image A). The domains do not fuse with each other, even after complete formation of the monomolecular films at 2 or 5 °C; rather, they show constrained deformation (image B). Such a growth pattern has been discussed in detail previously.27,28 For temperatures g20 °C the domains, however, can fuse, even where a large fraction of fluidlike phase is available to increase their sizes (image C). Although the bulk concentrations do not change the domain shapes below 13 °C, they have little effect on increasing the branching at higher temperatures, particularly above 20 °C. This is expected from the increased growth rate of formation with higher bulk concentrations. Although at lower temperatures a discrimination in the size distribution of the domains is observed, the shape is certainly circular. At g20 °C, small size domains having compact shapes are occasionally observed (image D). The branched domains in this temperature region do not always grow equally. Some arms become elongated and some of them are prohibited from growing by other domains, although they do not touch each other (image E). 3. Nonequilibrium Growth of Domains. To observe the effect of growth rate on the domain shapes, we disrupted the equilibrium by a temperature jump from 19 to 15 °C. Figure 7 shows the change of temperature and surface pressure with time during the temperature jump. This experiment was carried out with a 2.2 × 10-5 M aqueous solution of 2-HEL. The initial surface pressure in the figure is the equilibrium value at 19 °C. The arrows indicate the positions of the BAM images which are presented in Figure 8. For every temperature there is a critical bulk concentration below which a phase transition is not possible due to low 2-D surface concentration.28 At a concentration of 2-HEL equal to 2.2 × 10-5 M, a phase transition occurs at 15 °C but does not occur at 19 °C. This conclusion becomes clear if we consider surface pressure at equilibrium, 35 mN m-1 (Figure 7), which is lower than the expected πc (from Figure 3). Thus, a jump of temperature allows for a very rapid rate of formation of the
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Figure 4. Isothermal growth process of the domains at 15 °C with a 2.2 × 10-5 M solution of 2-HEL with time: (A) 1480 s, (B)1610 s, (C) 1930 s, (D) 2125 s, (E) 2350 s, and (F) 3420 s. Image sizes are 400 µm × 300 µm.
domains. In this case the increased formation rate provides nonequilibrium conditions in the adsorbed monolayers. The domains start to grow rapidly in a fractal-like structure just after completion of the temperature jump (Figure 8, images A, B). After growing to a certain size, the domains relax to the normal growth pattern within 25 min (Figure 8, image D or E). During normal growth of domains at this temperature, both growing and broadening of the arms of the fingering domains take place simultaneously with time (Figure 4). Contrary to the normal growth, the fractal domains relax rapidly to isothermal growth patterns which then become larger
(Figure 8, image F) as the adsorption continues until equilibrium is reached again. The nuclei density of the domains is much higher than that for the isothermal course of domain formation. This is typical for a nucleation and growth process. Similar experiments at 13 and 18 °C have also been performed with 1.9 × 10-5 and 2.5 × 10-5 M solutions with a temperature jump from 17 and 22 °C, respectively (Figure 9). At 13 °C, it is found that the domain shapes remain unaltered with the exception of the smaller size of the domains (image A) in comparison with that in the isothermal growth. However, at 18 °C the domains show a similar behavior to that found at 15 °C (image B).
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Figure 5. Typical domain shapes and textures in the domains at different temperatures. The images were obtained with different concentration solutions corresponding to Figure 2. The image D at 13 °C was obtained with 2.2 × 10-5 M solutions. Image sizes are 400 µm × 300 µm.
4. Textures in Domains. The most interesting feature is the characteristic stripe texture of the domains at lower temperatures (Figure 5). Each domain has a number of stripes depending on the size as well as the temperature. At the very beginning of the domain formation, there are only two or three stripes which increase with the increasing size of the domains. At 2 °C, the separate stripes undergo continuous narrowing and eventually merge to a core defect which lies on the peripheral line of the domain (image A). The other end of the stripes remains parallel and vanishes at the peripheral line separately. At 5 °C,
the core defect is also present but seems to be a little far from the peripheral line (image B). However, for g10 °C, such a core defect may not be present or, if present, it is far from the domain boundary (image C). Another characteristic feature is that the number of the stripes decreases with increasing temperature. With almost equal size of domains, seven, six and three stripes are shown in the figure at 2, 5, and 10 °C, respectively. The widths of the stripes are about 50, 70, and 100 µm for these three temperatures, respectively. At 13 °C, the stripes are not well defined. Image D shows another type
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Figure 6. Growth characteristics of the domains of 2-HEL under different conditions. Images A and B are with 1.4 × 10-5 M solution at 5 and 2 °C, respectively, and all others are with 3.0 × 10-5 M solution at 20 °C. (A) two touching domains which are just deformed, (B) constrained deformation without fusion, (C) fusion of the domains, although a large portion of fluid phase is available, (D) some compact shape domains together with fingering domains, and (E) inhibition in growth of some arms due to long-range dipole-dipole repulsion. Image sizes are 400 µm × 300 µm.
of characteristic texture in which the internal stripe shows fingering. This is also the critical temperature for the shape transition of the domain from the circular to the fingering pattern. Domains show branching in their structures having no internal anisotropy at higher temperatures (g15 °C). Discussion The presence of a cusp point on the π-t curves is indicative of the existence of a first-order phase transition
in the adsorbed monolayers at the air-water interface (Figure 2).24-30 The initial rapid rise of the surface pressure in each of these curves is related to the adsorption of the amphiphile to form a uniform layer of molecules, i.e., a fluidlike phase on the water surface. The cusps followed by the plateau regions are due to the formation of condensed domains during the phase transitions. The experimental results suggest that, for every temperature, there is a minimum bulk concentration necessary to achieve the critical 2-D surface concentration for the phase
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Figure 7. Change of the temperature (I) and the surface pressure (II) with time during temperature jump experiment. The initial surface pressure is the equilibrium value at 19 °C obtained after 2 h of adsorption from 2.2 × 10-5 M solution of 2-HEL. The vertical arrows indicate the points of BAM images shown in Figure 8.
transition. The absence of the cusp point in the π-t curve as well as the domains at g26 °C suggests that this is the critical temperature. Above this temperature the cohesive energy against the kinetic energy of the molecules does not permit the existence of a condensed phase in the monolayers. However, from the viewpoint of cmc, it can be stipulated that, above the critical temperature, increased bulk concentration leads to micellization and therefore impedes the condensed domain formation by not allowing sufficient surface concentration. BAM observation confirms the conclusions drawn from the π-t curves. Whether condensed domains can form in the monolayers is governed by the delicate balance between the cohesive energy difference of condensed and expanded phases or line tension and the kinetic energy of the molecules. Muller et al.34 showed that the line tension between a solidlike phase and a fluidlike phase is on the order of 5 pN, which can be converted to the cohesive energy difference of the molecules between the two phases by multiplying it by the molecular width, 0.5 nm at the periphery of a condensed domain. This accounts for a cohesive energy difference of ≈2.5 × 10-21 J molecule-1, which is almost comparable to that of the kinetic energy of the molecules, kT, in two-dimensions. Therefore, it is expected that domains will be formed only when the cohesive energy difference or line tension dominates over the kinetic energy of the molecules. With an increase in the temperature, the line tension decreases, whereas the kinetic energy of the molecules increases. Thus, there should be a temperature, i.e., the critical temperature, at or above which condensed domain formation is not possible. For our system this temperature is around 26 °C. Below the critical temperature, condensed domains are formed, if the 2-D surface concentration that depends on the bulk concentration in adsorbed monolayers is sufficiently high. Once the domains are formed, the equilibrium shapes of the domains depend partly on the competition between the line tension and dipole-dipole repulsion of the molecules.5,6 Since we are dealing with adsorbed monolayers that are in a pseudoequilibrium state, growth rate instability or supersaturation has negligible effect on the domains during the isothermal course of formation. At lower temperature, the molecules have higher cohesive energy that supersedes over the dipole-dipole repulsion between the molecules. As a result, the molecules are compactly bound to form circular (34) Muller, P.; Gallet, F. Phys. Rev. Lett. 1991, 67, 1106.
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domains to reduce the surface area of the molecules (Figure 5). With increasing temperature the line tension decreases. Therefore, at 15 °C, the domains show a fingering pattern which branches into fractal-like domains for a further decrease in line tension as the temperature increases. Suresh et al.8 suggested that the unstable growth of the condensed domains in myristic acid at higher temperatures is due to the diffusion-limited growth. Our observation, although similar to theirs, suggests that the fingering pattern of 2-HEL is rather stable and exists up to fusion with other domains (Figure 4). Moreover, the effect of impurities on the domain shape9,10 is negligible in the case of 2-HEL, because the most probable impurities (e0.5%, reactants dodecanoyl chloride or 2-iodoethyl laurate) have lower surface activity and prefer to remain in the bulk. Thus, it is the competition between line tension and dipole-dipole repulsion that governs such a growth pattern in our case. We should also take the growth kinetics of domains into consideration. At lower temperatures the line tension is sufficient over the dipole-dipole repulsion to prevent any change in the domain shape during the growth process. The shape of these domains remains unaffected, even with the increased rate of formation with a temperature jump (Figure 9, image A). However, at higher temperatures (g15 °C), where the line tension is comparatively low, domains are very much affected by the growth rate, which will be discussed later. There should certainly be a compromise between the growth rate instability and the line tension that leads to the relaxation of the shape of domains. The growth of the domain is prohibited in the region of highly dense nuclei. This accounts for some compact shape domains at higher temperatures, where the nuclei density is high (Figure 6, image D). Meunier et al.15,35 suggested that an anisotropic contribution to the line tension is essential to stabilize a defect point inside or at the boundary of the domains. The presence of defect points at lower temperatures for the domains of 2-HEL indicates the existence of the anisotropic line tension in this temperature region. The line tension at higher temperatures should be isotropic in nature, because the molecules in these domains are not tilted, as could be revealed considering the uniform brightness of the BAM images. Anisotropy in the line tension does not permit the domains to be fused as found at lower temperatures, whereas isotropic line tension allows the domains to be fused while touching each other. The line tension is a short-range interaction, the dipolar forces on the other hand, are long ranged. The repulsive long-range interactions between two domains can exist, even on the order of a few tens of micrometer in distance.18,36 At higher temperatures, where the line tension is low compared to dipole-dipole repulsion, the domains should be vulnerable to the long-range forces. This can explain qualitatively why the growth of some arms is prohibited, causing overall distortion in the domain shape (Figure 6, image E). The another possible reason can be the smaller number of molecules in the fluidlike phase between the two close domains. These molecules do not show the tendency to distribute between the neighboring domains. Theoretically, the anisotropic line tension can also cause twisted domains, because the length of the arms of the side with the largest line tension is as short as possible. This reason can be ruled out in our case, because only the arms of the domains in the vicinity of the (35) Rivie`re, S.; Meunier, J. Phys. Rev. Lett. 1995, 74, 2495. (36) Rivie`re, S.; He´non, S.; Meunier, J.; Albrecht, G.; Boissonnade, M. M.; Baszkin, A.; Phys. Rev. Lett. 1995, 75, 2506.
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Figure 8. Nonequilibrium growth of domains and their relaxation with time at 15 °C with 2.2 × 105 M solution of 2-HEL. Image sizes are 300 µm × 300 µm.
other domains have impeded growth and/or the line tension is isotropic in this temperature region. However, if the domains touch each other for some reason such as movement of the monolayers, the domains fuse due to isotropic line tension, as described above. Long-range dipole-dipole repulsion is expected to be low compared to high line tension at lower temperatures, and therefore, it cannot deform the domains until they touch each other (Figure 6, image A). Very rapid compression of the spread monolayer and therefore the high rate of formation were reported to change the circular domain into a fractal-like structure.13,14
We also find the same behavior of formation of fractal structure in the domains at e15 °C in adsorbed monolayers by increasing the rate of formation (Figure 8). The fractal structures are observed because the molecules on the peripheral line of the domains formed by high growth rate cannot be diffused rapidly to the relaxed state. However, the domains relax to their equilibrium shapes within 25 min, because the line tension at this temperature does not permit the existence of fractal domains. In this case the domains grow to a definite size rapidly due to supersaturation, but further growth is prohibited because such domains are unstable and therefore relax quickly to
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BAM observation clearly reveals that, for g15 °C, the molecules remain almost perpendicular to the surface, which causes uniform brightness all over the domains. Below this temperature the tilted molecules form textures in the domains.21,22 There appears to be a continuous change of the tilt angle of the molecules toward zero with increasing temperature. Thus, it is expected that, for every temperature, the molecules in the domains have a particular tilt angle and form domains with almost equal width of the stripes. Since tilt angle or tilt azimuthal angle can be measured by grazing incidence X-ray diffraction (GIXD) analysis, these experiments are in progress. Conclusions
Figure 9. Typical nonequilibrium pattern at two different temperatures: A (13 °C) and B (18 °C). The experiments were done with 1.9 × 10-5 and 2.5 × 10-5 M solutions by the temperature jump from 17 and 22 °C, respectively. Images were taken at the beginning stage after completion of the temperature jump. Image sizes are 400 µm × 300 µm.
their equilibrium shapes by capturing the molecules. But at lower temperatures, the growth rate is not sufficiently rapid to distort the shape of the domains because the line tension or the resultant relaxation at this temperature always dominates over this growth rate. The stripe texture in the domains is caused by the sudden jump of the tilt azimuthal direction of the molecules across a defect line that separates a stripe from its neighbor.18,28 On the other hand, the jump of the tilt azimuthal direction in a domain causes anisotropy, which ultimately leads to the formation of segments of different brightness in a domain. All the stripes in a domain in our case appear with almost identical brightness, which indicates that the degree of jump of the molecular tilt azimuthal angle is relatively small. Across the stripes, the tilt azimuth of the molecules varies continuously to the extent that the contrast between two ends of the stripe is detectable weakly by BAM. The molecules in the neighboring stripes are oriented in a similar way.
We discussed the formation of domains with a variety of morphological and textural features in adsorbed monolayers of 2-HEL at the air-water interface. The morphology of the domains in these monolayers responds to the experimental variables similarly as those reported for the spread monolayers. The isothermal course of domain growth can be considered to be in a pseudoequilibrium state, and supersaturation caused by the temperature jump allows for nonequilibrium domain shapes that relax readily into their normal growth patterns. Both texture and morphology show a characteristic variation with temperature. Stripe textures are observed when the domains are circular in shape up to 13 °C. Above this temperature, the domains show a fingering pattern with uniform molecular orientation. The domains show a similar effect of increasing branching in their shapes with increased temperature as well as an increased formation rate. However, we feel confident that increased branching at higher temperatures is related to the competition between line tension and dipole-dipole repulsion, although the possible effect of the increased formation rate cannot be ruled out. We can also neglect the effect of impurities on the growth pattern because the expected trace amount of impurities in our case prefers to remain in the bulk. These results clearly demonstrate that the instability in the domain shape is induced when the line tension is comparatively low. Condensed domains in adsorbed monolayers are formed only when the bulk concentrations within the limit of cmc can provide the sufficient 2-D surface concentrations necessary for the phase transition. The critical temperature for the condensed domain formation in Gibbs monolayers is the temperature at which the cmc does not allow the existence of the phase transition by favoring micellization over adsorption. Acknowledgment. We are thankful to Assoc. Prof. M. Yoshida of this Department for his help during the synthesis of the amphiphile and to Assoc. Prof. N. Suzuki of this laboratory for useful discussion. We also thank Prof. R. A. Dluhy of the University of Georgia for the grammatical corrections of the manuscript. Part of this research is supported by SVBL of Utsunomiya University. LA991710P
