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Sequential Collapse Transitions in a Langmuir Monolayer E. Hatta Nanoelectronics Laboratory, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan Received October 27, 2003. In Final Form: January 26, 2004 Unusual sequential collapse transitions are investigated in a lignoceric acid Langmuir monolayer. The nucleation of monolayer collapse is first initiated in the solid, S, phase but at remarkably low surface pressure where small three-dimensional (3D) granular dots appear. The density of nucleation centers increases, and the 3D dots prevail over the monolayer (surface roughening regime) as the surface pressure increases, but individual dots neither grow very much in size nor evolve into other shapes such as stripes or elongated dots. On further compression the second collapse mode manifests itself by highly anisotropic, global crack arrays (anisotropic cracking regime) where the surface pressure “kink” appears in the isotherm. In the latter regime, various forms of 3D curved filaments develop in the crack regions, and they break into smaller fragments with a typical relaxation time (∼60 ms).
Introduction Langmuir monolayers have been used as a means of studying physical, chemical, and biological problems in two dimensions, phase transitions,1 wetting,2 twodimensional fluid dynamics and microrheology,3,4 membrane physics,5 etc. The lattice structure of the many phases and the complex polymorphism of the various mesophases intervening between the two-dimensional (2D) gas and solid phases have been unraveled with the application of glazing incidence X-ray diffraction (GIXD),6 polarized fluorescence microscopy,7 and Brewster angle microscopy,8,9 while the correlations between each phase and the macroscopic flow and mechanical properties have, as yet, been less explored. Besides phase transitions in two dimensions, much attention has recently been paid to collapse transitions where the monolayers break into the third dimension perpendicular to the water surface, and this has been intensively investigated with video microscopy.10-13 2D-3D transition has been considered in detail by nucleation and growth theoretically.14 The study of collapse transitions is essential for the understanding of the formation mechanism of lipid bilayers and 3D higher ordered structures such as vesicles, twisted ribbons, and giant folds.15 Moreover, collapse transitions provide a (1) Rivie`re-Cantin, S.; He´non, S.; Meunier, J. Phys. Rev. E 1996, 54, 1683. (2) Khattari, Z.; Heinig, P.; Wurlitzer, S.; Steffen, P.; Lo¨sche, M.; Fischer, Th. M. Langmuir 2002, 18. 2273. (3) De Koker, R.; McConnell, H. M. J. Phys. Chem. B 1998, 102, 6927. (4) Brooks, C. F.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1999, 15, 2450. (5) Lipp, M. M.; Lee, K. Y.; Waring, A.; Zasadzinski, J. A. Biophys. J. 1997, 72, 2783. (6) Bibo, A. M.; Knobler, C. M.; Peterson, I. R. J. Phys. Chem. 1991, 95, 5591. (7) Schwartz, D. K.; Knobler, C. M. J. Phys. Chem. 1993, 97, 8849. (8) Overbeck, G. A.; Mo¨bius, D. J. Phys. Chem. 1993, 97, 7999. (9) Henon, S.; Meunier, J. J. Chem. Phys. 1993, 98, 9148. (10) Gopal, A.; Lee, K. Y. C. J. Phys. Chem. B 2001, 105, 10348. (11) Hatta, E.; Fischer, Th. M. J. Phys. Chem. B 2002, 106, 589. (12) Ybert, C.; Lu, W.; Mo¨ller, G.; Knobler, C. M. J. Phys. Chem. B 2002, 106, 2004. (13) Lu, W.; Knobler, C. M.; Bruinsma, R. F.; Twardos, M.; Dennin, M. Phys. Rev. Lett. 2002, 89, 146107. (14) Vollhardt, D. Adv. Colloid Interface Sci. 1993, 47, 1. (15) Micelles, Monolayers, and Biomembranes; Jones, M. N., Chapman, D., Jones, M., III., Eds.; John Wiley & Sons: New York, 1994.
unique opportunity for studying the formation of intriguing 2D to 3D spatiotemporal patterns.16,17 While the collapse transition is usually characterized macroscopically by the “collapse pressure” at which either a kink or a plateau appears in the isotherm upon overcompression of the monolayer, the protrusions into three dimensions from the water surface were found to occur in the form of monolayer buckling,18 topographic instabilities,19 and shear-induced fracture20 at pressures well below the “collapse pressure”. The origin of such mechanical instabilities may be ascribed to the nature of microscopic head-head and tail-tail interactions in constituent amphiphilic molecules.21 The effects of head-head and tail-tail interactions on the collapse behavior in monolayers can be studied by decoupling them. In simple longchain fatty acid monolayers, the head-head interactions can be changed through dissociation of the headgroups (COOH to COO-H+) by increasing the subphase pH, while the tail-tail interactions can be changed by varying the chain length. Both interactions can affect the positional and orientational order of the monolayers, but the relative significance of these interactions on the rheological properties of monolayers has been less understood. A delicate balance between head-head and tail-tail interactions may be the cause of an unexpected behavior of the mechanical properties in monolayers.11 We use a lignoceric (tetracosanoic) acid for the study of collapse transitions in monolayers. This material is one of the saturated fatty acids and has the longest hydrophobic tail that can be prepared in the form of a Langmuir monolayer. Attractive forces are exerted between long-chain molecules via van der Waals forces. An increase in subphase pH due to the addition of monovalent cations tends to increase the attractive forces between dissociated and undissociated headgroups via hydrogen bonding as well as to cause disorder in the herringbone packing of the backbone plane of the fatty acid hydrocarbon tails due to the formation of a mixture of two kinds of headgroups in the monolayer.22 (16) Hatta, E.; Nagao, J.; Suzuki, D. Eur. Phys. J. B 1999, 11, 609. (17) Hatta, E.; Nagao, J. Phys. Rev. E 2003, 67, 041604. (18) Saint-Jalmes, A.; Gallet, F. Eur. Phys. J. B 1998, 2, 489. (19) Schief, W. R.; Touryan, L.; Hall, S. B.; Vogel, V. J. Phys. Chem. B 2000, 104, 7388. (20) Maruyama, T.; Laugher, J.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1998, 14, 1836. (21) Angelova, A.; Vollhardt, D.; Ionov, R. J. Phys. Chem. 1996, 100, 10710.
10.1021/la036014a CCC: $27.50 © 2004 American Chemical Society Published on Web 04/10/2004
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Figure 1. π-A isotherms in lignoceric acid Langmuir monolayers at pH 7.0 (solid line) and pH 7.8 (dotted line) and at 20 °C.
The interplay between tail-tail and head-head interactions would thus possibly result in some mechanical instability in the monolayer where long-chain molecules would easily become unstable, forming a monolayer through the coupling of the monolayer structure with mechanical stress. In this paper we report the occurrence of sequential collapse transitions where surface-roughening collapse is followed by anisotropic cracking in a lignoceric acid Langmuir monolayer. The occurrence of such a collapse sequence is unusual, since only a single collapse mode is normally observed above the critical collapse pressure upon single barrier compression of a monolayer. The existence of a characteristic length scale, the crack direction, and its evolution in time characterize each regime of the transition. In the anisotropic cracking regime, 3D curved filaments grow in the crack regions and finally break into smaller fragments. Experimental Section Monolayers of lignoceric acid (tetracosanoic acid, C24; 99% pure, Sigma Chemicals) dissolved in 0.5 mmol of chloroform (97% pure, Kanto Chemicals) were spread onto a subphase (Millipore Mill-Q system filtered water, 18.0 MΩ cm) in most experiments of this study. For comparison several experiments were carried out with a subphase containing 1.0 mmol of salt (CdCl2, Rare Metallic, purity 99.999%). All experiments were performed at 20.0 ( 0.2 °C. The pH values of the subphase from 7.0 to 7.8 were adjusted with NaHCO3. These materials were used without further purification. It has been established that phase contrast microscopy (PCM) is essential for following collapse morphologies and their dynamics.11 Cracks in the monolayer at the air-water interface were monitored via three-dimensional aggregates protruding from the cracks using phase contrast microscopy (NIKON, OPTIPHOT-2) equipped with a CCD camera (Hamamatsu, C2400-77H) followed by an image processor (Hamamatsu, DVS-3000). The incident light was transmitted through the bottom of a homemade glass trough, placed on the microscope stage. The crack evolution was recorded at a frequency of 30 frames/s with constant monitoring of the π-A isotherms with a Wilhelmy plate balance. The width of the trough used was 10 cm, and the monolayers were compressed at a low barrier speed (1 cm/min) to diminish the kinetic effects of barrier compression.
Results and Discussion Figure 1 shows π-A isotherms in lignoceric acid Langmuir monolayers at pH 7.0 and 7.8. The isotherms exhibit a transition from a liquid expanded (LE) to a liquid (22) Datta, A.; Kmetko, J.; Richter, A. G.; Yu, C.-J.; Dutta, P. Langmuir 2000, 16, 1239.
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condensed (LC) phase at a surface pressure of 3.1-4.0 mN/m and for an area of 21-22 Å2/molecule. These values are smaller than those (8-10 mN/m and 22-25 Å2/ molecule) previously reported at pH 4.0.23,24 The plateau pressures at the surface area of about 21-22 Å2/molecule have been decreased, and the isotherms in this region have become featureless with increasing pH, which is consistent with the general forms of the isotherms observed for fatty acid monolayers with an increase in subphase pH.25 This result shows that with an increase in pH the tilted-untilted phase boundary has been pushed down to lower surface pressure. This suggests that an increase in the subphase pH drives the monolayer toward a phase with less tilted tails and closer packing even at lower surface pressures, probably due to the formation of a compact and complex 2D mixture of dissociated and undissociated headgroups and closely packed hydrophobic tails due to van der Waals interactions.22 Both the monolayers exhibit very similar sequential collapse transitions. Figure 2 shows the evolution of sequential collapse transitions upon monolayer compression at pH 7.0. Each image was taken at the corresponding points (i.e., a, b, c, and d) in the isotherm (solid line) shown in Figure 1. The dark and bright regions in the images correspond to the 3D collapse structure and the coexisting monolayer, respectively. The monolayer is compressed from left to right in all images. It can be seen from the images of collapse evolution that the collapse of the monolayer is initiated by 3D granular dots protruding from the monolayer immediately after the end of the plateau region in the isotherm (Figure 2a). It is well-known that an increase in subphase pH leads to a lowering of the surface pressure of the phase transition.26 The monolayer is probably in the S phase at the onset of collapse.27 In relation to the onset of the collapse mode at very low surface pressure in the S phase, Schlossman et al. found that on barrier compression the fully relaxed or equilibrium monolayers collapse at surface pressures considerably less than those at which nonequilibrium ones collapse.27,28 Our observation and their result suggest that the issue of equilibrium and relaxation in monolayers and the relevant mechanical properties should be further examined. Further compression of the monolayer steadily increases the number of 3D dots over the monolayer, and the whole area is covered with numerous fine dots at the final stage in this regime (referred to as “the surface roughening regime” 11) (Figure 2b). Interestingly, those individual nucleated dots neither grow significantly in size nor develop into stripes or other elongated shapes.17 On further compression the onset of the second stage of monolayer collapse is manifested by the occurrence of anisotropic crack arrays (“the anisotropic (23) Ekelund, K.; Sparr, E.; Engblom, J.; Wennerstro¨m, H.; Engstro¨m, S. Langmuir 1999, 15, 6946. (24) Kajiyama et al. observed a rather high plateau pressure of nearly 12 mN/m in the isotherm of a lignoceric acid monolayer at pH 5.8 and at 20 °C and the L2-CS transition under these conditions (Bull. Chem. Soc. Jpn. 2001, 74, 765). The observation of the transition, however, seems not to be consistent with the well-known, generalized π-T phase diagram. See, for example: Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779. The two intervening phases (i.e., L2′ and S) between the L2 and CS phases may have been missed. The high compression speed (120 mm2 s-1) they adopted may be related to the appearance of its high plateau pressure. (25) Petty, M. C. Langmuir-Blodgett films: an introduction; Cambridge University Press: Cambridge, 1996. (26) Shih, M. C.; Bohanon, T. M.; Mikrut, J. M.; Zschack, P.; Dutta, P. J. Chem. Phys. 1992, 96, 1556. (27) Schlossman, M. L.; Schwartz, D. K.; Pershan, P. S.; Kawamoto, E. H.; Kellogg, G. J.; Lee, S. Phys. Rev. Lett. 1991, 66, 1599. (28) Schwartz, D. K.: Schlossman, M. L.: Pershan, P. S. J. Chem. Phys. 1992, 96, 2356. (29) Bohanon, T. M.; Lee, A. M.; Ketterson, J. B.; Dutta, P. Langmuir 1992, 8, 2497.
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Figure 2. Evolution of sequential collapse transitions in a lignoceric acid Langmuir monolayer at pH 7.0. The images a, b, c, and d were taken at the points (a) π ) 5.2 mN/m, (b) π ) 39.3 mN/m, (c) π ) 46.0 mN/m, and (d) π ) 47.8 mN/m indicated in the isotherm at pH 7.0 shown in Figure 1. The scale bar represents 100 µm.
cracking regime”,11 Figure 2c,d). The transition from the surface roughening to the anisotropic cracking regime is also characterized by the appearance of a kink in the isotherm. In the latter regime, anisotropic cracks with a finite width (∼20 µm) become arranged in a common direction. The crack speed cannot be evaluated accurately in this case because individual cracks propagate across the image from top to bottom in less than 1/30 s, the frame rate of the video recorder. Only a single collapse mode was observed in our investigations of other fatty (i.e., stearic and arachidic) acid monolayers with shorter aliphatic chains. In these studies, the monolayers changed from the L2 to the LS (-S) phase upon uniaxial barrier compression at the same temperature (20 °C) as the experiment described above. The reason the monolayer collapses sequentially is not clear at present, but we can study the origin of the onset of monolayer collapse during the low surface pressure phase by other means. The formation of a spontaneous assembly of molecules with zero surface pressure on the water surface has already been observed (Figure 3). This suggests that there is a strong attraction between the long tails of the molecules. Moreover, in the presence of divalent cations (Cd2+) and at zero surface pressure, lignoceric acid monolayers exhibit many collapsed regions within isolated domains (Figure 4). The occurrence of spontaneous, concentric collapse within domains without the application of a substantial external stress indeed reflects the fact that in the presence of divalent metal ions attractive forces that are too strong to allow the formation of monolayers of uniform thickness are exerted between molecules with long hydrophobic tails through both tail-tail and head-head interactions. From the above results, the delicate balance between headhead and tail-tail interactions may cause the sequential collapse transitions observed. Thus, it seems possible that the fracture in a monolayer, as seen in Figure 2b, which cannot be deduced from its π-A isotherm, occurs even at a sufficiently low surface pressure in the S phase depending on the packing manner of the constituent molecules. The cross-sectional area of the headgroups is generally different from that of the tails where some strain would
Figure 3. 3. PCM image of a lignoceric acid monolayer at pH 7.0 and at zero surface pressure. A large domain of spontaneously assembled molecules is seen in the center region of the image. The curved domain boundary can be seen in the lower left part, while another domain boundary is seen in the upper right part. The scale bar represents 100 µm.
be required to compensate for the mismatch. From the viewpoint of this geometric frustration, it might be easier to induce a structural instability from the mechanical stress due to the strong attractive forces between the long tails in a lignoceric acid monolayer. Disorder in a monolayer is normally created by tail-tail interactions caused by increasing temperature or decreasing length of the tail. In the present study partial dissociation of the headgroups by a relatively high pH due to the presence of monovalent metal ions in the subphase can lead to a disorder of the backbone planes of the tails by the creation of a 2D complex of dissociated and undissociated headgroups with hydrogen bonding.22 In fact, an atomic force microscopy (AFM) study by Ekelund et al. demonstrated that monolayers prepared on a buffer of pH 7 exhibit a worse film quality than those at pH 4.23 The presence of such disordered tail packing may assist in promoting frustration in the monolayer. From the above considerations the onset of monolayer collapse in the low surface pressure phase
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Figure 4. PCM image of a lignoceric acid monolayer in the presence of 1 mmol of Cd2+ ions (pH 7.0) at zero surface pressure. In a large isolated domain in the center region of the image many concentric collapsed regions can be seen. Some smaller anisotropic domains (which also have collapsed regions inside) locate around the large domain. The scale bar represents 100 µm.
indicates that the interplay of compactness and disorder in the packing of tails drives the monolayer to collapse spontaneously without substantial compression of the monolayer. In the surface roughening regime 3D domains nucleate at random locations to the uniaxial barrier compression and show a very low in-plane growth. This behavior would be understood by the nucleation-growth collision mechanism.14,21 In this mechanism multilayer growth from the water surface is favored by enhanced headgroup interactions through hydrogen bonding (between dissociated and undissociated headgroups in our case) due to decreased in-plane growth rates of the 3D structures.21 This collapse mode must not be regarded as a precursor for the subsequent anisotropic crack growth since the latter mode emerges after the 3D dots are spread over the whole water surface area. In the anisotropic cracking regime, a welloriented anisotropic assembly of aligned cracks grows at an angle of 70° ( 3° to the compression direction. We cannot identify the phase definitely by phase contrast microscopy since it is insensitive to molecular tilt and the azimuth of monolayer and thus the transition between two different phases. The occurrence of the anisotropic cracking, however, may be explained if we assume that monolayer enters into the higher solid, CS, phase. Bohanon et al. showed that in heneicosanoic acid (C21) surface tension anisotropy is observed in the CS phase in uniaxially compressed monolayers.29 If surface tension
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anisotropy develops, it does mean that a shear stress is being applied to a solid monolayer. Ghaskadvi et al. indeed found that a finite static shear modulus exists only in the CS phase.30 Given that the monolayer enters into the CS phase at the second stage of collapse transitions in our study, the shear stress on the monolayer could be a significant contributory factor for the anisotropic cracking. The clear picture, however, must rely on the future identification of the phase close to the onset of the second collapse mode. In the anisotropic cracking regime the creation of 3D curved filaments with fairly uniform thickness (6-10 µm) followed by breakdown of the filaments into smaller fragments with a finite relaxation time (∼60 ms) is seen in the crack region (Figure 5). The 3D filaments in the cracks often seem to form regularly in the initial stages (the second frame of Figure 4a and the upper part of the second frame of Figure 5b). In contrast to the “Ries” mechanism,31 which is often referred to as the mechanism for monolayer collapse where the monolayer breaks off to create double-layer ribbons or platelets on the underlying monolayer via weakening, folding, and bending processes, the 3D filaments in our study seem not to locate on the underlying monolayer but to bridge and afterward locate between two broken monolayer edges. Moreover, the width of our filaments is 2 orders of magnitude larger than that of the ribbons created by the Ries mechanism. These features indicate that distinct collapse mechanisms operate in each case. In the previous modulation crack study,11 in contrast to the growth of anisotropic cracks in monolayers reported here, the cracking speed itself was rather slow (100-300 µm/s) and the creation of 3D filaments that followed was not observed, at least, on the micrometer length scale. The viscous nature of the monolayer effectively slows the crack-opening process in monolayer collapse. It is noteworthy that the evolution of 3D filaments is slow enough to track its process roughly in this study. The 3D filaments observed here are definitely nonequilibrium structures that form and break only through a particular kinetic pathway, i.e., monolayer collapse from the preexisting monolayer. Many types of amphiphilic molecules are known to self-assemble in solution to form cylindrical tubules and helical ribbons, and a variety of models have been proposed to explain the formation of these high-curvature structures, which can be divided into two main categories: those based on the chiral elastic properties of the material and those based on nonchiral effects such as electrostatic interaction and orientational elasticity.32 In forming curved filaments our elementary components (i.e., the monolayers) are certainly nonchiral, and the former chirality-based scenario may be excluded. Not only the enhanced headgroup interactions but also the strong cohesion between long hydrocarbon chains may
Figure 5. Evolution of 3D filaments created in different crack lines [(a) π ) 48.8 mN/m; (b) π ) 49.1 mN/m]. The crack region in (a) is enclosed for clarity. In the initial stage, relatively long 3D filaments develop in the crack region, and some of them form a regular arrangement (the second frame in (a) and the upper part of the second frame in (b)) and then finally break into smaller segments (the fourth frame in both (a) and (b)). The scale bar represents 100 µm.
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be a significant contributory factor for the formation of 3D curved filaments in the anisotropic cracking regime. Some mechanism must thus be considered, taking into account the filament’s overall curvature and its nonequilibrium nature. The Ries mechanism allows a collapsed monolayer to form a bilayer structure only if the conceptual framework of monolayer curvature is introduced for both edges. The nonequilibrium, long-length-scale mechanism that leads a monolayer to a curved 3D filament should be explored. Conclusions We have found sequential collapse transitions in a lignoceric acid Langmuir monolayer. The surface rough(30) Ghaskadvi, R. S.; Bohanon, T. M.; Dutta, P.; Ketterson, J. B. Phys. Rev. E 1996, 54, 1770. (31) Ries, Jr, H. E.; Swift, H. Langmuir 1987, 3, 853 and references therein. (32) Selinger, J. V.; Spector, M. S.; Schnur, J. M. J. Phys. Chem. B 2001, 105, 7157.
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ening regime characterized by the nucleation of 3D granular dots and their prevalence over the monolayer is already initiated at low surface pressure, probably in the S phase. The onset of monolayer collapse at low surface pressure indicates that the interplay between head-head and tail-tail interactions induces a structural instability in the monolayer. The second collapse mode manifests itself in the form of anisotropic, global crack arrays (anisotropic cracking regime), signified by the appearance of a kink in the isotherm. The onset of the anisotropic cracking may be associated with the existence of a finite shear modulus in the monolayer. The mechanical properties of the monolayers in the distinct solid (i.e., S and CS) phases should be further examined. In the anisotropic crack region various forms of 3D curved filaments evolve and break into smaller fragments with a typical relaxation time (∼60 ms). LA036014A
