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Nonequilibrium Structures in 1-Monopalmitoyl-rac-glycerol Monolayers U. Gehlert* and D. Vollhardt Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12 489 Berlin, Germany Received December 11, 1995. In Final Form: October 11, 1996X Brewster angle microscopy is used for investigations of nonequilibrium structures in 1-monopalmitoylrac-glycerol monolayers. The extent of branching of the condensed phase domains correlates with the supersaturation and thus with the compression rate of the monolayer. Dendritic growth is favored at intermediate compression rates, while tip splitting occurs at higher compression rates. The shape relaxation of unstable branched structures into nearly round equilibrium domains is shown by Brewster angle microscopy and described by a time development of the roundness. The optical anisotropy observed within the nonequilibrium structures allows the identification of the main growth direction of the dendrites with respect to the lattice directions.
Introduction In recent years new methods have extended the knowledge of various two-dimensional monolayer phases.1-7 Domains of condensed phase surrounded by a phase of lower density have been observed with an exciting variety of sizes and shapes. These include for instance circular,4,8 spiral,9 and unstable branched structures.10-13 The different shapes depend not only on the type of amphiphilic molecule but also on experimental factors such as temperature, modification of the water subphase, impurity content, spreading technique, and compression rate. Unstable branched structures are usually a consequence of nonequilibrium conditions.14 Fractal-like structures or dendrites appear in compressed monolayers during rapid decrease in temperature12 and also in monolayers compressed at high rates.15 Using fluorescence microscopy, Akamatsu and Rondelez16 have described a temperature-induced domain-wall instability in fatty acid monolayers. At high temperatures, near the critical temperature, fractal-like structures were observed which relax very slowly to their equilibrium shapes. At lower temperatures the domains have compact shapes. The appearance of branched structures with increasing temperature was ascribed to a decrease in the line tension,17 which tends to zero approaching the critical point. FractalX Abstract published in Advance ACS Abstracts, December 15, 1996.
(1) Kenn, R. M.; Bo¨hm, C.; Bibo, A. M.; Peterson, I. R.; Mo¨hwald, H.; Als-Nielsen, J.; Kjaer, K. J. Phys. Chem. 1991, 95, 2092-2097. (2) Als-Nielsen, J.; Mo¨hwald, H. In Handbook on Synchrotron Radiation; Ebashi, S., Koch, M., Rubenstein, E., Eds.; North-Holland: Amsterdam, Oxford, New York, Tokyo, 1994; Vol. 4, pp 1-53. (3) Gehlert, U.; Vollhardt, D. Prog. Colloid Polym. Sci. 1994, 97, 302-306. (4) Gehlert, U.; Weidemann, G.; Vollhardt, D. J. Colloid Interface Sci. 1995, 174, 392-399. (5) Henon, S.; Meunier, J. Rev. Sci. Instrum. 1991, 62, 936-939. (6) Ho¨nig, D.; Mo¨bius, D. Thin Solid Films 1992, 210/211, 64-68. (7) Vollhardt, D.; Gehlert, U.; Siegel, S. Colloid Surf. A 1993, 76, 187-195. (8) Henon, S.; Meunier, J. J. Chem. Phys. 1993, 98, 9148-9154. (9) McConnell, H. M. Annu. Rev. Phys. Chem. 1991, 42, 171-195. (10) Miller, A.; Knoll, W.; Mo¨hwald, H. Phys. Rev. Lett. 1986, 56, 2633-2636. (11) Knobler, C. M. Science 1990, 249, 870-874. (12) Suresh, K. A.; Nittmann, J.; Rondelez, F. Biophys. Lett. 1988, 6, 437-443. (13) Gehlert, U.; Siegel, S.; Vollhardt, D. Prog. Colloid Polym. Sci. 1993, 93, 247. (14) Ben-Jakob, E.; Garik, P. Nature 1990, 343, 523-530. (15) Lo¨sche, M.; Mo¨hwald, H. Eur. Biophys. J. 1984, 11, 35-42. (16) Akamatsu, S.; Rondelez, F. J. Phys. II 1991, 1, 1309-1322.
like growth in phospholipid monolayers has been studied by Mo¨hwald et al.18-23 and has been explained by a mechanism of constitutional supercooling due to different solubilities of impurities (fluorescent markers) in the two phases. For DPPC and DMPE monolayers the same structures were found without fluorescent markers using Brewster angle microscopy (BAM).24-26 Weidemann and Vollhardt have shown that the behavior of the two substances differs with respect to the shape relaxation of the branched domains.27 Recently dendritic crystallization could be observed in different amphiphilic monolayers.28-30 This work presents nonequilibrium pattern growth including dendritic structures in monolayers of 1-monoglycerides. These are excellent modell substances for studying two-dimensional phase behavior. Under equilibrium conditions both circular- and cardioid-shaped domains can be observed by BAM.4 The shape of the cardioid domains is caused by the anisotropy of the line tension. A remarkable feature of the circular domains is a sevenfold substructure. The different brightnesses of subdomains are due to regions of different molecular orientation. The tilt angle within a monolayer domain possesses a defined value whereas the chain tilt azimuth is changed at each segment boundary. The analyses of the BAM experiments have shown that the aliphatic chains are tilted radially.4 X-ray data indicate that the chains are tilted to the nearest neighbor direction of a centered rectangular lattice with (17) Suresh, K. A.; Nittman, J.; Rondelez, F. Europhys. Lett. 1988, 6, 437-443. (18) Fischer, A.; Lo¨sche, M.; Mo¨hwald, H.; Sackmann, E. J. Phys. Lett. 1984, 45, 785-791. (19) Lo¨sche, M.; Rabe, J.; Fischer, A.; Rucha, U.; Knoll, W.; Mo¨hwald, H. Thin Solid Films 1984, 117, 269-280. (20) Miller, A.; Knoll, W.; Mo¨hwald, H. Phys. Rev. Lett. 1986, 56, 2633-2638. (21) Miller, A.; Mo¨hwald, H. J. Chem. Phys. 1987, 86, 4258-4265. (22) Mo¨hwald, H. Thin Solid Films 1988, 159, 1-15. (23) Kenn, R. M.; Bo¨hm, C.; Bibo, A. M.; Peterson, I. R.; Mo¨hwald, H.; Als-Nielsen, J.; Kjaer, K. J. Phys. Chem. 1991, 95, 2092-2097. (24) Weidemann, G.; Vollhardt, D. Colloids Surf. A 1995, 100, 187202 (25) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590-4592. (26) Akamatsu, S.; Bouloussa, O.; To, K.; Rondelez, F. Phys. Rev. A 1992, 46, 4504-4507. (27) Weidemann, G.; Vollhardt, D. Thin Solid Films 1995, 264, 94103. (28) Vollhardt, D.; Gutberlet, T.; Emrich, G.; Fuhrhop, J.-H. Langmuir 1995, 11, 2661-2668. (29) Knobler, C. M.; Stine, K.; Moore, B. G. Springer Proc. Phys. 1990, 52, 131-140. (30) Emrich, G.; Vollhardt, D.; Gutberlet, T.; Kling, B.; Fuhrhop, J.-H. Prog. Colloid Polym. Sci. 1995, 98, 266-268.
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the tilt azimuth parallel to the a axis.31 The segment boundaries can be considered to be low-energy lattice rows. The interdependence of the lattice parameters and the number of segments indicates that the lattice structure influences the inner structure of a condensed phase domain.32 Much has been learned about the morphological properties of 1-monoglycerol monolayers under equilibrium conditions. However there are still unanswered questions concerning the nonequilibrium structures, which are as follows: (1) What is the relation between domain shape and supersaturation? (2) How are the macroscopic directions of a dendrite related to the lattice directions of the two-dimensional crystal structure? In this paper, the classification of Ben-Jakob and Garik is applied for the various nonequilibrium morphologies in monolayers.14 Experimental Section A Brewster angle microscope from NFT (Go¨ttingen), mounted on a Langmuir film balance from LAUDA (Lauda-Ko¨nigshofen), is used to observe the microscopic structures of the monolayer. The light reflected from the surface is collected by a lens and detected with a CCD (charge-coupled device) camera. The resulting signal is recorded on video. Optical anisotropy at the monolayer can be detected by introducing an analyzer to the reflected beam path. The spatial resolution of the method is approximately 4 µm. Experimental details of BAM have been described previously.33 1-Monopalmitoyl-rac-glycerol was obtained from Sigma (Deisenhofen) with a purity of approximately 99%. Special attention must be paid to the purity of the water subphase and the solvent because impurities influence the nucleation of the condensed phase domains. BAM was used to test the water subphase with and without spreading solvent. n-Heptane for spectroscopy, Merck (Darmstadt), and the ethanol p.A., Merck, are dust-free. A mixture (9:1 heptane/ethanol) was used to dissolve the 1-monopalmitoyl-rac-glycerol. The subphase was ultra pure water with a specific resistance of 18.2 MΩ/cm, purified using a Millipore desktop, Millipore (Eschborn). After the spreading liquid was spread and evaporated, the dynamic investigation of monolayer compression was carried out with an automatic Langmuir film balance. The balance was equipped with a temperature control unit, and the system was flushed with nitrogen to prevent dust contamination of the aqueous surface. The experiments were performed at different compression rates at a fixed temperature of 23 °C.
Results and Discussion Growth of Nonequilibrium Domains. Two-dimensional condensed phase domains of 1-monopalmitoyl-rac-glycerol appear during the first-order phase transition in the plateau region of the π-A isotherm. The images of Figure 1 show a morphology diagram of these domains as a function of the compression rate. Each part of Figure 1 is taken in the moment of compression stop at equal area per molecule distinguished by the compression rates. At slow reduction of molecular area the supersaturation is negligible, so that the domains can obtain nearly their equilibrium shapes (Figure 1a). At higher compression rates the domains start to become irregular (Figure 1b). A further increase in compression rate and thus in supersaturation causes dendritic structures (Figure 1c). The arms of the dendrites start at the initial nucleus and grow continously with stable tips without branching. The dendritic shape is due to a growth anisotropy, indicating (31) Brezesinski, G.; Scalas, E.; Struth, B.; Mo¨hwald, H.; Bringezu, F.; Gehlert, U.; Weidemann, G.; Vollhardt, D. J. Phys. Chem. 1995, 99, 8758-8762. (32) Weidemann, G.; Gehlert, U.; Vollhardt, D. Langmuir, 1995, 11, 864-871. (33) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590-4592.
Figure 1. Morphology diagram of condensed phase domains of 1-monopalmitoyl-rac-glycerol on stopping the compression (A ) 0.32 nm2/molecule, T ) 23 °C). The bars represent 100 µm. (a) Compact condensed phase domain. Compression rate: 8 × 10-3 nm2/(molecule min). (b) Irregular-shaped domain. Compression rate: 2.3 × 10-2 nm2/(molecule min). (c) Dendriticshaped domain. Compression rate: 4.7 × 10-2 nm2/(molecule min). (d) Transition state between dendritic-shaped domain and fractal-like domain. Compression rate: 0.17 nm2/(molecule min). (e) Fractal-like condensed phase domain. Compression rate: 0.22 nm2/(molecule min).
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Figure 2. Surface pressure-time (π-t) diagram after stop of the compression for the lowest and highest compression rates of figure 1 (A ) 0.38 nm2/molecule, T ) 23 °C). (a) Lowest compression rate: 8 × 10-3 nm2/(molecule min). Curve fit parameters: π0 ) 5.5 mN/m, ∆πt)0 ) 0.17 mN/m, τ ) 1.4 × 10-2 s-1, cT ) 1.5 × 10-4 mN/(m s). (b) Highest compression rate: 0.24 nm2/(molecule min). Curve fit parameters: π0 ) 5.8 mN/ m, ∆πt)0 ) 0.58 mN/m, τ ) 0.11 s-1, cT ) 3.2 × 10-4 mN/(m s).
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rate, the boundary length of the condensed phase already formed, and the incorporation rate of the molecules into the condensed phase. A measure of the supersaturation is accessible by the difference of the surface pressure of the monolayer compressed to a fixed area (π) and the surface pressure at the same area for equilibrium (π0). The surface pressure approaches this equilibrium value with time. The decrease of the surface pressure is due to the reduction of the supersaturation by the transition of molecules from the phase of lower density to the condensed phase. The relative supersaturation can be obtained by
ϑ ) (π - π0)/π0
(1)
The pressure difference is also correlated to a difference in the density of the fluid phase. The corresponding change of the area fraction can be calculated from the actual area per molecule and the area requirement of the condensed and the fluid phase. The calculated change of the area of the condensed phase is less than 5% of the absolute area of the condensed phase. This is too small to be detected by an analysis of the domain area, so that the area fraction could not be used to quantify the supersaturation. Figure 2a shows the time development of the surface pressure following a compression into the plateau region of the π-A isotherm at the lowest rate shown in Figure 1a. For a compression at the highest rate and resulting fractal-like domains (Figure 1e) the π-t diagram is presented in Figure 2b. Experimental data have been fit to an empirical function of the following form:
π ) π0 + ∆πt)0 exp(-τt) - cTt
(2)
that the incorporation of the molecules in the condensed phase is favored in defined directions. The higher the compression rate, the more branched domain structures can be observed. A jump of the surface pressure into the plateau region of the π-A isotherm leads to a high supersaturation. Under these conditions fractal-like structures are formed (Figure 1e). The growth of the branches occurs in each direction with the same probability. That means branched structures do not reflect growth anisotropy in contrast to the dendrites. The domains first grow with split tips. If the supersaturation is reduced by a further transition of the fluid phase to the condensed phase, the tips become stable. Consequently the domains are more branched in the center than in the outer region. At compression rates between those yielding dendrites and fractal-like structures, the domain shape is also intermediate. Domains result which clearly show main arms, but these are split two or three times (Figure 1d). Hence the growth is favored in defined directions and the shape reflects a growth anisotropy. The nature of the so-called tip-splitting transition, where the tip of a growing branch splits into two or more parts, is not yet clear and is of theoretical interest.34 The question is whether it is possible to use the word "transition" or if it is better to think of a gradual crossover between dendritic and fractal-like morphology. Supersaturation is a significant quantity in contributing to the extent of domain branching. With an ideal pressure jump the surface pressure would increase as for the fluid phase, if nucleation and growth would be neglegted. With a real pressure jump the supersaturation realized at a defined area per molecule is related to the compression
where ∆πt)0 is the absolute supersaturation for t ) 0, t is the time, τ is the time constant of decreasing pressure, and cT is the temperature constant. The slight decrease in the surface pressure at the end of the curve is due to a slight decrease in temperature. This is taken into account by the linear term in the equation. Random fluctuations in temperature lead to positive and negative terms corresponding to a slight decrease or increase of temperature. The shifts of the temperature are introduced by the thermostat. Even a change of 0.1 °C corresponds to a shift of the surface pressure of about 0.1 mN/m in the two-phase coexistence region. Relaxation of Nonequilibrium Domains. The way the domain shapes change with time-dependent surface pressure relaxation can be observed with BAM. Immediately after a high-rate monolayer compression, one can follow the continued growth of the split tips of a fractallike structure for some seconds. This corresponds to the decrease of the supersaturation as shown in Figure 2b. Since this process is very fast and the field of view is very small (about 1 mm2), a quantitative description of the growth kinetics could not be realized. In the moment of compression stop the branched structures start to relax to compact domains within approximately 5 min. This shape transformation is affected by the minimization of the line energy. A sequence of relaxing domain shapes is shown in Figure 3a-c. In this example the initial nonequilibrium domain is a transition stage between a fractal-like and a dendritic domain. Relaxation stages as seen in Figure 3 can also arise from monolayer compression with corresponding rates (see Figure 1). As shape parameter the roundness (r) of the domains which were formed during the shape relaxation has been determined from the relation
(34) Gliozzi, A.; Levi, A. C.; Menessini, M.; Scalas, E. Physica A 1994, 203, 347-358.
r ) 4πA/u2
(3)
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Figure 3. (a-c) Sequence of relaxing domain shapes after compression stop in the plateau region of the π-A isotherm (A ) 0.38 nm2/molecule, T ) 23 °C). (d) Domain roundness-time (r-t) diagram with designated arrows corresponding to the images of a-c.
where A is the domain area and u is the domain perimeter. The roundness increases with time (Figure 3d). Using an image-analysis software package, the final roundness was calculated to be 0.8 instead of 1 as expected for circular domains. This difference can be ascribed to the perimeter determined by the imaging software, which is longer than that in reality due to blurring of the images. The blurring of the image biased toward one axis. Only a small part of the image is sufficiently sharp and well illuminated. Nonequilibrium Dendrites. The shape of nonequilibrium dendrites can be interpreted in light of the relation between microscopic growth directions and lattice rows of the molecule chains. The seven branches starting from the dendrite origin reflect with different brightness (Figure 4a). The molecules of each arm of a dendrite have a distinct molecular orientation. The angle included by two adjacent arms has been estimated. The angle distribution indicates a most probable angle between 45° and 50° (Figure 4b). This is in good agreement with the angle of the bisectors of two segments in the sevenfold equilibrium domains.4 From the angle distribution it is evident that a dendrite arm corresponds to one segment of an equilibrium domain. This result is in good agreement with the shape relaxation experiments. Figure 5 shows a snapshot of a nonequilibrium domain in a shape relaxation stage after compression stop. This structure indicates quite nicely that the initial seven dendrite arms transform to the segments of the sevenfold equilibrium domains. However the number of branches within a dendrite varies from five to seven. Figure 6a shows both a sevenfold and a sixfold dendrite. BAM observations indicate that generally within a sixfold dendrite one angle is larger (arrow) than the rest, which are approximately the same. The angle distribution of dendrites with six arms clearly shows a second maximum at about twice the maximum angle (Figure 6b). This clearly indicates that at the position of
the large angle in a six-fold dendrite one arm is not developed. It can be seen from Figure 6a that one arm of the sevenfold dendrite has grown into the gap of the absent arm of the sixfold dendrite. These results suggest that the initial growth of the dendrites affects the local concentration field. As a consequence direction dependent growth rates can prevent the formation of one or two of the dendrite arms and lead to statistically distributed arm lengths. The appearance of nonequilibrium structures differing in number of branches allows conclusions to be drawn concerning the formation of two different equilibrium domain structures.4 Because circular- and cardioidshaped domains appear when the system has nearly relaxed to equilibrium-shaped domains, it seems likely that the position of the original point of the segment boundaries is caused by the domain growth. If the domain growth is prevented in one direction and five- or six-arm structures are developed, the contact point of the segments should be situated on the edge of the equilibrium shape. These domains have a cardioid-shaped boundary due to the anisotropic contribution of the line tension. Circular domains with a segment center in the middle of the domain arise only if the growth rate of the nonequilibrium structures was the same for all directions. Now we consider the formation of the condensed phase with a low compession rate. Although by BAM only near equilibrium domain shapes are observable, it can be assumed that a wall instability can also occur during an early stage of the domain growth. The initial stage of the domains is outside the resolution of BAM. Local concentration fields during domain nucleation and growth can induce local non-equilibrium conditions and, following from that, direction dependent growth. After further domain growth, two relaxed equilibrium shapes of the domains are made visible with BAM. So it cannot be
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Figure 4. (a) BAM image of optical anisotropy within a sevenfold dendrite (A ≈ 0.4 nm2/molecule, T ) 23 °C). (b) Distribution of the angles included by two arms of the sevenfold dendrite (number of dendrites: 31). The precision of the determined segment angles is about 4°.
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Figure 6. (a) Brewster angle image of optical anisotropy within a sixfold dendrite A ≈ 0.4 nm2/molecule. (b) Distribution of the angles included by two arms of the sixfold dendrite (number of dendrites: 36).
direction along low-energy lattice rows. Grazing incidence X-ray diffraction studies connected with a geometrical analysis revealed that the chains in the circular domains are tilted along the segment bisector to the nearest neighbor lattice direction projecting the chains on the surface.32 It has been shown by BAM that the dendrite arms correspond to the segments of a compact domain. Therefore the arms of a dendrite are along the azimuthal chain tilt direction of each segment. This allows the identification of the main growth direction of the dendrites with respect to the lattice directions as the [10]-direction. Conclusions
Figure 5. Condensed phase domain in a shape relaxation stage (A ≈ 0.3 nm2/molecule, T ) 23 °C).
discounted that the appearance of the two equilibrium shapes is caused by the domain growth. From Figure 6a it is obvious that the side branches have the same chain orientation and growth direction as the adjacent domain arm. This indicates chain tilt
1-Monopalmitoyl-rac-glycerol is an excellent model substance for studying two-dimensional nonequilibrium phase behavior. As a result of nonequilibrium, domainwall instability in monolayers of 1-monopalmitoyl-racglycerol, induced by increasing the compression rate, has been observed by BAM and described qualitatively by a morphology diagram. While dendritic shape shows growth anisotropy, fractal-like structures do not reflect growth anisotropy. The supersaturation, which can be determined by the surface pressure relaxation after stopping the compression in the plateau region of the π-A isotherm, can be correlated to the domain-wall instability.
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On stopping after fast compression, the domain shape relaxes into the circular equilibrium shape. During the first seconds of the relaxation the supersaturation is reduced due to the growth of the branched domain tips. This process occurs during the steep surface pressure decrease in the π-t diagram. Comparing the equilibrium structure with nonequilibrium dendrites, it can be shown that a dendrite arm corresponds to one segment in the circular domain. On the basis of this result the relation between the distinct growth directions of a nonequilibrium structure and the lattice direction of the two-dimensional lattice of the
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molecule chains could be clarified. The growth direction of the dendrites is along the densest lattice rows. Acknowledgment. Financial assistance from the Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie is gratefully acknowledged. We are indebted to support by Prof. Mo¨hwald (Max-PlanckInstitut fu¨r Kolloid- und Grenzfla¨chenforschung, Berlin) and Prof. Findenegg (Technische Universita¨t, Berlin). We thank E. Scalas (Universita¨t Mainz) for helpful discussion. LA951531H
