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Langmuir 1992,8, 160-163
Capillary Wave Propagation on Water Covered with Inhomogeneous Monolayers: Liquid/Gas Coexistence Films Kenjiro Miyano' Department of Applied Physics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo-113, Japan
Kaoru Tamada Tsukuba Research Laboratory, Japan Synthetic Rubber Co., Ltd., 25 Miyukigaoka, Tsukuba-305, Japan Received April 10, 1991. In Final Form: August 8, 1991 Externally generated capillary wave propagation has been studied on water whose surface was covered with a monolayer in the liquid/gas coexistence phase up to 1kHz. A simultaneous morphology observation with a fluorescence microscope enabled us to make a one-to-one correspondence between the fraction of the liquid film and the propagation characteristics. It was found that the liquid film does not affect the capillary wave significantly until it covers more than 90% of the water surface, which indicates that the dynamic elasticity of the liquid monolayer below 1kHz is extremely low. It was also noted that the bubbles (the gas phase) were very stable against coalescence, implying that the line tension of the liquid phase is quite low. These findings suggest that the liquid phase in equilibrium with the gas phase is in a very shallow intermolecular potential. It was confirmed that the surface waves do not affect the morphology of the monolayer.
Introduction Capillary wave propagation on water covered with a monolayer has been studied extensively.' The propagation characteristics have been well understood, at least at the phenomenological level, when the film is homogeneous. However, when the monolayer is inhomogeneous, hardly any attempts have been made to elucidate the consequence of the inhomogeneity on the capillary waves except for occasional remarks that the propagation characteristics fluctuate a lot; further investigation into the cause of the fluctuation was not possible because of the lack of means for independent characterization of the inhomogeneity. The fluctuation due to the inhomogeneity could have been mistaken for the problem of the measurement system and thus ignored. With the advent of fluorescence microscopy,2 however, it has been widely realized that an inhomogeneous monolayer is not an exception; indeed, monolayers are very often inhomogeneous at low pressures. It is, therefore, highly worthwhile to study the capillary wave propagation on water with a spread monolayer which shows a wellcharacterized inhomogeneity. We have started a systematic study toward this goal. In this paper, we report the results of our first attempt at dealing with a liquid/gas coexistent film. Experimental Procedure The experimental setup is shown schematically in Figure 1. The basic construction was the same as that of the capillary wave probe which has been described previously.3 In addition to the capillary wave probe, a fluorescence microscope was mounted on the same x-y stage, which could be moved to any part of the trough (25 cm X 17 cm). The Wilhelmy plate previously used to monitor the surfacepressure (a)was replaced with a Langmuirtype horizontal pressure sensor since the former was found to be not reliable when the film became stiff or viscous. (1) Miyano, K. In Light Scattering by Liquid Surfaces;Langevin, D., Ed.; Marcel Dekker: New York, in press. (2) See for example, Mohwald, H. Thin Solid Films 1988,159,1, and references therein. ( 3 ) Miyano, K. Langmuir 1990, 6,1254.
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Figure 1. Schematic diagram of the experimental setup. SIT CAMERA
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Figure 2. A wave-generating blade and a small mirror attached to the objective holder for the simultaneous capillary wave measurement and microscope observation. The monolayer in the liquid/gas coexistenceregion is naturally quite mobile: a small disturbance (draft, temperature gradient, etc.) can cause alarge-scaleflow. With the setup shown in Figure 1 in which the field of view of the microscope was not the same as the scanning area of the capillary wave probe, we could not make sure that the state of the film viewed under the microscope stayed the same when the capillary wave probe was moved to the location of the microscope observation. We have therefore devised a small capillary wave outfit which allowed us to make the microscope observationand the capillary wave measurement simuitaneously. As shown in Figure 2, a small generating blade and a small mirror were attached to the objective holder. The field of view thus fell directly on the capillarywavepath. Because 0 1992 American Chemical Society
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Langmuir, Vol. 8, No. 1, 1992 161
of the space limitation, we could not scan the laser beam reliably in this configuration. The capillary wave propagation distance was hence fixed (- 2 cm)in this measurementand only the change in the amplitude and the phase relative to those on a film-free water were noted. It should be cautionedthat only a small fraction of the total path was observable. The amplitude of the capillary wave at the generator could be held constant by keeping the microscope image focused all the time and thus maintaining a constant separation between the wave generating metal blade and the water surface. When the monolayer was well compacted and immobile, the usual scanning scheme (Figure 1) was also employed. The fluorescencemicroscope was fitted with an SIT camera connected to a TV monitor. The image was recorded on videotape,which was later analyzed with an image processor. In this study, it is important that the fluorescent image faithfully reflects the presence and the absence of the film material. In this respect, the doping method used in most of the previous fluorescencemicroscopystudies? in which fluorescentprobe was added to a nonfluorescent monolayer, was not workable here. We, therefore, chose a cyanine dye (1) (3-0ctadecyl-2-[3-(3-octadecyl-2-benzothiazolinylidene)-l-propyl] benzothiazolium perchlorate) as the monolayer material; it fluoresces strongly in orange under green light excitation and was found to exhibit a clear gas-liquid transition. It was dissolved in a 1:3 mixture of spectroscopic grade ethanol and chloroform to a concentration of 0.3 mM/L. The amphiphile was purchased from Wako Pure Chemical Industries, Ltd., and was used without further purification.
dye I
The water for the subphase was distilled and filtered through a Mill-Q system. The temperature was 21 "C. The data analysisposed a difficultproblem, since notheoretical treatment has ever appeared for the surface wave propagation on water covered with an inhomogeneous monolayer. We thereforeproceeded as follows: the data were analyzed using the conventional surface wave dispersion relation3 (pw2- yk3 - pgk
+ 2ipuk2)[ipw(m2+ k2)- mk2cl + [i(yk3+ pgk) + 2pumk](2puk2+ ik3t) = o
(1)
with the following definitions: k is the complex wavenumber (=kr + ikj), g is the gravitation acceleration, y is the surface tension, w is the angular frequency of the capillary wave, p and p are the density and the shear viscosity of water, respectively, c is the complex uniaxial elastic modulus (=cr + ici), and m2 = k2 - iwp/p
With the measured k and y determined from y = ywater - T , the elastic modulus c was then calculated from eq 1. The parameter e was studied as a function of the liquid film fraction of the monolayer. We looked for any anomalous behavior which might be a signature of the breakdown of our assumption that the film was homogeneous.
Results and Discussion A pressure-area (FA) diagram is shown in Figure 3 together with the microscope images taken a t the respective areas which are indicated by arrows. The bright region is the liquid phase and the dark area is where the molecules are scarce (the gas phase). The monolayer showed some area relaxation while being held (- 10 min) at a constant pressure above 1mN/m as seen in the decompression cycle. On second compression, the isotherm followed the decompression curve.
v-
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r 90%
Area /nm2 molecule-1 Figure 3. Pressure-area isotherm for a compression-decompression cycle. The area relaxation occurred when the pressure was held above 1mN/m for 10min. The pictures are fluorescence microscope images (a 250 pm X 250 pm section) taken at the corresponding area in the decompressioncycle. The bright parts are the condensed film (liquid) and the dark parts are the gas phase. The liquid film fraction in each image is shown above the respective picture. We searched for the area of low density and made capillary wave measurements there in order to obtain the data points at low fluid film fraction in Figure 4. The surface pressure of the monolayer when spread was below the resolution of our pressure sensor. The film, however, exhibited a remarkable inhomogeneity seen under the fluorescencemicroscope, even if care was taken to spread the solution uniformly. The scale of the inhomogeneity was of the order of several centimeters or more. It was quite disturbing because it seemed as though the water surface was contaminated and the contamination hindered the initial spread of the monolayer. However, the large-scale inhomogeneity went away when the film was reexpanded after a compression. This suggests that the initial inhomogeneitywas due to the spreading process itself. It is sometimes observed with a dye that a film initially dispersed over the entire trough area retracts into a large blob after a while. It may be related to how the solvent evaporates, but the details still remain to be understood. In order to avoid the initial large-scale inhomogeneity, we compressed the monolayer to the surface pressure of a few mN/m. A t this point, the film appeared quite uniform and featureless under the microscope. The monolayer was then expanded and the morphology observation and capillary wave measurement were performed. Shown in Figure 3 are a series of microscope images during this decompression cycle. The results of the microscope observation and the capillary wave measurements described below were reproducible on repeated compression and expansion subsequent to the first compression. Three frequencies chosen for the surface wave were 240, 500, and 920 Hz. The lower frequency was limited by the reflection from the trough walls when the monolayer was absent and the higher frequency by the attenuation when the film was fully compacted. The number above each picture in Figure 3 indicates the percentage of the area covered by the liquid film in the respective photograph. It has been obtained by first binarizing the image and taking the ratio of the number of the bright pixels over the entire image. A t large A, the liquid fraction is far below the value expected from the average density of the monolayer, because we searched over the trough for the area of low coverage. Naturally, most of the rest of the area was covered with the liquid film. We needed to take measurements a t low coverage
Miyano and Tamada
162 Langmuir, Vol. 8, No. 1, 1992 k
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Figure 6. Relative motion of two points on the water surface
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Figure 4. Film elastic modulus vs liquid film fraction. o a
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0.5 1.0 1.5 2.0
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Surface Pressure / mN.m" Figure 5. Film elastic modulus vs surface pressure. The solid curve is the static elasticity calculated using eq 2. in order to complete the abscissa in Figure 4. Note that what is relevant to us is the liquid fraction a t the point of capillary wave measurement, not the average over the entire trough. We will quote the value thus obtained in the following analysis. As the area was expanded, the film appeared uniform down to about 0.1 mN/m. At this point, small bubbles began to appear. They were stable in that they did not disappear or coalesce as long as the pressure was maintained within the duration of our measurement (- 10min). They were not caused by the heating effect of the microscope, since there were areas where no bubbles were found a t the same pressure. As the area was expanded further, the bubbles grew in size. By the time the bubbles covered 10% of the water surface, the pressure was immeasurably small. The vapor pressure, thus, seemed to be nearly zero in this material a t room temperature. Therefore, the nonzero pressure, albeit small, when the bubbles first began to appear is disturbing, because this implies that the equilibrium vapor pressure is higher in smaller bubbles. This is just the opposite to what one might expect if one assumes a positive line tension of the liquid monolayer. This point will be discussed later. The film elastic modulus E calculated from eq 1 is plotted in Figure 4 as a function of the fraction of the liquid film coverage and in Figure 5 as a function of the surface pressure together with the equilibrium film elastic modulus E , defined by = aria In A
(2) The overall behavior of the dynamic elastic modulus e, agrees with E,, However, the equilibrium modulus seems to be consistently larger than tr in both Figures 4 and 5. This is troubling since it should physically be the other way around (see discussions below). A detailed analysis showed that tr calculated from eq 1 is not very sensitive to the variation of the measured values of k and y (ywater - T ) , while the error bar for ti is quite large. Thus the fact t,
during the capillary wave passage. The monolayer undergoes the contraction and expansion regardless of ita size or shape because of the local coupling to the surface motion of the water. The dashed circles show the subphase motion in the bulk.
that e, is smaller than ts is not likely to be due to the uncertainty in the measurement. Since the main thesis of the current study is to investigate the effect of the inhomogeneity, we will leave this problem for a future study. Note in passing that a single capillary wave measurement, i.e. the determination of a complex k (two knowns) a t a given o,is not sufficient to uniquely calculate y and complex t (three unknowns) a t the same time. One could, in principle, make measurements a t various frequencies and determine y and t as adjustable parameters in a certain model. In practice, however, the frequency range accessible to the current setup is rather limited, making an attempt along this line not realistic. In our previousstudy,3 on the other hand, y could be determined from a capillary wave measurement because t had been known to be very large beforehand (solid monolayer) and hence y was a unique function of k (cf. Figures 1 and 2 in ref 3). The absence of the influence of the liquid film up to the coverage of 90% is remarkable. One might argue that this is altogether reasonable, because the P A curve shows ts = 0. However, when one considers the compression process in the microscopic level, there should be a difference between t, and the elastic modulus the capillary wave experiences in an inhomogeneous monolayer. Under a uniformcompression in the coexistence region, the pressure does not change because the gas condenses into the liquid. The density in the liquid phase remains the same; the liquid phase simply grows. On the other hand, when the capillary wave is involved, the liquid density should change locally as the following argument shows. Let us note that the fluid (subphase water) motion in the capillary wave is such that the surface periodically expands and contracts as the wave passes by. The monolayer on the surface undergoes the same motion since the monolayer cannot escape from the surface (see Figure 6). This is the mechanism through which the film elasticity modifies the capillary wave propagation characteristics. Because this interaction occurs locally, i.e. the stress in the monolayer occurs regardless of its shape or size, one expects that the effect of the monolayer on the capillary wave is proportional to its coverage. The result in Figure 4 is just the contrary. Even though the size of the microscope field of view is about 1mm and thus it would be difficult to be sure about the state of the monolayer in the entire path length of the capillary waves, it is not likely that the inhomogeneity of the film was such that the liquid phase was consistently absent in the area not seen under the microscope. We therefore have to conclude that the film in the liquid phase (in the conventional notation it should be classified as a "liquid expanded" phase) is extremely compressible. In other words, the condensed phase is in a very flat intermolecular potential well. That the intermolecular interaction in the liquid phase is weak can be seen from pictures in Figure 3 as well. The intricate network made of fine threads indicates that the
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Langmuir, Vol. 8, No. 1, 1992 163
line tension of the liquid phase is virtually zero. In three dimensions, the surface tension can be related to the shape of the intermolecular potential well V(r) as4 y
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Kr4[dV(r)/drlg(2)(r)dr
(3)
where g(2)(r)is the two-body correlation function. If a similar argument is applicable to the line tension of a monolayer, the weakness of the line tension immediately implies that the intermolecular potential is again very flat a t the equilibrium position in the liquid phase. Some studies on the line tension of a monolayer5 and a t a contact region of three bulk liquids6 have appeared. Although a fully quantitative measurement is yet to be done, the line tension is of the order of 10-lo N and it is either positive or negative. If the bubbling process under expansion occurs in equilibrium, the fact that the bubbles do not coalesce implies that the line tension is negative. When the film pressure is in equilibrium with the negative pressure of the bubbles, the line tension K is obtained from6 K
= -AWb
(4)
where AT is the pressure change due to the line tension and Fb is the radius of the curvature of the bubbles (the negative curvature of the liquid film). The diameters of the bubbles are found to be 1-10 pm from the video image a t a = 0.07 mN/m. The line tension is therefore about (-0.4 to -4) X 10-lo N, which is in the same order of magnitude of the literature value cited above. Although we have discussed our data in terms of the intermolecular potential, the concept of such a potential in monolayers should not be confused with the threedimensional counterpart. In a three-dimensional liquid or gas, the all intermolecular configuration space is accessible, over which the intermolecular potential is defined. On the other hand, in monolayers, the intermolecular configuration is greatly restricted because of the unidirectional and planar arrangement of molecules. The shape of the potential, therefore, could be highly dependent on the details of the molecular arrangement not readily revealed in the a-A curve for instance, and it should be cautioned that the effects observed here could be only particular to the material studied. We can argue, however, that our observations are of more general value. That the intermolecular interaction in monolayers is different from the one in the three-dimensional form is of course nothing new. The critical temperature of pentadecanoic acid7 a t the liquid/gas transition, for instance, is very low (26.27 "C). Its critical pressure (ac= 0.174 mN/ m), if translated into three dimensions, is only 1atm. The critical temperatures of monolayers with long alkyl chains are in general close to room temperature and, therefore, the smallness of the line tension and the large dynamic compressibility are not surprising. We feel that our dye 1 also falls in this category. (4) Kirkwood, J. G.; Buff, F. P. J. Chem. Phys. 1949,17, 338. (5) Some remarks have been made for the line tension of the solid phase: McConnell, H. M.; Keller, D.; Gaub, H. J.Phys. Chem. 1986,90, 1717. Theoretical treatments have been given by Andelman, D.; Brochard, F.; Joanny, J.-F. J . Chem. Phys. 1987,86,3673, and McConnell, H. M.; Moy, V. T. J . Phys. Chem. 1988,92,4520. (6) Toshev, B. V.; Platikanov, D.; Scheludko, A. Langmuir 1988, 4, 489. (7) Kim, M. W.; Cannell, D. S. Phys. Reu. Lett. 1975, 35, 889; Phys. Rev. A: Gen. Phys. 1976, 13,411.
Capillary waves on films of dipalmitoylphosphatidylcholine in the liquid/gas coexistence region have been studied with a light scattering method? in which relatively large elastic constants (er and ci) have been found in contrast to our results. One possibility for this discrepancy is that a relaxation process exists in the frequency range between 1 and 5 kHz (the lowest frequency used in the light scattering study). It may simply be that the material constants of the two monolayers are different. However, we would like to point out another possibility of inhomogeneity peculiar to the as-spread monolayer. Current study was prompted because of the lack of reproducibility in the capillary wave measurements of asspread liquid monolayers. A typical liquid monolayer as oleic acid consistently displayed a significant inhomogeneity seen with the capillary wave when spread from a solution. The degree of the inhomogeneity, however, was not reproducible a t all. Nonetheless, the f i b became quite uniform and transparent to the capillary wave ( 6 0) once it was compressed slightly ( - 1 mN/m) and reexpanded to the original area. One might expect that the as-spread monolayer is more uniform than the reexpanded film after compression. The behavior of the cyanine dye 1 is contrary to expectation, as described before, and we assume that the same holds for oleic acid also. The inhomogeneity seen with the capillary waves tended to fade away with dye 1, which seemed to coincide with the microscope observation of "melting" of the solidlike flakes formed at the time of spreading. This process took about 1 h. Spreading less solution did not improve the homogeneity. With oleic acid being a liquid in the bulk a t room temperature, one expects that the initial inhomogeneity seen with the capillary wave goes away much faster. However, it lingered longer in this case and did not disappear completely in 1 h. Since the morphology of the oleic acid film cannot be observed with the fluorescence microscope, we are not sure of the nature of the inhomogeneity. But it must be more than a simple blob of liquid monolayer, which is invisible with the capillary wave. Many monolayers show drastically different morphology once compressed and r e e ~ p a n d e d .It ~ is also sometimes noted that the *-A diagram depends on the spreading solvent.lo The macroscopic morphology of the as-spread monolayer naturally affects the a-A diagram3if the monolayer is condensed (droplets or icebergs) and therefore should be taken into account when discussing the detailed feature of the isotherm especially on the first compression. This precaution should also be applied in interpreting fluctuations in relatively local measurements other than the capillary waves, e.g. the surface potential. We are currently extending this work to a solid/gas coexistence phase.
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Acknowledgment. This work was supported in part by a Grant-in-Aid for Developmental Scientific Research from the Ministry of Education, Science and Culture and a Grant for International Joint Research Project from NEDO, Japan. Registry No. 1, 53533-50-9. (8) Sauer, B. B.; Chen. Y.-L.; Zogrfi, G.; Yu, H. Langmuir 1988, 4, 111. (9) McConnell, H. M.;Tamm,L. K.;Weis,R. M.Roc. Natl. Acad. Sci. U.S.A. 1984, 81, 3249. (10)Cook, H. D.; Ries, H. E. J. Phys. Chem. 1956,60,1533. Mingins, J.; Owens, N. F.; Iles, D. H. J . Phys. Chem. 1969, 73, 2118.
