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Temperature and Flow Rate Dependence of the Velocity Profile during Channel Flow of a Langmuir Monolayer Ani Ivanova, M. Levent Kurnaz, and Daniel K. Schwartz*,† Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 Received December 18, 1998. In Final Form: April 6, 1999 Brewster angle microscopy was used to observe the surface pressure-driven flow of various fatty acid Langmuir monolayers through a narrow channel. In the tilted liquid crystalline phases (L2, L2′, and Ov), the velocity profile was generally parabolic at low flow rates, evolved to a nearly triangular shape at higher flow rates, and often returned to a parabolic shape at very high flow rates (when it was possible to observe them). In the L2 phase, the critical flow rates for the transitions between flow profiles showed a marked decrease with increasing temperature. However, the critical flow rates were insensitive to temperature in the L2′ and Ov phases. The temperature dependence of these critical flow rates for each of the three chain lengths studied (octadecanoic, eicosanoic, and docosanoic acids) is nearly identical if one adjusts the temperatures by the typical 5 °C per methylene group in order to consider equivalent positions in the generalized fatty acid monolayer phase diagram. This suggests that the non-Newtonian flow behavior is specifically linked to the structures of the mesophases themselves and not due to effects such as coupling to the subphase or a simple correlation to the polydomain structure of the monolayers.
Introduction Interfacial flow, including that of surfactant monolayers, is understood to be an important aspect of processes that are at the heart of the structure and stability of multiphase materials such as foams and emulsions.1 For example, the drainage rate of foams and the coalescence rate of emulsion droplets are affected by the interfacial rheology of adsorbed surfactants. When interfacial rheology is considered in models of these processes, however, it is generally only at the level of a simple Newtonian twodimensional viscosity. Such a simplification is not warranted, however, given the complexity of the phase diagrams of various monolayer systems that has emerged in the past decade2sin particular, the ubiquitous appearance of liquid-crystalline phases. In fact, recent studies of flow in Langmuir monolayers have uncovered a variety of non-Newtonian behavior in the mesophases including flow-induced orientational alignment,3,4 unexpected maxima in viscoelastic moduli,5 and unusual velocity profiles in channel flow.6 Observations of non-Newtonian behavior in monolayers have been mostly empirical; i.e., there is no fundamental understanding of the correlation between monolayer structure and flow behavior. In fact, there are several possible sources for unusual flow behavior. One involves the details of the coupling between the underlying liquid subphase and the monolayer. Several studies have demonstrated, for example, that the velocity profile in channel flow is sensitive to the ratio of the surface and bulk viscosities.7-10 Other possibilities involve the struc† Phone: 504/862-3562.Fax: 504/865-5596.E-mail: dks@mailhost. tcs.tulane.edu.
(1) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interfacial Transport Processes and Rheology; Butterworth-Heinemann: Stoneham, MA, 1991. (2) Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207. (3) Maruyama, T.; Fuller, G.; Frank, C.; Robertson, C. Science 1996, 274, 233. (4) Maruyama, T.; Lauger, J.; Fuller, G. G.; Frank, C. W.; et al. Langmuir 1998, 14, 1836. (5) Ghaskadvi, R. S.; Ketterson, J. B.; Dutta, P. Langmuir 1997, 13, 5137. (6) Kurnaz, M. L.; Schwartz, D. K. Phys. Rev. E 1997, 56, 3378.
ture within the monolayer itself, spanning a wide range of length scales.11 The molecular order within the relevant phases is hexatic. The molecules possess a long-range bond-orientational order; however, true crystalline positional order is absent due to a proliferation of point dislocations typical for 2D systems. The rheology of even simple hexatic phases of point particles may not be completely understood. In addition, since there is longrange orientational order which is coupled to the azimuthal tilt direction, the structure of the tilted hexatic phases is anisotropic. Macroscopically, however, a monolayer sample is not a single orientational domain. In fact, monolayers are typically composed of a mosaic of small domains (5100 µm in size) that are separated by distinct boundaries. These domains are often observed to maintain their integrity during flow. This complicates the rheology since we must consider the possibilities that the domains will slip along each other11 (adding a distinctive relaxation time scale) or that the boundaries may be elastic (they have a line tension). It is clear that one type of experiment alone will not resolve all of these issues. The approach we take in this manuscript, therefore, is to present a systematic study of channel flow, throughout the various tilted hexatic phases, as a function of flow rate, temperature, and alkyl chain length. On one hand, this allows us to determine which aspects of the flow behavior are well correlated to the known 2D phase behavior in the monolayers. On the other hand, the trends we observe (with temperature, for example) could be compared with similar trends in other flow properties (such as viscosity or relaxation times) measured by independent techniques. Experimental Details Octadecanoic (C18), eicosanoic (C20), or docosanoic acid (C22)sCH3(CH2)n-2COOH (>99%, Sigma)swas deposited from (7) Sacchetti, M.; Yu, H.; Zografi, G. J. Chem. Phys. 1993, 99, 563. (8) Schwartz, D. K.; Knobler, C. M.; Bruinsma, R. Phys. Rev. Lett. 1994, 73, 2841. (9) Stone, H. A. Phys. Fluids 1995, 7, 2931. (10) Turati, V.; Ferrari, C.; Relini, A.; Rolandi, R. Langmuir 1998, 14, 1963. (11) Bruinsma, R.; Halperin, B. I.; Zippelius, A. Phys. Rev. B 1982, 25, 579.
10.1021/la981742x CCC: $18.00 © 1999 American Chemical Society Published on Web 05/20/1999
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Figure 1. (a-c) Typical sequence of BAM images during eicosanoic acid monolayer flow from top to bottom. Distinctive features of the domain boundaries (some examples are indicated by arrows) are followed frame-by-frame in order to generate the velocity profile across the channel. chloroform (Fisher Spectranalyzed) solution onto the surface of water (Millipore Milli-Q UV+) contained in a custom-built Teflon Langmuir trough. The pH of the pure water in equilibrium with atmospheric CO2 was 5.7 ( 0.1. Previous work suggests that phase behavior and rheology of carboxylic acid monolayers are insensitive to small variations in pH in the absence of divalent cations.12 The temperature of the subphase was controlled to within (0.1 K using a combination of a recirculating water bath and thermoelectric Peltier elements and monitored with a Teflon encapsulated thermocouple probe. The surface pressure was measured using a filter paper Wilhelmy plate and a R&K electrobalance. The trough was equipped with one motor-driven Teflon barrier and a second “slave” barrier that could be clamped in place to allow monolayer compression or mechanically linked to the motorized barrier to allow the translation of the entire monolayer without compression. Between these two Teflon barriers was placed a stationary barrier made of glass and hydrophobized by treatment with octadecyltrichlorosilane. The glass barrier incorporated two channels 25 mm in length, one approximately 1 mm wide which was used for flow visualization using Brewster angle microscopy (BAM)13,14 and a second with a variable width, 0-10 mm. The second channel was used to create a twodimensional “flow divider” to permit the control of particularly low flow rates through the microscope channel. After the monolayer was brought to the desired surface pressure (π ) 21 mN/m) and temperature, the slave barrier was coupled to the motorized barrier and the monolayer was forced through the channels in the stationary glass barrier by slowly moving the motorized barriers in concert at a controlled speed. The surface pressure was chosen as the minimum value for which the unusual velocity profiles were previously observed.6 The monolayer in the channel was viewed by means of a custom-built BAM.6 BAM is sensitive to the anisotropy created (12) Yazdanian, M.; Yu, H.; Zografi, G.; Kim, M. W. Langmuir 1992, 8, 630. (13) He´non, S.; Meunier., J. Rev. Sci. Instrum. 1991, 62, 936. (14) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590.
Figure 2. Velocity profiles during monolayer flow of octadecanoic acid at π ) 21 mN/m and T ) 10 °C. The dashed lines represent the best parabolic fit to the data. The solid line is a fit to a power law model. (a) At low flow rates the profile is approximately parabolic. (b) At higher flow rates a triangular profile is observed. (c) At even higher flow rates the profiles becomes parabolic again. by the molecular tilt; hence, the monolayer appears as a mosaic of domains, each gray level corresponding to a different azimuthal tilt direction.15 We used the naturally occurring distinctive shapes of the domain boundaries as markers to follow the monolayer during flow (see Figure 1). The BAM image was videotaped and later analyzed frame by frame in order to extract the velocity profile. For each temperature and chain length, the monolayer flow was observed and analyzed for 10-12 different flow rates, where the centerline velocity (vcen) was in the range 10-3000 µm/s.
Results A typical sequence of velocity profiles is shown in Figure 2 for octadecanoic acid at 10 °C, where the monolayer is in the L2 phase. At low flow rates (Figure 2a, vcen ) 35 (15) He´non, S.; Meunier, J. J. Phys. Chem. 1993, 98, 9148.
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Discussion
Figure 3. Flow-rate/temperature “phase diagram” of the velocity profile for various fatty acid monolayers at π ) 21 mN/ m. The horizontal axis, labeled T20, refers to temperatures adjusted to be appropriate for eicosanoic acid, i.e., octadecanoic acid data are offset by +10 °C and docosanoic acid data are offset by -10 °C. The letter “P” indicates regions where the velocity profile is parabolic, and “T” represents a triangular profile. Various symbols refer to different chain lengths of the fatty acid as annotated. The vertical dashed lines indicate phase boundaries: the L2′ phase is below 15 °C, the L2 phase is at intermediate temperatures, and the Ov phase is above about 28 °C. Other lines are simply guides to the eye.
µm/s) the velocity profile across the channel is nearly parabolic. Upon increase of the flow rate to vcen ) 300 µm/s (Figure 2b), the velocity profile is noticeably sharpened - nearly triangular. At even higher flow rates (Figure 2c, vcen ) 1000 µm/s) the profile returns to a parabolic shape. “Sharp” transitions between profile shapes with increasing flow rate were not observed; in fact, the profiles gradually evolved from one shape to another over a small range of flow rates. This range was approximately 10% of the applicable critical flow rate. The shape of the velocity profile for all chain lengths, temperatures, and flow rates studied is summarized in Figure 3. The data are cast in the form of a flow-rate/temperature “phase diagram” for the velocity profile. The symbols “P” and “T” denote regions where the velocity profile is parabolic and triangular, respectively. The temperature is exact for C20, offset by +10 °C for C18, and offset by -10 °C for C22. Within the L2 phase, the critical flow rates for the P f T transition and the reentrant T f P transition decrease dramatically with increasing temperature for all three chain lengths. In fact, both the trend and the absolute values of these critical flow rates are remarkably consistent for the different chain lengths, once the temperature offset is taken into account. Within the L2′ and Ov phases, however, the critical flow rates are insensitive to temperature. In fact, within the Ov phase, the low flow rate parabolic profile has disappeared; i.e., the profile is triangular for even the lowest flow rates. In the L2′ phase, the transition to the triangular profile is not observed until a flow rate where vcen ) 2700 µm/s. We cannot observe the reentrant transition to a parabolic profile within this phase (or even in the low-temperature region of the L2 phase). It is possible that this is simply a limitation of our experimentsour camera does not permit us to analyze flow rates faster than about 3000 µm/s.
As we noted previously, the relatively sharp transitions between different types of velocity profiles suggest that the effect is not related to coupling to the subphase.6 In fact, the direct measurement of surface viscosity suggested that it should dominate the subphase viscosity.6,9 The current data confirm this conclusion. For example, the critical flow rate is insensitive to temperature in the L2′ phase even though the viscosity is known to increase significantly with temperature in this phase.5 Thus it appears that the unusual flow behaviors in these condensed phases are related to the 2D phases themselves and not to the interaction of the monolayer with the subphase. The data also indicate that the flow behavior is closely related to the particular mesophase. The critical flow rates for different chain lengths overlay each other remarkably well when offset by temperatures corresponding to the offset in the known phase boundaries. This suggests a correlation between the rheology and the generalized phase diagram. In addition, the evolution of the critical flow rates with temperature is dramatically different in the various mesophases; they vary with temperature in the L2 phase but are constant in the L2′ and Ov phases. This suggests that the flow behavior depends on the details of the molecular ordering in the different mesophases. This dependence must be subtle since all three phases are tilted hexatics. The phases are distinct only in that the molecules are tilted toward their nearest neighbor in the L2 phase and toward the next-nearest neighbor in the L2′ and Ov phases. It is interesting to note that Maruyama et al. observed a significant difference in the response to extensional flow in these phases; molecules in the L2′ phase were aligned by the flow while those in the L2 phase did not align. The domains were simply distorted.3,4 Conclusion The velocity profile of fatty acid monolayers was measured during flow through a narrow channel using BAM. In general, the velocity profile evolved from parabolic to triangular and back to parabolic with increasing flow rate. The critical flow rates for these transitions decreased dramatically with increasing temperature in the L2 phase but were insensitive to temperature in the L2′ and Ov phases. The critical flow rates in fatty acids of different chain lengths were identical if the temperatures were offset to be consistent with the generalized fatty acid phase diagram. These results imply that the unusual behavior of the velocity profile is closely related to the particular molecular packing of the various mesophases and is not simply a consequence of coupling to the subphase or of the polydomain nature of the monolayers. Acknowledgment. This work was supported by the National Science Foundation (Grant No. CTS-9733281), the Louisiana Education Quality Support Fund Contract LEQSF(1996-99)-RD-B-12, and the donors of the Petroleum Research Fund. LA981742X
