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Microrheology of a Sheared Langmuir Monolayer: Elastic Recovery and Interdomain Slippage Ani T. Ivanova,† Jordi Igne´s-Mullol,‡ and Daniel K. Schwartz*,§ Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 Received December 18, 2000. In Final Form: March 16, 2001 Brewster angle microscopy was used to study the microrheological response of fatty acid Langmuir monolayers subjected to shear flow. Slippage of domains past each other was observed during shear, and elastic recovery of domain shape was monitored following the cessation of shear. Experiments were performed as a function of shear rate, total strain, and temperature in two tilted hexatic monolayer phases, L2 and Ov. Three regimes were found as a function of temperature. At low temperature (T ) 17 °C), the degree of slippage and recovery was shear rate independent. At high temperature (T g 25 °C), the recovery decreased and the slippage increased systematically with increasing shear rate. At an intermediate temperature (T ) 21 °C), a distinct transition from low-temperature to high-temperature behavior was observed at a shear rate of 0.35 s-1. These regimes correlated precisely to previous observations of parabolic or triangular velocity profiles in monolayer channel flow. Taking all temperatures and shear rates into account, there was a one-to-one correspondence between slippage and recovery, suggesting that the two are directly related. These results suggest a fundamental correspondence between macroscopic monolayer rheology and domain-level processes.
Introduction Surfactant molecules are widely used as stabilizers for liquid dispersions, such as emulsions and foams. It is generally recognized that the formation of monolayer films at fluid-fluid interfaces reduces the interfacial tension and, therefore, the driving force for phase separation in these multiphase systems. However, the effect of the adsorbed monolayer on the interfacial rheology (i.e., interfacial viscosity and elasticity) is an equally important factor in the inhibition of drop coalescence and coarsening.1 Insoluble monolayers of surfactant molecules at the airwater interface are frequently used as model systems for studies of interfacial rheology. Langmuir monolayers (LM) are convenient for these experiments because thermodynamic conditions (including surface concentration) can be precisely controlled, various rheological measurements can be performed, and flow can be visualized directly using Brewster angle microscopy (BAM) or fluorescence microscopy. Most recent studies have focused on fatty acid molecules because the two-dimensional phase behavior is well understood and one can relate the rheological response to the known molecular organization. Fatty acid molecules display a variety of phases as a function of surface pressure and temperature, including hexatic liquid-crystalline (LC) phases.2,3 These phases are characterized by a local lattice arrangement of molecular headgroups as well as by long-range order of the molecular * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: 303-735-0240. Fax: 303492-4341. † Current address: Division of Engineering and Applied Science, Harvard University, Cambridge, MA 02138. ‡ Current address: Departament de Quı´mica Fı´sica, Universitat de Barcelona, Martı´ i Franque`s 1, E-08028 Barcelona, Spain. § Current address: Department of Chemical Engineering, University of Colorado, Boulder, CO 80309. (1) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interfacial Transport Processes and Rheology; Butterworth-Heinemann: Boston, 1991. (2) Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207. (3) Kaganer, V.; Mohwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779.
tilt direction that gives rise to a domain structure. Thus, a monolayer in a hexatic liquid-crystalline phase typically appears as a mosaic of domains (50-100 µm in size) with distinct boundaries. Studies involving flow of fatty acid LM provide evidence of non-Newtonian behavior within the liquid-crystalline phases. Examples include reports of unusual (sharp) velocity profiles in channel flow,4,5 nonlinear response to applied shear stress,6 an unexpected peak of the monolayer viscosity as a function of surface pressure,6-8 and alignment of the monolayer under shear.9-12 In some cases, the observations could be correlated with the complex structure of the monolayer within the hexatic phase. For example, we have recently shown that the details of the shear-induced orientational alignment of a monolayer in the Ov phase is consistent with an alignment of the underlying hexagonal lattice in the flow direction.11 Our earlier studies of LM flow through a narrow channel5 revealed an evolution of the velocity profile from a parabolic to a triangular shape as a function of temperature and flow rate. The results suggested that the behavior of the velocity profile is related to the particular packing of the various monolayer mesophases; however, the mechanism of the unusual behavior remains unclear. Recently, we reported observations of transient behavior of the velocity profile in the channel flow in one of the LC phases, the L2 phase.13 These transient effects appear to be related to the total strain in the system and suggest the importance of the monolayer elasticity in the (4) Kurnaz, M. L.; Schwartz, D. K. Phys. Rev. E 1997, 56, 3378. (5) Ivanova, A.; Kurnaz, M. L.; Schwartz, D. K. Langmuir 1999, 15, 4622. (6) Ghaskadvi, R. S.; Ketterson, J. B.; Dutta, P. Langmuir 1997, 13, 5137. (7) Ghaskadvi, R. S.; Carr, S.; Dennin, M. J. Chem. Phys. 1999, 111, 3675. (8) Ghaskadvi, R. S.; Dennin, M. Langmuir 2000, 16, 10553. (9) Maruyama, T.; Fuller, G.; Frank, C.; Robertson, C. Science 1996, 274, 233. (10) Maruyama, T.; Lauger, J.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1998, 14, 1836. (11) Ignes-Mullol, J.; Schwartz, D. K. Phys. Rev. Lett. 2000, 85, 1476. (12) Igne´s-Mullol, J.; Schwartz, D. K. Nature 2001, 410, 348. (13) Ivanova, A. T.; Schwartz, D. K. Langmuir 2000, 16, 9433.
10.1021/la001764v CCC: $20.00 © 2001 American Chemical Society Published on Web 04/26/2001
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Figure 2. Three distinctive features (A, B, and C) on a domain boundary are followed with time to evaluate the shape parameter δ ) cot R. Part a shows a domain at rest. In part b, the domain is under shear, AD′ is the line parallel to shear direction and the angle of rotation φ * 0. The domain deformation is ∆ ) cot R0 - cot R ) cot R0 - cot(R′ + φ). Figure 1. A schematic diagram of the shear flow cell device.
flow response. Because the monolayer within the LC phases has a multidomain structure, the line tension of domain boundaries is a possible source of elastic stress. In addition, in the situations when the velocity profile was triangular, the distribution of domain widths across the channel showed that the degree of domain stretching was systematically less than expected given the amount of strain that the monolayer had experienced. This implied that elasticity of domain boundaries and/or slippage between domains resisted domain stretching; these domain-level processes may contribute to the flow response. The current work examines the role of domain boundaries during monolayer flow. We performed shear “creep” experiments under conditions where a parabolic or a triangular velocity profile was previously observed in channel flow. BAM14-16 was used to observe domain shapes under shear deformation and subsequent domain shape relaxation after cessation of shear. In similar experiments, Maruyama and co-workers10 previously found that deformation of individual domains in the L2 phase (in extensional or shear flow) was generally affine, except at very low rates of strain where asymmetrical deformation was observed. Our observations of individual domains in the L2 and Ov phases were also consistent with affine deformation; however, we found that deformations of multidomain clusters were generally nonaffine. In the analysis presented here, the discrepancy between the deformation of individual domains and the deformation of multidomain groups is interpreted as slippage of neighboring domains at their boundaries. Although other mechanisms are possible, this way of parametrizing the phenomenon leads to an intuitive perspective. The analysis of BAM images also demonstrates that domains recover elastically after cessation of shear and the extent of domain recovery is directly related to the amount of slippage during shear. Moreover, the recovery/slippage behavior as a function of temperature and shear rate shows a correlation to the velocity profile behavior in channel flow. The current results provide suggestive evidence that the elasticity of domain boundaries and domain slippage play a role in the previously observed non-Newtonian flow of the monolayer. Experimental Details The Shear Cell Experiment. The shear cell consisted of two rotating Viton O-rings separated by a 2 cm gap. Each band was stretched between two Delrin rollers connected to a dc motor by spur gears such that the two bands moved at the same speed (Figure 1). A constant velocity gradient was created across the gap with a stagnation line between the bands. Thus, a specific monolayer domain sheared in the channel between the bands could be observed for long periods of time along that line. The (14) He´non, S.; Meunier, J. Rev. Sci. Instrum. 1991, 62, 963. (15) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590. (16) He´non, S.; Meunier, J. J. Phys. Chem. 1993, 98, 9148.
shear device was mounted on a vertical translation stage that allowed for easy adjustment of the device relative to the water surface. The Langmuir monolayer for the shear experiment was contained in a custom-built Teflon trough, equipped with a motorized barrier that moved at a controllable speed. The surface pressure was monitored by a filter paper Wilhelmy plate and a R&K electrobalance. The subphase temperature was adjusted by a combination of a recirculating water bath and thermoelectric Peltier elements and monitored by a Teflon encapsulated thermocouple probe. The clean water subphase (Millipore Milli-Q UV+) was first brought to the desired temperature and then the eicosanoic or docosanoic acid (>99%, Sigma) monolayer was deposited from chloroform (Fisher Spectranalyzed) solution. Afterward, the monolayer was compressed to the desired surface pressure (∼22 mN/m). Before starting the shear, we generally waited for 1/2-1 h for the domains to grow larger so that deformations were more easily observed. Before each experiment, the shear bands were adjusted to be parallel to each other and to the water surface. They were tightened so that they moved smoothly, without slipping on the rollers. Because chloroform could dissolve the O-ring material and cause contamination of the monolayer, the bands were kept in the subphase during the time of monolayer deposition and were raised to the surface only after solvent evaporation was complete. Raising the bands did not cause any observable effect on the monolayer appearance and properties. The top edges of the bands were adjusted to barely show above the water to minimize meniscus effects. In a typical creep experiment, we applied a constant shear rate in the range of 0.015-0.95 s-1 for a finite period of time. The total amount of strain was in the range 0.4-1. After cessation of shear, the monolayer was observed for possible domain shape relaxation for 5-7 min. Sometimes, the surface pressure dropped slightly after the monolayer was sheared for some time, and the desired pressure was adjusted by compression before a subsequent experiment. The BAM was focused on the stagnation line between the two bands where the monolayer has a long residence time. The location of the stagnation line was determined directly from BAM observations during steady shear. We recorded images of a monolayer during shear and after shear had stopped. The subphase temperature, the surface pressure, and the shear device motor speed were controlled by Labview software. The voltage applied to the motor controller was displayed on the screen by a video overlay device (RS-232, model 500, Outland Technology Inc.) and was recorded simultaneously with the BAM images. Analysis of Domain Deformation and Relaxation. To quantify the deformation of an individual domain under shear, we defined a shape parameter δ ) cot R, where R is the angle between a line connecting two distinctive features (A and B) on a domain boundary and a line, parallel to the flow direction, that originates from one of these features (Figure 2). NIH Image software was used to digitize the flow “movies” and to analyze the BAM images. We measured the coordinates of the distinctive features A (xa, ya) and B (xb, yb) on a domain boundary and determined the initial value of the shape parameter prior to the onset of shear, δ0. We accounted for possible domain rotation that would affect the measured value of δ using a third distinctive feature, C, on the boundary of the domain. The shape parameter is given by δ ) cot R ) cot(R′ + φ), where R′ is the angle formed between line AB and the line parallel to shear and φ is the rotation angle (see
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Figure 4. Definition of the angles used in the calculation of slippage. (a) Distinctive features on the boundary of domain 1 are used to calculate the deformation of the domain, ∆1. (b) Distinctive features from the boundaries of adjacent domains, domain 1 and domain 2 (A and C from domain 1 and E from domain 2), are used to find the deformation ∆1+2 ) cot β - cot β0 of the “composite” domain. Slippage is calculated as S ) 1 - ∆1/∆1+2. 2) were selected from the boundary of the composite domain. In calculating δ, the possible angle of rotation φ was also determined and taken into account as described above. Analogously, the deformation ∆1+2 of the composite domain was calculated as ∆1+2 ) δ - δ0 ) cot β - cot β0, where δ0 ) cot β0 is the composite domain shape parameter when the monolayer is at rest and δ ) cot β is the shape parameter at time t after shear was applied. The slippage S was calculated as
Figure 3. (a) The applied rate of strain during an idealized shear creep experiment. (b) Domain deformation and recovery as a function of time in the same experiment as part a. The amount of domain recovery is calculated as r ) (∆max - ∆∞)/ ∆max. (c) A typical curve of domain deformation and recovery. The example shown is for a docosanoic acid monolayer at T ) 27 °C in the L2 phase. Filled symbols represent domain deformation under shear at a shear rate of 0.04 s-1, and open symbols represent domain recovery after cessation of shear. Time 0 indicates when the shear device was stopped. Figure 2). The assumption that domain shape transformations are linear leads to CD/CB ) C0D0/C0B0 ) k, where point D0 marks the intercept between line B0C0 and the line originating from A0 and parallel to shear direction (CD is the distance between points C and D). The angle of rotation φ (Figure 2b) can be then calculated by the following equation:
cos φ )
k(yb - yc) + yc - ya
x[k(xb - xc) + xc - xa]2 + [k(yb - yc) + yc - ya]2
The measured values of φ were generally very small, in the range 0-2°. Finally, the deformation ∆ of a domain at any given time was determined as ∆ ) δ - δ0 , where δ0 is the shape parameter of a domain at rest (before shear is applied) and δ is the shape parameter of a domain at time t. The value of ∆ is, in fact, the strain of the domain but we choose to call it “deformation” in order to distinguish it from overall strain which may be different because of possible slippage. The deformation parameter ∆ was determined as a function of time during shear by analyzing consecutive image frames. Domain recovery was extracted from images recorded after shear has stopped and was calculated as r ) (∆max - ∆∞)/∆max, where the value for r ranges from 0, for no recovery, to 1, for complete recovery. Figure 3 illustrates the time dependence of the applied shear strain and domain deformation during an idealized creep experiment as well as actual deformation data for a typical experiment. Analysis of Domain Slippage. The shape parameter defined to measure domain deformation and recovery is also convenient to perform analysis for slippage between neighboring domains. We determined the shape parameter δ ) cot β of a “composite” domain that includes two neighboring domains, d1 and d2 (Figure 4). Distinctive features A (from domain 1) and E (from domain
S)1-
cot R - cot R0 ) 1 - ∆1/∆1+2 cot β - cot β0
where ∆1 is the deformation of domain 1. The value of S ranges from 0, when there is no slippage and the monolayer behaves as a single sheet, to 1, when the shear strain in the monolayer is completely accounted for by domain slippage.
Results and Analysis We have observed the deformation and relaxation processes for isolated domains in two tilted hexatic liquid crystalline phases, L2 and Ov. Our earlier channel flow studies in those phases5 revealed an evolution of the velocity profile across the channel from a parabolic to a triangular shape as a function of shear rate and temperature (Figure 5). The solid symbols in Figure 5 represent the critical flow rates for the transition from a parabolic to a triangular profile. To correlate the role of individual domains to our previous channel flow measurements, we studied domain recovery and slippage in various locations of the flow rate/temperature “phase diagram” of the velocity profile. For a range of shear rates between 0.015 and 0.95 s-1, we explored the domain recovery at different temperatures, that is, under conditions where a parabolic profile, a triangular profile, or a transition between velocity profiles was previously observed (Figure 5). Figure 6 shows a typical sequence of BAM images of a docosanoic acid monolayer, captured at different times in a creep experiment. Figure 6a-c illustrates domain deformation under applied shear, and Figure 6d-f shows domain recovery after shear was stopped. Arrows in the figure indicate distinctive features on a domain boundary that are followed with time to analyze the domain deformation. Generally, cessation of shear resulted in some elastic recovery of the domain. Domain relaxation was rapid within the first 5-10 s, whereas for longer observation times (∼5 min) domain shape recovery was insignificant. Image analysis was also performed to explore the possibility of slippage between neighboring domains during shear deformation. A sequence of BAM images in Figure 7 illustrates an example of domain slippage in a
Microrheology of a Sheared Langmuir Monolayer
Figure 5. A portion of the flow rate/temperature phase diagram of the velocity profile for surface-pressure-driven channel flow for various fatty acid monolayers at π ) 21 mN/m. The horizontal axis, T20, refers to temperatures adjusted for eicosanoic acid. The letter “P” indicates regions where the velocity profile is parabolic, and “T” represents a triangular profile. The solid symbols represent the transition from a parabolic to a triangular profile for fatty acids with various chain lengths (see inset). The vertical dashed line indicates the phase boundary between the L2 and the Ov phases. The diamond symbols mark the locations in the diagram where shear experiments were performed. The dotted line is a guide to the eye drawn through the solid symbols.
docosanoic acid monolayer under shear at γ˘ ) 0.1 s-1. Slippage between domains was observed at all temperatures. The effect of shear rate on both recovery and slippage is illustrated in Figure 8. At T ) 17 °C (parabolic velocity profile), the fractional domain shape recovery, r, had an approximately constant value (∼0.3), regardless of the rate of shear from 0.02 to 0.7 s-1 (Figure 8a). Domain slippage was in the range 0.28-0.3 and also appeared to be independent of the rate of shear. However, under thermodynamic conditions where a triangular velocity profile has been reported (T > 25 °C), domain recovery was quite sensitive to the shear rate, as shown in Figure 8b. At very low shear rates, domains recovered to nearly their original shape, whereas an increase in shear rate resulted in reduced recovery. A dramatic decrease in recovery (from 0.85 to 0.15) was observed over a relatively small range of shear rates, from 0.01 to 0.17 s-1 (note the different scales in the horizontal axes of Figure 8a,b). Recovery was also measured for various values of total strain at a given rate of shear. Although there was a slight decrease in recovery for very high values of strain, the effect was subtle compared to the dependence on shear
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rate. The data in Figure 8 correspond to experiments where the total strain was in the range 0.3-0.6. Interdomain slippage was also shear rate dependent for T > 25 °C; it increased with increasing shear rate (Figure 8b). Moreover, the increase in the amount of slippage at higher shear rates appears to be related to the decreasing domain recovery for the corresponding conditions. Figure 8c represents a plot of domain recovery/slippage as a function of shear rate at T ) 21 °C. As seen in Figure 5, at this temperature the velocity profile during channel flow undergoes a transition from a parabolic to a triangular shape within the range of shear rates we apply. For shear rates lower than 0.35 s-1, recovery and slippage were in the range 0.25-0.3 and were shear rate independent. At γ˘ ∼ 0.35 s-1, however, we observed a distinctive break in both the recovery and slippage behavior; further increase of shear rate results in reduced domain recovery and a corresponding increase of slippage. The “transition” shear rate of 0.35 s-1 is identical to the shear rate for which the velocity profile in channel flow was previously observed to evolve from a parabolic to a triangular shape at this temperature. We extracted characteristic times for domain recovery from the plots of deformation versus time by fitting the rapid part of the recovery curve to an exponential function, r(t) ) ∆∞ + (∆max - ∆∞) exp(-t/τ), where τ is the relaxation time. The measured relaxation times are plotted as a function of the rate of shear in Figure 9. The graphs illustrate that the relaxation time for domain recovery depends on the rate at which the monolayer was originally sheared; τ ≈ 8-10 s for very small shear rates and decreases to τ ≈ 2 s with an increase of shear rate. This observation is true for both the situations in which the extent of domain recovery was shear rate dependent (open circles in Figure 9) as well as when the amount of recovery was independent of shear rate (filled circles in Figure 9). In Figure 10, we plot the values of domain recovery calculated at various temperatures and shear rates versus domain slippage for the corresponding conditions. As Figure 10 indicates, there is a universal relationship between recovery and slippage; that is, higher slippage corresponds to a decrease in the amount of domain recovery, regardless of shear rate or thermodynamic conditions. Discussion All of our BAM observations of monolayer flow necessarily focus on the location and motion of domain boundaries. This means that motion in the monolayer can be followed only at discrete locations. For example,
Figure 6. BAM images of an eicosanoic acid monolayer at T ) 18 °C demonstrating domain deformation at a shear rate of 0.04 s-1 and recovery after cessation of shear: (a) prior to onset of shear, (b) 8 s after onset of shear, (c) 17 s after onset of shear, (d) 5 s after cessation of shear, (e) 23 s after cessation of shear, and (f) 60 s after cessation of shear. Arrows indicate distinctive features on the domain boundary used for image analysis.
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Figure 8. Domain recovery r (circles) and slippage S (triangles) as a function of shear rate: (a) T ) 17 °C, (b) T > 25 °C, and (c) T ) 21 °C. Figure 7. BAM images of a docosanoic acid monolayer under shear at a shear rate of 0.1 s-1 demonstrating nonaffine deformation of a multidomain aggregate. This is interpreted as due to interdomain slippage. Arrows indicate specific features on the domain boundaries used for image analysis. (a) Prior to the onset of shear; (b) 7 s after the onset of shear; (c) 13 s after the onset of shear. The white line connecting the three different features is drawn to guide the eye and shows that the “bright” domain and the neighboring “dark” domain slip past each other. In the absence of slippage, the three features would remain aligned during shear.
velocity profiles in channel flow are extracted by following distinctively shaped features on domain boundaries; there is no way to determine the monolayer velocity at an arbitrary location within a uniformly shaded domain. In the present observations, this limitation makes it impossible to provide absolute proof of domain slippage. In principle, one would like to demonstrate that the velocity is discontinuous at a domain boundary. Clearly, this cannot be done using our methods. Our approach here has been to infer the slippage of domains by comparing the deformation of multidomain aggregates to that of individual domains. These observations suggest slippage at domain boundaries, but other mechanisms could possibly lead to the nonaffine deformation. Although we do not know the molecular-level mechanisms that lead to slippage between domains, it is useful to consider a phenomenological model involving a thin lubricating layer of a fluid phase between domains (the layer thickness may be on the order of molecular dimen-
Figure 9. Relaxation times τ for domain shape recovery as determined by an exponential fit vs shear rate. The filled and open symbols denote data obtained at T ) 17 °C and T > 25 °C, respectively.
sions). To make the model concrete, we assume two neighboring domains of width w and viscosity η separated by a layer of a different monolayer phase with a width b and viscosity ηb (where b , w). It is straightforward to calculate the velocity profile across such a three-layer model by demanding the continuity of shear stress at the boundaries. Apparent slippage of the two domains in this model is due to shear within the thin middle layer and is
Microrheology of a Sheared Langmuir Monolayer
Figure 10. Domain recovery vs slippage for all temperatures and shear rates.
given by the expression
(
S) 1+
)
2wηb bη
-1
which is independent of the shear rate. As expected, the slippage approaches unity in the limit that ηb becomes very small. If the fluid in the boundary layer is Newtonian (constant ηb), the slippage is independent of shear rate, similar to the monolayer behavior at low temperature. An increase of slippage with increasing shear rate (as is observed at higher temperatures) would be consistent with shear thinning of the lubricating fluid; the extreme case would be frictional coupling between domains. If we consider a model where neighboring domains are coupled by a purely frictional force (as opposed to a viscous fluid boundary layer) with frictional stress given by f, the domains do not slip until viscous shear stress exceeds the frictional stress. The slippage for this model is described by the expression
S)
{
0
f g ηγ˘
f 1ηγ˘
f < ηγ˘
which increases with shear rate (γ˘ ) once the viscous shear stress exceeds the stress due to friction. The distinctive change of the slippage behavior as a function of shear rate at intermediate temperatures can be (simplistically) considered a transition from viscous to frictional coupling between neighboring domains. Figure 10 indicates a correlation between the decreasing amount of domain recovery and increasing interdomain slippage regardless of shear rate and thermodynamic conditions. This implies that there is a universal trend describing the domain recovery and slippage behavior. The direct relationship between recovery and slippage suggests that they are two parts of the same phenomenon, even though one is measured during shear and the other after shear has ceased. It is possible that slippage dissipates stored elastic energy, thus reducing elastic recovery. The time scales for domain recovery after cessation of shear depend on the shear rate at which the monolayer was originally sheared, as indicated in Figure 9. The fact that domain behavior after cessation of shear
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is related to the conditions under which shear was applied explicitly demonstrates a memory effect of domain dynamics. The dependence of elastic recovery and interdomain slippage on shear rate is qualitatively different at different temperatures; these phenomena are shear rate independent under conditions where a parabolic velocity profile was observed (T ) 17 °C) and shear rate dependent at temperatures (T > 25 °C) for which the velocity profile was triangular. This suggests a direct relationship between the domain dynamics and the velocity profile behavior. Moreover, the distinct change of the behavior of domain recovery and slippage at the shear rate γ˘ ∼ 0.35 s-1 (at T ) 21 °C) is remarkably consistent with the transition between a parabolic and a triangular shape of the velocity profile that occurs at the same temperature and shear rate. Thus, the temperature and flow rate dependence of the velocity profile in channel flow seem to be correlated to the domain dynamics of the monolayer. Although we do not presently propose a specific mechanical model that relates the domain-level processes of slippage and recovery to the macroscopic, continuum, rheological behavior of the monolayer, it seems clear that they are directly related and that such a model might be developed. Conclusions Brewster angle microscopy was used to monitor the domain structure of fatty acid Langmuir monolayers during shear creep experiments. Video images were analyzed to determine the degree of interdomain slippage during shear and the elastic recovery of domain shape following the cessation of shear. The behavior of slippage and recovery as a function of temperature and shear rate correlated directly to previous measurements of parabolic and triangular velocity profiles in surface-pressure-driven channel flow. At low temperature (T ) 17 °C) where channel flow velocity profiles are parabolic, the degree of slippage and recovery were shear rate independent consistent with viscous coupling between domains. At high temperature (T > 25 °C) where velocity profiles are triangular, the recovery decreased and the slippage increased systematically with increasing shear rate suggesting a pseudo-frictional coupling between domains. At an intermediate temperature (T ) 21 °C) where a transition was previously observed between parabolic and triangular velocity profiles at a shear rate of 0.35 s-1, a distinct change in slippage and recovery behavior (from low-temperature to high-temperature behavior) was observed at an identical rate of shear. The slippage and recovery measurements obtained at all temperatures and shear rates fell onto a universal curve, suggesting that the degree of elastic recovery after cessation of shear depends directly on the amount of interdomain slippage during shear. These results illustrate an explicit connection between microrheology (domain-level processes) and macroscopic continuum rheological measurements. Acknowledgment. This work was supported by the National Science Foundation (Award No. 9733281) and the Camille Dreyfus Teacher-Scholar Award Program. LA001764V
