Langmuir 2000, 16, 10553-10555
10553
Notes Alternate Measurement of the Viscosity Peak in Heneicosanoic Acid Monolayers R. S. Ghaskadvi and Michael Dennin* Department of Physics and Astronomy, University of California, Irvine, California 92697-4575 Received May 19, 2000. In Final Form: September 28, 2000
Many materials of technological and biological importance, such as foams, emulsions, paints, polymer melts, and so forth, fall under the general heading of complex fluids. These fluids exhibit a range of interesting behavior in response to external stresses and strains, such as viscoelasticity, shear-thinning, and shear-thickening. Major advances have been made in the understanding of the flow properties of complex fluids; however, our understanding is far from complete. One challenge is that the properties of complex fluids are generally influenced by structure on both the mesoscopic level, in the form of domains, and the microscopic level. Because of their twodimensional nature, Langmuir monolayers present a unique opportunity to study the relative importance of the mesoscopic and microscopic degrees of freedom. Unlike most three-dimensional complex fluids, with Langmuir monolayers it is possible to directly observe the dynamics on the mesoscopic scale while simultaneously measuring the viscoelastic response. Langmuir monolayers consist of amphiphilic molecules that are confined to the air-water interface.1,2 The equilibrium phase behavior of fatty acid monolayers is particularly well understood.3,4 There are a number of liquid-crystalline phases that possess structure on both the microscopic and the mesoscopic scales. These phases are examples of two-dimensional complex fluids. In this paper, we present results on viscosity measurements of a particular phase, the L2 phase, in a particular fatty acid, heneicosanoic acid (C21). Both the microscopic and mesoscopic structures of this phase have been detailed using X-ray diffraction,5 fluorescence microscopy,6 and Brewster angle microscopy.7 The L2 phase is characterized by hexatic ordering of the headgroups and orientational ordering of the tilt azimuth. In general, the hexatic lattice is stretched along one axis. However, there is a single pressure, for each temperature, at which the lattice is a perfect hexagon. In this paper, the term “pressure” refers to the surface pressure of the monolayer defined as Π ) γw - γ, where γw is the surface tension of pure water and γ is the surface tension with the monolayer present. On the mesoscopic scale, the L2 phase typically exhibits a random domain structure.7 The domains are on the order (1) McConnell, H. M. Annu. Rev. Phys. Chem. 1991, 42, 171. (2) Mohwald, H. Annu. Rev. Phys. Chem. 1990, 41, 441. (3) Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207. (4) Kaganer, V. M.; Mohwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779. (5) Lin, B.; Shih, M. C.; Bohanon, T. M.; Ice, G. E.; Dutta, P. Phys. Rev. Lett. 1990, 65, 191. (6) Schwartz, D. K.; Knobler, C. M. J. Phys. Chem. 1993, 97, 8849.
of 10-100 µm, and each domain corresponds to a different overall orientation of the tilt azimuth. The viscosity of Langmuir monolayers has been studied for many years.8 However, it is only recently that the complex nature of their flow behavior has been appreciated. The wide range of phenomena that has been reported includes alignment of domains,9 a nonlinear shear modulus,10 anomalous pressure dependence of the complex shear modulus,10,11 and “stretched exponential” stress-relaxation.12 Also, recent work has shown that under certain conditions, different methods of probing the viscosity result in different conclusions concerning the shear dependence of the viscosity.13 In this paper, we focus on the anomalous pressure dependence of the complex shear modulus reported for C21.10 In the L2 phase of C21, Ghaskadvi et al. have shown that the dissipative part of the complex shear modulus, G′′, is strongly correlated with the symmetry of the underlying hexatic lattice.10 The lattice shape changes from a “broad” hexagon to a “tall” hexagon as the film is compressed in the L2 phase. As this change is continuous, there is an intermediate pressure, Πhex, at which the lattice is exactly hexagonal. At the same time, G′′ is anomalous: increasing in magnitude as a function of pressure, reaching a maximum value at a pressure Πpeak ) Πhex, and then decreasing in magnitude until the L2/L2′ phase transition occurs. This suggests a strong correlation between G′′ and the lattice structure that is currently not understood. For fluids with a linear response, the relationship between G′′ and the viscosity, η, is simply G′′ ) ωη. For such a fluid, both η and G′′ would be expected to have the same pressure dependence. However, for the monolayers G′′ is dependent on both amplitude and frequency10 and η is shear-rate dependent.13,14 Therefore, G′′ and η are not simply related. In particular, one possible source for the nonlinear behavior of G′′ and η is the dynamics of the mesoscopic domains. For a large enough strain, the domains of the L2 phase are stretched by an applied shear flow.9 In contrast, small amplitude oscillations were used to measure G′′,10 and the domains were not significantly distorted. In addition to being a source of nonlinear behavior, one might expect the domain dynamics to result in different pressure dependences for η and G′′. For many bulk fluids with shear-rate-dependent viscosities, there is an empirical relationship between G′′ and η, known as the Cox-Merz relationship.15 This relationship has not been confirmed for monolayer sys(7) Riviere, S.; Henon, S.; Meunier, J.; Schwartz, D. K.; Tsao, M. W.; Knobler, C. M. J. Chem. Phys. 1994, 101, 10045. (8) Edwards, D. A.; Brenner, H.; Watson, D. T. Interfacial Transport Processes and Rheology; Butterworth-Heinemann: Boston, MA, 1991. (9) Maruyama, T.; Fuller, G.; Frank, C.; Robertson, C. Science 1996, 274, 233. (10) Ghaskadvi, R. S.; Ketterson, J. B.; Dutta, P. Langmuir 1997, 13, 5137. (11) Brooks, C. F.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1999, 15, 2450. (12) Ghaskadvi, R. S.; Bohanon, T. M.; Dutta, P.; Ketterson, J. B. Phys. Rev. E 1996, 54, 1770. (13) Kurnaz, M. L.; Schwartz, D. K. Phys. Rev. E 1997, 56, 3378. (14) Ivanova, A.; Kurnaz, M. L.; Schwartz, D. K. Langmuir 1999, 15, 4622. (15) Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619.
10.1021/la0006925 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/22/2000
10554
Langmuir, Vol. 16, No. 26, 2000
Notes
Figure 1. Two Brewster angle microscope images of the monolayer: (a) the monolayer without an applied shear and (b) the monolayer during an applied shear. Each image is a 0.5 mm × 0.5 mm section of the trough.
tems, but if it holds, then one would expect G′′ and η to have the same pressure dependence. For monolayers, confirmation of the Cox-Merz relationship is complicated by the strong amplitude dependence of G′′.10 Therefore, in this paper we focus on the pressure dependence at a single frequency and shear rate. We report on the comparison of the pressure dependence of η, determined by a Couette viscometer, and G′′, determined by a torsion pendulum technique. For measurements of η, the monolayer is subjected to a continuous, steady rate of strain that results in significant distortions of the domains. We use the torsion pendulum measurements to directly compare G′′ and η for the same film. Our two-dimensional Couette viscometer is described in detail in ref 16. The trough consists of a segmented Teflon outer barrier that is immersed into water in a circular dish. The barrier is used to compress and expand the monolayer and maintains a circular shape over the entire range of compression. A circular knife-edge torsion pendulum hangs by a wire so that it just touches the water surface. It is centered with respect to the outer barrier. The wire is hung from a coil that is placed in an external magnetic field. The coil is used to measure the angular position of the rotor. A Langmuir monolayer is made at the annular air-water interface between the outer barrier and the rotor knife-edge. The viscometer has two main modes: steady Couette flow and oscillatory motion of the torsion pendulum. In steady Couette flow, the equilibrium position, θ1, of the rotor is measured. Then, a two-dimensional Couette flow is generated by rotating the outer barrier at a constant angular speed. The Couette flow causes a torque τ on the rotor that displaces it to a new equilibrium position θ2. The magnitude of the torque is given by τ ) k(θ2 - θ1), where k is the torsion constant of the wire. After rotating the barrier for 5 min to achieve equilibrium, θ2 is measured, and then the rotation is stopped. This procedure was repeated for each value of pressure. For the measurements reported here, a shear rate of 0.03 s-1 was used. For oscillatory shear, an external torque is applied to the rotor by manipulating the external magnetic field and the current through the coil. The in-phase and out-ofphase response of the rotor is used to measure the complex shear modulus G ) G′ + iG′′. Here, G′ measures the elastic response of the monolayer, and G′′ measures the viscous response of the monolayer. For these measurements, a (16) Ghaskadvi, R. S.; Dennin, M. Rev. Sci. Instrum. 1998, 69, 3568.
Figure 2. For both plots, the open squares are the measured values of G′′ (the left-hand axis) and the closed squares are the measured values of the viscosity η (the right-hand axis). Both quantities are plotted versus the surface pressure Π. (a) This plot covers the range 0 < Π < 14 mN/m. It illustrates the peak in both G′′ and η in the L2 phase and the phase transition to the L2′ phase at approximately 10.8 mN/m. (b) An expanded view of the box region in (a). Here, the axes have been shifted to emphasize the coincidence of the peaks in G′′ and η.
frequency of ω ) 0.5 rad/s and an amplitude of 3.5 mrad (∼130 µm at the rotor edge) were used. The C21 monolayer was made from a chloroform solution of 99% pure heneicosanoic acid purchased from Fisher and used without additional purification. The solution was placed on the aqueous subphase with a microsyringe and allowed to relax for 20 min before compression to facilitate the evaporation of the solvent. All the data presented here were taken at 9 °C. The surface pressure Π was measured using a standard Wilhelmy plate technique. The subphase was deionized water that had been passed through a Millipore filter to obtain water with a resistivity in excess of 18 MΩ.
Notes
Figure 1 presents Brewster angle microscope images of the film. Figure 1a shows the unsheared monolayer. Figure 1b shows the monolayer during steady shear. These images highlight the large distortions introduced by the steady shear. Figure 2 presents the results for both η and G′′ as functions of the surface pressure. Both methods clearly exhibit a peak value at approximately Π ) 5.4 mN/m. This is in agreement with the results of ref 10 and is consistent with the peak in both η and G′′ corresponding to Πhex. The magnitudes of the viscosities are not directly comparable because of the dependence of viscosity on shear rate and the dependence of G′′ on frequency and amplitude. In summary, we have shown that the peak in η of C21 acid in the L2 phase corresponds to the peak in G′′. Therefore, the peak in η also correlates with the microscopic structure of the monolayer. Furthermore, the
Langmuir, Vol. 16, No. 26, 2000 10555
measurement of η involves large values of the applied strain and correspondingly large motions of the domains that are not present in the measurement of G′′. This provides strong evidence that the domain motions do not alter the pressure at which maximum dissipation occurs in the L2 phase. Though these results do not provide a detailed explanation of the peak in viscosity or G′′, they represent an important additional piece in the puzzle. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and an award from the Research Corporation for support of this work. Also, additional funding was provided by grant CTS-9874701 from the National Science Foundation. LA0006925
