5630
Langmuir 1996, 12, 5630-5635
Deformation and Relaxation Processes of Mono- and Bilayer Domains of Liquid Crystalline Langmuir Films on Water Jo¨rg La¨uger, Channing R. Robertson, Curtis W. Frank, and Gerald G. Fuller* Department of Chemical Engineering, Stanford University, Stanford, California 94305-5025 Received June 21, 1996X Flow deformation and relaxation of mono- and bilayer domains of a thermotropic liquid crystal at the air-water interface have been studied by means of simultaneous application of extensional flow fields and Brewster angle microscopy measurements. In an extentional flow, mono- and bilayer domains are found to be distorted into long, stringlike domains that are stable. This is due to the absence of Rayleigh instabilities in the two-dimensional case, which otherwise lead to the occurrence of a break-up mechanism in three dimensions. However, small fluctuations in the domain thickness lead to defects that can cause breakup of the string domains followed by a retraction of the two domain ends due to line tension effects. In relaxation experiments covering both the high deformation bola-shaped regime and the small-deformation regime of slightly deformed domains, the line tensions of mono- and bilayer domains were determined. Both deformation regimes yielded the same values for the line tension of the mono- and bilayer cases. However, the line tension of the bilayer was found to be about 10 times higher than that of the monolayer. It is believed that this large difference is a result of a strong attractive dipole-dipole interaction force in the interdigitated bilayer.
Introduction The introduction of structure and orientation sensitive methods for investigating Langmuir monolayers at the air-water interface such as second harmonic generation,1 fluorescence2 and polarized fluorescence microscopy,3 and Brewster angle microscopy (BAM)4,5 has led to considerable progress in the understanding of such two-dimensional (2D) systems over the past decade.6-10 A wide number of chemical substances such as phospholipids, fatty acids, alcohols, polymers, and thermotropic liquid crystals are known to form insoluble monomolecular films on water surfaces. These molecular assemblies are often used as models of systems such as biological membranes and have a wide range of possible technical applications.11 Since many technically important processes such as Langmuir-Blodgett deposition involve flow fields in monolayers, the flow behavior of these systems is of interest. In fact, the observed domain anisotropy in transferred films has been related to surface flows in the monolayer during the deposition process.12 Furthermore, by using a rotating trough device, Benvegnu and McConnell showed that surface shear flows can elongate lipid monolayer domains to a so-called bola shape.13 In three dimensions, droplet deformation is governed * Corresponding author. X Abstract published in Advance ACS Abstracts, October 15, 1996. (1) Rasing, T.; Shen, Y. R.; Kim, M. W.; Grub, S. Phys. Rev. Lett. 1987, 55, 1597. (2) Lo¨sche, M.; Mo¨hwald, H. Rev. Sci. Instrum. 1984, 55, 1968. (3) Moy, V. T.; Keller, D. J.; Gaub, H. E.; McConnell, H. M. J. Phys. Chem. 1986, 90, 3198. (4) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590. (5) He´non, S.; Meunier, J. Rev. Sci. Instrum. 1991, 62, 936. (6) Ulman, A. An Introduction to Ultrathin Organic Films; Academic Press: New York, 1990 (7) Roberts, G. Langmuir-Blodgett Films; Plenum Press: New York, 1990 (8) Mo¨hwald, H. Annu. Rev. Phys. Chem. 1990, 41, 441. (9) McConnell, H. M. Annu. Rev. Phys. Chem. 1991, 42, 171. (10) Knobler, C.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207. (11) Swalen, J. D.; Allara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelachvili, J.; McCarthy, T. J.; Pease, R. F.; Rabolt, J. F.; Wynne, K. J.; Yu, H. Langmuir 1987, 3, 932. (12) Daniel, M. F.; Hart, J. T. T. J. Mol. Electron. 1985, 1, 97. (13) Benvegnu, D. J.; McConnell, H. M. J. Phys. Chem. 1992, 96, 6820.
S0743-7463(96)00617-8 CCC: $12.00
by two parameters: the viscosity ratio between the dispersed phase and the matrix, and the capillary number Ca, which is the ratio between hydrodynamic stress and interfacial stress. In the case of Newtonian droplets in a Newtonian matrix, and for an extensional flow with an extensional strain rate ˘ , Ca can be expressed as
Ca )
Rηm˘ σ
(1)
where R represents the equilibrium radius of a drop, ηm is the viscosity of the matrix, and σ is the interfacial tension. It has been shown that highly deformed threedimensional droplets are unstable as soon as the wavelengths of capillary distortions are larger than the circumference of the droplets. A distortion within an elongated particle causes a flow of material away from the distortion, and the circumference at the distortion decreases. This leads to a decrease in interfacial area, and the circumference at the distortion tends to go to zero.14 These Rayleigh instabilities cause the onset of a break-up mechanism and break the droplet into smaller particles. An elongational flow is known to be generally more effective in breaking up droplets than a simple shear flow.15,16 A stringlike structure has been found recently also in the shear deformation of a three-dimensional, bicontinuous, two-phase morphology where both phases are continuous and have an interconnected structure.17 In contrast, at the location of a distortion no closed circumference exists in the two-dimensional case. Therefore, in two dimensions no Rayleigh instabilities can occur and an elongational flow field is expected to produce a long stringlike structure. In the case of a dispersed morphology, however, no flow-induced stringlike structure is known in three dimensions. (14) Tomotika, S. Proc. R. Soc. London 1935, A150, 322. (15) Acrivos, A.; Lo, T. S. J. Fluid Mech. 1978, 86, 641. (16) Hinch, E. J.; Acrivos, A. J. Fluid Mech. 1980, 98, 305. (17) Hashimoto, T.; Matsuzaka, K.; Moses, E.; Onuki, A. Phys. Rev. Lett. 1995, 74, 126.
© 1996 American Chemical Society
Liquid Crystalline Langmuir Films on Water
The key parameter determining the stability and the shape of two-dimensional monolayer domains is the line tension, which expresses the action of short range interactions and is opposed by long range interactions mainly due to electrostatic forces. At the present time, only a small number of experimental determinations of the line tension are available. Mu¨ller and Gallet measured a liquid-solid line tension of amphiphilic monolayers using the rate of activated homogeneous nucleation.18 Benvegnu and McConnell developed a method that allows the calculation of the line tension of lipid monolayers from the relaxation rate after a shear distortion of domains.13 In general, it has been found that the observed shapes are elliptical for weak flows and become bola-shaped at high deformations. The method of Benvegnu and McConnell assumes that the domains relax from a bola-shaped state. Recently, experiments were reported by Mann et al.19 on a polymeric monolayer using relaxation both from bolashaped domains and from slightly deformed, elliptically shaped domains. Both relaxation processes resulted in the same line tension value. The flow fields used in these previous studies were simple shear flow or not well defined flows, i.e. jet flow above the monolayer or dragging a needle through the monolayer. A different approach was used by Rivie`re et al.20 in the coexistence region between the liquid expanded phase (L1) and the liquid-condensed phase (L2) of a long chain fatty acid monolayer by using surface potential and BAM measurements. The presence of a long range repulsive dipolar interaction between the two phases leads to strong domain deformations when the domains are close to each other. The strength of the electrostatic forces was measured by surface potential measurements and the line tension of the L1/L2 interface was deduced from the balance between the electrostatic forces and the line tension. The purpose of this paper is to report on BAM measurements on both flow deformation and relaxation of mono- and bilayer domains of 4′-octyl-1,1′-biphenyl-4carbonitride (8CB) subject to well defined two-dimensional extensional flows. Figure 1 sketches the different structures that are possible with this system and their locations on the surface pressure isotherm. Additionally, the five different regimes as discussed by Xue et al. are marked in Figure 1.21 Previous experiments have shown that monolayers of this system collapse during compression and form stable bilayer domains on top of the monolayer.21-23 The monolayer region and the bilayer region are referred to as region I and region III, respectively. The region where the uniform monolayer is compressed is called region II. Using BAM to visualize the structure, circular bilayer domains (structure B) were found in the absence of flow in region III. These bilayer domains undergo coalescence upon further compression and finally form an almost perfect bilayer film on top of the monolayer.22,23 Additional compression of the bilayer in region IV induces collapse to even thicker domains with odd numbers of layers (region V). The collapse of the 8CB monolayer to a trilayer is accompanied by an increase in the surface pressure followed by a large plateau and evolves as a first-order transition in an orderly manner, in contrast to the collapse of most other monolayer films. Therefore, 8CB films offer a unique possibility to investigate the dynamical properties (18) Gallet, F.; Mu¨ller, P. Phys. Rev. Lett. 1991, 67, 1106. (19) Mann, E. K.; He´non, S.; Langevin, D.; Meunier, J.; Le´ger, L. Phys. Rev. E 1995, 51, 5708. (20) Rivie`re, S.; He´non, S.; Meunier, J.; Albrecht, G.; Boissonnade, M. M.; Baszkin, A. Phys. Rev. Lett. 1995, 75, 2506. (21) Xue, J.; Jung, C. S.; Kim, M. W. Phys. Rev. Lett. 1992, 69, 474. (22) Friedenberg, M. C.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1994, 10, 1251. (23) de Mul, M. N. G.; Mann, J. A. Langmuir 1994, 10, 2311.
Langmuir, Vol. 12, No. 23, 1996 5631
Figure 1. Schematic representation of different structures occurring during the compression and re-expansion of the 8CB monolayer. The locations of the different structures are indicated by letters in the surface pressure isotherm.
of multilayer domains in flow fields. Re-expansion from the point where the whole area is covered by the bilayer leads to a foam structure where circular holes in the bilayer (structure C) occur which again coalesce by further decompression. As shown later, by further re-expansion into the monolayer regime a similar foam structure can be found also in the monolayer, which consists of circular holes in the monolayer (structure D). If monolayer molecules are tilted with respect to the water surface normal, domain structures can be formed, which can be visualized in a BAM experiment by use of a polarization analyzer in the path of the reflected light. Such domain structures have been found for various fatty acids, where one individual domain consists of molecules which all have the same azimuthal orientation angle for the tilt direction.24,25 Molecules in different domains have different azimuthal orientation angles, which lead to a difference in the reflectivity of the monolayer film and are responsible for the contrast differences seen in the BAM images. The molecules in the 8CB monolayers are known to be tilted from the air-water interface by an angle of 71 ( 2°.26 Therefore, a domain structure in which the individual domains are distinguished by different azimuthal orientation angles of the molecular tilt might be expected in BAM observations by using a polarization analyzer in the path of the reflected light. However, correlation length measurements using X-ray techniques on thin solid 5CB and 7CB films indicate that typical sizes of individual domains are on the order of 81 and 94.5 Å, respectively.27 These are too small to be seen in a BAM experiment with a typical lateral resolution of 5-10 µm. In the following, we will present data on the elongation of monolayers as well as bilayer domains and of holes in both types of layers. We demonstrate that domain breakup can occur under conditions of high deformation (24) Ho¨nig, D.; Mo¨bius, D.Thin Solid Films 1992, 210-211, 64. (25) Overbeck, G. A.; Ho¨nig, D.; Mo¨bius, D. Thin Solid Films 1994, 242, 213. (26) Guyot-Sionnest, P.; Hsiung, H.; Shen, Y. R. Phys. Rev. Lett. 1986, 57, 2963. (27) Leadbetter, J.; Richardson, R. M.; Colling, C. N. J. Phys., Colloq. 1975, 36, C1-37.
5632 Langmuir, Vol. 12, No. 23, 1996
La¨ uger et al.
to stringlike domains that are subject to instabilities. Furthermore, we measure the line tension of the monoand bilayer domains and the holes in these layers during the relaxation of both high-deformation, bola-shaped and slightly elliptically shaped domains and holes. Background Domain Relaxation. At high deformations twodimensional domains assume a bola-shaped structure consisting of two almost circular disks connected by a thin string. By approximating the structure to be two circular disks of radii R that are much larger than the width w of the connecting string, we can estimate the line tension by observing the shape relaxation process, as shown recently by Benvegnu and McConnell.13 The force bringing the two disks back together is the line tension and is opposed by the viscous drag of the subphase. By equating these two forces and neglecting electrostatic effects, one obtains the following expression for the line tension in the low Reynolds number limit:
8 λ ) ηRU 3
(2)
η is the viscosity of the subphase (i.e. the water), and U is the velocity of a single bola. Therefore, the relaxation of the bola is governed by a nearly constant velocity of the connected bolas as they come together. By neglecting the electrostatic contribution, it is possible to determine the line tension experimentally by measuring the radii of individual bolas and their velocities. Analysis of the shape relaxation in the case of slightly deformed domains proceeds differently. Here one defines a deformation D by D ) L/W - 1, where L and W are the length and the width of an elliptically deformed domain, respectively. In the small-deformation case, D e 1 and the relaxation is expected to be exponential; i.e., D ∝ exp(-t/Tc), where Tc is a characteristic relaxation time. It can be shown that, for certain experimental conditions, dissipation by the subphase viscosity η dominates the surface viscosity effects, and from a simple dimensional analysis one would expect
Tc ∝
ηR2 λ
(3)
In fact, assuming an incompressible monolayer, Stone and McConnell derived the expression28
Tc )
5π ηR2 16 λ
(4)
Therefore, the measurement of the deformation relaxation in the small deformation limit also allows an estimation of line tension. Again electrostatic effects have been neglected. This assumption is reasonable as long as individual domains are sufficiently far apart from each other, and only such cases were considered in the analysis. The long range dipole-dipole interactions between domains are then small because dipole forces decrease rapidly with separation proportional to r-4 whereas interactions on shorter length scales (i.e. dipole-dipole interactions within a single domain) are included in the measured line tension. Experimental Section A 110 mm × 700 mm symmetric compression KSV-5000 Langmuir-Blodgett trough (KSV, Helsinki) located in a class 1000 clean room was used. 8CB (BDH Ltd.) was dissolved in (28) Stone, H. A.; McConnell, H. M. Proc. R. Soc. London 1995, A448, 97.
Figure 2. Top view of the four-row mill and the convection, shielding showing the direction of the roller rotation, the flow field, and the stagnation point. The stagnation point of the flow field and the point of observation of the BAM experiment coincide and are at the center of the device. chloroform (Baker HPLC grade) at a concentration of 0.5 mg/mL and approximately 100 µL of this solution was spread with a microsyringe on deionized water, purified by a Milli-Q system (Millipore Corp.). All experiments described here were performed at a subphase temperature of 18 °C. Bulk 8CB is crystalline at this temperature and has a transition from crystalline to smectic A at 21.5 °C. However, it has been shown that the monolayer phase diagram remains unchanged within the temperature range 10-38.7 °C.21 Different mono- and bilayer regimes were accessed by compression and re-expansion of the barriers at a rate of 10.0 mm/min. A Wilhelmy plate was used to monitor the surface pressure Π and established an independent confirmation of the collapse point of the monolayer. Surface potential measurements were performed by using a surface potential meter based on the vibrating capacitor method (KSV 5000SP). The surface potential meter was calibrated by applying different known voltages within the range of the measurements. The Brewster angle microscope setup was described earlier.22 BAM images were recorded on videotape and digitized using a frame grabber. After a correction of the geometric distortion due to the oblique incident angle associated with the BAM optics, we analyzed the digitized images with the help of image analysis software (NIH-Image 156 ppc). An extensional flow field was applied by a four-row mill, as illustrated in Figure 2. BAM measurements were performed at the stagnation point of the flow field, where material has a long residence time. In the absence of an applied flow the 8CB monoand bilayer domains underwent movement due to convection in the subphase and in the air above the monolayer. This made it difficult to measure relaxation processes upon cessation of flow, where it is desirable to monitor the same domains over long time scales. Therefore, additional shielding was constructed, which reduced the convection problem considerably and allowed relaxation measurements to be made. The geometrical dimensions of the four-row mill and the shielding follow suggestions by Fuller and Leal29 and Higdon.30 The flow behavior of a monolayer can be characterized by the Reynolds number, which is the ratio of inertial to viscous forces. Since 8CB has a low surface viscosity, inertial effects strongly influence the flow behavior. For that reason, the observed monolayer deformation requires time to accelerate to a steady flow upon start up of the rollers and to decelerate upon cessation of roller motion. (29) Fuller, G. G.; Leal, L. G. J. Polym. Sci., Polym. Phys. Ed. 1981, 19, 557. (30) Higdon, J. J. L. Phys. Fluids A 1993, 5, 274.
Liquid Crystalline Langmuir Films on Water
Langmuir, Vol. 12, No. 23, 1996 5633
Figure 3. Surface pressure-area and surface potential-area isotherms during compression of the film at a temperature of the water subphase of 18 °C. Two different measurements of the potential are shown.
Results and Discussion Surface Pressure and Surface Potential Isotherm. Figure 3 shows the surface pressure, Π, as a function of the area per molecule, A, obtained by compressing the 8CB film. The dominant feature of the isotherm is the strong increase of the pressure at an area per molecule of A ) 48 Å2 followed by a large plateau between the areas per molecule of 40 and 9 Å2. At higher compressions, a second increase in the surface pressure occurs followed by a second plateau. The isotherm is discussed in terms of different regions following Xue et al.21 Region I, where the surface pressure is almost zero down to an area per molecule of 48 Å2, is referred to as the gaseous phase. The gaseous phase consists of dispersed monolayer domains (structure A in Figure 1). The steep rise in surface pressure below 48 Å2 signals the formation of an uniform monolayer at the water surface. In region II (48 Å2 > A > 40 Å2) Π increases and the initially homogeneous monolayer is compressed. At A ) 40 Å2 the monolayer collapses and region III begins. This region is characterized by stable bilayer domains formed on top of the monolayer (structure B) and is identified by BAM images. Further compression of the bilayer down to an area per molecule of A ) 9 Å2 causes an almost perfect trilayer to be formed. The second increase at A ) 9 Å2 marks the beginning of region IV, in which the bilayer on top of the monolayer is compressed until region V is reached and the trilayer collapses to form multilayers. This multilayer formation is not as ordered as the bilayer formation, and domains representing different numbers of layers are found in BAM experiments. Additionally, the surface potential was measured, and the results from two different experiments are also included in Figure 3. In the monolayer regime (region I) the surface potential is spatially very inhomogeneous, showing strong fluctuations. Since the surface potential is directly proportional to the dipole density in the thin film, this reflects a nonuniform distribution of the monolayer molecules in the gaseous phase, in conformity with the BAM observations to be discussed later. Once a homogeneous monolayer is formed in region II, the fluctuations vanish and the surface potential increases due to the compression of the monolayer, which increases the dipole density. After reaching region III, the surface potential slightly decreases although the number of molecules per unit area increases. This finding strongly supports the picture of an interdigitated bilayer on top of the monolayer as proposed by various groups.21-23 Interdigitation causes the dipoles to cancel each other, and no further increase in the surface potential is measured.
Figure 4. Bilayer domains (white) on top of the monolayer (black) at A ) 20 Å2 before (a) and after (b) applying an extensional flow field.
Breakup of Monolayer and Bilayer Domains. By varying the area per molecule, we obtained four different structures, as described earlier in Figure 1. These are monolayer domains (structure A), holes within the monolayer (i.e. a two-dimensional monolayer foam; structure D), bilayer domains on top of the monolayer (structure B), and holes in the bilayer (i.e. a two-dimensional bilayer foam; structure C). Flow experiments on all four of these structures were performed. Figure 4 shows an example of a bilayer domain at A ) 20 Å2. Figure 4a represents the initial structure prior to flow, and Figure 4b shows the result of applying an extensional flow. Due to the absence of Rayleigh instabilities in two dimensions, the domains are highly elongated and stringlike structures are formed. A similar flow behavior was found in all four cases. Under certain circumstances, however, the long stringlike domains will eventually break, as shown in Figures 5 and 6 for the cases of a hole in the monolayer and a bilayer domain, respectively. In the sequence of Figure 5 it can be seen that at the location where the long stringlike domain finally breaks a defectlike inhomogeneity occurs before the breakup starts. In the bilayer case shown in Figure 6, circular and string domains can be seen simultaneously. This is due to the fact that there exists a critical domain size for large deformation that depends on the elongation rate and the line tension. If the domains are larger than this critical size, they are deformed, whereas the smaller domains remain circular. Unfortunately, due to the inability to follow individual domains to a steady state deformation before they move out of the field of view, such a critical domain size could not be determined. However, once a string domain is formed, a breakup of such a domain can occur, but only at a defect point such as the example shown in Figure 6. The arrow in Figure 6a marks a small circular domain. Above and below this domain two stringlike domains are stretched to a very thin thickness almost below the resolution limit of the BAM. It can be seen that a breakup process of one of the stringlike domains is initiated at the location where this stringlike domain is pressed against the small circular domain. This small domain serves as a defect that induces a local stress concentration on the stringlike domain, causing it to fail at that location. The two ends snap away in opposite directions, as indicated
5634 Langmuir, Vol. 12, No. 23, 1996
Figure 5. Breakup of a highly elongated hole in the monolayer at A ) 60 Å2: (a) t ) 0 s; (b) 1.5 s; (c) 1.57 s; (d) 1.73 s; (e) 2.23 s.
by the arrows in Figure 6b-f. The velocities of the two ends decrease from 2.14 mm/s immediately (0.67 s) after the breakup (6b) to 0.3 mm/s at 2.5 s after the breakup (6f). Relaxation Processes. As pointed out earlier, it is possible to obtain the line tension of mono- and bilayer domains by measuring the relaxation of distorted domains back to their equilibrium, circular shape. Figure 7, for example, shows the relaxation of an extended bilayer domain. In Figure 7a-c the domain has a typical bolashape consisting of two almost circular disks connected by a thin string of bilayer material. In Figure 7d the connecting string becomes thicker and the domain assumes an elliptical shape which further relaxes to a circular disk. Due to convection, it is often not possible to follow the entire relaxation process, but according to eq 2 it is sufficient to analyze the relative velocity of a single end of the bolas over a certain period of time to calculate the line tension. In the small-deformation limit the relaxation times of only slightly elongated domains are measured, and the line tension can be obtained using eq 4. An example of such a relaxation process is shown in Figure 8 for a monolayer domain on the water subphase. Relaxation processes have been analyzed in the monolayer as well as in the bilayer case. In each case, both kinds of structures (i.e. domains atop and holes within the layer) and both kinds of relaxation processes (i.e. bola relaxation and small-deformation relaxation) were investigated. In this manner four different experiments were performed for each kind of layer. An inspection of the time scales in Figures 6 and 7 shows that the relaxation is considerably slower in the monolayer case compared to the bilayer,
La¨ uger et al.
Figure 6. Breakup of a highly elongated thin bilayer domain at A ) 27 Å2. Arrows mark the point of the breakup just before breakup (a) and the two ends after the breakup (b-f), respectively: (a) t ) 0 s; (b) 0.033 s; (c) 0.16 s; (d) 0.49 s; (e) 1.16 s; (f) 2.66 s.
Figure 7. Relaxation of an elongated bilayer domain at A ) 27 Å2: (a) t ) 0 s; (b) 0.67 s; (c) 1.33 s; (d) 2.0 s; (e) 2.17 s; (f) 2.5 s.
and therefore, the line tension values obtained in a quantitative analysis are expected to be lower in the monolayer. Figure 9, in which all results are summarized, confirms this finding. Moreover, it can be seen that for both kinds of layers all four different types of relaxation processes, i.e. small deformation of layer domains, small deformation of holes in the layer, bola-shaped layer, and bola shaped hole in the layer, lead to the same line tension values. The data in Figure 9 are plotted against the radius of the domains or the radius of the bola disks, respectively,
Liquid Crystalline Langmuir Films on Water
Figure 8. Relaxation of a hole in the monolayer after a small deformation at A ) 70 Å2: (a) t ) 0 s; (b) 8 s; (c) 16 s.
Langmuir, Vol. 12, No. 23, 1996 5635
for different monolayer systems,13,17,19,20 indicating that monolayers of different chemical structures such as fatty acids, phospholipids, polymers, and thermotropic liquid crystals have all similar line tension values. However, the bilayer line tension is almost 10 times higher compared with the monolayer line tension. Two explanations of the high bilayer line tension are possible. The interaction between the monolayer and the bilayer influences the relaxation behavior of the bilayer domains. If the bilayer was able to move more easily on top of the monolayer due to a weak connection between mono- and bilayer (i.e. a possible lubrication effect), the bilayer domains would relax faster to equilibrium, leading to a higher effective line tension. Moreover, in eqs 2 and 4 the water viscosity was used as subphase viscosity in calculating the line tension. However, the bilayer domains are not in direct contact with the water surface; instead, the monolayer resides between the water subphase and the bilayer. In principle, an improved estimation of the bilayer line tension should take the monolayer viscosity into account, but unfortunately the monolayer viscosity for the 8CB monolayer is unknown. However, a second possible explanation is believed to be more reliable. As pointed out in earlier work and confirmed by the surface potential measurements, the bilayer consists of interdigitated 8CB molecules. Due to this interdigitated structure the molecules in the bilayer are oriented antiparallel to each other and separated only by approximately half the distance compared with the distance of the molecules in the monolayer. Additionally, the bilayer molecules are oriented perpendicularly to the water surface and are completely above the water, whereas the monolayer molecules are strongly tilted by 72° with respect to the water surface normal, and the hydrophilic polar cyano-biphenyl headgroup is at least partially covered with water molecules. Therefore, the resulting attractive dipole-dipole interactions in the bilayer are believed to be strong compared to dipole forces in the monolayer. This attractive force leads to an increase in the measured line tension. Conclusions
Figure 9. Line tension vs radius for all eight different cases. The radius of the bola ends in the bola case and the radius of the circular structure after relaxation in the case of small deformation were taken, respectively.
and no influence of the radii is found in either case over the experimentally limited accessible radius range. By taking averages over all values in each layer case the line tensions for the monolayer and the bilayer on top of the monolayer are λ ) (1.2 ( 0.3) × 10-12 N and λ ) (1.1 ( 0.2) × 10-11 N, respectively. The line tension of the monolayer is of the same order as found by various groups
It has been shown that the absence of Rayleigh instabilities leads to stable stringlike domains in the flow deformation of two-dimensional Langmuir mono- and bilayer domains of 8CB on the water surface. Therefore, two-dimensional structures consisting of stringlike domains are easily formed by deformation processes of Langmuir monolayers providing the possibility to obtain anisotropic monolayer structures with possible unique properties. The eventual breakup of such stringlike domains occurs at defect locations, such as interactions with neighboring domains. Both the relaxation of bolashaped domains and the relaxation of slightly deformed domains yield the same line tension values in the monolayer and the bilayer case, respectively, providing more confidence for further applications of the underlying models to line tension measurements. Acknowledgment. J.L. thanks H. McConnell for helpful discussions and gratefully acknowledges the support of the Alexander-von-Humboldt Foundation through a Feodor-Lynen-Fellowship. Partial support was provided by the NSF-MRSEC Center on Polymer Interfaces and Macromolecular Assemblies (CPIMA). LA960617N
