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Liquid Crystalline and Solid Stripe Textures in Langmuir Monolayers E. Hatta and Th. M. Fischer* Max Planck Institute of Colloids and Interfaces, Am Mu¨ hlenberg 1, D-14476 Golm, Germany Received January 23, 2002. In Final Form: April 29, 2002 Textures of the molecular orientation of molecules in a Langmuir monolayer of pentadecanoic acid (PDA) are compared with similar textures of monomeric and polymeric pentacosadiynoic acid (PCA) monolayers. Both acids PDA and PCA (monomeric and polymeric) exhibit stripe textures with characteristic modulations of the molecular orientation. Using laser heating, we may cleave or deform the stripes in monomeric PCA. The relaxation of the stripes reveals that the stripes in monomeric PCA are solid stripes with a finite Young’s modulus of the order E ) 5-30 mN/m in contrast to those in PDA, which are hexatic with a vanishing Young’s modulus.
Introduction There exists a rich variety of different solid, liquid condensed, liquid, and gaseous phases in Langmuir monolayers of simple amphiphiles.1 The close resemblance of liquid condensed (LC) monolayer phases to free-standing thermotropic liquid crystalline films could be shown experimentally by optical observation of the texture of such films on the micron scale as well as by X-ray diffraction studies revealing the local microscopic arrangement of the molecules. The textures are usually characterized by the c-director, which is the averaged projection of the molecular axis of the rodlike molecules onto the film plane. If the axes in the film are denoted by x and y, then the x and y components of the c-director are denoted by cos φ and sin φ, with φ being the tilt azimuth angle. From a mechanical point of view, liquid phases can sustain only isotropic stress. If one applies a shear, that is, anisotropic, stress, liquids react with flow, while solids react with an elastic deformation. This is the reason a two-dimensional (2d) liquid can change its shape with little cost of line energy ∆E (of the order ∆E ) λ∆P, with λ being the line tension (pN) and ∆P the change in perimeter), provided the shape change occurs along an isochor. A liquid condensed phase behaves like a liquid and has a vanishing shear, respectively Young’s modulus; however, shape changes of the liquid condensed phases are associated with a change in energy due to the boundary conditions imposed on the c-director, leading to orientation elastic deformations, characterized by Franck elastic constants.2,3 Two-dimensional solids withstand shear, and if they melt (via dislocation unbinding),4-6 their Young’s modulus must exceed a value of Emin ) 16πkBTm/Amol, where Tm is the melting temperature and Amol is the area per molecule of the 2d solid. One liquid condensed texture characteristic for monolayers of achiral amphiphiles,7,8 also seen in freely (1) Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779. (2) Selinger, J. V.; Nelson, D. R. Phys. Rev. A 1989, 39, 3135. (3) Fischer, T. M.; Bruinsma, R.; Knobler, C. M. Phys. Rev. E 1994, 50, 413. (4) Kosterlitz, M.; Thouless, D. J. J. Phys. C 1973, 6, 1181. (5) Nelson, D. R.; Halperin, B. I. Phys. Rev. B 1979, 19, 2457. (6) Nelson, D. R. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic Press: London, 1983; Vol. 7, pp 2-93.
suspended films of chiral liquid crystals,9 is a stripe texture. Stripe textures are periodic variations of the tilt azimuth φ slowly varying within a stripe and discontinuously jumping between the stripes. Stripe textures are caused by the head-tail asymmetry in monolayers, which allows for free energy terms linear in the gradient of the c-director.10 Stripe textures of achiral mesogens also occur as surface phases in freely suspended hexatic liquid crystalline films.11 Straightforward methods to determine the mechanical properties of liquid condensed or solid phases measure the force needed for a certain deformation of a monolayer structure. Indeed, such methods have been employed using glass fibers to determine the 2d Young’s modulus of solidlike monolayer rods12 in Langmuir monolayers of NBD stearic acid. Recently, the use of laser tweezers and laser heating13 greatly simplified the local mechanical handling of monolayers, and we make use of this technique in order to deform and cleave stripe textures in monolayers. As we will show, stripe textures occur not only in liquid condensed but also in solid monolayer phases and their behavior upon thermomechanical manipulation is quite different depending on the nature of the phase. Experimental Section Thermomechanical experiments have been performed in pentadecanoic acid (PDA) and monomeric and polymerized 10,12pentacosadiynoic acid (PCA), because both amphiphiles exhibit stripe textures. PDA is a simple long-chain fatty acid. Long-chain fatty acids form monolayers, which have been analyzed in great detail over the past decades.1 Polydiacetylene single crystals, either in bulk or in Langmuir monolayers, have received much attention14-16 because they are model systems for (7) Ruiz Garcia, J.; Qiu, X.; Tsao, M. W.; Marshall, G.; Knobler, C. M.; Overbeck, G. A.; Mo¨bius, D. J. Phys. Chem. 1993, 97, 6955. (8) Schwartz, D. K.; Ruiz Garcia, J.; Qiu, X.; Selinger, J. V.; Knobler, C. M. Physica A 1994, 204, 606. (9) Langer, S. A.; Sethna, J. P. Phys. Rev. A 1986, 34, 5035. (10) Selinger, J. V. In Complex Fluids; Materials Research Society Symposium Proceedings, Vol. 248; Materials Research Society: Pittsburgh, PA, 1992; p 29. (11) MacLennan, J.; Seul, M. Phys. Rev. Lett. 1992, 69, 2082. (12) Bercegol, H.; Meunier, J. Nature 1992, 356, 226. (13) Wurlitzer, S.; Lautz, C.; Liley, M.; Duschl, C.; Fischer, Th. M. J. Phys. Chem. B 2001, 105, 182. (14) Bloor, D.; Chance, R. R. Polydiacetylenes: Synthesis, Structure, and Electronic Properties; Martinus Nijhoff: Dordrecht, The Netherlands, 1985. (15) Ulman, A. Ultrathin Organic Films; Academic Press: San Diego, 1991.
10.1021/la025571e CCC: $22.00 © 2002 American Chemical Society Published on Web 06/26/2002
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Figure 1. Brewster angle microscope image of a stripe texture of a PDA monolayer (T ) 12 °C, π ) 6.8 mN/m). investigating the physics of low-dimensional electrical17,18 and optical19,20 phenomena in organic polymers. This monomer monolayer is polymerized from the solid state condition topochemically; that is, if the tails of the molecules in the monomer monolayers are not oriented properly with respect to their neighbors, polymerization may be inhibited. Here the focus is switched to the ability of PCA to form extended stripe patterns. PDA was obtained from Sigma and claimed to be 99+% pure. Without further purification, it was spread from chloroform (p.a. Merck) onto pure water (Millipore Milli-Q at 18 MΩ) contained in a home-built Teflon trough. PCA was purchased from Wako Pure Chemical Industries, Ltd., and PCA monomers were spread onto the pure water from benzene without further purification. Benzene was chosen because larger domains can be obtained with this solvent. A highly concentrated solution (10 mmol) was spread onto the water surface to an average molecular area of 23 Å2 after the water surface area was bounded to a small area (50 cm2). The use of a concentrated solution confined to a small spreading area was crucial for the formation of stripe and spherulite textures.21 Lower concentrations (say, 0.5-1 mmol) resulted in mosaic textures.22 No specific precautions to prevent oxygen-assisted polymerization of the monolayer were taken. Polymerization of PCA was carried out on the water/air surface with the monolayer prepared as indicated above by 15 min exposure of the monolayer to an UV lamp (λ ) 254 nm, 12 W). The distance from the lamp to the monolayer surface was 15 cm. The Langmuir monolayers were visualized by Brewster angle microscopy (BAM) using an Ar+ laser. The monolayer also was exposed to a Nd:YAG IR laser with focus on the water/air surface. A second 20× objective was added to the BAM with the focus arranged so that it coincides with the field of view of the Brewster angle microscope. The power P of the IR laser (after the objective) was adjustable in a range between 50 mW and 2 W. The IR laser locally heats the subphase. The temperature increase ∆T at the center of the hot spot is proportional to the laser power ∆T ) RP with R ) 10 K/W. The device has been described in more detail elsewhere.13
Results Figure 1 shows Brewster angle microscopy images of PDA (T ) 12 °C, π ) 6.8 mN/m), Figures 2 and 3, of monomeric PCA (T ) 18 °C, π ) 25 mN/m), and Figure 4, of polymerized PCA (T ) 18 °C, π ) 25 mN/m). PDA shows typical stripe textures of the LC phase with a stripe width of B ) 54 µm consistent with those reported by Ruiz Garcia et al.7 Monomeric PCA shows a coexistence of spherulites (Figure 2) and stripes (Figure 3). In PDA and monomeric PCA, the gray value (tilt azimuth) gradually changes on moving from one edge of the stripe to the other. (16) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley-Interscience: New York, 1991. (17) Heeger, A. J. Rev. Mod. Phys. 2001, 73, 681. (18) Hoofman, R. J. O. M.; Siebbeles, L. D. A.; de Haas, M. P.; Hummel, A. J. Chem. Phys. 1998, 109, 1885. (19) Osaheni, J. A.; Jenekhe, S. A.; Perlstein, J. J. Phys. Chem. 1994, 98, 12727. (20) Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic Press: Orlando, 1987. (21) Yamada, S.; Hatta, E.; Mukasa, K. Jpn. J. Appl. Phys. 1994, 33, 3528. (22) Gourier, C.; Alba, M.; Braslau, A.; Daillant, J.; Goldmann, M.; Knobler, C. M.; Rieutord, F.; Zalczer, G. Langmuir 2001, 17, 6496.
Figure 2. Brewster angle microscope image of a spherulite texture of a PCA monomer monolayer (T ) 18 °C, π ) 25 mN/ m).
Figure 3. Brewster angle microscope image of a stripe texture of a PCA monomer monolayer (T ) 18 °C, π ) 25 mN/m).
Figure 4. Brewster angle microscope image of a stripe texture of a polymerized PCA monolayer (T ) 18 °C, π ) 25 mN/m).
Upon polymerization, the stripes become more homogeneous inside, while the contrast between individual stripes increases (Figure 4). In all experiments, the contrast between the stripes can be inverted by rotating the analyzer of the BAM. Therefore, the contrast is due to differences in the c-director, not due to differences in thickness. The surface tension of water depends on temperature. Switching on the IR laser, which is focused onto the monolayer, locally heats the subphase and creates a temperature gradient pointing in the direction of the laser focus. As a result, a surface stress gradient pointing radially outward is associated with this temperature gradient. It tends to reduce the initially homogeneous surfactant concentration in the center of the hot spot. The stress gradient associated with the surfactant concentration gradient may be strong enough to balance the stress gradient due to the heating. However, if one further increases the laser power, the concentration gradient induced stress gradient becomes too weak to maintain mechanical equilibrium. One or more 2d cavitation gas bubbles open with an outward flow of the subphase constantly sweeping the heated region free of surfactant molecules.23 (23) Khattari, Z.; Hatta, E.; Kurth, D. G.; Fischer, Th. M. J. Chem. Phys. 2001, 115, 9923.
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Figure 6. Cleavage and bending (-4.5-0 s) (deformation D ) 86 µm) of monomeric PCA stripes using laser heating (T ) 18 °C, π ) 25 mN/m, P ) 0.6 W). At t ) 0, the laser heating is switched off, and the bend stripe (width B ) 73 µm, length L ) 825 µm) straightens (D˙ ) 2160 µm/s), thereby reducing the gas area between the bend stripe and the other stripes.
Figure 7. Brewster angle microscope image of a crack across the stripes of a polymerized PCA monolayer (T ) 18 °C, π ) 25 mN/m). The contrast decreases with time when permanently locally heated. Figure 5. (a) Brewster angle microscope image of the formation (0-7.6 s) and relaxation (7.6-15.1 s) of cavitation bubbles in PDA using laser heating (T ) 11 °C, π ) 6.8 mN/m, P ) 0.10 W). The heating is switched on at t ) 0 s and switched off at t ) 7.6 s. (b) Brewster angle microscope image of the formation (0-6.68 s) and relaxation (6.68-8.6 s) of a single cavitation bubble in PDA by laser heating (T ) 11 °C, π ) 9.6 mN/m, P ) 0.13 W). The laser heating is switched on at t ) 0 s and switched off at t ) 6.68 s.
In Figure 5, we show such 2d cavitation bubbles in a stripe texture of PDA. The cavitation instability occurs at a fairly low power of the IR laser (P ≈ 0.1 W). Circular cavitation bubbles form showing no anisotropy parallel or perpendicular to the stripes. They nucleate at random locations inside or at the edge of a stripe. Their radius is largest in the focus and decreases with the distance of the cavitation bubbles from the IR laser focus. The number of nucleation sites decreases with the surface pressure. At low pressure, π ) 6.8 mN/m, many cavitation bubbles nucleate and create a foamlike structure (Figure 5a). At higher pressure, π ) 9.6 mN/m, only one cavitation bubble nucleates (Figure 5b). In monomeric PCA, cavitation happens anisotropically and always occurs between, and never inside, the stripes (Figure 6). Cracks of gaseous PCA phase appear, cleaving the PCA stripes. Obviously, the yield stress of the solid phase is lowest near the stripe edges, and cracks nucleate and propagate along those edges. In most cases, once the heating is strong enough to cleave the stripes, the result is a complete cleavage. Monomeric PCA can be easily cleaved into individual stripes with a local heating power in the range of P ∼ 0.7 W. Moderate heating (0.2-0.5 W) only partially cleaves the stripes resulting in a deformed
stripe where it is cleaved off the other stripe. The deformation can be a stretch or bend deformation or a combination of both. In a bend deformation, the cleaved edge of the deformed stripe is compressed (as determined by measuring the arc length between characteristic points at the edge before and after the cleavage), while the opposite side is stretched resulting in a neutral line in the middle of the stripe. In a stretch deformation, both edges of the stripe increase in length. The bending deformation is dominant for a relatively small deformation, while a large deformation leads to homogeneous stretching (∆L/L ∼ 5-10%). The typical behavior of the polymer monolayer upon local heating differs from that of the monomer. It was impossible to cleave polymerized stripe textures. Instead, the overall contrast decreases and especially at low pressures, the orientation order is partially destroyed. Some of the tension created by the heating is released by cracks travelling approximately perpendicular to the stripes as shown in Figure 7 (T ) 18 °C, π ) 25 mN/m). Very rarely, the polymer monolayer breaks into small platelets but never along the boundaries. If one switches off the laser heating during the cleavage, temperature gradients relax very quickly (on the time scale of τ ≈ A/β ) 0.7 ms; Α ≈ 100 µm2 for the heated region, and β ) 1.42 × 10-7 m2/s is the thermal diffusivity of water), while the mass transport is slow. Only after thermal equilibration can we expect mechanical equilibration to occur. In PDA, mechanical relaxation occurs via a decrease in cavitation bubble size as a function of time24 and via the nucleation of liquid condensed domains with virtual defects called boojums25 inside the cavitation bubbles.
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∇‚v ) 0
(3)
where p denotes the hydrodynamic pressure in the threedimensional (3d) subphase. The translational invariance of the problem in the y direction renders the problem a two-dimensional one, and one may employ the method of the stream function ψ defined via Figure 8. Scheme of a gaseous monolayer slit of width D closing with velocity V and coupled to a 3d subphase of viscosity η.
In monomeric PCA, cavitation bubbles between stripes caused a stretch-bend deformation of the stripes (Figure 6, t ) 0 s). The bent stripes can return to the original position due to their elasticity when switching off the laser (Figure 6, t ) 0.4-0.12 s). The relaxation of the deformation is fast (τ ≈ 10 ms) but slower than the thermal relaxation (τ ≈ 1 ms). After the relaxation, the cleaved stripes do not coalesce to form a continuous liquid condensed stripe phase. They remain separated by a thin gas film between the stripes. Repeated heating and cooling cycles on the same position cause plastic deformation, such that the bend-stretch relaxation time of the stripe increases with each cycle until finally the bent stripe does not return to its original position. In polymerized PCA, heating caused a decrease of orientational order and cracks perpendicular to the stripes. These effects are irreversible such that no relaxation upon switching off the laser is observed. The only effect is a reduction of the area occupied with gas such that the width of the cracks decreases when the laser heating is switched off. In the following, we focus on the relaxation dynamics of the bend stripes in monomeric PCA and show that monomeric PCA is a 2d solid with finite Young’s modulus.
∂ψ ∂ψ ) vz and ) -vx ∂x ∂z and obeying the biharmonic equation
V vx(z ) 0) ) [Θ(x + D/2) - Θ(x - D/2)] 2
(1)
vz(z ) 0) ) 0 where Θ(ξ) denotes Heaviside’s function. The subphase velocity v is found from solutions of the Stokes equation
-∇p + η∆v ) 0
(2)
and the continuity equation (24) Khattari, Z.; Hatta, E.; Heinig, P.; Steffen, P.; Fischer, Th. M.; Bruinsma, R. Phys. Rev. E 2002, 65, 041603. (25) Schwartz, D. K.; Tsao, M.-W.; Knobler, C. M. J. Chem. Phys. 1994, 101, 8258.
∇4ψ ) 0
(5)
1 ω ) ∆ψ 2
(6)
The vorticity
fulfills the Laplace equation and hence can be written as
ω ) -Im W
(7)
where W is an analytic function of the complex variable x + iz. One of the simplest analytic functions with poles at the edges of the slit is
W)
i V i 2π x - D/2 + iz x + D/2 + iz
[
]
(8)
It is straightforward to construct the corresponding stream function
ψ)
Theoretical Here we analyze the relaxation kinetics of the bend stripes. First, we calculate the viscous pressure created when both stripes are pressed together, and second, we analyze the driving pressure. Three models are presented assuming the driving pressure for the stripe relaxation to originate from elastic, orientation elastic, or line tension energies. The validity of the models for the description of the experiments in monomeric PCA (Figure 6) is then discussed. Hydrodynamic Viscous Pressure. Consider a fluid/ air interface at z ) 0 covered by an infinite slit along the y axis of width D, bounded by two symmetrically arranged solid surface phases and closing with velocity V ) -D˙ (Figure 8). Both the gas phase and the solid phases are considered incompressible, such that the surface velocity at the interface is completely described by
(4)
x + D/2 V x - D/2 z arctan - arctan 2π z z
[
]
(9)
which solves the biharmonic equation subject to the boundary conditions (1) at the surface. The surface pressure πs onto one of the solid interfaces necessary for such a compression is then given by
πs )
2
∂v
∞ ∞ ∂ψ x dxη (z ) 0) ) -∫D/2+δ dxη 2 (z ) 0) ) ∫D/2+δ ∂z ∂z
ηV D ln (10) π δ
[]
and δ ≈ ηDs/K is a cutoff length, where the assumption of incompressibility breaks down at the slit edges. Ds is the surface diffusion constant, K ) -Γdσ/dΓ is the elasticity, σ is the surface tension, and Γ is the surface concentration of the monolayer. Typical values of δ range from 0.1 to 10 nm such that we find the estimate 9 < ln(D/δ) < 14 for the logarithmic correction factor. Equation 10 relates the surface pressure acting at the slit edges to the closure velocity V of the slit. Elastic Pressure. The laser heating in the experiments leads to a deformation of the outermost stripe, which in general is a combined elastic stretch and bend deformation. For simplicity, in the theoretical treatment of the elastic deformation we will treat only the case of a pure stretch and a pure bend deformation (Figure 9a,b). Stretch Deformation. For the case of a pure stretch deformation, we assume that the stripe is fixed at the points A and A′ in Figure 9a. Deforming of the initially straight stripe of length
R L ) 2R sin 2
(11)
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)
x R
(18)
where x ) 0 denotes the position of the neutral line. To obtain the total energy U stored in this bend deformation, we must integrate the energy density u ) (E/2)2 over the stripe area to find
U)L
3
2
3
B/2 ELB 8 DB dx u(x) ) ) E 3 ∫-B/2 3 L 24R2
(19)
The surface pressure πs is then given by
πs )
1 ∂U 16 B3D ) E 4 L ∂D 3 L
(20)
Balancing this pressure with the viscous pressure (10) yields Young’s modulus: Figure 9. (a) Scheme of a stretch deformation of the stripe. (b) Scheme of a bend deformation of the stripe. At the neutral line (dashed line), the length of the deformed stripe equals the undeformed length.
toward a stripe of curvature R uniformly elongates the stripe to
L + ∆L ) RR
(12)
thereby creating a slit of width
(
D ) R 1 - cos
R 2
)
E)-
D L
R≈
L2 8D
(13)
F ) FB + FS
(22)
∫A dx dy21K6(∇φ)2
(23)
( )
(24)
with
∆L 8 D2 ≈ L 3 L2
FB ) where
(14) c)
The total energy U due to the stretching is
1 ∆L 2 32 BD4 ) E 3 U ) BLE 2 L 9 L
( )
(15)
where B denotes the width of the stripe and E is Young’s modulus. The surface pressure πs created by the stretching is then given by
πs )
(21)
Hexatic Orientation Elastic Energy. The equilibrium stripe texture of PDA has been explained by an orientation elastic Landau type free energy of a liquid crystalline hexatic phase, which for textures, where the average molecular orientation is locked to the hexatic orientation, takes the simple form
In the limit of small deformations R f 0, we might express the bend angle R, the stripe curvature 1/R and the strain ∆L/L in terms of L and D by combining eqs 11-13:
R≈8
L4 D 3 ηD˙ 3 ln 16π B D δ
cosφ sin φ
denotes the c-director, and K6 denotes the hexatic Franck constants. The surface energy FS depends on the relative orientation of the c-director with respect to the boundary. If we assume that the anchoring of the c-director does not change upon deformation, then the only changes occur in FB. Textures minimizing FB satisfy the Laplace equation
∆φ ) 0
(25)
3
1 ∂U 128 BD ) E 4 L ∂D 9 L
(16)
Balancing this pressure with the viscous pressure (10) yields an expression for Young’s modulus.
L4 D 9 ηD˙ ln E)128π BD3 δ
(17)
Bend Deformation. In a bend deformation, the length of the stripe does not change on average during the deformation. At the neutral line in the middle of the stripe, the length does not change. Beyond the neutral line, there is a length increase, while the side of the stripe facing the extended LC region shortens. (Figure 9b). The strain dependence normal to the neutral line (the x direction) is linear and given by
A curved 60°-splay stripe of thickness B is described by
φ(r,ψ) ) ψ +
πr-R 3 B
(26)
where the stripe extends over (R - B/2) < r < (R + B/2), where r,ψ are polar coordinates and the excess free energy due to the bending of the stripe is
FB(R) - FB(R ) ∞) )
K
R+B/2 6 r dr 2 ) ∫0R dψ∫R-B/2 2r
BD2 32K6 3 (27) L which translates into a surface pressure trying to straighten the stripes
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πs )
1 ∂FB BD ) 64K6 4 L ∂D L
Hatta and Fischer
(28)
Balancing this pressure with the viscous pressure (10) yields the Franck elastic constant
K6 ) -
L4 D 1 ηD˙ ln 64π BD δ
(29)
Line Tension. The bending also increases the line energy which is proportional to the line tension λ and leads to a Laplace pressure:
πs )
2λ 16λD ) R L2
(30)
Considering this pressure as the dominant driving force, for the deformation relaxation we obtain
λ)-
ηL2D˙ D ln 16πD δ
(31)
Equations 17, 21, 29, and 31 offer three different interpretations for the stripe shortening. Equation 17 or eq 21 holds for a solid, while eq 29 should apply for hexatic liquid condensed phases and eq 31 for a liquid. If the stripes were solid stripes, then eq 17 or eq 21 must result in a Young’s modulus satisfying
E > 16πkBTm/Amol
(32)
For a liquid condensed stripe, we would expect a Franck elastic constant of the order
K6 ≈ kBTc
(33)
where Tc is the hexatic to liquid transition temperature. The line tension is expected to be of the order
λ ≈ πc(∆A)1/2
(34)
where πc is the transition pressure between both phases and ∆A is the difference in the area per molecule of both phases. A comparison of eqs 17, 21, 29, and 31 with eqs 32-34 shows which of the models is reasonable. For the stripe relaxation in monomeric PCA (L ) 825 µm, B ) 73 µm, D ) 86 µm, D˙ ≈ 2160 µm/s, η ) 1.1 × 10-3 Ns/m2,26 and δ ) 0.1-10 nm), the interpretation of the stripes as solid stripes (eqs 17 or 21) yields reasonable results: E ) 5-30 mN/m for Young’s modulus, which should be compared with Emin ) 44.2 mN/m (using Amol )23 Å and Tm3d ) 62 °C) as obtained from (32). The interpretation as a 2d hexatic yields Franck elastic constants (eq 29) of (26) Landolt Bo¨rnstein IV/1, 6th ed.; Springer: Berlin, 1955; pp 600, 613.
K6 ) 8-12 × 10-12 J, 9 orders of magnitude larger than expected from (33), and K6 ≈ 4.8 × 10-21 J (using Tc ≈ 50 °C), and the line tension calculated from (31), λ ) 3-5 nN, is 4 orders of magnitude larger than expected from (34), λ ≈ 0.31 pN (using πc ≈ 1 mN/m and ∆A ≈ 10 Å2). Also, the plastic deformation observed after repeated heating cycles should not occur if the straightening of the stripes were due to the line tension between the phases. It is therefore clear that the stripe patterns in monomeric PCA are solid stripes in contrast to those in PDA which are hexatic stripe textures. One might ask, what are the important chemical differences between different amphiphiles that might cause some to be crystalline and others liquid crystalline? The interrelation between the chemical structure and the phase behavior cannot easily be deduced. Slight changes of the headgroup and/or alkyl chain length may cause drastic effects to the phase diagram. For example, the phase diagrams of long-chain fatty acids, alcohols, and esters, which have been studied in great detail, differ. Those differences can be understood only when taking into account the effective headgroup sizes due to hydration shells and conformational changes such as E-Z isomerization in the esters. The phase diagram of PCA has not been analyzed in detail, and variations in the results depending on the spreading solution are reported to occur.22 To unravel the chemical reason for the PDA monolayer being liquid crystalline and the PCA being solid, clearly more experiments on the detailed microscopic arrangement of monomeric PCA within the stripe phase are needed. Conclusions Stripe textures of the molecular orientation of molecules in a Langmuir monolayer appear in a variety of different amphiphiles and within hexatic liquid condensed and solid phases. In a monomeric monolayer of PCA, spherulite textures coexist with stripe textures. Cavitation of the hexatic PDA monolayer caused by local heating is not correlated with a specific position on the stripes. In solid monomer PCA, cavitation always occurs at the stripe edges thereby cleaving the stripes. The relaxation of the solid monomer PCA stripes is due to their Young’s modulus which is of the order E ) 5-30 mN/m. In polymerized PCA, cavitation occurs via crack formation perpendicular to the stripe pattern. The chemical reason for the different behaviors of PDA and monomeric PCA is not clear. Further studies are needed to clarify this issue. Acknowledgment. We thank H. Mo¨hwald for generous support and stimulating discussions. E. Hatta thanks the Max-Planck-Gesellschaft for providing a Max-Planck fellowship. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) with a Heisenberg Fellowship to T.M.F. and by Grant No. Fi 548/3-1. LA025571E
