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Disorder in Langmuir Monolayers. 1. Disordered Packing of Alkyl Chains G. Weidemann, G. Brezesinski, D. Vollhardt,* and H. Mo¨hwald Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, 12489 Berlin, Germany Received February 13, 1998. In Final Form: July 27, 1998 Grazing incidence synchrotron X-ray diffraction (GID) studies of Langmuir monolayers of several substances such as 2-monopalmitoyl-glycerol, 2-hexadecanol, and 2-hydroxypalmitic acid reveal diffraction patterns that indicate a disordered packing of alkyl chains. The diffracted intensity is distributed along a characteristic arc in reciprocal space. A relation between in-plane lattice and two parameters, polar tilt angle and tilt azimuth, is derived in order to describe the observed distribution that results from the superposition of the diffracted intensities of different lattices. It is possible to ascribe the diffraction patterns unambiguously to a variation of the tilt azimuth. Variation of the polar tilt angle was ruled out. A detailed analysis of the distributed intensity allows one to obtain at least the polar tilt angle and the lattice spacing perpendicular to the tilt azimuth in the limit of a lattice with nearest-neighbor tilt.
I. Introduction The order in Langmuir monolayers is of considerable interest. Grazing incidence synchrotron X-ray diffraction (GID) was established as a powerful tool to study the packing of amphiphiles at the air-water interface.1-3 It allowed the identification of the phases of fatty acid monolayers as a model system,4,5 the study of the influence of chirality on the packing and the phase behavior of amphiphilic monolayers,6 and the analysis of the influence of the molecular structure on the packing of alkyl chains in phospholipid monolayers.6,7 So far, the alkyl chains in monolayers of most substances were found to have cross sections similar to those of the free rotator phase of n-alkanes.8-10 Alkyl chains in a more crystalline state occur only for certain substances with very long chains11 or strong hydrogen bonds.12-15 In the diffraction patterns of certain substances, the intensity is distributed along a characteristic arc in the (1) Als-Nielsen, J.; Mo¨hwald, H. In Handbook on Synchrotron Radiation; Ebashi, S., Koch, M., Rubenstein, E., Eds.; Elsevier: Amsterdam, Oxford, New York, Tokyo, 1994; Vol. 4, pp 1-53. (2) Kjaer, K. Experimental Stations at HASYLAB; January 1994; pp 88-89. (3) Als-Nielsen, J.; Jacquemain, D.; Kjaer, K.; Lahav, M.; Leiveiller, F. Leiserowitz, L. Phys. Rep. 1994, 246, 251-321. (4) Kenn, R. M.; Bo¨hm, C.; Bibo, A. M.; Peterson, I. R.; Mo¨hwald, H.; Als-Nielsen, J.; Kjaer, K. J. Phys. Chem. 1991, 95, 2092-2097. (5) Kaganer, V. M.; Peterson, I. R.; Kenn, R. M.; Shih, M. C.; Durbin, M.; Dutta, P. J. Chem. Phys. 1995, 102, 9412-9422. (6) Struth, B.; Scalas, E.; Brezesinski, G.; Mo¨hwald, H.; Bringezu, F.; Bouwman, W. G.; Kjaer, K. Nuovo Cimento Soc. Ital. Fiz. D 1994, 16, 1545-1550. (7) Brezesinski, G.; Dietrich, A.; Dobner, B.; Mo¨hwald, H. Prog. Colloid Polym. Sci. 1995, 98, 255-262. (8) Dorset, D. L.; Moss, B.; Wittmann, J. C.; Lotz, B. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 1913-1917. (9) Doucet, J.; Denicolo, I.; Craievich, A.; Collet, A. J. Chem. Phys. 1981, 75, 5125-5127. (10) Doucet, J.; Denicolo, I.; Craievich, A.; Germain, C. J. Chem. Phys. 1984, 80, 1647-1651. (11) Dutta, P. In Phase Transition in Surface Films 2; Taub, H., et al., Eds.; Plenum: New York, 1991; pp 183-200. (12) Gehlert, U.; Weidemann, D.; Vollhardt, D.; Brezesinski, G.; Wagner, R.; Mo¨hwald, H. Langmuir 1998, 14, 2112-2118. Gehlert, U. PhD Thesis, Technical University Berlin, 1996. (13) Melzer, V.; Weidemann, G.; Vollhardt, D.; Brezesinski, G.; Wagner, R.; Struth, B.; Mo¨hwald, H. J. Phys. Chem. 1996, 101, 47524758. (14) Melzer, V.; Weidemann, G.; Vollhardt, D.; Brezesinski, G.; Wagner, R.; Struth, B.; Mo¨hwald, H. Supramol. Sci. 1996, 4, 391-397.
space described by the in-plane and out-of-plane scattering vector components. In the present paper, we focus our attention on such substances. The aims are to gain an understanding of the reasons for this feature and to obtain more information about the packing of the alkyl chains from a detailed analysis of the diffraction patterns. The diffracted intensity of substances such as 2-monopalmitoyl-glycerol, 2-hexadecanol, and 2-hydroxypalmitic acid cannot be interpreted in terms of a well-defined lattice. It rather seemed to result from the superposition of the diffracted intensities of different lattices, which might differ with respect to the polar tilt angle or the tilt azimuth of alkyl chains. To develop an understanding of the observed disordered chain packing, a relation between the in-plane lattice and the alkyl chain packing is derived. A discussion of the area requirement of headgroups and alkyl chains suggests that disorder is induced by a misfit of headgroups and alkyl chains that cannot be compensated by the tilt of the alkyl chains. II. Experimental Section The subphase water used for the experiments was purified by a Millipore desktop (Millipore, Eschborn, Germany). 2-Monopalmitoyl-glycerol and DL-2-hexadecanol were purchased from Sigma (Deisenhofen, Germany) (approximately 99%), and DL-2-hydroxypalmitic acid was obtained from Avocado Research Chemicals, (Heysham, England) (approximately 98%). The substances were used without further purification. The heptane (UVASOL) and ethanol (p. A. grade), which are used to prepare spreading solutions (9:1), were obtained from Merck (Darmstadt, Germany). For the studies of 2-hydroxypalmitic acid monolayers, the pH of the subphase was adjusted to 2 with HCl (Titrisol) from Merck. Grazing incidence X-ray diffraction experiments were performed using the liquid surface diffractometer on the undulator beamline BW1 at HASYLAB, DESY (Hamburg, Germany).2 The monolayer has to be considered as a twodimensional powder. The beam was made monochromatic (15) Vollhardt, D.; Emrich, G.; Melzer, V.; Weidemann, G.; Gehlert, U. in Short and Long Chains at Interfaces, Proceedings of the XXXth Recontres de Moriond; Daillant J., et al., Eds. Editions Frontieres: Gifsur-Yvette, France, 1995; pp 149-154.
10.1021/la980188o CCC: $15.00 © 1998 American Chemical Society Published on Web 10/02/1998
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by a beryllium crystal (002). The wavelength was 1.481 Å (except for the 2-monopalmitoyl-glycerol experiments, where it was 1.338 Å). The beam was adjusted to strike the surface with an angle of incidence Ri ≈ 0.85Rc, where Rc (Rc ≈ 0.14°) is the critical angle for total internal reflection. The diffracted intensity was monitored by a linear position-sensitive detector (PSD) (OED-100-M, Braun, Garching, Germany) as a function of the vertical scattering angle Rf. To record the intensity as a function of the horizontal scattering angle 2θ, this detector was rotated around the sample. The in-plane divergence of the diffracted beam was restricted to 0.09° by a Soller collimator in front of the PSD. According to the geometry of diffraction1-3 the scattering vector Q can be written in terms of an in-plane component, Qxy, with
Qxy )
2π cos2 Ri + cos2 Rf - 2 cos Ri cos Rf cos 2θ (1) λx
Figure 1. Description of the coordinate system of the molecule in terms of azimuthal tilt angle Ψ (with respect to the a axis) and polar tilt angle t (a). The in-plane lattice is correlated to the lattice perpendicular to the chain axis by an elongation along the tilt azimuth. A lattice vector g⊥ perpendicular to the tilt azimuth remains unchanged, while a vector g| parallel to the tilt azimuth b n| is elongated by 1/cos(t) (b).
and an out-of-plane component, Qz, with
Qz )
2π (sin Ri + sin Rf) λ
(2)
The intensities were least-squares fitted as a Lorentzian parallel to the water surface and as a Gaussian normal to it. From the in-plane reflex positions the spacings of the two-dimensional lattice can be obtained.
Qxy )
2π dhk
(3)
The out-of-plane scattering vector component is determined by the molecular form factor and can provide information about the polar tilt angle t and the tilt azimuth Ψ of the rodlike alkyl chains. According to the cylinder model,1,3 the scattering vector components at maximum intensity are related to these two parameters hk Qhk z ) Qxy cos Ψhk tan t
2 fwhm(Qxy)
(5)
III. Geometrical Relations between In-Plane Lattice, Tilt Azimuth, and Polar Tilt Angle Assuming a defined lattice perpendicular to the chain axis, it is possible to calculate the in-plane lattice from the tilt azimuth Ψ and the polar tilt angle t (Figure 1a). The main idea is that the in-plane lattice is correlated to the lattice perpendicular to the chain axis by an elongation along the tilt azimuth. A lattice vector g⊥ perpendicular to the tilt azimuth remains unchanged, while a vector parallel to the tilt azimuth g| is elongated by 1/cos(t) (Figure 1b)
g⊥ )
go⊥
and
in an orthonormal system with vectors parallel and perpendicular to the tilt azimuth [ b n|, b n⊥] (Figure 2). The vector b go is then
b g o ) (go cos Ψo, go sin Ψo)
go⊥ g| ) cos t
(6)
where b g is a vector of the in-plane lattice and b g a vector of the lattice perpendicular to the chain axis. The transformation of an arbitrary vector b g can be described
(7)
go. where Ψo is the tilt azimuth with respect to the vector b The vector of the in-plane lattice can be obtained by a b|, where f ) 1/cos(t) simple substitution of b n| by fn
(
(4)
The full width at half-maximum (fwhm) is related to the positional correlation length ξ. For an exponential decay of positional correlation as observed in liquid crystals (corresponding to a Lorentzian as reflex profile), it is
ξ)
Figure 2. Lattice vector in an orthonormal system [n b|, n⊥] with basis vectors parallel and perpendicular to the azimuthal tilt direction (lattice perpendicular to the chains).
)
cos Ψo , go sin Ψo b g ) go cos t
(8)
The same algorithm can be used to calculate the lattice perpendicular to the chain axis from the in-plane lattice, if f ) cos(t) is used. To calculate the peak positions as a function of tilt azimuth and polar tilt angle, the d values (i.e., the interplanar spacing) have to be calculated. The spacing of lattice planes is considered as a vector d ) (d0 cos Ψo/cos t, do sin Ψo), where Ψo is now the tilt azimuth with respect to this vector (i.e., with respect to the normal of the lattice plane). The square of the absolute d value results then from
d2 ) d2o
(
cos2 Ψο + sin2 Ψo cos2 t
)
(9)
which can be simplified to
(
)
1 - cos2 t d2 ) d2o 1 + cos2 Ψο cos2 t
(10)
d2 ) d2o (1 + cos2 Ψο tan2 t)
(11)
or
o
With eq 3, it is possible to calculate the Qxy values of the reflection from the lattice plane.
Disorder in Langmuir Monolayers
Qxy )
2π o
d
x1 + cos2 Ψo tan2 t
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(12)
The Qz value is defined by eq 4. At first glance, both the square of the Qxy value and the square of Qz value depend on cos2 Ψ tan2 t. However, Ψ is the azimuth of the inplane lattice, whereas Ψo is the azimuth in the plane perpendicular to the chain axis. The relation between Ψo and Ψ can be derived by substituting g1 in Figure 2 by g1/cos t to derive the corresponding plot in the water surface.
tan Ψ ) cos t tan Ψ0
(13)
Ψo - Ψ remains quite small for small polar tilt angles. Even for the quite large polar tilt angle of t ) 35°, it amounts to about 6°, resulting in a deviation of about 7% for the Qz value. Neglecting this difference, a direct relation between Qxy and Qz can be derived from eqs 12 and 4:
Q2z + Q2xy )
4π2 d2o
(14)
The alkyl chains in Langmuir monolayers of most common amphiphiles, such as palmitic acid, methyl palmitate, ethyl palmitate,16 palmityl acetate,17 1-monopalmitoyl-glycerol,18 and 1-hexadecyl-glycerol,19 have a cross-sectional area of about 20.0 Å2 as in the free rotator phase of n-alkanes.8-10 In this case, the lattice perpendicular to the chain axis is expected to be hexagonal or almost hexagonal. Assuming a hexagonal lattice in the plane perpendicular to the chains, then all do values are equal, and all peaks are shifting on the same curve as if the tilt azimuth or the polar tilt angle were varied. Even for quite large polar tilt angles, the peak positions deviate only slightly from this curve. IV. Effect of the Headgroup on the Alkyl Chain Packing Until now, attention was focused on the packing of the alkyl chains. However, simple amphiphiles consist of a headgroup and one or more alkyl chains. In most cases, the headgroup requires a larger area Axy than the alkyl chains Ao. To adapt to the lattice of the headgroups, the area requirement of the alkyl chains can be increased by a tilt of the chains to Ao/cos(t). To illustrate the distortion of the lattice due to the tilt, it is useful to consider the six nearest neighbors of an alkyl chain. In a free rotator phase, the alkyl chains are expected to pack hexagonally perpendicular to their axis. The nearest neighbors are then situated on a circle. As discussed above, the tilt of the chains gives rise to an elongation of the lattice only in the tilt direction, which transforms the circle into an ellipse (Figure 3a). Considering a single molecule in an hexagonal lattice, the cross section of the alkyl chain can be represented by a circle. In most cases, the headgroup is larger than the alkyl chain. To overcome this mismatch, the chain needs to be tilted, transforming the projection of the chain onto (16) Weidemann, G.; Brezesinski, G.; Bringezu, F.; de Meijere, K.; Vollhardt, D.; Mo¨hwald H. J. Phys. Chem. 1998, 102, 148-153. (17) Weidemann, G.; Brezesinski, G.; Vollhardt, D.; Mo¨hwald H. J. Phys. Chem. 1998, 102, 1224-1228. (18) Brezesinski, G.; Scalas E.; Struth, B.; Mo¨hwald, H.; Bringezu, F.; Gehlert, U.; Weidemann, G.; Vollhardt, D. J. Phys. Chem. 1995, 99, 8758-8762. (19) Scalas, E.; Brezesinski, G.; Mo¨hwald, H.; Kaganer, V. M.; Bouwman, W. G.; Kjaer, K. Thin Solid Films 1996, 284/285, 56-61.
Figure 3. Elliptical description of the geometry of nearest neighbors of an alkyl chain. (a). The alkyl chain needs to adapt to the headgroup to pack in a lattice. A tilt of the alkyl chain (symbolized by a circle) gives rise to an elongation in the tilt direction resulting in the dashed ellipse. If the headgroup (symbolized by the bold ellipse) is larger (b) or smaller (c) perpendicular to the tilt direction despite the tilt of the chain, a misfit remains (compare dashed with bold ellipses), which can only be compensated by a distortion of the chain packing (d,e).
the water plane into an ellipse (Figure 3b,c dashed lines). However, it is quite unlikely that this projection of the chain and that of the headgroup are of the same size perpendicular to the tilt azimuth. The headgroups (symbolized by the bold ellipse) are often larger (Figure 3b) or smaller (Figure 3c) than the chains in this direction. This remaining misfit cannot be compensated so long as both the chain packing remains hexagonal and the crosssectional area Ao of the alkyl chains is preserved. However, the latter is supported by the observation of Aovalues of about 20.0 Å2 for various substances with tilted alkyl chains.6,7,16-19 Furthermore, the Aovalues for a single substance do not significantly depend on the polar tilt angle. Consequently, only an additional distortion of the chain packing (i.e., a transformation of the circle in Figure 3b,c to an ellipse in Figure 3d,e) allows an adaptation of the chain lattice to the headgroup lattice. A larger headgroup then requires an elongation of the chain cross section perpendicular to the tilt azimuth (Figure 3d). Accordingly, the distortion of the chain packing (referring to the plane perpendicular to the chain axis) is perpendicular to that of the in-plane lattice due to the tilt of the molecule. A smaller headgroup gives rise to a contraction of the chain cross section perpendicular to the tilt azimuth (Figure 3e). The chain packing and the in-plane lattice are then distorted in the same direction. To test this assertion, the chain packing can be calculated using the relation derived above. For most substances, we found that the headgroups are larger, for instance myristic and palmitic acid,16 palmityl acetate,17 1-monopalmitoyl-glycerol,18 1-hexadecyl-glycerol,19 2-hexadecanol, 2-hydroxypalmitic acid, and 2-monopalmitoylglycerol (present work). However, the alkyl chains of most amphiphiles with 16 or fewer carbon atoms are in a free rotator phase. Consequently, the chains are expected to prefer a hexagonal packing. This results in the following two questions: (1) Does a limit for the distortion of the alkyl chains in the free rotator phase exist? (2) What is the consequence if the misfit becomes so large that its compensation requires a distortion that exceeds this limit? V. Experimental Results and Discussion 2-Monopalmitoyl-glycerol (Figure 4) monolayers were studied at 13 °C. Diffraction patterns were recorded at
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Figure 5. Contour plots of diffracted intensity versus in-plane scattering vector component Qxy and out-of-plane scattering vector component Qz for a monolayer of 2-monopalmitoylglycerol at 13 °C.
Figure 4. Surface pressure (π)-molecular area (A) isotherms and chemical formulas of 2-monopalmitoyl-glycerol (a), 2-hexadecanol (b), and 2-hydroxypalmitic acid (c).
18, 25, and 40 mN/m. At 18 and 25 mN/m, two intensity maxima according to the (02) and the degenerate (11), (11 h ) peaks of a lattice with alkyl chains tilted toward nearest neighbors (NN) can be identified (Figure 5). However, in addition to these peaks, diffracted intensity is also distributed along a curve. This looks like a superposition of the peaks of lattices which differ with respect to the polar tilt angle or the tilt azimuth. The distributed intensity increases from 18 to 25 mN/m. At 40 mN/m, the degenerate (11),(11 h ) peak cannot be identified, as its intensity is too low compared to the distributed intensity. 2-Hexadecanol (Figure 4) shows a different behavior (Figure 6). All diffracted intensity is distributed along a curve at 10, 20, and 30 mN/m. However, the part at high Qz and low Qxy now shows a sharp edge toward low Qxy values. A similarly distributed scattered intensity
(Figure 7) was found for 2-hydroxypalmitic acid (for isotherm, see Figure 4). To understand these differences in the intensity distributions, the peak positions for alkyl chain lattices were calculated as a function of the polar (t) and azimuthal (Ψ) tilt angle according to eqs 4 and 12. To do so, it was assumed that the chains have a hexagonal packing perpendicular to the chain axis which does not vary with the polar and azimuthal tilt angle. This assumption is only partly justified, but it allows the study of the general shape of the intensity distribution. Furthermore, a constant cross-sectional area of 20.5 Å2 is assumed. At first glance, this appears to be rather high, but our experiments showed that this is quite realistic (further discussion). In section III, it was shown that all peaks are approximately located on the same curve as long as the packing of the alkyl chains is hexagonal. However, different types of intensity distributions are observed. Although the curve is the same if the tilt azimuth and the polar tilt angle are varied, the distribution of the peaks along the curve is different. First, the tilt azimuth was kept constant, and the polar tilt angle was varied (Figure 8a,b). Two cases were considered: lattices of alkyl chains tilted toward nearest neighbors (NN) and toward next nearest neighbors (NNN). Neither pattern is in agreement with the observed diffracted intensity: For NN-tilted chains, all lattices give rise to a peak at Qz ) 0 Å-1 and the same Qxy (in the same position as the peak for t ) 0
Disorder in Langmuir Monolayers
Figure 6. Contour plots of diffracted intensity versus in-plane scattering vector component Qxy and out-of-plane scattering vector component Qz for a monolayer of 2-hexadecanol at 25 °C.
but not shown in Figure 8a for clarity), whereas the other peak is distributed along a curve (Figure 8a). Consequently, the peak at Qz ) 0 Å-1 is expected to be much more intense than the intensity distributed along the curve (Figure 9a, dashed line). As the experimental curves do not show such an intense peak at Qz ) 0 Å-1, we can exclude this case. The distribution of the peaks on the curve obtained for a varying polar tilt angle and NNNtilted chains (Figure 8b) is also not in agreement with the observed intensity distributions. Now the number of peaks with a Qz value smaller than half the maximum Qz value is much larger than the number of those with higher Qz. Furthermore, all degenerate peaks, which are expected to have twice the intensity of nondegenerate peaks, have a Qz value smaller than half the maximum Qz value. Hence, the intensity is expected to fall to a lower value at half the maximum Qz value (Figure 9a, dotted line), a feature which was not found in any experimental intensity distribution.
Langmuir, Vol. 14, No. 22, 1998 6489
Figure 7. Contour plots of diffracted intensity versus in-plane scattering vector component Qxy and out-of-plane scattering vector component Qz for a monolayer of 2-hydroxypalmitic acid on a subphase with pH 2 at 24 °C.
At first glance, the contour plots of the experimental diffraction patterns suggest a decrease of intensity with increasing Qz. Such a decrease of diffracted intensity with increasing Qz is also observed for substances that show sharp peaks, such as 1-monopalmitoyl-glycerol.18 This decrease of intensity results from a broadening of peaks with increasing Qz which might be introduced by deviations of the monolayer from the horizontal due to the meniscus or waves.20 If the intensity is integrated over the whole Qxy range, the maximum of the experimental intensity distributions is at high Qz (Figure 9b-d). Agreement with this finding is achieved if the polar tilt angle is assumed to remain constant and the tilt azimuth is postulated to vary (Figure 9a, solid line). Now the peaks are distributed quite continuously along the curve in the (20) Howes, P. B.; Kjaer, K. Annual Report 1996; Hamburger Synchrotronstrahlungs-labor HASYLAB am Deutschen Elektronensynchrotron DESY, p 445.
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Figure 8. Peak positions for lattices with varying polar tilt angles or varying tilt azimuth: (a) varying polar tilt angle and tilt toward nearest neighbors, (b) varying polar tilt angle and tilt toward next nearest neighbors, and (c) varying tilt azimuth and a constant polar tilt angle. The Ψ values given in parentheses are with respect to the in-plane lattice; the other values are with respect to the chain packing (where 30° corresponds to a NNN direction).
Qxy-Qz plane (Figure 8c), and only at maximum Qz and minimum Qxy does an accumulation of peaks occur (the peaks for Ψo ) 20°-30° coincide). The former is in agreement with all experimental diffraction patterns (Figures 5-7). The latter is impressively reproduced in the diffraction patterns of 2-hexadecanol and 2-hydroxypalmitic acid. Here, the accumulation of peaks at the end of the curve gives rise to the sharp edge toward low Qxy at high Qz. The diffraction patterns of 2-monopalmitoylglycerol have a different shape. The two peaks at 18 mN/m correspond to a lattice with NN-tilted chains (Ψo ) 0°). If attention is focused on the peaks for Ψo ) 0°-10° in Figure 9, one sees that the degenerate (11),(11 h ) peak is split into two peaks. One shifts with increasing Ψ to higher Qz and higher Qxy, and the other shifts to lower Qz and lower Qxy. This explains the asymmetric shape of the degenerate (11),(11 h ) peak in Figure 5. The (02) peak is found to shift with varying tilt azimuth only slightly to lower Qxy but strongly to higher Qz. This, again, is in agreement with the experimentally observed intensity distribution.
Figure 9. Scattered intensity integrated over the whole Qxy range as a function of Qz. (a) Intensity distributions calculated from the reflex positions given in Figure 8 assuming Gaussian reflex profiles of equal intensity with a fwhm of 0.3 Å-1 (corresponding to a molecule length of about 20 Å). (b-d) Intensity distributions obtained for the three substances studied.
The different shapes of the diffraction patterns of 2-monopalmitoyl-glycerol and 2-hexadecanol evidently result from a different preferred tilt azimuth with respect to the lattice. The sharp edge of the intensity distribution in the diffraction patterns of 2-hexadecanol indicates that the preferred tilt direction is NNN, whereas the preferred tilt direction is NN in 2-monopalmitoyl-glycerol monolayers. This also becomes evident from the peak profile in the xy-direction at high Qz (Figure 10). In the case of preferred NN-tilt (Figure 10, left image) the peak at high h ) peak. The two Qz corresponds to the degenerate (11),(11
Disorder in Langmuir Monolayers
Langmuir, Vol. 14, No. 22, 1998 6491 Table 2. Peak Positions and fwhm (Below Each Peak Position) for 2-Hexadecanola 2-hexadecanol, 25 °C
Qxy
10 mN/m
1.449 0.020 1.456 0.018 1.463 0.017
20 mN/m 30 mN/m
Figure 10. Peak profiles of 2-monopalmitoyl-glycerol at 25 mN/m (Qz ≈ 0.9 Å-1) (left image, symmetric peak for preferred NN-tilt) and 2-hexadecanol at (Qz ≈ 0.7 Å-1) (right image, asymmetric peak for preferred NNN-tilt). Table 1. Peak Positions and fwhm (Below Each Peak Position) for 2-Monopalmitoyl-Glycerol 2-monopalmitoylglycerol, 13 °C 18 mN/m 25 mN/m 40 mN/m
02 Qxy (Å-1) Qz (Å-1) 1.447 0.027 1.450 0.027 1.466 0.047
11,11 h Qxy (Å-1) Qza (Å-1)
0
1.26
0.86
0
1.30
0.80
0
2-hexadecanol, 25 °C
02 (NNN)b Qxy (Å-1) Qz (Å-1)
0
1.33
0.75
0
1.36
0.62
0
1.41
0.49
02 Qxy (Å-1)
Qz (Å-1)
1.452 0.018
0.15 0.32
40 mN/m
11,11 ha Qxy (Å-1) Qza (Å-1) 1.472 0.013
0.30 0.27
a At 40 mN/m, peak positions and the fwhm according to a lattice with NNN-tilted chains can be determined. b At 10, 20, and 30 mN/m, the xy-position of the (02) peak in the limiting case of NNNtilted chains cannot be determined as precisely as usual, and its fwhm(Qxy) cannot be determined with a tolerable accuracy.
Table 3. Peak Positions and fwhm (Below Each Peak Position) for 2-Hydroxypalmitic Acid 2-hydroxypalmatic acid, pH 2, 24 °C
02 (NN) Qxy (Å-1) Qz (Å-1)
18 mN/m
The position of the degenerate (11),(11 h ) peak cannot be determined as precisely as usual, and its fwhm cannot be determined with a tolerable accuracy. At 40 mN/m, the position of the peak also cannot be determined with a tolerable accuracy. a
peaks shift with varying tilt azimuth in opposite directions, and the peak profile remains symmetric. In the case of preferred NNN-tilt (Figure 10, right image), the peak at Qz corresponds to the nondegenerate (02) peak, which shifts with varying tilt azimuth only to higher Qxy, and the peak profile becomes asymmetric. The substances studied here differ not only with respect to the diffraction pattern but also with respect to the development of the intensity distribution with increasing surface pressure. For 2-monopalmitoyl-glycerol (Figure 5), peaks of a single lattice can be identified at 18 and also at 25 mN/m (Table 1). The variation of the tilt azimuth seems to increase with increasing surface pressure. For 2-hexadecanol (Figure 6), an opposite trend is observed. Here, the peaks corresponding to a lattice with NNNtilted chains become more pronounced with increasing surface pressure. At 40 mN/m, the peak positions can be determined (Table 2). The lattice parameters are a ) 4.907 Å, b ) 8.654 Å, and the in-plane area per molecule Axy is 21.2 Å2. The chains now are only slightly tilted by about 12°, and the cross-sectional area amounts to 20.8 Å2. The intensity distribution of 2-hydroxypalmitic acid allows no determination of a lattice at any pressure. However, in each diffraction pattern presented here, one characteristic value can be determined very precisely: the position of the intensity maximum in the xydirection at Qz ) 0 Å-1 (Tables 1-3). This corresponds to the (02) peak of a lattice with NN-tilted chains, from which the length of the b axis (bNN) can be calculated. If the diffraction curve ends in a sharp edge toward low Qxy, both the Qxy and the Qz positions of the (02) peak of a lattice with NNN-tilted chains can also be determined (Tables 5 and 6). The precision of Qxy is one order of magnitude lower than usual, and the fwhm cannot be estimated with reasonable precision. However, it allows the estimation of the length of the b axis in the limiting case of NNN-tilted chains (Tables 5 and 6). As the (02) peak almost does not shift in the z-direction, Qz can be determined with the usual precision and allows the
02 (NN) Qz (Å-1)
(Å-1)
25 mN/m 35 mN/m 45 mN/m
1.450 0.040 1.454 0.035 1.461 0.029 1.471 0.019
02 (NNN)a Qxy (Å-1) Qza (Å-1)
0
1.35
0.57
0
1.38
0.52
0
1.40
0.47
0
1.43
0.37
a The xy-position of the (02) peak in the limiting case of NNNtilted chains cannot be determined as precisely as usual, and the fwhm cannot be determined with a tolerable accuracy.
Table 4. Lattice Parameters for 2-Monopalmitoyl-Glycerol 2-monopalmitoyl-glycerol, 13 °C aa (Å)
b (Å)
18 mN/m 25 mN/m 40 mN/m
8.684 26.5 8.667 25.2 8.571
a
6.09 5.82
Axy (Å2) t (deg) Ao (Å2) 40 36
20.3 20.3
The a-spacing cannot be determined as precisely as usual.
Table 5. Characteristic Parameters Which Can Be Determined for 2-Hexadecanol at 10, 20, and 30 mN/m: Polar Tilt Angle t, the b-Spacing in the Limiting Case of NN-Tilted Chains bNN, and That in the Limiting Case of NNN-Tilted Chains bNNNa 2-hexadedanol, 25 °C
bNN (Å)
bNNNb (Å)
t (deg)
10 mN/m 20 mN/m 30 mN/m
8.672 8.631 8.589
9.45 9.24 8.91
>30 25 19
a At 40 mN/m, the diffraction pattern can be ascribed to a single lattice with NNN-tilted chains. The lattice parameters are a ) 4.907 Å, b ) 8.654 Å, Axy ) 21.2 Å2, t ) 12°, and Ao ) 20.8 Å2.b bNNN cannot be determined as precisely as usual.
calculation of the polar tilt angle for 2-hexadecanol and 2-hydroxypalmitic acid (Tables 5 and 6). Until now, attention was focused on the interpretation of the diffraction patterns. Now the information obtained is used to discuss the reason for a distorted packing of alkyl chains. The bNN value provides insight into the lattice perpendicular to the tilt azimuth. For each substance, it is larger than 8.66 Å at the lowest surface pressure investigated. Assuming the chains to be packed hexagonally perpendicular to their axes, this value
6492 Langmuir, Vol. 14, No. 22, 1998
Weidemann et al.
Table 6. Characteristic Parameters Which Can Be Determined for 2-Hydroxypalmitic Acid: Polar Tilt Angle t, the b-Spacing in the Limiting Case of NN-Tilted Chains bNN, and that in the Limiting Case of NNN-Tilted Chains bNNN
Å at 25 mN/m to 40 Å at 40 mN/m. This corresponds to an increased variation of the tilt azimuth with increasing surface pressure. In 2-hydroxypalmitic acid monolayers, the positional correlation length is found to increase from about 50 Å at 18 mN/m to about 100 Å at 45 mN/m.
2-hydroxypalmitic acid, pH 2, 24 °C
bNN (Å)
bNNNa (Å)
t (deg)
Conclusions
18 mN/m 25 mN/m 35 mN/m 45 mN/m
8.666 8.643 8.601 8.543
9.45 9.11 8.98 8.79
23 21 19 15
Langmuir monolayers of several substances, such as 2-monopalmitoyl-glycerol, 2-hexadecanol, and 2-hydroxypalmitic acid, reveal diffraction patterns, in which the diffracted intensity is distributed along a characteristic arc. For hexagonal packing of alkyl chains (i.e., a hexagonal lattice in the plane perpendicular to the chains), all peaks are approximately located on a circle. Deviations from this curve result from a distortion of the alkyl chain packing. The observed diffraction patterns were identified as the superposition of lattices with varying tilt azimuth of alkyl chains. A variation of the polar tilt angle cannot explain the observed intensity distributions. The better understanding of the shape of the intensity distributions allows the determination of characteristic parameters of the lattice. The b-spacing in the limiting case of NN-tilted chains (bNN) provides insight into the lattice perpendicular to the tilt azimuth. For the substances studied, this spacing is much larger than that of an undistorted alkyl chain (b ) 8.32 Å, corresponding to a cross-sectional area of 20.0 Å2 typical for a free rotator phase of alkyl chains). Even the high cross-sectional area of 20.8 Å2 cannot explain the high bNN values. Evidently, the chain packing is considerably distorted. A simple discussion of the geometry of the headgroup and alkyl chain lattices shows that the chain packing needs to be distorted to allow an adaptation of alkyl chains to headgroups which are too large perpendicular to the chain tilt direction. Obviously, a limit for the distortion of the alkyl chain packing does exist in a free rotator phase, and disorder is induced when the distortion exceeds this limit. We find disorder if bNN amounts to about 8.6 Å for polar tilt angles t < 30° or to about 8.7 Å for 30° < t < 40°.
a
bNNN cannot be determined as precisely as usual.
corresponds to a cross-sectional area of 21.6 Å2. Thus, perpendicular to the chain tilt azimuth, the headgroup is much larger than an alkyl chain. Consequently, the chain packing is considerably distorted. This also becomes evident from the observation that, in the experimental curves, the Qxy value changes less with Qz than suggested by our calculations. These large bNN values result in a large variation of the tilt azimuth. Increasing surface pressure decreases the bNN value slightly, thereby decreasing the misfit between headgroup and alkyl chain. Whether the misfit produces a variation of the tilt azimuth depends on the polar tilt angle, which is also decreasing with increasing surface pressure. At smaller tilt angles, this variation occurs even with smaller misfits, whereas at larger tilt angles the molecules are able to compensate such small misfits without azimuth variation. This explains the differences in scattering behavior as a function of surface pressure observed for the different substances. For 2-hexadecanol, the cross-sectional area of alkyl chains is very high (20.8 Å2). Obviously, the methyl chain branching causes a widening of the chain packing. The polar tilt angles found for this substance are rather small. A similar behavior is found for 2-hydroxypalmitic acid. 2-Monopalmitoyl-glycerol behaves differently: the polar tilt angles are high, but the cross-sectional area of alkyl chains is only slightly increased (Ao ) 20.3 Å2). Evidently, a large headgroup leads either to a widening of the chain packing or to large polar tilt angles. For all substances, the positional correlation length can be evaluated from the (02) peak in the limiting case of NN-tilted chains. 2-Hexadecanol reveals the lowest fwhm (Qxy), and the positional correlation length ξ amounts to more than 100 Å. The positional correlation length in 2-monopalmitoyl-glycerol layers decreases from about 70
Acknowledgment. Financial assistance from the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie is gratefully acknowledged. The authors are grateful to C. DeWolf and V. M. Kaganer for helpful discussions. We also thank K. Kjaer for help with setting up the X-ray experiment. LA980188O
