Molecular Orientation in Langmuir Films of 12-Hydroxystearic Acid

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Langmuir 1998, 14, 6249-6255

6249

Molecular Orientation in Langmuir Films of 12-Hydroxystearic Acid Studied by Infrared External-Reflection Spectroscopy H. Sakai* and J. Umemura Institute for Chemical Research, Kyoto University, Uji, Kyoto-Fu 611-0011, Japan Received September 8, 1997. In Final Form: August 5, 1998 12-Hydroxystearic acid is known to exhibit a wide plateau region between 0.3 and 0.95 nm2/molecule in the π-A isotherm. In situ polarized FT-IR external-reflection spectra of Langmuir (L) films of 12hydroxystearic acid on the water surface were recorded under various surface areas, and the molecularorientation angles were quantitatively evaluated. At the final stage of the plateau region (0.4 nm2/molecule), the orientation angle of the hydrocarbon chain was about 55° from the surface normal. Upon monolayer compression, however, the angle decreased to about 28° in the solid-phase region. This change corresponds well to the result in Langmuir-Blodgett films that was reported earlier. In addition, it was elucidated that the hydrocarbon chain tended to become random during the surface pressure relaxation.

Introduction Langmuir (L) films at the air-water interface exhibit various types of π-A isotherms (various phase transitions) depending on their molecular nature.1-3 Specifically, bipolar molecules show striking π-A isotherms.4-22 It is of considerable concern in many aspects to unravel the molecular configuration in L films under corresponding π-A isotherms. In a normal L film such as that of monopolar fatty acid, the polar group attaches to the water * To whom correspondence should be addressed. Present address: Heian Jogakuin (Saint Agnes’) College, Nampeidai, Takatsuki, Osaka-Fu 569-1092, Japan. FAX: 81-726-96-4919. E-mail: [email protected]. (1) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience Publishers: New York, 1966. (2) Langmuir-Blodgett Films; Robert, G. G., Ed.; Plenum Press: New York, 1990. (3) Ulman, A. An Introduction to Ultrathin Organic Films; Academic Press: Boston, 1991. (4) Adam, N. K.; Jessop, G. Proc. R. Soc. London Ser. A 1926, 112, 376. (5) Adam, N. K.; Danielli, J. F.; Harding, J. B. Proc. R. Soc. London Ser. A 1934, 147, 491. (6) Davies, J. T. Trans. Faraday Soc. 1948, 44, 909. (7) Goddard, E. D.; Alexander, A. E. Biochem. J. 1950, 47, 331. (8) Jeffers, P. M.; Daen, J. J. Phys. Chem. 1965, 69, 2368. (9) Tinoco, J.; Ghosh, D.; Keith, A. D. Biochim. Biophys. Acta 1972, 274, 279. (10) Cadenhead, D. A.; Mu¨ller-Landau, F. Biochim. Biophys. Acta 1973, 307, 279. (11) Cadenhead, D. A.; Mu¨ller-Landau, F. J. Colloid Interface Sci. 1974, 49, 131. (12) Cadenhead, D. A.; Kellner, B. M. J.; Mu¨ller-Landau, F. Biochim. Biophys. Acta 1975, 382, 253. (13) Ueno, M.; Kawanabe, M.; Meguro, K. J. Colloid Interface Sci. 1975, 51, 32. (14) Tachibana, T.; Hori, K. J. Colloid Interface Sci. 1977, 61, 398. (15) Kellner, B. M.; Cadenhead, D. A. J. Colloid Interface Sci. 1978, 63, 452. (16) Tachibana, T.; Yoshizumi, T.; Hori, K. Bull. Chem. Soc. Jpn. 1979, 52, 34. (17) Kellner, B. M. J.; Cadenhead, D. A. Chem. Phys. Lipids 1979, 23, 41. (18) Nagarajan, M. K.; Shah, J. P. J. Colloid Interface Sci. 1981, 80, 7. (19) Vogel, V.; Mo¨bius, D. Thin Solid Films 1985, 132, 205. (20) Lewis, T. J.; Taylor, D. M.; Llewellyn, J. P.; Salvagno, S.; Stirling, C. J. M. Thin Solid Films 1985, 133, 243. (21) Menger, F. M.; Richardson, S. D.; Wood, M. G., Jr.; Sherrod, M. J. Langmuir 1989, 5, 833. (22) Hasegawa, T.; Umemura, J.; Takenaka, T. Thin Solid Films 1992, 210/211, 583.

surface, while the hydrophobic chain directs away from the surface. In a bipolar molecule it is more complicated, since the molecule has two separated polar groups. 12-Hydroxystearic acid has a wide plateau region in the π-A isotherm. To date, some studies on the acid have been performed by surface pressure and surface potential measurements,14,16,18,21 and it has been accepted that the plateau represents the process during which the hydroxy group is forced out of the water surface as the film is compressed. These methods clarified the macroscopic features of this L film. However, the microscopic aspects have not been studied yet, except for the indirect study of Langmuir-Blodgett films of 12-hydroxystearic acid by Fourier transform infrared (FT-IR) metal overlayer attenuated total reflection (ATR) spectroscopy,22 in which the change of the molecular orientation was qualitatively clarified. Various methods can be applied to elucidate the microscopic profile of L films; grazing-incidence X-ray diffraction,23-25 optical second-harmonic generation,26 sum-frequency vibrational spectroscopy,27 Raman spectroscopy,28 and infrared spectroscopy.29-44 Among these, infrared spectroscopy has the advantage of being easy to (23) Kjaer, K.; Als-Nielsen, J.; Helm, C. A.; Tippman-Krayer, P.; Mo¨wald, H. J. Phys. Chem. 1989, 93, 3200. (24) Kenn, R. M.; Bo¨hm, C.; Bibo, A. M.; Peterson, I. R.; Mo¨wald, H.; Als-Nielsen, J.; Kjaer, K. J. Phys. Chem. 1991, 95, 2092. (25) Wang, J.-L.; Leveiller, F.; Jacquemain, D.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1994, 116, 1192. (26) Rasing, Th.; Shen, Y. R.; Kim, M. W.; Grubb, S. Phys. Rev. Lett. 1985, 55, 2903. (27) Guyot-Sionnest, P.; Hunt, J. H.; Shen, Y. R. Phys. Rev. Lett. 1987, 59, 1597. (28) Kawai, T.; Umemura, J.; Takenaka, T. Chem. Phys. Lett. 1989, 162, 243. (29) Dluhy, R. A.; Cornell, D. G. J. Phys. Chem. 1985, 89, 3195. (30) Dluhy, R. A. J. Phys. Chem. 1986, 90, 1373. (31) Mitchell, M. L.; Dluhy, R. A. J. Am. Chem. Soc. 1988, 110, 712. (32) Fina, L. J.; Tung, Y.-S. Appl. Spectrosc. 1991, 6, 986. (33) Tung, Y.-S.; Gao, T.; Rosen, M. J.; Valentini, J. E.; Fina, L. J. Appl. Spectrosc. 1993, 47, 1643. (34) Sakai, H.; Umemura, J. Chem. Lett. 1993, 2167. (35) Gericke, A.; Michailov, A. V.; Hu¨hnerfuss, H. Vibr. Spectrosc. 1993, 4, 335. (36) Gericke, A.; Hu¨hnerfuss, H. J. Phys. Chem. 1993, 97, 12899. (37) Buontempo, J. T.; Rice, S. A. J. Chem. Phys. 1993, 98, 5825. (38) Buontempo, J. T.; Rice, S. A. J. Chem. Phys. 1993, 98, 5835. (39) Blaudez, D.; Buffeteau, T.; Cornut, J. C.; Desbat, B.; Escafre, N.; Pezolet, M.; Turlet, J. M. Appl. Spectrosc. 1993, 47, 869.

S0743-7463(97)01016-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/25/1998

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use, nondestructive against samples, and sensitive to changes in the molecular conformation. In a previous study44 the polarized FT-IR external-reflection spectra (ERS) of L films of stearic acid and cadmium stearate were recorded. In the stearic acid monolayer, the orientation angle of the hydrocarbon chain from the surface normal decreased from 20° to almost 0° upon monolayer compression. In the cadmium stearate monolayer, on the other hand, the orientation angle (near 0°) did not change upon monolayer compression. In the present work, FT-IR/ERS of the L film of 12hydroxystearic acid on the water surface was measured under various surface areas and the molecular-orientation angles were quantitatively evaluated. In addition, the mechanism of surface pressure relaxation was also investigated using this method. Mechanisms of monolayer instability have attracted a growing interest, and in order to clarify them many researchers have studied pressure changes at constant surface areas 45-52 or surface-area changes at constant pressures.53-57 These relaxations are due to the viscoelasticity of the film and therefore are dynamic phenomena. Consequently, in situ examination needs to be conducted for these phenomena. X-ray diffraction was used to study a microscopic relaxation mechanism in Langmuir films of heneicosanol.58 FT-IR/ ERS is also deemed to be appropriate for this purpose. Clarification on the molecular behavior is not only important for the understanding of the phenomenon itself but also of the stability of the L film, which is the essential factor in fabricating Langmuir-Blodgett films. So far, limited work has been done on the spectral study of surface pressure relaxation,52 especially on the quantitative analysis. It is thus the object of this study to investigate the structural change at the molecular level in the L film during the surface pressure relaxation using FT-IR/ERS. Experimental Section 12-Hydroxystearic acid (99% purity) was purchased from Sigma and used without further purification. All other reagents were either highly pure (>98%) or of spectroscopic grade. Distilled water was prepared by a modified Mitamura Riken Model PLS-DFR automatic lab still consisting of a reverse-osmosis module, an ion-exchange column, and a double distiller. (40) Blaudez, D.; Buffeteau, T.; Cornut, J. C.; Desbat, B.; Escafre, N.; Pezolet, M.; Turlet, J. M. Thin Solid Films 1994, 242, 146. (41) Flach, C. R.; Brauner, J. W.; Mendelsohn, R. Biophys. J. 1993, 65, 1994. (42) Pastrana-Rios, B.; Flach, C. R.; Brauner, J. W.; Mautone, A. J.; Mendelsohn, R. Biochemistry 1994, 33, 5121. (43) Ren, Y.; Meuse, C. W.; Hsu, S. L.; Stidham, H. D. J. Phys. Chem. 1994, 98, 8424. (44) Sakai, H.; Umemura, J. Bull. Chem. Soc. Jpn. 1997, 70, 1027. (45) Rabinovitch, W.; Robertson, R. F.; Mason, S. G. Can. J. Chem. 1960, 38, 1881. (46) Gabrielli, G.; Guarini, G. G. T.; Ferroni, E. J. Colloid Interface Sci. 1976, 54, 424. (47) Tabak, S. A.; Notter, R. H.; Ultman, J. S. J. Colloid Interface Sci. 1977, 60, 117. (48) Bois, A. G.; Panaiotov, I. I.; Baret, J. F. Chem. Phys. Lipids 1984, 34, 265. (49) Bois, A. G.; Baret, J. F.; Kulkarni, V. S.; Panaiotov, I. I.; Ivanova, M. G. Langmuir 1988, 4, 1358. (50) Adams, J.; Buske, A.; Duran, R. S. Macromolecules 1993, 26, 2871. (51) Wang, L.-F.; Kuo, J.-F.; Chen, C.-Y. Colloid Polym. Sci. 1995, 273, 426. (52) Sakai, H.; Umemura, J. Chem. Lett. 1996, 465. (53) Neuman, R. D. J. Colloid Interface Sci. 1976, 56, 505. (54) Vollhardt, D.; Retter, U. J. Phys. Chem. 1991, 95, 3723. (55) Vollhardt, D.; Retter, U.; Siegel, S. Thin Solid Films 1991, 199, 189. (56) Vollhardt, D.; Retter, U. Langmuir 1992, 8, 309. (57) Wang, L. F.; Kuo, J. F.; Chen, C. Y. Mater. Chem. Phys. 1995, 40, 197. (58) Lin, B.; Peng, J. B.; Ketterson, J. B.; Dutta, P.; Thomas, B. N.; Buontempo, J.; Rice, S. A. J. Chem. Phys. 1989, 90 2393.

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Figure 1. π-A isotherm of 12-hydroxystearic acid on the water surface at 25 °C. The L films of 12-hydroxystearic acid were prepared by spreading 4.5 or 9.0 µL of 8.12 × 10-4 M benzene solution of the acid on the water surface at pH 4.0, controlled by HCl. A trough with an 80 × 22 mm2 effective surface area attached to a Specac 19650 monolayer/grazing angle accessory was used. An S. T. Japan Model STJ-100 wire-grid polarizer with 1300 line/mm Al wires on KRS-5 was settled just above the water surface to optimize the polarization.59 Although a band-pass filter was used in the previous study, due to concern that the infrared radiation may perturb the L film,60 it was not used in the present work, because the film had significant surface pressure and the molecules were hardly perturbed within the measurement time scale. In fact, the spectra appeared the same within the experimental error regardless of whether the filter was used or not. In this way, the spectra could be measured in a wide wavenumber range. FT-IR/ERS of L films were recorded on a Nicolet Magna 850 FT-IR spectrophotometer equipped with a DTGS detector with a resolution of 8 cm-1. For selecting the best incident-beam condition, measurements were conducted at several incident angles with p- and s-polarized beam. Finally, the incident angle of 40° with an s-polarized beam was chosen. First, the background spectrum was collected with 1500 scans at the pure water surface, and then the solution was spread out. After waiting for 10 min to allow the solvent to be completely evaporated, the L film was compressed to various surface areas, and FT-IR/ERS were recorded with 300-600 scans. Unfortunately, due to the apparatus design, measurements covering a wide range of surface area could not be performed. Measurements were carried out at surface areas from 0.80 to 0.48 and from 0.40 to 0.21 nm2/molecule, separately. In addition, FT-IR/ERS were measured during the surface pressure relaxation. As in the previous experiment, the background spectrum was collected with 1500 scans for the water surface, and then 9.0 µL of benzene solution was spread out. After 10 min of evaporation, the L film was compressed at a constant velocity of 0.03 nm2 molecule-1 min-1 down to the surface area of 0.21 nm2/molecule, which is typical of the solid-phase region. Immediately after the compression, 50 FT-IR/ERS were successively recorded with 100 scans each. The transmission spectra of isotropic KBr pellets of 12hydroxystearic acid (0.0222, 0.0422, 0.0648, 0.0845, 0.1083 mg in 200 mg KBr) and the temperature dependence (from 25 °C to 75 °C) of one pellet (0.1083 mg) with a resolution of 8 cm-1 were recorded on the same FT-IR spectrophotometer with 300 scans for determining the extinction coefficient of the bulk state. The π-A isotherm and surface-pressure-relaxation isotherm were measured with a Wilhelmy balance attached to a Kyowa Interface Science Model HBM-AP Langmuir trough. The compression velocity was 0.0205 nm2 molecule-1 min-1 in the measurement of the π-A isotherm and 0.03 nm2 molecule-1 min-1 in the surface-pressure-relaxation isotherm. All experiments were performed at 25 °C.

Results and Discussion π-A Isotherm. The π-A isotherm of 12-hydroxystearic acid at 25 °C is shown in Figure 1. It consists of a liquid(59) Mendelsohn, R.; Brauner, J. W.; Gericke, A. Annu. Rev. Phys. Chem. 1995, 46, 305. (60) Sakai, H.; Umemura, J. Langmuir 1997, 13, 502.

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Figure 2. FT-IR/ERS of an L film of 12-hydroxystearic acid measured by an s-polarized beam at a surface area of 0.21 nm2/ molecule.

expanded (LE) region, plateau (P) region, and solid (S) region. The limiting area, which is the extrapolated area of the solid region at zero pressure, is 0.23 nm2/molecule. This area is a little larger than that of stearic acid (0.2 nm2/molecule)44 because of the additional hydroxy group. It is presumed in some studies14,16,18,21 that the molecule is bent with both the carboxyl group and the hydroxy group attached to the water surface in the liquid-expanded region, the molecule is straight with only the carboxyl group on the water surface in the solid region, and the plateau represents the process during which the hydroxy group is forced out of the water surface as the film is compressed. Polarized FT-IR External-Reflection Spectra. Figure 2 shows the ERS of an L film of 12-hydroxystearic acid at 0.21 nm2/molecule between 4000 and 500 cm-1. In this frequency region the antisymmetric and symmetric CH2 stretching bands (νa(CH2) and νs(CH2)) at ca. 2917 and 2850 cm-1, respectively, the carbonyl stretching band (ν(CdO)) at ca. 1720 cm-1, the CH2 scissoring band (δ(CH2)) at ca. 1470 cm-1, and the bands of water at ca. 3580, 1660, and 850 cm-1 were observed. In the external reflection measurements of L films on the water surface, the reflection absorbances appear positive or negative (upward or downward) depending on the direction of the transition moment, the angle of incidence, and the polarization of the incident beam. At the present condition, the observed IR bands of the film mentioned above show negative reflection absorbances, while the bands of water show positive reflection absorbances. Although the discussion about the water bands was not made in this article, the bands could be simulated by the calculation that was introduced below. The wavenumber (1720 cm-1) of the carbonyl stretching band reveals that the carbonyl groups form hydrogen bonds.36 In addition, the surfactant molecule in the L film was not ionized, since the carboxylate stretching bands did not appear between 1600 and 1400 cm-1. From the number of peaks of the CH2 scissoring band and their frequencies, the crystal system of the sample can be recognized. Unfortunately, however, due to the low resolution and the weak intensity of the band in the present measurement, the precise estimation was difficult. From now on the discussion is concentrated upon the CH2 stretching bands. The ERS of L films of 12-hydroxystearic acid in the CH2 stretching region are presented in Figure 3 under various surface areas. At a first glance, it is observed that the intensities of the antisymmetric and symmetric CH2 stretching bands increase as the film is compressed. Wavenumber of νa(CH2). It is known that the wavenumber of the νa(CH2) band is sensitive to the

Figure 3. FT-IR/ERS of the L film of 12-hydroxystearic acid measured by an s-polarized beam at various surface areas.

Figure 4. Wavenumber of νa(CH2) in the L film of 12hydroxystearic acid vs surface area. The error bars are estimated from observed band shape distortions and noise levels in the background region.

conformation of the molecule.34,61,62 Figure 4 shows the plot of the wavenumber of the νa(CH2) band presented in Figure 3 against the surface area. The errors were estimated from the observed band shape distortions and noise levels in the background region. The value of ca. 2919 cm-1 in the small surface areas is indicative of the mainly all-trans conformer of the alkyl chain with less gauche conformers, and higher wavenumbers in the surface areas larger than 0.48 nm2 molecule-1 indicate inclusion of gauche conformers, although the errors in the latter regions are very large. Peak Intensities. The peak intensities of νa(CH2) and νs(CH2) bands for the 12-hydroxystearic acid film shown in Figure 3 are plotted against the surface area in Figure 5. The error bars are estimated from the spectral noise in the baseline region. The intensity data were first calibrated for the surface density, since the peak intensity is contributed by the surface density, the molecular conformation, and the molecular orientation. The calibration was based on the difference in the surface density to the point at surface area 0.23 nm2/molecule, which is the limiting area of the solid region. After the calibration, information about the molecular configuration can be extracted explicitly. Although the peak intensities of both bands are invariant at large surface areas, the absolute peak intensities increase upon monolayer compression at surface areas smaller than 0.4 nm2/molecule. Calculation of Molecular Orientation. For calculating the molecular orientation, the formulas derived by (61) Snyder, R. G.; Strauss, H. L.; Elliger, C. A. J. Phys. Chem. 1982, 86, 5145. (62) Casal, H. L.; Mantsch, H. H. Biochim. Biophys. Acta 1984, 779. 381.

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Figure 5. Peak intensities of νa(CH2) (O) and νs(CH2) (b) in the L film of 12-hydroxystearic acid vs surface area. The error bars are estimated from the spectral noise in the baseline region.

Hasegawa et al.63 were used as in the previous paper.44 These formulas are suitable for studying L films, because one can calculate the molecular-orientation angles using only one polarized beam measurement. Of course, the method employing both the p- and s-polarized beams is more precise if the L-film structure is stable with time. However, the state of L films sometimes changes, especially during the surface pressure relaxation, as shown below, and hence the present method is better in such a case. In this study only an s-polarized beam was used, and three-layer model that comprises air/film/water was employed for the theoretical considerations. The air and water were assumed isotropic and the film was considered uniaxial. For a theoretical calculation of the reflection absorbance, the optical constants of the media, the angle of incidence, film thickness, and wavelength of the band are needed. Among these parameters, the thickness, the index of refraction, and the extinction coefficient of the film were considered to depend on the molecular orientation, and it was assumed that the rest of parameters did not depend on the molecular orientation. An ellipsoid of the extinction coefficient was considered because of the optical anisotropy of the uniaxial crystal in the L film. This ellipsoid relates the extinction coefficient in bulk to that in the film through the orientation angle of the transition moment. By comparing the calculated value with the observed value, the most appropriate orientation values can be determined. Furthermore, since the directions of the transition moment of two bands, νa(CH2) and νs(CH2), and the hydrocarbon chain axis are mutually orthogonal, the molecular orientation can be calculated. The extinction coefficients of the peak maxima of the νa(CH2) and νs(CH2) bands of stearic acid in bulk at a resolution of 8 cm-1 are 0.231 and 0.136, respectively, at room temperature.44 The extinction coefficients of 12hydroxystearic acid at a resolution of 8 cm-1 could be determined by comparing the transmission intensities of KBr pellets of stearic acid and 12-hydroxystearic acid. However, since the peak wavenumbers of the bands changed markedly in the L film of 12-hydroxystearic acid upon compression, as shown above, the extinction coefficient for each band with a particular wavenumber must be decided. The transmission intensities of the KBr pellet were measured at various temperatures, and the extinction coefficients for bands with particular wavenumbers could be determined (0.1488-0.1152 at νa(CH2) and 0.0958-0.0741 at νs(CH2)) therefrom. These values seem to be smaller than expected. We think the reasons are as follows: (1) the resolution was 8 cm-1, (2) the methylene (63) Hasegawa, T.; Takeda, S.; Kawaguchi, A.; Umemura, J. Langmuir 1995, 11, 1236.

Figure 6. The orientation angles of the transition moments of (A) νa(CH2) (O) and (B) νs(CH2) (b) in the L film of 12-hydroxystearic acid vs surface area.

chain is divided by a hydroxy group in the molecule of 12-hydroxystearic acid, and (3) the redistribution of electrons occurs near the hydroxy group, thus affecting the methylene intensities. The formulas were modified about the refractive index and the film thickness, because the molecular-orientation angle changes very much upon monolayer compression in the present case, as shown below. The refractive index of the L film changes depending on the molecular orientation according to eq 1 (see Appendix),

n2o )

(

2nx2nz2

)

1/2

nz2(cos2 γ + 1) + nx2 sin2 γ

(1)

where γ is the molecular orientation angle of the hydrocarbon chain from the surface normal, n2o is the ordinary refractive index of the film, and nx (1.48) and nz (1.56)64 are the molecular-fixed refractive index directed perpendicular and parallel to the molecular axis, respectively. The film thickness also depends on the molecular orientation. The simple equation such as h2 ) 25 cos γ is sometimes used in the estimation of the film thickness,33 where h2 is the film thickness in angstroms. However, since the orientation angle is large in the present case, as shown below, eq 2 seems to be more precise:

h2 ) 25 cos γ + 5.4 sin γ

(2)

This equation was derived by taking into account the length (25 Å) and width (5.4 Å) of the 12-hydroxystearic acid molecule. Figure 6 shows the orientation angles of the transition moments, νa(CH2) and νs(CH2), of the L film of 12hydroxystearic acid against the surface area. The angles of the transition moments of two bands are roughly 60° from the surface normal at the initial stage of the plateau region; however, upon further compression, the angles start to increase at the final stage of the plateau region and reach almost 70° in the solid-phase region. (64) Paudler, M.; Ruth, J.; Riegler, H. Langmuir 1992, 8, 184.

Langmuir Films of 12-Hydroxystearic Acid

Figure 7. Molecular-orientation angle in the L film of 12hydroxystearic acid vs surface area.

The orientation angles of the hydrocarbon chain axes of 12-hydroxystearic acid in the L film plotted against the surface area are shown in Figure 7. Although the error in the estimation of the orientation angle is very large, it is centered roughly at 55° from the surface normal in the plateau region. However, upon monolayer compression, the angle decreases at surface areas smaller than 0.4 nm2/ molecule, and reaches about 28° in the solid-phase region. As mentioned above, the alkyl chain contains more gauche conformer in the plateau region; hence the molecule cannot be regarded as a planar one. In this case, the angle represents the average of all methylene segments. Considering both facts that in the plateau region the hydrocarbon chain contains more gauche conformer and the angle of 55° is very close to the random orientationalangle 54°, it does not conflict with the disordered state of molecules. Since the error bar is very large in the orientation angle in the plateau region, the detail is not clear; however, it starts to decrease from the final part of the plateau. This tendency coincides well with the results of an ATR study in LB films.22 As the film is compressed, the conformation gets to be ordered and the angle starts to show a value that represents the molecular orientation literally. In the solid region, the conformation is almost all-trans, as revealed by the wavenumber of νa(CH2). Therefore, the molecule can be regarded as being almost planar, and the change of the angle corresponds to the change of the orientation. To paraphrase, the orientation angle is represented properly at a surface area smaller than 0.4 nm2/molecule and just indicates the disordered state at a surface area larger than 0.4 nm2/molecule. Generally, the molecules form an island in the Langmuir film when the surface density is low. Rigorously speaking, the orientation analysis may need to incorporate this concept. However, the area of the IR spot is about 1 cm2. The result becomes the average of this area. Because the area is usually much larger than the size of islands, the average of the surface density is the same as the homogeneous film. Here, we treat the system as the average. The angle of 28° in the solid-phase region is larger than that of stearic acid, probably because the hydroxy group hinders the vertical orientation of the hydrocarbon chain. On compression, the molecules become vertical and slide. It is presumed that the hydrogen bond formation occurs through the hydroxy group when the molecular angle reaches about 28°. According to the X-ray diffraction measurements conducted on a powder of 12-hydroxystearic acid,16 its crystal structure resembles that of the B-form of stearic acid, whose crystal angle is 27.24°.65 This crystal angle is very close to our result. Moreover, (65) Goto, M.; Asada, E. Bull. Chem. Soc. Jpn. 1978, 51, 2456.

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Figure 8. Surface-pressure-relaxation isotherm of the L film of 12-hydroxystearic acid compressed to the surface area of 0.21 nm2/molecule.

the hydrogen bond formation is verified in that powder sample of 12-hydroxystearic acid by IR.16 Finally, we will add some comments on the refractive index. Fortunately or not, the result for the calculated angle was almost the same (difference of about 0.5°) regardless of the usage of eq 1. This is because the molecularly-fixed refractive indices directed perpendicular and parallel to the molecular axis of 12-hydroxystearic acid are not so different from each other. This equation seems to become more significant in the case where the two refractive indices are appreciably different. Surface Pressure Relaxation. When an L film is compressed and held at a certain surface area, the surface pressure decreases. This is because the L film is not in thermodynamic equilibrium. As the cause of monolayer instability, some mechanisms have been presumed such as a transition between two two-dimensional phases, a desorption into the bulk phase, the collapse of the film into a three-dimensional state, and so on.45-58 In the present work, an L film of 12-hydroxystearic acid was compressed to a surface area of 0.21 nm2/molecule, which is typical of the solid-phase region, and then the surface pressure and FT-IR/ERS were recorded with the time lapse in order to examine the structural change at the molecular level during the surface pressure relaxation. Figure 8 shows the surface-pressure-relaxation isotherm of the L film of 12-hydroxystearic acid compressed to the surface area of 0.21 nm2/molecule. We defined t ) 0 as the time that the barrier was stopped. Initially, the pressure steeply decreases and then the decrease becomes more and more gradual. The trend somewhat resembles that of stearic acid compressed to the LS region.52 In a previous paper52 it was reported that the mechanism of the pressure relaxation in the L film of stearic acid was the collapse of the monolayer. Some molecules in the compressed monolayer slip out upward in order to release the excess pressure, and transform from trans to gauche conformer by acquiring free space. Then, the surface pressure decreases owing to the decrease in number of molecules in the two-dimensional monolayer. Moreover, it is well accepted that a monolayer is metastable above its equilibrium spreading pressure (ESP), and the formation of three-dimensional structures occurs.66 It is reported that the ESP of 12-hydroxystearic acid is 5.7 mN/ m.67 We can anticipate that the mechanism of the relaxation is collapse. For further analysis, we considered the transition from monolayer to three-dimensional structure by analogy with the chemical reaction. A curve fit was conducted by using (66) Kato, T.; Matsumoto, N.; Kawano, M.; Suzuki, N.; Araki, T.; Iriyama, K. Thin Solid Films 1994, 242, 223. (67) Rakshit, A. K.; Zografi, G.; Jalal, I. M.; Gunstone, F. D. J. Colloid Interface Sci. 1981, 80, 466.

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entation angles were quantitatively evaluated. At the final stage of the plateau region (0.4 nm2/molecule) the orientation angle of the hydrocarbon chain was found to be about 55° from the surface normal; however, upon further monolayer compression, the angle started to decrease and reached about 28° in the solid-phase region. In addition, it was elucidated that the hydrocarbon chain tended to be disordered during the surface pressure relaxation. Appendix Figure 9. Peak intensities of νa(CH2) in the L film of 12-hydroxystearic acid vs time after compression.

the rate of reaction equation. As a result, the pressurerelaxation isotherm could be fitted with a first-order equation:

π - πe ) (π0 - πe) exp(-kt)

Our purpose is to derive equations of the ordinary and extraordinary indices of refraction depending on the molecular orientation in the L film. An index ellipsoid was introduced as

x2 y2 z2 + + )1 nx2 ny2 nz2

(3)

where π, π0, and πe are the surface pressure at time t and 0, and at equilibrium, respectively, and k is a rate constant. Since the π-A isotherm is linear in the pressure range of this relaxation measurement, the surface pressure is proportional to the surface concentration and hence it can be used in the equation instead of the concentration. It seems natural that the slip-out rate from the monolayer depends on the surface pressure. The surface pressure reaches a certain value at infinite time; the transition from monolayer to three-dimensional state stops at a certain extent. Only the molecules that cause extra surface pressure contribute to pressure relaxation. In addition, it can be concluded that desorption did not occur, because the pressure converged. The rate constant k was 0.029. The same analysis was conducted about the L film of stearic acid in the LS region using the result that was reported previously.52 Its rate coefficient was 0.18; namely, the pressure reached the equilibrium value much faster than that of 12-hydroxystearic acid. Since the rate constant does not depend on the concentration in the case of first-order formulation, the difference of the rate is due to the nature of the L film. This seems to be due to the high viscosity of the L film of 12-hydroxystearic acid by hydrogen bond formation through the hydroxy group. It also manifests in the different behavior after ordinary collapse pressure; the pressure decreases rapidly in stearic acid, while in 12-hydroxystearic acid the pressure starts to increase slowly. To confirm the process that was mentioned above, FTIR/ERS were recorded during the surface pressure relaxation. Figure 9 shows the peak intensities of νa(CH2) in the L film of 12-hydroxystearic acid against time after compression. The absolute value of the peak intensity changes in the manner similar to that of the surface pressure. Conducting the curve fit with eq 3, the rate constant was 0.021, which was close to that of the surface pressure. In addition, the molecular orientation was calculated with the results of ERS. It was found that the molecular angle actually changed from 23.3 to 32.1°. According to the mechanism of collapse, the increase of the angle is due to the random orientation of the slippedout hydrocarbon chains.

(A1)

where x, y, and z are the principal dielectric axes and nx, ny, and nz are the principal indices of refraction.68 It was supposed that the index ellipsoid can be adapted for each molecule. First of all, the molecule was considered to be standing vertically, and the principal dielectric axes (the moleculefixed axes) were matched with the space-fixed axes X, Y, and Z. The surface of an L film is in the XY plane, and the Z axis is the direction of the surface normal. The molecule was then rotated around the fixed molecular center of mass through three angles; counterclockwise rotation φ about the Z axis, counterclockwise rotation θ about the line of nodes N, which is defined as the intersection of the XY and xy planes, and counterclockwise rotation χ about the z axis. The angles θ and φ are polar coordinates, where θ is the angle between the Z and z axes, namely molecular orientation in the L film, and φ is the angle from the X axis to the projection of the z axis on the XY plane. The rotation can be expressed in a matrix form69

() ( x y z

)

cosφ cosθ cosχ - sinφ sinχ sinφ cosθ cosχ + cosφ sinχ -sinθ cosχ -cosφ cosθ sinχ - sinφ cosχ -sinφ cosθ sinχ + cosφ cosχ sinθ sinχ cosφ sinθ sinφ sinθ cosθ

)( ) X Y Z

(A2)

Equation A3, which is the equation of the index ellipsoid, represented in terms of the space-fixed axes, was derived by substituting eq A2 into eq A1:

[{(cos φ cos θ cos χ - sin φ sin χ)X + (sin φ cos θ cos χ + cos φ sin χ)Y + (-sin θ cos χ)Z}2/nx2] + [{(-cos φ cos θ sin χ sin φ cos χ)X + (-sin φ cos θ sin χ + cos φ cos χ)Y + (sin θ sin χ)Z}2/ny2] + [{(cos φ sin θ)X + (sin φ sin θ)Y + (cos θ)Z}2/nz2] ) 1 (A3)

Conclusion

Then, the film was assumed to be uniaxial, which means that angle φ is distributed randomly from 0 to 2π. By space averaging eq A3 about angle φ and taking into

Polarized FT-IR external reflection spectra of Langmuir films of 12-hydroxystearic acid on the water surface were measured under various surface areas as well as during the surface pressure relaxation, and the molecular ori-

(68) Born, M.; Wolf, E. Principles of Optics, 5th ed.; Pergamon Press: Oxford, U.K., 1975. (69) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955.

Langmuir Films of 12-Hydroxystearic Acid

Langmuir, Vol. 14, No. 21, 1998 6255

account the well-known relations

∫0

2π

sin φ dφ 2π

∫0

2π

)

∫0

)

∫0

2π

sin φ dφ 2π

cos φ dφ 2π

2π

2

ne2 ) nx2ny2nz2

)0

(A4)

(A8)

2

cos φ dφ 2π

)

1 2

(A5)

we obtained the final form eq A6:

(

cos2 θ cos2 χ + sin2 χ cos2 θ sin2 χ + cos2 χ + + 2nx2 2ny2

) (

cos2 θ cos2 χ + sin2 χ sin2 θ 2 X + + 2nz2 2nx2

) (

sin2 θ cos2 χ cos2 θ sin2 χ + cos2 χ sin2 θ 2 + Y + + 2 2 2ny 2nz nx2 2

2

ny2nz2 sin2 θ cos2 χ + nz2nx2 sin2 θ sin2 χ + nx2ny2 cos2 θ

)

Here, no and ne are the ordinary and extraordinary indices of refraction of the L film, respectively. Since nx, ny, and nz are unknown, eqs A7 and A8 cannot be used to calculate no and ne. However, the ordinary and extraordinary indices of refraction have been obtained for a film in which the molecule is vertically oriented.64 The extraordinary index of refraction of vertically oriented film could be regarded as nz, which is the molecular-fixed refractive index directed parallel to the molecular axis. It can be assumed that nx and ny are equal, because these two directions are not so different geometrically. The ordinary index of refraction can be considered as equal to nx ()ny). As a result of the above discussion, these two simplified equations were obtained:

sin θ sin χ cos2 θ 2 + Z ) 1 (A6) ny2 nz2

no2 )

Equation A6 can be considered as another index ellipsoid. The ultimate aim is to calculate the principal indices of refraction of this index ellipsoid:

2nx2ny2nz2 2

2

ne2 )

ny nz (cos θ cos χ + sin χ) + nz2nx2(cos2θ sin2χ + cos2χ) + nx2ny2 sin2θ 2

nz2(cos2 θ + 1) + nx2 sin2 θ nx2nz2 nz2 sin2 θ + nx2 cos2 θ

(A9)

(A10)

Acknowledgment. The authors thank Professor Masaru Nakahara of this laboratory for his kind support throughout the duration of this study.

no2 ) 2

2nx2nz2

2

(A7)

LA971016E