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J. Phys. Chem. B 2001, 105, 11178-11185
Simultaneous Evaluation of Molecular-Orientation and Optical Parameters in Ultrathin Films by Oscillators-Model Simulation and Infrared External-Reflection Spectrometry Takeshi Hasegawa,*,† Jujiro Nishijo,† Junzo Umemura,‡ and Wolfgang Theiss§ Kobe Pharmaceutical UniVersity, Motoyama-kita, Higashinada-ku, Kobe 658-8558, Japan; Institute for Chemical Research, Kyoto UniVersity, Gokasho, Uji, Kyoto-fu 611-0011, Japan; and M. Theiss Hard- and Software, Dr.-Bernhard-Klein-Strasse 110, D-52078 Aachen, Germany ReceiVed: May 8, 2001; In Final Form: August 5, 2001
A new analytical technique is presented for the simultaneous evaluation of molecular orientation and optical parameters in organic ultrathin films on a dielectric substrate by integration of oscillators-model simulation analysis and infrared external-reflection (ER) spectroscopy. The surface-normal and -tangential components of vibrational TO and LO modes in the film were independently represented by two dielectric dispersion functions with the use of Kim’s oscillators models. The reflection absorbance of each band in the ER spectra was analyzed by use of the two functions on the assumption of the anisotropic optical system. Two p-polarization infrared ER spectra observed at two angles of incidence were subjected to an optimization calculation, so that the parameters in the two functions were simultaneously converged. The converged results yielded refractive-index dispersions and orientation angles at the same time. As an example study, the molecular structure in a 5-monolayer cadmium stearate Langmuir-Blodgett (LB) film has been analyzed with the new technique. The evaluated optical parameters were consistent with other experimental results. The new technique has also revealed the fine molecular orientation around the R-carbon atom, which has not been shown experimentally thus far. The new method proved to enable us to discuss fine properties in thin condensed matter without using library values of optical parameters.
Introduction Langmuir-Blodgett (LB) films attract much interest from various fields in terms of nanoarchitectures, whose layer structures are easily controlled, which results in many possibilities for gas sensors,1 constructing mimic biomolecules,2 and so on. Molecular orientation analysis of an organic ultrathin film is a crucial matter to develop new molecular assemblies with specific functions. For the analysis of the organic thin films, Fourier transform infrared (FT-IR) spectrometry is one of the best analytical methods for its ultrahigh sensitivity, quantitativity, and abundance of chemical information. FT-IR spectrometry has, indeed, proved to be suitable for the quantitative evaluation of molecular orientation in monolayer-level films via polarization measurements.4,5 When physical properties of an ultrathin film are discussed using FT-IR spectra, two major matters have been focused on: band intensity and band location. Molecular orientation change is directly reflected by band intensity. The band intensity, in principle, obeys Beer’s law (A ) c), which relates absorbance (A) to absorptivity () of a band and concentration (c) at a unit cell length, in which the absorptivity is a scalar value. In an anisotropic media such as LB films, however, the absorptivity becomes a tensor, which makes the law complicated. In recent years, fine theoretical studies of the correlation between the absorptivity tensor and the electric field of irradiated infrared light have become possible in some cases.4,5 * To whom correspondence should be addressed. Fax: 078-435-2080. E-mail:
[email protected]. † Kobe Pharmaceutical University. ‡ Kyoto University. § M. Theiss Hard- and Software.
On the other hand, band location that is influenced by optical effects has also been an important physical issue. Since Berreman published a paper6 dealing with the band shift that is specifically found in ultrathin films on metal with p-polarization at an oblique angle of incidence, the shift has been highly noticed. The most important point of Berreman’s effect is that it is not derived from a chemical reaction, but from a pure optical effect. In this way, the band intensity and the band shift are both crucial to investigate finely the characteristics of the films. Nevertheless, it is unfortunate that they have been discussed separately thus far. For the band intensity analysis, Parikh and Allara4 developed a powerful algorithm by use of Yeh’s 4 × 4 transfer matrix method7 to theoretically regenerate the observed infrared spectra. Yeh’s method can take optical anisotropy into account through dielectric tensors. Prior to the theoretical analysis, they measured an infrared spectrum of an isotropic sample, so that the wavenumber dispersion of the absorption index (k) for each band is evaluated. A certain molecular orientation was assumed for the evaluation of the anisotropic absorption-index dispersion. With the anisotropic dispersion functions, the real part of the anisotropic refractive index was finally evaluated by the Kramers-Kronig transformation. By changing the orientation angles, iterative calculations were performed until the simulated spectrum became close to the observed spectrum. In a similar concept, on the other hand, Hasegawa et al.5 proposed another idea to evaluate the orientation angles. They merged Drude’s optically anisotropic theory7 into Hansen’s optical theory9 for stratified layers to yield a calculation algorithm of absorbance that is a function of molecular orientation. With this method, the orientation angles were evaluated directly from the observed band intensities without
10.1021/jp011739d CCC: $20.00 © 2001 American Chemical Society Published on Web 10/19/2001
Evaluation of Parameters in Ultrathin Films using iterative calculation, and they were found to be reliable in comparison to the results by X-ray analysis. In any case, however, we have a common issue that it is necessary to have reliable optical parameters such as refractive index, absorption index, and other related parameters before the analysis. In the conventional methods, the optical parameters have been evaluated by techniques other than FT-IR spectrometry, such as ellipsometry or by Kramers-Kronig transform analysis of bulk samples. This technical difference sometimes causes analytical errors due to sample-preparation difference or unexpected optical effects. Of note is that this technical difference often causes difference of band position (shift) due to the difference of optical geometries. Besides, the matter of band shift has not been directly discussed with respect to the molecular orientation. Nevertheless, the optical interaction between lattice vibration and electromagnetic field (phonon-photon interaction) should be discussed carefully. It has been known that a vibrational mode of interest sometimes appears shifted to the higher wavenumber side in a reflection-absorption (RA) spectrum than the position in a transmission one, when the vibrational mode is in a lowwavenumber region and its intensity is strong.10 This effect was not attributed to a chemical reaction of the chemical group with the substrate. Instead, it was attributed to the effect of TO (transverse-optic)-LO (longitudinal-optic) splitting.10 TO and LO modes are intrinsically degenerated in a material of condensed matter, when infrared ray is not irradiated on the material. When an infrared ray is irradiated on the material, however, the TO mode is shifted to the lower-wavenumber side from the equilibrium wavenumber that is evaluated by factorgroup analysis.11 This makes the two modes split, but the LO mode is ordinarily not observable in optically thick material, since the LO mode could not be coupled with the electromagnetic wave that is the transverse wave. The transverse electromagnetic wave induces alternately directed dipole zones that are perpendicular to the wave-propagation vector. When the thickness of the film is sufficiently less than half-length of the wavelength of the infrared ray, on the other hand, a uniformly directed dipole zone is formed in the film, in which a conserve field (scalar potential) is generated. In this atmosphere, the electric field can be interacted with the LO mode, which makes the LO mode active in infrared spectra of ultrathin layers, even for amorphous layers. Of note is that the TO-LO splitting has not been discussed in terms of the molecular structure and orientation in the film. The theory of TO-LO splitting represented by Berreman’s effect is usually discussed by use of static and dynamic dielectric functions with charge bunching.12 This conceptual technique is quite convenient to consider the appearance of LO modes in infrared spectra of thin films. The theory of Berreman’s effect, however, depends on an assumption that the film material is optically isotropic.6 In other words, the theory intrinsically does not provide us with any information about anisotropic molecular structure and orientation. If the inplane and out-of-plane components of a dielectric dispersion can be evaluated experimentally, the components would be expected to give useful information for the molecular orientation analysis in the film. Fortunately, p-polarization infrared spectra observed on a nonmetallic (dielectric) substrate contain both components.5 In the present paper, therefore, the mechanism of the TOLO splitting occurring in organic molecular assemblies is discussed first. This discussion enables us, before the theoretical analysis, to understand which band would be split significantly
J. Phys. Chem. B, Vol. 105, No. 45, 2001 11179
Figure 1. Schematic molecular models of a metal salt of stearic acid when the molecular axis is (a) perpendicular and (b) parallel to the film surface. The metal ion is not drawn.
and which band would not be split significantly. Further, it also enables us to evaluate the molecular orientation in ultrathin films on nonmetallic substrates. For the spectral simulation, the surface-normal and -tangential components of the dielectric property of the film are individually expressed by an oscillatorsmodel function. By employing optimization calculation of the model functions to observed p-polarization external-reflection spectra, optical parameters including the TO-LO splitting effect have been readily evaluated. Molecular orientation angles have also been evaluated by use of oscillator strengths obtained from the optimized anisotropic dielectric functions, instead of using absorption indices. As a result, the orientation analysis and the evaluation of optical parameters can be achieved simultaneously. Theoretical Basis. A. Vibrational Mode Perpendicular or Parallel to the Molecular Axis. LB films are planar organic molecular assemblies, in which a lateral pressure in the film packs long monomer species, in most cases. In each long monomer molecule, vibrating parts are connected through chemical bonds. In the case of cadmium stearate, for example, the structurally dominant part is the hydrocarbon chain, in which sixteen methylene groups are connected almost linearly. This can be considered as a connection of several kinds of oscillators: the symmetric and antisymmetric CH2 stretching, the CH2 wagging and scissoring vibration modes, and so on. It should be noted that the transition-moment directions of the symmetric and the antisymmetric CH2 stretching vibration (νs(CH2) and νa(CH2)) modes and the CH2 scissoring vibration (δ(CH2)) mode are always perpendicular to the molecular (hydrocarbon chain) axis when the hydrocarbon chain has all-trans zigzag conformation. The TO-LO theory was intrinsically constructed on a linear chain-vibration model with the nearest-neighbors approximation. The chain molecule in the present study can also be used as the linear chain-vibration model. Therefore, in this paper, “molecular axis” is used as the linear chain image. With this simple model, the three modes mentioned above generate transverse vibrational waves to the molecular axis, which yield TO modes in an LB film (Figure 1a). On the other hand, the transition-moment direction of the CH2 wagging vibration (ω(CH2)) mode is parallel to the molecular axis, which generates a LO mode. In this manner, if a vibrational mode of interest is perfectly perpendicular or parallel to the molecular axis, the vibrational mode can be categorized into either TO or LO mode. Of note is that, in this case, any vibrational mode does not cause a splitting. When the molecular axis is perfectly perpendicular to the film surface (Figure 1a), the TO and LO modes are individually observed by infrared transmission and RA spectrometries,
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respectively.10 When the molecular axis is tilted (Figure 1b), however, the TO and LO modes appear in both transmission and RA spectra, since both modes give surface-normal and -tangential components. In this case, it should be noted that an identical mode appears at an identical wavenumber in both transmission and RA spectra. In other words, when we find a mode that appears at an identical wavenumber in both transmission and RA spectra, it means that the mode does not cause the TO-LO splitting, which suggests that the transition moment is almost perpendicular or parallel to the molecular axis (not to the film surface). Regardless, we sometimes observe minute wavenumber difference between transmission and RA spectra (less than 1 cm-1).10 This is because the absorption-index (k) dispersion against the wavenumber has a different shape from that of the imaginary part of complex dielectric-dispersion (2) due to the extraordinary dispersion,11 which is a purely optical effect. In infrared spectra, especially in a high-wavenumber region, this effect can be ignored. B. Vibrational Mode Oblique to the Molecular Axis. When a vibrational mode of interest has an oblique angle to the molecular axis, the situation becomes complicated. The symmetric COO- stretching vibration (νs(COO-)) mode in cadmium stearate is an example for this case (Figure 1a). As schematically presented in Figure 1b, its vibrational mode has components both perpendicular and parallel to the molecular axis. Since the perpendicular and parallel components generate transverse and longitudinal waves, respectively, in the molecule, such a mode results in the TO-LO splitting. When the molecule stands on the substrate perpendicularly, the TO and LO modes are individually observed by infrared transmission and RA spectrometries, respectively. In many cases, the band appearing in the RA spectrum has a higher wavenumber than that in the transmission one. It is well-known that this wavenumber shift obeys the Lydanne-Sachs-Teller (LST) law.11,13 Therefore, when we find a wavenumber difference for an identical mode in infrared transmission and RA spectra, the difference suggests that the vibrational mode has an oblique angle to the molecular axis. When the molecular axis is tilted to the film surface, the situation becomes more complex. The TO and LO modes split from an identical vibrational mode are individually split again into surface-normal and -tangential components. This means that the TO and LO modes appear in both transmission and RA spectra. C. Oscillators-Model Representation of Dielectric Function. Optical absorption is theorized well by a dielectric wavenumberdispersion function. This function is known as Lorentz’s oscillators model,14 and it is frequently used to explain optical properties of insulator and semiconductor materials particularly in the wavenumber region of visible light. When a metallic material is analyzed, a special case of the Lorentz model is used, which is known as Drude’s model.14 These oscillators models are useful to discuss the material property in the infrared region, since the vibrations of electrons can be conceptually replaced by that of atoms. One-phonon absorption in the infrared region is strongly correlated to a TO mode that induces a transition dipole moment. In a Lorentz’s model, the complex dielectric function (E˜ ) of an organic thin-layer material in the wavenumber domain is written as
˜ (ν) ) ∞ +
∑j χj ) ∞ + ∑j
4πFjν0j2
ν0j2 - ν2 - iγjν
(1)
Here, ∞ is the dielectric constant measured in electromagnetic waves, and it corresponds to a baseline of the dielectric dispersion curve. Each term in the summation (χ) represents an oscillator that corresponds to a band in a spectrum. Therefore, j is the number of bands in the spectrum to be analyzed. The band center (resonance position) and a damping factor are expressed by ν0 and γ, respectively. The square root of the numerator of eq 1 is called the “oscillator strength” and corresponds to the number of the oscillators in a unit volume.13 When the molecules in the thin-layer material are highly ordered, the dielectric property of the layer becomes anisotropic. In the present study, an assumption of uniaxial anisotropy5 is introduced for convenience of calculation, in which surfacenormal (z) and surface-tangential (x-y) directions are discriminated from each other. Then, oscillator models in the z and x-y directions are individually prepared: E˜ z and ˜ x-y. With these uniaxially anisotropic dielectric functions, infrared RA spectra were generated by an anisotropic calculation process.5 To determine an appropriate balance of ˜ z and ˜ x-y for each band, at least two spectra are necessary. In the present study, two spectra measured at two different angles of incidence were prepared for the analysis. Note that s-polarization spectra have no information for ˜ z. Therefore, only p-polarization spectra were collected. Material and Methods GaAs wafers were chosen as the substrate of LB film. The wafers were kindly provided by Sumitomo Electric Co. The wafers have an optically flat (100) crystalline surface, and the back side is coarse. The infrared ray incident through the flat surface is scattered at the coarse surface.15 Therefore, the internal reflection in the GaAs wafer does not affect the reflection spectra. In other words, the thickness of the wafer can be set to infinity in the spectrum simulation. For the chemicals and preparation method of the LB film, the reader is referred elsewhere.5 For the optimization of the parameters, the optical simulation software SCOUT2 was used, which was created by one of the authors (W. T.). In the present study, the so-called Kim’s oscillators function16 that is available in the software was used in place of the conventional Lorentz’s oscillators function. In Kim’s function, the damping factor is replaced by τ to have the simulation curve fit better to the observed spectrum by using the following equation.
χj )
4πFjν0j2 ν0j - ν - iτjν 2
2
[ (
; where τj ) γj exp - Rj
ν - ν0j γj
)] 2
(2) This function is more useful for various kinds of band shapes, since it enables the simulated curve to be continuously switched between Lorentz and Gaussian curves. The switching parameter is represented by Rj. After a rough setting of the parameters by comparing the calculated spectrum to the observed one, all the parameters were simultaneously converged by using the socalled “downhill SIMPLEX” algorithm.17 Results and Discussion Infrared p-polarization ER spectra of a five-monolayer cadmium stearate LB film deposited on a GaAs wafer were measured at various angles of incidence as presented in Figure 2. As reported in the literature,5,18,19 a surface-normal transition
Evaluation of Parameters in Ultrathin Films
Figure 2. Infrared p-polarized ER spectra of a 5-monolayer LB film of cadmium stearate deposited on GaAs measured at angles of incidence: 25°, 50°, 60°, and 80° from the surface normal.
Figure 3. Simulation spectra (dashed line) after the convergence of the optimization calculation, which are overlaid on observed ppolarization spectra (solid line). The calculation was simultaneously performed for the two spectra measured at angles of incidence of (a) 25° and (b) 50°. The analytical region is 2700-3100 cm-1.
moment appears as a positive band, while a surface-tangential transition moment appears as a negative band in the reflectionabsorption unit for p-polarized ER spectra when the angle of incidence is smaller than Brewster’s angle for the air/substrate interface (73° for GaAs). Above the Brewster angle, however, the sign of the bands changes as shown by the spectrum at 80°. This means that the infrared p-polarized ER spectra greatly respond to both molecular-orientation angle and the angle of incidence. Transmission spectrometry with an oblique angle of incidence and attenuated total reflection (ATR) spectrometry20 can also detect both surface-normal and -tangential components of a transition moment. Nevertheless, the ER spectrometry with p-polarized light is more responsive to the direction of a transition moment, since the direction is more strongly reflected as the sign of band. For the optimization of simulated spectra to the observed ones, two ER spectra were selected from Figure 2. Since the experimental precision drops when the angle of incidence is close to the Brewster angle for the p-polarization,5 the spectra measured at 25° and 50° were selected for the optimization. The optimization calculation was performed for the wavenumber regions 2700-3100 and 1300-1700 cm-1 individually. The higher-wavenumber region is presented in Figure 3, in which the spectra measured at 25° and 50° are shown. It is found that the band intensity in the spectrum at 50° is stronger than that at 25°, as theoretically expected.5 Another notable feature is that the spectral shape around 2875 cm-1 is recognizably different from each other. In the spectrum at 50°, the band at 2875 cm-1 has a positive shape, although its absolute intensity itself is negative. This strongly suggests that there is a positive band hidden in the neighbor bands. This is also true for the
J. Phys. Chem. B, Vol. 105, No. 45, 2001 11181 shape of the in-plane asymmetric CH3 stretching vibration (νa(CH3)-ip) band at ca. 2963 cm-1.15 In this region, there are minute bands at approximately 2953 (νa(CH3)-op) and 2963 cm-1, and the latter band shows a minute but a positive peak in the spectrum at 50°. These clear differences are not found in transmission and RA spectra. This shows, in this manner, that infrared p-polarization ER spectrometry is highly sensitive to the angle of incidence, which means that this spectrometry is information rich. If we could have a set of appropriate dielectric dispersion curves (z and x-y) that accounts for both ER spectra (at 25° and 50°), the dielectric dispersion would clarify the optical property of the LB film. For that purpose, the surface-normal and -tangential components of the dielectric dispersion function were individually modeled by use of several bands. The anisotropic calculation of the reflection absorbance was performed with the use of the two model dielectric dispersions simultaneously. The calculated reflection-absorption curves after the convergence (simulated spectra) are plotted by the dotted lines in Figure 3, which are found to be almost identical to the observed spectra plotted by the solid lines. For the adequate convergence of the simulated spectra, eight bands were found to be necessary to model the dielectric dispersions. The eight bands are listed in the top eight rows in Table 1. The band positions are automatically converged values, which are beautifully consistent with the band positions reported by Parikh and Allara.4 This means that the optimization calculation is reliable and the evaluated values are chemically meaningful. Of note is that some weak-intensity bands as the antisymmetric and the symmetric CH2 stretching vibration bands of the R-carbon are readily resolved by the optimization, which are not recognizable in the raw spectra. In this manner, the optimization analysis has a good potential to reveal the fine spectral characteristics. Each complex dielectric dispersion function (E˜ (ν)) for the two components (surface-normal and -tangential) obtained by the optimization calculation was converted to a refractive-index dispersion (n˜ (ν)) by use of the next relationship that holds when the magnetic permeability is unity.13,14
n˜ (ν) ) n + ik ) x˜ (ν)
(3)
The real (n) and imaginary (k) parts in the calculated refractiveindex dispersions are presented in Figure 4 by the dotted and solid lines, respectively. The k-dispersion curves for the x-y and z-directions are found to be very similar in shape to those of transmission and RA spectra (Figure 5a) of the same LB film. This proves that the evaluation of the dielectric dispersion functions has been readily performed. These results remind us of a matter discussed in subsection A in Theoretical Basis. Therefore, we can roughly conclude that the molecular axis is nearly perpendicular to the film surface. Although transition moments of the CH3 group have oblique angles to the molecular axis, the TO-LO splitting is not observed. This is because the absorption indices (k) of the modes are very minor. The real part of the refractive-index dispersions is also of interest. From the base values (˜ in eq 1) of the dielectric dispersion functions, n in the x-y and z directions were obtained to be 1.50 and 1.54, respectively. In a previous study, these values were cited from literature19 to be 1.48 and 1.56, which were obtained from ellipsometric analysis. The values in the present study are close to the literature values, which suggests again that the analytical results are reliable and useful. The same analysis was performed for the lower-wavenumber region (1300-1700 cm-1; Figure 6). In this region, a dramatic change in spectral shape happened. In the spectrum at 25°, the
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TABLE 1: Bands Required for the Optimization, and Evaluated Orientation Anglesa
a
bands
wavenumber (cm-1)
νa(CH3)-ip νa(CH3)-op νa(R-CH2) νa(CH2) νs(CH2) + FR νs(CH3) νs(R-CH2) νs(CH2) νa(COO) δ(CH2)1 δ(CH2)2 νs(COO)-LO νs(COO)-TO
2962.0 2956.1 2923.9 2919.8 2890.6 2878.4 2860.4 2852.2 1543.8 1477.2 1466.7 1435.8 1422.0
fine assignments ip of CCC backbone plane* op of CCC backbone plane* op of CCC backbone plane* op of CCC backbone plane* op axis, ip of backbone plane* ip CCH3, ip CCC* op axis, ip CCC backbone* op axis, ip CCC backbone* Factor splitting of δ(CH2) Factor splitting of δ(CH2) LO mode by νs(COO) TO mode by νs(COO)
orientation angle (deg) 8.0 (inaccurate) 89.8 85.5 75.6 87.7 7.5 86.7 80.2 76.8 85.5 87.2 See the text. See the text.
Band positions were automatically yielded by the optimization process. b After earlier work.4
Figure 4. Refractive-index dispersion curves obtained from the calculated dielectric functions in the wavenumber range of 2700-3100 cm-1. The real (n) and imaginary (k) parts are represented by the dashed and solid lines, respectively. The surface parallel and normal components are shown in parts a and b, respectively.
Figure 5. Infrared RA (dashed line) and transmission (solid line) spectra of 5-monolayer cadmium stearate LB films deposited on a goldevaporated glass slide and on a GaAs wafer, respectively. The higher and lower wavenumber regions are separately shown in parts a and b, respectively.
Figure 6. Simulation spectra (dashed line) after the convergence of the optimization calculation, which are overlaid on observed ppolarization spectra (solid line). The calculation was simultaneously performed for the two spectra measured at angles of incidence of (a) 25° and (b) 50°. The analytical region is 1300-1700 cm-1.
νs(COO-) band at around 1430 cm-1 is very weak in intensity and has a complex shape, whereas the same band appears as a strongly positive peak in the spectrum at 50°. Regardless, the optimization calculation was readily performed, as presented by the dotted curves in Figure 6. Since the signal-to-noise ratio
Figure 7. Refractive-index dispersion curves obtained from the calculated dielectric functions in the wavenumber range of 1300-1700 cm-1. The real (n) and imaginary (k) parts are represented by the dashed and solid lines, respectively. The surface parallel and normal components are shown in parts a and b, respectively.
of the spectrum measured at 25° is poor due to the lower sensitivity compared to the angle near the Brewster angle, the optimization accuracy becomes less than the previous analysis for the higher-wavenumber region. The results are, however, still useful for the present study. The calculated refractive-index dispersions of the surfacenormal and -tangential components are presented in Figure 7a and b, respectively. As found in the analysis of the higherwavenumber region, each dispersion curve of k corresponds to transmission and RA spectra of the film (Figure 5). Here, in the lower-wavenumber region, the νs(COO-) band is clearly found at different position that depend on the optical geometry. In Figure 7a, the band is located at 1422 cm-1, whereas the same band appears at 1436 cm-1 in Figure 7b. This different band positions were automatically obtained by the optimization calculation. In the conventional sense, it is possible to consider that the two bands are from two different modes. One of the possible ideas is that the CH2 bending mode of the R-carbon is shifted to a low wavenumber position, as reported for octanoic acid. The band intensity of this mode (approximately 1470 cm-1), however, should be much less than that from other methylene groups. Since the intensity of the band at around 1470 cm-1 is weak as shown in Figure 6a, the band from the R-carbon should be invisible. Therefore, this idea due to the R-carbon is denied. In the present case, the TO-LO splitting is an accepted mechanism that causes the band shift.6,10 Of note is that, in the observed transmission and RA spectra, the νs(COO-) band appears at 1423 and 1433 cm-1, respectively (Figure 5b). These band locations are very close to the wavenumbers obtained by the optimization calculation. According to Berreman, the two different band locations found in the transmission and RA spectra are assigned to the TO and LO modes, respectively. Therefore, the two locations of the peak tops in the k-dispersion
Evaluation of Parameters in Ultrathin Films
J. Phys. Chem. B, Vol. 105, No. 45, 2001 11183
Figure 8. Dispersion curve of the absorption index (k) of nonoriented cadmium stearate molecules (thick line) evaluated by use of the k-lines shown in Figures 4 and 7. The surface-parallel and -normal components of k are plotted by dashed and thin solid lines, respectively. The wavenumber region is split into the two regions shown in parts a and b.
curves are concluded to correspond to the TO and LO modes. As mentioned in subsection B of Theoretical Basis, the νs(COO-) band could possibly cause the splitting due to the oblique angle to the molecular axis and the charge density of the group. Therefore, it is reasonable that the band in the ER spectra is decomposed into two components. In other words, this optimization calculation of the anisotropic functions has clearly revealed the TO-LO splitting in organic molecular assemblies. It is of interest here that the νa(COO-) mode does not show a clear TO-LO splitting. During the optimization calculation, the band in the ER spectra at 1544 cm-1 seems to be a singlecomponent band (Figure 7). In fact, both transmission and RA spectra show that the band appears at almost the same position (Figure 5b). This strongly suggests that this mode is nearly perpendicular to the molecular axis, according to the discussion in subsections A and B of Theoretical Basis. As shown later, in fact, the tilt angle of this mode to the molecular axis is nearly perpendicular. In this manner, molecular orientational information would be obtained if the TO-LO splitting would be recognized experimentally. Besides, the absorption indices in x-y and z directions (kx-y, kz) are known to be related to that of bulk sample (kbulk) as (for a uniaxial system):5
3kbulk ) 2kx-y + kz
(4)
With this equation, a dispersion curve of kbulk was estimated as presented in Figure 8. The TO and LO bands of the νa(COO-) mode are mixed to yield a almost single-component band. In Figure 9, a nonpolarized transmission spectrum of cadmium stearate in a KBr pellet is presented, in which cadmium stearate microcrystallites is dispersed. The KBr spectrum is very similar to the kbulk dispersion curve estimated above. The νs(COO-) band in the KBr spectrum has an asymmetric shape, and the peak top was found at 1425 cm-1, which accompanies a shoulder band at 1430 cm-1 on closer inspection. In this manner, the KBr spectrum is found to be explained well by the two dispersion curves obtained from the ER spectra. This proves again that the analytical technique in the present study is very useful. Then, the molecular orientation was analyzed by using parameters obtained by the optimization. When the direction of a transition moment is perpendicular or parallel to the molecular axis (A in Theoretical Basis), the tilt angle of a TO or a LO mode from the surface-normal becomes the orientation angle that we want. As mentioned in subsection C in Theoretical Basis, oscillator strengths can be used in place of integral band intensities. Let us assume that the oscillator strength of the mode
Figure 9. Infrared transmission spectrum of cadmium stearate dispersed in a KBr pellet in the two wavenumber regions (parts a and b). For the band resolution, a second-derivative spectrum of the spectrum in part b is presented in part c.
and its surface-tangential and -normal components are represented by Ω0, Ωx-y, and Ωz, respectively. From the uniaxial assumption, the following equation holds when the orientation angle from the surface normal is φ.
Ω02 ) Ω02 sin 2 φ + Ω02 cos2 φ ) 2Ωx-y2 + Ωz2
(5)
This equation yields the following ones:
1 Ωx-y2 ) Ω02 sin2 φ 2
(6)
Ωz2 ) Ω02 cos2 φ
(7)
Therefore, the orientation angle, φ, can be deduced as
(
Ωx-y Ωz
φ ) tan-1 x2
)
(8)
For example, when the strengths in the x-y and z directions are calculated to be the same as each other, φ is calculated as 54.7°, which is the so-called magic angle. The magic angle is obtained when the transition moments are nonoriented (Ωx-y ) Ωz). Therefore, this evaluation equation is appropriate for the uniaxial system. With this analytical procedure, orientation angles were calculated for all vibrational modes except for the νs(COO-) mode as presented in Table 1. In a previous paper, the angle of the νa(COO-) mode could not be calculated. In the paper, the absorption index of the band was estimated by way of a KBr transmission spectrum. In a KBr pellet, however, the order of microcrystallites is random, and molecular conformation would be different from that in the LB film. In this situation, it is possible that the mode generates a LO mode as well as a TO one, which makes the band wider. In fact, on very close inspection, the KBr spectrum (Figure 9a and b) presents a νa(COO-) band at 1544 cm-1 with a shoulder at 1554 cm-1. The presence of the minor bands is confirmed by performing second-derivative calculation (Figure 9(c)). This broadening of the band due to the TO-LO splitting causes decrease of the band height, which makes the evaluation of the absorption index
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Hasegawa et al.
Figure 10. Evaluated molecular orientation of cadmium stearate molecule in the 5-monolayer LB film on GaAs. All the angles are calculated on the assumption of the uniaxial angular-distribution except the angle of 40.5°.
incorrect. In the present study, this flaw was removed, since the optical parameters were evaluated from the identical sample used for the orientation analysis. The angle of the band (76.8°) is reasonable with the previous rough evaluation: nearly perpendicular to the molecular axis. For a very weak band like the νa(CH3)-ip band, the analytical accuracy is expected to be poor. With these angles, the tilt angle of the molecular axis was calculated. Since the molecular axis is perpendicular to both the νa(CH2) and νs(CH2) modes, the tilt angle is calculated5 to be 17.5° from the surface normal (Figure 10). The present result is a little larger than the previous result (14.7°). In the present study, however, the tilt angle at the R-carbon can be separately evaluated with the angles of the νa(R-CH2) and νs(R-CH2) modes. The tilt angle at the R-carbon was calculated to be 5.6° from the surface-normal. This suggests that the R-carbon plays the role of a connection part between the molecular axis and the headgroup. The previous result for the tilt angle can be considered as an averaged angle over the whole hydrocarbon chain. On the other hand, when a transition moment has an oblique angle to the molecular axis, the same analysis cannot be performed, since the mode yields both TO and LO modes. In this case, the TO and LO bands are individually analyzed, and oscillator strengths of both TO and LO modes (ΩTO and ΩLO) must be evaluated. To do that, each strength is calculated by eq 5 with the use of the x-y and z components of each oscillator strength. With the strengths, the tilt angle of the transition moment to the molecular axis, φ, is calculated by the following equation.
φ ) tan-1
( ) ΩTO ΩLO
(9)
This equation is very similar to eq 8, but it does not have the factor, x2. Since TO and LO modes are not distributed uniaxially, x2 is not necessary for the calculation of the orientation angle. Of note is that the orientation angle is defined as the angle from the molecular axis. With this method, the tilt angle of the νs(COO-) mode from the molecular axis was evaluated to be 40.5° (Figure 10). Since the molecular axis has a tilt angle of 17.5° from the surfacenormal, the tilt angle of νs(COO-) mode from the surfacenormal is roughly evaluated to be 23.0°. Previously,5 the tilt angle was evaluated to be 18.5°. Because of a similar problem
in the analysis of the νs(COO-) mode, the previous result might have an analytical error due to the evaluation of the absorption index by use of the KBr spectrum. In this way, it is suggested that a clear TO-LO splitting takes place when a vibrational mode has a large oblique angle (near 45°) to the molecular axis, whereas the splitting is minor when the angle is less than 15° (or more than 75°), which is demonstrated by the νs(COO-) and νa(COO-) bands. These are consistent with the discussion in Theoretical Basis. It may be possible to still consider that the splitting of the COO- stretching vibration band is derived not from TO-LO splitting, but from crystal-field effect that is known as factor splitting, since the terminal groups are packed two-dimensionally. If this physical model is true, however, the νa(COO-) band would also appear at two largely different positions in transmission and RA spectra. To comprehensively understand all the results, therefore, it is appropriate to take the TO-LO splitting model as a suitable mechanism. Conclusion The new analytical technique presented in this study is valid for the spectra of films on dielectric substrates, since the ER spectra contain information of both surface-normal and -tangential components of vibrational modes. In RA spectrometry that is performed on a metallic substrate, however, only surfacenormal components are detected in p-polarization spectra irrespective of angle of incidence, which means that angle-ofincidence dependent RA spectra are degenerated in information. To analyze the RA spectra, therefore, the conventional analytical methods are still valid. Nevertheless, the present study has suggested that the ER spectrometry by use of two observed infrared ER spectra is quite powerful for the analysis of molecular orientation and the optical-parameters evaluation. Since the spectra were commonly used for both analyses, the analytical precision was very high, and optimization accuracy was also high. This analytical method would be useful for various thin films particularly when the optical characteristics (parameters) are unknown. Acknowledgment. This work is financially supported by Grant-in-Aid for Scientific Research on Priority Areas (A), “Dynamic Control of Strongly Correlated Soft Materials” (No. 413/13031074) from the Ministry of Education, Science, Sports, Culture, and Technology. References and Notes (1) Emelianov, I. L.; Khatko, V. V. Sens. Actuators B, Chem. 1999, 60, 221-227. (2) Wong, J. Y.; Park, C. K.; Seitz, M.; Israelachvili, J. Biophys. J. 1999, 77, 1458-1468. (3) Ishino, Y.; Ishida, H. Langmuir 1988, 4, 1341-XX. (4) Parikh, A. N.; Allara, D. L. J. Chem. Phys. 1992, 96, 927-945. (5) Hasegawa, T.; Takeda, S.; Kawaguchi, A.; Umemura, J. Langmuir 1995, 11, 1236-1243. (6) Berreman, D. W. Phys. ReV. 1963, 130, 2193-2198. (7) Yeh, P. J. Opt. Soc. Am. 1981, 72, 507-513. (8) Drude, P. Ann. Phys. U. Chem. N. F. 1889, 32, 584-625. (9) Hansen, W. N. J. Opt. Soc. Am. 1968, 58, 380-390. (10) Yamamoto, K, Ishida, H. Vib. Spectrosc. 1994, 8, 1-36. (11) Kudo, K. Hikaribussei-Kiso (Introduction to Optical Solid-State Physics); Ohm-Sha: Tokyo, 1996; pp 75-78. (12) Harbecke, B.; Heinz, B.; Grosse, P. Appl. Phys. A 1985, 38, 263. (13) Ibach, H.; Luth, H. Solid-State Physics: An Introduction to Principles of Materials Science; Springer: New York, 1995. (14) Kittel, C. Introduction to Solid State Physics, 5th ed.; Wiley: Chichester, 1986.
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