Optical and Spectroscopic Characteristics of Oleate Adsorption As

May 19, 2004 - Nan Qiu , Jing Zhang , Lirong Zheng , Guangcai Chang , Takeshi Hashishin , Satoshi Ohara , Ziyu Wu. RSC Advances 2014 4, 16033 ...
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Optical and Spectroscopic Characteristics of Oleate Adsorption As Revealed by FTIR Analysis Keqing Fa,*,† Tao Jiang,‡ Jakub Nalaskowski†, and Jan D. Miller*,† Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, and Department of Mineral Engineering, Central South University, Changsha, Hunan, 410083, People’s Republic of China Received January 14, 2004. In Final Form: April 9, 2004 Fourier transform infrared transmission (FTIR/TS), external reflection (FTIR/ERS), and internal reflection (FTIR/IRS) spectroscopies are three important sampling techniques for the study of adsorbed surfactants. The optical and spectral characteristics of a three-phase system were calculated using theoretical simulation and discussed based on experimental results for oleate adsorption at the air/water interface and at the water/fluorite interface. It is shown that a thorough understanding of the optical properties and spectral characteristics from FTIR analysis helps to improve the experimental design and explanation of experimental results and is important to properly quantify surfactant interfacial adsorption phenomena.

1. Introduction In modern Fourier transform infrared (FTIR) spectroscopy, there are about 10 sampling techniques, including transmission, total internal reflection (or attenuated total reflection), external reflection, diffuse reflectance infrared Fourier transform (DRIFT), mull film, and other techniques.1 Among these techniques, transmission (TS), total internal reflection (IRS), and external reflection (ERS) spectroscopies are three of the most important and most often used sampling techniques in surface and interfacial research. In the past, FTIR/ERS and FTIR/IRS have been combined with other analytical methods to study complicated systems and chemical processes.2-9 A significant research progress with respect to FTIR spectra sampling techniques was the quantitative measurement of interfacial phenomena in the past decade.10-14 The transmission sampling technique is relatively simple, and collected absorption spectra are usually strong and well-defined. FTIR/TS spectra are thus frequently used as references for ERS and IRS spectra. However, transmission sampling offers less interfacial information than FTIR/ERS and FTIR/IRS sampling techniques. Both * Corresponding authors. Keqing Fa: e-mail, [email protected]; phone, 801 581 6814; fax, 801 5814937. † University of Utah. ‡ Central South University. (1) Stuart, B.; George, W. O.; McIntyre, P. S. Modern Infrared Spectroscopy; John Wiley & Sons: New York, 1996. (2) Hansen, W. N. Advances in Electrochemistry and Electrochemical Engineering; Wiley-Interscience: New York, 1973; Vol. 9, Chapter 1. (3) Hwang, M.; Kim, K. Langmuir 1999, 15, 3563. (4) Kajiyama, T.; Zhang, L.; Uchida, M.; Oishi, Y.; Takahar, A. Langmuir 1993, 9, 760. (5) Flach, C. R.; Brauner, J. W.; Mendelsohn, R. Appl. Spectrosc. 1993, 47, 982. (6) Simon-Kutscher, J.; Gericke, A.; Hu¨hnerfuss, H. Langmuir 1996, 12, 1027. (7) Myrzakozha, D. A.; Hasegawa, T.; Nishijo, J.; Imae, T.; Ozaki, U. Surf. Sci. 1999, 427-428, 107. (8) Overs, M.; Hoffmann, F.; Scha¨fer, H. J.; Hu¨hnerfuss, H. Langmuir 2000, 16, 6995. (9) Hoffmann, F.; Hu¨hnerfuss, H.; Stine, K. J. Langmuir 1998, 14, 4525. (10) Buontempo, J. T.; Rice, S. A. J. Chem. Phys. 1998, 7, 5825. (11) Jang, W. H.; Miller, J. D. Langmuir 1993, 9, 3159. (12) Jang, W.-H.; Miller, J. D. J. Phys. Chem. 1995, 99, 10272. (13) Sperline, R. P.; Song, Y.; Freiser, H. Langmuir 1997, 13, 3727. (14) Frey, S.; Tamm, L. K. Biophys. J. 1991, 60, 922.

FTIR/ERS and FTIR/IRS in situ sampling systems can be described by a three-phase model. The optics and spectra in FTIR/ERS and FTIR/IRS sampling are different because they use different optical fields to probe interfacial films. Although there have been several theoretical calculations of the optics and spectra for the FTIR/ERS and FTIR/IRS sampling techniques, the descriptions and comparison of FTIR/ERS and FTIR/ IRS sampling are still not common for the same surfactant film.15-18 Of particular importance is the quantitative determination of surfactant adsorption density and molecular conformation in the interfacial region in order to understand the nature of the resulting surface state. To achieve the quantitative analysis of surfactant adsorption, the relationship between optical constants, the spectra collected in a three-phase system, and some key experimental parameters must be understood. Unfortunately, these issues have not been completely discussed in the literature. Especially, the proper utilization of FTIR spectra for quantitative surfactant adsorption measurements has seldom been discussed theoretically based on the calculation of spectra and electric fields. This paper thus presents the calculated electric field intensity and spectra for FTIR/ERS and FTIR/IRS sampling techniques for selected systems. Individual factors involved in the three-phase systems are considered in detail. Effects of optical properties of the third phase and the proper selection of spectral peaks for quantitative measurements are discussed. 2. Three-Phase System The typical FTIR/ERS and FTIR/IRS experimental setups are schematically illustrated in Figure 1. These systems typically include three layered phases: the incident phase; the second phase, which is the organic film being probed; and the third phase. For FTIR/ERS, the refractive index n1 of the incident phase (rare phase) is smaller than the refractive index n3 of the substrate (15) Mcintyre, J. D. E. Advances in Electrochemistry and Electrochemical Engineering; Wiley-Interscience: New York, 1973; Vol. 9, Chapter 2. (16) Harrick, N. J. Internal Reflection Spectroscopy; John Wiley & Sons: New York, 1979. (17) Mielczarski, J. A. J. Phys. Chem. 1993, 97, 2649. (18) Hansen, W. N. J. Opt. Soc. Am. 1968, 58, 380.

10.1021/la049869b CCC: $27.50 © 2004 American Chemical Society Published on Web 05/19/2004

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Figure 1. The typical FTIR/ERS (a) and FTIR/IRS (b) experimental setup. For FTIR/ERS, the refractive index n1 for the incident phase is smaller than the refractive index n3 for the third phase, n1 < n3. For FTIR/IRS, n1 > n3 and the incident angle at each reflection must be greater than the critical angle. The infrared light is guided inside the FTIR IRE.

phase (dense phase). The detected signal is the reflected IR radiation in the incident phase from the interface between phase 1 and 2 and the interface between phase 2 and 3, as shown in Figure 1a. For FTIR/IRS, the refractive index n1 of the incident phase (dense phase) is larger than the refractive index n3 of the substrate phase (rare phase) as shown in Figure 1b. When the incident angle is larger than the critical angle θc ) sin-1(n3/n1), the total internal reflection occurs and an evanescent optical field is generated in phase 3. The guided IR radiation inside the internal reflection element (IRE) experiences multiple reflections at both sides of the IRE crystal. However, the spectra and electric field intensities in this paper are all calculated for single reflection. A parallelepiped IRE crystal is often used because polarization experiments can be performed with this geometry. The first phase for both FTIR/ERS and FTIR/IRS is required to be transparent in the mid-infrared region, which indicates that the k1 value is zero or small enough to be ignored. The second phase (film) is thin by definition, and its thickness is much smaller than the radiation wavelength (d , λ). The electric fields in the first and second phase are the sum of incident and reflected components. For FTIR/ERS, the transmitted light in the third phase passes out of the system. For FTIR/IRS, the evanescent wave results from the dramatic attenuation of IR radiation in the direction of light propagation. Light shifts a short distance along the interface and is reflected back to the first phase with an angle at 2θ (θ, incident angle with respect to the surface normal) with respect to the incident light. More descriptions of the evanescent wave can be found in the literature.19-21 The fundamental theory for electromagnetic fields is described by the (19) Hecht, E. Optics; Addison-Wesley: Reading, MA, 1990; Chapter 4. (20) Balanis, C. A. Advanced Engineering Electromagnetics, John Wiley & Sons: New York, 1989; Chapter 5. (21) Wolf, E.; Born, M. Principles of Optics; Cambridge University Press: Cambridge, 1999; Chapter 1.

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Maxwell equations. Fresnel coefficients can be derived from the application of Maxwell equations for the threephase system with appropriate boundary conditions. Hansen et al. have developed equations to calculate electric fields in all three phases and the reflectivity for the whole system.2,18 These equations were used in this paper for the calculation of electric fields and spectra. The spectral absorbance is calculated as A ) -log(R/ R0), where R and R0 are the reflectivities of the system with and without the surfactant film, respectively. In the calculation of whole spectra, both R and R0 are calculated using all the optical constants of three phases at each frequency in this research. By definition, R0 is the reflectivity of a two-phase system. Due to the multiple reflections in a single-crystal IRE, the signal-to-noise ratio (S/N) in FTIR/IRS spectra is usually satisfactory. The FTIR/ERS technique can be used to probe those systems that are not accessible for FTIR/ IRS. It has been used to probe the air/water interface and metal surfaces.22-27 Due to only one reflection from the surface, the signal-to-noise ratio is usually low, especially in the case of the low reflective dielectric substrates.28-29 The carboxyl region is very difficult to properly investigate due to the overlap of carboxyl peaks with the characteristic water vapor peaks.30-37 When polarized spectra are collected, the S/N ratio is further reduced due to the presence of the polarizer, which blocks half of the incident radiation. According to photodetection theory, the S/N ratio is proportional to the square of incident radiation power.38 3. Electric Field Intensity and Spectral Characteristics The local electric field intensity and spectral characteristics of a three-phase system have been discussed to some extent in the literature. Harrick has used the concepts of penetration depth and effective thickness for FTIR/IRS to indirectly describe spectral dependence on parameters such as the incident angle and absorption coefficient.16 His calculation helps to understand the nature of the attenuation of FTIR/IRS. Also, he has shown that the electric field in the first phase is of standing wave periodicity. However, most of his calculation concerned a two-phase system and FTIR/IRS. Hansen also calculated the electric field intensity and spectral absorbance to some extent for both FTIR/ERS and FTIR/IRS to verify the validity of tractable absorption equations.2 However, most (22) Allara, D. L.; Swalen, J. D. J. Phys. Chem. 1982, 86, 2700. (23) Allara, D. L.; Nuzzo, R. G. Langmuir 1985, 1, 52. (24) Sakai, H.; Umemura, J. Langmuir 1998, 14, 6249. (25) Dluhy, R. A.; Cornell, D. G. J. Phys. Chem. 1985, 89, 3195. (26) Dluhy, R. A. J. Phys. Chem. 1986, 90, 1373. (27) Dluhy, R. A.; Stephens, S. M.; Widayati, S.; Williams, A. D. Spectrochim. Acta, Part A 1995, 51, 1413. (28) Yen, Y.-S. J. Phys. Chem. 1989, 93, 7208. (29) Blaudez, D.; Buffeteau, T.; Desbat, B.; Flurnier, P.; Ritcey, A.M.; Pezolet, M. J. Phys. Chem. B 1998, 102, 99. (30) Le Calvez, E.; Blaudez, D.; Buffeteau, T.; Desbat, B. Langmuir 2001, 17, 670. (31) Gericke, A.; Huhnerfuss, H. Thin Solid Films 1994, 245, 74. (32) Gericke, A.; Simon-Kutscher, J.; Huhnerfuss, H. Langmuir 1993, 9, 3115. (33) Overs, M.; Hoffmann, F.; Schafer, H. J.; Huhnerfuss, H. Langmuir 2000, 16, 6995. (34) Simon-Kutscher, J.; Gericke, A.; Huhnerfuss, H. Langmuir 1996, 12, 1027. (35) Blaudez, D.; Buffeteau, T.; Cornut, J. C.; Desbat, B.; Escafre, N.; Pezolet, M.; Turlet, J. M. Appl. Spectrosc. 1993, 47, 869. (36) Flach, C. R.; Gericke, A.; Mendelsohn, R. J. Phys. Chem. B 1997, 101, 58. (37) Gericke, A.; Michailov, A. V.; Huhnerfuss, H. Vib. Spectrosc. 1993, 4, 335. (38) Kasap, S. O. Optoelectronics and Photonics; Prentice Hall: Upper Saddle River, NJ, 2001.

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Figure 2. A three-phase system for both FTIR/ERS and FTIR/ IRS. The three phases are distinguished by distinct optical constants. The film is the second phase sandwiched between the incident and the third phase. The polarized electric fields are illustrated for all three phases. Figure 4. FTIR transmission spectra of 2.4 nm thick calcium dioleate film.

Figure 3. Optical constants refractive index n and absorption coefficient k of calcium dioleate as a function of wavenumber (cm-1) (adapted from ref 39).

of the earlier calculations have not compared the electric field intensity and spectral properties of FTIR/ERS with those of FTIR/IRS. Further, the relationship between the spectral property and the optical constants of all the three phases has not been investigated in detail. Figure 2 shows the three-phase system used for FTIR/ ERS and FTIR/IRS sampling. Three optically distinct phases are distinguished by refractive indices ni and absorption coefficients ki, i ) 1, 2, 3. The film to be probed is the second phase sandwiched between the first (incident) and the third (substrate) phase. 3.1. Thin Films. The hypothetical film that was examined in the present research was a fatty acid/salt molecular layer at semisoluble mineral surfaces, such as fluorite and calcite, and at the air/water interface. Optical constants for the fatty acid/salt films were taken from the literature,39 as shown in Figure 3. The refractive index n and absorption coefficient k of fluorite in the mid-IR range 3000-1000 cm-1 are almost constant, about 1.43 and 0.0, respectively. The process and nature of oleate adsorption at fluorite and calcite surfaces are very complicated and involve time-dependent behavior.40 IR characteristic peaks (39) Mielczarski, E.; Mielczarski, J. A.; Cases, J. M. Langmuir 1998, 14, 1739.

of oleate adsorbed at calcium-bearing mineral surfaces have been observed to change with change in ion concentrations, contact modes of minerals with solution, pH, time, and temperature.41-44 In this regard, optical constants of the adsorbed film may vary with the solution and surface chemistry. The calculated spectra are mainly determined by optical constants, particularly the absorption coefficient k. One very important point emphasized here is that although the spectral simulation is able to offer insights into the experimental design and explanation of experimental results, it should not be used as evidence to verify the proposed adsorption state. Because the optical constants for oleate films were measured from solution precipitates, the calculated spectra only represent the spectral characteristics associated with these precipitated compounds. 3.2. Spectra of Calcium Dioleate Film. Simulated spectra of a 2.4 nm thick film of calcium dioleate for FTIR/ TS, FTIR/ERS, and FTIR/IRS sampling techniques are shown in Figures 4-6. The calcium oleate spectra show two strong vibrational regions: the -CH2 stretching from 3050 to 2800 cm-1 and the carboxyl -COO- stretching from 1700 to 1400 cm-1. The absorbances are positive in the FTIR/TS and FTIR/IRS spectra but negative in the FTIR/ERS spectrum. Besides, the three spectra have different magnitudes in absorbance and are dependent on the polarization of the incident radiation. As reported in the literature, the spectra in FTIR/ERS and FTIR/IRS not only depend on film optical properties but also on the experimental setup.10,12,14 Because the film in all three sampling techniques was the same, the observed difference was caused by the experimental setup. To illustrate this point, the absorbances of the same oleate film in FTIR/ ERS and FTIR/IRS spectra were calculated as a function of beam incident angle and results are shown in Figure 7a,b. 3.3. Incident Angles. The wavenumber selected for calculation of the effect of the incident angle on the spectral (40) Finkelstein, N. P. Trans. 1nst. Min. Metall. 1989, 98, c157. (41) Lu, Y.; Miller, J. D. J. Colloid Interface Sci. 2002, 256, 41. (42) Miller, J. D.; Misra, M. In Mintek 50: International Conference on Mineral Science and Technology; Council for Minerals Technology: Randburg, South Africa, 1984; Vol. 1, p 33. (43) Hu, J. S.; Misra, M.; Miller, J. D. Int. J. Miner. Process. 1986, 18, 57. (44) Hu, J. S.; Misra, M.; Miller, J. D. Int. J. Miner. Process. 1986, 18, 73.

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Figure 5. FTIR/ERS spectra of calcium dioleate: incident angle, 20°; d ) 2.4 nm; n1 ) 1.0, k1 ) 0.0; n3 ) 1.43, k3 ) 0.0.

Figure 6. FTIR/IRS spectra of calcium dioleate: incident angle, 75°; d ) 2.4 nm; n1 ) 1.43, k1 ) 0.0; n3 ) 1.0, k3 ) 0.0.

absorbance and on 〈E2〉 was 2923.8 cm-1, a position in the CH2 stretching region. Research interests are not only to illustrate the spectral properties of oleate films but also to make quantitative measurements such as the surfactant adsorption density and/or molecular orientation angle at surfaces. CH2 stretching peaks are most frequently used for this type of measurement. There is no doubt that the calculation and explanation are also useful for any other spectral region such as carboxyl stretching vibrations. It can be seen immediately from Figure 7 that in both FTIR/ ERS and FTIR/IRS the absorbance is highly related to the beam incident angle and polarization. In FTIR/ERS, however, the spectrum absorbance is not sensitive to the incident angle when the incident angle is smaller than 20° with respect to the surface normal as shown in Figure 7a. Around the Brewster angle, the S/N ratio is enhanced significantly for p-polarization light. When the incident angle is larger than the Brewster angle, the absorbance for p-polarization is still very strong but its sign is opposite to that for s-polarization. When nonpolarized IR radiation is used, the absorbances of the two polarization spectra cancel each other and the net S/N ratio is diminished thereby. To get a satisfactory S/N ratio, the incident angles ought to be close to but smaller than the Brewster angle.

Figure 7. Calculated FTIR/ERS and FTIR/IRS spectral absorbance at 2923.8 cm-1 for a 2.4 nm thick calcium dioleate film at a fluorite surface as a function of incident angle. (a) n1 ) 1.0, k1 ) 0.0; n2 ) 1.5694, k2 ) 0.246; n3 ) 1.43, k3 ) 0.0. (b) n1 ) 1.43, k1 ) 0.0; n2 ) 1.5694, k2 ) 0.246; n3 ) 1.0, k3 ) 0.0.

To quantitatively compare spectra collected in different chemistry conditions, incident angles should be smaller than 20°, which eliminates the influence of incident angles. In the whole range of incident angles, the magnitude of absorbance for s-polarization decreases monotonically with an increase in the incident angle. In FTIR/IRS, the incident angle must be larger than the critical angle. The critical angle is determined by refractive indices of the first and third phase but is independent of the refractive index of the second phase. It is evident that the FTIR/IRS spectrum absorbance is significantly dependent on the incident angle in the range of θ > θc and polarization as shown in Figure 7b. In Figure 5, FTIR/ERS spectra for two polarizations are nearly identical. But the absorbance magnitudes for two polarizations in FTIR/IRS spectra are significantly different as shown in Figure 6. This difference decreases with an increase in incident angles as the results in Figure 7b demonstrate. However, even at very high incident angles such as 80°, the absorbance magnitudes of the two polarizations are still significantly different. As described

Characteristics of Oleate Adsorption

above, multiple reflections along the IRE result in the FTIR/IRS spectra usually being well-defined and strong. Therefore, it is possible to get satisfactory signals by setting the incident angle at larger values such as around 75°. When the incident angle is set higher, the penetration depth and effective thickness are smaller.16 Under such a circumstance, spectral signals are mainly collected from the interfacial region. Theoretical calculation according to the formula from Harrick16 shows that the smallest penetration depth and effective thickness are about 0.1 micron. Thus, even though the incident angles are set high, a large proportion of signal is still from the bulk solution. It can be concluded that it is unreasonable to use FTIR/IRS spectra to probe the interfacial water structure as has been demonstrated in the literature.45 Also, a change in adsorbed surfactant conformation is identified by only a small shift in peak position from gauche state to trans state when a large proportion of the signal comes from the bulk solution. The spectral absorbance dependence on the incident angle and polarization state can be illustrated by the calculation of the square of local electric fields in three phases because light intensity (energy per unit area per unit time) is proportional to the square of the electric field. The components of 〈E2〉 are shown in Figure 8. The inset in Figure 8 indicates the locations in the three-phase system for 〈E2〉 calculation. Due to the continuity of electric fields across the boundary and very small thickness of the film, the x and y components of 〈E2〉 in all the three locations are almost the same. The subscripts 1, 2, and 3 for x and y components are thus dropped in the rest of this paper. But the z component is discontinuous across the interface. For FTIR/ERS (Figure 8a), the x and y components are dominant and have similar magnitude at low incident angles. They decrease with an increase in the incident angle. The absorbance for s-polarization thus has the behavior shown in Figure 7a because the molecules experience less excitation per unit area per unit time with an increase in the incident angle when the 〈E2X〉 decreases. Each z component in the three phases has a maximum around an incident angle of about 60°. The sum of x and z components 〈E2X〉 and 〈E2Z〉 results in the sign change and enhancement of signal around the Brewster angle for p-polarization. Around this angle, molecule dipoles have experienced more excitation from the ground state. It is not surprising that the electric field components shown in Figure 8b for FTIR/IRS are larger than those shown in Figure 8a for FTIR/ERS. Larger magnitudes of 〈E2〉 indicate that the electric fields are trapped in the interfacial region. As a consequence, the S/N ratio in FTIR/ IRS sampling is better than that in FTIR/ERS even for a single reflection. In the range of θ > θc, the y component 〈EY2〉 among all the interacting components (〈EX2〉, 〈EY2〉, and 〈EZ22〉) is dominant, which results in the s-polarization spectra having larger absorbance magnitudes than the p-polarization (Figure 7b). To obtain a satisfactory S/N ratio, which is important for quantitative measurements or when the reflective index of the IRE is large, the incident angle should be set close to the critical angle. 3.4. The Effect of n2, k2. The calculation of spectral absorbance and 〈E2〉 with respect to n2 and k2 is going to reveal the fundamental relationship between the spectra and the material optical property to be probed. Spectral absorbance change with respect to n2 and k2 for FTIR/ ERS is shown in Figure 9. According to the KramersKronig dispersion relation, n and k are not independent (45) Hancer, M.; Sperline, R. P.; Miller, J. D. Appl. Spectrosc. 2000, 54, 139.

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Figure 8. Electric field intensity 〈E2〉 in a three-phase system as a function of incident angle. (a) FTIR/ERS: air (n1 ) 1.0, k1 ) 0.0)/thin film of calcium dioleate (n2 ) 1.5694, k2 ) 0.246, d ) 2.4 nm)/fluorite (n3 ) 1.43, k3 ) 0.0). (b) FTIR/IRS: fluorite (n1 ) 1.43, k1 ) 0.0)/thin film of calcium dioleate (n2 ) 1.5694, k2 ) 0.246, d ) 2.4 nm)/air (n3 ) 1.0, k3 ) 0.0). The inset shows the calculation points.

of each other.46-49 Therefore, it is interesting to calculate spectral absorbances as a function of combination of n and k. Figure 9a shows that in the range of k2 from 0.123 to 0.492, which is the typical range for organic materials, spectral absorbance magnitude using the FTIR/ERS technique increases with an increase in n2 values. For all the k2 values selected, the absorbance magnitude increases linearly with an increase in n2 in the range from 1.2 to 2.0. Plots in Figure 9a indicate that equations similar to Beer’s law can be derived for quantitative measurements. This observation is further illustrated in Figure 9c. Figure 9b,d shows that at the incident angle of 20°, 〈EX2〉 and 〈EY2〉 (46) Buffeteau, T.; Le Calvez, E.; Desbat, B.; Pelletier, I.; Pezolet, M. J. Phys. Chem. B 2001, 105, 1464. (47) Lee, S.; Sung, C. S. P. Macromolecules 2001, 34, 599. (48) Ren, Y.; Kato, T. Langmuir 2002, 18, 6699. (49) Buffeteau, T.; Blaudez, D.; Pere, E.; Desbat, B. J. Phys. Chem. B 1999, 103, 5020.

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Figure 9. Calculated FTIR/ERS spectral absorbance and electric field 〈E2〉 components (at 2923.8 cm-1) in a three-phase system (θ ) 20°, d ) 2.4 nm) as a function of optical constants of the film. (a,b) n1 ) 1.0, k1 ) 0.0; k2 ) 0.246 (for b); n3 ) 1.43, k3 ) 0.0. (c,d) n1 ) 1.0, k1 ) 0.0; n2 ) 1.5694 (for d); n3 ) 1.43, k3 ) 0.0.

decrease with increases in n2 and k2 and the rates of change are similar. Meanwhile, 〈EZ22〉 decreases significantly with increases in n2 and k2, which means that the absorbance change for p-polarization is faster than that for s-polarization. The spectral absorbance and 〈E2〉 relationships with respect to n2 and k2 for FTIR/IRS are shown in Figure 10. When k2 is small (