Langmuir 1997, 13, 7211-7216
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Investigation of the Molecular Organization in Langmuir-Blodgett Films Using Polarized Infrared Spectra: Comparison of Two Methods H. Hui-Litwin,† L. Servant,*,‡ M. J. Dignam,§ and M. Moskovits Department of Chemistry, University of Toronto, 80 Saint George Street, Toronto, Ontario M5S 1A1, Canada Received June 24, 1997X We compare two methods for obtaining structural information on Langmuir-Blodgett films from polarized infrared spectroscopy. For sufficiently uniform films, we have already shown (refs 11 and 12) that all polarized spectroscopic properties could be characterized by a single quantity that we call the “electrical surface susceptibility tensor”, γ˜ . The imaginary parts of the susceptibility tensor could be readily obtained from reflectance measurements with the electric field parallel (Im(γt)) and perpendicular (Im(γn)) to the plane of the film, independently of any specific properties of the film. This, in turn, could be related to the characteristics of individual molecules comprising the film, and their geometric disposition if the molecules are assumed to be interacting dipoles, which corrects, to a large extent, for the local field effects. We report the results of an infrared study performed on a dipalmitoylphosphatidylethanolamine monolayer. Attenuated total reflection spectra for both s and p polarization were recorded, and the spectra of Im(γt) and Im(γn), as well as those of the imaginary part of the refractive index (kt and kn), are presented. Finally, the information deduced from the Im(γx) and kx (x ) s, p) are compared, and the molecular orientation is discussed both in terms of Im(γx) and kx. We show that by using this approach one obtains more truthworthy measurements of the disposition of oriented molecules at surfaces than those obtained from absorption coefficients.
1. Introduction Organic thin films offer an attractive method of designing molecular materials for various applications. The properties of such films arise not only from the specific characteristics of the molecules but also from their arrangement within the film.1,2 Polarized infrared spectroscopy has been widely used to obtain information on molecular organization. Since the infrared (IR) absorption depends on the relative orientation of the incident electric field and of the dipole transition moment belonging to the molecular vibration, it is possible to obtain information on the orientation of the molecules by using polarized radiation. In most studies incorporating this approach, the reflectance spectra of a film lying on a substrate are recorded for the electric field parallel and perpendicular to the incident plane. The reflectance is defined as the ratio of the reflected intensity of the film-covered substrate to that of the bare substrate. The results are then discussed in terms of a three-phase stratified model, with an anisotropic film of thickness d, lying between the ambient and the substrate phase.3-6 Here, the connection between the spectroscopic observables and the mean molecular orientation can be derived in principle, but it is not a simple † Now at Centre for Infection and Biomaterials Research, The Toronto Hospital, Bell Wing, Ground Fl., Rm. 631, 200 Elizabeth St., Toronto, ON M5G 2C4, Canada. ‡ Now at Laboratoire de Spectroscopie Mole ´ culaire et Cristalline, URA 124 CNRS, Universite´ Bordeaux I, 351, Cours de La Libe´ration, 33405 Talence Cedex, France. Author to whom correspondence should be sent. § Deceased. X Abstract published in Advance ACS Abstracts, December 1, 1997.
(1) Roberts, G. Langmuir-Blodgett films; Plenum Press: New York, 1990. (2) Ulman, A. An Introduction to Ultrathin Organic films; Academic Press: London, 1991. (3) Buontempo, J. T.; Rice, S. A. J. Chem. Phys. 1993, 98, 5825. (4) Ahn, D. J.; Franses, E. I. J. Phys. Chem. 1992, 96, 9952. (5) Chollet, P. A. Thin Solid Films 1980, 68, 13. (6) Parikh, A. N.; Allara, D. L. J. Chem. Phys. 1992, 96, 927.
S0743-7463(97)00676-8 CCC: $14.00
one. The problem arises from the contribution of the radiation-induced dipole moment to the local electric field experienced by the oscillators. In general, the local electric field acting on a molecule is modified by the electric field radiated by all the surrounding induced dipoles. As a consequence, in an anisotropic medium, the effect of the local field is to alter the direction of the transition moments so that they do not correspond with those of an equivalent set of well-separated molecules. As pointed out by several authors,1,2 the problem of taking into account local field effects in evaluating molecular parameters is not a simple task.3-10 The Lorentz-Lorenz local field expressions are likely to be invalid for ordered Langmuir-Blodgett (LB) systems, where more detailed calculations are required.7 With this in mind, we developed a new approach to evaluate the optical response of an anisotropic molecular layer, taking into account the local field effect, and directly connecting it to measurable spectroscopic quantities.11-15 We show in particular, that the reflectance spectra of a thin uniaxial film lying on a substrate could be understood by considering the elements of a single tensor: the electric surface susceptibility tensor (γ˜ ), which is related simply to the density of the induced dipoles per unit area. In addition, we show that the imaginary parts of the tangential and normal components of γ˜ (Im(γt) and Im(γn)) could be readily obtained directly from the experimental data, without any assumptions regarding film (7) Cnossen, G.; Drabe, K.; Wiersma, D. A. J. Chem. Phys. 1992, 97, 4512. (8) Brossard, Ch.; Kupfer, M.; Florsheimer, M.; Borer, T.; Gunter, P.; Tang, Q.; Zahir, S. Thin Solid Films 1992, 210/211, 198-201. (9) Shen, Y. R. Annu. Rev. Phys. Chem. 1989, 40, 327. (10) Munn, R. W.; Shabat, M. M. J. Chem. Phys. 1993, 99, 10059. (11) Servant, L.; Dignam, M. J. Thin Solid Films 1994, 242, 21. (12) Servant, L.; Dignam, M. J. Unpublished work. (13) Bardwell, J.; Dignam, M. J. Fourier Transform Polarimetry. In Fourier transform Infrared Characterization of Polymers; Ishida, H, Ed.; Plenum Publishing Corp.: New York, 1987. (14) Dignam, M. J. Fourier Transform Polarization Spectroscopy. Appl. Spectrosc. Rev. 1988, 24 (1&2), 99. (15) Dignam, M. J.; Moskovits, M.; Stobie, R. W. Trans. Faraday Soc. 1971, 67, 3306.
© 1997 American Chemical Society
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on the film and P1 is the effective dipole moment induced, for example, by the electric field of an incident infrared beam. The tangential and normal components of γ˜ , γt, and γn can be related to the corresponding components of the bulk dielectric constants of the array n and t, through the equations13,14
γt ) (t/3 - 1)d
(2a)
γn ) (1 - 3/n)d
(2b)
where d is the thickness or assumed thickness of the array. When n and t are substituted into the Fresnel reflection equations applicable to a film that is on average uniaxial and resting on a planar, isotropic substrate, the reflection coefficient for the system is readily expanded in orders of d/λ. On dropping terms of order (d/λ)2 and smaller,13-15 one obtains (for internal reflection)
ln(rv0/rv) ) i2(ω/c) cos θin[Xt + Yv(Xt - Xn) - d] (3)
Figure 1. Structure of DPPE.
properties, e.g., its thickness. Hence γ would depend only on the precision and accuracy of the spectroscopic measurements. In this study, we compare two approaches used to characterize a model monomolecular film on the basis of its reflectance spectra: the new approach, based on Im(γx), x ) s, p, and the more conventional treatment, involving the determination of the imaginary part of the optical constants (kt, kn). The film is a monolayer of the phospholipid dipalmitoylphosphatidylethanolamine, DL(DPPE), whose structure is shown in Figure 1. In section 2, we briefly review the theory behind the surface electric susceptibility approach, emphasizing the aspects that can be directly used for the interpretation of the experimental data. Section 3 describes the preparation of the DPPE monolayers and the experimental procedure. In section 4, we present the spectra in terms of Im(γ) and k and compare the information they provide concerning molecular orientation.
where v ) s or p according to whether the radiation is s or p polarized, rv and rv0 are the complex reflection coefficients for the film-covered and bare surface respectively, ω is the angular frequency, c and θin are the speed of light and the angle of incidence in medium 1, respectively, and i ) x-1. The remaining terms are defined as follows
[
Yp ) cot2 θin Xt )
γ˜ E1 ) 4πP1
(1)
In this expression, E1 is the incident electric field acting
,
(1/3 - 1)
-1
,
Ys ) 0
Xn )
γn (1 - 3/1)
(4a)
(4b)
where the subscripts 1 and 3 identify parameters related to the phases containing the incident and evanescent waves, respectively, and the dielectric functions are represented by , with n and t being the principal dielectric tensor for the fields parallel to and transverse to the surface normal, respectively. These expressions show clearly that the measurable quantity ln(rv0/rv) is proportional to γt and γn. Moreover, in the case of an absorption band, γt and γn are complex valued and from eq 3 we have
2. Theory The approach presented in refs 11 and 12 was intended to capture the effects of the local field on the spectroscopic observables. In this paper, we will treat the case of internal reflection spectroscopy (attenuated total reflection (ATR)), where the incident medium is the bulk substrate phase and the film is in the ambient phase. For simplicity, we assumed that the monolayer could be treated as a set of randomly oriented biaxial domains, each of which is represented by a regular planar array of point polarizable elements, with identical polarizabilities, and situated in identical sites (one element per unit net). For such an array, immersed in a dielectric continuum of dielectric constant 3 (where the subscript 3 refers to the ambient), and arranged on a surface of an isotropic dielectric continuum 1 (1 ) substrate), it is then possible to define the surface susceptibility tensor γ˜ which is 4π times the polarization per unit area in excess of that in the absence of the film divided by the electric field in the ambient:
γt
]
1 3
Im(γt) ) Im(γn) )
(1/3 - 1) 4(ω/c) cos θ
(1 - 3/1)
ln(Rs0/Rs)
(5a)
[(ln(Rs0/Rs)(1 + 1/Yp) -
4(ω/c) cos θ
(ln(Rp0/Rp))/Yp] (5b) A connection may be established between the electric surface susceptibility and the microscopic structure of the film, starting from a model of randomly oriented biaxial domains involving a single localized transition dipole per unit area, all the transition dipole moments being oriented in the same direction: the θ, φ direction, where θ is the tilt angle of the long molecular axis from the film normal and φ is the azimuthal angle. The randomness of the azimuthal orientations of the domains results in a monolayer with optical properties of a uniaxial thin film with its optic axis normal to the film; furthermore, we were able to obtain an analytical expression for Im(γt) and Im(γn) as a function of molecular paramaters of the film. In the case of a hexagonally packed monolayer (i.e., each domain is considered as an hexagonal array), the local field effect can be incorporated through a single
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Langmuir, Vol. 13, No. 26, 1997 7213
constant:
a1 )
∑i
ni
(6)
2ri3
which is present in the various analytical expressions describing the optical properties of the system.11,12 In eq 6, ni is the number of sites in the net at distance ri from the central site. For a hexagonal net, a1 ) 5.515/a3, where a is the nearest neighbor separation. For very dilute films (a being large), a1 tends to zero and the local field effect vanishes, otherwise, a1 has a nonvanishing value, that is related to the lattice constant of the hexagonal array. The results that finally emerged from this analysis are as follows: (i) For an absorption band, the frequency at the maxima of Im(γt) and Im(γn), i.e., ω(γt) and ω(γn) respectively, depend on the tilt angle θ and a1 but are identical for both Im(γt) and Im(γn), which is significant since this is not the case for kt and kn.11 (ii) A useful dichroic ratio, facilitating the direct interpretation of experimental data and taking into account the local field effect, can be defined in terms of Im(γ):11
Dγ )
Im(γt) Im(γn)
1 ) G(a1R⊥0) tan2 θ ) 2 1 + 3a1R⊥0 - 4(a1R⊥0)3 1 tan2 θ (7) 0 3 2 (1 - a R ) 1 ⊥
assuming the principal elements of the polarizability tensor of a given vibrational mode, corresponding to fields perpendicular and parallel to the transition dipole moment, take the form
R⊥ ) R⊥0,
R| ) R|0 +
( )
ω 1ω0
s
2
( )
- iΓ
ω ω0
(8)
where R⊥0 and R|0 are real valued constants representing the high-frequency response, while s is the oscillator strength for the absorption band, Γ is the relative bandwidth, and ω0 is the resonance angular frequency. In other words, the effect of the local field appears explicitly in this definition of the dichroic ratio through a1, accounting for the lattice, and through R⊥0, the highfrequency limit of the polarizability, accounting for the polarizability of the vibration being considered, at a given wavelength. Note that only the perpendicular highfrequency part of the polarizability contributes to eq 7. This definition of the dichroic ratio has the advantage of including explicitly the geometric arrangement of the molecules within the film (through a1) and it can be evaluated directly from measurable quantities (eqs 5a,b). 3. Experimental Section Langmuir-Blodgett Films Fabrication. DL-DPPE (Sigma, 98% purity) was dissolved in 0.88:0.098:0.196 hexanes:methanol: chloroform to give a final concentration of 0.2 mg/mL and sonicated at 50 °C for at least an hour prior to spreading. The solutions were kept in a freezer for storage for no longer than 3 months. A Lauda Film Balance (Sybron Brinkmann, 1974) was used. Prior to each deposition, the trough was cleaned with ACS 2-propanol and methanol. The subphase was distilled deionized water (IWT double cartridge system, Rolen Industries, Toronto, Canada), with resistivity >60 MΩ cm. After filling the trough with the subphase, the pressure sensor was calibrated using the cross and weight set provided by Lauda. A monolayer was spread by applying 500-600 µL of solution dropwise to the water surface. Fifteen minutes was allowed for
Figure 2. Surface pressure-area curves of DPPE monolayer spread from methanol-hexanes-chloroform mixture. solvent evaporation. The film was then compressed at 0.9 cm/ min until the desired surface pressure was reached. The film was allowed to equilibrate an hour before deposition. A typical pressure-area isotherm of DPPE monolayer on aqueous subphase is shown in Figure 2. The area per molecule at a surface pressure of 30 mN/m is approximately 40 Å2, which agrees well with previously reported values.16 Depositions were carried out with a Newport Linear Actuator 850 series, Model PMC100 at a speed of approximatively 0.15 mm/s. A spring-loaded frame with Teflon holding blocks secured the prism during deposition. After each run, the prism was cleaned by immersion in 3:1 CHCl3/ MeOH solution and sonicating for 3 h at 60 °C, and the solvent was changed every hour. FTIR Spectroscopy. Infrared spectra were recorded with a Bomem M110 upgraded to an MB100 equivalent, equipped with a liquid nitrogen cooled mercury cadmium telluride MCT detector. The spectra were collected at a resolution of 4 cm-1. The sample chamber was purged overnight with a Balston air purification system, which removed CO2 and water vapor. A square ZnSe prism (55 × 55 × 3 mm., face angle θ ) 45°) manufactured by Harrick Scientific Corp. (Ossining, NY) was used for ATR measurements. We designed a square prism in order to be able to detect possible in-plane anisotropy; after the film was deposited, we checked that the spectra obtained by rotating the prism 90° could be exactly superimposed onto the original spectra, establishing that the film was uniaxial. For DPPE monolayers, it was found that satisfactory signal to noise ratios could be obtained for as few as 50 scans. For room temperature scans, 250 scans were coadded. The prism was mounted in a sample holder in the spectrometer during scanning. The holder consisted of two copper slabs, with the prism sandwiched between them. The inside surfaces of the holder were coated with a gold layer (Applied Physics, Toronto, Canada). In order to ensure that the ambient medium was air, the cell was built such that thermal contact was made only between the prism and the holder at the outer perimeter of the prism.
4. Results and Discussion The reflectance spectra in (s) and (p) polarization, obtained by taking the ratio of the spectra of the filmcovered prism to the one of the bare prism, are shown in Figure 3. These spectra show the CH2 stretching mode (16) Huang, W. T.; Levitt, D. G. Biophys. J. 1977, 17, 111.
7214 Langmuir, Vol. 13, No. 26, 1997
Figure 3. Polarized rv/rv0 ATR spectra (v ) s, p) of DPPE monolayer deposited on a ZnSe prism.
Figure 4. Spectra of the imaginary parts of the optical constants, kt and kn, of the DPPE monolayer, as deduced from the Dignam and Bardwell modified Kramers-Kronig approach (thickness of the film, d ) 0.0025 µm; high-frequency refractive index, N ) 1.5).
region (2800-3000 cm-1) and a number of bands involving a mixture of CH2 wagging, twisting, and rocking vibration in the 1000-1500 cm-1 region. Also apparent is a strong absorption band at about 1740 cm-1 due to the stretching of the CdO group (ν(CdO)) and a singlet band due to the scissoring mode of the CH2 (δ(CH2)) at 1468 cm-1. The presence of a single band for the scissoring CH2 mode can be explained if the monolayer has a hexagonal bidimensional packing; the subcell contains only one molecule.17 The bands in the 1075-1225 cm-1 region are characteristic of the phosphate-stretching modes. The reflectance spectra were processed in order to extract the normal and transverse components of the imaginary part of the refractive indicies (kt, kn), using an approach developed by Bardwell and Dignam.13,14 In this method, it is necessary to specify a thickness d for the film and a value for the high-frequency limit of the refractive index N: we took N ) 1.5 and d ) 0.0025 µm. By contrast, no assumption are needed to get (Im(γt), Im(γn)) spectra: they are straightforwardly obtained from experimental data via eqs 5a,b. The resulting k and γ spectra are displayed in Figures 4 and 5. The overall appearance of the spectra is similar for k and Im(γ) in terms of the presence of the various bands and their relative intensities for a given polarization. For example, four bands in the CH stretching mode region are seen in (17) Tasumi, M.; Shimanouchi, T. J. Chem. Phys. 1965, 43, 1245.
Hui-Litwin et al.
Figure 5. Spectra of Im(γt) and Im(γn) of the DPPE monolayer, as deduced from eqs 5a,b.
the spectra showing the normal components of both Im(γ) and k: the two strong bands at 2920 and 2850 cm-1 are assigned to the methylene antisymmetric and symmetric stretching modes, respectively, and the weaker bands near 2950 and 2870 cm-1 are due to the asymmetric and symmetric stretching modes of the terminal methyl group.18 The phosphate stretching mode region is dominated by two main features near 1225 and 1075 cm-1 that have been assigned to the PO2 asymmetric and symmetric stretching modes, respectively.19 Furthermore, it should be emphazised that a number of weak bands superimposed onto the PO2 asymmetric stretch mode, due to acyl chain methylene wagging, are apparent in both the kn and Im(γn) spectra. However, for all vibrationnal modes, the difference between the frequency at the maxima of Im(γt) and Im(γn) (i.e., ω(γt) - ω(γn)), is systematically smaller than the corresponding one for kt and kn (ω(kt) - ω(kn)), which is consistent with the theory, predicting that ω(γt) and ω(γn)) should be identical for Im(γt) and Im(γn), in contrast with ω(kt) and ω(kn). The molecular orientation within the film was determined using the CO stretching mode and the localized CH2 symmetric and asymmetric stretching modes, in order to infer the average tilt angle θ of the hydrocarbon chains from the surface normal. The two dichroic ratios which are naturally defined for γ or k are
Dγ ) Im(γt)/Im(γn)
(10a)
Dk ) kt/kn
(10b)
In the case of k spectra and for an uniaxial film, a straightforward relation exists between θ and Dk, assuming the absorption to be due to a single isolated transition dipole moment, tilted by an angle θ from the film normal. Such a relation, which is, of course, approximate as it neglects local field effects, holds only for dilute films. In order to evaluate the average tilt angle from Dγ, using eq 7, we need to know a1 and R⊥0. The DPPE monolayer being hexagonally packed (as evidenced from the singlet δ(CH2) scissoring mode) eq 5 was used to obtain a1. From the pressure-area isotherm displayed in Figure 2, it can be seen that the area per molecule at 30 mN/m is 40 Å2, which leads to an area per alkyl chain roughly equal to 20 Å2, and the corresponding interchain distance is about a ) 4.8 Å. This value is consistent with (18) Cameron, D. G.; Casal, H. H.; Mantsch, H. H. Biochemisry 1980, 19, 3665. (19) Lafrance, D.; Marion, D.; Pezolet, M. Biochemistry 1990, 29, 4592.
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Table 1. The Average Tilt Angles of Dipole Moments for (DL)DPPE Monolayers Deposited onto ZnSe, Obtained from the Absorption Index, kv, v ) s, p vibrational mode
(a)
transition dipole angle (deg)
CH2 asym str CH2 sym str CdO stretch
65.9 69.1 61.0
av hydrocarbon chain tilt angle
32.8
Table 2. The Average Tilt Angles of Dipole Moments for (DL)DPPE Monolayers Deposited onto ZnSe, Obtained from Im(γv), v ) s, p vibrational mode
transition dipole angle (deg)
CH2 asym str CH2 sym str CdO stretch
75.8 77.8 72.4
av hydrocarbon chain tilt angle
18.8
previouly reported X-ray data,5 giving a ) 4.6 Å. We obtain finally a1 ) 0.05 Å-3. The evaluation of R⊥0 is less straightforward; it represents the high-frequency contribution limit of the polarizability of the localized mode under study. An exact calculation of the polarizability requires a complete quantum mechanical solution and is only possible for very simple molecules. However, a good approximation may be obtained from the molar refraction MR20,21 through the relation MR ) (4/3)πNAR (NA being the Avogadro constant). It is well-known that the molar refraction for a particular moiety is the sum of its contributing bond refractions. This is a well established procedure involving the vector sum of tabulated bond polarizabilities. Since most of the tabulated values refer to the Na D-line, the resultant polarizability is in the required high-frequency limit. For example, the bond refraction for the CH bond is approximately 1.69 cm3.20 Therefore, MR for the CH2 group takes the value 2(1.69) ) 3.38 cm3, which finally gives an estimate of the polarizability R⊥0 ) 1.34 Å3. Using a1 ) 0.05 Å-3, one gets G(a1R⊥0) ) 1.48 (eq 7). As an example, for the CH2 asymmetric stretch dipole at room temperature, using band area, one obtains D ) 14.73. Substituing D and G values into eq 7, one obtains 75.8° as the angle of the CH2 asymmetric stretch dipole tilt from the z axis. Similarly, the angle of the dipole of the CH2 symmetric stretch comes out to be 77.8°. The average tilt angle for the hydrocarbon chains (θ) can be obtained from the average angles of the transition dipole moments calculated for the CH2 asymmetric (θasym) and symmetric (θsym) stretching modes through the relationship22
cos2 θasym + cos2 θsym + cos2 θ ) 1
(11)
The angles calculated for the transition moments of three vibrations and the resulting values of the tilt angle of the DPPE chains are presented in Tables 1 and 2, based on the dichroic ratios Dk and Dγ, respectively, and evaluated from the ratios of the corresponding integrated intensities. The definition of the tilt angles is given in Figure 6. In general, the angles of the transition dipoles appear to be systematically underestimated by approximately 10° and hence the value of the chain tilt is overestimated by approximatedly 13° when kv is used as opposed to γv. These differences are due to the local fields, which are ap(20) Denbigh, K. G. Faraday Soc. Trans. 1940, 36, 936. (21) Smith, R. P.; Martensen, E. M. J. Chem. Phys. 1960, 32, 502, 508. (22) Hasegawa, T.; Takeda, S.; Kawaguchi, A.; Umemura, J. Langmuir 1995, 11, 1236.
(b)
Figure 6. The orientation of the transition dipole moments with respect to the molecular axis. The average angle between the film normal and the CdO stretching transition dipole moment, θCdO, is shown in (a), whereas the average angles between the film normal and the hydrocarbon chain axis, θ, and the CH2 asymmetric stretching dipole moment, θCH2(asym) and the CH2 symmetric stretching dipole moment, θCH2(sym) are shown in (b); M is the transition dipole moment.
proximately taken into account in the latter approach and neglected in the former. On the basis of the values of Dγ associated with the CH2 stretching vibrations, together with eq 9, one determines, θ, the tilt angle of the hydrocarbon chains from the surface normal to be 18.8 ( 1.7°. This is consistent with the inclination determined for the transition dipole moment associated with the CO vibration which is found to be tilted 72.4 ( 1.1° from the film normal, implying a chain tilt angle of 17.6°. For a well-packed layer of phospholipid molecules, the chains of the molecules are expected to be aligned close to the film normal. A range of tilt angles has been reported in the literature, on the basis of a variety of measurements techniques, for the DPPE chains. Single crystal X-ray analysis of DL-DLPE12 indicated that the chains are essentially perpendicular to the film plane. The confidence limit indicated in ref 12 encompass a small tilt angle such as the one we find. 5. Conclusion We considered the molecular information that could be obtained from polarized infrared spectroscopy, using a
7216 Langmuir, Vol. 13, No. 26, 1997
new method based on the surface susceptibility tensor approach. Using this treatment, the sample is modeled as a layer of discrete particles, characterized by its electric surface susceptibility rather than a continuous film. It can be shown that the electric surface susceptibility is directly related to the number of induced dipole moments per unit area, the imaginary part of which is a more accurate measure of the absorption properties of the molecules since it includes the effect of fields induced by neighboring molecules. In addition, the expressions relating the reflectance to Im(γ) are simple and direct.
Hui-Litwin et al.
Using DPPE monolayers as a model system, it was found that the spectra of the imaginary part of the susceptibility tensor yielded tilt angles that were consistently approximately 10° smaller than those deduced from the imaginary parts of the anisotropic optical constants. Such discrepancies illustrate and emphasize the importance of the local field in interpreting and extracting the molecular orientation from polarized spectroscopic data. LA970676G
