Infrared Spectroscopic Analysis of Sub-Monolayer Perfluoropolyether Z-Tetraol Films Used in Boundary Lubrication Robert J. Waltman HGST/Western Digital Company, 5601 Great Oaks Parkway, San Jose, CA 95119 USA
Infrared specular reflection spectra of Z-Tetraol on a gold substrate was simulated and studied experimentally. The simulated spectra were obtained using a classical dispersion analysis coupled with solutions of Maxwell’s equations for transmission and reflection of electromagnetic radiation. The simulated spectra, which are based on a randomly oriented sample, provide excellent fits for Z-Tetraol over a wide film thickness range. Spectroscopic data are provided for the Z-Tetraol –(CF2O)p–(CF2CF2O)q– main chain. The differences in the transverse and longitudinal optical infrared spectra are discussed for off-normal reflection spectra in the thin film limit. Corrections to the infrared reflection spectra for sub-monolayer coverage using effective medium theory are also discussed. Index Headings: Perfluoropolyethers; Reflection infrared spectroscopy; Boundary lubricants.
INTRODUCTION Perfluoropolyether (PFPE) liquids are widely used in technology as vacuum pump fluids,1 hydrodynamic or elastohydrodynamic lubricants in space engineering devices,2 and as boundary lubricants in computer harddisk drives.3 In order to assess or monitor the chemical integrity of the PFPE liquids as a function of the device life, many of these applications require suitable analytical tools that are capable of detecting minute physical interactions and chemical changes at interfaces. One such tool, infrared spectroscopy, in particular Fourier transform infrared (FT-IR), has been widely used.4 Thin film coatings applied on metal surfaces present additional problems for an analysis using infrared spectroscopy. Due to specular reflection from the metal surface, complicated optical interference effects render this analysis significantly less straightforward than one using transmission spectroscopy. The interference depends on the film thickness, angle of incidence, polarization of the incoming electric field, and the absorption characteristics of the metal substrate and overlaying films. In general, when the film is very thin, specular reflection tends to simplify; however, one should not interpret this as a cardinal rule. For example, longitudinal optical excitations, while infrared (IR) inactive in the bulk, become observable as a result of finite film thickness effects.5 Specular reflection in the infrared spectral region is completely simulated once the optical constants are known for the metal substrate and coated films. With the Received 22 July 2013; accepted 18 December 2013. E-mail: [email protected]. DOI: 10.1366/13-07229
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optical constants, specular reflection spectra may be easily calculated from solutions to Maxwell’s equations. Thus, a computer can be used to provide complex refractive indices over the infrared, and in turn calculate reflection spectra for any film thickness, angle of incidence, or polarization of the incident electric field. In the computer disk industry, specular reflectance infrared spectroscopy is well used to monitor changes in the composition of the disk surface. For example, contaminants that adsorb onto the disk surface or chemical and physical changes induced in the PFPE boundary lubricant film itself as a result of slider–disk interactions are all amenable to analysis using specular reflection infrared spectroscopy. In order to facilitate the interpretation of such spectra, we investigate herein the infrared spectroscopy of the Fomblin Z fluid ‘‘Z-Tetraol’’ and report its optical constants and oscillator parameters. Z-Tetraol is used in the computer disk industry as a boundary lubricant film because it is truncated by OH end groups that provide adhesion to the underlying rigid disk. The main chain is composed of a copolymer of perfluoromethylene- and perfluoroethylene-oxide monomer units. HOCH2 CHðOHÞCH2 OCH2 CF2 OðCF2 OÞp ðCF2 CF2 OÞq CF2 CH2 OCH2 CHðOHÞCH2 OH
EXPERIMENTAL SECTION Z-Tetraol was obtained from Solvay Solexis under the trade name Z-Tetraol-GT (q/p = 1.0, Mn = 2200). Samples of Z-Tetraol were applied to gold or sodium chloride substrates by spin coating the liquids from a hydrofluoroether solvent. Sample thicknesses were measured by relating the infrared integrated absorbance of a characteristic absorption band to film thickness. For thin films (, 20 A˚), film thicknesses were quantified using electron spectroscopy for chemical analysis (ESCA) using a Phi Quantum 2000 ESCA system using a takeoff angle of 458 and an electron mean free path of 25 A˚ (Fig. 1).6 Thicker films were quantified ellipso-metrically using a Rudolph Research Auto-El III. Infrared spectroscopic measurements were performed using a Nicolet Magna Model 560 Infrared Spectrometer. A standard specular reflection adapter (Harrick, New York) was used to maintain the proper angle of incidence to the sample.
REFLECTANCE MEASUREMENTS AND CALCULATIONS An account of the method used to determine the refractive index of the PFPE based on the perfluoropro-
0003-7028/14/6805-0593/0 Q 2014 Society for Applied Spectroscopy
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FIG. 1. The FT-IR thickness calibration to ESCA for Z-Tetraol in the ultrathin 10 to 20 A˚ regime.
pyleneoxide monomer unit, –[CF(CF3)CF2O]–, has been reported.7 Therefore, only those details pertinent for this report will be given. In essence, the method treats the polymer as consisting of a collection of Lorentzian oscillators whose band centers, widths, and strengths are obtained from a transmission infrared absorption spectrum. The oscillator parameters are then used to compute the complex dielectric function, which in turn is equated to the complex refractive index. These, along with the refractive index of the metal (gold substrate), are combined with the solutions of Maxwell’s equations for transmission and reflection of electromagnetic radiation at interfaces. As an orientation for the optical parameters describing the specular reflection, consider the three-layer system as the air–perfluoropolyether–gold system shown in Fig. 2. Hence, the three refractive indices are n1 = 1.0, for air; for polyperfluoroether, n~2 ¼ n2 þ ij2
ð1Þ
for the gold substrate, n~3 ¼ n3 þ ij3
ð2Þ
In Eqs. 1 and 2, n2 and n3 are the real parts of the refractive indices for the polyperfluoroether and gold, respectively, while j2 and j3 are the imaginary parts, respectively. In the calculations that follow, the angle of incidence for the infrared light is maintained at 718 from normal, and h is defined as the perfluoropolyether (PFPE) film thickness. The optical constants for the PFPE were individually related to wavenumber through a dispersion analysis. Since the dispersion analysis is only performed on the PFPE, the subscript 2 will be dropped in the following discussion for the sake of brevity. The refractive index for the PFPE is cast in the form of the dielectric constant as e ¼ ð˜ n2 Þ2 ¼ er þ iei
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ð3Þ
FIG. 2. Illustration of the three layer system, air–PFPE–gold, used for the dispersion analysis and reflectance calculations.
where e r ¼ n 2 j2
ð4Þ
ei ¼ 2nj
ð5Þ
and
Using Eqs. 4 and 5, the following expressions for n and j are obtained. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 2 2 n ¼ er þ ei þ er ð6Þ 2 j2 ¼
1 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2r þ e2i er
ð7Þ
The real and imaginary part of the dielectric constant, er and ei, were determined using the classical dispersion analysis reported by Spitzer and Kleinman8 and Maeda and Schatz9 as given below: er ¼ eo þ
j¼N X
4pqj m2j
j¼1
m2j m2 ðm2j m2 Þ2 þ c2j m2j m2
ð8Þ
and ei ¼
j¼N X j¼1
4pqj m2j
ðm2j
cj m j m 2 2
m Þ þ c2j m2j m2
ð9Þ
where the summation is over the N oscillators in the system; eo is the short wavelength dielectric constant; mj is the frequency of the jth oscillator; the damping constant, cj, is related to the band width at half-height by cj ¼
Dmð1=2Þ mj
ð10Þ
and qj is related to the oscillator strength by qj ¼
ð˜ nAj Þ 4p3 m2j
ð11Þ
To ln dm T
ð12Þ
where Aj ¼
1 h
Z
n˜ is the mean refractive index, and To/T is the inverse of the transmittance. To obtain n and j it is necessary to have the short wavelength contribution to the dielectric constant, i.e., in this case the electronic contribution, the number of oscillators, and their frequency, width, and strength. The short wavelength contribution to the dielectric was taken as the value measured at the 0.6328 lm line of a He/Ne laser.10 The real part of the refractive index for ZTetraol at this wavelength was 1.298. The refractive index for gold was taken from a Drude model fit11 using a damping frequency (xs) of 216 cm1 and a plasma frequency (xp) of 7.25 3 104 cm1. Both n3 and j3 were calculated using the following expressions: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n32 ¼ e21 þ e22 þ e1 ð13Þ 2 j23 ¼
1 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e21 þ e22 e1
ð14Þ
where e1 ¼ e‘
e2 ¼
x2p x2 þ x2s
x2p xs þ xx2s
x3
ð15Þ
ð16Þ
e‘ = 1.0, and x is the frequency at which a particular value for the dielectric constant is required. The process of obtaining a dispersion analysis is, in essence, an iterative process where initially the integrated absorbance, Aj, is obtained using transmission spectra. Subsequently, the spectra are fit to Eqs. 6 and 7. The reflectance in the infrared was calculated following the formalism given by Born and Wolfe.12 The equations for the reflection coefficients for the components of the electric field parallel and perpendicular to the plane of incidence at interfaces 12 and 23 are well known and can be found in a previous publication.7 With these equations, the reflectance spectra may be calculated for any Z-Tetraol film thickness and angle of incidence. The experimental reflection IR spectra reported herein are obtained using p-polarized light, and so the calculated reflectance spectra are also p-polarized.
RESULTS AND DISCUSSION The experimental transmission IR spectrum for ZTetraol is first shown in Fig. 3a. The various IR absorption bands from the –(CF2O)p–(CF2CF2O)q– main chain in the 1400–900 cm1 region are attributed
FIG. 3. (a) The experimental transmission infrared spectrum for a 0.044 lm Z-Tetraol film on a NaCl substrate. (b)–(d) The HF/6-31G(d) computed IR spectra for the Z-Tetraol model C9F20O5 as a function of the half-height band widths 75, 50, and 16 cm1. (e) The HF/6-31G(d) computed IR spectra for the Z-Tetraol model C9F20O5 as a ‘‘stick spectrum’’ showing all of the oscillators between 1400 and 900 cm1. All of the computed IR spectra are uniformly scaled in wavenumber (cm1) by 0.84 to match the transmission experimental spectrum at 1200 cm1.
primarily to the numerous C–F, C–O, and C–C stretching vibrations that are coupled and hence create a rather broad envelope that is difficult to deconvolve. Since the oscillator parameters derived from the transmission spectrum will be used as the basis for the reflectivity calculations to be shown later, we first provide some qualitative understanding of the relationship between the observed transmission IR spectrum and the oscillators that produce the absorption bands. We use the power of ab initio calculations13 to provide insight into the ZTetraol transmission IR spectrum. The Z-Tetraol model structures used to calculate the IR spectra are summarized in Fig. 4. All of the model structures are fully optimized geometries with no computed imaginary frequencies. The total energy for each model structure is specified in the figure caption. For reasons to be disclosed below, we have chosen the C9F20O5 as the model structure for Z-Tetraol. The computed C9F20O5 IR spectra are shown in Fig. 3b–3e below the experimental IR spectrum. All of the computed vibrations in this wavenumber regime (1600–900 cm1) are presented as a ‘‘stick’’ spectrum in Fig. 3e. The number of normal modes is large (27), and all contribute to the IR spectrum. When the ab initio computed IR spectrum is modeled as a series of Lorentzian oscillators whose band widths at halfheight are increased systematically from 16 to 75 cm1,
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FIG. 4. The HF/6-31G(d) optimized geometries for some Z-Tetraol model structures. The total energies (Hartree) are 1532.36476835 (C5F12O2); 2155.60932077 (C7F16O4); 2703.97148593 (C9F20O5); 3252.33567964 (C11F24O6); 3800.69987200 (C13F28O7).
the broad absorption band in the experimental spectrum is increasingly reproduced. This is an artificial exercise simply used to render the computed IR spectrum more similar to the experimental IR spectrum to compensate for the deficiencies of having used smaller model structures (Fig. 4) for the purposes of computational tractability. At the experimental molecular weight of 2200, the stoichiometry of the Z-Tetraol main chain (excluding end groups) is approximately C30F60O20. Our largest model structure is C13F28O7. Figure 5 further illustrates the effect
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of model size and the computed IR spectrum. With increasing model size, contributions to the IR band shape from the end group vibrations are increasingly reduced to render the computed IR spectrum more like the experimental spectrum. Figure 5 indicates that the experimental IR spectrum can be reproduced adequately using a nine carbon atom model structure for Z-Tetraol. Thus the computed IR spectrum for the C9F20O5 model structure is greatly simplified to approximately eight ‘‘major’’ group vibrations at the 16 cm1 resolution (Fig. 3). The computed
FIG. 5. The HF/6-31G(d) computed transmission IR spectra for the Z-Tetraol model structures as a function of main chain length.
potential energy distribution for these ‘‘bands’’ is summarized in Table I. Except for the C–C stretching vibration at the scaled 1340 cm1, most of the other normal modes are combinations of C–O and C–F stretching vibrations. The use of correlated wavefunctions often improves the computed IR spectrum even at the modest 6-31G(d) basis set. This aspect was explored for the C9F20O5 model structure, and the results are shown in Fig. 6. While the correction factor for the normal mode frequencies is greatly improved from the 0.84 used to correct the Hartree–Fock (HF) to 0.96 for the density
functional theory (DFT) frequencies, the computed IR spectra are qualitatively similar after all. Thus HF/631G(d) data were used throughout. Guided by the ab initio computed IR results, eight oscillator parameters were used to fit the experimental transmission spectrum. The film thickness, integrated intensities, band centers, and widths extracted from the transmission spectrum are listed in Table II. These data were in turn used to generate the optical constants using the dispersion analysis described herein. The quality of the oscillator parameters listed in Table II to generate
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TABLE I. Potential energy distribution (PED) of the major IR bands for C9F20O5 computed at HF/6-31G(d).
TABLE II. Oscillator parameters for a 0.044 lm film of Z-Tetraol GT.
Computed Computed band Band No. band center center (cm1) Scaled 3 0.84 Fig. 1 (cm1)
Band center (cm1)
1 2 3 4 5 6 7 8
1595 1511 1467 1442 1411 1323 1236 1038
1340 1269 1232 1211 1185 1111 1213 1019
PED C–C str C–F str (CF3); C–O str; C–C str C–O str; C–F str C–O str; C–F str C–O str; C–F str C–O str C–O str; C–F str C–O str; C–F str; C–O–C bend
the optical constants was assessed by first computing the transmission IR spectra from which they were derived. This is shown in Fig. 7, directly below the experimental transmission spectrum. The side-by-side comparison indicates an excellent fit between the experimental and simulated transmission IR spectra and indicates that the oscillator parameters derived using this methodology are useful and can be used in a general manner. We now discuss IR reflection spectra of Z-Tetraol. Figure 8a directly compares the transmission and the reflection spectra of Z-Tetraol. Qualitatively they are different enough such that the spectra could be misinterpreted as originating from different materials. However, this is not the case. One needs to account for the
1297.1 1266.0 1225.0 1194.7 1144.6 1120.0 1095.9 1070.2
Integrated area (cm1)
Band width (cm1) at half-height
0.22 0.24 1.97 1.21 0.74 0.21 0.43 0.51
60.0 34.0 60.0 45.0 43.0 28.0 35.0 38.0
fact that both transverse optical (TO) and longitudinal optical (LO) excitations are associated with each resonance term in the dielectric function that can be observed in the IR spectra.5,14,15 When the IR radiation is normal to the sample surface, only TO vibrations are detected due to the transverse character of the electromagnetic radiation. However, in reflection spectroscopy employing IR radiation at angles off-normal to the surface, both LO and TO surface modes can be excited in the thin film limit.5 The TO and LO modes are separated in frequency using the Lyddane–Sachs–Teller relation16 where the LO frequency is shifted to a higher wavenumber from that of the TO frequency by an amount that is approximately proportional to the absorption strength, i.e., the stronger the absorption the greater the shift of the LO frequency. One can then begin to understand why the experimental reflection and transmission spectra shown in Fig. 8a are so different. Figure 8b shows the TO and LO energy loss functions that are calculated from the optical constants given in Table II. The LO spectrum, Im(1/e), is calculated using Eq. 17.16 Imð1=eÞ ¼
FIG. 6. A comparison of the C9F20O5 computed transmission IR spectrum between the HF and B3LYP theories at the 6-31G(d) basis set. The B3LYP spectrum is uniformly scaled in wavenumber (cm1) by 0.96 to match the HF spectrum.
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ei er 2 þ ei 2
ð17Þ
For the reflection IR spectra, the incident infrared radiation for both simulated and observed cases is ppolarized with an angle of incidence equal to 718. The experimental reflection spectrum contains an appreciable contribution from the LO vibrations. Observed and computed specular reflection spectra for Z-Tetraol are now shown in Figs. 9b and 9a, respectively, as a function of film thickness between 2 and 27 A˚. This thickness range covers the actual film thicknesses typically used in hard-disk drives. All of the experimental spectra were recorded using gold as a substrate. As the results show, excellent agreement between the observed and simulated reflectance IR spectra is qualitatively obtained with one exception. In the experimental spectra, the band center of the main absorption band at 1283 cm1 is observed to shift to a lower wavenumber (cm1) with decreasing film thickness, Fig. 10a. This experimental feature is not reproduced in the simulated reflectance spectra, Fig. 9a, for these ultrathin films. The shift in the band center with decreasing film thickness is experimentally observed for film thicknesses below approximately 15 A˚. The dispersive surface energy versus Z-Tetraol film thickness on
FIG. 7. The experimental and calculated transmission spectra for a 0.044 lm Z-Tetraol film on NaCl. The calculated spectrum is derived from the oscillator parameters specified in Table II. The calculated spectrum is offset in the y-axis by 2% for ease of comparison to the experimental spectrum.
FIG. 8. (a) Plots comparing the experimental transmission and p-polarized reflection infrared spectra of Z-Tetraol. The transmission spectrum is on NaCl, while the reflection spectrum is on Au at an angle of incidence of 718. (b) The calculated TO and LO spectrum of Z-Tetraol using the oscillator parameters in Table II.
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FIG. 9. Plots comparing the experimental and calculated specular reflection infrared spectra of Z-Tetraol on gold as a function of film thickness at an angle of incidence = 718. The experimental film thicknesses in (b) are 1.6, 3.3, 4.6, 6.8, 9.6, 13.3, 14.6, 18.3, 27.4 A˚ in increasing reflectivity. The calculated reflection spectra are shown in (a) and (c), where (a) is uncorrected and (c) is corrected using EMA (effective medium approximation).
carbon films (not Au) is also observed to decrease with decreasing film thickness to reach an asymptotic or limiting value near 15 A˚ (Fig. 10c). The changes in the dispersive surface energy are related to film coverage.17 The asymptotic value in the dispersive surface energy is taken as an indication for full surface coverage. By analogy, the shift in the IR band center is attributed to surface coverage effects. This band shift may be reproduced in the calculated reflection IR spectra by correcting the computed dielectric constant as a function of wavenumber using the effective medium theory (EMT).
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EMTs describe randomly mixed composites in terms of a spatially homogeneous electromagnetic response. Assuming an increasingly ‘‘patchy coverage’’ with decreasing Z-Tetraol film thickness below the monolayer thickness, the averaging effects in the dielectric constant as a function of wavenumber are simulated by mixing the refractive indexes for air and Z-Tetraol. Here we employ the ‘‘power law’’ approximation:18 eaeff ¼
N X i¼1
fi eai
ð18Þ
and the changes in the dispersive surface energy, Figs. 10a and 10c.
CONCLUSIONS This study reports useful spectroscopic data for the ZTetraol perfluoropolyether. The oscillator parameters reported herein can be used to calculate reflection spectra for any film thickness and any angle of incidence. We have shown that reflection and transmission spectra do not necessarily match, since LO excitations are possible in the thin film limit of offnormal reflection spectroscopy. In the sub-monolayer film thickness regime, the reflection IR spectrum is further complicated by ‘‘patchy coverage.’’ This could be corrected using effective medium theory and treating the composite film dielectric constant as deriving from a film/air mixture. ACKNOWLEDGMENT The author is indebted to J. Pacansky for many fruitful discussions on IR specular reflection and dispersion analysis.
FIG. 10. Plots comparing the changes in (a) band center; (b) fractional coverage in the effective medium approximation that best matches the experimental reflection spectrum in Fig. 9; and (c) changes in the dispersive surface energy as a function of Z-Tetraol film thickness.
eeff, fi, and ei are the effective dielectric constant of the composite, volume fraction, and the dielectric constant of the ith phase. In our calculations, we have chosen to use a = ½ for no reason other than to demonstrate that the band center shift could be corrected using an EMT treatment. The value of a is related to the geometry of the scatterers, where a = ½ is attributed to cylindrical shaped scatterers.18 The power law is used here since it can be applied to both dilute and dense mixture composites and is appropriate for the thickness range covered in these studies.19 The results of applying the EMT to the calculated reflection spectra below full surface coverage are shown in Fig. 9c. Note the shift in the band center to lower wavenumbers with decreasing film thickness. The fractional coverage required to simulate the experimental reflection spectrum is plotted in Fig. 10b. The plot is correlated to the band center shift
1. L. Holland, L. Laurenson, P.N. Baker, H.J. Davis. ‘‘Perfluoropolyether–a Vacuum Pump Fluid Resistant to Electron Induced Polymerization’’. Nature. 1972. 238(5358): 36-37. 2. T. Kaldonski, P.P. Wojdyna. ‘‘Liquid Lubricants for Space Engineering and Methods for Their Testing’’. J. KONES. 2011. 18(1): 163184. 3. A.M. Scarati, G. Caporiccio. ‘‘Frictional Behaviour and Wear Resistance of Rigid Disks Lubricated with Neutral and Functional Perfluoropolyethers’’. IEEE Trans. Magn. 1987. 23(1): 106-108. 4. K. Merchant, P. Mee, M. Smallen, S. Smith. ‘‘Lubricant Bonding and Orientation on Carbon Coated Media’’. IEEE Trans. Magn. 1990. 26(5): 2688-2690. 5. D.W. Berreman. ‘‘Infrared Absorption at Longitudinal Optic Frequency in Cubic Crystal Films’’. Phys. Rev. 1963. 130(6): 2193-2198. 6. M.F. Toney, C.M. Mate, D.J. Pocker. ‘‘Calibrating ESCA and Ellipsometry Measurements of Perfluoropolyether Lubricant Thickness’’. IEEE Trans. Magn. 1998. 34(4): 1774-1776. 7. J. Pacansky, C.D. England, R.J. Waltman. ‘‘Infrared Spectroscopic Studies of Poly(perfluoropropyleneoxide) on Gold Substrates: A Classical Dispersion Analysis for the Refractive Index’’. Appl. Spectrosc. 1986. 40(1): 8-16. 8. W.G. Spitzer, D.A. Kleinman. ‘‘Infrared Lattice Bands of Quartz’’. Phys. Rev. 1961. 121(5): 1324-1335. 9. S. Maeda, P.N. Schatz. ‘‘Absolute Infrared Intensity Measurements in Thin Films’’. J. Chem. Phys. 1961. 35(5): 1617-1621. 10. J.D. Swalen, R. Santo, M. Tacke, J. Fischer. ‘‘Properties of Polymeric Thin Films by Integrated Optical Techniques’’. IBM J. Res. Dev. 1977. 21(2): 168-175. 11. M.A. Ordal, L.L. Long, R.J. Bell, S.E. Bell, R.R. Bell, R.W. Alexander, Jr., C.A. Ward. ‘‘Optical Properties of the Metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the Infrared and Far Infrared’’. Appl. Opt. 1983. 22(7): 1099-1119. 12. M. Born, E. Wolf. ‘‘Principles of Optics’’. Oxford, UK: Pergamon Press, 1970. Pp. 36-47. 13. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. AlLaham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill,
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B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople. Gaussian 03, Revision D.01. Wallingford, CT: Gaussian, Inc., 2004. 14. Y.-S. Yen, J.S. Wong. ‘‘Infrared Reflectance Properties of Surface Thin Films’’. J. Phys. Chem. 1989. 93(20): 7208-7216. 15. M.A. Karakassides, D. Petridis, D. Gournis. ‘‘Infrared Reflectance Study of Thermally Treated Li and Cs-Montmorillonites’’. Clays Clay Miner. 1997. 45(5): 649-658. 16. M.F. Al-Mudhaffer, M.A. Nattiq, M.A. Jaber. ‘‘Linear Optical Properties and Energy Loss Function of Novolac: Epoxy Blend Film’’. Archives Appl. Sci. Res. 2012. 4(4): 1731-7140.
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17. H. Chen, M.S. Jhon. ‘‘Relationship Between Surface Coverage and End Group Functionality of Molecularly Thin Perfluoropolyether Films’’. J. Appl. Phys. 2008. 103(7): 07F536-1-07F536-3. 18. P.H. Zhou, L.J. Deng, B.-I. Wu, J.A. Kong. ‘‘Influence of Scatterer’s Geometry on Power-Law Formula in Random Mixing Composites’’. Prog. Electromagn. Res. 2008. 85: 69-82. 19. W.M. Merrill, R.E. Diaz, M.M. LoRe, M.C. Squires, N.G. Alexopoulos. ‘‘Effective Medium Theories for Artificial Materials Composed of Multiple Sizes of Spherical Inclusions in a Host Medium’’. IEEE Trans. Antennas Propag. 1999. 47(1): 142-148.
Infrared specular reflection spectra of Z-Tetraol on a gold substrate was simulated and studied experimentally. The simulated spectra were obtained using a classical dispersion analysis coupled with solutions of Maxwell’s equations for transmission and reflection of electromagnetic radiation. The simulated spectra, which are based on a randomly oriented sample, provide excellent fits for Z-Tetraol over a wide film thickness range. Spectroscopic data are provided for the Z-Tetraol –(CF2O)p–(CF2CF2O)q– main chain. The differences in the transverse and longitudinal optical infrared spectra are discussed for off-normal reflection spectra in the thin film limit. Corrections to the infrared reflection spectra for sub-monolayer coverage using effective medium theory are also discussed. Index Headings: Perfluoropolyethers; Reflection infrared spectroscopy; Boundary lubricants.
INTRODUCTION Perfluoropolyether (PFPE) liquids are widely used in technology as vacuum pump fluids,1 hydrodynamic or elastohydrodynamic lubricants in space engineering devices,2 and as boundary lubricants in computer harddisk drives.3 In order to assess or monitor the chemical integrity of the PFPE liquids as a function of the device life, many of these applications require suitable analytical tools that are capable of detecting minute physical interactions and chemical changes at interfaces. One such tool, infrared spectroscopy, in particular Fourier transform infrared (FT-IR), has been widely used.4 Thin film coatings applied on metal surfaces present additional problems for an analysis using infrared spectroscopy. Due to specular reflection from the metal surface, complicated optical interference effects render this analysis significantly less straightforward than one using transmission spectroscopy. The interference depends on the film thickness, angle of incidence, polarization of the incoming electric field, and the absorption characteristics of the metal substrate and overlaying films. In general, when the film is very thin, specular reflection tends to simplify; however, one should not interpret this as a cardinal rule. For example, longitudinal optical excitations, while infrared (IR) inactive in the bulk, become observable as a result of finite film thickness effects.5 Specular reflection in the infrared spectral region is completely simulated once the optical constants are known for the metal substrate and coated films. With the Received 22 July 2013; accepted 18 December 2013. E-mail: [email protected]. DOI: 10.1366/13-07229
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optical constants, specular reflection spectra may be easily calculated from solutions to Maxwell’s equations. Thus, a computer can be used to provide complex refractive indices over the infrared, and in turn calculate reflection spectra for any film thickness, angle of incidence, or polarization of the incident electric field. In the computer disk industry, specular reflectance infrared spectroscopy is well used to monitor changes in the composition of the disk surface. For example, contaminants that adsorb onto the disk surface or chemical and physical changes induced in the PFPE boundary lubricant film itself as a result of slider–disk interactions are all amenable to analysis using specular reflection infrared spectroscopy. In order to facilitate the interpretation of such spectra, we investigate herein the infrared spectroscopy of the Fomblin Z fluid ‘‘Z-Tetraol’’ and report its optical constants and oscillator parameters. Z-Tetraol is used in the computer disk industry as a boundary lubricant film because it is truncated by OH end groups that provide adhesion to the underlying rigid disk. The main chain is composed of a copolymer of perfluoromethylene- and perfluoroethylene-oxide monomer units. HOCH2 CHðOHÞCH2 OCH2 CF2 OðCF2 OÞp ðCF2 CF2 OÞq CF2 CH2 OCH2 CHðOHÞCH2 OH
EXPERIMENTAL SECTION Z-Tetraol was obtained from Solvay Solexis under the trade name Z-Tetraol-GT (q/p = 1.0, Mn = 2200). Samples of Z-Tetraol were applied to gold or sodium chloride substrates by spin coating the liquids from a hydrofluoroether solvent. Sample thicknesses were measured by relating the infrared integrated absorbance of a characteristic absorption band to film thickness. For thin films (, 20 A˚), film thicknesses were quantified using electron spectroscopy for chemical analysis (ESCA) using a Phi Quantum 2000 ESCA system using a takeoff angle of 458 and an electron mean free path of 25 A˚ (Fig. 1).6 Thicker films were quantified ellipso-metrically using a Rudolph Research Auto-El III. Infrared spectroscopic measurements were performed using a Nicolet Magna Model 560 Infrared Spectrometer. A standard specular reflection adapter (Harrick, New York) was used to maintain the proper angle of incidence to the sample.
REFLECTANCE MEASUREMENTS AND CALCULATIONS An account of the method used to determine the refractive index of the PFPE based on the perfluoropro-
0003-7028/14/6805-0593/0 Q 2014 Society for Applied Spectroscopy
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FIG. 1. The FT-IR thickness calibration to ESCA for Z-Tetraol in the ultrathin 10 to 20 A˚ regime.
pyleneoxide monomer unit, –[CF(CF3)CF2O]–, has been reported.7 Therefore, only those details pertinent for this report will be given. In essence, the method treats the polymer as consisting of a collection of Lorentzian oscillators whose band centers, widths, and strengths are obtained from a transmission infrared absorption spectrum. The oscillator parameters are then used to compute the complex dielectric function, which in turn is equated to the complex refractive index. These, along with the refractive index of the metal (gold substrate), are combined with the solutions of Maxwell’s equations for transmission and reflection of electromagnetic radiation at interfaces. As an orientation for the optical parameters describing the specular reflection, consider the three-layer system as the air–perfluoropolyether–gold system shown in Fig. 2. Hence, the three refractive indices are n1 = 1.0, for air; for polyperfluoroether, n~2 ¼ n2 þ ij2
ð1Þ
for the gold substrate, n~3 ¼ n3 þ ij3
ð2Þ
In Eqs. 1 and 2, n2 and n3 are the real parts of the refractive indices for the polyperfluoroether and gold, respectively, while j2 and j3 are the imaginary parts, respectively. In the calculations that follow, the angle of incidence for the infrared light is maintained at 718 from normal, and h is defined as the perfluoropolyether (PFPE) film thickness. The optical constants for the PFPE were individually related to wavenumber through a dispersion analysis. Since the dispersion analysis is only performed on the PFPE, the subscript 2 will be dropped in the following discussion for the sake of brevity. The refractive index for the PFPE is cast in the form of the dielectric constant as e ¼ ð˜ n2 Þ2 ¼ er þ iei
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ð3Þ
FIG. 2. Illustration of the three layer system, air–PFPE–gold, used for the dispersion analysis and reflectance calculations.
where e r ¼ n 2 j2
ð4Þ
ei ¼ 2nj
ð5Þ
and
Using Eqs. 4 and 5, the following expressions for n and j are obtained. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 2 2 n ¼ er þ ei þ er ð6Þ 2 j2 ¼
1 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2r þ e2i er
ð7Þ
The real and imaginary part of the dielectric constant, er and ei, were determined using the classical dispersion analysis reported by Spitzer and Kleinman8 and Maeda and Schatz9 as given below: er ¼ eo þ
j¼N X
4pqj m2j
j¼1
m2j m2 ðm2j m2 Þ2 þ c2j m2j m2
ð8Þ
and ei ¼
j¼N X j¼1
4pqj m2j
ðm2j
cj m j m 2 2
m Þ þ c2j m2j m2
ð9Þ
where the summation is over the N oscillators in the system; eo is the short wavelength dielectric constant; mj is the frequency of the jth oscillator; the damping constant, cj, is related to the band width at half-height by cj ¼
Dmð1=2Þ mj
ð10Þ
and qj is related to the oscillator strength by qj ¼
ð˜ nAj Þ 4p3 m2j
ð11Þ
To ln dm T
ð12Þ
where Aj ¼
1 h
Z
n˜ is the mean refractive index, and To/T is the inverse of the transmittance. To obtain n and j it is necessary to have the short wavelength contribution to the dielectric constant, i.e., in this case the electronic contribution, the number of oscillators, and their frequency, width, and strength. The short wavelength contribution to the dielectric was taken as the value measured at the 0.6328 lm line of a He/Ne laser.10 The real part of the refractive index for ZTetraol at this wavelength was 1.298. The refractive index for gold was taken from a Drude model fit11 using a damping frequency (xs) of 216 cm1 and a plasma frequency (xp) of 7.25 3 104 cm1. Both n3 and j3 were calculated using the following expressions: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n32 ¼ e21 þ e22 þ e1 ð13Þ 2 j23 ¼
1 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e21 þ e22 e1
ð14Þ
where e1 ¼ e‘
e2 ¼
x2p x2 þ x2s
x2p xs þ xx2s
x3
ð15Þ
ð16Þ
e‘ = 1.0, and x is the frequency at which a particular value for the dielectric constant is required. The process of obtaining a dispersion analysis is, in essence, an iterative process where initially the integrated absorbance, Aj, is obtained using transmission spectra. Subsequently, the spectra are fit to Eqs. 6 and 7. The reflectance in the infrared was calculated following the formalism given by Born and Wolfe.12 The equations for the reflection coefficients for the components of the electric field parallel and perpendicular to the plane of incidence at interfaces 12 and 23 are well known and can be found in a previous publication.7 With these equations, the reflectance spectra may be calculated for any Z-Tetraol film thickness and angle of incidence. The experimental reflection IR spectra reported herein are obtained using p-polarized light, and so the calculated reflectance spectra are also p-polarized.
RESULTS AND DISCUSSION The experimental transmission IR spectrum for ZTetraol is first shown in Fig. 3a. The various IR absorption bands from the –(CF2O)p–(CF2CF2O)q– main chain in the 1400–900 cm1 region are attributed
FIG. 3. (a) The experimental transmission infrared spectrum for a 0.044 lm Z-Tetraol film on a NaCl substrate. (b)–(d) The HF/6-31G(d) computed IR spectra for the Z-Tetraol model C9F20O5 as a function of the half-height band widths 75, 50, and 16 cm1. (e) The HF/6-31G(d) computed IR spectra for the Z-Tetraol model C9F20O5 as a ‘‘stick spectrum’’ showing all of the oscillators between 1400 and 900 cm1. All of the computed IR spectra are uniformly scaled in wavenumber (cm1) by 0.84 to match the transmission experimental spectrum at 1200 cm1.
primarily to the numerous C–F, C–O, and C–C stretching vibrations that are coupled and hence create a rather broad envelope that is difficult to deconvolve. Since the oscillator parameters derived from the transmission spectrum will be used as the basis for the reflectivity calculations to be shown later, we first provide some qualitative understanding of the relationship between the observed transmission IR spectrum and the oscillators that produce the absorption bands. We use the power of ab initio calculations13 to provide insight into the ZTetraol transmission IR spectrum. The Z-Tetraol model structures used to calculate the IR spectra are summarized in Fig. 4. All of the model structures are fully optimized geometries with no computed imaginary frequencies. The total energy for each model structure is specified in the figure caption. For reasons to be disclosed below, we have chosen the C9F20O5 as the model structure for Z-Tetraol. The computed C9F20O5 IR spectra are shown in Fig. 3b–3e below the experimental IR spectrum. All of the computed vibrations in this wavenumber regime (1600–900 cm1) are presented as a ‘‘stick’’ spectrum in Fig. 3e. The number of normal modes is large (27), and all contribute to the IR spectrum. When the ab initio computed IR spectrum is modeled as a series of Lorentzian oscillators whose band widths at halfheight are increased systematically from 16 to 75 cm1,
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FIG. 4. The HF/6-31G(d) optimized geometries for some Z-Tetraol model structures. The total energies (Hartree) are 1532.36476835 (C5F12O2); 2155.60932077 (C7F16O4); 2703.97148593 (C9F20O5); 3252.33567964 (C11F24O6); 3800.69987200 (C13F28O7).
the broad absorption band in the experimental spectrum is increasingly reproduced. This is an artificial exercise simply used to render the computed IR spectrum more similar to the experimental IR spectrum to compensate for the deficiencies of having used smaller model structures (Fig. 4) for the purposes of computational tractability. At the experimental molecular weight of 2200, the stoichiometry of the Z-Tetraol main chain (excluding end groups) is approximately C30F60O20. Our largest model structure is C13F28O7. Figure 5 further illustrates the effect
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of model size and the computed IR spectrum. With increasing model size, contributions to the IR band shape from the end group vibrations are increasingly reduced to render the computed IR spectrum more like the experimental spectrum. Figure 5 indicates that the experimental IR spectrum can be reproduced adequately using a nine carbon atom model structure for Z-Tetraol. Thus the computed IR spectrum for the C9F20O5 model structure is greatly simplified to approximately eight ‘‘major’’ group vibrations at the 16 cm1 resolution (Fig. 3). The computed
FIG. 5. The HF/6-31G(d) computed transmission IR spectra for the Z-Tetraol model structures as a function of main chain length.
potential energy distribution for these ‘‘bands’’ is summarized in Table I. Except for the C–C stretching vibration at the scaled 1340 cm1, most of the other normal modes are combinations of C–O and C–F stretching vibrations. The use of correlated wavefunctions often improves the computed IR spectrum even at the modest 6-31G(d) basis set. This aspect was explored for the C9F20O5 model structure, and the results are shown in Fig. 6. While the correction factor for the normal mode frequencies is greatly improved from the 0.84 used to correct the Hartree–Fock (HF) to 0.96 for the density
functional theory (DFT) frequencies, the computed IR spectra are qualitatively similar after all. Thus HF/631G(d) data were used throughout. Guided by the ab initio computed IR results, eight oscillator parameters were used to fit the experimental transmission spectrum. The film thickness, integrated intensities, band centers, and widths extracted from the transmission spectrum are listed in Table II. These data were in turn used to generate the optical constants using the dispersion analysis described herein. The quality of the oscillator parameters listed in Table II to generate
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TABLE I. Potential energy distribution (PED) of the major IR bands for C9F20O5 computed at HF/6-31G(d).
TABLE II. Oscillator parameters for a 0.044 lm film of Z-Tetraol GT.
Computed Computed band Band No. band center center (cm1) Scaled 3 0.84 Fig. 1 (cm1)
Band center (cm1)
1 2 3 4 5 6 7 8
1595 1511 1467 1442 1411 1323 1236 1038
1340 1269 1232 1211 1185 1111 1213 1019
PED C–C str C–F str (CF3); C–O str; C–C str C–O str; C–F str C–O str; C–F str C–O str; C–F str C–O str C–O str; C–F str C–O str; C–F str; C–O–C bend
the optical constants was assessed by first computing the transmission IR spectra from which they were derived. This is shown in Fig. 7, directly below the experimental transmission spectrum. The side-by-side comparison indicates an excellent fit between the experimental and simulated transmission IR spectra and indicates that the oscillator parameters derived using this methodology are useful and can be used in a general manner. We now discuss IR reflection spectra of Z-Tetraol. Figure 8a directly compares the transmission and the reflection spectra of Z-Tetraol. Qualitatively they are different enough such that the spectra could be misinterpreted as originating from different materials. However, this is not the case. One needs to account for the
1297.1 1266.0 1225.0 1194.7 1144.6 1120.0 1095.9 1070.2
Integrated area (cm1)
Band width (cm1) at half-height
0.22 0.24 1.97 1.21 0.74 0.21 0.43 0.51
60.0 34.0 60.0 45.0 43.0 28.0 35.0 38.0
fact that both transverse optical (TO) and longitudinal optical (LO) excitations are associated with each resonance term in the dielectric function that can be observed in the IR spectra.5,14,15 When the IR radiation is normal to the sample surface, only TO vibrations are detected due to the transverse character of the electromagnetic radiation. However, in reflection spectroscopy employing IR radiation at angles off-normal to the surface, both LO and TO surface modes can be excited in the thin film limit.5 The TO and LO modes are separated in frequency using the Lyddane–Sachs–Teller relation16 where the LO frequency is shifted to a higher wavenumber from that of the TO frequency by an amount that is approximately proportional to the absorption strength, i.e., the stronger the absorption the greater the shift of the LO frequency. One can then begin to understand why the experimental reflection and transmission spectra shown in Fig. 8a are so different. Figure 8b shows the TO and LO energy loss functions that are calculated from the optical constants given in Table II. The LO spectrum, Im(1/e), is calculated using Eq. 17.16 Imð1=eÞ ¼
FIG. 6. A comparison of the C9F20O5 computed transmission IR spectrum between the HF and B3LYP theories at the 6-31G(d) basis set. The B3LYP spectrum is uniformly scaled in wavenumber (cm1) by 0.96 to match the HF spectrum.
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ei er 2 þ ei 2
ð17Þ
For the reflection IR spectra, the incident infrared radiation for both simulated and observed cases is ppolarized with an angle of incidence equal to 718. The experimental reflection spectrum contains an appreciable contribution from the LO vibrations. Observed and computed specular reflection spectra for Z-Tetraol are now shown in Figs. 9b and 9a, respectively, as a function of film thickness between 2 and 27 A˚. This thickness range covers the actual film thicknesses typically used in hard-disk drives. All of the experimental spectra were recorded using gold as a substrate. As the results show, excellent agreement between the observed and simulated reflectance IR spectra is qualitatively obtained with one exception. In the experimental spectra, the band center of the main absorption band at 1283 cm1 is observed to shift to a lower wavenumber (cm1) with decreasing film thickness, Fig. 10a. This experimental feature is not reproduced in the simulated reflectance spectra, Fig. 9a, for these ultrathin films. The shift in the band center with decreasing film thickness is experimentally observed for film thicknesses below approximately 15 A˚. The dispersive surface energy versus Z-Tetraol film thickness on
FIG. 7. The experimental and calculated transmission spectra for a 0.044 lm Z-Tetraol film on NaCl. The calculated spectrum is derived from the oscillator parameters specified in Table II. The calculated spectrum is offset in the y-axis by 2% for ease of comparison to the experimental spectrum.
FIG. 8. (a) Plots comparing the experimental transmission and p-polarized reflection infrared spectra of Z-Tetraol. The transmission spectrum is on NaCl, while the reflection spectrum is on Au at an angle of incidence of 718. (b) The calculated TO and LO spectrum of Z-Tetraol using the oscillator parameters in Table II.
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FIG. 9. Plots comparing the experimental and calculated specular reflection infrared spectra of Z-Tetraol on gold as a function of film thickness at an angle of incidence = 718. The experimental film thicknesses in (b) are 1.6, 3.3, 4.6, 6.8, 9.6, 13.3, 14.6, 18.3, 27.4 A˚ in increasing reflectivity. The calculated reflection spectra are shown in (a) and (c), where (a) is uncorrected and (c) is corrected using EMA (effective medium approximation).
carbon films (not Au) is also observed to decrease with decreasing film thickness to reach an asymptotic or limiting value near 15 A˚ (Fig. 10c). The changes in the dispersive surface energy are related to film coverage.17 The asymptotic value in the dispersive surface energy is taken as an indication for full surface coverage. By analogy, the shift in the IR band center is attributed to surface coverage effects. This band shift may be reproduced in the calculated reflection IR spectra by correcting the computed dielectric constant as a function of wavenumber using the effective medium theory (EMT).
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EMTs describe randomly mixed composites in terms of a spatially homogeneous electromagnetic response. Assuming an increasingly ‘‘patchy coverage’’ with decreasing Z-Tetraol film thickness below the monolayer thickness, the averaging effects in the dielectric constant as a function of wavenumber are simulated by mixing the refractive indexes for air and Z-Tetraol. Here we employ the ‘‘power law’’ approximation:18 eaeff ¼
N X i¼1
fi eai
ð18Þ
and the changes in the dispersive surface energy, Figs. 10a and 10c.
CONCLUSIONS This study reports useful spectroscopic data for the ZTetraol perfluoropolyether. The oscillator parameters reported herein can be used to calculate reflection spectra for any film thickness and any angle of incidence. We have shown that reflection and transmission spectra do not necessarily match, since LO excitations are possible in the thin film limit of offnormal reflection spectroscopy. In the sub-monolayer film thickness regime, the reflection IR spectrum is further complicated by ‘‘patchy coverage.’’ This could be corrected using effective medium theory and treating the composite film dielectric constant as deriving from a film/air mixture. ACKNOWLEDGMENT The author is indebted to J. Pacansky for many fruitful discussions on IR specular reflection and dispersion analysis.
FIG. 10. Plots comparing the changes in (a) band center; (b) fractional coverage in the effective medium approximation that best matches the experimental reflection spectrum in Fig. 9; and (c) changes in the dispersive surface energy as a function of Z-Tetraol film thickness.
eeff, fi, and ei are the effective dielectric constant of the composite, volume fraction, and the dielectric constant of the ith phase. In our calculations, we have chosen to use a = ½ for no reason other than to demonstrate that the band center shift could be corrected using an EMT treatment. The value of a is related to the geometry of the scatterers, where a = ½ is attributed to cylindrical shaped scatterers.18 The power law is used here since it can be applied to both dilute and dense mixture composites and is appropriate for the thickness range covered in these studies.19 The results of applying the EMT to the calculated reflection spectra below full surface coverage are shown in Fig. 9c. Note the shift in the band center to lower wavenumbers with decreasing film thickness. The fractional coverage required to simulate the experimental reflection spectrum is plotted in Fig. 10b. The plot is correlated to the band center shift
1. L. Holland, L. Laurenson, P.N. Baker, H.J. Davis. ‘‘Perfluoropolyether–a Vacuum Pump Fluid Resistant to Electron Induced Polymerization’’. Nature. 1972. 238(5358): 36-37. 2. T. Kaldonski, P.P. Wojdyna. ‘‘Liquid Lubricants for Space Engineering and Methods for Their Testing’’. J. KONES. 2011. 18(1): 163184. 3. A.M. Scarati, G. Caporiccio. ‘‘Frictional Behaviour and Wear Resistance of Rigid Disks Lubricated with Neutral and Functional Perfluoropolyethers’’. IEEE Trans. Magn. 1987. 23(1): 106-108. 4. K. Merchant, P. Mee, M. Smallen, S. Smith. ‘‘Lubricant Bonding and Orientation on Carbon Coated Media’’. IEEE Trans. Magn. 1990. 26(5): 2688-2690. 5. D.W. Berreman. ‘‘Infrared Absorption at Longitudinal Optic Frequency in Cubic Crystal Films’’. Phys. Rev. 1963. 130(6): 2193-2198. 6. M.F. Toney, C.M. Mate, D.J. Pocker. ‘‘Calibrating ESCA and Ellipsometry Measurements of Perfluoropolyether Lubricant Thickness’’. IEEE Trans. Magn. 1998. 34(4): 1774-1776. 7. J. Pacansky, C.D. England, R.J. Waltman. ‘‘Infrared Spectroscopic Studies of Poly(perfluoropropyleneoxide) on Gold Substrates: A Classical Dispersion Analysis for the Refractive Index’’. Appl. Spectrosc. 1986. 40(1): 8-16. 8. W.G. Spitzer, D.A. Kleinman. ‘‘Infrared Lattice Bands of Quartz’’. Phys. Rev. 1961. 121(5): 1324-1335. 9. S. Maeda, P.N. Schatz. ‘‘Absolute Infrared Intensity Measurements in Thin Films’’. J. Chem. Phys. 1961. 35(5): 1617-1621. 10. J.D. Swalen, R. Santo, M. Tacke, J. Fischer. ‘‘Properties of Polymeric Thin Films by Integrated Optical Techniques’’. IBM J. Res. Dev. 1977. 21(2): 168-175. 11. M.A. Ordal, L.L. Long, R.J. Bell, S.E. Bell, R.R. Bell, R.W. Alexander, Jr., C.A. Ward. ‘‘Optical Properties of the Metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the Infrared and Far Infrared’’. Appl. Opt. 1983. 22(7): 1099-1119. 12. M. Born, E. Wolf. ‘‘Principles of Optics’’. Oxford, UK: Pergamon Press, 1970. Pp. 36-47. 13. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. AlLaham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill,
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B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople. Gaussian 03, Revision D.01. Wallingford, CT: Gaussian, Inc., 2004. 14. Y.-S. Yen, J.S. Wong. ‘‘Infrared Reflectance Properties of Surface Thin Films’’. J. Phys. Chem. 1989. 93(20): 7208-7216. 15. M.A. Karakassides, D. Petridis, D. Gournis. ‘‘Infrared Reflectance Study of Thermally Treated Li and Cs-Montmorillonites’’. Clays Clay Miner. 1997. 45(5): 649-658. 16. M.F. Al-Mudhaffer, M.A. Nattiq, M.A. Jaber. ‘‘Linear Optical Properties and Energy Loss Function of Novolac: Epoxy Blend Film’’. Archives Appl. Sci. Res. 2012. 4(4): 1731-7140.
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17. H. Chen, M.S. Jhon. ‘‘Relationship Between Surface Coverage and End Group Functionality of Molecularly Thin Perfluoropolyether Films’’. J. Appl. Phys. 2008. 103(7): 07F536-1-07F536-3. 18. P.H. Zhou, L.J. Deng, B.-I. Wu, J.A. Kong. ‘‘Influence of Scatterer’s Geometry on Power-Law Formula in Random Mixing Composites’’. Prog. Electromagn. Res. 2008. 85: 69-82. 19. W.M. Merrill, R.E. Diaz, M.M. LoRe, M.C. Squires, N.G. Alexopoulos. ‘‘Effective Medium Theories for Artificial Materials Composed of Multiple Sizes of Spherical Inclusions in a Host Medium’’. IEEE Trans. Antennas Propag. 1999. 47(1): 142-148.
