where ρ=Iρ(0)/Is(0) and A (d)pseu=1-Iρ(d)/Iρ(0), is a pseudo absorption spectrum of the film. Based on a first-order approximation of the series expression of lnx, i.e. lnx≈1-(1/x) for x>1/2, the true absorbance spectrum of the film, A(d) can then be approximated as follows:

where R is the reflectance. By substituting A(d)pseu solved from Equation (6-4) into Equation (6-5), we obtain

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As a first order approximation, it is reasonable to consider ρ as a constant over the entire mid-IR range. For metallic substrates at near grazing incidence, ρ is very close to and less than 1, and in contrast, γ may very from zero to infinity depending on the preferential polarization of the optical setup. However, if the polarizing effects of all optical parts of the PM-IRRAS setup are minimized, γ can be kept very close to 1. A(d) in general should be positive according to Equation (6-6), since whenγρ<1 the surface bands on an experimental PM-IRRAS spectrum defined by Equation (6-2) are oriented upwards above the J2(ψ0) curve, and subsequently the normalized PM-IRRAS signal is greater than 1, and whenγρ<1, the surface bands are oriented downwards below the J2(ψ0) curve and subsequently the normalized signal is less than 1. For a typical sample, i.e. an organic thin film on a gold-coated substrate, ρ≈0.95 (at σ=1000cm-1, ρ varies very little across the entire mid-IR spectrum) and γ≈1, Equation (6-6) then reduces to:

Equation (6-7) can be utilized to quickly convert a normalized PM-IRRAS spectrum to a conventional absorbance spectrum. Figure 6.7 shows a directly measured absorbance spectrum of a poly-l-lysine film on a gold-coated glass substrate collected by using a Smart SAGATM grazing angle accessory (top) and a converted absorbance spectrum of the same sample, collected by using dual-channel PM-RRAS and processed by Equation (6-7) (bottom). The grazing angle difference between the regular IRRAS (80°) and PM-IRRAS (83°) was also factored in for the calculation of the converted absorbance spectrum. It can be seen that the converted absorbance spectrum matches well the spectrum directly measured by regular IRRAS as illustrated by the band intensity at 1664cm-1, i.e. 0.00123 vs. 0.00138 absorbance, respectively. The tremendous advantages of dual-channel PM-IRRAS over conventional IRRAS in terms of SNR and clean removal of moisture contamination are also clearly demonstrated.

补上昨日的：
6.4.5 Application Examples
As a very sensitive technique, PM-IRRAS has been used to characterize thin films on reflective substrates in many fields. Thin films of this kind with thickness of <400A are generally well suited for PM-IRRAS. The most common applications are studies of Langmuir Blodgett (LB) (monolayer) organic films on highly reflective metallic substrates such as gold or gold-coated materials. In addition, PM-IRRAS has also been used to study monolayer films on water/air interfaces, a much more challenging environment for conventional IRRAS detection where water absorbs IR very strongly.

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Monolayers on metallic substrates. PM-IRRAS spectra of monolayers or submonolayers can be obtained easily in less than one minute due to the high sensitivity of the technique and the high reflectivity of metallic substrates. Illustrated in Figure 6.8 is the PM-IRRAS spectrum of cadmium arachidate on gold measured at 4cm-1 resolution in ~20sec. Figures 6.9 and 6.10 show unnormalized and normalized/converted PM-IRRAS spectra of decanethiol (C10H22S) and tetradecanethiol (C14H30S) films on gold-coated glass substrates respectively. The PEM modulation efficiency was adjusted to regions around 1500cm-1 and 3000cm-1 respectively for measuring absorbance spectra were calculated using Equation (6-7) and absorbance values are on a similar scale to monolayers as obtained with a different and rather tedious approach.

Characterization of lubricants on hard disks. The drive for continuing improvement in storage capacity and miniaturization of data storage media of hard disks used in moderns computers has increased the demand for highly sensitive analytical tools that allow fast and reliable measurements of thin films. PM-IRRAS is one of the very successful techniques widely utilized in analyzing computer hard disks. A typical hard disk has multilayered films deposited/coated on a aluminum substrate. Its cross section view is shown Figure 6.11. In order to increase the storage capacity of a hard disk, the distance between the read/write (R/W) head and the magnetic media layer where the data are stored must be as short as possible. A thin layer of lubricant protects the data stored in the magnetic medium of the hard disk from corrosion and contact with R/W head. The lifetime and performance of hard disk drives are critically dependent on the thickness of lubricants on the surface. Over supply of lubricant wound increase the stiction force on disk drive motors at startup and shortage of lubricant does not protect the disk from damage due to excessive wear and corrosion.