Optical constants of the substrate

From a practical point of view the consequences of TOF dispersion are important only for short intrinsic fluorescence decay times of to < 1 nsec. Figure 8.15 shows an example with to = 50 psec and realistic optical constants of the substrate. The intensity maximum in Fb(t) is formed at At 30 psec after (5-excitation. After this maximum, the fluorescence decays with an effective lifetime of r ff = 100 psec that increases after long times to t > > 500 psec. The long-lived tail disappears as soon as there is some fluorescence reabsorption, and for Ke = K there is practically no difference to the intrinsic decay curve (curve 3 in Figure 8.15). 

The amplitude ratio of the AC to DC components is equal to -cos(2ip), and ip is related to the optical constants of the substrate, film, and ambient, the wavelength of the light, incidence angle and film thickness through the Drude equation (47). 

Having obtained values of A and p for the electrode/solution interface of interest, or more commonly detected changes as the electrode potential is varied, the next step is to relate these values to the properties of the interface. As with all reflection techniques, this is usually done in terms of a three layer model consisting of bulk substrate/interfacial region/bulk solution as shown in Fig. 10.10. Assuming the optical constants of the substrate and solution and the film thickness are known, it is possible to obtain unique values of the effective optical constants of the interphase from A and p [15]. The optical characteristics of any phase are simply defined by p, the magnetic permeability (usually equal to unity) and either the wavelength dependent complex dielectric constant defined by Equation (10.11)... 

Optical models of the interaction of polarized radiation with plane parallel layers are based on Maxwell s equations. Many derivations have ajqieared in the literature. The most generalized models treat the probed material as an n-layered system with an arbitrary variation in optical properties with distance. Optical modeling was first applied to an isotropic monolayer deposited on an aqueous subphase by Dluhy (25). In this work, it was established that when the optical constants of the substrate are lower than the monolayer, non-zero electric field intensities exist in three dimensions, unlike the cases of grazing-angle reflection from metal surfaces or normal transmission spectroscopy. 

IRRAS spectra of a monolayer of octadecylsiloxane (ODS) on a silicon substrate measured at several incidence angles are shown in Figure 13.18. Also shown in this figure are the spectra that are calculated by assuming that the ODS is present as an all-trans hydrocarbon chain tilted by 10°. Note that only when the spectrum is measured with p-polarized radiation above Brewster s angle is the absorbance positive, as it is for metallic substrates. Under all other conditions, the effect of the adsorbate is to cause the reflectance to increase above the value for the clean substrate. Thus, a knowledge of the optical constants of the substrate is vital if optimal IRRAS spectra of thin Aims on dielectric substrates are to be measured. 

An excess of substrate is required in order to guarantee a constant reaction rate during hi least 3 ruin. lil B systcui wiui hu insoluble Cuuipuiiciii, a iuciai liuii Qi enzyme to substrate cannot be considered. The optical density of the substrate is limited to 1.000 at 450 urn for reasons of sensitivity. Consequently, the enzyme concentration should be kept as iow as possible, in the present assays a final enzyme couceatratiou of 0.3 mg/L is used. 

Fig. 5. AR/R calculated as a function of incident angle

The exact optical model describing multiple internal reflections, which are important for thin films where the penetration depth of the light 8 is larger than the layer thickness. Because of this part, iph depends on the layer thickness and the optical constants of both substrate and layer. This optical part mainly explains the observed variation in iph(df) found in the photocurrent spectra. 

In order to interpret the reflectance spectrum, modeling of the interface is the key issue. For example, in the simulation above, we tacitly made some assumptions. One is that the change of the optical properties of the substrate and refractive index of the solution immediately adjacent to the film surface are independent of potential and the presence of the film. The use of the Fresnel model with optical constants is based on the assumption that the phases in the three-strata model are two-dimen-sionally homogeneous continua. However, if the adsorbed molecule is a globular polymer which possesses a chromophore at its core, a better model of the adsorption layer would be a homogeneously distributed point dipole incorporated in a colorless medium. To gain closer access to the interpretation of the spectrum, a more precise and detailed model would be necessary. But this may increase the number of adjustable parameters and may demand a too complex optical treatment to calculate mathematically. Moreover, one has to pile up approximations, the validity of which cannot easily be confirmed experimentally. 

This equation is the so-called basic ellipsometric equation. It contains R and R which depend on the optical properties of the reflecting system, the wavelength of the light X the angle of incidence cp and the experimentally measurable parameters Pand A. For the reflection at a clean interface, the Rp and R are the Fresnel coefficients (246) of the single uncovered interface. They depend only on the refractive indices of the two adjacent phases and the angle of incidence. For systems that do not absorb light the optical constants of the two bulk phases (ambient and substrate media) are usually obtained from the experimental values of P and A for the clean interface (denoted by subscript 0 via Eq. (111). For a layer-covered interface, multiple reflections and refractions take place within the layer (Fig. 24). 

In this section, only the optical constants of isotropic films determined by the multiwavelength approach in IRRAS will be discussed. The optical constants are assumed to be independent of the film thickness, and any gradient in the optical properties of the substrate (Section 3.5) is ignored. This undoubtedly lowers accuracy of the results. Anisotropic optical constants of a film are more closely related to real-world ultrathin films. At this point, it is worth noting that approaches to measuring isotropic and anisotropic optical constants are conceptually identical An anisotropic material shows a completely identical metallic IRRAS spectrum to the isotropic one if the complex refractive index along the z-direction for the anisotropic material is equal to that for the isotropic one [44]. However, to... 

These layers were deposited by magnetron sputtering on A1 substrates maintained at temperatures of 25° and 250°C. The spectrum obtained by IRRAS for the film deposited at 25°C (Fig. 3.68a) shows an intense vlo absorption band at 725 cm . In the spectrum of the film deposited at 250°C, the maximum of this band is shifted to higher frequencies, and its FWHM is smaller than that in the spectrum of the film obtained at 25°C. The resulting spectral dependences of n2(v) and k2 v) for the MgO layers are presented in Fig. 3.68Z . The optical constants of the layer sputtered on the 250°C substrate are close to those of a MgO crystal. The lower frequency and larger bandwidth of the / 2(v) band suggest an amorphous phase in the layer. 

Another error in the optical constants 2 and 2 of the layer, calculated from experimental values of R/R, is caused by an uncertainty in the optical constants n-i and of the substrate. The partial derivatives d(AR/R)/dti- k =consu 9(A/ // )/9 3 3=const were calculated for cp = 75° and ti2, with k2 in the range from 0 to 3 [458], It was found that the relative error in AR/R generated from W3 and 3 (whose accuracy is 20%) is less than 0.5% and can be neglected. Moreover, if the optical constants of an ultrathin film are measured using the technique of Yamamoto and Ishida [7], the optical constants of the metal substrate do not matter, and those of any real metal can be employed. 

As depicted in Fig. 2.7, a bifunctional racemic substrate consisting of its enantiomers A and B is enzymatically resolved via a first step to give the intermediate enantiomeric products P and Q. The selectivity of this step is governed by the constants and k. Then, both of the intermediate monoester products (P, Q) undergo a second reaction step, the selectivity of which is determined by k-2 and k4, to form the enantiomeric final reaction products R and S. As a result, the optical purity of the substrate (A, B), the intermediate monoester (P, Q), and the final products (R, S) are a function of the conversion of the reaction, as shown by the curve in Fig. 2.7. The selectivities of each of the steps (E and Ef) can be determined experimentally and the optical purities of the three species e.e.A/B, e.e.p/Q, and e.e.jys can be calculated [57, 58]. Free shareware computer programs for the analysis, simulation, and optimization of such processes can be obtained over the internet [59]. 

In the Air Sandwich design, the active layer is coated onto a transparent substrate and is located within an air gap sandwich structure. Thus, no overcoat is needed. The laser beam is focused through the substrate onto the active layer and consequently the mechanical and optical properties of the substrate play an important part in optical disk construction. The substrate should be highly transparent ("85X) at the laser wavelength and optically uniform. Optical uniformity not only includes constant, standard path length, but low, uniform birefringence as well. The requirement of low birefringence arises from the use of... 

From the change in optical constants of the film covered surface compared to the bare surface, one can calculate from first principles the thickness and refractive index of the film using the equations derived by Drude. The sensitivity of the measurement is dependent primarily on the differences in refractive index of the solution and film, and the film and substrate. 

It is apparent from Eqs. (29) that the R/R spectra of a surface film on an absorbing substrate do not always allow for a straightforward interpretation of the film optical constants. The spectra are by no means transmission-like but are markedly influenced by the optical properties of the substrate. Therefore, it appears to be desirable to evaluate directly the film dielectric function, 2 = 2 f 2, from the experimentally determined quantity R/R rather than attempting a detailed interpretation of the AR/R spectra alone. In the following, we briefly discuss three different methods for evaluating film optical constants. 

The basis of Method II may be deduced from Figure 6-3. To do this, let us consider the ideal case, in which the x-rays involved are monochromatic, all influences of composition are absent, the simplest x-ray optics obtain, and excitation of a characteristic line in the film by a characteristic line of the substrate does not occur. Suppose now that a beam of intensity Iq falls upon a metal film d cm thick to excite a characteristic line of intensity Id- The contribution to Id of a volume element of constant area and of thickness dx, located at depth x, is... 

In the M. trichosporium OB3b system, a third intermediate, T, with kmax at 325 nm (e = 6000 M-1cm 1) was observed in the presence of the substrate nitrobenzene (70). This species was assigned as the product, 4-nitrophenol, bound to the dinuclear iron site, and its absorption was attributed primarily to the 4-nitrophenol moiety. No analogous intermediate was found with the M. capsulatus (Bath) system in the presence of nitrobenzene. For both systems, addition of methane accelerated the rate of disappearance of the optical spectrum of Q (k > 0.065 s-1) without appreciatively affecting its formation rate constant (51, 70). In the absence of substrate, Q decayed slowly (k 0.065 s-1). This decay may be accompanied by oxidation of a protein side chain. 

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