Optical constants measurements

In this section, the spectral optical constants measured for BPA-PC In the IR are presented first. Using these data, the relationships between IR-RA absorbance values and BPA-PC functionality concentration were determined for a range of applicable film thicknesses using an optical model of the IR-RA experiment. 

A) MEASUREMENT OF THE OPTICAL CONSTANTS OF MATERIALS USING ELLIPSOMETRY... 

Smectites are stmcturaUy similar to pyrophylUte [12269-78-2] or talc [14807-96-6], but differ by substitutions mainly in the octahedral layers. Some substitution may occur for Si in the tetrahedral layer, and by F for OH in the stmcture. Deficit charges in smectite are compensated by cations (usually Na, Ca, K) sorbed between the three-layer (two tetrahedral and one octahedral, hence 2 1) clay mineral sandwiches. These are held relatively loosely, although stoichiometricaUy, and give rise to the significant cation exchange properties of the smectite. Representative analyses of smectite minerals are given in Table 3. The deterrnination of a complete set of optical constants of the smectite group is usually not possible because the individual crystals are too small. Representative optical measurements may, however, be found in the Uterature (42,107). 

The unknown parameters of the model, such as film thicknesses, optical constants, or constituent material fractions, are varied until a best fit between the measured P and A and the calculated P/ and A/ is found, where m signifies a quantity that is measured. A mathematical function called the mean squared error (MSE) is used as a measure of the goodness of the fit ... 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Marvel, Dec, and Cooke [J. Am. Chem. Soc., 62 (3499), 1940] have used optical rotation measurements to study the kinetics of the polymerization of certain optically active vinyl esters. The change in rotation during the polymerization may be used to determine the reaction order and reaction rate constant. The specific rotation angle in dioxane solution is a linear combination of the contributions of the monomer and of the polymerized mer units. The optical rotation due to each mer unit in the polymer chain is independent of the chain length. The following values of the optical rotation were recorded as a function of time for the polymerization of d-s-butyl a-chloroacrylate... 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

It is the intensity of light transmitted by a sample of path length . It can be shown that t = (16 ir/3)R so that Eqs. (22) and (40) may be expressed with r in place of R0 and an optical constant H (= 16 jtK/3) in place of K. Although r is usually too small to be measured as such directly, some experimental results are often reported in the form of He/t even though Kc/Rg is the measured quantity. 

A Varian Cary 100 model UWis spectrophotometer was used for optical absorbance measurements. The absorbance measrrrements were conducted in situ for the study of the kinetics of adsorption process. In all experiments, the size and mass of ACC was kept as constant as possible (about 18.0 0.1 mg). Weighed ACC pieces were pre-wetted by leaving in water for 24 h before use. The idea of using pre-wetted ACC originates from previons findings that pre-wetting enhances the adsorption process [9, 11],... 

A very common and useful approach to studying the plasma polymerization process is the careful characterization of the polymer films produced. A specific property of the films is then measured as a function of one or more of the plasma parameters and mechanistic explanations are then derived from such a study. Some of the properties of plasma-polymerized thin films which have been measured include electrical conductivity, tunneling phenomena and photoconductivity, capacitance, optical constants, structure (IR absorption and ESCA), surface tension, free radical density (ESR), surface topography and reverse osmosis characteristics. So far relatively few of these measurements were made with the objective of determining mechanisms of plasma polymerization. The motivation in most instances was a specific application of the thin films. Considerable emphasis on correlations between mass spectroscopy in polymerizing plasmas and ESCA on polymer films with plasma polymerization mechanisms will be given later in this chapter based on recent work done in this laboratory. 

The real and imaginary parts of the complex refractive index satisfy Kramers-Kronig relations sometimes this can be used to assess the reliability of measured optical constants. N(oj) satisfies the same crossing condition as X(w) N (u) = N( — u). However, it does not vanish in the limit of indefinitely large frequency lim JV(co) = 1. But this is a small hurdle, which can be surmounted readily enough by minor fiddling with JV(co) the quantity jV(co) — 1 has the desired asymptotic behavior. If we now assume that 7V( ) is analytic in the top half of the complex [Pg.28]

Equation (2.62) is not merely a mathematical curiosity from (2.61) it follows that at a given frequency w the optical constants are determined by the reflectance and phase however, if the reflectance is measured over a sufficiently large range of frequencies about w, the phase can be obtained from... 

These methods and their variations are the principal means of measuring optical constants. As noted, none of them is clearly superior in all instances... 

A good review article on optical constants and their measurement is that by Bell (1967). Determination of optical constants from reflectance measurements is treated by Wendlandt and Hecht (1966) and from internal reflection spectroscopy by Harrick (1967). Ellipsometric techniques are discussed at length by Azzam and Bashara (1977). 

Another kind of effective or average optical constants involves mixtures of different particles such as atmospheric aerosols or soils. Effective optical constants for compacted samples of these mixtures might be inferred from reflectance and transmittance measurements as if the samples were homogeneous. But scattering or extinction calculations based on these optical constants would not necessarily be correct. 

An example of practical importance in atmospheric physics is the inference of effective optical constants for atmospheric aerosols composed of various kinds of particles and the subsequent use of these optical constants in other ways. One might infer effective n and k from measurements—made either in the laboratory or remotely by, for example, using bistatic lidar—of angular scattering fitting the experimental data with Mie theory would give effective optical constants. But how effectual would they be Would they have more than a limited applicability Would they be more than merely consistent with an experiment of limited scope It is by no means certain that they would lead to correct calculations of extinction or backscattering or absorption. We shall return to these questions in Section 14.2. 

The 1/to4 high frequency limit for R can be useful in determining optical constants from Kramers-Kronig analysis of reflectance data (see Section 2.7). Reflectances at frequencies higher than the greatest far-ultraviolet frequency for which measurements are made can be calculated from (9.15) and used to complete the Kramers-Kronig integral to infinite frequency. 

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