Optical constants defined

Where Mw 1 the weight average molecular weight or the apparent molecular weight in the cape of copolyraerp, is the second virial coefficient, and K is an optical constant defined as... 

The expressions for scattered light intensity (and Rayleigh ratio) must be corrected by dividing by the appropriate Cabannes factor. Effectively this is equivalent to replacing the optical constant K as defined in Eq. (24) by Kf and by 2 Kfj for unpolarised and vertically polarised incident light respectively. 

In the next section, we will develop a simple model to predict the frequency dependence of the relative dielectric constants si and 2 of a given material. At that point, we will be able to determine the measurable optical magnitudes defined in Chapter 1 at any particular wavelength (or frequency) if the relative dielectric constants (and thus n and k) are known at that wavelength. 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

The scattering function Kc/Rg is the quantity directly related to the physical properties of interest. It consists of an optical constant K times the concentration, divided by the Rayleigh ratio. The constant K is defined by... 

A simple way to determine the relationship between molecular weight and intensity of scattered light is to recast Equation (4.4) by defining an optical constant K using Equation (4.5) and Ro, the Rayleigh factor (Equation (4.6)). 

It is customary also to define another optical constant H such that... 

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

The real part n of this optical constant is the well-known refractive index of the medium, while its imaginary part k is its absorption coefficient. The propagation of an optical wave inside the medium along axis z, for instance, is then defined by the propagation of its electric vector E as... 

It is also customary to define another optical constant K such that [cf. Eq. (4.92)]... 

Materials are characterized optically by their optical constants, i.e. the extinction coefficient and refractive index. The extinction coefficient k is the imaginary part of the complex refractive index N = n - ik It assumes the role of an index of attenuation. If this attenuation is caused by true absorption alone, it is termed the absorption coefficient k. The absorption (or extinction) constant is defined as a( = 4 n (J X, 1. Finally, 1 dB cm"1 = 4.34 a ... 

A crystal exposed to a stress S will show a change of its impermeability. The photo-elastic (or elasto-optic) constants, P. p are defined by... 

The purpose of obtaining spectral data on the complex refractive Index of polycarbonate polymer was to permit detailed Interpretations to be made of the IR-RA spectra collected In situ on metal-backed films of this material. Several of the principal methods for obtaining the optical constants n and k of an Isotropic medium have been reviewed by Humphreys-Owen [18]. All of the methods outlined are Insensitive to k when k Is close to zero, which Is the case for frequencies between absorbance bands. For this study, a polarlmetrlc technique (method D In Ref. 18) was chosen to obtain the optical constants of BPA-PC. To apply this method, the ratio of surface reflectances Rp/Rg at two large, but well-separated, angles of Incidence (9 ) was obtained for BPA-PC In the IR. Rp Is defined as the reflectance measured for a sample using radiation polarized parallel to the Incidence plane and R... 

In conformity with all ellipsometers, a DOAP detects the change in polarization of an initially polarized laser beam (of well-defined and known polarization) after reflection from the surface of interest, by dividing the total signal into four polarization components. After an elaborate calibration routine [99], the optical constants of Ae sample were obtained from the Fresnel equations, provided that die angle of incidence and the refractive index of the ambient medium, e.g. air, were known. The whole instrument was originally designed to measure emittance and the optic parameters result as a by-product fi om this process, see e.g., [100] obtained with a / -DOAP. 

The left-hand side of Equation (9-43) corresponds to the reduced scattered light intensity by all N molecules in the volume F, and is called the Rayleigh ratio R. Defining the optical constant k as... 

A quantitative analysis of the electromagnetic response begins with the evaluation of the optical constants of a system (complex dielectric function, complex conductivity, etc.) from the experimentally accessible quantities such as reflectance, transmission or absorption. It is convenient to discuss the response of metals and superconductors in terms of the complex conductivity ), defined from J(o)) = o(ci))E(co) where J is the current vector and E is the electric field vector. All optical constants are interrelated through simple analytical expressions and contain the same physical information. The advantage of the conductivity notation is that o(co) has no singularity at ft) = 0. Also, an extrapolation of ai(tft) to ft) —> 0 yields the dc conductivity of a metal. 

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)... 

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