Angular dependence 602 INDEX

Figure 12. (a) Index ellipsoid defined by ne and no with a ray of light propagating in an arbitrary direction OP (b) an ellipse that is formed by the intersection of the plane normal to OP and the index ellipsoid. The principal axes of this ellipse are the angularly dependent index ne (9) and the angularly independent index nQ. 

For Markovian block copolymers the formula is valid analogous to formula (Eq. 58), however factor (Q + e)-1 stands instead of the sum over index v. Thus, in the region of angles 6, at which the inequality Q <3C s holds, the angular dependence of the amplitude of scattering 1(6) of a melt of proteinlike heteropolymers turns out to be identical to that of Markovian heteropolymers with e = i. Essentially, this coincidence disappears for the values of angle 6 at which inequality Q fii is not valid. 

Fig. 6. Lower part angular dependence of the non-normalized static scattering intensity I(q) observerd with latex particles (R=265 nm). Upper part dependence of r/q =D on the scattering angle in dynamic LS. The sharp downturn at large scattering angles results from a weak back reflection of light on the boundary of the aqueous solution to the index matching bath, that consisted of toluene. This reflection results from the difference in the refractive indices of water (n = 1.333) and toluene (n =1.51). Reprinted with permission from [182]. Copyright [1982] American Society...

Figure 4. Open circles, angular dependence of the second-order scattered light intensity (hyper-Rayleigh scattering from 1064 to 532 nm) for a suspension of purple membrane patches of bacteriorhodopsin before any solubilization has taken place. Solid curve best fit to the data by combining the nonlinear hyperpolarizability of retinal with the linear refractive index of the upo-protein.

The Rayleigh-Gans equation for the angular dependence of the intensity of the scattered light is given for spherical particles of low refractive index by the equation [45] ... 

At any total scattering energy E, elements of the multichannel S matrix In the RLM are labelled by the total angular momentum Index I, and by the Initial and final vibrational quantum numbers v and v. Equations for physical observables in the BCRLM have been given previously (24-26), and we only summarize the final results here, In order to establish a common notation. The opacity function gives the Impact parameter dependence of the reaction probabilities. 

The step-free energy k Ts(T) can be conveniently introduced by considering the interfacial tension of interfaces which are tilted through an angle 8 relative to a low-index lattice plane (fig. 65). For small 9 the angular-dependent surface tension takes the form... 

In the following analysis, we assume that the mixed LB film is a non-absorbing medium for the following two reasons (1) Since the molar ratio of p-carotene to barium stearate is 1 10 in the mixed LB fihn, the number of the barium stearate molecules predominates in the film (2) The angular dependence of reflectance for the mixed LB fihn fits the theoretical curves for the non-absorbing medium calculated using the refractive index of barium stearate (1.462) (Blodgett, 1935). 

It was shown that the transition moment of the )3-carotene molecule is isotropically distributed in the plane of the SC film. As regards the normal direction ofthe film, the observed angular dependence ofboth reflectance and transmittance was in excellent agreement with the theoretical curves calculated assuming the isotropic absorbing medium. This means that the refractive index ofthe SC film is isotropic in the normal ofthe film. Since the refractive index can be directly related to the polarizability of a molecule using Clausius-Mosotti s law and a transition moment linearly depends on the polarizability, the present investigation reveals that the transition moment of the /3-carotene molecule is isotropically distributed both in the plane and in the normal of the SC film. The transition moment lies parallel to the molecular axis of /3-carotene, hence we can conclude that the /3-carotene molecules are randomly oriented in the SC film. 

In Eqs. (25)-(27), we subdivided configuration space into sectors, eacli labeled by the index i the boundary between sectors in each coordinate system is formed by curves on which the propagation variables (R, u, and p, respectively) are constant. Since the wavefunction expansion may change from sector to sector, the functions f, F, g, G, h, and H depend parametrically on the i index, as well as the total angular momentum index J and the adiabatic bend quantum numbers A and A2. 

Mielczarski and Mielczarski [41], who first reported the effect of phonon absorption of a substrate on IRRAS, found that the substrate band absorption depth can vary in magnitude and sign, being very sensitive to small changes in factors such as angle of incidence and thickness of the deposited layer. For fused quartz, the angular dependence of the absorption depth of the substrate band AR(polarized radiation is depicted in Fig. 2.15a, which shows the maximum value of AR at sa 80°. Moreover (Fig. 2.15 ), the absorption depth depends not only on the thickness of the layer but also on its refractive index. 

---