Anisotropy reflectance functions

This is identical in form to the equation for V (z) in an isotropic material. But of course R hkl (8) is quite different from any isotropic reflectance function. For a cubic material an anisotropy factor can be defined as... 

In DLS, the molecular anisotropy reflects the stmcture factor through rotational motions. The correlation function for lyv contains the decay by rotational diffusion. For example, the correlation functions for Jw and Ivh for a thin rod in dilute solution are, respectively, expressed as... 

Complex Anisotropy is studied in texture goniometers (p. 193) as a function of sample orientation. If the study is aiming at quantitative analysis of scattering data, the absorption correction may become an issue. Conversely, by choosing a special kind of scanning modus (e.g., symmetrical reflection SAXS SRSAXS), the absorption correction problem can be simplified. 

Figure 8.12. Radial distribution of the reflectance as a function of the anisotropy parameter g. The upper curves...

Strambini and Galley have used tryptophan anisotropy to measure the rotation of proteins in glassy solvents as a function of temperature. They found that the anisotropy of tryptophan phosphorescence reflected the size of globular proteins in glycerol buffer in the temperature range -90 to -70°C.(84 85) Tryptophan phosphorescence of erythrocyte ghosts depolarized discontinuously as a function of temperature. These authors interpreted the complex temperature dependence to indicate protein-protein interactions in the membrane. 

If molecules are involved, isotropic potential functions are in general not adequate and angular dependences reflecting the molecular symmetries may have to be accounted for. In general, up to five angular variables may be needed, but in many cases the anisotropies may be described rigorously by fewer angles. We must refer the reader to the literature for specific answers (Maitland et al., 1981) and mention here merely that much of what will interest us below can be modeled in the framework of the isotropic interaction approximation. 

The final rotational state distributions of the products in the fragmentation of a polyatomic molecule contain additional clues about the intra- and intermolecular dynamics, especially about the coupling in the exit channel. In realistic as well as model studies it has been observed that the rotational state distributions of the photodissociation products reflect the angular dependence of the wave function at the transition state and the anisotropy of the PES in the exit channel [4, 9, 10]. HO2 is no exception. 

As long as the concentration of the small molecule is low (<5%), the scattered intensity due to concentration fluctuations will be negligible relative to the density or anisotropy fluctuations. In polystyrene, the HV spectrum will not have any contribution due to concentration fluctuations, but in principle there could be a contribution due to the diluent anisotropy. The average relaxation time will be determined by the longest time processes and thus should reflect only the polymer fluctuations. The data were collected near the end of the thermal polymerization of styrene. Average relaxation times were determined as a function of elapsed time during the final stages of the reaction... 

In similar work, Sipe, Moss and Van Driel [84] determined a functional form of the rotational anisotropy for cubic centrosymmetric media. Their derived expressions for the total reflected p- and s-polarized SH fields from perfectly terminated (111) and (100) crystals under p- and s-polarized excitation take the form... 

The photo-dissociation dynamics at 193 nm was analyzed in detail and the observed rotational state distribution was obtained by using the rotation reflection principle by Schinke and Stasemler [53]. All rotational state distributions depend sensitively on the anisotropy of the dissociative potential energy surface. These are interpreted as a mapping of the bound state wave function onto the quantum number axis. The mapping is mediated by the classical excitation function determined by running classical trajectories onto the potential energy surface within the dissociative state. This so-called rotation-reflection principle... 

Strikingly, the solvation dynamics for all mutants are nearly the same. All correlation functions can be best described by a double exponential decay with time constants of 0.67 ps with 68% of the total amplitude and 13.2 ps (32%) for D60, 0.47 ps (67%) and 12.7 (33%) for D60G, and 0.53 ps (69%) and 10.8 ps (31%) for D60N. Relative to SNase above, the solvation dynamics are fast, which reflects the neighboring hydrophobic environment. We also measured the anisotropy dynamics and, as shown in the inset of Fig. 33, the local structure is very rigid in the time window of 800 ps. This observation is consistent with the inflexible turn (-T30W31-) in the transition from the second /1-sheet and the second x-helix (Fig. 31). Thus, the three mutants, with a charged, polar, or hydrophobic reside around the probe (Fig. 34) but with the similar time scales of... 

Figure 33. Hydration correlation functions c(t) probed by W31 in hTrx and two mutants in reduced states. The three functions are strikingly similar, indicating a similar local solvent environment upon mutation. The inset shows the fluorescence anisotropy dynamics of W31. The nearly constant r(t) reflects a very rigid local structure.

---