Anisotropy of polarization

Fig. 2.5. The geometry adopted in calculating the degree of polarization V and the anisotropy of polarization of fluorescence 77 at excitation by linear polarized light beam directed along the a -axis with E z.

From the form of Eq. (2.33) it becomes understandable why the anisotropy of polarization 7Z is sometimes called the degree of alignment. From the point of view of the determination of the magnitude of the polarization moments bPo the measurement of 71 is preferable, as compared with that of V, all the more so if one bears in mind that the population bPo appears only as a normalizing factor for all other bPQ and does not influence the shape of the probability density p(B,multipole moment dependence of V and 71 for various types of radiational transition (A = 0, 1) can be obtained using the numerical values of the Clebsch-Gordan coefficient from Table C.l, Appendix C. 

If the excited molecules undergo disorienting collisions before emitting light, then the bpQ of various rank K relax at different rates T/c. The anisotropy of polarization % permits us to find the ratio between the population relaxation rate To and that of the alignment relaxation r2 ... 

Table 3.5. The dependence of the intensity, anisotropy of polarization degree of polarization V and degree of circularity C on the pumping parameter x at the classical limit J — oo...

Table 3.6. Expressions for anisotropy of polarization 1Z(J), degree of polarization V J) and degree of circularity C(J) for all types of dipole transitions, J being the quantum number of the initial level. Summation is over M from — J to J. 

S. Wozniak and S. Kielich. Effective optical anisotropy of polar molecules from Rayleigh light scattering studies. J. Phys. Paris), 36 1305-1315 (1975). 

Dipole moment and Kerr effect measurements are frequently used for conformational analyses, e,g., the recent studies of the phosphepanes (88) and 1,3,2,5-dioxasilaphosphorinanes (89). On the other hand the anisotropy of polarization and conformational analysis of triphenylphosphine, trimesityl-phosphine, and their chalcogenides also incorporated Raleigh scattering measurements (c/. ref. 236), whilst conformation studies of 1,3,5-dioxaphosphorinanes combined dipole moments with n.m.r. or u.v. data or reactive field calculations. ... 

In addition to the above mentioned research, the authors of [84] have also performed calculations for Li+, Na, K+, Be, Mg + and Ca + complexes of G-tetrads. Calculations showed that for an isolated quartet, the metal ion with the smallest ionic radius in their respective groups (lA and IIA) form more stable complexes. Other properties such as the HOMO-LUMO gap and polarizability have also been analyzed. The variation in the polarizability has been studied with respect to the movement of cations along the central cavity of the quartet to show that such movement leads to a large anisotropy of polarization and hence the refractive index (q) thereby creating optical birefringence which have potential apphcations in biomo-lecular imaging. 

Han, X., Gross, R.W. (1992) Nonmonotonic alterations in the fluorescence anisotropy of polar head group labeled fluorophores during the lamellar to hexagonal phase transition of phospholipids.[see comment]. Biophys. J. 63, 309-316. 

R Merlin, C Colvard, MV Klein, H Morkoc, AY Cho, AC Gossard. Raman-scattering in superlattices—Anisotropy of polar phonons. Appl Phys Lett 36 43-45, 1980. 

The anisotropy fiinction r t) = (/ (t) -1+ 21 t)) is detemiined by two polarized fluorescence transients / (t) and/j (t) observed parallel and perpendicular, respectively, to the plane of polarization of the excitation pulse. In tlie upconversion experiment, the two measurements are most conveniently made by rotating the plane of polarization of the excitation pulse with respect to the fixed orientation of the input plane... 

The anisotropy of the product rotational state distribution, or the polarization of the rotational angular momentum, is most conveniently parametrized tluough multipole moments of the distribution [45]. Odd multipoles, such as the dipole, describe the orientation of the angidar momentum /, i.e. which way the tips of the / vectors preferentially point. Even multipoles, such as the quadnipole, describe the aligmnent of /, i.e. the spatial distribution of the / vectors, regarded as a collection of double-headed arrows. Orr-Ewing and Zare [47] have discussed in detail the measurement of orientation and aligmnent in products of chemical reactions and what can be learned about the reaction dynamics from these measurements. 

Let us consider tire case of a donor-acceptor pair where tire acceptor, after capturing excitation from tire donor, can emit a photon of fluorescence. If tire excitation light is linearly polarized, tire acceptor emission generally has a different polarization. Common quantitative expressions of tliis effect are tire anisotropy of fluorescence, r, or tire degree of polarization,... 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

Thus, the process of PAN transformation under the effect of IR radiation proceeds with considerable self-acceleration. The irradiation of uniaxially oriented PAN films gives a polymer with a distinct anisotropy of optical properties, dichroism in the visible spectral region in particular. Figure 8 presents dichroism curves [D =/(X)] at various angles (ip) between the polarization plane and the orientation axis. The same figure shows the dependence D =f(uniaxially oriented film. 

Calibration. The quantitative transformation of polarization measurements into binding takes advantage of unique features of the FLPEP system. Weber s Law of the additivity of anisotropy is given by... 

Under some circumstances the rotationally anisotropy may be even further simplified for T-R energy transfer of polar molecules like HF (41). To explore this quantitatively we performed additional rigid-rotator calculations in which we retained only the spherically symmetric and dipole-dipole terms of the AD potential, which yields M = 3 (see Figures 1, 3, and 4). These calculations converge more rapidly with increasing N and usually yield even less rotationally inelastic scattering. For example Table 2 compares the converged inelastic transition probabilities... 

The fluorescence depolarization technique excites a fluorescent dye by linearly polarized light and measures the polarization anisotropy of the fluorescence emission. The fluorescence anisotropy, r, is defined as... 

Fluorescence polarization anisotropy of a ligand and its complexes with DNA or RNA can be given by the following expression ... 

The lowest energy structures were found to be the above carbon and above bond geometries (Fig. 6d and e, respectively). This is a function of the anisotropy of the electron density around the iodine and the geometry dependent polarization of the dihalogen. 

Piquemal J-P, Chelli R, Procacci P, Gresh N (2007) Key role of the polarization anisotropy of water in modeling classical polarizable force fields. J Phys Chem A 111 8170... 

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