Optical anisotropy coefficient

A sensitive approach for the analysis of molecular structures is the measurement of rotation time constants and optical anisotropy coefficients by relaxation electrooptical methods.The experimental procedure used for electrooptical investigations is relatively simple samples are subjected to electric field pulses, and the response due to field-induced alignment or field-induced reactions is recorded by spectrophotometric techniques. In the dichroism experiments, the absorbance of polarized light is measured under electric field pulses. The measured quantity, linear dichroism (LD), means that anisotropic absorption of plane or linearly polarized light has taken place. 

Today generator matrices F are known for many properties,10 among them the population of different conformers, the relative stability of macromolecular diastereoisomers, the mean-square end-to-end distance, the radius of gyration, the molecular dipole moment, the molecular optical anisotropy (and, with it, the stress-optical coefficient, the Kerr effect, depolarized light scattering, and the... 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

The stress-optical coefficient of PE networks is calculated, and results are compared with experimental data. Observed temperature coefficients of AT and the optical anisotropy for unswollen samples are much larger than those calculated using acceptable values of E(g), the energy of the gauche conformation, relative to that of Vans. It is concluded that observed temperature coefficients should Include some contributions other than those implied in the theory, i.e., those arising from the conformational change with temperature. 

Evidence of only a low barrier to inversion in Si—O—Si sequences could be important with regard to the interpretation of the statistical properties of silicone polymers. The effects are estimated for the temperature coefficients of the unperturbed dimensions, dipole moments, and the optical anisotropy for PDMS. 

In addition, the optical anisotropy of the statistical segment Aa calculated [50, 51] from the stress-optical coefficient C,... 

The role of the carrier density in M-I transitions is shown for an oriented sulfuric acid-polyparaphenylenevinylene (PPV-H2SO4) sample. The optical anisotropy of this oriented PPV sample, from dichroic ratio measurements at 1520 cm 1, is nearly 50 [15]. The value of pr continuously increases upon reducing the carrier density by systematically dedoping the sample, as shown in Fig. 3.4. However, it is difficult to locate the M I transition from the a vs. T plot alone. Instead, the W = d(lnmetallic regime with a weak negative TCR, then W shows a positive temperature coefficient at low temperatures. Moreover, this ensures that there is a finite conductivity as T —> 0. As pr increases, W(T) gradually moves from positive (metallic) to negative... 

The stress optical coefficient C merits special attention, because it leads directly to the parameter F2 that characterizes the optical anisotropy of the network chain under strain. F2 is defined by (13)... 

Equations (20) and (23) show that the average rotational friction coefficient W is proportional to the radius of gyration both for extended and symmetrical conformations. Hence, it is proportional to h (compare Eqs. (3) and (3 )p. 98). According to Eq. (46), optical anisotropy in the random chain conformation is also proportional to h in the Gaussian range (h/L -4 1). Hence, a Gaussian coil obeys the following equation... 

Recently, Foreman demonstrated that fe-linear terms in semiconductor heterojunctions [47] are enhanced near the interface, and that the associated mixing of Fg hh and Ih states is increased so that it influences the quantum-well Pockels effect. [48] The reduced symmetry in quantum well structures (from Td in the bulk to C2v) increases the optical anisotropy. The work in Ref. [47] shows that the A -linear splitting contributes significantly to this anisotropy because the C coefficients are often an order of magnitude larger in the heterojunctions than in the bulk materials. 

Figure 10 shows the optical absorption spectra of the single crystal of all-trans-/3-carotene measured upon irradiation with linearly polarized light parallel to the a- or fc-crystal axis. Large optical anisotropy for the molar extinction coefficient is seen in these spectra. This observation can be explained in terms of the molecular orientation of /3-carotene in the crystal (see Fig. 9). Since the molecular axis of /3-carotene is almost parallel to the fc-axis, the molar extinction coefficients along fc-axis should appear larger than those along a-axis. Based on the symmetry considerations, these spectra can be assigned to the transitions to the (//fc-axis) and B (//a-axis) molecular excitons, as illustrated in Fig. 10 (Chapman etal., 1967).

In this case, the optics of the interface is slightly complicated in view of the birefringence of the surface induced pre-nematic phase. The interface is now consisting of (i)the isotropic bulk liquid crystal, (ii) the surface induced, weakly optically uniaxial layer with a thickness of the nematic correlation length and with the optical axis perpendicular to the surface, and, (iii) an isotropic substrate (such as glass). If the optical anisotropy and the thickness of the anisotropic layer are small, the eUipticity coefficient at the Brewster angle> PB, can be calculated in the Drude approximation [1]... 

When an electric field is applied to a chemical system which exhibits both electrical and optical anisotropy, both the c, and the Cj terms in the fundamental Eq. (4.21) may be field dependent. Note that the usual extinction coefficients of optically anisotropic molecules reflect random average values ij of all chromophore orientations of the system when measured with polarized light. 

An is the difference in the refractive indices n in the plane of the dra i/ing direction and n perpendicular to iti n = (n, + 2n )/3 is the mean refractive index of the sample and Aa the difference of the polarizabilities of the statistical segment (Aa = optical anisotropy) parallel and perpendicular to the axis of the segment. The quotient of orientational birefringence and stress is defined as the stress optical coefficient C. From the simple model of the network chains the product CT (equation 3) should be independent of T if a slight temperature dependence of n is neglected. CT is proportional to the optical anisotropy of the statistical segment. 

Stress-optical coefficients have been determined using PDMS networks both unswollen and swollen with a variety of solvents. Only qualitative agreement was obtained, presumably because of the vanishingly small optical anisotropy of the PDMS chain. Similar studies have been carried out on other polysiloxanes —for example, on poly(methylphenylsiloxane) andpoly(tetramethyl-p-silphenylene-siloxane). ... 

Kochergin et al. 2004, 2005 Ruda and Shik 2011) and is basically understood. Consistently the Structural anisotropy of (110) porous Si also affects the dielectric properties in general, like the optical absorption coefficient and nonlinear susceptibility (Zabotnov et al. 2005 Timoshenko et al. 2003 Soboleva et al. 2005 Efimova et al. 2007a, b). 

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