Anisotropy ratios

The specific resistance of natural graphite crystals is ca Hem (room temperature) along the a axis parallel to the network basal plane. The resistance along the c axis (perpendicular to the basal plane) is ca 1 Q. The cja axis anisotropy ratio is, therefore, ca 10 . Screw dislocations within the crystal may short-circuit the current path parallel to the c axis and cause lower anisotropic ratios separation of planes may cause higher anisotropic ratios. 

Another quantity of interest in VCD spectroscopy is the anisotropy ratio, g, given by... 

Strictly speaking, the values of e, Ac, A, and AA need to be obtained by integration over the spectral band however, since, for a fundamental transition, the VCD and its parent absorption band have the same shape, the anisotropy ratio can be obtained, in the absence of interfering bands due to other transitions, by taking the ratios of intensities at corresponding spectral positions, such as peak locations. The anisotropy ratio is also of interest for theoretical reasons since it is a dimensionless quantity that can be compared to the results of calculations vide infra). 

Closing naphthyl ring. The induced dipole moment is then chirally disposed in relation to the inducing NH2 dipole moment. This mechanism, referred to as the dynamic polarization model (45), is shown to explain most of the observed VCD intensity in the synunetric NH2 stretching mode, >>nh2- The anisotropy ratio for this VCD band is ca. 10. Since an NH. . . x type hydrogen bond is possible in this molecule, a description based on vibrationally induced charge flow (currents) may also be riuitfiil, similar to that proposed for a-phenyleth-ylamine. Sect. FV-B-2. 

The VCD spectra of a series of chiral allenes have been recorded at the University of Minnesota using a dispersive VCD instrument (113). The spectrum of one of these compounds has been verified by FTIR-VCD (23). The molecules have a phenyl and a carboxyl substituent on opposite ends of the allene, and alkyl or hydrogen substituents in die remaining two positions. All the corresponding (S)-(+) enantiomers, 46, exhibit a single positive VCD feature and the (/ )-(-) enantiomers, 47, a negative VCD feature, at 1945 cm , with an anisotropy ratio of ca. 4 X 10 . 

The geometry and electronic structure of the azide ion, Nj, is quite similar to that of allene. The rotational strength observed for the antisymmetric stretching vibration of the azide (2025 cm ) in azidomethemoglobin A (Figure 25), measured by Marcott, et al., is —3 x 10 esu cm, with an anisotropy ratio 0.02 (115). These values are two orders of magnitude or more greater than normally observed for VCD. 

The coefficient of anisotropy or anisotropy ratio for a mineral is expressed in a different way, in percent, by Guse (1975)... 

La2.xSrxCuo 98Mno 0204 and of the resistivity anisotropy ratio in Lai 97Sro o3Cu04 obtained in Ref. 4... 

Fig. 7a, b Average mass transfer coefficient as a function of a aquifer anisotropy ratio for several variances of the log-transformed hydraulic conductivity distribution b variance of the log-transformed hydraulic conductivity distribution where open circles represent numerically generated data and solid lines represent linear fits. All model parameter values are identical with those used in Fig. 6... 

Fig. 74. Anisotropic resistivity in nonstoichiometric rutile Ti02 x, where p and pc are a- and c-axis resistivities, respectively, (a) Anisotropy ratio p /ptf at —60°C vs. pat where p and Rtt decrease with increasing oxygen deficiency X. Rtt(c axis) < Rc(Ti) for pa < approx. 10 ohm-cm. The sharpness of the breakdown in pa with Rtt(a axis) is not apparent from this type of plot, (b) The o-axis and c-axis resistivities vs. temperature for composition G, a nonstoichiometric rutile. (Adaoted from Hollander and Castro (278).)...

Fig. 2 The VCD spectra of camphor with the anisotropy ratio on the order of magnitude of 10 5 are used as examples to illustrate the performance of several generations of FTIR-VCD spectrometers. Raw (bottom traces) and subtracted (top traces) VCD spectra of 0.6 M R-camphor in CC14 in a 0.10 mm CaF2 cell from 4,000 to 2,000 cm-1 are shown (a) SPM, single PEM only, for a pair of enantiomers. The subtracted spectrum is the true spectrum (b) SPM, single PEM, with only solvent baseline correction (c) SPM/RHWP, single PEM (SPM) with RHWP, with only solvent baseline correction (d) DPM, DPM only, with only solvent baseline correction (e) DPM/RHWP, with both DPM and RHWP, with only solvent baseline correction. Reproduced with permission from [41]. Copyright (2008) Springer...

An extreme example of the generation of a ring current is the azide stretch band at 2025 cm in the VCD spectrum of azidomethemoglobin A (Marcott et al., 1979). With an anisotropy ratio of 0.02 it shows the largest single molecule effect observed today. 

Fig. 17.3 Polarization anisotropy ratio as a function of reduced optical radius ka, where e is the dielectric constant of the material. Solid (broken) lines are the theoretical curves for Si (SiC) NWs. Circles (diamonds) are the experimental values for Si (SiC) NW optical phonon (TO) lines (With permission from reference [12]. Copyright (2006) by the American Physical Society)...

The Mie scattering model also helps explain the strong polarization anisotropy or antenna effects [9, 12] in the Raman scattering of semiconductor NWs, so named because of the selective Raman scattering of TM-polarized light by way of this structural resonance modulation. This behavior is quantifled in the polarization anisotropy ratio, calculated by an averaging of the squared held amplitudes of the product of incident and scattered flelds [12], determined from a Mie-type solution ... 

The striking different temperature dependencies for the in and out of plane resistances suggest an interpretation in terms of a non-Fermi liquid approach for 7 >r , although p (7) is not far from a conventional behavior. Figure 15 emphasizes the remarkable feature of (TMTSF)2PFj, namely, opposite temperature dependencies for interplane and chain resistivities above T . A temperature independent anisotropy ratio is indeed observed below 10 K in... 

Figure 16 Anisotropy ratio for the resistance along the a and c directions in...

As the temperature is decreased below T, , the anisotropy ratio remains temperature dependent, a feature that can hardly be tied with a Fermi liquid picture. It is only below 10 K in (TMTSF)2PF5 under 9 kbar that the ratio becomes constant in temperature suggesting a recovery of the usual Fermi liquid behavior (Fig. 16). 

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