Polarization correlation linear

Other solvatochromic probes have been proposed. Mukerjee et al. used nitrox-ides for this purpose, finding that their transition energies correlate linearly with Z and t (30). Brooker et al. prepared a polar merocyanine that shows a blue shift... 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

The electronic spectra of HgX2 (X = Cl, Br, I) have been measured in several solvents in an endeavour to characterize the solution structures of these compounds.144 The peak maxima correlate linearly with dielectric constants and Kosower s Z value for solvent polarity in... 

The primary standard betaine dye (44) is only sparingly soluble in water and less polar solvents it is insoluble in nonpolar solvents such as aliphatic hydrocarbons. In order to overcome the solubility problems in nonpolar solvents, the more lipophilic penta-t-butyl-substituted betaine dye (45) has additionally been used as a secondary reference probe [174]. The excellent Hnear correlation between the Ej values of the two dyes allows the calculation of t(30) values for solvents in which the solvatochromic indicator dye (44) is not soluble. Introduction of electron-withdrawing substituents e.g. Cl [323], F, CF3, C6F13 [324]) in the betaine molecule reduces the basicity of its phenolate moiety, which allows the direct determination of x(30) values for somewhat more acidic solvents. Moreover, the Hpophilic and fluorophilic penta(trifluoromethyl)-substituted betaine dye (46) is more soluble in nonpolar solvents e.g. hexafluoro-benzene) than the standard dye (44) [324]. Conversely, the solubility in aqueous media can be improved through replacement of some of the peripheral hydrophobic phenyl groups in (44) by more hydrophilic pyridyl groups, to yield the more water-soluble betaine dye (47) [325]. The Ej values of these new secondary standard betaine dyes correlate linearly with the x(30) values of (44), which allows the calculation of x(30) values for solvents in which only betaine dyes (45)-(47) are sufficiently stable and soluble for the UV/Vis spectroscopic measurements [324, 325]. 

It has been stated that, when specific hydrogen-bonding effects are excluded, and differential polarizability effects are similar or minimized, the solvent polarity scales derived from UV/Vis absorption spectra Z,S,Ei 2Qi),n, Xk E- ), fluorescence speetra Py), infrared spectra (G), ESR spectra [a( " N)], NMR spectra (P), and NMR spectra AN) are linear with each other for a set of select solvents, i.e. non-HBD aliphatic solvents with a single dominant group dipole [263]. This result can be taken as confirmation that all these solvent scales do in fact describe intrinsic solvent properties and that they are to a great extent independent of the experimental methods and indicators used in their measurement [263], That these empirical solvent parameters correlate linearly with solvent dipole moments and functions of the relative permittivities (either alone or in combination with refractive index functions) indicates that they are a measure of the solvent dipolarity and polarizability, provided that specific solute/ solvent interactions are excluded. 

The empirical treatment of solvent-solute interactions by means of the jt parameters was re-examined 15 years after their introduction16. It was concluded that AAAAdimethyl-4-nitroaniline (7), not used in the original introduction of the jt scale, is superior to N,N-diethyl-4-nitroaniline (5) employed originally, since the former is not appreciably affected by differences in band shapes in different solvents as the latter is, due to vibrational structure. An extensive table of v(7) in 229 solvents and the gas phase was provided (and found well correlated linearly with v(2)). New jt values were obtained for several solvents that differed somewhat from the previously established values4,7. The wavenumbers (in cm-1) of 7 were shown to depend on the polarizability (measured by the refractive index n) and the polarity (measured by the relative permittivity e) of the solvent for 66 non-aromatic solvents as follows (equation 10) ... 

Aminophenoxazone dyes were studied by Otsuki and Taguchi94 with respect to their solvatochromic behavior in non-hydrogen-bonding polar solvents. The absorption spectra of 7-A,A-dimethylamino-3-phenoxazone (77), its 7-A,A-diethylamino analog and its 1-methyl analog were measured in several neat solvents and in aqueous dioxane solutions and the peak positions correlated linearly with the jt scale. The fluorescence emission peak, however, was not linear with jt. ... 

Finally, we like to point out that our results can explain the observations that 0-H BDEs in phenols correlate with ap+. Because of the direct conjugation between the oxygen lone pair and the substituent, the polar stabilization of the phenol can be expected to follow a linear relationship with Op" rather than with ap+. This is also consistent with our computed APSE which correlates linearly with Op with a correlation coefficient of 0.984. Since the Up and the CTp+ scales differ in that Gp+ predicts much larger substituent effects for resonance donors (e.g. 0CH3 oh and NH2) and relatively smaller substituent effects for resonance attractors (e.g. CN and NO2), the overall relationship between ABDE and electron donating substituents. Thus to understand the substituent effects on the 0-H... 

With R=NMe2, the absorbance frequency remained at Vg, 25.6 X 10 cm but the emission Vg, varied from 23.6 in n-hexane to 16.3 in acetonitrile, while with R=H the absorbance remained at 27.4 and the fluorescence experienced a limited shift from 24.7 to 23.0. The Stokes shifts of these compounds were shown to correlate linearly with a solvent polarity parameter, as did the fluorescence quantum yield. ... 

Interest in the polarization correlation of photons goes back to the early measurements of the linear polarization correlation of the two photons produced in the annihilation of para-positronium which were carried out as a result of a suggestion by Wheeler that these photons, when detected, have orthogonal polarizations. Yang subsequently pointed out that such measurements are capable of giving information on the parity state of nuclear particles that decay into two photons. In addition, the polarization correlation observed in the two-photon decay of atoms is considered to be one of the few phenomena where semiclassical theories of radiation are inadequate and it is necessary to invoke a full quantum theory of radiation. The effect has also been used to demonstrate the phenomenon of quantum interference. ... 

While two-photon absorption spectroscopy has been widely applied for precision measurements of atomic structure, the polarization correlation of the simultaneous two-photon emission from the metastable Is state of atomic hydrogen has only been measured very recently. The emission of the coincident two photons can be described by a single state vector which determines the circular and linear two-photon polarization. Compared to the two-photon cascade experiments the polarization correlation of the simultaneous two-photon decay of metastable hydrogen is conceptually closer to the original proposals by Bell and Bohm for tests of the foundation of quantum mechanics. More than SO years have elapsed since the famous Einstein-Bohr debate on microphysical reality and quantum formalism. The present and future outcome of the hydrogen two-photon correlation experiment is considered to be a most crucial test with regard to the rivalry between quantum mechanics and local realistic theories. 

The diffusion coefficient correlates linearly with the viscosity T as was already shown in the case of a diffusion limited transport system (Figure 14). When using the empirical Kirkwood function, a linear relationship between k and obtained. Figure 15 shows that the use of a more polar solvent slows down the rate of decomplexation. Hence, the regime of the transport can be influenced by the solvent polarity. 

Furthermore, in a series of polyoxyethylene nonylphenol nonionic surfactants, the value of varied linearly with the HLB number of the surfactant. The value of K2 varied linearly with the log of the interfacial tension measured at the surfactant concentration that gives 90% soil removal. Carrying the correlations still further, it was found that from the detergency equation of a single surfactant with three different polar sods, was a function of the sod s dipole moment and a function of the sod s surface tension (81). 

According to a kinetic study which included (56), (56a) and some oxaziridines derived from aliphatic aldehydes, hydrolysis follows exactly first order kinetics in 4M HCIO4. Proton catalysis was observed, and there is a linear correlation with Hammett s Ho function. Since only protonated molecules are hydrolyzed, basicities of oxaziridines ranging from pii A = +0.13 to -1.81 were found from the acidity rate profile. Hydrolysis rates were 1.49X 10 min for (56) and 43.4x 10 min for (56a) (7UCS(B)778). O-Protonation is assumed to occur, followed by polar C—O bond cleavage. The question of the place of protonation is independent of the predominant IV-protonation observed spectroscopically under equilibrium conditions all protonated species are thermodynamically equivalent. 

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