Linear correlator

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... 

The Av is also correlated linearly with 19F of p-FC6H4X103. Besides these investigations, other linear free energy relationships for the hydrogen bond of sulphones with several... 

Diffusivity correlates linearly with the ratio of temperature and viscosity. Therefore the diffusivity can also be expected to correlate with relaxation time because the latter correlates with temperature and viscosity according to Eq. (3.6.1). Figure 3.6.3 illustrates the correlation between relaxation time and diffusivity with the gas/oil ratio as a parameter [13]. The correlation between diffusivity and relaxation time extends to hydrocarbon components in a mixture and there is a mapping between the distributions of diffusivity and relaxation time for crude oils [17]. 

Nuclear Quadrupolar Resonance. - A variety of dichlorophosphanes have n.q.r. 35C1 resonances whose average for each compound correlate linearly uith the total Taft constants.103 The spectra of a number of po1yf1uoroary1 hexachlorophosphazenes have been studied.104 A n.q.r. study of pentafluorophenyl-... 

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. 

PLS should have, in principle, rejected a portion of the non-linear variance resulting in a better, although not completely exact, fit to the data with just 1 factor. The PLS does tend to reject (exclude) those portions of the x-data which do not correlate linearly to the y-block. (Richard Kramer)... 

The relationship between the structure of 1,2,4-thiadiazolidines and their H NMR spectral solvent effects has been studied by measurement of the NMR chemical shift differences (Av) of 39 derivatives in various solvents (CgDg, CCU) for methyl or methylene groups attached to an sp2-hybridized nitrogen, Av correlates linearly with Hammett a constants and for those attached to an sp3 4-hybridized nitrogen, with Taft a° constants <1982AHC285>. 

Remarkably, the use of a fluorous biphasic solvent system in combination with a [Rh(NBD)(DPPE)]+-type catalyst (NBD = norbornadiene) copolymerized into a porous nonfluorous ethylene dimethacrylate polymer, resulted in an increased activity of the catalyst relative to a situation when only toluene was used as solvent [30]. The results were explained by assuming that fluorophobicity of the substrate (methyl-trans-cinnamate) leads to a relatively higher local substrate concentration inside the cavities of the polymer when the fluorous solvent is used. That is, the polymer could be viewed as a better solvent than the fluorous solvent system. This interpretation was supported by the observations that (i) the increase in activity correlates linearly with the volume fraction of fluorous solvent (PFMCH) and (ii) the porous ethylene dimethacrylate polymer by itself lowers the concentration of decane in PFMCH from 75 mM to 50 mM, corresponding to a 600 mM local concentration of decane in the polymer. Gas to liquid mass transport limitation of dihydrogen could be mled out as a possible cause. 

Figure 9.31 AFM image of a scalpel scratch used to determine the thickness of the polyethylene films grown on a Cr0v/Si02/Si(100) model catalyst. The polymer thickness correlates linearly with the reaction time (adapted from Thiine et at. [90]).

The calculations were performed at the semiempirical level using AMI parametrization. The results for the methyl chloride reaction (Table 8) supported Williams earlier findings for the methylammonium ion-ammonia reaction (p. 147) and the results by Wolfe and Kim in that the inverse secondary a-deuterium KIE arose from an increase in the C —H stretching force constants which accompanied the change from sp3 hybridization at the a-carbon in the reactant to the spMike hybridization in the transition state. More important, however, were the observations that (i) the total KIE is dominated by the vibrational (ZPE) component of the KIE with which it correlates linearly, and (ii) that the inverse contribution from the C —H(D) stretching vibrations is almost constant for all the reactions. Ibis suggests that the contribution from the other vibrations, i.e. the rest in Table 8, determines the magnitude of the KIE. In fact, Barnes and Williams stated that the... 

Obviously the n ionization energy is a function of the type, number and position of the substituents. The IP( n) values of 4-substituted quinuclidines correlate linearly with Taft s a values51 (Figure 3). 

Similarly, the minimal effective brain level, MEBL (nmol/g), required for the drug to interfere with the conditioned avoidance response of rats correlates linearly with IPav. The least-squares correlation is... 

The hydrophobicity of a packing is best described by the retention factor of a neutral hydrophobic compound, such as naphthalene or acenaphthene. More sophisticated methods are possible, but they are of little concern for the practitioner. The natural logarithms of the retention factors of both compounds correlate linearly for all 91 commercial packings tested. Thus we can use either one of these compounds as reference compounds for the hydrophobicity of a packing. We chose acenaphthene as our hydrophobic reference compound. 

Deprotonation energies for 9-substituted fluorenes, calculated using AMI semiem-pirical MO theory, correlate linearly with acidities determined experimentally for these heteroatom-substituted compounds. ... 

According to the Arrhenius law, the rate of reaction is correlated linearly to the increase in temperature, with the rate constant k given by... 

That H and C chemical shifts correlate linearly with charge density in carbonium ions and carbanions has been an operating... 

The aluminum content of the as-synthesized zeolites also influences their X-ray powder diffraction pattern. The height of the main peak in the patterns decreases with decreasing Si/Al ratio in the zeolite, but their width increases simultaneously so that the area remains practically constant for all samples. On the other hand, the dhki distance corresponding to the diffraction peak at 43 of 20 correlated linearly with the aluminum content of the zeolite (Figure 4). However, the lack of knowledge of the crystal structure of Beta zeolite makes it impossible to correlate the Al content and unit cell parameters. 

Hong et al. applied capillary EKC with dodecyltrimethylammonium-bromide/sodium dodecylsulfate (12.7/21.1 mM) vesicles to the separation of alkylphenones (Fig. 8A) and obtained better resolution than with sodium dodecylsulfate micelles (59). The logarithms of the retention factors for 20 neutral compounds of similar structures showed an excellent linear correlation with log Poct (R2 = 0.98). Similarly, Razak et al. (60) showed that the log capacity factors for interaction between neutral and positively charged analytes and cetyltrimethylammoniumbromide/sodium octylsulfate vesicles correlated linearly with the log Poa values. 

Quantitatively the Coulomb repulsion integral of SCF-calculations for SEM correlates linearly with Ig Ksem Equation (3)... 

Two issues now need be addressed (1) which atom(s) of each molecule should be considered for the correlation with the IPs and (2) what is the proper n value associated with the equations of Table 7.1. The form of the correlation (linear or other) is... 

---