Moment ratios

The moment ratios are dimensionless coefficients used to compare characteristics of distributions measured on different scales. 

The first step in data analysis is the selection of the best filling probability function, often beginning with a graphical analysis of the frequency histogram. Moment ratios and moment-ratio diagrams (with p as abscissa and as ordinate) are useful since probability functions of known distributions have characteristic values of p, and p. ... 

Frequency analysis is an alternative to moment-ratio analysis in selecting a representative function. Probability paper (see Figure 1-59 for an example) is available for each distribution, and the function is presented as a cumulative probability function. If the data sample has the same distribution function as the function used to scale the paper, the data will plot as a straight line. 

The conformational properties of trimer molecules modeling PVDB (S 100) and PVDF are analyzed by the molecular mechanics method of Boyd and Kesner [J. Chem. Phys. 1980, 72, 21791, which takes into account both steric and electrostatic energy. Total conformational energies are used to calculate a set of intramolecular interaction energies that, by means of the RIS model, allowed estimation of the characteristic ratios and dipole moment ratios of PVDB and PVDF under unperturbed conditions. 

Dielectric constants are determined for PDMS chains in the thermodynamically good solvent cyclohexane. Unfortunately, comparison of the experimental values of the dipole moment ratio with those predicted from RIS theory is complicated by pronounced specific solvent effects and comparison of experimental and theoretical values of the temperature coefficient is also difficult because of the very small magnitude of this coefficient. 

The configurational characteristics of PODME are established by calculations based on the RIS model. By using an appropriate set of conformational energy parameters, the characteristic ratio and the dipole moment ratio are evaluated. 

The characteristic ratio of atactic polylferf.-butyl vinyl ketone) is determined from light scattering and viscosimetry measurements, and at 300 K in benzene the dipole moment ratio and its temperature coefficient are measured. Calculations of Ca and Da based on a two-state RIS model, with parameters independently derived from a previously developed semiempirical potential energy surface and from epimerization equilibrium measurements for dimeric and trimeric oligomers, are in excellent agreement with the experimental results. The predicted temperature coefficient is positive but lower in magnitude than that observed. 

Values of the dipole moment ratio of PNS are obtained from dielectric measurements. From thermoelastic experiments, performed on polymer networks, the temperature coefficient of the unperturbed dimensions is determined. Analysis of these results using the RIS model is performed leading to the parameters given above. 

Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

Dielectric constants are determined for a fraction of PDET in benzene. The data indicate that the dipole moment ratio is somewhat higher than that of PEO, and its temperature coefficient is in the vicinity of 2ero. 

Values of the mean-square dipole moment, , of PDEI are determined as a function of temperature. The value of the dipole moment ratio is 0.697 at 303 K. Trifunctional model networks are prepared. From thermoelastic experiments performed on the networks over a temperature range 293 - 353 K, it is found that the value of the temperature coefficient of the unperturbed dimensions amounts to 1.05 0.17 K-1. The dipole moments and the temperature coefficients of both the dipole moments and the unperturbed dimensions are critically interpreted in terms of the RIS model, and are found to be in a reasonable agreement. 

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

Helical hydrophobic moment ratios, I , are evaluated for 34 polypeptides under conditions where the helix content is dictated solely by the short-range interactions operative in aqueous media. The mean-square helical hydrophobic moment is denoted by , and is the averaged of the squared hydrophoblcltles. This ratio would be one in absence of any correlation in the hydrophoblcltles of amino acid residues in helices. 

Averaged helical hydrophobic moment ratios are evaluated in order to assess the potential of amphiphilic regions contributing to the helix-helix interaction responsible for stabilization of tropomyosin dimers. These ratios yield profiles that are higher in the amino-terminal half than in the carboxyl-terminal half of a and p tropomyosin chains. The higher profiles found in the amino-terminal half of a tropomyosin may contribute to the greater stability of the dimer in this region. 

Triangular Matrix Representation of Dimensionless Helical Hydrophobic Moment Ratios Maroun, R. C. McCord, R. W. Mattice, W. L. Int. J. Biol. Macromoi. 1986, 8, 73. 

The two-exciton manifold consists of two types of doubly excited vibrational states. The first are overtones (local), where a single bond is doubly excited. The other are collective (nonlocal), where two bonds are simultaneously excited (43,50). We denote the former OTE (overtone two-excitation) and the latter CTE (collective two-excitation). A pentapeptide has 5 OTE and 10 CTE. The two-exciton energies are determined by the parameters gn in the Hamiltonian [Equation (17)], which in turn depend on the peptide group energies G , the anharmonicity An, and dipole moment ratio Kn, n = l,...,5. We set them equal for all CO units... 

The infrared spectra of a number of cyanato complexes are recorded in Table XIV. One of the compounds cp2M(OCN)2 (M = Ti,Hf) is incorrectly formulated. The infrared data are as listed, and N NMR [93) and mass spectral data [J45) support cp2Ti(OCN)2. However, the dipole moment ratios of the compounds suggest that they cannot both have the same type of coordination [422). Most cyanato complexes can... 

The already low melt elasticity of polymer made with Cr/alumina was further diminished when sulfate was added. This response is shown in Table 49. The sulfate level on a Cr/alumina catalyst was varied from 0 to 3.0 mmol SO4 g-1 A12C>3, followed by activation at 600 °C. Polymer was then made with each catalyst, and the elastic properties of these polymers are listed in Table 49. H2 was used in all these polymerization runs, although, in the absence of sulfate, less H2 was needed to maintain a similarly high MW. The MW of these polymers was found to increase significantly as sulfate was added. This trend probably reflects a diminished sensitivity to H2 rather than an increase in the natural MW (made without H2). The addition of sulfate to the catalyst also greatly narrowed the MW distribution, as indicated by the Mw/Mn and MyJ Mw moment ratios. Both ratios dropped significantly when sulfate was added. 

The 3E and p-complex structures resemble each other because both consist of one unit of spin or electronic angular momentum (S or L) coupled to the nuclear rotation (R). However, since fj, operates exclusively on electron spatial coordinates, any resemblance between the rotational-branch intensity patterns for 3S —1E+ and p-complex —1E+ transitions would seem to be coincidental. A 3E —1E+ transition will look exactly like a p-complex —1E+ transition if, in addition to satisfying Eqs. (6.3.47), the cr-orbital of the 1E+ state is predominantly of scr united atom character. Then the transition moment ratio will be... 

The moments ratio, Pa (equation (26)) is unity, which is obeyed reasonably well for non-diffusing species in ionic materials and for ionic melts. 

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