Correlation length, axial

The effect of these chain distortions is to isolate the alkali ions within shorter axial domains, the extent of which is reflected in the small correlation length, 25 A. The results of the neutron diffraction study by Aime el al. [Ill] seem to be more significant in the light of these recent findings. 

X-ray diffraction patterns of fibers spun from liquid crystalline melts of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) show a high degree of axial orientation. Several meridional maxima are detected which are aperiodic and also change in position and number with the monomer composition. The positions of these maxima can be predicted by calculating the theoretical scattering of random copolymer chains, in which the residues are represented by points separated by the monomer lengths. Both peak positions and intensities are reproduced when intraresidue interferences are allowed for in an atomic model for the random chains. This procedure also allows determination of the stiff-chain persistence (or correlation) length from the breadth of the maximum at d=2.lA which increases from 9 to 13 residues as the HBA content is increased from 25 to 75%. 

Axial blanket lengths must be chosen prior to the hydraulic calculations to establish the total fuel-element length. The axial blankets are sized primarily from economic studies performed at the core system level. Pressure loss across the fuel-element bundle is next calculated for the reference flow rate using empirical head-loss coefficients. Over the relevant range of Reynolds numbers, liquid-metal velocity profiles and pressure drops agree with those calculated from generalized correlations developed... 

An interesting improvement from the classical treatment of the bond under stress was proposed by Crist et al, [101], Considering the chain as a set of N-coupled Morse oscillators, these authors determined the elongation and time to failure as a function of the axial stress. The results, reported in Fig. 20, show a decreasing correlation between the total elastic strain before failure and the level of applied force with the chain length. To break a chain within some reasonable time interval (for example <10-3s) requires, however, the same level of stress (a0.7 fb) as found from the simpler de Boer s model. 

Correlations between the 0(5)-C(l) and C(l)-0(1) bond lengths in both axial and equatorial isomers demonstrated that (0)-cr (C-0) interactions stabilizing the SN1 transition states are already manifesting themselves in... 

Fig. 25 Plots of the sensitivity parameters and intercepts obtained from bond length-reactivity correlations for axial tetrahydropyranyl- [96], methoxymethyl- and a-glucosyl-OX versus their relative reactivities towards hydrolysis. Reprinted with permission from Kirby and Jones (1986).

A great number of olefinic compounds are known to photodimerize in the crystalline state (1,2). Formation of a-truxillic and / -truxinic acids from two types of cinnamic acid crystals was interpreted by Bernstein and Quimby in 1943 to be a crystal lattice controlled reaction (5). In 1964 their hypothesis on cinnamic acid crystals was visualized by Schmidt and co-workers, who correlated the crystal structure of several olefin derivatives with photoreactivity and configuration of the products (4). In these olefinic crystals the potentially reactive double bonds are oriented in parallel to each other and are separated by approximately 4 A, favorable for [2+2] cycloaddition with minimal atomic and molecular motion. In general, the environment of olefinic double bonds in these crystals conforms to one of three principal types (a) the -type crystal, in which the double bonds of neighboring molecules make contact at a distance of -3.7 A across a center of symmetry to give a centrosymmetric dimer (1-dimer) (b) the / -type crystal, characterized by a lattice having one axial length of... 

The pressure is presumed to vary smoothly throughout the length of the channel, so it can be expanded in a first-order Taylor series. The wall shear stress is presumed to come from an empirical correlation, since, by assumption, the model does not consider radial variations in the axial velocity. The control-surface integrals can be evaluated simply to yield an equation for the axial momentum balance... 

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