Molecular disorder parameter

Correlation times and activation energy parameters obtained from different techniques may or may not agree with one another. Comparison of these data enables one to check the applicability of the model employed and examine whether any particular basic molecular process is reflected by the measurement or whether the method of analysis employed is correct. In order to characterize rotational motion in plastic crystals properly it may indeed be necessary to compare correlation times obtained by several methods. Thus, values from NMR spectroscopy and Rayleigh scattering enable us to distinguish uncorrelated and correlated rotations. Molecular disorder is not reflected in NMR measurements to this end, diffraction studies would be essential. 

In the absence of dynamic and static disorder, all partially filled band systems would exhibit coherent transport over long distances. With static and dynamic disorder, the modulation of the simple molecular orbital or band structure by nuclear effects entirely dominates transport. This is clear both in the Kubo linear response formulation of conductivity and in the Marcus-Hush-Jortner formulation of ET rates. The DNA systems are remarkable for the different kinds of disorder they exhibit in addition to the ordinary static and dynamic disorder expected in any soft material, DNA has the covalent disorder arising from the choice of A, T, G, or C at each substitution base site along the backbone. Additionally, DNA has the characteristic orientational and metric (helicoidal) disorder parameters arising from the fundamental motif of electron motion along the r-stack. 

If the difference in atomic number between the absorber element and the backscattering element is >10 and if only one kind of element backscatters, EXAFS spectra can be analyzed readily to provide local structural data on adsorbed species. However, because the electron mean free path, thermal and static disorder parameters (Debye-Waller factors), and coordination number for an absorber environment cannot be determined a priori with sufficient accuracy, EXAFS data for suitable reference compounds of known molecular structure must be used to help interpret the EXAFS spectrum for an interfaeial region. 

The X-ray molecular disorder is immediately recognized by GIPAW method when experimental and theoretical shielding NMR parameters are compared. The scatter of points shown in Fig. 2.42B and C, both for tensor parameters and isotropic values exclude the drawing of acceptable linear correlation. These correlations have been greatly improved when periodic model with fuU optimization of position of heavy atoms and protons was used for calculation of GIPAW parameters. 

In the present section a number of modern physical concepts for the description of the structure of crosslinked polymers is used the thermodynamic concept, the cluster model of amorphous state structure of polymers, fractal analysis, irreversible aggregation models and the thermal cluster model. Within the frameworks of the thermodynamic approach the interconnection of structural and molecular characteristics of crosslinked polymers with disorder parameter 8 is considered [69]. According to the concept [69] the indicated parameter, connected with the thermal mobility of molecules near the melting temperature, is expressed by Formula 1.28. Since p. is given by Equation 1.29 then Relationship 1.30 can be received from combination of Equations 1.28 and 1.29. 

With increasing values of P the molar volume is in progressively better agreement with the experimental values. Upon heating a phase transition takes place from the a phase to an orientationally disordered fee phase at the transition temperature where we find a jump in the molar volume (Fig. 6), the molecular energy, and in the order parameter. The transition temperature of our previous classical Monte Carlo study [290,291] is T = 42.5( 0.3) K, with increasing P, T is shifted to smaller values, and in the quantum limit we obtain = 38( 0.5) K, which represents a reduction of about 11% with respect to the classical value. 

Fig. 59 Phase diagram for blend consisting of two symmetric PS-6-PI block copolymers of different molecular weights in parameter space of temperature and fraction of higher molecular weight copolymer, . disordered state lamella A PS cylinder. From [179]. Copyright 2001 American Chemical Society... 

The variation of the Chin-Gilman parameter with bonding type means that the mechanism underlying hardness numbers varies. As a result, this author has found that it is necessary to consider the work done by an applied shear stress during the shearing of a bond. This depends on the crystal structure, the direction of shear, and the chemical bond type. At constant crystal structure, it depends on the atomic (molecular volume). In the case of glasses, it depends on the average size of the disorder mesh. 

A switch to double-angle vectors given by Eq. (2.3.12) not only significantly simplifies the treatment of orientation phase transitions in planar systems of nonpolar molecules but also leads to a number of substantial inferences on the transition nature. First of all note that the long-range-order parameter t] (vanishing in a disordered phase and equal to unity at T = 0) in a -dimensional space (specified by the orientations of long molecular axes) can be defined as ... 

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