Molecular deformation factor

In the kinetic equation (4.35), transient free energy of the elastic chain deformation controls ratio of the rate constants (4.36) while effects of molecular orientation are accounted for by the concentration factor A w 0,i). The concentration factor reduces to unity for the case of isotropic systems, assumes values above unity in the range of enhanced orientation, and below unity in the range of reduced orientation. Equation (4.35) introduces effects of molecular deformation and orientation of chain segments. 

The expression of the orientation function derived on the basis of the real network model differs markedly from those obtained in previous treatments. The strain function includes the non-affine molecular deformation consecutive to restriction on junction fluctuations and distorsions of constraint domains. The configurational factor for the real chain accounts also for local intermolecular orientational correlations. 

Two factors need to be accounted for in the calculation of the so-called r -struc-ture of a molecule from LCNMR data. The first is the effect of molecular harmonic vibrations on the observed dipolar splittings, which has been generally recognized since the late 1970s [22] most LCNMR stmctures published since 1980 contain these corrections. The second factor is molecular deformations caused by interaction of the solute with the medium (due to correlations between molecular vibrations and solute reorientations), which as might be expected, are more important for some liquid crystals than others. These effects have been widely recognized since the early 1980s, and have been studied in detail (see for example [15, 23-26]). Procedures to correct for these effects have been published [27], and solvent systems which produce minimal structural distortions have been identified [12, 28, 29]. The problem and its solution have recently been re-emphasized by Diehl and coworkers [30]. 

Although scaling of the computed vibrational frequencies using a single, global, scale factor is common, the first scaling methods applied to ab initio force constants used several different scale factors to correct for systematic errors in different types of molecular deformations, e.g.. 

Durihg recent years a considerable amount of re-.search has been undertaken to understand what in the makeup of a polymer affects the processability. In the late 1980s, the Rubber Manufacturers Association in the United States undertook a research project with the Department of Polymer Engineering at the University of Akron to evaluate the laboratory equipment available using specially made butadiene-acrylonitrile polymers with different acrylonitrile levels, molecular weights, and molecular weight distributions. The results from the study confirmed that, from the processing variables viewpoint, the major factors are frequency (shear rate), temperature (temperature), and deformation (strain). 

Both sets of experiments seem to support the proportionality of crack opening displacement 5C = 2w and molecular mass Mc between crosslinks as indicated by the slope 1 in the double logarithmic plot (Fig. 7.5). Even if Mc had to be adjusted due to doubts about the front factor in Eq. (4.3), the proportionality would stay unaffected. Consequently, the size of the deformation zone ahead of the crack is determined by the length of the molecular strands in the chemical network. 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

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