Orientation averages predicted

The predicted diffusion behavior of benzene showed the familiar anisotropy observed for other molecules in silicalite, although evolving over a far longer time period. The calculated diffusion coefficients at temperatures between 200 and 500 K varied by 6 orders of magnitude. The orientationally averaged value at 300 K is 1.1 X 10-12 m2/s, approximately 1-2 orders of... 

We have shown the importance of local free stream velocity (uqo) in controlling deposition velocity. There may be a relationship between Uo and time-of-wetness, either through variations in synoptic conditions or through heat transfer and evaporation. Such an interaction could modify the estimation of an effective annual average SO2 deposition rate. As mentioned above, one must also account for surface orientation in predicting time-of-wetness. 

These questions form the topics of discussion for sections 11.2, 11.3 and 11.4, respectively. In extremely highly drawn material, a great deal of modification of the original structure of the polymer must have taken place and most of the chains are essentially parallel to the draw direction, so that (cos 0) and Pjicos 6)) are both close to 1. It is difficult to describe theoretically and in detail how molecular orientation takes place under these circumstances and thus to predict the small departures from unity for such materials. Discussion of the prediction and use of orientation averages is therefore limited to materials of moderate draw ratios. Models used for interpreting the properties of highly oriented polymers are discussed in sections 11.5 and 11.6. 

Equations (A.7) also show that, in general, the prediction of a property that depends on a tensor of rank I will require knowledge of orientation averages of order /. The elastic constants of a material are fourth-rank tensor properties thus the prediction of their values for a drawn polymer involves the use of both second- and fourth-order averages, in the simplest case P ico O)) and P (x>s6)), and thus provides a more severe test of the models for the development of orientation. The elastic constants are considered in section 11.4. 

There are two possible sources for the discrepancies between measured and predicted elastic constants when the orientation averages used are determined from models for molecular orientation the models may be incorrect and neither Voigt nor Reuss averaging may be appropriate. In order to examine the second of these possibilities more directly it is necessary to determine the orientation averages experimentally. 

The general case is predicted to lie in between some examples on the possibility of obtaining the different cases are given later, together with parallel orientation averages and (see Sect. 15). 

Electron affinities for 35 substituted nitrobenzenes have been reported and provided a comprehensive data set for the examination of substituent effects38. The data were used to derive Taft gas-phase substituent parameters and discussed qualitatively based on frontier orbital molecular theory38. The rate constants for the exo-energetic electron-transfer reactions were found to be close to those predicted by the ADO (average dipole orientation) theory38. 

One of the most talked-about dream targets of synthesis, dodeca-hedrane (123), has been studied repeatedly by the MM method (128,235). Recent MM2 calculations (234) predict a heat of formation of 22.15 kcal/mol, incidentally equal to the average from the two previous values 45 .28 by the Allinger 1971 force field, and -0.22 kcal/mol by the Schleyer force field (26a). In the If, structure a very high strain energy is predicted by these two force fields because of the perfect eclipsed orientation of all the C—C as well as C—H bonds. Ermer calculated twisted conformations for this molecule with the CFF and confirmed that the I, structure was the GMEC (324,324a). 

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