Internal rotation angles

As the most notable contribution of ab initio studies, it was revealed that the different modes of molecular deformation (i.e. bond stretching, valence angle bending and internal rotation) are excited simultaneously and not sequentially at different levels of stress. Intuitive arguments, implied by molecular mechanics and other semi-empirical procedures, lead to the erroneous assumption that the relative extent of deformation under stress of covalent bonds, valence angles and internal rotation angles (Ar A0 AO) should be inversely proportional to the relative stiffness of the deformation modes which, for a typical polyolefin, are 100 10 1 [15]. A completly different picture emerged from the Hartree-Fock calculations where the determined values of Ar A0 AO actually vary in the ratio of 1 2.4 9 [91]. 

In an effort to correlate the conformational features of polysilane derivatives with their properties, calculations are performed to determine the relative stabilities of the conformational states of the meso and racemic diads of polysilapropylene. Energy maps are constructed in terms of internal rotation angles to calculate the average properties of the chain. The calculations show that the difference In energy between the various states of the meso and racemic dlad Is small. Hence, PSP can be considered to be more flexible than the analogous carbon polymer, PP. The characteristic ratios of the unperturbed end-to-end distances for the /so- and syndiotaclic PSP are less than those for the PP of corresponding tacticity. 

For a number of SRMs C H, i.e. ( ) isa proper subgroup of This fact has been established by determining the group H directly. In the case where a principle axis coincides with an internal rotation axis for all values of the internal rotation angle, but not being a covering symmetry axis, we have... 

The initial guess structure is subjected to a total energy minimisation by slightly modifying the internal rotation angles in order to reach a microscopic structure in a mechanical equilibrium, i.e. corresponding to a true potential energy minimum. 

Fig. 124 Mean change of the internal rotation angles of the main-chain C-C bonds at - 40 °C and 50 °C (from [78])...

The observed activation energy comes from a change of the intramolecular energy of the chain with the rotating ester group and it increases with the amplitude of the main-chain internal rotation angle changes. 

The total change of internal rotation angles of the main-chain C - C bonds in the case of CMIM20 is weaker (55°) than for PMMA (58.5°). Furthermore, one observes a gradual increase of this total angular change when the MMA... 

Figure 136 shows the amplitude and extent of the internal rotation angle changes for PMMA and CMIM20. 

The glutarimide cycle, due to the additional CH2 group, is less rigid than the maleimide one and can undergo distortions of the internal rotation angles of its C - CH2 - C part. 

MMA ester group Tt-flips, associated with internal rotation angle changes of the backbone C - C bonds, including both the MMA backbone bonds and the Cq - CH2 - Cq sequence of the glutarimide cycles... 

The energy calculations were performed without fixing the fiber identity period, the only assumption being that the chain forms a helical structure, that is, the set of internal rotation angles repeats along the subsequent monomeric units of the chain. For the calculation the internal rotation barriers, van der Waals interactions [mainly after Scheraga (31)], and dipole-dipole interactions were taken into account. 

Polypropylene and polyacetaldehyde are the simplest of the above polymers, having only two internal rotation angles, x and Tg, in the main chain. Figure 1 shows the potencial energy contour map for polyacetaldehyde. The crosses indicate the potential minima, and the closed circles the x-ray structure determined by Natta et al. (28). The two minima correspond to the right- and left-hand helices. 

The results of the first four polymers are listed in Table I the internal rotation angles of the main chain, x. and x , the number of monomeric units per turn, N, for the calculated stable conformations, and also the values for the structure determined by x-ray analyses. In the case of polypropylene, the number of monomeric units per turn is 2.91, very close to the x-ray value of 3.0. This result for polypropylene is essentially the same as those of Natta et al. (32) and Liquori et al. (33). For the three other polymers, good agreements were also obtained between the predicted models and x-ray structures in spite of the simple assumption of considering only intramolecular interactions. This... 

Table II. Internal Rotation Angles of Poly(ethylene Oxybenzoate) cx-Form on the Process of Analysis (U)...

In 1961 a molecular model of a (7/2) helix [Figure 6(a)] was proposed by the author and his coworkers (13.) based on the information from x-ray, infrared, and Raman spectroscopy, but the crystal structure could not be determined at that time. After ten years, owing to the development of methods and apparatus, especially the constrained least-squares method and a vacuum cylindrical camera with a radius of 10 cm, the crystal structure has been determined as shown in Figure 6(c) (22.). The internal rotation angles are considerably distorted from the uniform helix, although the molecular conformation is essentially the (7/2) helix and close to the TTG sequences. 

Figure 8.26. Internal rotor potential for the H20-C02 complex (upper panel). The dotted line corresponds to ab initio scaled calculation. The lower panel shows the variation in the intermolecular CO bond with internal rotation angle. (From Block et al. [1992].)...

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