Chains bond rotation

Figure 14.6 Schematic representation of a single polymer chain molecule that has numerous random kinks and coils produced by chain bond rotations.

Molecular Shape Molecular entanglements occur when the chains assume twisted, coiled, and kinked shapes or contours as a consequence of chain bond rotations. 

Rosenbluth algorithm can also be used as the basis for a more efficient way to perform ite Carlo sampling for fully flexible chain molecules [Siepmann and Frenkel 1992], ch, as we have seen, is difficult to do as bond rotations often give rise to high energy rlaps with the rest of the system. 

A cycloalkane is a saturated cyclic hydrocarbon with the general formula C H2 . In contrast to open-chain alkanes, where nearly free rotation occurs around C, -C bonds, rotation is greatly reduced in cycloalkanes. Disubstituted cycloalkanes can therefore exist as cis-trans isomers. The cis isomer has both substituents on the same face of the ring the trans isomer has substituents on opposite faces. Cis-trans isomers are just one kind of stereoisomers—isomers... 

Figure 3-7. A simplified picture of a //wi-v-polyacelylcne chain with conformational disorder the right part of the chain is rotated with respect to its left part over the angle .

Ea = Arrhenius activation energy Es = excess stress energy AEr = potential barrier for bond rotation Eel = molecular elastic energy F = mean force potential f = average force on the chain fb = bond breaking force H0 = Hookean spring constant kB = Boltzmann constant... 

The carbon chains of samrated fatty acids form a zigzag pattern when extended, as at low temperamres. At higher temperatures, some bonds rotate, causing chain shortening, which explains why biomembranes become thinner with increases in temperamre. A type of geometric isomerism occurs in unsaturated fatty acids, depending on the orientation of atoms or groups around the axes of double bonds, which do not allow rotation. If the acyl chains are on the same side of the bond, it is cis-, as in oleic acid if on opposite sides, it is tram-, as in elaidic acid, the tram isomer of oleic acid (Fig-... 

Not only are steric interferences intolerably severe in the fully extended configuration XI it is usually impossible to eliminate them altogether through bond rotation, as may be seen from models. Even when the substituents are no larger than methyl, as in polyisobutylene (X = Y=CH3), steric interferences are so great as to preclude construction of a scale model for any configuration of the chain if the normal C—C and C—H distances and the usually accepted van der Waals radii are used. If Stuart models are used, in which the van der Waals... 

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Fig. 81.—Potential energy associated with bond rotation as a function of angle, (a) Symmetrical potential according to Eq. (23) (b) and (c) potential energy functions with lowest minimum at 0=0 corresponding to the planar zigzag form of a polymethylene chain. These curves were calculated by Taylor. 0...

Since the additions are normally stereospecific with respect to the alkene, if an open-chain intermediate is involved it must collapse to product more rapidly than single-bond rotations that would destroy the stereoselectivity. 

We have added a companion option to PBUILD, PRANDOM which eases considerably the problem of finding good conformations of a polymer segment. PRANDOM automatically selects all of the polymer backbone and/or side chain bonds and will randomly select rotations for each bond. In a few minutes, one can not only build a polymer fragment, but also set up a Monte-Carlo search of its conformational space. However, even this cannot solve the problems for large models (pentamer or larger), again due to the number of bonds to be rotated. 

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