Restricted bond angles

The characteristic ratio is larger than unity (C > 1) for all polymers. The physical origins of these local correlations between bond vectors are restricted bond angles and steric hindrance. All models of ideal polymers ignore steric hindrance between monomers separated by many bonds and result in characteristic ratios saturating at a finite value Coo for large numbers of main-chain bonds ( — oo) (see Fig. 2.4). Thus, the mean-... 

As seen above, the key result of the freely jointed chain statistics and incorporation of local conformational details such as restricted bond angles and dihedral angles is that R ) is always proportional to the chain length, that is, the size exponent v = 1/2, as long as the excluded volume effect is absent. The only... 

The persistence vectors vividly portray the correlations between bonds of the chain. These correlations are due to the combined effects of narrowly restricted bond angles, preferences for one or more rotational states over others and the interdependence of rotations about neighboring bonds. The persistence of a freely jointed chain is just the first bond. Transverse components are necessarily null. 

Taking the length per repeat unit (i.e., bond angles already considered) as 0.78 nm in each instance, evaluate the factors (1 + cos 0)/(l - cos (p) and cos (p for each polymer. Ignoring the difference between 130 and 140°C, do you find the difference in steric hindrance between the tributyrate and tri-caprylate to be what you expected Is the effect of temperature on the 1q value of cellulose tributyrate what you expected Briefly explain each answer. For each polymer, calculate r if n = 10 also do this for the hypothetical chain with no restrictions to rotation and having the same repeat length. 

Id. Influence of Bond Angle Restrictions.—In all real polymer chains the direction assumed by a given bond is strongly influenced by the direction of its predecessor in the chain. The orientation of other nearby bonds (second, third, and possibly fourth neighbors) may also exert an appreciable influence, but the orientation of the immediate predecessor usually is of greatest importance. The exact nature of these restrictions on the direction assumed by a given bond... 

The second step is the molecular dynamics (MD) calculation that is based on the solution of the Newtonian equations of motion. An arbitrary starting conformation is chosen and the atoms in the molecule can move under the restriction of a certain force field using the thermal energy, distributed via Boltzmann functions to the atoms in the molecule in a stochastic manner. The aim is to find the conformation with minimal energy when the experimental distances and sometimes simultaneously the bond angles as derived from vicinal or direct coupling constants are used as constraints. 

Such a model ignores restrictions on the bond angles and dihedral angles imposed by the local chemical structure. This may be taken care of empirically by defining a characteristic ratio, Cm, where... 

General theories of molecular structure have been advocated by different groups in the past but their applicability has been restricted to the shape, Le. bond lengths and bond angles, of small molecules. Two types of approaches deserve special mention ... 

C b2 is the effective bond length , b. For the case of the bond angle restriction on the random walk ... 

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