Vibrations (stretching of bonds, bending of bond angles) are usually described by Hooke's Law or a Morse potential. In discussions of the static conformations of polymers, such as the characteristic ratio, approximations are often used in which the bond lengths (or bond lengths plus bond angles) are considered to be constant.
Torsions involve the rotation about bonds. No torsion exist in H2O, because the three atoms describe a plane. But a single torsion is present in H2O2. The two oxygen atoms and a hydrogen atom describe a plane, but two such planes exist, depending on which hydrogen atom is chosen. Torsion about the O-O bond in HO-OH changes the orientation of these two planes.
Changes in the torsion angles are the dominant means by which flexible polymer molecules change from one conformation to another. Unfortunately, the polymer literature does not contain a single convention for the numerical description of the torsion angles. Instead two different conventions are widely used. The two conventions agree that the zero of the torsion angle at the B-C bond is achieved when the four defining atoms, AB-CD, are in a common plane. But they disagree on whether the arrangement should be
Symmetric (E does not depend on the sign of the torsion angle) torsion potential energy functions are often represented using
E = (Eb/2)[1 + cos (nphi)]
where Eb is the barrier height, the absolute value of n is the number of minima, and its sign determines whether there is a maximum or minimum at the zero of the torsion angle, phi. For example, the three-fold torsion about the C-C bond in ethane, with minima in the staggered conformations, uses Eb = 12 kJ/mol and n = 3, MS Fig. III-1. More complicated torsions can often be represented by a sum of two or more such terms, with different values of En and n.
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