The qualitative model of a chirally perturbed polyisocyanate chain, with lone helical sequences separated by helical sense reversals, has been interpreted quantitatively by statistical thermodynamics. The change of the specific optical rotation with temperature depends on the following: The energy of a helix sense reversal, Er; the energy difference per monomer unit between the opposing helical senses, 2Eh; the degree of polymerization, N. Three cases of dynamic equilibrium are considered: (1) Equilibrium between purely right-handed (P) and purely left-handed (M) short polymers; (2) equilibrium between many long alternating P and M helical sequences, separated by helix reversal states, in a very long polymer chain; (3) the general case of polymers of any length, including (1) and (2) as special cases. Calculations of the relationship between optical activity [α]D and temperature prove that both cases 2 and 3 make an excellent fit to the corresponding measurements on poly((R)-1-deuterio-n-hexyl isocyanate) of Mw 870000, in dilute chloroform and hexane solutions. In this fit of the experimental data to the theory, cases 2 and 3 differ somewhat, yielding values of 2Eh and Er near to 1 and 4000 cal/mol. The results confirm a cooperative model proposed to account for the unusual sensitivity of this polymer to asymmetric deuterium substitution and yield the energy bias of the isotope effect, which would otherwise be extremely difficult to measure. The calculated average lengths of helical sequences, evaluated from Er, are too large to attribute the long-known flexibility of high molecular weight poly(n-alkyl isocyanates) to kinks at the reversals between otherwise stiff helical segments. Consequently the present results support strongly, though indirectly, the model of smooth bending with the global dimensions of these polymers dominated by local segmental motion.
ASJC Scopus subject areas
- Colloid and Surface Chemistry