Molecular-Weight Dependence of the Optical Rotation of Poly((R)-2-deuterio-n-hexyl isocyanate)

The extraordinarily large optical rotations [α] of poly((R)-2-deuterio-n-hexyl isocyanate) were investigated with a particular emphasis on the chain length dependence of [α]. Data for [α] in hexane, 1-chlorobutane, and dichloromethane were obtained as functions of temperature and degree of polymerization N and analyzed by a statistical mechanical theory developed recently (Lifson, S.; Andreola, C.; Peterson, N. C.; Green, M. M. J. Am. Chem. Soc. 1989, 111, 8850). The theory is based on a model whereby a polymer chain consists of an alternate sequence of M helix (left-handed) and P helix (right-handed), interrupted by helix reversal points, and [α] originates from the excess presence of the P helix over the M helix due to the chiral substitution of a deuterium atom on the side chain. Detailed analysis of [α] vs N data substantiated the validity of the theory and allowed a separate estimate of enthalpic and entropic contributions to the isotope effect, revealing that the P helix dwells in a slightly narrow but deep energy well in the conformational space compared with the M helix. In hexane at 25 °C, this isotope effect favors the P helix over the M helix by 0.74 cal mol^-1 on a monomer unit basis, implying that the P helix would exist in excess of the M helix only by 0.12%. However, for a long chain with N = 2000, this minute excess is amplified by the cooperative mechanism to 67:33 in [α], whereas the helix reversal costs 3900 cal mol^-1 and appears only once in 762 units on the average.