In polyisocyanates composed only of randomly distributed (R) and (S) units, the chiral optical properties of the polymer are far out of proportion to the enantiomeric excess of the monomers. This highly disproportionate relationship, which arises from a majority-rule effect among these enantiomeric units on the helical sense of the backbone, is now found to be unaffected, within certain limits, by the overwhelming presence of achiral units randomly distributed along the chain. This experimental result can be explained quantitatively by an analysis based on the one-dimensional random-field Ising model, which shows that dilution of the chiral units with achiral units increases the helical domain size in a manner that compensates for the dilution. In qualitative terms, since the random-field domain size is limited by the “objection” of the minority units to the helical sense dictated by the majority units, dilution of this “objection” acts to increase the domain size. As long as this domain size is not limited by the chain length or by thermal fluctuations, the achiral dilution will not reduce the optical activity of the polymer.

Mechanism of the transformation of a stiff polymer lyotropic nematic liquid crystal to the cholesteric state by dopant-mediated chiral information transfer Green, M.M.

Optical rotation (OR) of random copolymers of chiral 2,6-dimethylheptyl isocyanate (NIC) and achiral hexyl isocyanate (HIC) was measured as a function of mole fraction x of the chiral monomer, temperature, and molecular weight, with hexane, 1-chlorobutane, and dichloromethane as the solvents. The data as a function of molecular weight were analyzed by the statistical mechanical theory of copolymers developed (Gu, H.; et al. Polym. J. 1997, 29, 77−84), in which a polyisocyanate chain is modeled by an alternating sequence of left-handed and right-handed helices occasionally interrupted by helical reversals. The theory involves two parameters, the left-handed−right-handed free energy bias, 2ΔG h, and the helical reversal free energy, ΔG r. With appropriate values for these parameters, the experimental OR values were well described by the theory. When compared with poly((R)-i-deuterio-n-hexyl isocyanate (i = 1, 2), the values of ΔG r were nearly the same but those of |2ΔG h| were much larger:  71 ± 14 cal/mol for the terpene derived chiral unit vs 1∼2 cal/mol for the deuterated chiral monomer units. These free energy values are reasonable considering the chemical structures of the respective chiral monomer units.

Human experience informs us of the two extreme consequences of crowding: random behavior of the individuals, in which each takes a singular path; and cooperative behavior, in which the individuals in the crowd act in a predictable uniform manner, such as in a military organization These extremes find parallels in the crowded situations encountered at the molecular level, exemplified for the former by glassy states, such as often encountered in polymeric materials,1 or for the latter, in the uniform archetypal arrangements of crystals or liquid crystals. Here we review the cooperative characteristics of uniform arrangements that take a chiral form and explore how these characteristics lead to left‐ and right‐handedness. These studies lead us to understand the basis of amplification of chirality in regular arrays, in which small influences have large consequences, and how chiral cooperativity acts in the resolution of conflict between influences favoring left‐ and right‐handedness.2