Cooperative Chiral Order in Copolymers of Chiral and Achiral Units

Polyisocyanates can be synthesized with chiral and achiral pendant groups distributed randomly along the chains. The overall chiral order, measured by optical activity, is strongly cooperative and depends sensitively on the concentration of chiral pendant groups. To explain this cooperative chiral order theoretically, we map the random copolymer onto the one-dimensional random-field Ising model. We show that the optical activity as a function of composition is well-described by the predictions of this theory.Comment: 13 pages, including 3 postscript figures, uses REVTeX 3.0 and epsf.st

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals--increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [L. M. Lopatina and J. V. Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.Comment: 7 pages, including 2 postscript figures, uses REVTeX 4.

Theory of Chiral Order in Random Copolymers

Recent experiments have found that polyisocyanates composed of a mixture of opposite enantiomers follow a chiral ``majority rule:'' the chiral order of the copolymer, measured by optical activity, is dominated by whichever enantiomer is in the majority. We explain this majority rule theoretically by mapping the random copolymer onto the random-field Ising model. Using this model, we predict the chiral order as a function of enantiomer concentration, in quantitative agreement with the experiments, and show how the sharpness of the majority-rule curve can be controlled.Comment: 13 pages, including 4 postscript figures, uses REVTeX 3.0 and epsf.st