Torsional defects, dielectric response and dynamics of comb polymer liquid crystals

Nematically and smectically ordered teeth of comb polymers are known to be coupled to the backbone. We speculate that if suitable chemistry can make this coupling torsional as well, then dipolar correlations can be induced in addition to quadrupolar order. We then predict an activated dielectric response mirroring the creation of torsional defects in the tooth order. The susceptibility becomes large, eventually proportional to the degree of polymerization, N_p. A model for the diffusional dynamics of these defects can be calculated exactly and gives an exponential variation of the dielectric relaxation time. At low temperatures this relaxation time ultimately varies as N²_p. Analogous conclusions are drawn about possible non-linear optical effects in comb polymer liquid crystals.