Mean-field theory for interchain orientational ordering of conjugated polymers

Abstract

We consider a generalized anisotropic planar-rotor model on a triangular lattice for interchain orientational ordering of undoped and doped polyacetylene, and investigate the effects of various terms on the symmetry and the range of stability of the observed herringbone (HB) phases. Dipole, quadrupole, and octopole interactions are included in the model with sixfold crystal-field anisotropy and are analyzed within the mean-field theory. The relative strength of these interactions can be estimated from the observed setting angle of the HB phase with the help of the smallness of crystal-field anisotropy. A model where the polymer chain is represented by a ‘‘quadrupolar’’ mass density only has various phases as the temperature and the interaction parameters are varied. Among them, the HB phase is found below a critical temperature $T_c$ for some range of the parameter space, and the setting angle of the HB phase is 45° and independent of temperature. Competition between quadrupole and other interactions such as dipole or octopole, parametrized by the ratio of interaction strengths λ, results in an additional phase transition at $T_c^{\mathcal{’}}$(λ) and makes the setting angle vary with the temperature below $T_c^{\mathcal{’}}$(λ). For a model with quadrupole and octopole terms, there are two degenerate states of the setting angle related by θ’=π/2-θ. This degeneracy does not reflect a symmetry of the system and is lifted by the dipole terms. For a model with quadrupole and dipole interactions, the setting angle increases as the temperature is reduced below $T_c^{\mathcal{’}}$(λ). From these results, we conclude that quadrupole and dipole interactions are important terms to explain experimental observations. Effects of crystal-field anisotropy resolve the twofold degeneracy, destroy the critical behavior associated with $T_c^{\mathcal{’}}$(λ), and make the setting angle temperature dependent over the entire range of temperature below $T_c$. Crucial information on the interaction parameters of the model can be obtained through the temperature dependence of the setting angle of the HB phase.