Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers.

Mikhail A Osipov,Alexander A Antonov,Maxim V Gorkunov

doi:10.3390/polym12061262

Abstract

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

Highlights

Rod-coil copolymers usually undergo a transition from the isotropic to nematic and into the orthogonal lamellar phase or directly into the lamellar phase [7,8,9,10] which is similar to liquid crystal materials
We propose a more general density functional theory of rod-coil diblock copolymers which enables one to describe the orientational and translational order in the hexagonal phase
It has been shown that the density functional theory of rod-coil diblock copolymers can be used to describe in detail both the microphase separation and the orientational ordering of rod fragments both in the lamellar and in the hexagonal phases

Summary

Introduction

Rod-coil block copolymers are very interesting soft matter systems which are composed of copolymer macromolecules with flexible and rigid parts of various chemical structure including rod-like fragments of semiconducting polymers [1,2], polypeptides [3,4] and polysaccharides [5,6]. The free energy expansion is valid only in the vicinity of the transition into the isotropic phase and in the case of weak segregation: the equilibrium density of monomers contains only one Fourier harmonic and is proportional to the corresponding translational order parameter [23,24] This theory does not account for the induced orientational order of rod fragments in the lamellar phase which has been observed experimentally [7,8]. One notes that the theory [49] is based on the self-consistency equations for the translational and orientational order parameters and does not employ the free energy expansion in terms of the order parameters It may be approximately valid in the case of relatively strong segregation and at low temperatures when the order parameters are not small and the densities are nonlinear functions of the order parameters containing many.

Density Functional Approach to the Theory of Block Copolymers

Free Energy of the Orthogonal Lamellar Phase

Free Energy of the Hexagonal Phase

Minimization of the Free Energy and Phase Diagrams

Discussion and Conclusions