Molecular theory of liquid-crystal ordering in rod-coil diblock copolymers

Abstract

Molecular-statistical theory of rod-coil diblock copolymers is proposed using the general density functional approach which enables one to consider the cases of both weak and strong segregation. The free energy of the system is expressed as a functional of the phase-space densities of rod and coil monomers, which depend on the orientational and translational order parameters. Temperature-concentration phase diagrams are obtained and the profiles of all order parameters are calculated numerically by minimizing the polymer free energy. The lamellar phase is shown to possess strong orientational order which is partially induced by the phase structural anisotropy. The enhanced stability of the lamellar phase is determined by a combination of the microphase separation effects and the emergence of long-range smectic order.

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod–coil diblock copolymers

“…6(a), which is obtained similarly to those in Ref. 42 . Resolving numerically the values of all three parameters α 1,2,3 we observe that over the whole diagram the coefficients α 1 and α 3 are positive reaching the values 0.7-0.8 in the bottom left corner.…”

“…The general density functional theory of rod-coil diblock copolymers developed by the authors before 42 has been generalised to the case of the tilted lamellar phase. One notes that such a density functional theory is based on the selfconsistent equations for the equilibrium densities of rod and coil monomers and for the corresponding orientational and translational order parameters and hence it cam be used both in the case of both weak and relatively strong segregation.…”

“…Recently the classical density functional approach, which is successfully used in the molecular theory of liquid crystals [36][37][38][39][40] and inhomogeneous fluids 41 , has been applied by the authors to rod-coil diblock copolymers 42 . In the density functional approach the free energy is expressed as a functional of the equilibrium densities of rod and coil monomers which are obtained by minimization of the free energy functional.…”

“…The free energy also depends on the direct correlation functions between rod and coil monomers in the reference system of noninteracting copolymer chains. The molecular theory 42 is based on the self-consistency equations for the translational and orientational order parameters and does not employ the expansion in terms of the order parameters. Thus it is valid in the case of relatively strong segregation and at low temperatures when the equilibrium monomer densities are nonlinear functions of the order parameters containing many Fourier harmonics.…”

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

“…Very recently, the general density functional approach, which is successfully used in the molecular theory of liquid crystals [43][44][45][46][47] and inhomogeneous fluids [48], has been applied by the authors to develop an analytical molecular-statistical theory of rod-coil diblock copolymers [49]. In this approach, the free energy is expressed as a functional of the equilibrium densities of rod and coil monomers which are obtained self-consistently by minimization of the free energy functional.…”