Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers
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HEORY AND SIMULATION
Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers M. A. Osipova,b, M. V. Gorkunovc,*, and A. A. Antonovc aDepartment
of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, Scotland, United Kingdom Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, 119991 Russia c Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Moscow, 119333 Russia *e-mail: [email protected] bTopchiev
Received November 11, 2019; revised March 4, 2020; accepted April 18, 2020
Abstract—The general density functional approach is used to develop a molecular-statistical theory of rodcoil diblock copolymers which is valid in the case of both weak and strong segregation. The free energy of the rod-coil copolymer is expressed as a functional of the number densities of rod and coil monomers which depend on the translational and orientational degrees of freedom. The equilibrium densities are determined by minimization of the free energy functional and depend on the orientational and translational order parameters of the monomers. The order parameters are calculated numerically by minimization of the free energy taking into account the incompressibility condition within the formalism of Lagrange multipliers. Phase diagrams are obtained and the profiles of orientational and translational order parameters are presented as functions of temperature and the fraction of coil fragments. It is shown that the lamellar phase possesses strong orientational order and the stability of the phase is increasing with the increasing fraction of rod monomers. DOI: 10.1134/S0965545X20050132
INTRODUCTION Rod-coil block copolymers are composed of macromolecules which include both rigid and flexible fragments. They are characterized by rich polymorphism and the orientational order of rigid rods in different phases including, in particular, the lamellae and the hexagonal one. These copolymer systems are very interesting from the fundamental point of view because they combine the properties of liquid crystals and block copolymers and enable one to get an insight into the mutual role of microphase separation effects and the effects of smectic liquid crystal ordering. Rodcoil block copolymers may contain rod-like fragments of various chemical structure and may be applied in polymer photovoltaics [1–3], LEDs [4–6], and high strength polymer composite fibers [7–10]. The first theory of rod-coil block copolymers has been developed by Semenov and Vasilenko using a simple lattice model in which the orientational order of rigid rods was assumed to be perfect [11]. Thus in this theory, only a transition from the nematic to the lamellar phase could be considered. A more general theory of rod-coil copolymers has been developed using the Landau–de Gennes expansion of the free energy in terms of the one-particle density and the orientational order parameters [12, 13]. The coefficients
of such expansion have
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