Abstract
A molecular-statistical theory of coil-rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic mechanisms. The first mechanism resembles a low dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.
Highlights
Rod–coil block copolymers attract significant attention as they combine anisotropic properties of smectic liquid crystals and microphase-separation properties of coil–coil block copolymers
For a better insight into the role of the polymer molecule asymmetry, we study the phase behavior of a coil–rod–coil triblock copolymer keeping the total fraction of coil fragments fixed and varying the ratio of the lengths of coil fragments, which is effectively expressed by the ratio of their partial fractions f c1 / f c2
We have developed a molecular theory of phase transitions and liquid crystal ordering in coil–rod–coil triblock copolymers, employing the same density functional theory that has been used before in our theoretical studies of rod–coil diblock copolymers [41,42]
Summary
Rod–coil block copolymers attract significant attention as they combine anisotropic properties of smectic liquid crystals and microphase-separation properties of coil–coil block copolymers. The authors have developed a novel molecular-statistical theory of rod–coil diblock copolymers [41,42,43] employing the same general density functional theory, which has been used before in the description of nematic and smectic liquid crystals [18,44,45,46,47,48] This theory is based on the free energy functional, which depends on the one-particle distribution functions of rod and coil segments and is not expanded in powers of the order parameters. In the region close to the disordered phase, the theory can Symmetry 2021, 13, 1834 be reduced to the corresponding Landau–de Gennes theory [42], as it employs the same correlation functions calculated for Gaussian chains Such a molecular-statistical theory is computationally simpler than the full SCFT theory (being not so precise, ) and can be efficiently used to evaluate numerically all order parameter profiles.
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