Molecular Theories of Liquid Crystals

Osipov, Mikhail A.

doi:10.1002/9783527619276.ch3ba

Cited by 10 publications

(2 citation statements)

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“…A molecular theory of coil-rod-coil triblock copolymers can be developed using the general density functional theory, which has been applied before to nematic and smectic liquid crystals [44][45][46][47][48][49]. In such a theory, the free energy F of a multicomponent polymer system depends on one-particle number densities ρ ν (r, ω), which depend both on the positional r and orientational ω degrees of freedom of the segments of type ν and which satisfy the normalization condition ρ ν (r, ω)drdω = f ν M, where f ν is the relative fraction of segments of type ν, while M is the number of macromolecules.…”

Section: Molecular Theory Of Coil-rod-coil Triblock Copolymersmentioning

confidence: 99%

“…Recently, 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.…”

Section: Introductionmentioning

confidence: 99%

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Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

2021

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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.

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