Liquid-crystalline behavior of rod-coil diblock copolymers

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Abstract
The exact mean-field phase behavior of the Semenov–Vasilenko model for rod-coil diblock copolymers is studied by applying self-consistent field techniques. The behavior depends on three quantities: the rod/coil immiscibility χN, the coil volume fraction f, and the ratio ν of the characteristic coil to rod dimensions. When χN≲5, the rods and coils mix producing a nematic phase, and at larger χN, they microphase separate forming a lamellar phase. The nonlamellar phases expected at f≳0.7 are not treated here. The lamellar phase is typically a smectic-C structure with monolayers of tilted rods. A thorough understanding of the model is achieved by closely examining segment distributions and various contributions to the free energy. The tilt angle θ is generally controlled by a competition between rod/coil interfacial tension and stretching of the coils. Lowering f reduces the latter contribution, causing θ→0 and producing a continuous transition to a smectic-A structure. Beyond that, there is a tendency to form structures with the rods arranged in bilayers, but this is strongly suppressed by a large steric penalty. We suggest that small amounts of solvent can greatly alleviate this penalty, and therefore could significantly affect some aspects of the phase behavior.