Strain-induced instabilities in hexagonal columnar phases

Abstract

Structural instabilities in the hexagonal-packed cylinder phase of block copolymers subject to uniaxial tension orthogonal to the column axis are investigated theoretically. For small strains, a Landau elastic free energy density which is identical to that for hexagonal columnar liquid crystals can be used to determine the threshold and form of the instability, which can be of two types. In the first the distortion field is scalar and the columns or rods are modulated in thickness, while in the second the distortion field is a vector, resulting in saddle-splay curvature. A detailed theoretical analysis of the instability is presented for asymmetric diblock copolymers near the ordering transition. For these materials, the first-order phase transition to the hexagonal-packed rod phase is induced by composition fluctuations and belongs to the Brazovskii class. The coefficients in a series expansion of the Brazovskii free energy density are identified with the elastic constants in the elastic free energy density, enabling them to be calculated from a microscopic random phase approximation model. It is thus shown that small uniaxial strains should induce a transition from the hexagonal rod phase to a ``modulated rod'' structure above a critical strain.