The deterministic proliferation of the orientation of hexagonally packed cylinders (HEX) from the twinned body-centered cubic (BCC) phase is investigated by synchrotron small-angle X-ray scattering (SAXS) and rheo-optical methods for di-and triblock copolymers of styrene and isoprene (SI and SIS). Repeated heating and cooling cycles starting from an initially aligned HEX produce a proliferation of cylinder orientations from successively twinned BCC states. The evolution of the orientation distribution of HEX cylinders produces a decrease in the birefringence and increase in the modulus with each successive generation. The cylinder axes of the degenerate HEX states coincide with the 〈111〉 directions of the twinned BCC due to the epitaxial growth of cylinders from the twinned BCC. The distribution of the cylinder axes of the degenerate HEX states among the 〈111〉 directions of the twinned BCC is found to be affected by memory of the prior HEX state, which decays with annealing time in the BCC state.

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γ 12 cos θ 12 + γ 23 cos θ 23 + T ) γ 13 cos θ 13(1)

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