Chirality in block copolymer melts: mesoscopic helicity from intersegment twist.

We study the effects of chirality at the segment scale on the thermodynamics of block copolymer melts using self-consistent field theory. In linear diblock melts where segments of one block prefer a twisted, or cholesteric, texture, we show that melt assembly is critically sensitive to the ratio of random coil size to the preferred pitch of cholesteric twist. For weakly chiral melts (large pitch), mesophases remain achiral, while below a critical value of pitch, two mesoscopically chiral phases are stable: an undulated lamellar phase and a phase of hexagonally ordered helices. We show that the nonlinear sensitivity of mesoscale chiral order to preferred pitch derives specifically from the geometric and thermodynamic coupling of the helical mesodomain shape to the twisted packing of chiral segments within the core, giving rise to a second-order cylinder-to-helix transition.