Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers*

Formation of the Frank-Kasper (FK) sigma phase in compositionally asymmetric A-B diblock copolymer melts has been shown using self-consistent mean-field theory (SCFT) to be associated with conformational asymmetry, b_A/b_B > 1, where b is the statistical segment length. Small-angle X-ray scattering and rheological measurements performed with narrow dispersity poly(styrene)-b-poly(butadiene) (PS-PB) diblocks show an absence of the FK sigma phase whereas poly(ethylethylene)-b-poly(lactide) (PEE-PLA) diblocks exhibit a wide composition window of this complex phase, where both systems have b_A/b_B = 1.3. This behavior is associated with block self-concentration expressed through the invariant degree of polymerization N(bar) = Nb⁶/v² in which v is the statistical segment volume. A direct analogy will be drawn between the role of N(bar) in FK phase formation in diblocks and the value N_e(bar) that defines the universal crossover from Rouse to reptation dynamics in homopolymer melts, where the block values of N(bar) for PEE-PLA and PS-PB are less than and greater than N_e(bar), respectively.