LAMELLAR DIBLOCK COPOLYMER GRAIN-BOUNDARY MORPHOLOGY .3. HELICOID SECTION TWIST BOUNDARY ENERGY

The helicoid section morphology allows a diblock copolymer lamellar ph ase to maintain microphase separation across a twist grain boundary. T he interface between the two microphases in the grain boundary region approximates a stack of sections of the helicoid minimal surface. Grai n boundary energies were calculated for the helicoid section morpholog y both as a function of diblock chain characteristics and as a functio n of grain boundary twist angle. The basic approach to grain boundary energy calculation is to formulate a general expression for local free energy density as a function both of chain characteristics and of the local curvature of the interface. The local energy density is then in tegrated over the mathematical model for the Scherk grain boundary. Tw o general methods of calculation were used, and the results where then compared. First, a self-consistent field model was formulated in whic h average energies per chain were calculated for all the possible inte rfacial curvature environments encountered by diblocks in the helicoid section morphology. A second general approach utilized a continuum (H elfrich) model for interfacial deformation in which moduli are used to impose energetic penalties for curvature of the interface in the grai n boundary region. The helicoid section grain boundary energies were c ompared to energies of a competing twist boundary morphology, the Sche rk surface, which was analyzed in the preceding paper of this series. It was found that the energies of both the Scherk morphology and the h elicoid section increase with increasing twist. The Scherk and helicoi d section energies are comparable at low twist angles, less than about 15 degrees. Both morphologies are observed in this twist range. For h igher twist angles, where only the Scherk morphology is observed, the helicoid section boundary energy becomes prohibitively high due to a c ompression of the lamellar layers.