Macromolecules, Vol.27, No.3, 849-861, 1994
Lamellar Diblock Copolymer Grain-Boundary Morphology .2. Scherk Twist Boundary Energy Calculations
The Scherk surface morphology allows a diblock copolymer lamellar phase to maintain microphase separation across a twist grain boundary. The interface between the two microphases in the Scherk grain boundary approximates a minimal surface consisting of a doubly periodic array of saddle surfaces. Grain boundary energies were calculated for the Scherk surface morphology as a function of diblock chain characteristics and as a function of grain boundary twist angle. The basic approach to grain boundary energy calculation is to formulate a general expression for the local free energy density asa function of chain characteristics and of the local curvature of the interface. The local energy density is then integrated over the mathematical model for the Scherk grain boundary. Two general methods of calculation were used, and the results were then compared. First, a self-consistent-field (SCF) model was formulated in which average energies per chain were calculated for all the possible interfacial curvature environments encountered by diblocks in the Scherk morphology. G second approach utilized a continuum (Helfrich) model for interfacial deformation in which moduli are used to impose energetic penalties for curvature of the interface in the grain boundary region. The application of this approach to block copolymers was provided by the model of Wang and Safran. The Wang and Safran model yielded results which agreed quite closely with those found using the SCF calculation.