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A mesoscopic model of a diblock copolymer is used to study the motion of agrain boundary separating two regions of perfectly ordered lamellar structuresunder an oscillatory but uniform shear flow. The case considered is a grainboundary separating lamellae along the so called parallel orientation (withwavevector parallel to the velocity gradient direction) and along thetransverse orientation (wavevector parallel to the shear direction). In themodel considered lamellae in the parallel orientation are marginal with respectto the shear, whereas transverse lamellae are uniformly compressed instead. Amultiple scale expansion valid in the weak segregation regime and for low shearfrequencies leads to an envelope equation for the grain boundary. This equationshows that the grain boundary moves by the action of the shear, with a velocitythat has two contributions. The first contribution, which arises from thechange in orientation of the grain boundary as it is being sheared, describesvariations in monomer density in the boundary region. This contribution isperiodic in time with twice the frequency of the shear and, by itself, leads tono net motion of the boundary. The second contribution arises from a freeenergy increase within the bulk transverse lamellae under shear. It is alsoperiodic with twice the frequency of the shear, but it does not average tozero, leading to a net reduction in the extent of the region occupied by thetransverse lamellae. We find in the limit studied that the velocity of thegrain boundary can be expressed as the product of a mobility coefficient timesa driving force, the latter given by the excess energy stored in the transversephase being sheared.

Motion of a Transverse/Parallel Grain Boundary in a Block Copolymer under Oscillatory Shear Flow