We identify a finite wave-number instability of a 90° tilt grain boundary in three-dimensional lamellar phases which is absent in two-dimensional configurations. Both a stability analysis of the slowly varying amplitude or envelope equation for the boundary, and a direct numerical solution of an order parameter model equation are presented. The instability mode involves two-dimensional perturbations of the planar base boundary, and is suppressed for purely one-dimensional perturbations. We find that both the most unstable wave numbers and their growth rate increase with ε, the dimensionless distance away from threshold of the lamellar phase.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - Mar 2005