Cubic to Cylindrical Transition in Diblock Copolymers Induced by Strain

I consider the problem of a body centered cubic (bcc), spherical meso-structure subjected to a uniform strain. Such a phase occurs for diblock copolymer melts when the fraction of the minority block, f, is roughly between 0.05 and 0.12. I determine how the spherical structure distorts when a strain is applied and find that the deformation is ellipsoidal. I then calculate the free energy cost of such a deformation and the bulk deformation constants i.e., elastic modulii. I also consider the stability of the deformed spherical morphology (ellipsoids) vs a cylindrical morphology and the approximate change in the phase boundary between the two morphologies as a function of strain. I consider how one may use this method, together with an applied electric field, to induce a cylindrical morphology from an initial bcc melt. If this were possible, this process would offer one avenue to reduce the radius of the cylinders, below the limit of the bulk cylindrical phase. This could lead to the possibility of nanowires with smaller radii.