Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

The nucleation of a droplet of stable cylinder phase from a metastablelamellar phase is examined within the single-mode approximation to theBrazovskii model for diblock copolymer melts. By employing a variational ansatzfor the droplet interfacial profile, an analytic expression for the interfacialfree-energy of an interface of arbitrary orientation between cylinders andlamellae is found. The interfacial free-energy is anisotropic, and is lowerwhen the cylinder axis is perpendicular to the interface than when thecylinders lie along the interface. Consequently, the droplet shape computed viathe Wulff construction is lens-like, being flattened along the axis of thecylinders. The size of the critical droplet and the nucleation barrier aredetermined within classical nucleation theory. Near the lamellar/cylinder phaseboundary, where classical nucleation theory is applicable, critical droplets ofsize 30--400 cylinders across with aspect ratios of 4--10 and nucleationbarriers of 30--40 k_B T are typically found. The general trend is to largercritical droplets, higher aspect ratios and smaller nucleation barriers as themean-field critical point is approached.Comment: 14 pages, 6 figures, submitted to J. Chem. Phy