SELF-ASSEMBLY OF LINEAR BLOCK-COPOLYMERS - RELATIVE STABILITY OF HYPERBOLIC PHASES

A simple model is described for the chain entropy of strongly segregated linear diblock copolymers which involves a generalization of rubber elasticity theory to curved as well as stretched rubberlike materials. The theory admits calculation of the chain entropy contribution to the free energy of any copolymer microdomain geometry, as a function of the effective surface tension at the domain boundaries (between strongly segregated blocks) and the geometry of the domains. In the absence of global packing constraints, the theory predicts the formation of hyperbolic interfaces (which include bicontinuous microdomain geometries) between the segregated blocks for a significant range of molecular concentrations, as well as the standard lamellar, cylindrical, and spherical geometries. Once the relevant global constraints for pure copolymer systems are imposed, planar, cylindrical and spherical phases dominate, due to the severe geometrical limitations required for uniform space filling by the assembled diblock molecules. The analysis suggests that the formation of exotic hyperbolic phases, such as bicontinuous or mesh mesostructures, requires the relaxation of global constraints.