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

A simple model is described for the chain entropy of strongly segregat ed 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 t he free energy of any copolymer microdomain geometry, as a function of the effective surface tension at the domain boundaries (between stron gly segregated blocks) and the geometry of the domains. In the absence of global packing constraints, the theory predicts the formation of h yperbolic interfaces (which include bicontinuous microdomain geometrie s) between the segregated blocks for a significant range of molecular concentrations, as well as the standard lamellar, cylindrical, and sph erical geometries. Once the relevant global constraints for pure copol ymer systems are imposed, planar, cylindrical and spherical phases dom inate, due to the severe geometrical limitations required for uniform space filling by the assembled diblock molecules. The analysis suggest s that the formation of exotic hyperbolic phases, such as bicontinuous or mesh mesostructures, requires the relaxation of global constraints .