Topological effects on the Lifshitz point of block copolymer/homopolymer blends

The influence of copolymer topology on the phase behavior of binary blends containing AB-type block copolymers and A homopolymers is studied by examining the instability modes of the system using the random-phase approximation. Depending on the concentration of the homopolymers, the blends could undergo microscopic or macroscopic phase separation, forming one ordered phase or two coexisting phases. The transition between these two distinct behaviors occurs at the Lifshitz point (LP), at which the wavelength of the most unstable mode diverges. We demonstrate that AB-type copolymers with identical block compositions but distinct chain topologies have different abilities to solubilize homopolymers, and their LPs exhibit two distinct, continuous (second-order) or discontinuous (first-order), features connected by a tricritical point. A more complex behavior featuring the coexistence of two instability modes with different finite length scales is also observed in multiblock copolymer/homopolymer blends. These behaviors are shown to be independent of specific chain models.