Microphase Separation of Block Copolymer Rings

Phase segregation properties of ring block copolymers are discussed using the theory of Leibler, ignoring the topological constraints specific to ring polymers. We find that the ordering properties of ring diblocks are similar to those of linear copolymers with a reduced chemical length N. For a melt of symmetric diblock rings, there is microphase separation for a demixing interaction larger than (_χN)* = 17.8; this is about 1.7 times that required for segregation of linear diblocks with the same structure. The wavelength of the ordering mode is about 0.67 of that for the equivalent linear diblock melt. Deep into the strongly-segregated state, the wavelength of lamellar domains composed of rings is 2^−2/3 = 0.63 times that of linear diblock lamellae with the same N.