Theory of microphase separation in multiple segment-type statistical multiblock copolymers with arbitrary block molecular weight distributions

A Landau free energy is derived for the weak segregation regime (WSR) of melts belonging to a very general class of statistical multiblock copolymers, referred to as "multiple segment-type statistical multiblock copolymers." Copolymer chains in this class consist of sequences of up to M = 2 chemically different types of segments, organized into sequences of blocks of varying lengths (molecular weights). The possible sequences of blocks that are encountered in the copolymer chains, as far as their type is concerned, are described by a first-order Markov process, while the block molecular weight distributions of these M types of blocks are completely arbitrary. The number of blocks per chain is assumed to be large. This class of copolymers is sufficiently general to encompass all industrial relevant bulk statistical multiblock copolymers, such as all known thermoplastic elastomers. The particular free energy considered is just one realization of an even more general Landau free energy which is applicable to the WSR of melts of all conceivable copolymers, including homopolymers and all possible blends. The derivation of this Landau free energy is given in Appendix A.