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Statistics of polymer chains with unit sequences obtained via spatial patterns
Design of polymer sequences is a tool to control macromolecular self-assembly for biopolymers and synthetic polymers. We consider the A and B monomer unit sequences created via the modification of polymers in a condensed state in accordance with the spatial positions of monomer units. The conformations of polymer chains in bulk can be described as random trajectories using the diffusion-type equations. The length distributions of blocks, which are the chain parts consisting of monomer units of the same type, are calculated for core-shell globules of single macromolecules (the protein-like copolymers) and for melts with the geometrical patterns of lamellae, hexagonally packed cylinders, and balls in a body-centered cubic lattice. The sequence characteristics are compared with those obtained by the computer simulations. Additionally, the related topics of evolutionary conformation-dependent process of mutations, the energetically favorable sequences of monomer units for core-shell globules, and self-assembly of random block AB copolymers will be discussed.