Conformation-dependent sequence design of polymer chains in melts

Abstract

Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling, the probability distributions of block length k being calculated. The problem is similar to that of gambler’s ruin and first passage time in probability theory but the consideration is generalized to 3D and the domains of different shapes are considered. In any domain, the probability distribution can be described by the asymptote ∼k −3/2 at moderate values of k if the spatial size of the block is less than the smallest characteristic size of the domain. For large blocks, the exponential asymptote exp(−const ) is valid, d as being the asymptotic domain length (a is the monomer unit size). The number average block lengths and their dispersities change linearly with the domain size for lamellae, cylinders, and balls, when the domain is characterized by a single characteristic size. If the domain is described by more than one size, the number average block length can grow nonlinearly with the domain sizes and the length d as can depend on all of them.