Conformation-dependent sequence design of polymer chains in melts

TL;DR

This paper explores how conformation-dependent sequence design influences polymer self-assembly in melts, analyzing probability distributions of block lengths and their relation to microphase-separated morphologies through analytical and simulation methods.

Contribution

It introduces a novel approach to designing polymer sequences based on conformation, providing analytical and simulation insights into block length distributions and their impact on microphase morphologies.

Findings

Probability distributions follow a ~k^{-3/2} asymptote for moderate block sizes.

Large blocks exhibit exponential decay in their probability distribution.

Number average block lengths depend linearly on domain size for single-scale morphologies.

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 $k$, which are analogous to the first-passage probabilities, are calculated analytically and determined from the computer simulations. 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 $exp(-const \, k a^2/d_{as}^2)$ 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 block length 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 das can depend on all of them.