Discrete-to-continuum simulation approach to polymer chain systems: Subdiffusion, segregation, and chain folding

Abstract

A discrete-to-continuum approach is introduced to study the static and dynamic properties of polymer chain systems with a bead-spring chain model in two dimensions. A finitely extensible nonlinear elastic potential is used for the bond between the consecutive beads with the Lennard-Jones (LJ) potential with smaller ${(R}_{c}{=2}^{1/6}\ensuremath{\sigma}=0.95)$ and larger ${(R}_{c}=2.5\ensuremath{\sigma}=2.1)$ values of the upper cutoff for the nonbonding interaction among the neighboring beads. We find that chains segregate at temperature $T=1.0$ with ${R}_{c}=2.1$ and remain desegregated with ${R}_{c}=0.95$. At low temperature $(T=0.2)$, chains become folded, in a ribbonlike conformation, unlike random and self-avoiding walk conformations at $T=1.0$. The power-law dependence of the rms displacements of the center of mass ${(R}_{\mathrm{c}.\mathrm{m}.})$ of the chains and their center node ${(R}_{\mathrm{cn}})$ with time are nonuniversal, with the range of exponents ${\ensuremath{\nu}}_{1}\ensuremath{\simeq}0.45\ensuremath{-}0.25$ and ${\ensuremath{\nu}}_{2}\ensuremath{\simeq}0.30\ensuremath{-}0.10$, respectively. Both radius of gyration ${(R}_{g})$ and average bond length $(〈l〉)$ decrease on increasing the range of interaction ${(R}_{c})$, consistent with the extended state in good solvent to collapsed state in poor solvent description of the polymer chains. Analysis of the radial distribution function supports these observations.