Behaviors of a Polymer Chain in Channels: From Zimm to Rouse Dynamics

Abstract

The effects of confinement and hydrodynamic interactions on single-chain diffusion behaviors are studied by using a combination of molecular dynamics and multiparticle collision dynamics simulations. For polymers in free space, the simulation results showed that the diffusion coefficient D∞ for long chains scales with the chain length N as D_∞ ∼ N^(–ν) (ν = 0.588), consistent with the Zimm dynamics, but it deviates from the Zimm dynamics for short chains. For polymers confined in channels with width H, the diffusion coefficient is found to follow two different scaling relations. The observed behaviors could be understood by introducing a microscopic hydrodynamic length ξₕ, below which the overall effect of hydrodynamic interactions becomes less important. For a confined chain, the diffusion behavior exhibits a crossover from Zimm (nondraining) to Rouse (free draining) dynamics as the channel size H decreases. When H is larger than ξₕ, the confinement experienced by the polymer chain is weak and the diffusion coefficient scales as D ∼ H^(0.7), in accordance with the prediction of blob theory; when H is smaller than ξₕ, D becomes independent of H, implying a free draining condition. A general analytical expression of D is derived by extending the partially permeable sphere model to the blob scale, which gives a quantitative description of the transition from Zimm to Rouse dynamics as H decreases.

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