The conformation of a polymer chain subjected to periodic straining fields of arbitrary amplitude Ω and modulation frequency ω is studied in the Rouse model of polymer dynamics in the high-frequency limit ωτR ≫ 1 where τR is the Rouse relaxation time. We specialize to the case of sinusoidal time dependence, but our results are expected to be general. We calculate the dimensionless mean square extension μ of a polymer segment containing s monomers, defined as the ratio of the mean square size to the equilibrium value. For simple shear we find μ = 3 + λ 2f1(φ) for large segments, ωτs ≫ 1, where τS is the segment relaxation time, λ ≡ Ω/ω, and f1 is a nonuniversal function of the phase, φ ≡ ωt, of the straining field. For small segments, ωτs ≪ 1, we find μ = 3 + λ2√ωτsf2(φ) with nonuniversal f2. In extensional flow the extension along the stretching axis is derived: μ = f3(φ, λ) for ωτs ≫ 1 and μ = 1 + √ωτ sf4(φ, λ) for ωτs ≪ 1 (again f3 and f4 are nonuniversal). These results are interpreted in terms of blobs of relaxation time ∼ω-1: the chain of blobs deforms affinely in the flow, but within a blob the polymer has time to relax. In the nonlinear régime (λ ≳ 1) the blobs are strongly distorted and the polymer within a blob relaxes to an elongation well beyond its equilibrium size such that its dimensions vary linearly with number of monomers. In the case of elongational flow, the fluctuations in the velocity field entirely suppress the "yo-yo" instability that has been conjectured to play an important role in the phenomenon of drag reduction.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry