Normal modes of stretched polymer chains

Abstract

We consider the normal modes and the response to a small oscillating force of one tethered polymer chain. The chain is originally stretched either by a force f applied at free end (case 1), giving a cigar shape, or by a uniform flow (case 2), giving a trumpet shape. Stretched chains can be understood as Rouse chains of impenetrable blobs : For case 1, the blobs are all identical and the long-wavelength modes are renormalized Rouse modes. A small oscillating driving force (f+ f 1 cos wt) distorts the chains up to a distance x = (f/ηw) 1/2 , where η is the solvent viscosity. For case 2, the size of the blobs decreases from the free end to the attachment point. The modes are described by zero-order Bessel functions, but the dispersion relation of the p'th mode is still of the Rouse type (1/τ p ∼ p 2 ). The penetration length of the distortion induced by a small oscillatory force applied at the free end is x = V/ω, where V is the solvent velocity. All our results hold as well for an ideal or swollen chain.