Simple derivation of the first cumulant for the Rouse chain

TL;DR

This paper derives an exact, simple formula for the first cumulant of the dynamic structure factor in the Rouse model, capturing internal and diffusive motions of a polymer chain across all scattering wave vectors.

Contribution

It provides a novel, straightforward analytic expression for the first cumulant in the Rouse model, enhancing understanding of polymer dynamics in scattering experiments.

Findings

Exact formula valid for all wave vectors

Incorporates internal and diffusive motions

Simplifies analysis of polymer scattering data

Abstract

A simple analytic expression for the first cumulant of the dynamic structure factor of a polymer coil in the Rouse model is derived. The obtained formula is exact within the usual assumption of the continuum distribution of beads along the chain. It reflects the contributions to the scattering of light or neutrons from both the internal motion of the polymer and its diffusion, and is valid in the whole region of the wave-vector change at the scattering.