Quasi-elastic scattering by dilute, ideal, polymer solutions: II. Effects of hydrodynamic interactions

Abstract

Each moving unit of a long, flexible, molecule induces in the surrounding solvent a velocity field which reacts on the motion of other segments. This long-range hydrodynamic interaction modifies strongly the dynamical form factor $S(\mathbf{q}\mathrm{\omega })$ at low frequencies $\mathrm{\omega }$ and small scattering vectors $\mathbf{q}$. For neutron scattering ($q{R}_G\gg \mathit{1}$, where $R_G$ is the radius of gyration of the polymer), the frequency width $\mathrm{\Delta }{\mathrm{\omega }}_q$ of $S(q\mathrm{\omega })$ at fixed q becomes proportional to $q^3$ (for an ideal coil). Also the effect of stretching the molecule becomes more dramatic, since stretching greatly reduces the hydrodynamic interactions.