Dynamics of confined polymer chains

We study the motions of a single polymer chain trapped inside a very thin capillary (or slit). We incorporate all excluded volume effects and hydrodynamic interactions through a scaling analysis. We find that the Debye–Bueche approximation, which was qualitatively correct for three-dimensional dilute solutions, becomes completely incorrect for confined chains: the local fluctuations of the monomer concentration which are ignored in the Debye–Bueche picture allow for channels of easy flow of the solvent inside the chain. We obtain scaling formulas (with unknown numerical coefficients) for the diffusion constant and we also analyze the internal mode structure: inside a tube, for wavelengths larger than the diameter, we recover an unexpectedly simple structure of Rouse modes. Finally, we analyze the possibility of ’’sucking in’’ one chain inside a slightly tapered pore, by imposing a certain flow of the solvent. We find that the threshold pressure difference Δpc for aspiration of the chain depends only on the smallest diameter of the pore and is independent of the molecular mass. The magnitude of Δpc is not too large, and the experiment may be feasible.