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Nanofluidity of a polymer melt: Breakdown of Poiseuille's flow model

Capillary rise of polymer in thin tubes ≈40 nm in diameter (comparable to the size of individual polymer molecule) shows anomalous molecular-weight dependence (Shin K. et al., Nat. Mater., 6 (2007) 961). We suggest that this dependence reveals breakdown of macroscopic hydrodynamics characterized by the bulk viscosity and propose a new microscopic mechanism for transport along a thin capillary based on the reptation model. The crossover capillary diameter from microscopic to macroscopic flow D*≈70 nm for 105 molecular-weight polyethylene and is proportional to the molecular weight. We discuss how a new transport mechanism might affect boundary conditions in a capillary when undulations of the walls prevent the slipage of the flow. We discuss the relevance of nonlinear effects and show, that they might be observed at the very onset of capillary rise flow.