General approach to polymer chains confined by interacting boundaries. II. Flow through a cylindrical nano-tube.

The Laplace-Green's function methods of Paper I are extended to describe polymers confined in interacting, impenetrable cylindrical geometries, whose treatment is far more challenging than the slit and box geometries considered in Paper I. The general methods are illustrated with calculations (as a function of the polymer-surface interaction) of the free energy of confinement, the radial density profile, and the average of the drag force in the free draining limit, quantities that will be used elsewhere to analyze experiments of Wu and co-workers involving the flow of polymers through nanopores. All these properties are evaluated by numerical inverse Laplace transforms of closed form analytical expressions, a significant savings over the traditional eigenfunction approaches. The example of the confinement free energy for a 3-arm star polymer illustrates the treatment when a closed form expression for the Laplace transform is unavailable.