| Abstract: | Following Di Benedetto it is proposed that noncrystalline polymer regions possess an approximate semicrystalline order with chain bundles that are locally parallel along distances of several nanometers. Packing with on-average four nearest neighbors is assumed. A spherical molecule may move through such a substrate in two distinct ways: (a) along the axis of a “tube” formed by locally parallel chains or (b) perpendicular to this axis by two polymer chains separating sufficiently to permit passage of the molecule. The first process is relatively fast, generally requires little activation energy, and determines the effective jump length in diffusion. The second is responsible for the activation energy of diffusion, which is taken as the minimum energy necessary to produce a symmetrical chain separation which allows transfer of a molecule. This is calculated as a function of the penetrant diameter d and parameters Γ and β which characterize the interchain cohesion and chain stiffness, respectively. Γ is estimated from the polymer density and cohesive energy density by suitably linearizing a relation given by Di Benedetto for the potential between two polymer chains approximated as infinite strings of Lennard-Jones force centers. β is shown to be approximately obtainable from the polymer chain backbone geometry and bond rotation potentials. An expression for the diffusion coefficient D is developed which contains only one disposable parameter, the effective jump length. |
