Effect of chain flexibility on master curve behavior for diffusion coefficient

The diffusion coefficients of simple chain models are analyzed as a function of packing fraction, η, and as a function of a parameter C that is the density raised to a power divided by temperature to look at scalar metrics to find master curves. The central feature in the analysis is the mapping onto an effective hard site diameter, d. For the molecular models lacking restrictions on dihedral angle (e.g., freely jointed), simple mappings of molecular potential to d work very well, and the reduced diffusion coefficient, D*, collapses into a single-valued function of η. Although this does not work for the dihedral angle restriction case, assuming that d is inversely proportional to temperature to a power results in collapse behavior for an empirically selected value of the power. This is equivalent to D* being a single-valued function of C. The diffusion coefficient of a single-site penetrant in the chain systems also is found to be a scalar metric that can reduce the chain diffusion data for a given system to a single master curve.