Fractional moments and moments of time in boundary diffusion of random coil polymers

Equations for the evaluation of experiments in free diffusion of random coil polymers in dilute solution are derived. Moments of the concentration function with respect to the cell co-ordinate of whole or fractional order are employed. Weight-average diffusion coefficients raised to any positive power and hence negative moments of the molecular weight distribution can be obtained. Among the latter is M_n. Theta conditions are not required. For a narrow-distribution polymer, the linear concentration effect is eliminated in a simple way without additional experiments. Corresponding equations referring to moments with time as the variable of integration are deduced. These should be applied to experiments in bounded diffusion. The statistical weight in the averages is the reciprocal of the weight given by using moments of the cell co-ordinate. Thus the series of weight averages of diffusion coefficients raised to a negative power and positive moments of the molecular weight distribution are obtainable.