Universal behavior of flexible and wormlike polymers using relations derived from the blob theory and the statistical mechanical theory

The variation of the viscometric expansion factor of macromolecular chains, αη, as a function of the number of blobs of which these chains consist, N/Nc, obeys a universal law, both for wormlike and for flexible polymers. Using also wormlike and flexible polymers, we show that the factor relating the excluded volume parameter, z, to the static expansion factor, αG, varies with the number of statistical chain segments, in a universal manner. The universalities appear to be valid below chain lengths required for the appearance of a power law, and they do not seem to have an upper limit in molecular weight. For these two universalities concerning flexible and wormlike polymers we use relations derived from the blob theory [Polymer 20 (1979) 1083] and statistical mechanical theory [J. Chem. Phys. 57 (1972) 2843].