Ratios of average molecular weights and molecular weight distributions in polymers
Chong Wha Pyun · Journal of Polymer Science Polymer Physics Edition · 1979
Abstract If Mmin and Mmax are lower and upper bounds, respectively, to the molecular weights of different molecular weight species contained in a polymer, the weight‐average to number‐average molecular weight ratio Mw/Mn cannot exceed (1 + Mmax/Mmin)2/(4Mmax/Mmin). The ratio attains this maximum possible value if the masses of the two species with molecular weights Mmin and Mmax are equal and the masses of all the other species are negligibly small, corresponding to maximum spread in the molecular weight distribution within the specified bounds. Also for a given value of Mw/Mn = α, the Mmax cannot be smaller than [2α − 1 + 2α1/2(α − 1)1/2]Mmin. The minimum possible value of Mmax/Mmin consistent with α given is obtained in the case of maximum spread described above. If only one species is predominant, then both Mw/Mn and Mmax/Mmin approach unity, as is well known. Similar relations hold for the ratios of higher‐order average molecular weights for which the role of the mass fractions is replaced by higher‐order distribution functions.