Sedimentation equilibria of polydisperse non-ideal solutes. VI: Number-average molecular weight and molecular-weight distribution functions

Abstract

A method for the determination of number-average molecular weights, Mn, with the equilibrium ultracentrifuge has been developed. Results for six experiments show a root-mean-square deviation of 5.8 per cent with molecular weights obtained from osmotic pressure data, with a maximum deviation of 9.1 per cent and a mean deviation of -2.1 per cent. The method is applicable to substances of very high molecular weight, in contrast to the direct measurement of osmotic pressure, but the optical system now in use in connection with the ultracentrifuge requires a knowledge of Mz/Mw for the material under investigation, for best results. This is not a fundamental requirement of the method. Thermodynamic factors for polymer-solvent systems can also be calculated from sedimentation equilibrium experiments. A method for the construction of approximate molecular-weight distribution curves from four moments has been developed. Several examples of the applications of this method are shown. A molecular-weight distribution curve where Mn:Mw:Mz::1:2:3 appears to be rather common among several varieties of unfractionated polymers.