Statistics of linear macromolecules with a relatively short chain. IV. Molecular dimensions from viscosity and sedimentation

In the usual model of linear macromolecules the number of chain links, Z, is so assumed that in the calculation only the highest term in Z need be considered. This is correct if Z is infinite, and holds fairly well in the soft, flexible molecules, but fails completely in the stiffer ones—like cellulose—even for molecular weights of some hundred thousands. With the exact values for the effective distance of the chain elements the theory of the sedimentation constant and of the intrinsic viscosity yield results which fit the experiments much better than could be achieved by the simple theory of the infinite chain. In plotting log (M/[η]) and log [s] versus log M, a pair of the characteristic parameters α and a/b can be determined from the experiments. Since α = cos β is the mean cosine between two consecutive links, it measures the stiffness of the macromolecule. In the second parameter a is the hydrodynamic radius and b the length of the chain unit. The values for cellulose acetate in acetone are in good agreement with our knowledge about the cellulose.