Hydrodynamic behavior of short chain molecules. I. Extension of the Rouse–Zimm theory

The Rouse–Zimm formalism of hydrodynamic properties of long chain molecules (polymers) in solution is modified to extend its validity to the case of short chains. The modification introduces: (a) a realistic calculation of averages for the intrachain distances; (b) an exact solution of the eigenvalue equation in matrix form; (c) an approximate representation of short-range interactions (first and second order) by means of springlike forces between nonconsecutive chain segments. The theory is applied to the calculation of limiting viscosity numbers and the Flory–Fox constant of short polymethylene chains (number of segments ?50). Our results are compared with those from other theories.