Eigenvalues and the intrinsic viscosity of short Gaussian chains

Abstract

Exact eigenvalues which are central to the Gaussian chain theory for dilute solutions of linear polymers have been determined for short chains. This is done for a number of chain segments N ranging from 1 to 15 and taking into account the effects of hydrodynamic interaction between segments. Using these exact eigenvalues, the molecular weight dependence of the steady flow intrinsic viscosity [η] is determined together with the terminal relaxation time τ1 which is derivable from [η]. These theoretical results are compared with similar results obtained using approximate eigenvalues λp for N large and small eigenvalue index p. It is found that while the character of the dependence of the λp, [η] and τ1 on N is similar for both exact and approximate results, the numerical factors may differ significantly. Comparison of these results for [η] with measured values for polystyrene over a wide range of molecular weights gives good agreement with the exact theoretical results and some indication of the inexactness of the approximate results for N large. The τ1 derived from [η] are compared with values obtained independently from oscillatory flow birefringence measurements.