Exact and approximate eigenvalues and intrinsic functions for the Gaussian chain theory

Abstract Eigenvalues for the Gaussian chain theory for dilute solutions of linear polymers have been determined in an exact manner for chain segments up to 100 and for a wide range of hydrodynamic interaction. It is found that these exact results may be closely approximated by a simple equation. The intrinsic functions of the eigenvalues which describe the molecular weight dependence of the intrinsic viscosity and terminal relaxation time of the chain are presented using both the exact and the approximate eigenvalues. It is shown that by using the simple approximate calculation good results are easily determined. The approximate equation is available for manipulation and analysis of complex eigenvalue functions.