First we show that the Cox-Merz rule, that η(γ) is approximated by η
*(ω)|
γ=ω, exhibits considerable deviations for systems with very strong or weak damping functions for the strain-dependent relaxation modulus; here η
*(ω) is the complex viscosity. The deviation can be accounted for in view of the BKZ constitutive model. Secondly we propose an equation to approximate the first normal stress coefficient, ψ
1(γ), from the dynamic modulus, G′(ω); ψ
1(γ)≅2G′(ω)/ω
2|
γ=κ′ω. Here κ′ is an adjustable parameter. It is proved that this equation is almost equivalent to a Gleissle formula, ψ
1(γ)≅ψ
1+(t)|
γ=κ/t with κ′=/1.55, where ψ
1+(t) is the growth function of the first normal stress coefficient at the start-up of shear flow at the limit of zero rate of shear. The normal stress coefficient is approximated well over a wide range of rate of shear for the data by Laun of IUPAC A polyethylene and those for a solution of polystyrene with a narrow molecular mass distribution. The appropriate values of κ′ for these systems over moderate ranges of γ were 2.0 and 1.4, respectively. These values are related to the damping function through the BKZ model and may be estimated from the damping function, approximated as exp(-αt), with a relation κ′≅0.37/α.
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