Empirical equations for representing viscoelastic functions and for deriving spectra

Several equations containing two empirical constants are considered for representing G(t), G′(ω), J′(ω), and J(t) in the glass‐to‐rubber dispersion zone. With these equations, data on the NBS polyisobutylene can be closely represented. The relaxation spectrum H(τ) and the retardation spectrum L(τ) were derived exactly from the equations for G′(ω) and J′(ω), respectively. The derived equations have the same functional form, and thus H(τ) and L(τ) can be interconverted, under certain conditions, by employing an auxiliary equation that interrelates the relaxation and retardation times at which the spectra maximize. An exact transformation of an equation for G(t) gave a second equation for H(τ); from the constants in this equation, L(τ) was calculated. The methods for obtaining and interconverting H(τ) and L(τ) for polyisobutylene gave results that agree satisfactorily with literature data obtained by the usual approximation methods.