Logarithmic method for continuous relaxation spectrum and comparison with previous methods

Abstract

Various algorithms for determining relaxation time spectrum have been to the fore, because relaxation spectrum plays an important role in interconversion between various viscoelastic functions. In this study, a new algorithm is developed by means of double-logarithmic power series approximation and the Levenberg–Marquardt method. Compared with most previous algorithms, new algorithm is applicable not only to dynamic data but also to the Laplace transform of relaxation modulus, which is available for optical data from the generalized Stokes–Einstein equation or creep data with ringing. It is worth noticing that the new algorithm determines continuous relaxation spectrum without any additional parameters and precedent procedures. This paper suggests such framework of newly developed algorithm and its applications to various kinds of viscoelastic data.