l-TIE DETERMINATION OF POLYMER RELAXATION MODULI AND MEMORY FUNCTIONS USING INTEGRAL TRANSFORMS

In this paper we describe two numerical methods by which the relaxation modulus and memory function of a polymer can be determined from a set of discrete linear viscoelastic storage and loss moduli measurements. The first method involves expressing the linear viscoelastic data by means of a rational function (with certain constraints) and then taking the Laplace transform of that function. The second method is the Fourier transform. We apply the different methods to samples of commercial grade polyethylene and liquid crystal polymers and conclude that the Fourier transform route appears to perform best, although the Laplace transform method is adequate for highly polydisperse materials of modest molecular weight. The form of the relaxation modulus and memory functions obtained by these two routes is compared with those obtained from other rheological tests on the materials and the results discussed in terms of application to integral constitutive equations.