DECONVOLUTION OF POLYMER MELT STRESS-RELAXATION BY THE PADE-LAPLACE METHOD

Transient viscoelastic experiments such as shear stress relaxation can provide direct measurement of the stress relaxation modulus G(t). Since the strain establishment is not instantaneous, the measured stress must be regarded as the convolution product of the relaxation modulus with respect to the shear rate. If a Maxwellian analogy is assumed for the melt stress relaxation, then the main difficulty arises from the deconvolution procedure and from the unknown number of relaxation modes. The Pade-Laplace method based upon Pade approximants and the Laplace transform has been applied to shear stress relaxation experiments performed with melt samples of polystyrene and polypropylene. The major interest of this method lies in the fact that it detects through its own stability the number of modes necessary to fit the signal without any assumption. Moreover, it allows the determination of the n relaxation times tau(i) and their weights G(i). Finally, the mathematical properties of the Laplace transform can be used to perform the deconvolution of the signal.