Analysis of the Palierne model by relaxation time spectrum

Viscoelasticity of immiscible polymer blends is affected by relaxation of the interface. Several attempts have been made for linear viscoelasticity of immiscible polymer blends. The Palierne model (1990) and the Gramespacher-Meissner model (1992) are representative. The Gramespacher-Meissner model consists of two parts: ingredients and interface. Moreover, it provides us the formula of the peak of interface in weighted relaxation time spectrum, which enables us to analyze the characteristics relating to interface more obviously. However, the Gramespacher-Meissner model is a kind of empirical model. Contrary to the Gramespacher-Meissner model, the Palierne model was derived in a rigorous manner. In this study, we investigated the Palierne model through the picture of the Gramespacher-Meissner model. We calculated moduli of immiscible blend using two models and obtained the weighted relaxation time spectra of them. The fixed-point iteration of Cho and Park (2013) was used in order to determine the weighted relaxation spectra.