Linear viscoelastic models: Part I. Relaxation modulus and melt calibration

Abstract

Constitutive models for the linear viscoelasticity of polymers are presented for the relation between the relaxation modulus and the molecular weight distribution (MWD). We also compute the MWD from a simulated relaxation modulus curve by first obtaining the rheologically effective distribution (RED) as a function of time, and converting this into the MWD by melt calibration; that is, the relation between timescale and the molecular weight. This procedure has similarities with the widely used universal calibration with solved polymers. The main principles of our technique are applied here to familiar relaxation modulus data, for which we present two models: (1) an analytical model derived from control theory, which is known capable of modelling partially observed system and (2) a practical characteristic model for obtaining usable results. No relaxation time or spectrum procedures are used to model the process of linear viscoelastic relaxation. The use of relative calculations and melt calibration dispenses with the need to know the real chain structures such as branching and entangled chain dynamics, and the model remains useful for future investigations of polymer chain structures and dynamics, such as using tube theory.