Ideas about reptation, tube renewal and tube relaxation applied to the description of the non-linear viscoelastic behaviour in shear of some polydisperse polyethylene melts

Abstract

In melts of polydisperse linear polymers like high-density polyethylene (HDPE) the dynamics of a given macromolecule are affected by the renewal of the confining tube owing to movements of surrounding molecules, the more so according as the matrix contains more shorter molecules. At large strains, the relaxation of the tube due to the retraction of matrix molecules also contributes to stress relaxation. For long-chain branched molecules in a polydisperse melt like that of low-density polyethylene (LDPE), the dynamics are dominated by tube renewal and tube relaxation effects. It is argued that for melts of HDPE as well as LDPE the combination of these ideas leads to a rheological constitutive equation consisting of the sum of two integrals. Both integrands are factored into the product of a strain-independent time function and a time-independent nonlinear strain tensor. Using the relaxation spectrum from oscillation experiments and the nonlinear strain measure from first normal stress growth data, this equation satisfactorily describes the decay of the stresses after step strain or after cessation of steady shear flow for melts of two commercial HDPEs and of two LDPEs. For the HDPE samples one integral suffices, but for the LDPE melts the additional time and strain dependences of the integral relating to tube relaxation are indispensable for a good fit of the experimental curves.