Rheology of polydisperse polymers: relationship between intermolecular interactions and molecular weight distribution

An expression of the relaxation function of linear polydisperse polymers is proposed in terms of intermolecular couplings of reptative chains. The relaxation times of each molecular weight are assumed to be shifted according to a tube renewal mechanism accounting for the diffusion of the surrounding chains. The subsequent shift is applied to the relaxation function of each molecular weight obtained from an analytical expression of the complex compliance J^*(). Therefore the complex shear modulus G^*() is derived from the overall relaxation function using the probability density accounting for the molecular weight distribution and four species-dependent parameters: a front factor A for zero-shear viscosity, plateau modulus G_N⁰, activation energy E and characteristic temperature T. All the main features of the theology of polydisperse polymers are described by the proposed model.