Rheological behaviour of branched polymer molecules

Abstract

A theory is presented for describing the viscoelastic properties of star-shaped branched polymers in concentrated solutions or melts. We describe the dominant mode of relaxation as diffusion of the chain in a potential field as others have done. Some indication of the form of the potential function is obtained by studying the statistics of random lattice walks entangled with a net of obstacles. The theory is compared with experimental data on well characterized stars covering a wide range of branch-point functionality. We show that it correctly describes the molecular-weight dependence of the zero shear-rate viscosity, η₀, and the steady-state compliance, J^°_e, as well as the frequency dependence of the dynamic shear moduli, G′(ω) and G″(ω). Some comments are made about the behaviour of branched polymers with a structure more complex than stars.