Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties



A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (M̄w/M̄n <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of M̄w/M̄n and the Mark-Houwink exponent a. The resulting value of S2/Smath image (where S1 = Στp1, S2 = Σ(τp1)2, the τp's being the relaxation times and τ1 the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.