Modeling of synthesis and flow properties of propylene-diene copolymers

Copolymerization with nonconjugated dienes offers an attractive route for introducing long-chain branching in polypropylene. From a simplified set of rate equations for such copolymerization with a metallocene catalyst, we derive the probabilities of branch formation at different stages of the reaction in a semibatch reactor. Using these probabilities, we generate an ensemble of molecules via a Monte Carlo sampling. The knowledge of the branching topology and segment lengths allows us to compute the flow properties of the resins from computational rheology. We compare our model predictions with existing experimental data, namely the molar mass distribution and small amplitude oscillatory shear response, for a set of resins with varying diene content. The rheology data suggest that the entanglement time Ï.,e depends sensitively and in a well-defined fashion on the diene content

Characterization of low-molecular-weight polymers: Failure of universal calibration in size exclusion chromatography

Accurate measurement of molecular weights for polymers in the 500-5000 molecular weight range requires considerable care. Absolute methods such as membrane osmometry or light scattering are generally imprecise because of membrane permeation or low scattering intensity. Many polymers are too fragile to be studied by mass spectrometry. Other techniques, such as vapor phase osmometry, cryoscopy, and ebulliometry require calibration and data replication if accurate molecular weights are to be obtained. Size exclusion chromatography (SEC) also requires calibration but can be a very rapid  and accurate method if proper calibration can be achieved. SEC calibration is now often achieved via “universal calibration” (UC), which is based on the premise that polymers with the same hydrodynamic volume will have the same SEC retention time. At very low molecular weights, the UC approach is clearly invalid since intrinsic viscosities can become negative for certain polymers. We demonstrate here that the invalidity of the UC concept extends well outside this molecular weight region, up to at least1000 molecular weight for the polystyrene (PS)/polyisobutene (PIB) case. We have also tested whether PS, PIB, and n-alkanes elute at equivalent radii of gyration, R,. This approach leads to somewhat smaller errors than UC, but also is not adequate for accurate work. Another SEC issue in this molecular weight range, with the commonly used differential refractive index (DRI)  detector, is the variation of the detector response with molecular weight. This variation is proportional to l/Mn and, if neglected, can cause substantial overestimations of M, (e.g., 10-25%) in the SEC analysis of polydisperse samples in THF solvent. Theoretical and experimental data are presented for PS, PIB, and  polymethylmethacrylate, quantifying the error. Errors in light scattering weight-average molecular  weights caused by the RI variation can also be significant and depend on the molecular weight  distribution; accurate results can be obtained, but only if Mn is accurately known, even if dn/dc is measured on the sample under study. © 1995, Taylor & Francis Group, LLC. All rights reserved