Primitive chain network simulations for asymmetric star polymers.
For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and∕or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers.
Combinatorial Rheology of Branched Polymer Melts
An algorithm is presented for predicting the linear viscoelasticity of polydisperse polymers containing long side branches with arbitrary distributions of branch length and branch location along a backbone. The algorithm gives semiquantitative predictions of literature data for a wide range of polybutadiene melts, including monodisperse linear, star, mixed linear and star, pom-pom, and comb polymers. Huge differences (several orders of magnitude) are predicted in zero-shear viscosities for samples that have the same weight-average molecular weight (200 000) and the same branching fraction but have different branching structures. It is shown that information on branching structure can be inferred by combinatorially measuring rheological properties on series of blends of the branched polymer with a linear, or well-defined branched, polymer.
Changes in Quartz During Heating and the Possible Effects on Si Production
In Si and FeSi production, the main Si source is SiO2, in the form of quartz. Reactions with SiO2 generate SiO gas that further reacts with SiC to Si. During heating, quartz will transform to other SiO2 modifications with cristobalite as the stable high-temperature phase. Transformation to cristobalite is a slow process. Its rate has been investigated for several industrial quartz sources and has been shown to vary considerably among the different quartz types. Other differences in behavior during heating between these quartz sources, such as softening temperature and volume expansion, have also been studied. The quartz-cristobalite ratio will affect the rate of reactions involving SiO2. The industrial consequences and other implications of the observed difference between quartz types are discussed. Initial studies of industrial quartz were published by Ringdalen et al. In the current work, a new experimental method has been developed, and an investigation of several new quartz sources has confirmed the earlier observed large variation between different sources. The repeatability of the data has been studied and the effect of gas atmosphere investigated. The results from the earlier work are included as a basis for the discussion.