AbstractsMathematics

Control of end use properties of branched polymers such as low-density Polyethylene (ldPE) produced at industrial scale is difficult at the molecular level since experimental techniques fail to detect the most decisive microstructural properties. Therefore, mathematical models are important in predicting the interesting microstructural properties of polymers. Key assumptions are related to the random scission reaction (breaking can take place in any random position of the chain), being modeled as linear or ‘topological’ scission, and to allowing/disallowing gelation. An explanation of the decisive reactions, modeling assumptions and the potential modeling schemes is given in Chapter 1. In Chapter 2, the developed population balance model forms a sound basis for further investigations of molecular weight/degree branching distribution. In Chapter 3, the model from Chapter 2 has been developed further to investigate the effect of multiradicals and gelation on the molecular weight distributions. In Chapter 4, we provide a model of the molecular weight distribution under circumstances of ldPE for a tubular reactor and for a series of continuous stirred tank reactors. A set of models to calculate the contraction factor of the radius of gyration, which to maximum extent accounts for the radical polymerization kinetics, is presented in Chapter 5. A full 2-dimensional model of ldPE chain length/branching distribution is provided in Chapter 6. The focus of Chapter 7 was especially on the role of combination termination in the context of 2- and 3-dimensional population balance models, implying that a mathematically non-linear problem had to be addressed in those modeling schemes.