A mathematical model for determining the best process conditions for average Molecular weight and melt flow index of polypropylene

The present work describes a mathematical model based on a population balance approach for determining the effect of the reaction temperature and hydrogen amount on the vital final product properties including average molecular weight and polydispersity index and flow index of polypropylene and also the profile rate of the polymerization. The aim of this study was to find the best operating condition through a model which is validated by the experimental data. The software program was coded in MATLAB/SIMULINK. The model profile rates compared with the experimental results to show the accuracy of the model. In this study, it was concluded that increasing the reaction temperature until a certain limit is useful and improve some indices of the final product and after that rising the reaction temperature has a harmful effect on the indices. Exactly the same issue is true in the case of increasing the amount of hydrogen.               KEY WORDS: Mathematical modeling, Propylene polymerization, Melt flow index, Population balance, Average molecular weight, hydrogen Bull. Chem. Soc. Ethiop. 2019, 33(1), 169-182DOI: https://dx.doi.org/10.4314/bcse.v33i1.1

Hydrogen effect modeling on Ziegler-Natta catalyst and final product properties in propylene polymerization

Hydrogen, as chain transfer agent, effects on kinetic of propylene polymerization; consequently variation of hydrogen concentration leads to change final product properties and also activates site of used catalyst. This phenomenon is one of the most important process variables is to adjust the final product properties and optimize the operating conditions. This work has attempted to present a mathematical model that cable to calculate the most important indices of end used product, such as melt flow index, number and weight average molecular weight and poly dispersity index. The model can predict profile polymerization rates determining important kinetic parameters such as the activation energy, lumped deactivation reaction initial reaction rate and deactivation constant. The mathematical model was implemented in Matlab/Simulink environment for slurry polymerization in laboratory scale. The modeling approach is based on polymer moment balance method in the slurry semi-batch reactor. In addition, in this work have provided a model that calculating fraction activated sites catalyst via hydrogen concentration. The model was validated by experimental data from lab scale, reactor. The experimental and model outputs were compared; consequently, the errors were within acceptable range.               KEY WORDS: Mathematical modeling, Propylene polymerization, Kinetics study, Hydrogen response, population balance Bull. Chem. Soc. Ethiop. 2018, 32(2), 371-386.DOI: https://dx.doi.org/10.4314/bcse.v32i2.1

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum