A Hybrid Galerkin–Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization Kinetics

Population balance models describing not only the chain-length distribution of a polymer but also additional properties like branching or composition are still difficult to solve numerically. For simulation of such systems two essentially different approaches are discussed in the literature: deterministic solvers based on rate equations and stochastic Monte-Carlo (MC) strategies based on chemical master equations. The paper presents a novel hybrid approach to polymer reaction kinetics that combines the best of these two worlds. We discuss the theoretical conditions of the algorithm, describe its numerical realization, and show that, if applicable, it is more efficient than full-scale MC approaches and leads to more detailed information in additional property indices than deterministic solvers

From reactor to rheology in industrial polymers

This article reviews current efforts towards quantitative prediction of rheological properties of industrial polymer resins, based upon their polydisperse branched molecular structure. This involves both an understanding of how reactor and reaction conditions influence the distribution of chain lengths and branch placement (which is the province of reactor engineering) and an understanding of how the molecular structures in turn give rise to the rheology (the province of polymer physics). Both fields are reviewed at an introductory level, focussing in particular on developments in theoretical prediction of rheology for both entangled model polymers and industrial polymers. Finally, we discuss three classes of reaction for which the fields of reactor engineering and polymer physics have been truly combined to produce predictions from reactor to rheology

Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination

A model is developed that predicts branching architectures of polymers from radical polymerization with transfer to polymer and termination by disproportionation and recombination, in a continuously stirred tank reactor (CSTR). It is a so-called conditional Monte Carlo (MC) method generating architectures of molecules of specified dimensions. The relevant dimensions in the present case are the number of branch points, np, and the number of combined parts a molecule consists of, nc. These branch points and combination points together are decisive for the connectivity inside molecules. The modeling strategy is based on backtracking of the molecular growth history in terms of the chemical events determining connectivity, transfer to polymer and recombination termination. The recombination termination mechanism requires the model to develop parts of the architecture following several paths back to the initial primary polymers that form the starting points for the molecules. The algorithm requires the construction of probability density functions being evaluated using a fast Galerkin-FEM method. The architectures generated by the conditional Monte Carlo method are compared to those from a full MC method using several qualifiers. One of these is the number of initial primary polymers in a molecule as well as their lengths, another is the radius of gyration contraction factor. Perfect agreement is found between the architectures found by the conditional and full MC methods

Aufbau neuer Schwerpunkte der Umweltbildung im Oekospeicher Wulkow Schlussbericht

SIGLEAvailable from TIB Hannover: F04B1065 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Bundesstiftung Umwelt, Osnabrueck (Germany)DEGerman