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A recent numerical method has opened new opportunities in multidimensional population balance modeling. Here, this method is applied to a full three-dimensional population balance model (PBM) describing branching topology evolution driven by chain end to backbone coupling. This process is typical for polymer modification reactions, e.g., in polyethylene, where initially linear polymer chains undergo hydrogen abstraction, and subsequent branching or scission. Topologies are distinguished by chain ends, number of branches, and number of reactive ends. The resulting time dependent trivariate distribution is utilized to extract various distributive properties of the polymer. The results exhibit excellent agreement with data from Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

During mix melting of hyperbranched AB2- and linear CD-polycondensates distributive properties are changing by interchange reactions. Two mathematical modeling approaches are presented: (i) Simplified approach of monodisperse population of three-arm stars undergoing interchange reactions, both analytical and by Monte Carlo simulations, assuming interchange as subsequent scission and recombination of fragments. (ii) Full system of interchange and polycondensation/hydrolysis reactions with Monte Carlo simulations and kinetic model describing reactions of free groups (A, B, C, D) and bonds (AB, CD, BC, AD). MC simulations show that the final molecular weight and branching distribution is attained after 10% of reaction time. The change of structure, from few large fragments to more, smaller ones, is slower. [ABSTRACT FROM AUTHOR]

During mix melting of hyperbranched AB2- and linear CD-polycondensates distributive properties are changing by interchange reactions. Two mathematical modeling approaches are presented: (i) Simplified approach of monodisperse population of three-arm stars undergoing interchange reactions, both analytical and by Monte Carlo simulations, assuming interchange as subsequent scission and recombination of fragments. (ii) Full system of interchange and polycondensation/hydrolysis reactions with Monte Carlo simulations and kinetic model describing reactions of free groups (A, B, C, D) and bonds (AB, CD, BC, AD). MC simulations show that the final molecular weight and branching distribution is attained after 10% of reaction time. The change of structure, from few large fragments to more, smaller ones, is slower. [ABSTRACT FROM AUTHOR]

This study investigates several possible thermodynamic options (Sanchez-Lacombe, SAFT, Flory-Huggins, Soave-Redlich-Kwong) available in designing polymerization systems. Various results are predicted by these models with respect to monomer-polymer separation and polymer properties. These results show that it is essential to choose the proper thermodynamic model in order to get reliable results from simulation. The low density polyethylene (LDPE) process is presented as an industrial case study. [ABSTRACT FROM AUTHOR]

In every network, a distance between a pair of nodes can be defined as the length of the shortest path connecting these nodes, and therefore one may speak of a ball, its volume, and how it grows as a function of the radius. Spatial networks tend to feature peculiar volume scaling functions, as well as other topological features, including clustering, degree-degree correlation, clique complexes, and heterogeneity. Here we investigate a nongeometric random graph with a given degree distribution and an additional constraint on the volume scaling function. We show that such structures fall into the category of m-colored random graphs and study the percolation transition by using this theory. We prove that for a given degree distribution the percolation threshold for weakly connected components is not affected by the volume growth function. Additionally, we show that the size of the giant component and the cyclomatic number are not affected by volume scaling. These findings may explain the surprisingly good performance of network models that neglect volume scaling. Even though this paper focuses on the implications of the volume growth, the model is generic and might lead to insights in the field of random directed acyclic graphs and their applications.

The formation of metal soaps (metal complexes of saturated fatty acids) is a serious problem affecting the appearance and structural integrity of many oil paintings. Tailored model systems for aged oil paint and time-dependent attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy were used to study the diffusion of palmitic acid and subsequent metal soap crystallization. The simultaneous presence of free saturated fatty acids and polymer-bound metal carboxylates leads to rapid metal soap crystallization, following a complex mechanism that involves both acid and metal diffusion. Solvent flow, water, and pigments all enhance metal soap crystallization in the model systems. These results contribute to the development of paint cleaning strategies, a better understanding of oil paint degradation, and highlight the potential of time-dependent ATR-FTIR spectroscopy for studying dynamic processes in polymer films., (© 2018 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.)