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Monte Carlo simulations reveal long chain branching (LCB) topology based on kinetics of systems like low-density polyethylene (ldPE). Examining the topologies computed shows the majority of branch arms to be short as compared to backbone length, while also a significant branch-on-branch fine structure is observed. Until now, predicting scattering function P−1(θ) from LCB has only been successful for structures like simple combs or stars. Topologies in graph theoretical form are used to predict scattering function P−1(θ) and [ABSTRACT FROM AUTHOR]

A full extensive 2-dimensional (2D) model of low-density Polyethylene chain length/branching distribution is provided in this paper. 2D Population Balance Equations are solved by the Galerkin-finite element method to obtain the distributions, accounting for 2D ‘topological scission’; a manner to approximate random scission by an estimated fragment length distribution. Explicit assumptions have been made concerning the redistribution of branch points on scission fragments. The calculations without scission show that in the 2D case a finer grid of chain length is required in comparison to the 1-dimensional case because of the narrow shape of the branching distribution at the given chain length. With a fine grid, results are in exact agreement to Monte Carlo simulations, which demonstrates the success of the implementation. In the present implementation it was necessary to assume a fragment length independent redistribution of branch points, as was done in an earlier 2D model by Krallis et al. (2007) and Krallis and Kiparissides (2007) . We demonstrated that the shape of the branching density distribution is sensitive to this assumption. [ABSTRACT FROM AUTHOR]

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]

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]

Abstract: Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties in measurement and computation of scission effect and branchings of polymer. Our previous papers [Kim, D.M., et al., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR. Chemical Engineering Science 59, 699–718; Kim, D.M., Iedema, P.D., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor. Chemical Engineering Science, submitted for publication] are concerned with the scission reaction during ldPE polymerization and its effect on molecular weight distribution (MWD) of ldPE for various reactor types. Here we consider branching distributions as a function of chain length for CSTR and tubular reactor processes. To simultaneously deal with chain length and branching distributions, the concept of pseudo-distributions is used, meaning that branching distributions are described by their main moments. The computation results are compared with properties of ldPE samples from a CSTR and a tubular reactor. Number and weight average branchings and branching density increase as chain length increases until the longest chain length. The concentrations of long chain branching (LCB) are close to those of first branching moment in both CSTR and tubular reactor systems. The branching dispersity, a measure for the width of the branching distribution at a certain chain length, has the highest value at shorter chain length and then monotonously decreases approaching to 1.0 as chain length increases. Excellent agreements in branching dispersities between calculation with branching moments and prediction with assumption of binomial distribution for a tubular reactor and CSTR processes show that the branching distribution follows a binomial distribution for both processes. [Copyright &y& Elsevier]

Any two polymer molecules of the same length (n) and the same number of branch points (N) can have different properties, since they may possess distinct architectures. In this paper we present conditional Monte Carlo algorithms for the virtual synthesis of polyethylene (PE) catalyzed by one branch forming constrained geometry metallocene catalyst (CGC, 1C-system) or by a mixture of CGC and linear metallocene catalyst (2C-system) in a continuous stirred tank reactor. The condition for the Monte Carlo method consists of a fixed chain length distribution and degree of branching distribution. To calculate these distributions explicit algebraic relations are available Macromolecules 36 (2003) 10037. The synthesis method is a recursive algorithm that subsequently creates insertions of sub-structures containing numbers of monomer units and branch points according to one- or two-dimensional probability density functions. We developed a general 2C-algorithm and a simplified 1C-algorithm applicable for 1C-systems only. They provide an adjacency matrix describing the connectivity between the branch points, while separately (1C-method Macromol Theor Simul 12 (2003) 484) or simultaneously (2C-method) a vector containing the length of segments between branch points and terminal segments is generated Macromol Theor Simul 10 (2001) 855. Characterization of the architectures proceeds by calculating the topological variables seniority and priority as well as the radius of gyration Macromol Theor Simul 10 (2001) 870. As regards seniority and priority good agreement is found with results from the analytical approach Macromolecules 36 (2003) 10037 is found. 2C-architectures turn out to possess more comb-like structures than 1C-architectures. Concerning molecular sizes an interesting effect of the segment length distribution in 2C-molecules is observed. [Copyright &y& Elsevier]

It has been shown that scission kinetics strongly affects the molecular weight distribution (MWD) of low-density polyethylene (ldPE) in a continuous stirred tank reactor (CSTR). The present paper focuses on the effects of different chemical scission mechanisms, linear and topological scission, as well as mechanical scission on MWD in batch and tubular reactors. In contrast to the CSTR, a batch reactor MWD does not show bimodalities or long tails. The tubular reactor was modeled as an industrially representative system with four initiator injection points and a proper ‘cocktail’ of different initiators. Calculated MWD was compared to one experimentally determined with SEC-MALLS for a commercial tubular product and fair agreement was found. Typically, these MWDs are broad, but not bimodal. Sensitivity studies were performed as to scission kinetics and the effect of chain transfer agent (CTA). Both batch and tubular reactor were observed to be less sensitive to scission kinetics than a CSTR. In addition, alternative CTA injection strategies (downstream positions) were tested. These showed interesting behavior leading to very broad and bimodal MWD. The model allows following the MWD broadening along the tube. We conclude that batch and tubular ldPE reactors lead to completely different MWD behavior than a CSTR and that it is possible to manipulate it to a great extent. [Copyright &y& Elsevier]

The role of scission reactions in low-density polyethylene (ldPE) polymerization has recently been the subject of various modeling studies. The linear scission approximation leading to a uniform fragment length distribution, seems to describe the scission mechanism well. For linear scission the predicted bimodal molecular weight distribution (MWD) in the case of a CSTR agrees with that found by size exclusion chromatography (SEC). However, scission of branched polymers does not follow the linear scission model, since it leads to predominately long and short fragments. Therefore, we systematically compared the linear scission model with the newly proposed ‘topological scission’ model. We found a pronounced difference in MWD between linear scission, yielding a bimodality and topological scission, leading to a long tail in MWD. In addition we examined mechanical scission that could occur in stirred autoclave reactors due to mechanical action. Mechanical scission also turns out to generate bimodality in MWD. The molecular architecture of ldPE is also discussed in connection with scission kinetics and the topological scission model. [Copyright &y& Elsevier]