A Conditional Monte Carlo Method to Determine the Architectures of Metallocene Catalyzed Polyethylene

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 a conditional Monte Carlo algorithm for the virtual synthesis of metallocene‐catalyzed polyethylene (PE) in a continuous stirred tank reactor (CSTR). The condition for the Monte Carlo method consists of a fixed chain length distribution (CLD) and a degree of branching distribution (DBD). These distributions are calculated with a Galerkin finite element method. The synthesis method is a recursive algorithm that subsequently creates insertions of sub‐structures containing numbers of branch points according to a certain probability density function. This provides an adjacency matrix describing the connectivity between the branch points, while separately a vector containing the length of segments between branch points and terminal segments is generated. Characterization of the architectures proceeds by rheological features, seniorities and priorities, and molecular properties like the radius of gyration. Comparing the radii of gyration of metallocene polyethylene and low density PE (ldPE) shows the former to possess a more comb‐like structure on average. This is confirmed by the rheological characterization. The found bivariate seniority/priority distribution agrees well to the results of an analytical study of the same chemical system.

Constituting elements of the algorithm.     

A Study on the ordering of intercalated solvents in poly-benzyl-l-glutamate; In-situ raman and X-ray scattering investigations

A polymer/solvent system can form a gel due to specific interactions between the polymer and the solvent. For poly-benzyl-L-glutamate/solvent systems, gelation can be based on carbonyl or phenyl ring interactions, depending on the solvent. The present paper describes X-ray scattering and Raman investigations on cast films of poly-benzyl-L-glutamate (PBLG) and benzylmethacrylate (BzMA). The studies indicate that in the cast samples separate zones of PBLG and BzMA are present. Upon heating, the system homogenises and the PBLG molecules pack in a pseudo hexagonal lattice. At approximately 150°C a new reflection at 11.4 Å in the WAXS pattern arises. This reflection is attributed to structural ordering of the solvent, due to intercalation of the solvent molecules within the helices of PBLG. The observed changes in the WAXS pattern upon heating are supported by Raman experiments.     

Compositional heterogeneity in pectic polysaccharides: NMR studies and statistical analysis

Pectins are a class of heterogeneous polysaccharides used in the food industry as a result of their ability to form gels. They are primarily composed of a (1ŕ4)-α-D-galactopyranosyluronic acid backbone where the carboxylic acid group is methyl esterified at a level which depends on the source of the pectin and processing conditions used to isolate the material. Of considerable interest is the distribution of the free acid and methyl ester groups along this polymer chain. NMR spectroscopy, coupled with statistical analysis, is a powerful technique for the study of sequence distribution of monomers. Experimental conditions (temperature, pD) are reported which are appropriate for the analysis of pectic polysaccharides. Results are presented from a study of sequence distribution in native, modified, and fractionated pectins using ¹H and ¹³C solution NMR methods. The triad sequence information was examined using Bernoullian and Markovian probability models in conjunction with continuous Gaussian distribution and discrete models. Intermolecular heterogeneity in pectins results in triad frequencies which reflect the distribution of acid and ester monomers for native and base saponified pectins. Fractionation of pectin through physicochemical methods and subsequent spectroscopic analysis provide insight into this heterogeneity. Segregation into discrete polymer populations shows a structural diversity best approximated by a 3-component statistical model.     

Synthesis of Branched Polymer Architectures from Molecular Weight and Branching Distributions for Radical Polymerisation with Long‐Chain Branching,Accounting for Topology‐Controlled Random Scission

Branched polymers like LDPE are known to possess a wide range of architectures. In this paper a modelling approach is developed, describing the relation between architectures, chemistry and reactor conditions with the general objective of improving characterisation and controlling visco‐elastic properties. More specifically, the particular scission kinetics of branched molecules as strongly contrasting with linear scission is described. A new method to synthesise branched architectures is developed as an alternative to full Monte Carlo (MC) sampling. It employs MC sampling for coupling of primary polymers only. Graph theory is used as an efficient storage method containing all topological information of individual molecules. The algorithm synthesises molecules for any given combination of chain length (n) and number of branches (N). The explicit and detailed knowledge of branched architectures allows finding the correct topological scission kinetics. Distributions of fragment lengths and numbers of branches on fragments after scission are obtained, showing a preference for short and long fragments. Approximate functions describing this have been implemented in another model, predicting molecular weight (MWD) and degree of branching (DBD) distributions using a Galerkin finite element method. Topological scission is seen to give MWD broadening and a higher branching density for long chains. Distributions of longest end‐to‐end distances could be computed for all architectural alternatives for given n, N. In conclusion, it is demonstrated that this method yields distributions of architectures consistent with MWD/DBD for radical polymerisation with long‐chain branching and random scission.