Deconvolution of Molecular Weight Distributions Using Dynamic Flory‐Schulz Distributions

Abstract

Summary: The deconvolution of molecular weight distributions (MWDs) may be useful for obtaining information about the polymerization kinetics and properties of catalytic systems. However, deconvolution techniques are normally based on steady‐state assumptions and very little has been reported about the use of non‐stationary approaches for the deconvolution of MWDs. In spite of this, polymerization reactions are often performed in batch or semi‐batch modes. For this reason, dynamic solutions are proposed here for simple kinetic models and are then used for deconvolution of actual MWD data. Deconvolution results obtained with dynamic models are compared to deconvolution results obtained with the standard stationary Flory‐Schulz distributions. For coordination polymerizations, results show that dynamic MWD models are able to describe experimental data with fewer catalytic sites, which indicates that the proper interpretation of the reaction dynamics may be of fundamental importance for kinetic characterization. On the other hand, reaction dynamics induced by modification of chain transfer agent concentration seem to play a minor role in the shape of the MWD in free‐radical polymerizations.This Figure illustrates that MWDs obtained at unsteady conditions should not be deconvoluted with standard steady‐state Flory‐Schulz distributions.imageThis Figure illustrates that MWDs obtained at unsteady conditions should not be deconvoluted with standard steady‐state Flory‐Schulz distributions.

Investigation of Catalyst Fragmentation in Gas‐Phase Olefin Polymerisation: A Novel Short Stop Reactor

“…As shown in Figure 4A, B the polydispersity indices increase steadily as a function of the polymerisation time, which indicates that growth of the polymer chain probably takes place under non-steady state conditions at the very early stages of the polymerisation (in other words, given the time scales involved, the reaction is stopped before the larger chains have the opportunity to transfer off of the active site where they are growing). This behaviour can be studied, for example, through deconvolution of molecular weight distributions using a non-stationary approach, as proposed by Fortuny et al [27] This very useful technique can be used to give information about the polymerisation kinetics and the main features of the catalyst systems employed in the polymerisations. Figure 4 also shows that the average molecular weights can be influenced by the reaction conditions, for instance, the local monomer concentration at the active site.…”

Synthesis of Propylene/1‐Butene Copolymers with Ziegler‐Natta Catalyst in Gas‐Phase Copolymerizations, 1

“…Although copolymerization reactions can lead to bimodal MWDs because of the different monomer reactivities and active site specificities, it is important to emphasize (except for Figure 5C) that MWDs obtained here do not present significant bimodal behavior. According to Fortuny et al,22 the smooth and continuous variation of the operation conditions along the batch makes the development of multimodal behavior less probable. As a matter of fact, as shown previously, composition drift does not play a significant role in this process, which favors unimodal distributions.…”

Evolutionary computing approach for evaluating flory distribution curves in gel permeation chromatography: Study of the poly(1‐octene) system

“…Because of the high level of automation, sophistication, reliability, and reproducibility of GPC instrumentation, a much higher resolution of data can be produced for mechanistic studies in comparison to basic solvent extraction techniques; this makes it the best tool for understanding the MWD of polymers. The separation of the GPC curve into individual Flory distribution curves provides detailed information regarding the active site distribution on the basis of fractions that have distinct molecular weight profiles; this leads to a lot of insight into the polymerization mechanism 4–14. The deconvolution of the MWDs of polymer resins, which is used for the characterization of polymer resins with broad and/or bimodal MWDs, has been carried out by various methodologies, such as the Haarhoff‐Van der Linde function,4 commercial software (Scientist,5 Peakfit,6 Microsoft Excel Solver7), and the Levenberg–Marquardt and Golub–Pereyra methods 8…”

“…The separation of the GPC curve into individual Flory distribution curves provides detailed information regarding the active site distribution on the basis of fractions that have distinct molecular weight profiles; this leads to a lot of insight into the polymerization mechanism. [4][5][6][7][8][9][10][11][12][13][14] The deconvolution of the MWDs of polymer resins, which is used for the characterization of polymer resins with broad and/or bimodal MWDs, has been carried out by various methodologies, such as the Haarhoff-Van der Linde function, 4 commercial software (Scientist, 5 Peakfit, 6 Microsoft Excel Solver 7 ), and the Levenberg-Marquardt and Golub-Pereyra methods. 8 A genetic algorithm, based on Darwin's theory of natural evolution, is a numerical optimization algorithm that is highly suited for large-scale optimization problems.…”