Claudia Sarmoria

Recovery of molecular weight distributions from transformed domains. Part I. Application of pgf to mass balances describing reactions involving free radicals

We present a general framework for the application of a transform technique, probability generating functions (pgf), to mass balances that describe free radical reactions, in particular synthesis or modification of polyolefins. Contributions of specific reactions to the mass balances are identified and transformed separately, so that a modular approach is possible for the construction of the pgf balance equations for different free radical processes. This simplifies the transformation step hopefully making the method useful to more people. Three examples taken from the literature are transformed using this modular method showing its ease of use. In Part II of this work, the resulting transforms are inverted to recover the complete molecular weight distribution.

Recovery of molecular weight distributions from transformed domains. Part II. Application of numerical inversion methods

This work is a part of a study aiming at developing tools for the prediction of complete molecular weight distributions (MWDs) of polymers at the exit of a reactor. This reactor may be a synthesis reactor or one used to modify a preexisting resin. In this work, we analyse the suitability of three methods for the numerical inversion of probability generating functions (pgfs), those due to Papoulis, de Hoog and Garbow. The three methods have been proposed in the literature for the inversion of Laplace transforms. We show how to adapt them to the problem at hand, and apply them to two situations. The first one is the recovery of experimentally measured MWDs, through a process that consists of finding the pgf of the distribution, numerically inverting it and comparing the result with the known MWD. The second one is to solve the pgf balances of polymerisation systems with known MWDs, and comparing those MWD with the ones that result from the inversion with the three methods. We discuss the relative advantages of each inversion method and propose guidelines for their proper use with unknown MWD functions.

Model linear ethylene–butene copolymers irradiated with γ-rays

Two model linear polyethylenes of different molecular weights and very narrow molecular weight distributions were subject to γ-ray irradiation under vacuum. Irradiations were conducted at two temperatures: 25 and 135°C. Number average and weight average molecular weight of irradiated samples was measured by LALLS and membrane osmometry, and the distribution of molecular weights was studied by GPC. The presence of a low but measurable amount of scission was verified. A mathematical model of the irradiation process was developed, which gave very good predictions of the measured values.

Mechanism and molecular weight model for thermal oxidation of linear ethylene-butene copolymer

Abstract The mechanism of thermooxidative degradation at 80°C of a narrow distribution linear ethylene–butene copolymer has been described by determining the chemical modifications and molecular weight distribution changes occurring in the polymer chains, and successively fitting the experimental results with a mathematical model which allows scission and crosslinking reactions to occur simultaneously. Degradation takes place with autoacceleration and from the computer simulation a cubic dependence of the degree of crosslinking and degree of scission with exposure time was obtained. It was established that in this system scissions predominate over crosslinking, in accordance with the drop in average molecular weights and the concomitant accumulation of oxidation products.

Peroxide modification of polyethylene. Prediction of molecular weight distributions by probability generating functions

We present a mathematical model able to describe the complete molecular weight distributions of polyethylene during reactive modification by organic peroxides. The method is applicable to batch processes, such as modification in a press or a plug-flow extruder, and in its present form is valid up to the gel point. We apply probability generating function definitions to the mass balances of radical and polymer species in the reacting medium. Three different probability generating functions are applied, each one directly applicable either to the number, weight or chromatographic distributions. These generating functions are numerically inverted to obtain the corresponding calculated molecular weight distribution. Two different inversion methods are used, and their relative performances analyzed. Predictions are compared with qualitative experimental data obtained in a press. Model predictions on molecular weight distributions are in agreement with experimental trends.

Effect of the phenolic antioxidants on the structure of gamma-irradiated model polyethylene

Abstract High energy radiation has been successfully employed to modify the chemical structure of commercial polymers. It induces at least two types of reaction in polyethylene: crosslinking and chain scission. In addition the efficiency of the radio-induced reactions can be affected by the presence of antioxidants. The purpose of this work is to study the effect of the irradiation on a model polyethylene containing a phenolic type antioxidant. Samples containing 0.1% and 1% by weight of Irganox 1010 (Ciba-Geigy) were irradiated under vacuum at room temperature with different doses of gamma rays from a 60 Co source. Changes in structure and the average molecular weight were followed by gel permeation chromatography and low angle laser light scattering. The critical doses for gelation were determined as a function of the antioxidant concentration. Theoretical calculations to predict the evolution of molecular structure with extent of radiation were performed using a probability model. The agreement between the calculated and the measured molecular weights is very good.

Model polydimethylsiloxanes subjected to thermal weathering : effect on molecular weight distributions

We have subjected samples of model polydimethylsiloxanes of narrow molecular weight distribution to thermo-oxidation in an air circulating oven. Samples remained for up to 1760 h at 200°C under a standard atmosphere. Loss of average molecular weight and broadening of molecular weight distributions was observed. We have modeled the process assuming that both crosslinking and scission are present simultaneously. We have tried to interpret the experimental data in two different ways: either assuming that the ratio of crosslinking to scission was not constant, or that there is an induction period with no reaction before the polymer shows measurable effects of the attack. We discuss the relative merits of both interpretations.

Prediction of the full molecular weight distribution in RAFT polymerization using probability generating functions

Abstract In this work, a model for the RAFT polymerization following the slow fragmentation approach was developed in order to obtain the full molecular weight distribution (MWD) using probability generating functions (pgf). A combination of univariate and bivariate pgf is applied to deal with the univariate chain length distributions of macroradical, dormant and dead polymer chains, and the bivariate distribution of the two arms intermediate adduct. This allows rigorous modeling of the polymerization system without simplifying assumptions. For comparison purposes, the population balances were solved by direct integration of the resulting equations. Our results show that the pgf technique allows obtaining an accurate solution efficiently in terms of computational time. What is more, the model provides a detailed characterization of the polymer that could be of great help for grasp the process fundamentals.

Comprehensive Mathematical Modeling of Controlled Radical Copolymerization in Tubular Reactors

Abstract In this work a comprehensive mathematical model of the nitroxide mediated polymerization in tubular reactors is developed. The model is able to predict average molecular properties, such as the average molecular weights and copolymer composition. Besides, detailed calculation of the copolymer microstructure is included. The model is able to predict the bidimensional molecular weight distribution of the copolymer, the sequence length distribution, the global molecular weight distribution and the copolymer composition distribution. In particular, styrene-α methyl styrene and styrene-methyl metha-crylate copolymerizations are studied. Model outputs are consistent with known features of the system. The detailed information on the copolymer molecular structure provided by the model makes it a valuable tool for the process design.

Prediction of the Full Molecular Weight Distribution in RAFT Polymerization using Probability Generating Functions

In this work, a model for the RAFT polymerization was developed in order to obtain the full molecular weight distribution (MWD) using probability generating functions (pgf). For comparison purposes, the population balances were solved by direct integration of the resulting equations. Our results show that the pgf technique allows obtaining an accurate solution while drastically reducing the required computational time.