Molecular weight distribution modeling

Howardt describes a model system used to test the molecular weight distribution of a condensation polymer The polymer sample was an acetic acid-stabilized equilibrium nylon-6,6. Analysis showed it to have the following end group composition (in equivalents per 10 g) acetyl = 28.9,... 

Model Networks. Constmction of model networks allows development of quantitative stmcture property relationships and provide the abiUty to test the accuracy of the theories of mbber elasticity (251—254). By definition, model networks have controlled molecular weight between cross-links, controlled cross-link functionahty, and controlled molecular weight distribution of cross-linked chains. Sihcones cross-linked by either condensation or addition reactions are ideally suited for these studies because all of the above parameters can be controlled. A typical condensation-cure model network consists of an a, CO-polydimethylsiloxanediol, tetraethoxysilane (or alkyltrimethoxysilane), and a tin-cure catalyst (255). A typical addition-cure model is composed of a, ffl-vinylpolydimethylsiloxane, tetrakis(dimethylsiloxy)silane, and a platinum-cure catalyst (256—258). 

Generally, the models used for simulation of living polymers can be divided roughly into two classes, focused on static or dynamic properties of the LP or GM. The static models are mainly designed to study equilibrium conformational properties of the polymer chains, critical behavior at the polymerization transition, and molecular weight distribution... 

Mathematical models of the reaction system were developed which enabled prediction of the molecular weight distribution (MWD). Direct and indirect methods were used, but only distributions obtained from moments are described here. Due to the stiffness of the model equations an improved numerical integrator was developed, in order to solve the equations in a reasonable time scale. 

Calculated Molecular Weight Distributions. The calculated weight fraction distributions for the micro-mixed, segregated, and micro-mixed reactor with dead-polymer models for Runs 2, 5,... 

The fair degree of consistency observed in the values of <()j) for Seeds II and III and the excellent agreement between the experimental molecular weight distribution and those calculated with, lends credibility to the dead-polymer model. The... 

Ordinate values of the molecular weight distribution rather than molecular weight averages obtained from size exclusion chromatography were used in the modelling (3.9). [Pn] in Equation (1) can be transformed into (log M), the ordinate of the molecular weight distribution using (2) ... 

This model was found to enable prediction of molecular weight distributions of the product extrudate for initiator concentrations of 0.0 to 0.04 wt. % and temperatures of 200 and 220°C. However, several aspects of the model required further development ... 

Using the above model improvements, Figiue 4 shows the variation of the predicted molecular weight distributions with reaction time for an initiator concentration and efficiency of 0.9 wt% and 0.18 respectively. The need for kinetic data to test these predictions again provides motivation for development of experimental techniques to obtain samples at lower reaction time. 

Good agreement between the experimental and model generated molecular weight distribution for an initiator concentration of 0.9 wt. % and a temperature of 200°C. However, under these conditions the degradation reactions were likely complete by the reaction time of 18.6 s. 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

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