Modelling the Complete Molecular Weight Distribution in Chain Growth Polymerizations
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Modelling the Complete Molecular Weight Distribution in Chain Growth Polymerizations Ramiro Infante-Martínez, Enrique Saldívar-Guerra, Odilia Pérez-Camacho, Maricela GarcíaZamora, Víctor Comparán-Padilla Centro de Investigación en Química Aplicada, Saltillo, Coahuila. México
ABSTRACT This work shows the development of several models for chain-growth polymerizations that admit the direct calculation of the complete molecular weight distribution of the polymer. The direct and complete calculation implies that no statistical mean values are employed as in the moments method neither numerical approximations like in the minimum-squared based methods. The free radical polymerization of ethylene (LDPE) and the coordination via metallocenes polymerization of ethylene (HDPE) are taken as examples for analysis. In the free radical polymerization case, the conventional scheme for chain-growth polymerization is adopted, with steps for initiation, propagation, chain transfer to small species and the additional step of chain transfer to dead chains [1]. The kinetic parameter are obtained from the open literature. Two kind of reactors were modelled: batch and continuous stirred tank reactor. For this last case, a simulation strategy was considered in which the run started from an initial known population of dead chains. Results show that typical non-linear polymerization profiles for the molecular weight distribution are obtained. For the coordination polymerization of ethylene via metalocenes, the standard coordination model was employed [2]. A two-site catalyst was considered and kinetic parameters reported in the open literature were used. For this study an experimental program in a lab-scale reactor was undertaken in order to obtain modelling data [3]. Results show that the standard model adequately reproduces the experimental data in the kinetic and molecular attributes of the polymer. INTRODUCTION Coordination polymerization modeling The task of modelling starts from a simplified scheme including only the mechanistic steps [1,2]: initiation, propagation, hydrogen transfer, -hydride elimintation and monomolecular deactivation, as is showed in table I.
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Description
Chemical equation
Initiation
C* + M
P1
ki
Propagation
Pr + M
Pr+1
kp
-Hydride elimination
Pr
C* + Dr
kt
H2 transfer
Pr + H2
C* + Dr
ktrH
Cd + Dr
Pr Deactivation
Kinetic constant
C*
Cd
kdac
Table I Simplified mechanism for homopolymerization via metallocenes. This is a working model wich can easily be extended to include more polymerization steps, more than one catalytic site and even more than one monomer. As such, it can model the synthesis of linear HDPE. Several assumptions were taken to simplify the algebraic manipulations in the model derivation, such as: (1) Site activation (reaction between catalyst and
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