Polymer growing ends, model

Under the condition that the reaction capability is only affected by the nature of the last monomer unit of the growing polymer chain end (terminal model, Bernoulli statistics), the copolymerization equation can be transformed according to Kelen and Tudos ... 

The idea of particle inhomogeneity was supported experimentally by Williams [149], However, his representation of growth is more complicated. In phase II, the monomer concentration in the particle decreases with conversion, while the rate remains constant. The particle has a core with a relatively high polymer content surrounded by a monomer-rich layer (see Fig. 16). Polymerization occurs at the polymer—monomer interface. Under these conditions, monomer concentration at the interface remains constant, even when its amount in the particle decreases. Napper presented the idea of an exactly opposite composition of the monomer—polymer particle [150], The core should be enriched in monomer and surrounded by a layer with a higher polymer content. Van den Hul and van der Hoff found most growing ends of macromolecules at the particle surface [151], which supports Napper s model. 

Compared to poly(o -methylstyrene), this polymerization reaction is irreversible and there are few monomers left in solution at the end. To test our model, we use the same parameter values and turn off the back reaction to simulate the irreversible reaction. As shown in Figure 10.5, the polymer grows faster for an irreversible reaction as expected. 

According to an early model.13 1 there are two adjacent accessible positions at the catalytic site, each favoring the coordination of the prochiral monomer with one of its two faces if the growing polymer chain alternates between the two positions at each insertion step, syndiotactic propagation is ensured. Due to the successive finding of a chain-end stereocontrol, this model has to be rejected. 

For syndiotactic polypropylene the symmetric Bernoulli trial, expressed in m and r dyads, is quite adequate for the representation of experimental data, and agrees with the stereochemical control being exerted by the growing chain end (145, 409). In its turn, atactic polypropylene is considered as a mixture of the products of two superposed processes, of the type discussed for isotactic and syndiotactic polymers, and is described by a simplified two-state model (145). 

A further modification of the active-center model was based on the consideration that the vacancy in the active center is strongly shielded by the polymer chain, mainly by the CH2 and CH3 groups of the second monomer unit. As a result, the vacant site is blocked and inaccessible for olefin coordination. Kissin et al. suggest a polymerization center with two vacancies one shielded and the other open for complexation.344,345 After each insertion step the end of the growing polymer chain flips from side to side and the two vacant sites are alternately available for alkene coordination. 

Conversion of a randomly-coiled growing polymer into a helix affects the surroundings of its active end and, therefore, such a transformation is expected to modify the rate constant of propagation. This most interesting situation was visualised by Doty and Lundberg (36), and a model, taken from a paper by Weingarten (33) and shown in Fig. 16, illustrates how a helical structure might influence the monomer addition. 

In our studies an attempt was made to obtain detailed information on the mechanism of stereospecific diene polymerization initiated by several catalyst systems. To this end the structure and some chemical reactions of compounds used as models of the system "catalyst-growing polymer chain were studied in detail. 

The equilibrium constant of polyesterification is typically equal to that of the analogous model reaction between monofunctional compounds. This can be explained by the proposition [3] that the reactivity of a functional end-group in any growing polymer chain is independent of the degree of polymerization or chain-length. There have been several experimental verifications of this theory. Thus the equilibrium constant for the reaction between dimethyl terephthalate (DMT) and ethylene glycol at 280°C was found [31] to be 4.9 under certain conditions. Under identical conditions, the equilibrium constant for the model reaction was 5.0. 

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