Chain copolymerization sequence-length distribution

Statistical Models. Due to the difficulties involved in calculating the composition distributions by purely deterministic techniques, statistical methods have been developed from which not only the CCD can be obtained but also the sequence length distribution. These methods view the chain growth as an stochastic process having possible states resulting from the kinetic mechanisms. Early work on this approach was reported by Merz, Alfrey and Goldfinger (4) who derived the copolymerization equation and the SLD for the ultimate effect case. Alfrey Bohrer and Mark (19) and Ham (9) formalized this approach. 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

A knowledge of the ratio of the starting monomers and their copolymerization parameters enables the sequence length distribution to be calculated. The reactivity probabilities Pjj are defined (5,6) that give the probabihty of the monomer j adding to the polymer chain with the terminating monomer i ... 

On the contrary, when Vi V2 / 1, there is a tendency toward the appearance of a sort of order in the copolymer, that is toward formation of shorter sequences of identical monomer units if rir2 < 1 and of longer sequences if riV2 > 1. We may speak of alternating-like copolymers in the former case and of blocklike copolymers in the latter. The above example of the bag is no more valid if we wish to reproduce the detailed structures of copolymers, we must have two bags and put into each bag the sequences of each monomer (not the units as before ), with lengths distribution deduced from the copolymerization laws correspondingly to that copolymer composition and to that product of reactivity ratios, and then pick up alternatively one sequence from each bag, in such a way that sequences of each monomer occupy every second place in the polymer chain. 

Consequently, there can be a co-elution of species possessing different chain length and chemical composition. The influence of different comonomers copolymerized into the macromolecule on the chain size can be measured by the GPC elution of homopolymer standards of this comonomer. Unfortunately, the influence of the comonomer sequence distribution on the hydrodynamic radius cannot be described explicitly by any theory at present. However, there are limiting cases which can be discussed to evaluate the influence of the comonomer placement in a macro-molecular chain. 

In copolymerization, the presence of more than one type of monomer adds an extra degree of complexity to the kinetics. The different monomers form different radical structures, and the relative rates of chain growth depend on the structure of both monomer and radical. It is these propagation mechanisms that control polymer composition (the relative amounts of each monomer unit incorporated into the copolymer) and sequence distribution (the way in which these monomer units are arranged within the chain). Developing a set of mechanisms to describe how radical structure affects termination and transfer rates is required to represent copolymer chain length and molecular weight distributions. 

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