Coleman-Fox model

For NMR studies of polymer mixtures, the earliest approach proposed was the Coleman-Fox model.(5) This model assumes the coexistence of two interconverting Bemoullian propagating sites and was used extensively for poly(methyl methacrylate).(6-8)... 

This indicates that a close contact of the carbanion with the counterion favours isotactic placements as well as short sequence length (corresponding to persistence ratios below 1). In the system Cs/THF the marked non-Bernoullian behaviour can be described by Markovian statistics rather than the Coleman-Fox model, i.e. the penultimate monomer unit influences the stereochemistry of the monomer addition (29). This effect can be interpreted by decreasing external solvation (III,IV) and increasing intramolecular solvation (I,II). 

In this case the results are compared for the first-order Markov, second-order Markov and the Coleman Fox model. For the first-order Markov, the sequence intensities are calculated from the values of the conditional probability obtained from the... 

The Coleman-Fox two state model describes the situation where there is restricted rotation about the bond to the preceding unit (Scheme 4.3). If this is slow with respect to the rate of addition, then at least two conformations of the propagating radical need to be considered each of which may react independently with monomer. The rale constants associated with the conformational equilibrium and two values of Pirn) are required to characterize the process. 

Other propagation models are also possible. An example is an adaptation [48,55,65] of the Coleman-Fox [66] mechanism in which the polymerisation is considered to take place at two active sites, each with a different Bernoullian propagation probability (see chapter 2). 

Busico and co-workers [24] presents the main results of a 150 MHz C-NMR characterisation of polypropene fractions containing high amounts of syndiotactoid sequences, and of the statistical analysis of the spectroscopic data in terms of a Coleman-Fox type [25] two-site model taking into account the hypothesis of junctions between isotactoid and syndiotactoid sequences. 

Analysis of the poly(methyl methacrylate) sequences obtained by anionic polymerization was undertaken at the tetrad level in terms of two different schemes (10) one, a second-order Markov distribution (with four independent conditional probabilities, Pmmr Pmrr, Pmr Prrr) (44), the other, a two-state mechanism proposed by Coleman and Fox (122). In this latter scheme one supposes that the chain end may exist in two (or more) different states, depending on the different solvation of the ion pair, each state exerting a specific stereochemical control. A dynamic equilibrium exists between the different states so that the growing chain shows the effects of one or the other mechanism in successive segments. The deviation of the experimental data from the distribution calculated using either model is, however, very small, below experimental error, and, therefore, it is not possible to make a choice between the two models on the basis of statistical criteria only. 

The above equations show that although the model contains four independent parameters, the frequency of occurrence of triads are determined by only two independent parameters, u and v. From this it also follows that the condition that the triads have the distribution found by Bovey (5, 6) for methyl methacrylate—i.e., Pi = PiP4, is equivalent to u = v and not the more restricted condition u = v = 1 which arises from the Bernoulli triad model of Coleman and Fox (8). 

Coleman and Fox published an alternative mechanism [82], According to these authors, the propagating centres exist in two forms, each of which favours the generation of either the m or r configuration. When both centres are in equilibrium, and when this equilibrium is rapidly established, the chain structure can be described by a modified Bernoulli statistics [83, 84]. The configurations of some polymers agrees better with this model than with first-or even second-order Markov models [84, 85]. 

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