Penultimate model addition

From these results, it can be concluded, that the structure of the growing chain end not only influences the addition of the cationic monomer but also the propagation step with acrylamide [38]. Figure 13 shows a comparison of the experimental results with the penultimate model and the best fit using the Keh-len/Tiidos equations [71]. A better agreement can be observed particularly in the range of higher DADMAC content. 

In these models, the complex formed by the monomer pair competes with the individual monomer molecules for the propagation reaction with the radicals. There are two variations of this approach in the complex participation model, the pair of monomers form a complex and are added to the chain radical [106-109]. On the other hand, in the complex dissociation model, the complex participates in the propagation process, but dissociates upon reaction and only one of the monomers is added to the chain [101, 103]. Although there is ample experimental evidence for the existence of such complexes in these copolymerizations (such as the bright colors associated with them) [76], it is questionable whether the complexes actually participate in the propagation step [76]. Additionally, for several years, Hall and Padias have accumulated experimental and theoretical evidence that refutes the validity of the models based on complex participation [76, 77]. Both the complex participation and the penultimate models were combined in the so-called comppen model [110]. 

There are two cases to consider when predicting flie effect of solvent polarity on copolymerization propagation kinetics (1) the solvent polarity is dominated by an added solvent and polarity is thus independent of the comonomer feed ratio, or (2) the solvent polarity does depend on the comonomer feed ratio, as it would in a bulk copolymerization. In the first case, the effect on copolymerization kinetics is simple. The monomer reactivity ratios (and additional reactivity ratios, depending on which copolymerization model is appropriate for that system) would vary fi om solvent to solvent, but, for a given copolymerization system they would be constant as a function of the monomer feed ratios. Assuming of course that there were no additional types of solvent effect present, fliese copolymerization systems could be described by their appropriate base model (such as the terminal model or the explicit or implicit penultimate models), depending on the chemical structure of the monomers. 

Copolymerization models based upon a Bootstrap effect were first proposed by Harwood and Semchikov" (see references cited therein). Harwood suggested that the terminal model could be extended by the incorporation of an additional equilibrium constant relating the effective and bulk monomer feed ratios. Different versions of this so-called Bootstrap model may be derived depending upon the baseline model assumed (such as the terminal model or the implicit or explicit penultimate models) and the form of equilibrium expression used to represent the Bootstrap effect. In the simplest case, it is assumed that the magni-... 

Relationships between second-order Markov addition probabilities and penultimate model reactivity ratios have also been derived and can be found in [5]. Similarly, for the complex participation model, Cais et al have derived expressions which enable calculation of any given sequence from a knowledge of reactivity ratios and the equilibrium constant for complex formation determined by other methods [6]. 

In the explicit penultimate model, it is assumed that both the terminal and penultimate units of a polymer radical may affect the rate of the propagation reaction. As in the terminal model, side reactions are considered to be insignificant. The explicit penultimate model was first suggested in 1946 by Merz and co-workers (10), who derived equations for predicting the composition and sequence distribution under this model. A full description of the model—including an expression for ( p)— has since been provided by Fukuda and co-workers (11), and it is their notation that is used below. In addition, penultimate model equations for the case of terpolymerization have been published by Coote and Davis (12). 

In eqn [24], fi is the mole fraction of monomer i in the monomer mixture. In the penultimate models, two monomer-derived segments at each radical chain end are taken into account, for example, by the rate coefficient kuy which refers to addition of a monomer molecule j to a radical chain end where both terminal and penultimate units consist of spedes i. Equation [24] is used to derive q and also q =fejj/feji from measured compositions of monomer mixture and copolymer, fi and Fi, respectively. 

It is known that the penultimate unit influences the conformation of both model radicals and propagating radicals.32 3 Since addition requires a particular geometric arrangement of the reactants, there are enthalpic barriers to overcome for addition to take place and also potentially significant effects on the entropy of activation. Comparisons of the rate constants and activation parameters for homopropagation with those for addition of simple model radicals to the same monomers also provide evidence for significant penultimate unit effects (Section 4.5.4). 

The arrangement of monomer units in copolymer chains is determined by the monomer reactivity ratios which can be influenced by the reaction medium and various additives. The average sequence distribution to the triad level can often be measured by NMR (Section 7.3.3.2) and in special cases by other techniques.100 101 Longer sequences are usually difficult to determine experimentally, however, by assuming a model (terminal, penultimate, etc.) they can be predicted.7 102 Where sequence distributions can be accurately determined Lhey provide, in principle, a powerful method for determining monomer reactivity ratios. 

Analysis of the data collected by Hill et al. illustrates how a four parameter problem can be reduced to one involving only two parameters by appropriately formulating the problem. In addition an approach to fitting models directly to triad fraction data is shown. Our analysis confirms the conclusion made by Hill et al. that a penultimate effect does exist for both styrene and acrlyonitrile. 

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). 

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