Mayo chain

Figure 6.8 Effect of chain transfer to solvent according to Eq. (6.89) for polystyrene at 100°C. Solvents used were ethyl benzene ( ), isopropylbenzene (o), toluene (- ), and benzene (°). [Data from R. A. Gregg and F. R. Mayo, Discuss. Faraday Soc. 2 328 (1947).]...

Figure 17.15 Schematic diagrams of the main-chain conformations of the second zinc finger domain of Zif 268 (red) and the designed peptide FSD-1 (blue). The zinc finger domain is stabilized by a zinc atom whereas FSD-1 is stabilized by hydrophobic interactions between the p strands and the a helix. (Adapted from B.I. Dahiyat and S.L. Mayo, Science 278 82-87, 1997.)...

With the omission of the reinitiation reaction, this scheme is the same as that for polymerization with chain transfer and an expression (eq 28) for the degree of polymerization similar in form to the Mayo equation can be derived. 

This equation (eq. 5) is commonly known as the Mayo equation.1" The equation is applicable at low (zero) conversion and is invalidated if the rate constants are chain length dependent. 

While it is, in principle, desirable to take the limiting slope of the log CLD plot, in practice the limiting slopes are very susceptible to experimental noise and baseline choice issues. Moad and Moad24 have shown that very little error is introduced by systematically taking the slope over the top 10% or the top 20% of the chain length distribution. The values for the slopes will overestimate ln(0). However, because the discrepancy is systematic, the Mayo" analysis still provides a good estimate for C ( 6% error for the example in Figure 6.1). 

Assuming that the number average degree of polymerization (DP ) is determined by chain transfer to monomer and assuming unimolecular termination relative to propagation (i.e., chain breaking due to solvent, polymer, impurities are absent), the simple Mayo equation55 ... 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Fig. 15.—Sources of chain ends in styrene polymerization with benzoyl peroxide at 60°C. (Mayo, Gregg, and Matheson. )...

For further data on chain transfer between styrene and a wider variety of substances, see Gregg and Mayo." ... 

A similar mechanism of chain oxidation of olefinic hydrocarbons was observed experimentally by Bolland and Gee [53] in 1946 after a detailed study of the kinetics of the oxidation of nonsaturated compounds. Miller and Mayo [54] studied the oxidation of styrene and found that this reaction is in essence the chain copolymerization of styrene and dioxygen with production of polymeric peroxide. Rust [55] observed dihydroperoxide formation in his study of the oxidation of branched aliphatic hydrocarbons and treated this fact as the result of intramolecular isomerization of peroxyl radicals. 

The reaction of chain generation PhCH=CH2 + 02 —> free radicals was experimentally proved A. A. Miller and F. R. Mayo [54]... 

The polymerization of St with 56 as the initiator is considered to proceed via a reaction mechanism in Eq. (56), being identical to the models in Eqs. (18) and (20). The structure of both chain ends of the resulting polymer was confirmed by NMR using the deuterated St as the monomer. The polymerization with BPO and TEMPO without isolation of the adduct would also proceed via a similar path. In the absence of BPO, it has been reported that the radicals produced by spontaneous initiation according to the Mayo mechanism react with TEMPO to yield the adducts, and then they initiate polymerization [206]. 

J.R. Uhl, C.A. Bell, L.M. Sloan, M.J. Espy, T.F. Smith, J.E. Rosenblatt and F.R. Cockerill, Application of rapid-cycle real-time polymerase chain reaction for the detection of microbial pathogens the Mayo-Roche rapid anthrax test, Mayo Clin. Proc., 77 (2002) 673-680. 

Another innovation is the reinterpretation of the significance of the various chain-breaking constant ratios which several workers had determined by means of Mayo plots. 

It is an obvious next step to identify this termination reaction with the second order chain breaking reaction involving the agent X, which was shown up by the Mayo plots. The rate of this is given by the third term of equation ii ... 

The same form of rate equation and Mayo equation can also be obtained, though with different constants, on the assumption, made by Biddulph and Plesch when first discussing this work [77], that the chain breaking agent is the stannic chloride hydrate itself. Since this reaction too would be subject to deceleration by increasing viscosity, it is also compatible with the curves of Figure 9. 

The dependence of the DP on the water concentration shows that it attains a maximum, but at a water concentration which is so low that it could not be determined with any accuracy. At greater water concentrations the Mayo plots of 1/DP against [H20] are linear. If the slopes of these are represented by kjkp, i.e., if it is assumed that the concentration of chain breaking agent is equal to [H2Oj the values shown in Table 6 are obtained. 

If it is assumed that the dissociation constant, Ky, of the ion pairs is independent of the length of the polymer chain attached to the cation, the Mayo equation takes the form... 

If F, G, and H (or substances originating directly from them) are (potential) chain-breakers, the DP will be governed by a Mayo equation of the form ... 

Most probably, it is the conjugate anion which is the chain-breaking species mentioned above whose presence is signalled by the Second Mayo Plot. 

Finally, the dependence of the DP and DPD on conversion, on mQ and on c0 must always be obtained, so that chain-breaking reactions can be identified by means of Mayo plots. 

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