Statistical chain-scission

Depolymerization, elimination, and statistical chain-scission reactions can be used for polymer analysis. When the monomer is the main degradation product obtained, it can easily be identified by boiling point and refractive index. 

The rates and products of poly(vinyl alcohol) (PVA) photooxidation were measured over a temperature range of 30°-90°C. Oxidation was initiated with 253.7-nm light, and several model compounds were included. The PVA photooxidation rate was autocatalytic and relatively insensitive to temperature with the major products being carbon dioxide, acids, peroxides, polymeric p-hydroxyketone, and hydrogen peroxide. Acids were mostly formic acid and carboxylic acids at the polymer chain ends. Several molecules of carbon dioxide and acid were formed per statistical chain scission. The mechanism of the photooxidation of PVA is discussed. 

The total number of statistical chain scissions during oxidation, SG, was calculated from the following equation,... 

Number of statistical chain scissions calculated from Equation 1. 

Statistical chain scission, followed by (i) retro-polymerisation starting from the radical chain ends (e.g. PIB, PS) (ii) radical transfer and disproportionation (e.g. PE, iPP) and (Hi) stabilisation of the fragments, e.g. by cyclisation (PDMS). 

The formation of macro-radicals created by non-thermally stable structures is observed prior to statistical chain scission. The thermal behavior of PMMA at temperatures below major degradation depends on many factors that have to be considered, in particular during certain stabilizer-free polymerization processes with high levels of radical generation. 

Thus, transesterification causes branching as well as chain scission Let us consider the branching statistics for the case of a polycarboxylic acid and polyepoxide with groups of independent reactivity. The use of the statistical method is justified because neither the substitution effect nor the initiated chain growth are operative. If only addition esterification occurs (and indeed this reaction can be selectively accelerated by special catalysts the statistics is analogous to the polyamine-polyepoxide addition and even simpler because the substitution effect is here absent. The pgf s for the number of bonds issuing from polyacid (C) and polyepoxide (E) units read ... 

The model chosen to describe the degradation of polyethylene was random chain scission. Lenz (3,) in his section on degradation reactions of polymers cites work which supports the contention that polyethylene does thermally degrade in a random chain scission manner as opposed to depolymerization. For this model a statistical treatment has been developed by Montroll and Simha (). The extent of reaction may be related to the number average molecular weight by ... 

The chemical stability against chain scission and oxygen attack also plays a role in the application of plastics at still higher temperatures. The statistical probability of chain scission is indeed practically the same for linear chains, cross-linked network polymers, and ladder polymers. But, whereas, a chain scission in linear polymers leads to lower degrees of polymerization because of chain degradation, with consequent diminished mechanical properties, chain scission with, for example, a ladder polymer, still leaves one chain of the ladder intact since it is improbable that both chains of the ladder should break at exactly the same distance from each end (see also Chapter 23). 

On the other hand, if the chain scissions occur randomly along the polymer chains, as illustrated in Figure 2.4b, then there is a small chance that two scissions work together to produce a short chain, or one scission occurs a few units away from the chain end. Using statistical analysis, Hory (1953) obtained... 

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