Radical polymerization controlled chain length models

Another convenient and effective scheme for the approximate solution of a mathematical description of the polymerization reaction replaces the discrete variable of infinite range, polymer chain length, by a continuous variable. The difference-differential equations become partial differential equations. Barn-ford and coworkers [16,27,28] used this procedure in their analysis of vinyl (radical chain growth) polymerization. Zeman and Amundson [18,19] used it extensively to study batch and continuous polymerizations. Recently, Coyle et al. [4] have applied it to analysis of high conversion free radical polymerizations while Taylor et al. [3] used it in their modelling efforts oriented to control of high conversion polymerization of methyl methacrylate. A rather extensive review of the numerical techniques and approximations has been presented by Amundson and Luss [29] and later by Tirrell et al. [30]. 

In this chapter, three examples of the application of ESR to conventional radical polymerizations based on controlled/living radical polymerizations wUl be demonstrated. The first example is estimation of the effect of chain length on propagating radicals. The second example is the detection of chain-transfer reactions on the propagating radicals in polymerization of tert-butyl acrylate (tBA). The third example is investigation of penultimate unit effects using ESR analysis of dimeric model radicals of (meth)acrylates prepared by ATRA. 

Development of controlled radical polymerization techniques has stimulated basic research on radical chemistry in conventional radical polymerizations. Information on the effect of chain lengths on propagating radicals, chain-transfer reactions to polymers, and penultimate unit effects has been obtained from ESR observation of model radicals generated from radical precursors prepared by ATRP. Previously, it has been extremely difficult, even impossible, to obtain such information from ESR spectra during conventional radical polymerizations. The ESR study of radical polymerizations has made remarkable progress as a result of the combination of study of radicals formed as a result of various kinds of controlled radical polymerization techniques. 

Ito s model [68] bears resemblances to the model of Ref. [35], but is different by two aspects. Firstly, it assumes that the constant rate of the chain termination depends on the number of monomeric units (so-called polymerization degree) of tn and n radical chains taking part in the termination reaction and represents the sum of the independent contributions of m and n. Secondly, the dependence of the chain termination constant on the length of chains under two types of conditions is described the first condition is < n, controlled by segmental diffusion, and the second one is m > controlled by the reptation diffusion. In the reptation chemical mechanism of diffusion in the deep states of conversion the macroradicals move snake-like between the network joints. De Gennes connected a reptative moving of macroradicals with the dynamic properties of the medium with the use of scaling ratios [37-40] as applied in Refs. [41-46] for the description of constant chain termination in the late conversion state. 

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