Continuous free radical theory

We continue our study of chemical kinetics with a presentation of reaction mechanisms. As time permits, we complete this section of the course with a presentation of one or more of the topics Lindemann theory, free radical chain mechanism, enzyme kinetics, or surface chemistry. The study of chemical kinetics is unlike both thermodynamics and quantum mechanics in that the overarching goal is not to produce a formal mathematical structure. Instead, techniques are developed to help design, analyze, and interpret experiments and then to connect experimental results to the proposed mechanism. We devote the balance of the semester to a traditional treatment of classical thermodynamics. In Appendix 2 the reader will find a general outline of the course in place of further detailed descriptions. 

Lin and Chiu (1979) developed a theory for the MWD in a zero-one system that correctly predicts (where M is continuous rather than discrete) the free-radical lifetime distribution Ni leading to a value of 2 for P. The formalism of Lin and Chiu involves calculating the number of chains containing m monomer units. Their final results involve sequence summations over the range K m < oo. 

Our discussion of the kinetic theory of fracture in Section 1 has already indicated the manner in which applied stress can bring about a net accumulation of nwlecular breakages in a jxrlymeric solid. Since the stress is continuous throughout a specimen loaded in tension, these breakages are distributed throughout the material and can be detected by ESR in terms of a volume concentration of free radicals. 

In theory, the chain could continue to propagate imtil all the monomer in the system has been consumed, but for the fact that free radicals are particularly reactive species and interact as quickly as possible to form inactive covalent bonds. This means that short chains are produced if the radical concentration is high because the probabihty of radical interaction is correspondingly high, and the radical concentration should be kept small if long chains are required. Termination of chains can take place in several ways by (1) the interaction of two active chain ends, (2) the reaction of an active chain end with an initiator radical, (3) termination by transfer of the active center to another molecule which may be solvent, initiator, or monomer, or (4) interaction with impurities (e.g., oxygen) or inhibitors. 

The use of quantum chemistry to obtain the individual rate coefficients of a free-radical polymerization process frees them from errors due to kinetic model-based assumptions. However, this approach introduces a new source of error in the model predictions the quantum chemical calculations themselves. As is well known, as there are no simple analytical solutions to a many-electron Schrodinger equation, numerical approximations are required. While accurate methods exist, they are generally very computationally intensive and their computational cost typically scales exponentially with the size of the system under study. The apphcation of quantum chemical methods to radical polymerization processes necessarily involves a compromise in which small model systems are used to mimic the reactions of their polymeric counterparts so that high levels of theory may be used. This is then balanced by the need to make these models as reahstic as possible hence, lower cost theoretical procedures are frequently adopted, often to the detriment of the accuracy of the calculations. Nonetheless, aided by rapid and continuing increases to computer power, chemically accurate predictions are now possible, even for solvent-sensitive systems [8]. In this section we examine the best-practice methodology required to generate accurate gas- and solution-phase predictions of rate coefficients in free-radical polymerization. 

The Kolbe-type reaction has continued to receive much attention with particular emphasis on formic acid oxidation. However, the mechanism remains open to question. The mechanism given primary consideration at present is that originally suggested by Crum-Brown and Walker," who proposed direct electrochemical oxidation of the carboxylate ion with subsequent decomposition of the radicals which combine giving the hydrocarbon. This theory, known as the discharged ion and free radical mechanism, can be... 

Free-radical Initiated Processes.—A great deal of work has appeared concerning emulsion copolymerizations such as that of Khanna and Noonan who have described the syntheses of copolymers of acrylic esters with uniform composition by continuous polymerization processes. Emulsion processes will not be considered further here except to mention that the kinetics and current problems in the theory of emulsion polymerization have been reviewed as have many other aspects of this field. ... 

The line shape of the ESR spectrum can be calculated using the spin Hamiltonian H (f) for the nitroxide radical. The time dependence of the spin Hamiltonian describes the orientation-dependent part which contains terms characterizing the anisotropy of the A- and g-tensors, and terms characterizing the rotational reorientation of the free radical as a classic stochastic process using the Wigner rotation matrix elements. A comprehensive theory of ESR spectra of nitroxides has been described step-by-step in contributions to two monographs and papers cited therein. Computer programs suitable for calculation of theoretical line shapes of ESR spectra measured in continuous wave (CW) and pulse experiments have become indispensable tools for practical applications. The ESR spectra of nitroxides are also described in chapters 1 and 3 in this volume. 

Polyolefins.— The mechanism(s) of polyolefin photo-oxidation continue to be shrouded in complexities. Recently Geuskens has attempted to answer questions concerning the sensitized photolysis of hydroperoxides in these polymers in the presence of carbonyl groups. In contrast with the theory proposed above,it is suggested that a complex is formed and photolysed to produce a carboxylic acid and an ether directly (Scheme 19) rather than free hydroxyl radicals. 

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