Reaction 2 Free Radical Polymerization Kinetics

Here, gt takes into account one interesting feature of the free radical polymerization kinetics the auto acceleration in the rate of reaction (better known as the Trommsdorff or gel effect). The gel effect is taken into account in the model (42) by including the experimental correlation developed in [18] for the termination rate ... 

Polystyrene and poly(methyl methacrylate) polymerizations are typical of homogeneous bulk chain-growth reactions. The molecular weight distributions of the products made in these reactions are broader than predicted from consideration of classical, homogeneous phase free-radical polymerization kinetics because of autoacceleration (Section 6.13.2) and temperature rises at higher conversions. 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

Free-radical Polymerization Kinetics. A general scheme for these reactions is the following ... 

The polymerization rate is directly proportional to the monomer concentration for ideal free radical polymerization kinetics. Deviations from this first-order kinetics can be caused by a whole series of effects which must be checked by separate kinetic experiments. These effects include cage effects during initiator free radical formation, solvation of or complex formation by the initiator free radicals, termination of the kinetic chain by primary free radicals, diffusion controlled termination reactions, and transfer reactions with reduction in the degree of polymerization. Deviations from the square root dependence on initiator concentration are to be primarily expected for termination by primary free radicals and for transfer reactions with reduction in the degree of polymerization. 

Free radical polymerization kinetics has received much attention and many aspects of the process are well understood (see Chapter 4). Most academic investigations have been carried out in idealized conditions where the extent of monomer conversion is low. The classical expression for the rate of polymerization (Rp), in a single-phase reaction, is Eq. (13), where kp is the propagation rate coefficient, Cm is monomer concentration, J i is the initiation rate and kt is the termination rate coefficient [63]. 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

The various kinetic and thermodynamic factors involved in vinyl free radical polymerization have been considered for the case of a batch (or semi-batch) polymerization being carried out to very high conversion. In particular, computations have been done for the final stage of the reaction when monomer concentration is reduced from approximately 5 volume % to 0.5 volume %. 

Free radical polymerization of MMA is a well understood process. The kinetic mechanism neglecting the chain transfer reactions is given as follows (Odian (1970), Rudin (1982)). 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

Since this reaction is not affected by hydroquinone and galvinoxyl and does not initiate polymerization of styrene, it obviously occurs without the formation of free radicals. The kinetic parameters of the reactions of three hydroperoxides with triphenyl phosphite in different solvents are given in Table 17.2 [21]. 

A critical survey of the literature on free radical polymerizations in the presence of phase transfer agents indicates that the majority of these reactions are initiated by transfer of an active species (monomer or initiator) from one phase to another, although the exact details of this phase transfer may be influenced by the nature of the phase transfer catalyst and reaction medium. Initial kinetic studies of the solution polymerization of methyl methacrylate utilizing solid potassium persulfate and Aliquat 336 yield the experimental rate law ... 

In conclusion, several examples of free radical polymerizations under phase transfer conditions have been described in the literature since the initial reports in 1981. In all of these cases it is apparent that transfer of an active species from one phase to a second phase is intimately involved in the initiation step of the polymerization. However, it is also clear that these are complex reactions mechanistically, and one general kinetic scheme may not be sufficient to describe them all. The extent of phase transfer and the exact species transferred will depend to a large extent upon the nature of the two phases, upon the... 

Compared with free radical polymerizations, the kinetics of ionic polymerizations are not well defined. Reactions can use heterogeneous initiators and they are usually quite sensitive to the presence of impurities. Thus, kinetic studies are difficult and the results sensitive to the particular reaction conditions. Further, the rates of polymer formation are more rapid. 

It is interesting to note that due to their industrial importance, free radical polymerizations are the most studied reactions in chemistry. Furthermore, the kinetic approaches taken in this chapter are experimentally verified for essentially all typical free radical vinyl polymerizations. 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

There are a large number of chain reactions that are significant in industrial processes or play an important role for the environment. Classes of chain reactions that are relevant industrially include hydrogen/halogen reactions and pyrolysis of hydrocarbons, which are both discussed below, and free-radical polymerization discussed in many textbooks on kinetics. As an example of a chain reaction of significant environmental consequence, we will discuss formation of nitric oxide from fixation of atmospheric nitrogen. 

The oxidation of benzoin with cerium(IV) in perchloric acid solution is proposed to involve an interaction between Ce4+(aq.) ions and the keto alcohol, resulting in the formation of free radicals. The final product is benzoic acid.66 The rate of oxidation of crotyl alcohol with cerium(IV) is independent of the concentration of Ce(IV). The reaction induced polymerization of acrylonitrile indicating the formation of free radicals. The kinetics and activation parameters for the reaction have been determined.67 For the Ir(III)-catalysed oxidation of methyl ketones68 and cyclic ketones69 with Ce(IV) perchlorate, successive formation of complex between the reductant and Ce(IV) and then with the catalyst has been proposed. Results showed that in acidic solutions, iridium(III) is a more efficient catalyst than osmium and ruthenium compounds. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

These investigations have demonstrated the successful application of cyclodex-trins in polymer synthesis in aqueous solutions via free radical polymerization or via a oxidative recombination mechanism. Some special aspects of cyclodextrins were found concerning the kinetics, chain transfer reaction, and copolymerization parameters [63],... 

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