Free radical polymerization disproportionation

The free-radical polymerization of methacrylic monomers follows a classical chain mechanism in which the chain-propagation step entails the head-to-taH growth of the polymeric free radical by attack on the double bond of the monomer. Chain termination can occur by either combination or disproportionation, depending on the conditions of the process (36). 

The minimum polydispersity index from a free-radical polymerization is 1.5 if termination is by combination, or 2.0 if chains ate terminated by disproportionation and/or transfer. Changes in concentrations and temperature during the reaction can lead to much greater polydispersities, however. These concepts of polymerization reaction engineering have been introduced in more detail elsewhere (6). 

In the period 1910-1950 many contributed to the development of free-radical polymerization.1 The basic mechanism as we know it today (Scheme 1.1), was laid out in the 1940s and 50s.7 9 The essential features of this mechanism are initiation and propagation steps, which involve radicals adding to the less substituted end of the double bond ("tail addition"), and a termination step, which involves disproportionation or combination between two growing chains. 

The most comprehensive simulation of a free radical polymerization process in a CSTR is that of Konopnicki and Kuester (15). For a mechanism which includes transfer to both monomer and solvent as well as termination by combination and disproportionation they examined the influence of non-isothermal operation, viscosity effects as well as induced sinuoidal and square-wave forcing functions on initiator feed and jacket temperature on the MWD of the polymer produced. 

The free radical polymerization of HPMA in the presence of mercaptans involves two different initiation mechanisms (Scheme 2) [26]. One is the initiation by RS radicals from chain transfer agent the other appears to be the direct initiation by the primary isobutyronitrile (IBN) radicals formed by the decomposition of AIBN [27]. The RS are formed by either the free radical transfer reaction of alkyl mercaptans with the IBN radicals or the chain transfer reaction of an active polymer chain with the mercaptans. The initiation by the RS radicals produces the ST polymers with a functional group at one end of the polymer chain. The initiation by IBN radicals leads to nonfunctional polymer chains with an IBN end group. The presence of the polymers with IBN end groups effects the purity and the functionality of ST polymers. As expected, the production of nonfunctionalized polymer chains is affected by reaction conditions. The polymerization is mainly terminated by chain transfer reaction with the mercaptans, but other termination mechanisms, such as disproportionation and recombination, take place depending on the reaction conditions [26]. 

Although this mechanism is an oversimplification, it does give the basic idea. Chain termination is more complicated than in free radical polymerization. Coupling and disproportionation are not possible since two negative ions cannot easily come together. Termination may result from a proton transfer from a solvent or weak acid, such as water, sometimes present in just trace amounts. 

For classical free radical polymerizations the rate of propagation is proportional to the concentration of monomer and the square root of the initiator concentration. Termination usually occurs through a coupling of two live radical chains but can occur through disproportionation. The rate of termination for coupling is directly proportional to initiator concentration. The DP is directly proportional to monomer concentration and inversely proportional to the square root of the initiator concentration. 

Taylor in 1925 demonstrated that hydrogen atoms generated by the mercury sensitized photodecomposition of hydrogen gas add to ethylene to form ethyl radicals, which were proposed to react with H2 to give the observed ethane and another hydrogen atom. Evidence that polymerization could occur by free radical reactions was found by Taylor and Jones in 1930, by the observation that ethyl radicals formed by the gas phase pyrolysis of diethylmercury or tetraethyllead initiated the polymerization of ethylene, and this process was extended to the solution phase by Cramer. The mechanism of equation (37) (with participation by a third body) was presented for the reaction, - which is in accord with current views, and the mechanism of equation (38) was shown for disproportionation. Staudinger in 1932 wrote a mechanism for free radical polymerization of styrene,but just as did Rice and Rice (equation 32), showed the radical attack on the most substituted carbon (anti-Markovnikov attack). The correct orientation was shown by Flory in 1937. In 1935, O.K. Rice and Sickman reported that ethylene polymerization was also induced by methyl radicals generated from thermolysis of azomethane. 

For anionic polymerizations in protic media, you get the same expressions as those obtained for free radical polymerization with termination by disproportionation (p is still the probability of chain growth, but now 1 -p is the probability of chain transfer). Again, the averages and distributions you can obtain are only valid for low degrees of conversion. For cationic polymerization, there are several types of transfer and termination reactions that occur m most reactions, so you... 

Free-radical polymerization with chain breaking exclusively by disproportionation or chain transfer yielding unreactive radicals produces a Schulz-Flory mole-fraction distribution. 

The distribution is as in free-radical polymerization with termination by disproportionation or terminating chain transfer (eqn 10.45 in Section 10.3.4) and, with increase of the progression factor as conversion increases, in step-growth polymerization of bifimctional monomers (eqn 10.19 in Section 10.2.3). According to eqn 10.81, the progression factor is... 

Free-radical polymerization requires initiation to produce free radicals that link up with monomer molecules to produce reactive centers. Additional monomer molecules are then added successively at these centers. In this way, a small family of polymer radicals acts as an assembly line to produce "dead" polymer. The most common termination mechanisms are reactions of two polymer radicals with one another, either by coupling to yield one larger dead polymer molecule or, more rarely, by disproportionation to convert... 

It is believed that most macroradicals terminate in free-radical polymerizations predominantly or entirely by combination. Experimental measurements of polymer systems are scanty, however. It can be expected that disproportionation will be... 

There is an important difference between the distributions calculated for equilibrium, bifunctional step-growth polymerization in Chapter 5 and for the free-radical polymerizations with termination by disproportionation or chain transfer that are being considered here. The distribution functions in the step-growth case apply to the whole reaction mixture in the free-radical polymerization this distribution describes only the polymer which has been formed. There is obviously a strong parallel between the probability S of this section and the extent of reaction p used in the step-growth calculations in Chapter 5. Many authors use the same symbol for both parameters. Different notations are used here, however, for clarity. 

Flory Statistics of the Molecular Weight Distribution. The solution to the complete set (j - I to j = 100,000) of coupled-nonlinear ordinary differential equations needed to calculate the distribution is an enormous undertaking even with the fastest computers. However, we can use probability theory to estimate the distribution. This theory was developed by Nobel laureate Paul Floty. We have shown that for step ipolymeiization and for free radical polymerization in which termination is by disproportionation the mole fraction of polymer -with chain length j is... 

The most important free-radical chain reaction conducted in industry is the free-radical polymerization of ethylene to give polyethylene. Industrial processes usually use (/-Bu())2 as the initiator. The t-BuO- radical adds to ethylene to give the beginning of a polymer chain. The propagation part has only one step the addition of an alkyl radical at the end of a growing polymer to ethylene to give a new alkyl radical at the end of a longer polymer. The termination steps are the usual radical-radical combination and disproportionation reactions. 

Problem 6.44 Consider a case of free-radical polymerization where termination involves both disproportionation and coupling of chain radicals but chain transfer reactions can be neglected. Derive an expression for the distribution function for the degree of polymerization of polymer in terms of the kinetic chain length and the ratio of termination by disproportionation to that by coupling [65]. Simplify the expression for two limiting cases where (a) termination is solely by coupling and (b) termination is solely by disproportionation. 

Figure 8.2 Number fraction and weight fraction distribution of the degree of polymerization with i/ = 50 for anionic "living" polymers and for free-radical polymerization (with termination by disproportionation). (Problem 8.8)...

Equations (6.105) and (6.106) for apply to free-radical polymerization following ideal kinetics in which termination of chain growth occurs only by mutual reaction (coupling and disproportionation) of chain radicals. Combining Eqs. (6.100) and (6.105) one may write... 

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