Radical reactions chain length

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Gas-phase radiolysis can sometimes result in chain reactions involving H atoms or other radicals. As in other cases with chain reactions, termination is due to either recombination or reaction with other radicals. Typical chain length is -1000 or more. Some specific examples will be considered in Sect. 5.2. 

The species RNO participates in five types of reactions pertinent here. At high NO pressures, it acts as a catalyst for the conversion of NO to N2 + N02. It is regenerated in the reaction chain lengths to 100 have been achieved. At the same time, it is also consumed by a reaction first-order in NO to produce N20 and RO radicals. At lower NO pressures, dimerization of RNO is an important process. Another possibility for RNO species with an a hydrogen atom is isomerization to the oxime R =NOH. This reaction proceeds with considerable activation energies for small radicals and, thus, may not be important at room temperature. If the pressure of NO is sufficiently low, so that all the radicals are not scavenged by NO, RNO may react with the radicals, either by addition or disproportionation. 

The phenomenon of catalyst-inhibitor conversion1 2,143,356 may be understood and critical concentration of metal can be deduced by reference to Eq. (280). If decomposition of the hydroperoxide is the source of initiation, it must be formed as rapidly as it is consumed to maintain a steady rate. If termination by metal complex predominates, a steady state occurs when the right-hand side of Eq. (280) equals unity. No oxidation will occur when this quantity is less than unity. Hence, catalyst-inhibitor conversion is observed as the metal concentration is increased to the point that the chain length becomes less than unity. If termination occurs by the bimolecular reaction of peroxy radicals, a chain length of less than unity will result in the depletion of the hydroperoxide until the rate of initiation has decreased to the point where the chain length is unity again. No inhibition is expected or observed. 

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. 

In writing Eqs. (7.1)-(7.4) we make the customary assumption that the kinetic constants are independent of the size of the radical and we indicate the concentration of all radicals, whatever their chain length, ending with the Mj repeat unit by the notation [Mj ], This formalism therefore assumes that only the nature of the radical chain end influences the rate constant for propagation. We refer to this as the terminal control mechanism. If we wished to consider the effect of the next-to-last repeat unit in the radical, each of these reactions and the associated rate laws would be replaced by two alternatives. Thus reaction (7. A) becomes... 

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

The main reason that the decreases as the polymerization temperature increases is the increase in the initiation and termination reactions, which leads to a decrease in the kinetic chain length (Fig. 17). At low temperature, the main termination mechanism is polystyryl radical coupling, but as the temperature increases, radical disproportionation becomes increasingly important. Termination by coupling results in higher PS than any of the other termination modes. 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Radical Scavengers Hydrogen-donating antioxidants (AH), such as hindered phenols and secondary aromatic amines, inhibit oxidation by competing with the organic substrate (RH) for peroxy radicals. This shortens the kinetic chain length of the propagation reactions. 

In the literature on radical polymerization, the rate constant for propagation, ( is often taken to have a single value (i.e. kp( I) - kv(2) - kvQ) - kp(n) - refer Scheme 4.45). However, there is now good evidence that the value of k is dependent on chain length, at least for the first few propagation steps (Section 4.5.1), and on the reaction conditions (Section 8.3). 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

In conventional radical polymerization, the chain length distribution of propagating species is broad and new short chains are formed continually by initiation. As has been stated above, the population balance means that, termination, most frequently, involves the reaction of a shorter, more mobile, chain with a longer, less mobile, chain. In living radical polymerizations, the chain lengths of most propagating species are similar (i.e. i j) and increase with conversion. Ideally, in ATRP and NMP no new chains are fonned. In practice,... 

The self reaction of primary alkyl radicals gives mainly combination.118 For primary alkyl radicals [CH3(CH2)nCH2 ], kjkxa is reported to lie in the range 0.12-0.14, apparently independent of chain length (n=0-3).1,8,119... 

If the amount of termination by radical-radical reaction is neglected the degree of polymerization and the kinetic chain length are given by eq. 29 ... 

Radiolytic ethylene destruction occurs with a yield of ca. 20 molecules consumed/100 e.v. (36, 48). Products containing up to six carbons account for ca. 60% of that amount, and can be ascribed to free radical reactions, molecular detachments, and low order ion-molecule reactions (32). This leaves only eight molecules/100 e.v. which may have formed ethylene polymer, corresponding to a chain length of only 2.1 molecules/ ion. Even if we assumed that ethylene destruction were entirely the result of ionic polymerization, only about five ethylene molecules would be involved per ion pair. The absence of ionic polymerization can also be demonstrated by the results of the gamma ray initiated polymerization of ethylene, whose kinetics can be completely explained on the basis of conventional free radical reactions and known rate constants for these processes (32). An increase above the expected rates occurs only at pressures in excess of ca. 20 atmospheres (10). The virtual absence of ionic polymerization can be regarded as one of the most surprising aspects of the radiation chemistry of ethylene. 

Figures 1-4 show that when polymerizations were carried out at low concentrations of initiator and/or at low temperatures, the agreement between the model predictions and the experimental data is not so good. This is due to the fact that under those reaction conditions where R is low a large kinetic chain length is expected. When this is so, chain transfer to monomer becomes a reaction to be taken into account, since it markedly influences the chain length of the polymer being formed. A decrease in the instantaneous degree of polymerization, due to chain transfer to monomer, will reduce the concentration of the entangled radicals and, consequently, a decrease in the rate of polymerization is expected.

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