Kinetic chain length radical

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. 

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. 

The block copolymer produced by Bamford s metal carbonyl/halide-terminated polymers photoinitiating systems are, therefore, more versatile than those based on anionic polymerization, since a wide range of monomers may be incorporated into the block. Although the mean block length is controllable through the parameters that normally determine the mean kinetic chain length in a free radical polymerization, the molecular weight distributions are, of course, much broader than with ionic polymerization and the polymers are, therefore, less well defined,... 

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 ... 

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.

Eqs. (26) and (27) apply irrespective of the nature of the initiation process it is required merely that the propagation and termination processes be of the second order. They emphasize the very general inverse dependence of the kinetic chain length on the radical concentration and therefore on the rate of polymerization. The kinetic chain length may be calculated from the ratios k /kt as given in Table XI and the rate of polymerization. Thus, for pure styrene at 60°C... 

At the same rate of polymerization, the kinetic chain length for vinyl acetate is over a hundred times that for styrene on account of the greater speed of propagation relative to termination for vinyl acetate. At a convenient rate of 10 moles/liter/sec., for example, each radical chain generated consumes on the average about 5X10 vinyl acetate units under the conditions stated. 

If reactions other than those considered so far did not take place to an appreciable extent, the average degree of polymerization would be directly related to the kinetic chain length v. Assuming termination by combination of radicals, as is indicated by experiments previously cited, each polymer molecule formed in a monoradical-initiated polymerization would consist of two kinetic chains grown from two other-... 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Kinetic vs. material chain. Kinetically, a chain reaction exists throughout the "life" of the radical, that is, from the initiation of a radical up to its termination by recombination or by disproportionation. The lifetime of a radical determines the so-called kinetic chain length Lp defined as the number of monomers consumed per initiating radical. Lp, by definition, can be calculated from the ratio between the propagation rate Rp to the initiation rate R, or, using steady-state hypothesis (Equation (1)), from the ratio between propagation rate to the termination rate Rt (Equation (3)). 

Equation (4) clearly shows that the number average degree of polymerisation Xn is inversely proportional to the reaction rate Rp, meaning that, in radical chain polymerisation high reaction rates are linked to low molecular masses and vice versa. One way to avoid this dilemma is to use emulsion polymerisation where the lifetime of a radical (i.e., the "kinetic" chain length) is independent of... 

Unlike ionic polymerizations, the termination of the growing free radical chains usually occurs by coupling of two macroradicals. Thus, the kinetic chain length (v) is equal to DP/2. The chemical and kinetic equations for bimolecular termination are shown below (Equations 6.17 and 6.18). 

The kinetic chain length v of a radical chain polymerization is defined as the average number of monomer molecules consumed (polymerized) per each radical, which initiates a polymer chain. This quantity will obviously be given by the ratio of the polymerization rate to the initiation rate or to the termination rate, since the latter two rates are equal. 

The number-average degree of polymerization X , defined as the average number of monomer molecules contained in a polymer molecule, is related to the kinetic chain length. If the propagating radicals terminate by coupling (Eq. 3-16a), a dead polymer molecule is composed of two kinetic chain lengths and... 

Consider the polymerization of styrene initiated by di-t-butyl peroxide at 60°C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rates of initiation and polymerization are 4.0 x 10 11 and 1.5 x 10 7 mol L 1 s 1, respectively. Calculate the values of (jkj), the initial kinetic chain length, and the initial degree of polymerization. Indicate how often on the average chain transfer occurs per each initiating radical from the peroxide. What is the breadth of the molecular weight distribution that is expected, that is, what is the value of Xw/Xnl Use the following chain-transfer constants ... 

It should be noted that the degree of polymerization in an emulsion polymerization is synonymous with the kinetic chain length. Although termination is by bimolecular coupling, one of the radicals is a primary (or oligomeric) radical, which does not significantly contribute to the size of a dead polymer molecule. The derivation of Eq. 4-7 assumes the absence... 

Peroxide crosslinking of the copolymer is more efficient than that of the homopolymer (Table 9-1). The process becomes a chain reaction (but with short kinetic chain length) involving polymerization of the pendant vinyl groups on the polysiloxane chains in combination with coupling of polymeric radicals. The crosslinking of EPDM rubbers is similarly more efficient when compared to EPM rubbers since the former contain double bonds in the polymer chain. 

In transfer reactions the growth of a chain is ended, for example, by transfer of a hydrogen atom from the molecule ZH, but at the same time a new polymer chain is started by the radical Z that is formed simultaneously. Thus, several macromolecules result from one primary radical therefore, the kinetic chain length, i.e., the total number of monomer molecules induced to be polymerized by one primary radical, is much larger than the degree of polymerization of the macromolecules formed. A general scheme is as follows ... 

The short kinetic chain lengths and different product mix at 155°C. in comparison with runs at 100°C. (Tables II and III) have three origins generally lower concentrations of isobutane at 155°C., higher rates of initiation, and more cleavage of tert-BuO radicals. To Reactions 1 to 7, 9, and 10 at 100°C., we need to add at 155°C. the terminating Reaction 12a, the nonterminating Reactions 10a and 12b, and the propa-... 

The quantum yield of photopolymerization, as well as the kinetic chain length ( p/ i), decrease with the square root of the absorbed light intensity. For an absorbed light intensity of 1.06 xlO-4 einsteins/1 x s and borate concentration of 10 mM the photopolymerization quantum yield is 1420. The quantum yield for radical generation is 0.067 [274], giving a kinetic chain length of 2.1 x 104, which compares favorably with the value of 2.9 x 104 reported for the UV photopolymerization of epoxy diacrylate/TMPTA in the presence of air [282]. 

Kinetic chain length is the number of substrate molecules that react during each kinetic chain. 100 C. Walling, Free Radicals in Solution, Wiley, New York, 1957, chap. 3. 

Much of the work with labelled initiators in radical polymerizations is quite independent of determinations of molecular weights, attention being focussed on kinetic chain lengths instead of on molecular chain lengths (10). In a sensitized polymerization, the rate of initiation is identified with the rate at which initiator fragments are incorporated in the polymer to calculate the rate of initiation, it is necessary only to determine the empirical formula shown previously for the recovered polymer and the overall rate of polymerization. No assumptions are required concerning the mechanism of termination or the frequency of transfer processes involving monomer, solvent or polymer. Errors can arise from three causes ... 

This process may well be understood in terms of intramolecular rearrangement of the disilane by a free radical chain mechanism, the average kinetic chain length being about 4. 

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