Chain transfer molecular distribution from

Throughout this section we have used mostly p and u to describe the distribution of molecular weights. It should be remembered that these quantities are defined in terms of various concentrations and therefore change as the reactions proceed. Accordingly, the results presented here are most simply applied at the start of the polymerization reaction when the initial concentrations of monomer and initiator can be used to evaluate p or u. The termination constants are known to decrease with the extent of conversion of monomer to polymer, and this effect also complicates the picture at high conversions. Note, also, that chain transfer has been excluded from consideration in this section, as elsewhere in the chapter. We shall consider chain transfer reactions in the next section. 

C. H. Bamford and H. Tompa, J. Polymer Sci.j 10, 345 (1953), first derive the moments of the distribution for the case of chain transfer to polymer. They then obtain the molecular weight distribution from these moments by appropriate mathematical methods. Their procedure should be applicable to a wide variety of polymerization mechanisms. 

RAFT polymerization of two anionic acrylamido monomers sodium 2-acrylamido-2-methylpropane-sulfonate, AMPS, and sodium 3-acrylamido-3-methyl-butanoate, AMBA, (Scheme 29) was conducted in water at 70 °C using 4,4/-azobis(4-cyanopentanoic acid) as the initiator and 4-cyanopentanoic acid dithiobenzoate as the RAFT chain transfer agent [80]. The synthesis was initiated either from one monomer or the other leading to narrow molecular weight distributions in both cases (Mw/Mn < 1.2). 

A number of interesting and non-obvious insights into molecular weight distributions can be gained from these simulations. For example, Fig. 3 demonstrates the effect of X on M IM as a function of C0 for irreversible chain transfer where C = 0. 

Initially the polymer molecular weight distribution obeys a Poisson distribution, typical of a chain growth reaction without chain transfer. Since the reactions are reversible, at a later stage, also the equilibration between the polymers becomes important and a broad distribution of molecular weights is obtained. As can be seen from Figure 16.5 the presence of linear alkenes causes chain termination (chain transfer) and thus low molecular weights are produced if the cycloalkenes are not sufficiently pure. 

For addition polymerisation without chain termination or chain transfer, eqns. (73) and (77) may be used for a batch reactor when fe = fep. Here, the growing chains have similar histories and hence the final molecular weight distribution can be very narrow. Similar results would be expected from a plug-flow reactor. The mole fraction of A , 7 , is given by... 

If free-radical polymerisation is carried out in an ideal back-mixed flow reactor, the concentrations of the reactant species become constant and the molecular weight distributions can be obtained from eqns. (83) and (84). Figure 8 shows how changes in P /Pn with conversion compare for the two reactor types. These plots represent idealised behaviour, in practice, Pw/Pn will be influenced by changes in at high conversion and by the occurrence of chain transfer reactions. 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

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 ... 

The mechanism of the polymerization of this monomer has been studied in far greater detail than any other. It is clear from the outset that a much more complex mechanism is involved than is the case for olefins. A large proportion of the initiator is used to form polymer whose molecular weight is only a few hundreds and the overall molecular weight distribution is so broad as to be rivalled only by those found in polyethylene produced by the high pressure process (19, 39). The initiator disappears almost instantaneously on mixing the reactants (19, 38). Under these conditions, an almost monodisperse polymer would be expected if chain transfer or termination processes are absent. 

Table II shows molecular weight distributions of products from monomer mixtures A and B using 3% dicumyl peroxide as initiator. The molecular weight distributions of the products from the six polymerizations are 3 or less. When, however, the percent of dicumyl peroxide was decreased in the reaction mixture, considerably wider molecular weight distributions resulted (Table III). With less initiator, the chains grow longer and terminate more often by chain transfer.

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