Termination kinetics molecular weight distributions

More recently it has been shown that in the polymerization with TT-crotylnickel iodide the order in monomer falls from a value close to unity at [M] below 0.5 mole 1" to below 0.5 at [M] > 4 mole 1 . These observations have been interpreted in terms of scheme (c) on p. 162, namely coordination of two monomer molecules with the catalyst and with most of the catalyst existing in the complex (inactive) state. The molecular weights of the polymers are double those calculated from the kinetic scheme put forward [61] and this is attributed to coupling of live polymer chains on termination [251]. Molecular weight distributions are binodal consistent with slow propagation and transfer. 

Due to the low reaction temperature and the use of chain terminator, the molecular weight distribution in interfacial synthesis is kinetically controlled and may be far from thermodynamic equilibrium. In two parametric studies Mills [179] and Munjal [180] have tried to model the full molecular weight distribution of polycarbonate. Varying the ratio of mass transfer/kinetic rates, they show how mass transfer limitations can lead to a higher polydispersity or a higher oligomer content. 

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,... 

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... 

Figure 8.16 Type of flow and kinetics influence the molecular weight distribution of polymer (a) duration of polymerization reaction (life of active polymer) is short compared to the reactor holding time (b) duration of polymerization reaction is long compared to the reactor holding time, or where polymerization has no termination reaction. Adapted from Denbigh (1947).

The molecular weight distribution and the average molecular weight in a free-radical polymerization can be calculated from kinetics. The kinetic chain length v is defined as the average number of monomers consumed per number of chains initiated during the polymerization. It is the ratio of the propagation rate to the initiation rate (or the termination rate with a steady-state approximation) ... 

The kinetic scheme with constant reaction of the polymer/monomer droplet increases fairly quickly with conversion, and the mobility of the polymer chains rapidly falls below the mobility of the monomer. The reduced diffusion of live polymer chains in the droplet will reduce the rate of termination of polymerization. The associated increase in the number of radicals will cause a rapid increase in the polymerization rate. This phenomenon is well known as the Trommsdorf or gel effect [8,9]. The gel effect causes a growth of the polymer chain length and widening of the molecular weight distribution (Figure 9.5). 

It is doubtful, however, that a true living system without termination or transfer exists in these polymerizations instead we believe that the narrow distributions may result from a combination of essentially instantaneous initiation, relatively long kinetic lifetime, and kinetic termination without transfer. H. Morawetz has derived an equation relating the molecular weight distribution to the relative rates of propagation and termination and the concentration of active species for such a case ( ). The equation accounts for the possible occurrence of narrow distributions, and we are presently experimentally investigating these calculations and predictions for the polymerization of the p-isopropyl monomer. 

Using the primary bromoacetyl-based pTHF macroinitiator (Mn=2100, Mw/Mn=1.20) with a CuBr/bpy catalyst for the ATRP of St resulted in poor initiation efficiency (—50%) and broad molecular weight distributions [353]. However, when the tertiary bromoisobutyryl-based pTHF macroinitiator was employed (Mn=1700, Mw/Mn=1.25), the kinetic plot had little deviation from linearity to suggest either slow initiation or termination and the molecular weights increased... 

Problem 6.43 The bulk polymerization of methyl methacrylate (density 0.94 g/cm ) was carried out at 60°C with 0.0398 M benzoyl peroxide initiator [64]. The reaction showed first order kinetics over the first 10-15% reaction and the initial rate of polymerization was determined to be 3.93x10 mol/L-s. From the GPC molecular weight distribution curve reported for a 3% conversion sample, the weight fraction of polymer of DP = 3000 is seen to be 1.7x10 . Calculate the weight fraction from Eq. (6.217) to compare with this value. [Use the following data Cj 0.02 Cm = 10- fk = 2.7 x 10 s kt = 2.55x10 L/mol-s fraction of termination by disproportionation = 0.85 ]... 

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