Average kinetic chain length

As there is no termination step in a true living polymerization, the growth of chains, once initiated, can stop only when the monomer is completely consumed. In a living polymerization with fast and complete dissociation of initiators the average kinetic chain length will thus be given by 

The maximum value of v is obtained at the completion of reaction or in the limit of r co as 

The average degree of polymerization represents the average number of monomer molecules polymerized per polymer molecule formed. In the case of monofunctional initiation [cf. Eq. (8.5)], the number of polymer molecules formed is equal to the number of chain centers (or initiators) and the number average degree of polymerization then is [cf. Eq. (8.29)] 

Problem 8.4 In an experiment (Szwarc et al., 1956), styrene (9.2 g) was added to 60 mL of tetrahydrofuran containing 3.3x10 mol of sodium naphthalene. Polymerization was carried out at -80°C and after completion (as determined by constant viscosity) an additional 7.7 g of styrene in 50 mL of tetrahydrofuran was added. The final yield was 16.6 g of polystyrene, i.e., about 100% conversion. Calculate the average molecular weight of the final polymer. 

Since sodium naphthalene causes bifunctional initiation, Eq. (8.34) is applicable. At complete conversion of monomer, 

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The average kinetic chain length r is defined as the number of monomer units consumed per active centre formed and is given by R fV (or R tV ). 

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. 

Other Useful Definitions. The number-average kinetic chain length, Vn, is the ratio of the rate of flie propagation rate to the rate of termination ... 

The ratio of the rate of polymerization and the rate of initiation is an important parameter in chain polymerization reactions and is known as average kinetic chain length y. This parameter gives the average number of monomer units per chain initiated. Using rel. (2.3.17) and (2.3.12) the expression for y can be obtained in the form ... 

The average kinetic chain length (u) or degree of polymerization (DP)... 

The Poisson distribution written in the bottom boxed equation of Fig. 3.31 approaches the binomial molar mass distribution for the case that p is small and the average kinetic chain length v = No/N is large, a condition approached for most hving polymers. It is an equation that can be calculated much more easily than the binomial distribution. Analyzing the Poisson distribution, one finds that polymerizations without termination lead to rather narrow molar mass distributions as discussed in Sect. 3.3 with Figs. 3.39 1. 

Gibbs free energy of polymerization enthalpy of polymerization entropy of polymerization residence time average kinetic chain length... 

It should be noted that is exactly the same as the average kinetic chain length in emulsion polymerization. This is simply because the termination reaction taking place in the monomer-swollen polymer particles involves a polymeric radical and an incoming oligomeric radical. 

The reduced molecular weight of the irradiated sample is less than the average kinetic chain length for the non-irradiated sample, hence for a given scission, less product is evolved and the stability is increased. 

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