Chain-length dependent termination

Subject headings polymerization / radical reactions / reaction kinetics / termination chain-length dependence... 

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

Most in depth studies of termination deal only with the low conversion regime. Logic dictates that simple center of mass diffusion and overall chain movement by reptation or many other mechanisms will be chain length dependent. At any instant, the overall rate coefficient for termination can be expressed as a weighted average of individual chain length dependent rate coefficients (eq. 20) 39... 

Table 5.1 Parameters Characterizing Chain Length Dependence of Termination Rate Coefficients in Radical Polymerization of Common Monomers 1...

Treatments (Smith-Ewart,79 pseudo-bulk77) have been devised which allow for the possibility of greater than one radical per particle and for the effects of chain length dependent termination. Further discussion on these is provided in the references mentioned above.77 751... 

Some of the issues associated with RAFT emulsion polymerization have been attributed to an effect of chain length-dependent termination.528 In conventional emulsion polymerization, most termination is between a long radical and a short radical. For RAFT polymerization at low conversion most chains are short thus the rate of termination is enhanced. Conversely, at high conversion most chains are long and the rate of termination is reduced. 

Effect of Chain-Length-Dependent Bimolecular Termination... 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

On the other hand, however, it is not straightforward to calculate the MWDs for intermediate cases using the conventional approach. A notable advantage of using an MC simulation technique is that it can be applied to virtually any type of emulsion polymerization, and can account for the chain-length-dependent bimolecular termination reactions in a straightforward manner [265]. Sample simulation results for instantaneous MWDs were shown [265] that were obtained using parameters for styrene polymerization that were reported by Russell [289]. 

Fig. 13 Effect of particle size on the instantaneous chain length distribution, where bimolecular terminations are chain-length dependent and are by disproportionation...

The chain-length-dependence of bimolecular termination reactions needs to be taken into account in order to be able to accurately estimate the MWD formed, except when very small polymer particles are formed and/or chain transfer reactions dominate over dead polymer chain formation. 

The traditional method of determining the monomer transfer constant is the Mayo method [294,295], where the inverse of the number average chain length Pn is extrapolated to zero polymerization rate. To obtain reliable values, one needs to measure rather large P values to high precision that can then be extrapolated to zero polymerization rate. In addition, linear extrapolation is not guaranteed if bimolecular termination reactions are chain-length-dependent [296]. 

The radical chain length depends on the mechanism of chain breaking. The most common of these is coupling. Here, the chain-breaking (and termination) rate is... 

Computational Aspects of Free Radical Polymerization Kinetics with Chain Length Dependent Termination... 

It is worthwhile to examine the forms of eq n (2) suggested by the existing models of chain length dependent termination reactions. O Driscoll (2) and Yasakawa (4) assumed a geometrical mixing rule expressed as,... 

But with chain length dependent termination this decrease should be less dramatic than without it. This is shown conceptually in Figure 2. 

Bamer-Kowollik, C. Russell, G. T. Prog. Polym. Sci. 2009, in press ( Chain-length-dependent termination in radical polymerization Subtle revolution in tackling a long-standing challenge ). 

Atre S V, Liedberg B and Allara D L 1995 Chain length dependence of the structure and wetting properties in binary composition monolayers of OH and CHg-terminated alkanethiolates on gold Langmuir 3882-93... 

---