Chain length dependence polymerization

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. 

Methods for measurement of kp have been reviewed by Stickler,340 41 van Herk Vl and more recently by Beuermann and Buback.343 A largely non critical summary of values of kp and k, obtained by various methods appears in the Polymer Handbook.344 Literature values of kp for a given monomer may span two or more orders of magnitude. The data and methods of measurement have heen critically assessed by IUPAC working parties"45"01 and reliable values for most common monomers are now available. 43 The wide variation in values of kp (and k,) obtained from various studies docs not reflect experimental error but differences in data interpretation and the dependence of kinetic parameters on chain length and polymerization conditions. 

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

Bamford43,59 63 has proposed a general treatment for solving polymerization kinetics with chain length dependent kt and considered in some detail the ramifications with respect to molecular weight distributions and the kinetics of chain transfer, retardation, etc. 

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. 

Because of the (chain-length dependent) restricted solubility of polymers in hydrocarbons, solution polymerization requires higher temperatures and / or higher pressures. Technologically, solution polymerization processes are similar to the high-pressure LDPE process, see chapter 3, and will not be discussed here. 

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]. 

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]. 

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

The absorption spectra of silylene polymers and telomers have been extensively reported and it has been shown that the position of the absorption maximum shifts to the red with increasing degree of polymerization (6,15-19). We and others have reported the existence of narrow, line like fluorescence with no observed vibrational structure for a number of medium and high molecular weight polymers (2,9,16,20,22). The narrow, line-like fluorescence and the chain length dependence of the absorption spectra both indicate substantial delocalization of the electronic states involved in the transitions. 

The chain length depends on the relative quantities of polymer and initiator that are used but also on the transfer frequency. The mass polydispersion of the produced polymer is always large. The lifetime of a radical varies from 10 1 to 10 seconds. The polymerization reaction stops spontaneously by deactivation. 

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 ). 

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