Length Dependence of kt

The discussion of the rate of bimolecular termination has, up to now, been mainly of a qualitative nature. The scaling of average or macroscopic kt values with viscosity, solvent effects and coil dimensions were discussed without much attention for the chain-length dependence of this process. This dependence originates from the simple fact that free-radical termination is a diffusion-controlled process. Consequently, the overall mobility of polymer chains and/or polymer chain ends determine the overall rate of radical loss in a polymerizing system. As small chains are known to be much more mobile than large ones, the chain length of radicals can be expected to have a profound effect on the termination kinetics. 

Macroscopic kt values are thus made up of a weighted sum of all possible termination events between macroradicals of different chain lengths, each being characterized by a different rate coefficient. These microscopic termination coefficients are usually depicted as kY, where i and j represent the chain lengths of the terminating macroradicals involved. The relation between the average kt, denoted as kC, and microscopic termination rate coefficients follows simply from equalizing the macroscopic and microscopic rates of the loss of radicals, and was first put forward by Allen and Patrick [138]  

In the older literature one can encounter quite a number of papers suggesting that bimolecular termination is not chain-length dependent e.g. 36, 66, 68, 139-143] Experimental evidence, however, has disproved these suggestions and numerous papers have proven termination to be chain-length dependent. The evidence takes several forms and has been obtained employing different experimental approaches, which can roughly be divided in three classes (i) termination studies of free-radical polymerizations, (ii) termination studies of non-propagating species and (iii) diffusion-controlled mimic reactions. 

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The chain length dependence of kt is normally quantified by the following equations A macroscopic—ie experimental—kt value may be obtained by the following averaging procedure (335) ... 

In the literature, numerous models have been reported describing the chain-length dependence of kt. Some of these are based on careful considerations of the motions of polymer chain ends, others are based on the translational diffusion of polymer coils as a whole and yet others use more empirical approaches. Not only are the models conflicting regarding their predictions and underlying mechanisms, also literature data do not yield an unambiguous picture about the chain-length dependence. Besides, because of the limitation of experimental techniques to the measurement of macroscopic termination rates, the validation of models is a cumbersome and difficult task. 

More recent examples can be found in the work of e.g. Matsumoto and Mizuta [154]. They found a chain-length dependence of kt by studying the free-radical polymerization of a substituted methacrylate trans-A-tert-hu. y cyclohexyl methacrylate) by ESR. Their results for for various monomer, initiator, transfer agent and viscosity modifier concentrations, could be summarized in terms of equation 2.11 by = 0.28 (10" < < 10 ). At larger chain... 

In the sections below it will be discussed how the kinetic information regarding the termination reactions can be extracted from the MWD. After a brief discussion of some of the work reported in literature, it will be shown that also here the single-pulse laser experiments have some very attractive features. Similarly to the case for studying the time-resolved data from these kind of experiments, also the MWD can reveal model-independent information about the chain-length dependence of kt. 

At first sight, the results shown in figure 3.29 do not look encouraging. The impact of the value of on the determination of the chain-length dependence of kt is rather large. 

A possible solution to the above problem may simply arise from the use of less flexible curve fit functions. Although these functions will be less sensitive towards noise, there is also the risk of losing too much flexibility in the fitting of the experimental data. If, for instance, a too simple function for the fitting of the experimental data would be used, it might not be possible to obtain the correct chain-length dependence of kt anymore. In other words, a too simple function ruins the model-independent nature of the time-resolved procedure, which is the key feature of this method. 

Chain-Length Dependence of kt for a Homologous Series of Acrylates A Qualitative Discussion... 

To obtain accurate quantitative information about the chain-length dependence of kt, several experimental parameters must first be tested. So far, only the results for experiments in which 20 pulses were applied have been shown. However, if the results might be (highly) dependent upon the amount of conversion, then a quantitative expression for the chain-length dependence of h has to include a conversion parameter. 

Furthermore, the MWD method should certainly be applied to study the effects of solvent quality upon the chain-length dependence of kt. As the solvent quality has a profound effect on the dimensions of polymer coils in solution, a change in this quality will reveal... 

In conclusion it can be said that the MWD method is capable of determining the chain-length dependence of kt model-independently. This method has been validated theoretically and, as long as the number MWD can be determined and scaled correctly, the method is robust and reliable. In this thesis, the first model-independent results have been reported for a set of three acrylates. These results will enable a better description of the overall kinetics of free-radical polymerizations and better predictions of the resulting MWDs and polymer properties. It is sincerely hoped that this method and lines of thought presented will find continuation in future scientific work by others in this field of great scientific interest and practical importance. 

Summarizing the above, it can be concluded that single-pulse pulsed-laser polymerization techniques are amongst the most powerful techniques that are nowadays available to study the chain-length dependence of termination reactions. When using a dedicated kinetic analysis, as presented in this thesis, model-independent data for the chain-length dependence of kt can be obtained. These data allow for better predictions for the MWD of the final polymer product and so of the final product properties. 

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