Scaling of the number MWD

In the above discussion little attention has been devoted to the exact scaling of the number MWD. In the simulations the value of [i ]o was exactly known and the number of radicals present after a certain time span at the end of the simulation, was also known. These numbers were used to scale the number MWD, leading to good agreement between input and output values of kt. However, these parameters are usually not known with great accuracy in real experimental studies while this is a essential prerequisite for obtaining accurate kt data Hence, problems due to inaccurate scaling of the MWD must be anticipated. 

In real experimental studies, there seem to be two basic routes that can be used to perform the scaling of MWDs (i) either [i ]o should be known and the number MWD should be scaled accordingly or (ii) the weight MWD should be scaled according to the conversion per laser pulse. Both methods scale the complete MWD (in the simulation results presented so far only a part of the MWD was rescaled) and are of limited accuracy. Consequently, additional systematic deviations will be introduced into the MWD method on top of the side reactions discussed above. It is therefore important to thoroughly investigate these effects. 

The above discussion about scaling the MWD by using k] values might seem to eliminate all problems that are encountered in the scaling of the MWDs. Unfortunately, this is not the case. Scaling of a complete number MWD to half the value of [7 ]o is not correct and also here the same parameter as used in the simulations, K res, must be introduced. This can be understood from the following reasons  

Determination of CLD Termination Rate Coefficients Theory Validation 

An accurate determination of after a certain time span (or at a specific chain length being smaller than the exclusion limit) is not very easy. Three options seem to be more or less readily available, here listed in order of preference  

---

Before discussing the parameters needed in the scaling of the number MWDs, some remarks regarding the quality of the SEC set-up should be made. Previous PLP studies of acrylates have reported a number of problems with broad and featureless MWDs, especially at higher temperatures [13, 16, 21, 32]. In this study, the MWDs obtained by PLP are fairly narrow, cf. for instance the MWDs as shown in figure 4.2 with typical MWD examples for acrylates as reported in several other studies [13, 16, 21, 25, 26], and up to 25°C the PLP peaks can clearly be distinguished from the background polymer. The experiments for EA... 

To increase the accuracy of the scaling of the number MWD, there seem to be two experimental techniques (or routes) that might prove to be useful. First of all, a combination of time-resolved single-pulse pulsed-laser polymerization with subsequent analysis of the MWD of the formed polymer product can be employed. From the time-resolved trace, accurate data on the radical concentration versus time can be deduced, which can then be used in the scaling of the number MWD. An alternative method to improve the scaling accuracy might arise form the use of mass-spectrometry techniques. Polymeric material with... 

In the kinetic analysis, the fact that termination and chain transfer are second and first order processes with respect to the radical concentration, respectively, can then be exploited. The scaling of the number MWD now has to be done such that the radical concentration versus time that is derived from this distribution, is in agreement with the amount of material that is found to originate from chain transfer to monomer. Hence, the degree of freedom in the scaling of the number MWD is limited by a second kinetic condition. It should be noted, however, that knowledge of the ratio of termination by combination over disproportionation is needed for that. 

A first idea about the effects of scaling can be seen directly from equation 3.34. This equation reveals that the parameter F is actually the scaling parameter of the number MWD and any inaccuracy in this parameter will linearly influence the apparent value of kt. Figure 3.27 shows the effects of the variation of the parameter Fby a factor 2 (the simulation results are identical to those presented by the figures 3.14 to 3.16). As expected, the differences... 

The investigations presented in this thesis have revealed that the MWD method is certainly a method with great potential for studying the chain-length dependence of termination reactions. However, the leap from the theoretical study presented in chapter 3 to the experimental one presented in chapter 4, introduces two additional complications (i) the correct shape of the number MWD must be determined and (ii) this number MWD must be scaled correctly. 

The solution of the first problem is easy to overcome and in this simulation section the number MWD was rescaled such as to correspond to the exact value of [i ]o. (Some discussion regarding scaling will be provided at the end of this section). The second problem cannot be overcome easily with a continuous integration procedure and was accepted as an inherent inaccuracy of the numerical procedure. 

In order to scale the number MWD correctly, the values of [i ]o and [i ]res must be known. As explained in the previous chapter, this can be accomplished by using good estimates for Df and average kt values. As we are working at very low conversions, both parameters will be estimated for the case of a bulk monomer solution in which no polymer is present. 

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. 

If the total number MWD were to be scaled to half the value of [i ]o, a kinetic deficiency of the MWD method will show up. Imagine for instance an experimentally obtained... 

The scaling factor V is no longer present and, hence, the values of 2i stem from a correctly scaled number distribution. If the maximum chain length of the MWD that is being... 

Before kinetic information can be extracted from this number MWD, two criteria must be met (i) the MWD must be of the correct shape and (ii) it must also be scaled correctly, according to equation 4.3. The former criterion, however, could be systematically violated in several ways. This can be the result of inaccurate SEC calibration, inaccurate Mark-Houwink coefficients, non-linear baseline drift, the occurrence of column broadening during a SEC analysis and the non-linear optical properties of a series of oligomers. It goes beyond the scope of this thesis to discuss all these effects. Here, the discussion will be limited to only two of these effects column broadening and non-linear optical properties of oligomers. 

---