Experimental Determination of Rp

It is appropriate at this point to briefly discuss the experimental procedures used to determine polymerization rates for both step and radical chain polymerizations. Rp can be experimentally followed by measuring the change in any property that differs for the monomer(s) and polymer, for example, solubility, density, refractive index, and spectral absorption [Collins et al., 1973 Giz et al., 2001 McCaffery, 1970 Stickler, 1987 Yamazoe et al., 2001]. Some techniques are equally useful for step and chain polymerizations, while others are more appropriate for only one or the other. Techniques useful for radical chain polymerizations are generally applicable to ionic chain polymerizations. The utility of any particular technique also depends on its precision and accuracy at low, medium, and high percentages of conversion. Some of the techniques have the inherent advantage of not needing to stop the polymerization to determine the percent conversion, that is, conversion can be followed versus time on the same reaction sample. 

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The reader is cautioned that there is often a considerable divergence in the literature for values of rate constants [Buback et al., 1988, 2002], One needs to examine the experimental details of literature reports to choose appropriately the values to be used for any needed calculations. Apparently different values of a rate constant may be a consequence of experimental error, experimental conditions (e.g., differences in conversion, solvent viscosity), or method of calculation (e.g., different workers using different literature values of kd for calculating Rt, which is subsequently used to calculate kp/kXJ2 from an experimental determination of Rp). 

The exact calculation of icorr for a given time requires simultaneous measurements of Rp and anodic and cathodic Tafel slopes (/> and be). Computer programs have been developed for the determination of precise values of /corr according to Eqs. (2) and (3). Experimental values of Rp (2p contain a contribution from the uncompensated solution resistance... 

Work in groups of three. Equation 3.75 can be re-written to reflect the fact experimental determination of polymerization rates typically yield a single rate constant, called the apparent rate constant, kapp, which is a composite of the three different rate constants, ki, kt and kp. If we call the rate of disappearance of monomer concentration, —d[M /dt the rate of polymerization, Rp, then we can rewrite Equation 3.75 as... 

However, experimental determination of logP does include correlation with such properties. For example, the ElogD method developed by Lombardo et al. [67] uses RP-HPLC retention data to determine octanol-water distribution coefficients at pH 7.4 for neutral and basic drugs in Pfizer. Moreover the authors used the same method to determine ElogD at pH 6.5, thus calculating important parameters for intestinal absorption [68],... 

Especially when calibrated with standard compounds relative to the classical shake-flask method, rp-HPLC is the method of choice for the experimental determination of partition coefficients. The liability to large variation in measured log for the highly lipophilic compounds (log > 5) subjects the experimental data to major uncertainties and for such molecules calculation is generally preferable (Taylor, 1990). Reported log P >1 (e.g. for some chlorinated dioxins up to 11), corresponding to concentration differences between the aqueous and the 1-octanol phase of about 10 and more are not exact values, but reflect the accuracy of the experimental analytical techniques used they may be subject to major uncertainties of 2 log units. The respective data have to be treated with great caution in QS AR studies, because at best they indicate the order of magnitude of the compounds lipophilicity. 

This equation is similar to that for the ordinary polymerization, indicating that Rp is independent of the concentration of P-N. In fact, the polymerization rate experimentally determined in the presence of P-N agreed with the rate of thermally initiated polymerization without any initiators. The production of the polymer induced a decrease in the Rvalue because of the gel effects, resulting in an increase in the rate. The suppressed gel effects in the presence of TEMPO have also been reported [233]. Catala et al. interpreted the independence of the polymerization rate from the nitroxide concentration with the terms of the association of domant species. However, there is no experimental evidence for the association [229,234,235]. 

Table 3-10 shows the values of the various concentrations, rates, and rate constants involved in the photopolymerization of methacrylamide as well as the range of values that are generally encountered in radical chain polymerizations. For the methacrylamide case, the experimentally determined quantities werei ,-, (Rp)s, [M], [I], kp/ltj1, ts, and kp/kf. All of the other... 

The determination of the individual rate constants requires the determination of kp, a difficult task and one that has not often heen performed well [Dunn, 1979 Kennedy and Marechal, 1982 Plesch, 1971, 1984, 1988]. The value of kp is obtained directly from Eq. 5-31 from a determination of the polymerization rate. However, this requires critical evaluation of the concentration of propagating species. The literature contains too many instances where the propagating species concentration is taken as equal to the concentration of initiator without experimental verification. Such an assumption holds only if Rp < Rt and all the initiator is active, that is, the initiator is not associated or consumed hy side reactions. 

Numerous recent reviews and guidelines have been published in this field [5,84,92]. Therefore, in this part, we summarize the basic principles only. Briefly, lipophilicity determination by RP-LC is based on the partitioning of the solute between an apolar stationary phase and a polar mobile phase. The experimental retention factor (log k)... 

In spite of these caveats, several experimental techniques can be applied generally. In solution, determination of percent conversion of monomer versus time of irradiation can be used to evaluate rates of polymerization, Rp. Relative or absolute rates of polymerization can be evaluated as a function of light intensity (Ia), monomer concentration, or in the presence of added inhibitors. In the presence of good inhibitors, the time of the inhibition period can be measured and related to the rate of initiation by... 

Experimentally determined retention times or capacity factors (k) generated by reverse phase, usually octadecylsilane (ODS), high performance liquid chromatography (RP-HPLC) have been used widely to estimate Kow values (McDuffie, 1981 Haky and Young, 1984 Sarna, 1984 Doucette and Andren, 1988). More recently, this approach has been used to directly estimate Koc (Vowles and Mantoura, 1987 Hodson and Williams, 1988 Szabo et al., 1990 Kordel et al., 1993 Kordel et al., 1995 Hong et al., 1996). This is not strictly an estimation method because it relies on the acquisition of experimental retention times. 

The contributions of (FC) to k t tend to be very large, as noted above, and the exponential dependence of ket on the experimental uncertainties in the determination of Franck-Condon parameters is often large enough to overwhelm the determination of 7/rp from rate constant measurements. This has made systematic studies of this parameter difficult and controversial. That is less than unity for many reactions, particularly of Co /Co couples, has been demonstrated by the contrasting effects (compared to Ru /Ru couples) of purely electroiuc, ion-pair charge transfer perturbations of the rate constant (this is a superexchange contribution), and by the complex dependencies of the electron-transfer rates of simple coordination complexes on the intensities of external magnetic fields. ... 

The effect of the pressure, temperature and pore radius on the separation factor is investigated also by Eichinann and Werner [19] using Eq. (9.34) with a constant and experimentally determined value of P for eiU gas membrane combinations, in contrast to Wu et al. who fitted the value of p for each gas membrane combination. Figure 9.14 shows the effect of the pressme ratio Pj. for different mean pressure levels P (assuming a linear pressure drop in the membrane) on the separation factor of a N2/CO2 mixture (ideal separation factor equals 1.25) in a membrane with pore radius Rp = 0.03 pm. 

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