Chain polymerization measurement rates

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. 

Five different types of rate constants are of concern in radical chain polymerization—those for initiation, propagation, termination, chain transfer, and inhibition. The use of polymerization data under steady-state conditions allows the evaluation of only the initiation rate constant kd (or kt for thermal initiation). The ratio kp/k J2 or kp/kl can be obtained from Eq. 3-25, since Rp, Rj, and [M] are measurable. Similarly, the chain-transfer constant k /kp and the inhibition constant kz/kp can be obtained by any one of several methods discussed. However, the evaluation of the individual kp, k ktr, and kz values under steady-state conditions requires the accurate determination of the propagating radical concentration. This would allow the determination of kp from Eq. 3-22 followed by the calculation of kt, kIr, and kz from the ratios kp/ltj2, ktr/kp, and kz/kp. 

The life-time, r, of the radicals can be determined from the ratio of overall rates of polymerization measured at the steady- and unsteady state as a result of intermittent illumination by the rotating sector. In Fig. 3.3-10 the rate constant, kp, of chain propagation (left) and kh that of termination (right), are plotted versus the pressure. Both rate constants increase with increasing temperature. The energy of activation of chain propagation is Ep = 37 kJ/mol, and that of chain termination is E, = 9.9 kJ/mol. The influence of pressure is... 

When the retarded polymerization proceeds at a measurable rate (i> ) and long chains are formed, it is better to use the approximations of Kice [7] or Jenkins [8],... 

Figure 14.8 shows TREPR field-swept spectra of the PMMA polymeric radical la in five different solvents at room temperature and similar concentrations. At first glance these spectra look very similar, but there are subtle differences, especially in the broader packets of lines from the polymeric radical. Even the lines not broadened by hyperfine modulation show slightly different linewidths and positions. In Fig. 14.9, kinetic profiles of the TREPR signal of the main-chain polymeric radical for each solvent are presented, obtained by measuring the intensity of one of the strong sharp central transitions in the spectra in Fig. 14.8. There are large differences in the decay rates of these signals at room temperature. The decay is fastest in dioxane (Fig. 14.9A), while in methylene chloride (Fig. 14.9B) and chloroform (Fig. 14.9C) it is slowest.

The use of chemical sensitizers such as benzoyl peroxide, cumene hydroperoxide, or azo-bis-isobutyronitrile, which decompose thermally to give free radicals in a convenient temperature range (i.e., 60 C to 150 C), makes it possible to study polymerizations over an extended temperature range. The form of the rate law with chemical initiations would be given by setting III = 2k (ln)< >i in Eq. (XVI.10.4). Here (In) is the initiator concentration, k I its specific rate constant of decomposition which can usually be measured independently, and is the efficiency with which its radicals initiate chains. The measure of t is subject to the difficulties already indicated in connection with the photolysis systems. ... 

The determination of the various rate constants (ki, kp, kt, kts, ktr) for cationic chain polymerization is much more difficult than in radical chain polymerization (or in anionic chain polymerization). It is convenient to use Rp data from experiments under steady-state conditions, since the concentration of propagating species is not required. The Rp data from non-steady-state conditions can be used, but only when the concentration of the propagating species is known. For example, the value of kp is obtained directly from Eq. (8.143) from a determination of the polymerization rate when [M J is known. The literature contains too many instances where [M" "] is taken equal to the concentration of the initiator, [IB], in order to determine kp from measured Rp. (For two-component initiator-coinitiator systems, [M" ] is taken to be the initiator concentration [IB] when the coinitiator is in excess or the coinitiator concentration [L] when the initiator is in excess.) Such an assumption holds only if Ri > Rp and the initiator is active, i.e., efficiency is 100%. Using this assumption without experimental verification may thus lead to erroneous results. 

Let US now examine if the chain length or degree of polymerization (jDP ) of a polymer product can be calculated from the measured rate of polymerization coupled with a knowledge of the relevant kinetic parameters. 

From Eqs. (1) and (2) it can be seen that the reaction rate is related to the evolution of the measured heat. For single reactions or one dominant reaction, like the propagation reaction in free-radical or chain polymerization processes, Qr is directly proportional to the measured heat generated by the reaction. For complex systems, where consecutive or parallel reactions with similar thermal contributions occur, the signal corresponds to the addition of all heat contributions, i.e. the macrokinetic. The final and simplified heat balance equation used for the polymerization part is given in Eq. (7) ... 

When AT,iV-dimethylaniline (DMA) or naphthalene is added to styrene-MA systems, the incorporation of MA in the copolymers is increased and the rate of copolymerization decreases.The rate drop is attributed to increased degradative chain transfer. Dimethylaniline-MA or naphthalene-MA complexes bring about a shift of monomer ratios in the copolymer. The free radicals which contribute to the chain transfer must be predominantly of the type that have a MA unit at the end, since it is known polystyryl radicals do not react with DMA donor. These free radicals react with the DMA-MA CTC to form transfer radicals with the MA component of the CTC. Thus, a low-grade MA-MA block is formed by a reinitiation mechanism and the MA content in the copolymer increases. This supports a CTC polymerization mechanism concept, since in more polar solvents or in the presence of donor additives the amount of donor monomer-MA CTC formed would be less and the rate of copolymerization reduced accordingly. Tsuchida and coworkers, from measured rate studies of the copolymerization of styrene with MA in a variety of solvents, support this concept and conclude that copolymerization of the styrene-MA pair clearly involves propagation in part by a CTC. 

Figure 1 shows the reactions of AH, and it can be seen that major processes using up AH are the formation of trimer, the MAH process, and chain transfer. The rate constants for all three of these reactions can be estimated in the following way (6,6a) If it is assumed that all of the trimeric product A-Sty is produced by an ene reaction (eq in Figure lA) rather than by radical recombination, reaction j, then the rate constant for the ene reaction of AH can be calculated from the rate of appearance of the trimer A-Sty measured by Buchholz and Kirchner (22) The rate constant for transfer of AH can be calculated from its transfer constant, obtained from our computer simulation (23), and the known value of k for styrene. And finally, the rate constant of the MAH reaction of AH can be calculated from the rate at which radicals are formed in styrene (calculated from the observed rate of thermal polymerization), assuming that all radicals come from this postulated MAH reaction. The steady state concentration of AH was measured by Kirchner, and is 6 x 10M at about 60 . 

Monomer conversion can be measured by different means dilatometry, spectrometry, sampling, and gravimetry for variable reaction times Rp is equal to the slope of the straight line drawn from the plot of the monomer conversion versus the reaction time. Knowing Ri, it is relatively easy to obtain k /kf. This value is an important feature of chain polymerizations indeed, for a same rate of initiation, this value is directly proportional to the rate of polymerization of the monomer considered it is also proportional to the average length of the polymer chains formed. Some typical values are given in Table 8.12. 

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. 

This suggests that polymerizations should be conducted at different ratios of [SX]/[M] and the molecular weight measured for each. Equation (6.89) shows that a plot of l/E j. versus [SX]/[M] should be a straight line of slope sx Figure 6.8 shows this type of plot for the polymerization of styrene at 100°C in the presence of four different solvents. The fact that all show a common intercept as required by Eq. (6.89) shows that the rate of initiation is unaffected by the nature of the solvent. The following example examines chain transfer constants evaluated in this situation. 

The absolute rate constants for attack of carbon-centered radicals on p-benzoquinone (38) and other quinones have been determined to be in the range I0M08 M 1 s 1.1 -04 This rate shows a strong dependence on the electrophilicity of the attacking radical and there is some correlation between the efficiency of various quinones as inhibitors of polymerization and the redox potential of the quinone. The complexity of the mechanism means that the stoichiometry of inhibition by these compounds is often not straightforward. Measurements of moles of inhibitor consumed for each chain terminated for common inhibitors of this class give values in the range 0.05-2.0.176... 

When one compares the brutto polymerization rate constants, a measure of the reactivity of monomers during cationic homopolymerizations is obtained. It was found for p-substituted styrenes that lg kBr increased parallel to the reactivity, which the monomers show versus a constant acceptor 93). The reactivity graduation of the cationic chain ends is apparently overcomed by the structural influence on the monomers during the entire process of the cationic polymerization. The quantitative treatment of the substituent influences with the assistance of the LFE principle leads to the following Hammett-type equations for the brutto polymerization rate constants ... 

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

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