Transfer and Cross-termination Kinetics

The midchain radical kinetics was studied by SP–PLP–EPR between 75 and 95 °C, where MCRs are the dominant radical species. The measured MCR concentration vs time profiles were fitted by PREDICI^® on the basis of the reaction steps listed in Figure 5.7.

Figure 5.7: Reaction steps implemented into the PREDICI^® model for fitting MCR concentration vs time profiles deduced from SP–PLP–EPR experiments between 75 and 95 °C. The composite-model parameters for SPR homo-termination, α_s, α_l, and i_c, were adopted for cross-termination from the low-temperature experiments described above.

Reaction Step Reaction Ref.

laser induced

initiation see text

SPR propagation Lacík et al.²⁹

SPR-SPR

homo-termination this work

backbiting this work

MCR propagation this work

SPR-MCR (cross-)

termination this work

5 Termination and Transfer Kinetics of Acrylamide in Aqueous Solution

78

The laser-induced decomposition of Darocur^® was assumed to be much faster than a single SPR propagation step.⁴⁷ The rate coefficient for addition of a monomer molecule to the photoinitiator-derived primary radical, ki, was estimated from ki = 10⁴∙kps, to ensure rapid initiation and to exclude an impact of initiation on the monomer concentration vs t profile.^47,179,180 The propagation rate coefficient, kps, including its dependence on AAm concentration in aqueous solution, was taken from literature.²⁹ SPR termination was estimated via the composite-model parameters deduced from the experiments at –5°C with only k_t^ss(1,1) being adjusted, by the correlation through fluidity, to the actual polymerization temperature. Backbiting was treated as independent of chain length with the restriction of at least three monomer units being required for MCR formation by a [1,5]-H-shift reaction. Even at high temperatures, no indication for β-scission was found. MCR propagation kinetics was assumed to exhibit the same dependency on monomer concentration as kps

, but to differ in absolute value. The associated rate coefficient, kpt

, was expressed by k_p^t = a∙k_p^s, with a being a fit parameter for each temperature.

As reported by Fröhlich et al., the composite-model parameters may differ for SPRs and MCRs.⁹⁹ PREDICI^® simulations using different values for αs, αl and ic of MCRs, however, showed no significant impact on the fitting result. Thus the MCR-SPR cross-termination rate coefficient, ktst, was implemented by ktst(1,1) = b∙k_t^ss(1,1) with the chain-length dependence being entirely contained in ktss(1,1). Note that ktst(1,1) and kttt(1,1), the MCR homo-termination rate coefficient, are hypothetical quantities introduced for applying the Composite Model. PREDICI^® simulations revealed that even extensive variation of the kttt(1,1) has only a negligible impact on the MCR concentration vs time traces within the range of polymerization conditions under investigation (see Appendices). The situation is different for chemically initiated polymerizations at temperatures at which the molar fraction of MCRs is very high. A similar conclusion had been reached for AA homopolymerizations.³⁸ Hence, the experimental MCR concentration vs time traces were fitted only for the rate coefficients kbb, kpt, and ktst(1,1). Within a first step, the measured maximum MCR concentration after applying the laser pulse, c_MCR^max, was fitted for k_bb. Within the second step, a, i.e., k_p^t, and b, i.e., ktst, were fitted to the measured decay in MCR concentration after passing the maximum MCR concentration. Finally, all three rate coefficients were simultaneously fitted. Note that a "typical" MCR concentration vs time profile exhibits specific regions which are sensitive toward one out of the rate coefficients mentioned above.

5.2 Termination and Transfer Kinetics of AAm

79 Sensitivity of MCR Concentration vs Time Profiles toward Transfer- and Termination Kinetics

It goes without saying that MCR formation by backbiting, and degradation by MCR propagation and cross-termination, can easily be separated by fitting the experimental MCR concentration vs time profiles.

It comes as no surprise that the rate of backbiting, i.e., dc_MCR/dt = k_bb·cSPR, determines cMCRmax, i.e., the maximum MCR concentration after applying the laser pulse. Since ktss(1,1) and thus cSPR are usually known from prior experiments, i.e., for AAm and BA, k_bb is easily accessible by fitting cMCRmax.

Figure 5.8: The simulated MCR concentration vs time profile for AAm polymerization (10 wt.% / H2O) at 95 °C (blue line) is identical to the one shown in Figure 5.9. The figure serves the purpose of illustrating the sensitivity of MCR concentration vs time profiles toward backbiting, MCR propagation and SPR-MCR cross-termination. The corresponding rate coefficients, i.e., k_bb, kpt and k_t^st(1,1), are depicted. k_t^ss(1,1) might be known from prior investigations. The regions dominated by one out of these three steps are colored. The dashed red line represents the fitting upon increasing ktst(1,1) and kbb but constant kpt such that the MCR maximum is correctly reproduced. The resulting fit is of poorer quality.

5 Termination and Transfer Kinetics of Acrylamide in Aqueous Solution

80

The decay of MCR concentration, on the other side, is given by the competition between MCR propagation and SPR-MCR cross-termination.

The latter one is more pronounced at high radical concentrations while k_p^t usually becomes apparent at higher delay times at which MCR-SPR cross-termination may be neglected due to the low SPR concentration. Thus, SP–

PLP–EPR allows for distinction between these processes and hence for a precise determination of k_p^t and k_t^st(1,1) as illustrated exemplarily for AAm (10 wt.% / H2O) at 95 °C in Figure 5.8. It is obvious that the formation and degradation of MCRs occur simultaneously during the whole reaction time. The colored regions in Figure 5.8 are related to the ones in which one process might be dominant. The simultaneousness of MCR formation and degradation results in a slight interdependency of the determined rate coefficients induced by the fitting procedure, e.g., a higher value for ktst(1,1) would lead to a higher number of kbb in order to compensate the faster degradation process. However, a higher ktst(1,1) would also change the shape of the MCR concentration vs time profile yielding a poorer fit of the experimental profile as demonstrated by the dashed red line in Figure 5.8. In case of both SPR and MCR concentration vs time profiles can be measured, the uncertainty in the rate coefficients may be further reduced.

Results from PREDICI^® fitting

Shown in Figure 5.9 are time-resolved MCR concentrations measured after applying a laser pulse at 75 and 95 °C. The two profiles differ in cMCRmax, and in the time required for reaching this maximum. That MCRs are not produced instantaneously, but by a consecutive reaction, as visualized by adding the simulated SPR concentration profile to the measured and fitted MCR traces for 95 °C (Figure 5.10). Shown in Figure 5.11 are the Arrhenius plots of k_bb for temperatures between 75 and 95 °C at both AAm concentrations, 10 and 20 wt.%. The uncertainty of the kbb data has been estimated by varying, during PREDICI fitting, the pulse-induced primary radical concentration within the reasonable range of ±20 percent in order to taking the noise into account.

5.2 Termination and Transfer Kinetics of AAm

81

0 20 40 60 80

0.0 0.5 1.0 1.5

2.0 exp. 95 °C

exp. 75 °C PREDICI^ 95°C PREDICI^ 75°C