Kinetics of polymerizations mediated by dithiobenzoates The following chapter has already been published in ref. [72]

The largest deviations from ideal (FRP) kinetics are observed during RAFT polymerizations mediated by dithiobenzoates. Considerable induction periods and rate retardation phenomena are observed in particular when cumyl dithiobenzoate (CDB) is used as the RAFT agent.

While induction periods are satisfactory explained by sluggish addition of monomer to the leaving group species, i.e. a lower polymerization rate is observed under pre-equilibrium conditions, rate retardation occurs over an extended conversion range. The fundamental reason for rate retardation has been under debate with great effort over the past years.

Various attempts have been made to understand this rate retardation behavior including slow fragmentation of the RAFT intermediate radical, INT^•,^[164] cross-termination between INT^• and a growing radical^[77] (see Scheme 7) and a combined model in which cross-termination is assumed to be restricted to very small growing radicals up to chain length three.^[165]

Depending on the particular model assumption, widely differing rate coefficients, k_β, have been deduced for fragmentation of INT^•. Thus for dithiobenzoate-mediated styrene polymerization, k_β values between 10⁻² s⁻¹ and 10⁵ s⁻¹ have been reported for identical polymerization conditions.[79, 166, 167]

TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION 131 The direct measurement of the lifetime of the intermediate radicals, INT^•, should allow for model discrimination. This kind of information will be obtained from the instationary SP-PLP-EPR approach (as described in chapter 5.3.5) which delivers concentrations of both intermediate and propagating radical species as a function of time after the SP. Modeling of the experimental data via a kinetic scheme implemented into PREDICI allows for the determination of the individual addition, kad, and fragmentation rate coefficient, k_β, rate coefficients.

In addition, the RAFT equilibrium constant, Keq may be deduced independently by the stationary approach (see chapter 5.3.5).

To produce main-equilibrium conditions in the initial stage of RAFT polymerization ETTP was used as the mediating agent for BA polymerization at −40 °C. ETTP carries a secondary ethyl propionate leaving group which mimics an SPR during BA polymerization (see section 4.1). The equilibrium constant determined via the stationary approach is depicted in Figure 42.

Figure 42. Ratio of intermediate radical and propagating radical concentrations, c_INT•/c_P• , plotted vs. ETTP concentration for BA polymerizations (1.5 mol· L⁻¹ in toluene) at −40 °C.

The slope of the straight-line fit yields the equilibrium constant, K_eq.

As detailed in section 10.3, the determination of Keq for BA polymerizations at elevated temperatures is complicated due to the occurrence of mid-chain radicals. However, an equilibrium constant for SPRs may be obtained at elevated temperatures, e.g., at 70 °C, by determination of cINT• and cP• from two independent experiments: The concentration of secondary propagating radicals, cP•, has been determined from the measured rate of polymerization and the known kp value of these radical species,^[143]as detailed in ref.^[168] The

132 TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION

resulting value is (5.2 ± 0.5) × 10⁻¹⁰ mol·L⁻¹ for BA polymerization carried out at a RAFT agent concentration of cRAFT = 2.0 × 10⁻² mol·L⁻¹. In addition, EPR spectra were taken during ETTP-mediated BA polymerization at 70 °C. The INT^• concentration (which is assumed to be dominated by INT^• species formed via addition of SPRs to the RAFT agent) is determined by double integration of the associated EPR component to be:

(3.9 ± 0.4) × 10⁻⁸ mol· L⁻¹. The resulting equilibrium constant is (75 ± 15) L·mol⁻¹, which value is close to Keq = 55 L·mol⁻¹ as reported by Kwak et al.^[168] for polystyryl dithiobenzoate-mediated styrene polymerization at 60 °C. The K_eq value estimated by the described procedure should be regarded as an upper limiting value of the “true” Keq for SPRs, since, at least to some extent INT^• species formed via MCR addition to RAFT species contribute to the total EPR-determined c_INT• used for the estimate of K_eq via eq. (28). From the K_eq values for BA polymerization at −40 °C and at 70 °C, the difference in activation energies, E_A(k_ad/k_β) = “E(K_eq)” = −49.5 kJ·mol⁻¹ is found. This number is in satisfactory agreement with the value of −40.5 kJ·mol⁻¹ determined by Arita et al.^[169] for CDB-mediated styrene polymerization.

In Figure 43, the measured time evolutions of INT^• and P^• concentrations after applying a laser pulse at t = 0 are shown (black lines), the experimental data is fitted to the kinetic scheme given in Scheme 7 via PREDICI simulation (best fit shown by gray lines).

Figure 43. Simulated and experimental concentration vs. time traces for propagating and intermediate radicals during BA polymerization (1.5 mol·L⁻¹ in toluene) at −40 °C. The initial ETTP concentration was 2.0 × 10⁻⁵ mol·L⁻¹. The input parameters for PREDICI^®

simulation were: kp = 2.27·10³ L·mol⁻¹·s⁻¹, ki = 2.27·10⁴ L·mol⁻¹·s⁻¹, c_R⁰ = 1.30·10⁻⁵ mol·L⁻¹, k_t^s,s(i,i) = 1.65·10⁸ L·mol⁻¹·s⁻¹, α_s = 0.85, α_l = 0.22, i_c = 30, and k_t^cross(i) = 0.25·k_t(i,i).

TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION 133 The chain-length dependence of ktcross

is adopted to be identical to the one measured for kts,s

. To check for the impact of cross-termination, parameter estimates have been carried out for various sizes of relative cross-termination rate, Ccross = ktcross

/kts,s

, with Ccross being varied from 0 to 1. The results obtained for the rate coefficients kad and kβ from the best fits upon variation of Ccross are depicted in Figure 44.

0.20 0.25 0.30

Figure 44. Results from fitting the experimental trace for ETTP-mediated BA polymerization at −40 °C for various adopted C_cross values. Upper part: k_β (squares, right axis) and k_ad (triangles, left axis); lower part: K_eq (circles). The shaded area indicates K_eq = (2.3 ± 0.6) L·mol⁻¹·s⁻¹ which value has been deduced from the stationary approach.

The optimized k_ad and k_β values in Figure 44 are associated with K_eq given in Figure 44 by the cyclic symbols. These values are matching the K_eq obtained from the stationary approach (shaded area in Figure 44) for values of C_cross ≤ 0.25. Simultaneous fitting of both concentration vs. time traces thus results in a narrow range for the size of cross-termination:

Ccross = 0.25 ± 0.05. The rate coefficients obtained for Ccross = 0.25, which allow for the best fit of both radical concentration profiles (see Figure 43), are:

kad = (1.4 ± 0.4) × 10⁶ L·mol⁻¹·s⁻¹ and kβ = (4.7 ± 1.5) s⁻¹. From these kad and kβ values, the equilibrium constant at – 40 °C is obtained to be Keq = (3.4 ± 0.6) × 10⁵ L·mol⁻¹. This number is in satisfactory agreement with Keq = (2.3 ± 0.6) × 10⁵ L·mol⁻¹, as obtained from the stationary approach (see Figure 42 and Figure 44).

Via the activation energy, EA(kad/kβ) = −49.5 kJ·mol⁻¹ (see above) and assuming that kad is associated with a low activation energy, e.g., of 8.4 kJ·mol⁻¹, as suggested by ab initio

134 TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION

quantum-chemical calculations for the addition of small radicals to dithioester compounds^[162], the activation energy of kβ is estimated to be EA(kβ) = 56.9 kJ·mol⁻¹. This number together with kβ measured for –40 °C results in a fragmentation rate coefficient of 3.1 × 10⁴ s⁻¹ at 60 °C, which is by orders of magnitude above kβ values predicted by the slow fragmentation model, e.g., k_β = 10⁻² s⁻¹ has been reported for CDB-mediated styrene polymerization at 60 °C. ^[79]

Recently, Chernikova et al.^[170] used a spin trap method for deriving a rate coefficient of 8·10⁻³ s⁻¹ for fragmentation of a tert-butyl radical from a dithiobenzoate intermediate radical at ambient temperature. This value is far from k_β determined from SP-PLP-EPR for acrylate SPR leaving moities. It appears reasonable that the value determined by Chernikova applies for pre-equilibrium conditions i.e. the order of magnitude difference may arise from the difference between acrylate leaving groups (present in the SP-PLP-EPR study) and the tert-butyl leaving group investigated by Chernikova. Moreover, the system studied by Chernikova is rather complex in that four types of radicals are present, which may pose further problems for evaluation of the rate coefficients. It is doubtfull whether the value determined by Chernikova may be used as an argument for a slow-fragmentation mechanism.

Since the SP-PLP-EPR experiments are of such quality and internal consistency, it can be concluded that slow fragmentation of the RAFT intermediate (with associated rate coefficients below the order of magnitude 10⁰ at −40 °C) does not occur in dithiobenzoate mediated polymerization of acrylates. Side reactions which may be induced by the specific conditions used for EPR measurement do not occur to an extent which may affect the determination of kad, kfrag, kt and Keq beyond the given error margins.

TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION 135 10.4.1. Comparison of EPR-derived parameters for the RAFT equilibrium with data

from ab-initio calculations

The results obtained for Keq and for the individual rate coefficients kad and kβ from chapters 10.2, 10.3 and 10.4 are summarized in Table 18 and compared to data from ab-initio calculations carried out in the group of M. Coote. Rate coefficients extrapolated to −40 °C are italized. The table was kindly provided by Wibke Meiser.^[171]

Table 18. Comparison of rate coefficients and equilibrium constants associated with the RAFT equilibrium of BA polymerization mediated via xanthates, trithiocarbonates and dithiobenzoates obtained from EPR experiments and ab-initio molecular orbital calculations.

Rate coefficients and equilibrium constants deduced via EPR methods satisfactorily match the ab-initio molecular orbital calculations for both trithiocarbonate- and xanthate-mediated polymerizations. To understand the pronounced difference in rate coefficient k_frag and K_eq for dithiobenzoate-mediated RAFT polymerization by orders of magnitude between EPR experiments and ab-initio calculations further reliable quantum chemical calculations should be carried out in the future to check for the reliability of such calculations in case of dithiobenzoate-mediated polymerization. So far, ab-initio calculation for dithiobenzoates

BA (1.5 M

136 TERMINATION,ADDITION AND FRAGMENTATION IN RAFT-POLYMERIZATION

have only be carried by a single research group. Intensive attempts of independent reproduction of the results for calculated k_frag values given in Table 18 by another group which is specialized on ab-initio calculations failed due to the complexity induced by delocalization of spin density in the aromatic ring of the intermediate radical.^[173]

DEACTIVATION IN ATRP 137