Kinetics of Fe-Mediated ATRP
4.1 Iron-Halide-Based Catalysts 1
4.1.2 Measurement of ATRP Rate Coefficients
It appeared particularly interesting to correlate the structural analysis of the complexes in monomer-free model systems with measurements of the activation and deactivation rate coefficients, kact and kdeact, respectively. For this purpose, a novel evaluation strategy was
40
Scheme 4.2: Mechanism for iron-bromide-mediated ATRP model systems; R-X refers to the dormant alkyl halide species, R• to the radical species and kt to the termination rate coefficient. Due to the absence of monomer, M, propagation cannot occur.
developed, which allows for determination of kact and kdeact in a single experiment. The ratio of kact and kdeact is referred to as Kmodel, whereas KATRP refers to the ratio of these coefficients for an actual polymerization.
Shown in Scheme 4.2 is the mechanism for iron-bromide-mediated ATRP model systems. The absence of monomer yields a simplified scenario by excluding chain-length dependent polymerization kinetics.
The reaction of [FeIIIBr3L]− with, e.g., ethyl 2-bromophenylacetate, EBrPA, as the alkyl halide results in oxidation to [FeIIIBr4]−. The accumulation of [FeIIIBr4]−, which is concurrent with termination of transient radicals according to Scheme 4.2, is referred to as persistent radical effect (PRE)156 and may be monitored via the ligand-to-metal charge transfer (LMCT) absorption at 21 200 cm−1 (Figure 4.5). The reaction rate may be controlled by adjusting the catalyst and initiator concentrations.
Alternatively, [FeIIIBr4]− concentration may be measured via the d-d transition between 9000 and 15 500 cm−1 (Figure 4.6) in experiments started with higher FeII concentrations.166 The increase in [FeIIIBr4]− concentration with time is quantitatively measured by integration of the absorbance between 13 600–12 225 cm−1 against a straight line passing through the absorbance points at these lower and higher limiting wavenumbers. Integration was performed over this low-wavenumber half-band of the FeIII-complex absorbance, as the sensitivity of the silicon diode detector is higher than in the 14 900–13 600 cm−1 region.
Quantitative analysis via integrated absorbances is mostly preferable over analysis via absorbance at the peak maximum position, as Beer-Lambert´s law better holds for vibrational intensity than for absorbance
4.1 Iron-Halide-Based Catalysts
41
28000 24000 20000
absorption
wavenumber / cm1
time
21200 cm1
15000 14000 13000 12000 11000 10000 9000 0.00
0.05 0.10 0.15 0.20 0.25 0.30
[FeIIIBr4]
absorbance
wavenumber / cm1 time
Figure 4.6: VIS/NIR spectral series of the [FeIIIBr4]− species as measured during the reaction of 10.0 mM FeBr2 with 33.3 mM EBrPA in NMP at 60 °C;
optical path length: d = 35.72 mm. By means of separately measured pure solvent spectra, the solvent absorption (dashed gray line) has been subtracted. The hatched area gives an example of the integration procedure by which [FeIIIBr4]− concentration is determined from the spectra.
at a specific wavelength. Calibration for quantitative analysis has been carried out via integrated absorbances using mixtures of 5 mM FeBr3
and of 10 mM FeBr2 without initiator.
In principle, the reaction may also be monitored via the decrease of absorbance of d–d-transitions of the FeII species centered around 4000 to
Figure 4.5: Plot of the [FeIIIBr4]− concentration as a function of time for the reaction of 0.67 mM FeBr2
and 0.68 mM EBrPA in solution of 2-butanone with 53 mM NMP at 60 °C. [FeIIIBr4]− is monitored via the associated absorbance at 21 200 cm−1.
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6000 cm−1 (Figure 4.3). Quantitative and time-resolved analysis of the FeIII species is, however, more appropriate because of the absence of strong background absorption of the solvent.
The measurement of [FeIIIBr4]− vs time consists of two parts (Figure 4.7): The pre-equilibrium state and the equilibrium state. First, Kmodel is evaluated from the equilibrium state according to a reported procedure:36 Equation 4.1 presents a modified expression for the PRE, which, in contrast to the classic equations by Fischer156 and Goto and Fukuda,157 is also applicable to high-conversion systems.36 [I]0 refers to [EBrPA] at time zero, [C]0 to [FeII]0, and [Y] to [FeIIIBr4]−.36 The integrated expression is given by Equations 3.8–3.10 in chapter 3.2.2.
t
The estimate of kt, which is required for using Equation 4.1, is carried out via the diffusion-controlled rate166 which scales with fluidity.200 An alternative approach for estimating kt of the ATRP model system is based on using the composite-model parameter kt1,1, which is obtained from pulsed-laser experiments for termination of two radicals of chain length unity after adjustment to the actual solvent viscosity.92,93 The kt values deduced by these two approaches differ by a factor of four, which translates into Kmodel being uncertain within a factor of two. The uncertainty of kt is considered to have the strongest impact on the accuracy of Kmodel. The estimates of kt via diffusion control (i.e., via fluidity) were used to determine Kmodel if not indicated otherwise.
The evaluation proceeds via a straight-line fit of F(Y) under equilibrium conditions as illustrates in Figure 4.8. Analysis of F(Y) and the estimate of kt = 3.0 × 109 Lmol−1s−1 from fluidity yields Kmodel = 6.0 × 10−7 for the reaction of 0.67 mM FeBr2 and 0.68 mM EBrPA in solution of 2-butanone and NMP (53 mM) at 60 °C.
It should be noted that Kmodel, which refers to total FeII content, is
4.1 Iron-Halide-Based Catalysts
43 Figure 4.7: Plot of [FeIIIBr4]− concentration vs time for the reaction of 0.67 mM FeBr2 and 0.68 mM EBrPA in solution of 2-butanone and NMP (53 mM) at 60 °C. kdeact was obtained by fitting the NIR-spectroscopically measured [FeIIIBr4]− concentration vs time trace using the measured value of Kmodel obtained under equilibrium conditions.
0 1000 2000 3000 4000 5000
496 498 500 502 504
F (Y)
time / h
equilibrium state pre-equilibrium state
Figure 4.8: Plot of the function F[Y] vs time for the reaction of 0.67 mM FeBr2 and 0.68 mM EBrPA in solution of 2-butanone with 53 mM NMP at 60 °C. The close agreement of the straight-line fit with the experimental data for t > 2800 s indicates that the equilibrium has been established for the activation and deactivation reactions.
0 1000 2000 3000 4000 5000
0.00 0.05 0.10 0.15
experiment fit of k
deact / [Lmols]:
9.0105 5.5105 3.0105
equilibrium state pre-equilibrium state
[FeIII Br4] / m
time / s
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the absence of TBA-Br or at high conversion, i.e., up to 90 % [FeIIBr3L]− being transformed to [FeIIIBr4]−. Well-controlled ATRPs operate at a rather constant FeII : FeIII ratio,105 which prevents any major impact of halogen transfer.
The second evaluation step consists of modeling the pre-equilibrium data, according to Scheme 4.2, via the PREDICI program package. Due to monomer being absent, the ATRP mechanism reduces to only three elementary reactions of activation, deactivation, and termination. kt is introduced as estimated via diffusion control. The measured value of Kmodel is used to substitute kact by Kmodel × kdeact. The rate coefficient kdeact is obtained by fitting the experimental [FeIIIBr4]− concentration vs time data. Figure 4.7 illustrates the close agreement of modeled and measured data by both lowering and enhancing kdeact by a factor of about 1.7. The simulations may also be applied toward selecting suitable catalyst and initiator concentrations. Low catalyst and initiator concentrations should be used to expand the pre-equilibrium region.
The outlined novel procedure is particularly attractive since all rate coefficients are accessible from a single experiment. With Cu catalysis, the established procedure for measuring kact is by radical trapping with 2,2,6,6-tetramethyl-1-piperidinyloxyl (TEMPO).35,39 This approach, however, fails with Fe-mediated system, since FeII is oxidized by TEMPO.
The activation–deactivation–equilibrium constant, KATRP, may also be determined from an actual polymerization; for details see chapters 4.2.3 and 6.3.2. As with analyzing Kmodel, the measurement of KATRP involves online spectroscopic detection of the conversion of the FeIII complex (or alternatively of FeII), and additionally of polymerization rate. The results for Kmodel and KATRP measured at 60 °C and ambient pressure will be discussed in the following. Measurements over an extended pressure and temperature range are detailed in chapter 6.3.