Determination of K model

As shown in the upper part of Scheme 4.1, the copper-mediated ATRP mechanism consists of reversible oxidation of a tetra-coordinated copper(I)-ligand complex, [Cu^ILⁿ]⁺[X]⁻, with an alkyl halide, R-X, to produce a penta-coordinated [Cu^IILⁿX]⁺[X]⁻ species and an alkyl radical, R^•.^[6,39] The activation rate coefficient is denoted by k^act, whereas the back reaction occurs with the deactivation rate coefficient, k^deact. The radical produced by the activation step may add to a monomer molecule, M, with the propagation rate coefficient kp and may terminate with another radical, with the rate coefficient k^t. Both k^p and k^t should be identical to the associated rate coefficients of conventional radical polymerization of M. The ratio kact to kdeact represents the ATRP equilibrium constant, KATRP = kact/kdeact. Higher KATRP is associated with faster ATRP.

The measurement of K^model in aqueous solution is especially challenging because of various side reactions. The most important side reaction is the potential dissociation of the penta-coordinated [Cu^IILⁿX]⁺[X]⁻ complex and formation of a hydrated halide ion, as shown in the lower part of Scheme 4.1.^[38] The equilibrium constant for the halide dissociation is denoted by K^X, which provides a measure for the strength of the halide complex. H2O molecules may occupy coordination

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Scheme 4.1: Suggested mechanism of Cu-mediated ATRP in aqueous solution; Lⁿ ligand with n complexing sites, R-X initiator, M monomer, R^• propagating radical, k^p propagation rate coefficient, k^t termination rate coefficient, Kx halide dissociation equilibrium constant, Kaq(Mt) equilibrium constant of water complexation, Kaq(X) equilibrium constant for hydration of the halide ion.

sites and substitute the halide ligand. This dissociation side reaction may lead to hydration of both the [Cu^IILⁿ]²⁺ and [X]⁻ species. These processes are quantified by the equilibrium constants K^aq(Mt) and Kaq(X), respectively. Due to the absence of halide the produced [Cu^IILn(H2O)]²⁺ is unable to deactivate radicals. The equilibria represented by K^aq(X) and K^aq(Mt) are established almost immediately. It appears justified to include these side equilibria into a single equilibrium constant, K^X.

To measure K^model and in order to avoid hydration and dissociation of the Cu^II-complex, up to 1000 equivalents NaBr relative to copper concentration have been added to the solution. Previous studies indicated that such high quantities of NaBr are required for shifting the equilibrium more or less quantitatively towards the ATRP-active halide complex.^[38]

Kmodel was determined from the [Cu^II(bpy)2Br]⁺[Br]⁻ complex concentration vs time traces for the monomer-free model system in water-PEO solutions. The [Cu^II(bpy)²Br]⁺[Br]⁻ concentration was measured via the Vis/NIR absorption of the copper d–d-transition.

Figure 4.1 shows a so-obtained spectral series for 7 mmol · L⁻¹ results from termination of radicals according to Scheme 4.1.

It has been reported that some Cu^I/ligand systems may disproportionate in aqueous solution.^[134] This is obviously not the case with the Cu^I-complex under investigation, at least not on the time scale of the experiments. Measurements over several hours, in the absence of the initiator R-X, showed no Cu^II evolution and no Cu⁰ was produced, π-system of bpy contributes to stabilization against disproportionation.

The equilibrium constant for the model system, Kmodel, was estimated from the Fischer-Fukuda-equation modified by Matyjaszewski et al.for systems with large equilibrium constants and non-equimolar initial concentrations, i.e., via the so-called F[Y]-function, ^[45]:

𝐹([Y]) = ( [I]₀[C]₀

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15000 14000 13000 12000 11000 10000 9000

absorbance

wavenumber / cm^1

t

t = 0

Figure 4.1: FT–Vis/NIR spectral series recorded during the reaction of 7 mmol · L⁻¹ Cu^I(Bpy)2Br, 91 mmol · L⁻¹ HEMA-Br and 500 equivalents of NaBr in a 50 wt.% water-PEO mixture at 22 °C and ambient pressure. The absorbance of the Cu^II complex increases with time t. The dashed lines denote the upper and lower limiting wavenumbers for integration.

Integrated absorbance due to the Cu^II complex was determined from the absorbance difference to the spectrum recorded at t = 0.

The initial concentrations of initiator and of the Cu^I-complex are represented by [I]⁰ and [C]⁰, respectively. The time-dependent concentration of the Cu^II complex is denoted by [Y]. Equation 4.1 holds for situations where only a single Cu^II-complex is present, i.e., without taking the dissociation of the [Cu^IILnX]⁺[Br]⁻ complex and subsequent halide hydration into account. Analysis of K^model via Equation 4.2 should however be valid at large excess concentration of NaBr.

0 1000 2000 3000 4000 0.0

0.2 0.4 0.6 0.8 1.0

5 eq NaBr 50 eq NaBr 1000 eq NaBr

normalized F[Y]-function

time / s

Figure 4.2: Plot of the normalized F[Y]-function vs. time for a reacting system containing 70 wt% water, 7 mmol · L⁻¹ Cu^I(Bpy)²Br, as well as 5, 50, and 1000 equivalents of NaBr at 22 °C with HEMA-Br acting as the initiator.

Shown in Figure 4.2 are three normalized F[Y]-functions plotted vs.

time t, measured with 5, 50 and 1000 equivalents of NaBr being added to a reacting mixture composed of 70 wt% water in PEO with 7 mmol · L⁻¹ [Cu^I(bpy)²]⁺[Br]⁻ and with HEMA-Br acting as the initiator. Straight-line behavior, as predicted by Equation 4.2, is only seen for the data measured upon the addition of 1000 equivalents of NaBr. The strong curvature of the F[Y]-function for 5 equivalents of NaBr and the weak curvature for 50 equivalents of NaBr indicate the presence of additional copper species at these lower NaBr levels. Straight-line behavior probably occurs from 300 to 500 equivalents NaBr on. Thus the analyses for Kmodel have been carried out with NaBr being present in large excess.

With the termination rate coefficient, k^t, being known, the slope of the linear F[Y]-plot yields the ATRP equilibrium constant K^model. For the low-molar-mass model system, kt may be identified with kt1,1, the rate coefficient for termination of two radicals of chain length unity, which is

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accessible from literature in conjunction with viscosity being measured for the particular solvent system.^[69] The viscosity of the solution depends on the water-PEO ratio as well as on the concentration of NaBr and has been measured by means of a falling ball viscometer for the pure solvents and for three solvent mixtures with and without excess NaBr. Alternatively, kt1,1 may be determined via pulsed-laser experiments in conjunction with highly time-resolved EPR spectroscopy.^[62] The two approaches result in k^t1,1 values which differ by a factor of 4. As k^t exhibits a square-root dependence, the associated

Br(2,2’-bipyridine)/HEMA-Br obtained in solvent mixtures of different PEO-water content at 22 °C. The solvent compositions include situations which mimic polymerization conditions. Most of the reported ATRPs with PEGMA were obtained at about 70 wt% water.[33,108,133]

Figure 4.3 shows the steep increase of K^model towards higher water relationship for the difference between K^model for H²O and polar solvents such as dimethyl formamide.^[42]

On the basis of linear solvation energy correlations and of electrochemical measurements, the Kamlet–Taft parameters predict Kmodel in a water environment to be by a factor of 10³ to 10⁴ above Kmodel

in a purely organic environment,^[42] which is in agreement with the data in Figure 4.3. It was also reported that K^model of the CuBr/Me⁶TREN system increases by a factor of 100 from an organic solvent toward pure water.^[47] Matyjaszewski et al. predicted K^model for CuBr/HMTETA in aqueous solution to be 5.9 · 10⁻⁵, which is close to our estimated value for the bipyridine system to be 2.5 · 10⁻⁵. Such difference in KATRP has also been observed for K^model with HMTETA and bipyridine in acetonitrile solution. For the initiator methyl 2-bromo-iso-butyrate

0 20 40 60 80 100 -18

-16 -14 -12

ln(K model)

water in wt %

Kmodel(100% H

2O) = 2.5  10^5

Figure 4.3: Plot of ln K^model vs. the weight fraction of water in H²O-PEO mixtures for the monomer–free model system CuBr/ 2,2’-bipyrdine at 22 °C.

The open squares are measured data to which the straight line has been fitted.

(MBriB), the resulting value for CuBr/HMTETA/MBriB is K^model = 2.8 · 10⁻⁸ which is about four times above the value for CuBr/Bpy/MBriB, K^model = 7.3 · 10⁻⁹.^[59,60]

K^model has additionally been measured as a function of pressure. The experiments were carried out from 500 to 2000 bar for 5 mmol · L⁻¹ Cu^I(bpy)²Br, at HEMA-Br concentrations between 40 and 70 mmol · L⁻¹, and in H2O-PEO mixtures containing 30, 50 or 70 wt.% water at 22 °C.

Plotted in Figure 4.4 are the obtained Kmodel data. Absolute Kmodel

increases with water concentration as shown for ambient pressure in Figure 4.3. The data in Figure 4.4 demonstrates that the relative increase in K^model with pressure is not affected by the water content. The slope to the straight lines in Figure 4.4 yields the reaction volume, ΔV^R, according to the relation:^[59]

64 indicates that the pressure effect results from the stronger contraction of the ligand sphere with the Cu^II-complex being a stronger Lewis acid than the Cu^I species, as has been suggested for polar organic solvents.^[59]

That ΔV^R does not significantly vary with solvent environment indicates that the pressure dependence reflects an intrinsic effect of the copper–

ligand system under investigation. Toward higher pressure, the penta-coordinated Cu^II-complex is favored over the tetra-coordinated Cu^I -complex because of reduced molar volume resulting from the higher oxidation state and the higher coordination.

0 1000 2000

Figure 4.4. Plot of ln K^ATRP vs. pressure at 22 °C for the monomer–free model system with 7 mmol · L⁻¹ Cu^Ibpy²Br in acetonitrile as well as in different H2O-PEO solvent mixtures. The slope of the straight lines yields the reaction volume, ΔV^R, for each mixture.