Solvent Effects on the Activation Rate Constant in Atom Transfer

Apr 29, 2013 - Center for Macromolecular Engineering, Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United Stat...
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Solvent Effects on the Activation Rate Constant in Atom Transfer Radical Polymerization Markus Horn and Krzysztof Matyjaszewski* Center for Macromolecular Engineering, Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States S Supporting Information *

ABSTRACT: Rate constants of activation (kact) for the reactions of tertiary alkyl halides with the ATRP catalyst CuIBr/1,1,4,7,10,10-hexamethyltriethylenetetramine (HMTETA) have been determined in 14 different solvents. The measurements have been performed at 25 °C by spectrophotometrically following the time-dependent absorbances of the CuII species. A large excess of 2,2,6,6-tetramethylpiperidinyl-1oxyl (TEMPO), which quantitatively trapped the alkyl radicals, ensured the irreversible generation of CuII. The rate constant for the least active solvent butanone is 30 times smaller than that of the most active solvent DMSO. In addition, the effect of increasing amounts of monomer in a solvent on the activation rate has been analyzed. A linear correlation of activation rate constants with previously determined equilibrium constants (KATRP) provides a Leffler−Hammond coefficient of 0.45. However, the activation rate constants do not correlate with dielectric constants and Dimroth’s and Reichardt’s ET(30) values. Application of the linear solvation energy relationship of Kamlet and Taft revealed that the dipolarity/polarizability π* of the solvent, i.e., nonspecific solvent−solute interactions, mainly accounts for solvent effects on kact, while the ability to donate a free electron pair is important for some solvents. Quantum chemical calculations showed that more polar solvents stabilize the CuII product complex to a higher degree than the CuI starting complex.

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INTRODUCTION Atom transfer radical polymerization (ATRP) is a powerful controlled radical polymerization method for alkenes.1 It is characterized by a uniform growth of all chains with high retention of chain-end functionality. The key to its controlling nature is the equilibrium between a dormant and an active state of the growing chain (Scheme 1), with the dormant state highly favored.

sufficiently high rates of activation and deactivation guarantee a controlled process with predictable properties of the polymeric product. These reaction parameters not only depend on the monomer, the temperature, the transition metal, the transferred group X, and the ligand used for the catalyst but also are affected by the solvent. Studies of activation rate constants have previously been performed.2 It was reported that the rate of activation is almost independent of the chain length during the polymerization of styrene in toluene and that bromine is much faster transferred than chlorine.2d The activation of 1-phenethyl bromide by CuIBr/4,4′-dinonyl-2,2′-bipyridine proceeded 5 times faster in acetonitrile than in ethyl acetate.2e In addition, comprehensive investigations on the effects of the ligand,3 initiator structure,4 pressure,5 and temperature6 were performed. Although the latter three studies allowed a profound understanding of the activation mechanism, they were exclusively conducted in acetonitrile. Quantitative reports about the influence of the solvent on kact are rare. In the present work, we determined activation rate coefficients for the model reaction between ethyl αbromoisobutyrate (EBiB) and CuIBr/1,1,4,7,10,10-hexamethyl-

Scheme 1. ATRP Equilibrium

In the activation step, a group X (usually a halogen atom) is formally transferred from an organic initiator to a metal (usually Cu) complex in the lower oxidation state, thereby forming the halido complex in the higher oxidation state. The reverse reaction represents the deactivation. Knowledge of the equilibrium constant KATRP and the rate coefficients kact and kdeact is crucial for designing a successful ATRP, as only a sufficiently small concentration of alkyl radicals as well as © XXXX American Chemical Society

Received: March 15, 2013 Revised: April 13, 2013

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triethylenetetramine (HMTETA) in 14 different solvents and derive a linear correlation which allows extrapolation of rate constants for other solvents. The catalyst was chosen for its relatively good solubility and because it does not disproportionate in polar solvents.7 As equilibrium constants, KATRP, have previously been determined in various solvents for this reaction,7 deactivation rate constants, kdeact, can be calculated.

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Time-resolved UV−vis spectrometry was employed to follow the evolution of the CuII species. The recorded curves were fitted by the monoexponential equation A = A0(1 − e−kobst) + C to obtain the apparent rate constants kobs. Activation rate constants were calculated by kact = kobs/[EBiB]0, as the initiator concentration can be approximated to stay constant over the course of the reaction. Both CuI and CuII species can reversibly associate with halide anions,7 as shown in eq 1 for the activator. Among the reaction parameters that affect the magnitude of the corresponding equilibrium constant K = kas/kdis, the nature of the solvent is most important.

EXPERIMENTAL SECTION

Activation rate and equilibrium constants were determined spectrophotometrically using either a Varian 5000 two-beam or an Agilent 8453 one-beam spectrometer. Solvents and monomers were dried and degassed before use. Gas-tight syringes were used for the transfer and the injection of solvents and solutions. Spectrophotometric titrations were performed by portionwise addition of a tetrabutylammonium bromide solution to Cu(TfO)2/HMTETA dissolved in the same solvent. Quantum chemical calculations have been performed with Gaussian 09.8 Typical Procedure for the Determination of Activation Rate Constants. Stock solutions of the catalyst (21 mg of CuBr and 42 μL of HMTETA in 10 mL of solvent), the initiator (100 μL of EBiB in 5 mL of solvent), and the trapping agent (117 mg of TEMPO in 5 mL of solvent) were prepared in a nitrogen atmosphere. A Schlenk flask, connected with a glass cuvette (d = 1 cm), was evacuated and backfilled with nitrogen several times and then filled with 2 mL of the solvent, 1 mL of TEMPO solution, and 1 mL of initiator solution. After addition of 1 mL of the catalyst solution, the measurement was started, and the absorbance of the Cu(II) species was recorded at or near its absorbance maximum. Typical Procedure for the Determination of Equilibrium Constants. Stock solutions of the catalyst (21 mg of CuBr and 42 μL of HMTETA in 10 mL of solvent) and the initiator (100 μL of EBiB in 5 mL of solvent) were prepared in a nitrogen atmosphere. A Schlenk flask, connected with a glass cuvette (d = 1 cm), was filled with 2 mL of the solvent and 2 mL of initiator solution. After addition of 2 mL of the catalyst solution, the measurement was started, and the absorbance of the Cu(II) species followed photometrically at or near its absorbance maximum. The corresponding molar absorbance was determined separately.

kas

[Cu I/HMTETA]+ + Br − HooI [Br−Cu I/HMTETA] active species

kdis

(1) I

As only halide-free complexes of Cu and a tetradentate amine ligand can activate the initiator,9 the question arose whether coordination of bromide to CuI might complicate our kinetic investigation. In order to analyze the effect of bromide anions initially present in solution, we performed additional experiments in some solvents using Cu(CH3CN)4BF4 instead of CuBr as catalyst precursor. The former compound contains the weakly coordinating tetrafluoroborate anion and should exclusively form the activator when mixed with the ligand. Figure 1 shows the absorbance increase during the reactions of EBiB with [CuI/HMTETA]+ in acetone due to the

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Figure 1. Exponential increase of the absorbance at 765 nm during the reactions of EBiB with [CuI/HMTETA]+ in acetone at 25 °C, [EBiB] = 26.7 mM, [TEMPO] = 30.0 mM: (a) using CuBr as catalyst precursor, [CuBr] = 3.07 mM, [HMTETA] = 3.09 mM; (b) using Cu(CH3CN)4BF4 as catalyst precursor, [Cu(CH3CN)4BF4] = 2.92 mM, [HMTETA] = 3.01 mM.

RESULTS Activation Rate Constants. All measurements were performed at 25 °C in dried, degassed solvents under pseudo-first-order conditions, using an excess of the initiator EBiB (usually 30 mM) with respect to the copper catalyst (usually 3 mM) which was generated in solution by mixing CuBr with the ligand HMTETA. In order to render the activation step irreversible, the established methodology of quantitatively trapping the transient alkyl radicals by a large excess of 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO, usually 30 mM) was used (Scheme 2).4,6

accumulation of CuII. Both curves show monoexponential behavior with almost identical activation rate constants, no matter whether CuBr or Cu(CH3CN)4BF4 was used for the catalyst. Similar results were obtained in acetonitrile and DMSO (Table 1). These results indicate that the effect of coordination of Br− to [CuI/HMTETA]+ is negligible in these three solvents. Table 2 reports the activation rate constants for all 14 solvents investigated, also containing the data from Table 1 which have been averaged for each of the three solvents. Additional experiments with variable concentrations of TEMPO or EBiB (see the Supporting Information) confirmed the independence of kact on [TEMPO] and the first-order dependence of kact on the initiator concentration, thus proving the operation of a second-order rate law. For 2 of the 14 solvents, methyl α-bromoisobutyrate (MBiB) was used instead of EBiB. Although the former compound is activated approximately 10−20% faster than the latter compound (in CH3CN, using CuIBr/pentamethyldiethylenetriamine, PMDE-

Scheme 2. Trapping of Alkyl Radicals by TEMPO

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Table 1. Second-Order Rate Constants kact for the Reactions of EBiB with [CuI/HMTETA]+ in Different Solvents at 25 °C Using Either CuBr or Cu(CH3CN)4BF4 as Catalyst Precursor solvent

catalyst precursor

acetone

CuBr Cu(CH3CN)4BF4 CuBr Cu(CH3CN)4BF4 CuBr Cu(CH3CN)4BF4

acetonitrile DMSO

Table 3. Second-Order Rate Constants kact for the Reactions of EBiB with [CuI/HMTETA]+ in Mixtures of DMSO and DMF with Monomers MMA and MA as Well as Methyl Propionate (MP) at 25 °C

kact/M−1 s−1 5.05 4.34 6.06 5.82 1.29 1.30

× × × ×

vol %a

−2

10 10−2 10−2 10−2

20 30 40 10 20 30 40

Table 2. Second-Order Rate Constants kact for the Reactions of EBiB with [CuI/HMTETA]+ in Various Solvents at 25 °C and Selected Solvent Parameters solvent anisole acetonitrile acetone butanone DMSO DMF dimethylacetamide formamide Nmethylpyrrolidonee propylene carbonatee MeOH EtOH 2-PrOH 2,2,2-TFE

kact/ L mol−1 s−1

dielectric constant εra

ET(30)b/ kcal mol−1

π*

37.1 45.6 42.2 41.3 45.1 43.2 42.9 55.8 42.2

0.73 0.75 0.71 0.67 1.00 0.88 0.88 0.97 0.92

46.0 55.4 51.9 48.4 59.8

0.83 0.60 0.54 0.48 0.73

7.38 5.94 4.70 4.17 1.30 2.58 1.33 8.39 2.73

× × × ×

10−2 10−2d 10−2 10−2

× × × ×

10−1 10−1 10−1 10−1

4.45 35.9 21.4 18.9 46.7 37.1 38.3 109f 32.6

1.12 1.11 2.24 1.38 6.84

× × × × ×

10−1 10−1 10−1 10−1 10−2

62.9 32.4g 25.0g 18.6g 26.5h

10 20 30 40

c

10 20 30

kact/L mol−1 s−1

kact/L mol−1 s−1

vol %a

MA/DMSO 8.85 × 10−1 50 6.87 × 10−1 60 5.36 × 10−1 MMA/DMSO 1.15 50 9.77 × 10−1 60 7.43 × 10−1 70 5.81 × 10−1 MP/DMSO 1.17 50 8.68 × 10−1 60 6.91 × 10−1 70 5.28 × 10−1 MA/DMF 2.48 × 10−1 40 2.29 × 10−1 50 2.09 × 10−1 60

4.54 × 10−1 3.23 × 10−1

4.52 × 10−1 3.70 × 10−1 2.98 × 10−1

4.21 × 10−1 3.14 × 10−1 2.53 × 10−1

1.74 × 10−1 2.58 × 10−1 1.27 × 10−1

a

Vol % of the methyl ester; the remainder consists of the indicated solvent.

Table 4. Equilibrium Constants KATRP for the Reactions of EBiB with CuIBr/HMTETA in Different Solvents at 25 °C solvent butanone formamide 2,2,2-TFE DMSOc

a

From ref 10 if not otherwise noted. bEmpirical solvent polarity parameters by Dimroth and Reichardt, from ref 11. cEmpirical dipolarity/polarizability parameters by Kamlet and Taft, from ref 12. d A value of kact (35 °C) = 0.14 L mol−1 s−1 has been reported in ref 3. e Methyl α-bromoisobutyrate (MBiB) was used as initiator. fFrom ref 13. gFrom ref 14. hFrom ref 15.

KATRP 1.55 2.83 7.82 2.59

× × × ×

10−9 a 10−6 b 10−9 10−9

A value of 2.45 × 10−9 was predicted in ref 7. bA value of 5.13 × 10−6 was predicted in ref 7. cMethyl α-bromopropionate (MBP) was used as initiator. a

Increasing the amount of MA in mixtures with either DMSO or CH3CN strongly reduced the ATRP equilibrium constant in reactions between bromine end-capped macroinitiators poly(MA)−Br and Cu IBr/tris[2-(dimethylamino)ethyl]amine (Me6TREN) or CuIBr/tris(2-pyridylmethyl)amine (TPMA).17 As the ligand of choice in the present work is HMTETA, we performed similar experiments and investigated the effect of increasing amounts of MA in DMSO on KATRP for the reactions of poly(MA)−Br and CuIBr/HMTETA in different mixtures of MA and DMSO (Table 5). The results not only allow for a comparison between the three ligands but also offer deeper insight into the relationship between rates and equilibria. In contrast to KATRP evaluations in pure solvents, where the evolution of the CuII species can be followed,7,16 measurements of KATRP under polymerization conditions require a different protocol.17 Here, the time-dependent concentrations of the monomer MA were recorded spectrophotometrically, and KATRP values were calculated with the help of eqs 2 and 3. For a detailed description of the experiments see the Supporting Information.

TA, as catalyst),6 this difference can be considered as negligible in view of the relatively large range of activation rate constants presented in Table 2. Because polymerizations cannot be conducted in pure solvents, but occur either in bulk or mixtures of monomers with solvents, we also studied the effect of increasing amounts of monomers in such mixtures on kact. Methyl acrylate (MA), methyl methacrylate (MMA), or methyl propionate (MP) as a saturated analogue of methyl acrylate was added to DMSO or DMF, and the same experimental procedure as described above was followed to determine the rates of activation of EBiB (Table 3). Equilibrium Constants. A thorough investigation of solvent effects on equilibrium constants KATRP = kact/kdeact has previously been performed using MBiB as initiator and CuIBr/ HMTETA as catalyst.7 Three more solvents, butanone, formamide, and trifluoroethanol, have been studied in the present contribution (Table 4) in order to enable a comprehensive rate-equilibrium analysis. The procedure for the determination of KATRP has previously been described in detail7,16 and shall not be repeated here (see also the Supporting Information).

−

d[M] [Cu IL] = k p[M][Pn•] = k p[M]KATRP[PnBr] dt [BrCu IIL] (2)

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Table 5. Equilibrium Constants KATRP for the Reactions of Poly(MA)−Br with CuIBr/HMTETA in Mixtures of Methyl Acrylate (MA) with DMSO at 25 °C

a

vol % MAa

c (MA)/ mol L−1

initiator

[MA]/[Init]/[CuIBr]/ CuIIBr2]/[HMTETA]

10 20 30 40 50 60

1.10 2.21 3.31 4.41 5.52 6.62

MBP EBiB EBiB EBiB EBiB EBiB

40/1/0.2/0.05/0.25 80/1/0.2/0.05/0.25 120/1/0.2/0.1/0.3 160/1/0.2/0.05/0.25 200/1/0.2/0.1/0.3 240/1/0.2/0.05/0.25

KATRP 7.29 9.99 4.64 3.73 1.37 1.49

× × × × × ×

10−9 10−9 10−9 10−9 10−9 10−9

The remainder is DMSO.

Figure 2. Plot of log kact (filled circles) and kdeact (open circles) vs log KATRP (KATRP from Table 4 and ref 7). *DMA = dimethylacetamide.

II

KATRP = −

[BrCu L] d ln[M] [Cu IL][PnBr]kp dt

KATRP = ΔΔG‡/ΔΔG0 of ca. 0.5 further implies an increase of KATRP by a factor of 4 when kact is doubled. In general, the influence of the solvent on kact is less pronounced than the influence of the initiator or the ligand structure: For example, ethyl bromophenylacetate as initiator is 1.8 × 105 times more reactive than methyl bromoacetate in the reaction with CuIBr/PMDETA in CH3CN,4 and Me6TREN as ligand is 3.2 × 103 times more reactive than its structural isomer HMTETA in the reaction of CuIBr with EBiB in CH3CN.3 Compared to these large ratios, an acceleration of the reaction between EBiB and CuIBr/HMTETA by a factor of 4 by changing the solvent from anisole to DMF is rather modest. A similar acceleration is achieved by raising the temperature from 0 to 40 °C for the reaction of EBiB with CuIBr/PMDETA in CH3CN.6 Activation Rates in Monomer−Solvent Mixtures. Addition of either methyl acrylate (MA) or methyl methacrylate (MMA) to DMSO caused the activation rate constants log kact for the reactions of EBiB with CuIBr/ HMTETA to decrease linearly with the volume fraction of DMSO (Figure 3). In order to investigate the possible

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Spectrophotometric Titrations. Complexes of CuII with tetradentate amine ligands usually exert higher affinities to bromide than the corresponding complexes of CuI,7,18 which can be explained by their larger coordination sphere. While CuI generally prefers four coordination sites (e.g., tetrahedral coordination), the geometry around CuII is most often either trigonal-bipyramidal or square-pyramidal. A bromidophilicity K = kas/kdis (cf. eq 1) of 4.6 × 104 M−1 was reported for [CuII/ HMTETA]2+ in acetonitrile,7 which implies that 94% of the CuII exists as [Br−CuII/HMTETA]+ after the reaction of EBiB with 3 mM CuI. The predominant species in the system CuBr2 + Me6TREN (3 mM in acetonitrile) was shown to be [Br− CuII/Me6TREN]+.18 In order to clarify the nature of the product of the activation step, we performed spectrophotometric titrations of CuII(TfO)2/HMTETA with tetrabutylammonium bromide (see the Supporting Information). Bathochromic shifts of the absorbance maxima in acetonitrile and DMSO occurred upon stepwise addition of Br−. In both cases, the spectra did not change any further after the addition of 1 equiv of bromide, indicating large bromidophilicities of [CuII/HMTETA]2+. Isosbestic points around 717 nm in CH3CN and 709 nm in DMSO suggest that only the two species [CuII/HMTETA]2+ and [Br−CuII/HMTETA]+ are involved in the stepwise transformation. The latter complex was therefore assumed to represent the main Cu species after quantitative bromine abstraction from the initiator in all investigated solvents.

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DISCUSSION Activation Rates in Pure Solvents. The activation rate constants for the reactions of EBiB with CuIBr/HMTETA in 14 different solvents differ by a factor of ∼30, with butanone being the least active and DMSO being the most active solvent. This interval is smaller than the interval of equilibrium constants KATRP, which have been studied under similar conditions previously.7 Whereas DMSO led to a 83 times higher value of KATRP than acetone for the reaction of MBiB with CuIBr/HMTETA, activation in the former solvent proceeds 29 times faster than in the latter solvent. Deactivation rate constants kdeact can be calculated from KATRP = kact/kdeact, and Figure 2 shows a fairly linear rateequilibrium relationship. It appears that a change of the solvent is accompanied by a change of both the activation and deactivation rate, with Δlog kact ≈ −Δlog kdeact; i.e., a higher value of KATRP is due to a higher value of kact and a lower value of kdeact. The Leffler−Hammond coefficient α = Δlog kact/Δlog

Figure 3. Plot of log kact for the reactions of EBiB with CuIBr/ HMTETA in different mixtures of DMSO with MA (blue), MMA (red), and MP (black) vs the volume fraction of the methyl esters; the regression straight line is drawn for methyl propionate, n = 8, R2 = 0.9955.

interaction of the double bond with the copper complex19 which could reduce the concentration of the active catalytic species, a series of experiments with a saturated methyl acrylate analogue, methyl propionate (MP), were performed. As can be seen in Figure 3, increasing the volume fraction of either MA, MMA, or MP in DMSO had almost the same effect on kact. This result can be rationalized by the very similar polarities of the three methyl esters, indicating that a medium effect is D

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Figure 5 further reveals that, in pure DMSO, MBiB as tertiary alkyl halide initiator is 17 times more reactive (in terms of the equilibrium constant KATRP) than the secondary alkyl halide macroinitiator poly(MA)−Br and 102 times more reactive than MBP. The penultimate unit effect in radical polymerizations affects propagation rate and equilibrium constants in ATRP and is mostly rationalized by steric reasons.20 The dependency of KATRP of the low molecular weight initiators MBiB and MBP on the composition of solvent/monomer mixtures can unfortunately not be studied. In Figure 6, activation rates (from Tables 2 and 3) and equilibrium constants (from Table 5) are plotted against the

operative. Hence, activation rates in pure MA, pure MMA, and pure MP should be almost identical. The effect of added monomer on kact is weaker in the case of DMF compared to DMSO (Figure 4). While the ratio kact(pure DMSO)/kact(pure MMA, extrapolated from Figure 3) is ∼9, the ratio kact(pure DMF)/kact(pure MMA) is only ca. 2.

Figure 4. Plot of kact for the reactions of EBiB with CuIBr/HMTETA in mixtures of MMA with DMSO or DMF.

ATRP Equilibria in Monomer−Solvent Mixtures. The dependence of equilibrium constants KATRP on the composition of DMSO/MA and CH3CN/MA mixtures has previously been studied using CuIBr/Me6TREN and CuIBr/TPMA.17 Linear correlations were observed between log KATRP and the volume fractions of the solvent, with a much steeper decline of log KATRP in DMSO than in CH3CN. As the order of decreasing polarity for the three solvents is DMSO > CH3CN > MA, this phenomenon may be ascribed to a medium polarity effect. It may be concluded that the decrease of KATRP is due to a decrease of the activation rate constant as well as an increase of the deactivation rate constant (see Figure 2). The impact of the solvent also seems to be dependent on the catalytic system under consideration: Compared to CuIBr/ Me6TREN and CuIBr/TPMA (Figure 5, blue and red), the dependency of KATRP on the solvent composition is less pronounced for CuIBr/HMTETA (Figure 5, black). While KATRP for the reaction of poly(MA)−Br with CuIBr/Me6TREN increases by a factor of 19 when the medium is changed from 60 to 20 vol % MA in DMSO, only a moderate increase by a factor of 5 is observed for CuIBr/HMTETA.

Figure 6. Plot of log KATRP (black, for the reactions of poly(MA)−Br with CuIBr/HMTETA) and log kact (red, for the reactions of EBiB with CuIBr/HMTETA) vs the volume fraction of methyl acrylate in DMSO; data from Tables 2, 3, and 5.

volume fraction of MA in DMSO. It is obvious that log KATRP drops faster than log kact, meaning that deactivation rates log kdeact must increase with increasing amount of MA. It has to be noted, however, that the activation rates in Figure 6 refer to reactions using EBiB as initiator, while the equilibrium constants refer to reactions using macromolecular poly(MA)−Br. This may account for the discrepancy between the ratios Δlog kact/Δlog KATRP = 0.45 in Figure 2 and 0.99/1.76 = 0.56 in Figure 6. Linear Solvation Energy Relationships. How does differential solvation affect the activation rate constant? Is there any characteristic solvent property that is responsible for this phenomenon, and is it possible to predict or at least estimate kact in other solvents? In the past, many attempts have been made to qualitatively describe solvent effects by correlating experimental observables like rate constants, equilibrium constants, or spectral absorbance data with physical properties of the solvents such as the dielectric constants. However, solvation of a solute is usually a complicated process that can involve dipolar interactions, dispersion forces, ionic interactions, hydrogen bonding, or Lewis acid−base adduct formation. As all these different aspects of solvation can hardly be reflected by any single physical entity, most of these attempts proved unsuccessful. Empirical measures of differential solvation proved to be more useful, as they naturally take all intermolecular interactions into account, and combine them to form empirical numbers, often termed “solvent polarity parameters”, generated on the basis of a reference system.10,21 Among many others, the following four sets of empirical solvent polarity parameters are perhaps the most often used. Winstein and Grunwald derived “ionizing powers” Y for solvents on the basis of ionization rate constants of various organic substrates.22 While Kosower’s Z-

Figure 5. Plot of log KATRP vs the volume fraction of MA in DMSO. Black: poly(MA)−Br reacting with CuIBr/HMTETA (this work); red: poly(MA)−Br reacting with CuIBr/TPMA (from ref 17); blue: poly(MA)−Br reacting with CuIBr/Me6TREN (from ref 17); green: MBiB reacting with CuIBr/HMTETA (from ref 7); yellow: MBP reacting with CuIBr/HMTETA (this work). E

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Figure 7. Plots of log kact vs (a) dielectric constants εr of the solvents and (b) ET(30) parameters; all data are from Table 2. *PC = propylene carbonate.

are not correlated with the corresponding dielectric constants of the solvents. Also, Dimroth’s and Reichardt’s ET(30) values are not related to kact (Figure 7b). Figure 8a, however, shows that the dipolarity/polarizability parameters π* by Kamlet and Taft serve as a good basis for

values are based on the solvatochromic shifts of the chargetransfer band of a pyridinium iodide,23 a pyridium phenolate betain was used as solvatochromic dye by Dimroth and Reichardt for the construction of their ET(30) scale (energy of transfer for compound no. 30, see Table 1).11,24 All three parameter sets were found to correlate fairly well with each other, whereas no relationship exists with the dielectric constants of the solvents. A similar solvatochromic approach to solvent polarities was made by Kamlet and Taft.25 In contrast to Kosower, Dimroth, and Reichardt, however, Kamlet and Taft split the overall process of solvation into individual contributions. Instead of a single dye, they used 47 different dyes in order to attenuate effects that might play a role in the interaction of a solvent with a specific dye.26 In the linear solvation energy relationship (LSER) (4), one form of the Kamlet−Taft equation, XYZ is the parameter of interest, with XYZ0 as its value in the gas phase or an ideal (nonsolvating) solvent. XYZ = XYZ0 + s(π * + dδ) + aα + bβ + h(δ H)2

Figure 8. (a) Plot of log kact vs π*; alcohols (open circles) have not been included in the linear regression (n = 10, R2 = 0.9150). (b) Plot of calculated log kact,cal = −3.63 + 2.28(π* + 0.22δ) + 0.47α + 1.30β + 0.000783(δH)2 vs experimental log kact,exp (n = 14, R2 = 0.8533). *NMP = N-methylpyrrolidone, DMA = dimethylacetamide, and PC = propylene carbonate.

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The parameters α and β represent the solvent’s ability to act as a hydrogen-bond donor and acceptor, respectively. π* is the dipolarity/polarizability which accounts for the stabilization of a charge or dipole by means of nonspecific interactions, and δ was later introduced as a polarizability correction term for polychlorinated (δ = 0.5) and aromatic (δ = 1) solvents.27 The Hildebrand solubility parameter δH is the square root of the cohesive energy density of a solvent, which quantifies intermolecular solvent−solvent interactions.28 The coefficients s, a, b, d, and h are solvent-independent and must be optimized for every reaction under consideration. Because π*, α, β, and δ are normalized and range from 0 to 1, their coefficients are a direct measure of the sensitivity to each individual contribution to the overall solvation process and thereby allow for a more detailed insight into the actual mechanism which dominates solvent effects. The Kamlet−Taft equation has been successfully used in a multitude of cases to linearly correlate experimental data (NMR, IR, UV spectral data, equilibrium and rate constants) with empirical solvatochromic parameters.29 The obtained correlation equations allowed predictions of reactions by extrapolation to other solvents, as long as the corresponding solvent parameters were known. In many of these cases, it was not necessary to use the complete set of parameters (π*, α, β, δ, δH) in order to get good correlations. As can be seen in Figure 7a, activation rate constants for the reactions of EBiB with CuIBr/HMTETA in different solvents

correlating kact values as long as methanol, ethanol, and isopropanol are excluded. For this reason, all four alcohols studied in the present work were excluded from the linear regression in Figure 8a. Interestingly, EBiB is much faster activated in alcohols than expected on the basis of the linear correlation with π* for the other solvents. When all adjustable parameters (XYZ0, a, b, s, d, and h) are used in a multiparameter least-squares minimization, i.e., taking into account all solvent-specific parameters in eq 4 (π*, α, β, δ, and (δH)2, see the Supporting Information), a fairly good correlation including all solvents is obtained (Figure 8b). The dipolarity/polarizability is still the dominant factor governing the activation rate of EBiB (s = 2.28, see the caption of Figure 8). However, Lewis acid−base interactions between the solvent and the copper species must not be neglected for some solvents (b = 1.30). The polarity of anisole, the only aromatic solvent (δ = 1, d = 0.22), and the hydrogen bond donor abilities of the solvents (α = 0.47) are of minor importance. Most of the squared Hildebrand solubility parameters (δH)2 are in a range from 100 to 200 (cal/cm3)1/2. The small value of h = 0.000 783 indicates that the solvent cavities in which the activations of EBiB take place are hardly changed during the reactions. The fact that it is the solvent polarity, characterized by the dipolarity/polarizability parameter π*, which dominates all F

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bipyramid with the two NMe2 groups located at the axial positions and an energetically favored square pyramid with Br at one corner of the square and a NMe2 group at the top of the pyramid (all optimized structures are depicted in Figure S8 of the Supporting Information). All three Cu complexes are more stable in DMSO than in acetone. However, the gain in stabilization energy by changing the solvent from acetone to DMSO is significantly bigger for the CuII complexes than for the CuI complex; i.e., the solvent affects the stability of [Br−CuII/HMTETA]+ to a higher degree than the stability of [CuI/HMTETA]+ (Figure 10).

solvent−solute interactions explains the observations in Figures 3 and 4: Because MA, MMA, and MP have similar polarities, the rate of activation of EBiB changes in a similar way when either of these three liquids is added to DMSO (Figure 3). The addition of DMSO to pure MMA, however, accelerates kact much stronger than the addition of DMF due to the higher polarity of the former solvent (Figure 4). Quantum Chemical Calculations. While, according to the transition state theory, Figure 2 tells us the relative positions of educts, transition states, and products for a specific solvent in a free energy diagram (Figure 9), the relative positions of these

Figure 10. Increasing the free energy of solvation of Cu complexes by changing the solvent from acetone to DMSO.

It should be noted that the states in Figure 9 involve not only the Cu complexes but also the initiator EBiB and the radical EiB*. However, the differences in solvation energies for both of the latter species between DMSO and acetone are almost identical (0.8 kJ mol−1), with DMSO being again the more stabilizing solvent. One can therefore conclude that starting materials, transition state, and products of the activation step are more stable, i.e. better solvated, in more polar solvents (like drawn in Figure 9). It is thus the different susceptibilities of the CuI and CuII species toward solvation that are mainly responsible for the solvent dependency of the activation rate.

Figure 9. Free energy diagram for the reactions of EBiB with [CuI/ HMTETA]+ in butanone and formamide at 25 °C; the origins of the scales were arbitrarily chosen to match the starting materials of the activation process.

states between different solvents remain unclear (parameter X in Figure 9). In fact, it is principally conceivable that changing the medium from butanone to the more polar formamide does not lead to a stabilization of all three states (like it is arbitrarily drawn in Figure 9), but to a destabilization. In order to investigate the effect of solvation on the actual species involved in the activation process, we compared the energies of the solvated states on a theoretical basis. The geometries of the two cationic complexes [CuI/HMTETA]+ and [Br−CuII/HMTETA]+ as well as EBiB and the radical EiB* were optimized using density functional methods. The B3LYP hybrid functional together with a mixed basis set consisting of 6-31G for the light atoms hydrogen, carbon, nitrogen, and oxygen, and LANL2DZ (Los Alamos National Lab 2 double ζ)30 for the heavy atoms copper and bromine including effective core potentials was employed. Both of these basis sets have been widely used along with DFT methods for studies of transition-metal-containing systems, and mixed basis sets of this type have been very popular in computational chemistry in recent years.31 After the optimized gas phase structures were confirmed to be minima on the potential energy surface by freqency calculations, single-point energy calculations including solvation by either acetone or DMSO were performed on the MP2(FC) level. Here, the basis sets were 6-31G(d) for the light atoms and cc-pVDZ for Cu and Br. Solvation was incorporated by the polarizable continuum model (PCM). Both complexes were assumed to contain no solvent molecules as ligand. The structure of [CuI/HMTETA]+ is characterized by four N atoms forming a slightly distorted tetrahedron around CuI. In the case of [Br−CuII/HMTETA]+, two minima were found which differ by ∼16.4 kJ mol−1 (ΔΔG298): a distorted trigonal

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CONCLUSION Activation rate constants kact, deactivation rate constants kdeact, and equilibrium constants KATRP for the activation−deactivation cycle in copper-catalyzed atom transfer radical polymerization are dependent on the solvent. In the reaction series using EBiB as initiator and HMTETA as ligand, a Leffler− Hammond coefficient of ∼0.5 was found for a linear rateequilibrium relationship, indicating that KATRP increases by a factor of 4 when kact doubles. This solvent dependency cannot be correlated with any single solvent property, such as the dielectric constants. However, values of kact in 14 different solvents could be linearized using the Kamlet−Taft approach. The dipolarity/polarizability π*, a measure of nonspecific solute−solvent interactions, shows the highest impact on kact, indicating that it is mostly the nonspecific “solvent polarity” that determines the magnitude of the activation rate. The higher the polarity of the medium, the faster the activation step, and the slower the deactivation step, eventually resulting in a higher value of KATRP. The formation of hydrogen bonds and Lewis acid−base adducts with the copper center cannot be neglected for some solvents, indicated by the respective Kamlet−Taft parameters α and β. Differential stabilization through solvation is stronger in the case of the product species [Br−CuII/HMTETA]+ compared to the starting material [CuI/ HMTETA]+, which is presumably due to the more pronounced dipolar nature of the former. It is mainly this difference between the two Cu complexes that renders the activation rate G

dx.doi.org/10.1021/ma400565k | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

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constant, and consequently the deactivation rate and equilibrium constant, solvent-dependent.

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ASSOCIATED CONTENT

* Supporting Information S

Detailed reaction conditions for the determinations of rate and equilibrium constants as well as additional figures for spectrophotometric titrations and theoretical calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (K.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Science Foundation (CHE 10-26060) and the members of the CRP Consortium at Carnegie Mellon University. The authors thank Hoyong Chung for experimental assistance and preliminary experiments. M.H. gratefully acknowledges financial support from the German Academic Exchange Service (DAAD).

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dx.doi.org/10.1021/ma400565k | Macromolecules XXXX, XXX, XXX−XXX