In Situ Spectroelectrochemical Investigations of the Redox-Active Tris

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In Situ Spectroelectrochemical Investigations of the Redox-Active Tris[4-(pyridin-4-yl)phenyl]amine Ligand and a Zn2+ Coordination Framework Carol Hua,† Amgalanbaatar Baldansuren,*,‡ Floriana Tuna,‡ David Collison,‡ and Deanna M. D’Alessandro*,† †

School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia School of Chemistry and Photon Science Institute, The University of Manchester, Manchester M13 9PL, United Kingdom

‡

S Supporting Information *

ABSTRACT: An investigation of the redox-active tris[4(pyridin-4-yl)phenyl]amine (NPy3) ligand in the solution state and upon its incorporation into the solid-state metal− organic framework (MOF) [Zn(NPy3)(NO2) 2·xMeOH· xDMF]n (MeOH = methanol and DMF = N,N-dimethylformamide) was conducted using in situ UV/vis/near-IR, electron paramagentic resonance (EPR), and fluorescence spectroelectrochemical experiments. Through this multifaceted approach, the properties of the ligand and framework were elucidated and quantified as a function of the redox state of the triarylamine core, which can undergo a one-electron oxidation to its radical cation. The use of pulsed EPR experiments revealed that the radical generated was highly delocalized throughout the entire ligand backbone. This combination of techniques provides comprehensive insight into electronic delocalization in a framework system and demonstrates the utility of in situ spectroelectrochemical methods in assessing electroactive MOFs.

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electronic swing adsorption,1 as cathode materials for battery applications, and in electrocatalytic schemes,12 among others. Metal−organic frameworks (MOFs) are particularly versatile redox-active materials because of the high level of systematic control and variation that is possible. It has previously been shown that the incorporation of a redox-active ligand and/or metal center will result in a framework that retains the redox activity of the ligand.13−21 Because the properties of the ligand are directly translated into the framework structure, the thorough investigation and characterization of the ligand properties in solution provides valuable insight into the properties of the solid-state material. Triarylamines are trisubstituted aromatic amines in which the central N atom is planar and the pendant aromatic rings are oriented in a “propeller-like” orientation, with each of the phenyl rings canted in the same direction.22 Triarylamines are capable of one-electron oxidation, which can be achieved through electrochemical or chemical processes to form the radical cation.23 Triarylamine units bridged by organic linkers have been widely studied in the field of organic mixed-valence chemistry,24 where powerful insight into the factors that govern

INTRODUCTION

Multifunctional materials whose properties can be altered as a function of their redox state are promising candidates for use in numerous applications.1−5 To obtain a thorough understanding of the material’s properties in its electrochemically accessible redox states, the application of in situ characterization methods are important alongside ex situ bulk techniques. In situ spectroelectrochemical techniques involve the direct application of an electrical stimulus to the material, where the spectral response is monitored as a function of the potential applied.6 While solution-state in situ spectroelectrochemical experiments have been well developed and paired with a number of different spectroscopic techniques such as UV/vis/near-IR (NIR), electron paramagentic resonance (EPR), NMR, IR, X-ray absorption spectroscopy (XAS), and optical fluorescence,7−9 the analogous solid-state in situ spectroelectrochemical experiments have received far less attention.5 Solid-state spectroelectrochemical experiments meet relatively greater challenges in terms of the experimental setup and subsequent data analysis.10 Many of the difficulties are associated with the inherent complex processes that occur during a solid-state electrochemical experiment, which include charge transport and diffusion of ions into the pores of the porous materials.11 Solid-state in situ spectroelectrochemical experiments can be applied to the analysis of materials that have potential use in © XXXX American Chemical Society

Special Issue: Metal-Organic Frameworks for Energy Applications Received: April 19, 2016

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DOI: 10.1021/acs.inorgchem.6b00981 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Solid-state structure of the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework as (a) an asymmetric unit, (b) a view along the a axis, and (c) a view along the c axis.

electrical, optical, and fluorescence properties that are sensitive to an applied electrical stimulus. A detailed understanding of the generation of the triarylamine radical cation has been achieved using electron paramagnetic resonance (EPR) techniques.35 Continuouswave (CW) EPR experiments provide information about spin-system-dependent interactions such as the g matrix and hyperfine coupling. Pulsed EPR can be applied to most samples of interest, and it allows better discrimination between different

electron transfer has been determined.22 Highly reversible oneelectron oxidation of triarylamines with their well-characterized electrochemical and spectral properties makes them attractive structural motifs for the design of multifunctional materials.25 The oxidized states of triarylamines have previously been exploited as hole-transport components in photoconductors and light-emitting diodes.26−34 Thus, redox-active materials incorporating these functional motifs should exhibit interesting B


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triarylamines (Figure 1a).37 The framework consists of one 3D network containing a series of (4,4′) nets. Ordered layers were observed along the c axis (Figure 1c), while pores are found along the a axis (Figure 1b). A solvent void-accessible volume of 17% was calculated using the SQUEEZE function in PLATON.38 This corresponds roughly to the mass loss below 123 °C in thermogravimetric analysis (TGA) of the framework, which is due to the liberation of MeOH from the pores (Supporting Information). Redox Properties. The redox properties of the NPy3 ligand have previously been determined in the [(n-C4H9)4N]PF6/ CH3CN electrolyte and are characterized by two broad irreversible oxidation processes (Supporting Information).13 The process at 0.70 V versus Fc+/Fc was assigned to oxidation of the pyridyl rings present in the ligand, while the process at 0.96 V versus Fc+/Fc involves one-electron oxidation of the triarylamine core to its radical cation.22,23,39 In light of the favored use of aprotic solvents for EPR measurements (vide infra), the redox properties of NPy3 were additionally investigated in the [(n-C4H9)4N]PF6/CH2Cl2 electrolyte. NPy3 exhibited markedly different redox properties in this electrolyte, with an irreversible peak observed upon oxidation, which became increasingly reversible with increased scan rates, indicating the domination of an electrochemical−chemical process at low scan rates (Supporting Information). The anodic shift of the oxidation peak from 0.75 to 1.4 V versus Fc+/Fc upon redox cycling appeared to indicate the formation of a film on the surface of the working electrode (Supporting Information). The redox properties of the [Zn(NPy3)(NO2)2·xMeOH· xDMF]n framework were investigated using solid-state electrochemical experiments in the [(n-C 4H9)4N]PF6/CH3CN electrolyte, where one irreversible redox process at 0.89 V versus Fc+/Fc was observed. This process was due to oxidation of the triarylamine core to its corresponding radical-cation state (Supporting Information) because oxidation of the pyridyl rings should be inhibited as a result of its coordination to Zn2+ through the N-atom donors on the ligand. UV/Vis/NIR Chemical and Spectroelectrochemical Oxidation. The UV/vis/NIR spectrum of the neutral [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework displayed bands at >20000 cm−1 due to the charge-transfer processes for the d10 Zn2+ metal center, which are overlaid on π-to-π* transitions of the aromatic triarylamine core (Supporting Information). Ex situ oxidation of [Zn(NPy 3 )(NO 2 ) 2 · xMeOH·xDMF]n was attempted using several different chemical oxidants (Supporting Information), with vapor diffusion of iodine proving to be the most successful. The appearance of a peak at 16000 cm−1 was indicative of the formation of the triarylamine radical cation. Vapor diffusion of bromine into the framework resulted in its dissolution, while attempted oxidation of the framework with Ce4+ did not result in any observable redox-state change. Chemical oxidation of NPy3 with NOBF4 in acetonitrile as monitored by solid-state UV/vis/NIR has previously been reported, where the appearance of a Gaussian-shaped peak at 11800 cm−1 (due to the localized D0 to D1 transition of the radical cation) and the red shift of the band at 23000 cm−1 to 17800 cm−1 upon oxidation were indicative of the formation of the triarylamine radical cation.13 The in situ UV/vis/NIR spectroelectrochemical experiment provides complementary information to the ex situ chemical oxidation experiments and provides insight into transient states

small interactions in the spin Hamiltonian. For instance, precise measurements of the smaller hyperfine interactions, which are readily masked by EPR broadening in the CW experiments, of the electron spin with remote nuclear spins in the environment can be achieved using techniques such as pulsed ENDOR. The extent of electron delocalization throughout the radical species is able to be elucidated by these selective pulsed EPR methods. The quantification of electron delocalization is particularly important in the development of lightweight conductive and charge-transfer materials, which have been demonstrated to exhibit novel and intriguing electronic properties.24,35 Herein, we describe the use of multiple in situ spectroelectrochemical experiments in the solution state paired with UV/ vis/NIR, EPR, and fluorescence spectroscopies for the investigation of the tris[4-(pyridin-4-yl)phenyl]amine (NPy3) ligand. The extent of electron delocalization and relevant information about the electronic and local structures of the electrogenerated radical cation were determined through pulsed EPR experiments. Solid-state in situ spectroelectrochemical experiments were performed on the novel [Zn(NPy3)(NO2)2· xMeOH·xDMF]n (MeOH = methanol and DMF = N,Ndimethylformamide) framework, allowing an investigation of the ligand-based processes in the solid state. This multifaceted approach has enabled deeper insight into the charge delocalization properties of electroactive MOFs, which are of interest as the basis for optical and electronic devices.

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RESULTS AND DISCUSSION Synthesis and Structure. The NPy3 ligand was synthesized via a Suzuki cross-coupling reaction between tris(pbromophenyl)amine and 4-pyridylboronic acid to yield the ligand as a bright-yellow crystalline solid.13,15 The incorporation of NPy3 into a coordination framework was achieved by heating the ligand with Zn(NO3)2·6H2O in a mixture of DMF and MeOH for 48 h at 80 °C to form [Zn(NPy3)(NO2)2· xMeOH·xDMF]n as yellow needles. Zinc oxide was formed during synthesis of the framework but was easily separated by hot filtration of the reaction mixture prior to cooling and crystallization of the framework, as was verified by the powder X-ray diffraction pattern (Supporting Information). The asymmetric unit of the [Zn(NPy3)(NO2)2·xMeOH· xDMF]n framework consisted of one NPy3 ligand coordinated by a Zn2+ ion (Figure 1a). Zn2+ contains a distorted tetrahedral coordination sphere, where the Zn2+ center is coordinated to three O atoms and one N atom. Two O atoms are bound in a bidentate manner from one NO2− ion, while the third O atom is bound in a monodentate manner to a second NO2− ion with the N atom from an NPy3 ligand. The presence of the NO2 groups bound to the Zn2+ center and detection of zinc oxide indicate that the Zn(NO3)2·6H2O precursor underwent decomposition during the course of the reaction. This may have been caused by reduction of the nitrate counterion by the triarylamine core, which can act as an oxidizing agent, resulting in formation of the nitrite anion. The subsequently formed triarylamine radical cation was presumably reduced to the neutral state by the MeOH in the reaction mixture. The presence of the nitrite anion was confirmed by inspection of the IR spectrum, where peaks at 1327, 1188, and 848 cm−1 corresponded well to the values previously reported (1351, 1171, and 850 cm−1).36 The central triarylamine core from the NPy3 ligand is oriented in a propeller-like configuration, which correlates well with previous reports of solid-state structures incorporating C


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Inorganic Chemistry that may be unable to be detected using the latter techniques.5 The spectrum of the neutral state of NPy3 is dominated by a band at 28140 cm−1 due to a highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) (S0 to S1) transition (Figure 2a). This band was at a lower energy

than that for analogous p-methoxy- and p-chloro-substituted triarylamine derivatives and may be due to the presence of an extended aromatic system.23 Three main processes were observed upon increasing the potential from 0 to 1.0 V in the UV/vis/NIR spectroelectrochemical experiment in the [(n-C4H9)4N]PF6/CH3CN electrolyte. The first process, where the potential was increased from 0 to 1.0 V, was characterized by the formation of bands at 23770 and 35000 cm−1, while the band at 28140 cm−1 decreased owing to oxidation of the N atoms on the pyridyl rings to form an N-oxide species (Figure 2a). The loss of the isosbestic points in the spectroelectrochemical experiment during this first step indicates that multiple processes are occurring concurrently, where several equilibria need to be established, corresponding to oxidation of the three pyridyl N centers. The UV/vis/NIR solution-state spectroelectrochemical experiments on 1,3,5-tris(4-pyridyl)benzene, which contains three pyridyl rings in a similar geometry with a redox-inactive core, confirmed the formation of an N-oxide species with an increase in the band at 35000 cm−1 (Supporting Information). The second process, involving the formation of a peak at 13690 cm−1 and a shoulder at 16540 cm−1, was ascribed to the formation of the triarylamine radical cation (Figure 2b). The band at 13690 cm−1 is due to a HOMO to single occupied molecular orbital (SOMO) (D0 to D1) transition of the triarylamine radical cation, while the shoulder at 16540 cm−1 arises from interaction of the molecule with the solvent, leading to the breaking of symmetry and a splitting of the degenerate D1 state.23 The final process consisted of oxidation of the triarylamine radical cation to the dication at 1.2 V (Figure 2c). The peak at 13690 cm−1 due to the radical-cation core decreased in intensity, while the band at 32000 cm−1 increased. These bands were indicative of the formation of the dication state and were assigned to a HOMO to LUMO transition.23 Because the Zn2+ center is redox-inactive, the spectral changes observed in the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework during the in situ solid-state spectroelectrochemical experiment are ascribed to ligand-based processes (Figure 3). Upon application of a positive potential of 1.5 V, a color change from light yellow to deep green/blue was accompanied by the appearance of an intense band at 13290 cm−1 and a broad band at 22220 cm−1 (Figure 3a). The band at 13290 cm−1 was assigned to the π-to-π* transition of the triarylamine radical cation, which was formed upon oxidation of the neutral triarylamine core. When the potential was held at 1.5 V, the radical-cation band decreased while a band at 21940 cm−1 appeared (Figure 3b), which was due to further oxidation of the radical-cation triarylamine core to the dication state. Application of a reducing potential (of 0 V) led to reduction of the oxidized [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework (Figure 3c) and a corresponding color change from deep blue/green of the oxidized state to the yellow of the neutral state. EPR Spectroelectrochemistry. The solution-state EPR spectroelectrochemical experiments for the NPy3 ligand were conducted in the [(n-C4H9)4N]PF6/CH2Cl2 electrolyte at room temperature, where dichloromethane was used as the solvent instead of acetonitrile because it is less polar and consequently absorbs less microwave radiation (Figure 4). CW EPR spectra display strong couplings of the electron spin to nuclei. The CW EPR spectrum in the solution state of NPy3 displayed a signal centered at g ≈ 2.0067 containing a 1:1:1 hyperfine splitting with an isotropic value of aiso = 23.0 MHz

Figure 2. Solution-state spectroelectrochemistry on NPy3 in the [(nC4H9)4N]PF6/CH3CN electrolyte over the potential range of 0−2.05 V, where the potential was held at (a) 0−1.0 V (acquired over 90 min), (b) 1.1 V (acquired over 25 min), and (c) 1.2 V (acquired over 65 min). D


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Figure 3. Solid-state spectroelectrochemistry on the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework in the [(n-C4H9)4N]PF6/ CH3CN electrolyte upon (a) increasing the potential from 0 to 1.5 V (over 12 min), (b) holding the potential at 1.5 V (over 9 min), and (c) reducing the potential from 1.5 to 0 V (over 9 min).

Figure 4. (a) EPR spectra of NPy3 at applied potentials of 1.5 (blue) and 1.8 V (red) in the [(n-C4H9)4N]PF6/CH2Cl2 electrolyte at 298 K (liquid solution). (b) Comparison between the experimental (black) and numerically simulated spectra (red) at 20 K (frozen solution). (c) EPR signals of the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework upon application of a potential of 1.0 V. The parameters for the numerical simulation are listed in the Supporting Information.

observed when a potential of 1.5 V was applied, along with a color change from bright yellow to green. These values agree well with previously reported EPR studies on triarylamine systems.35 As the potential was increased to 1.8 V, the intensity of the signal increased, indicating the generation of a larger quantity of the radical. This hyperfine-splitting pattern

indicated that the radical was primarily localized on the central N atom of triarylamine and was assigned to one-electron oxidation of triarylamine to its radical cation (Figure 4a).35 The E


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Inorganic Chemistry EPR spectrum of the electrochemically generated NPy3 radical was additionally obtained from a frozen solution of the ligand in the [(n-C4H9)4N]PF6/CH2Cl2 electrolyte at 20 K (Figure 4b). From the frozen CW spectrum, anisotropic information is able to be gained. The solid-state spectrum was found to exhibit g-factor values of 2.0045 and 2.0037 and anisotropic hyperfine values of 3.3, 58.9, and 3.3 MHz. A solid-state EPR spectroelectrochemical experiment was carried out on [Zn(NPy3)(NO2)2·xMeOH·xDMF]n, where the Zn2+ center is diamagnetic and EPR-silent. Upon application of a positive potential of 1.0 V to [Zn(NPy3)(NO2)2·xMeOH· xDMF]n, a typical EPR signal with hyperfine anisotropy was observed (g = 2.002), confirming that the radical was also generated in the solid state (Figure 4). This signal is comparable to the EPR spectrum of NPy3 in a frozen solution and is assigned to the triarylamine radical cation. As the potential was increased to 1.5 V, the signal intensity increased correspondingly. The solid-state EPR spectroelectrochemical experiment on the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework demonstrated that the radical-cation species were unambiguously generated, in agreement with the results of the UV/vis/NIR spectroelectrochemical measurements. Pulsed EPR. Due to their different spin properties and fundamental nuclear frequencies, separate contributions from the 14N and 1H nuclei in the EPR spectrum of NPy3 are expected. The use of CW EPR has allowed for one large 14N hyperfine coupling to be determined. Small hyperfine couplings present from the remaining 1H and 14N are unresolved, hidden under the inhomogeneous line width. The use of pulsed EPR techniques, such as HYSCORE and pulsed ENDOR, allows for elucidation of the hyperfine interactions, which are on the order of the nuclear Zeeman frequencies, and too small to be resolved by CW EPR. 14 N HYSCORE. The field-sweep electron-spin-echo (ESE) measurement, where a magnetic field sweep is performed, allows a field value to be selected for time-domain measurements, such as the HYSCORE experiment. A field value of 346.9 mT was chosen, for which only molecules with the appropriate g value satisfying the resonance condition were selected. An important topic in ESEEM/HYSCORE is characterization of the N atoms involved in either ligation of metal-ion centers or formation of hydrogen bonds with paramagnetic species, and either case implies spin-density delocalization or transfer (vide infra). It is well-known that the parameters of the 14 N spin Hamiltonian have typical values of the quadrupole coupling constant, 1−5 MHz, nuclear Zeeman frequency, νN ∼ 1.05 MHz, and isotropic hyperfine constant, aiso ∼ 0.1−5.0 MHz at X-band.40 The anisotropic hyperfine coupling is at least several times smaller than the isotropic constant. Therefore, the approximation of a pure isotropic hyperfine interaction has been used for the qualitative consideration of 14N powder-type ESEEM spectra.40−42 To confirm the presence of 14N in the local structure of the radical-cation species, HYSCORE experiments were performed, probing for its hyperfine interaction at the X band. The contour peaks in the (+, +) quadrant arise from weakly coupled N atoms with predominantly isotropic hyperfine interactions (Figure 5a). This spectrum features the three narrow contour peaks at ν0 ≈ 0.9 MHz, ν− ≈ 2.3 MHz, and ν+ ≈ 3.2 MHz (Figure S6), referred to as the cancellation condition42 in one of the two electron-spin (mS = ±1/2) manifolds with νeff±/K < 1.41 Detailed information on the cancellation condition for the

Figure 5. (a) X-band 14N HYSCORE spectrum of NPy3 recorded with τ = 136 ns at 346.9 mT, ∼9.7 GHz, and 20 K. The nuclear quadrupole frequency peaks assigned to ν0, ν−, and ν+ are shown in the (+, +) quadrant with fully stacked (top) and contour (bottom) plots. In the bottom plot, a number of contour lines were deliberately reduced in order to better show the locations of the correlation peaks (ν+, νdq) marked in the stacked presentation. The corresponding numerical simulation is shown in Figure S6. (b) X-band 1H HYSCORE spectrum of NPy3 recorded with τ = 136 ns at 346.9 mT and ∼9.7 GHz shown with the corresponding numerical simulation (red). (c) Cross-peak of 1 H shown in ν12 versus ν22 coordinates, where the red curve was defined by |ν1 ± ν2| = 2|1νH| with the proton Zeeman frequency 1νH ∼ 14.7 MHz. Regression analysis of the cross-peak is further shown in Figure S7.

observation of the three pure (or zero-field) nuclear quadrupole resonance frequencies is provided in the Supporting Information. These frequencies further determine the quadrupole coupling constant41,43,44 K ≈ 0.92 MHz and asymmetry parameter η ≈ 0.5 (given in Table 1). Table 1. Nuclear Quadrupole Frequencies and Isotropic Hyperfine Coupling of 14N in NPy3 Fulfilling the Cancellation Condition40,41 ν0 (MHz)

ν− (MHz)

ν+ (MHz)

νdq (MHz)

aiso (MHz)

κ (MHz)

η

0.9

2.3

3.2

5.5

2.2

0.92

0.5

There is a cross-correlation of the nuclear quadrupole resonance frequencies with the double-quantum frequency at νdq ≈ 5.5 MHz, marked as (ν+, νdq+)43,44 (Figure 5a). These correlation peaks possess a maximum at (5.5, 3.2) or (3.2, 5.5) MHz, when the double-quantum frequencies correlate from the opposite m S manifold with ν eff± /K > 1 (Supporting Information). From the nuclear quadrupole resonance frequencies, K and η can be determined and are used to F


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Inorganic Chemistry characterize the chemical type of the 14N atom and its electronic state.43,44 The double-quantum frequency provides the isotropic coupling constant, of the order of aNiso ≈ 2.3 MHz (Table 1). The corresponding numerical simulation45 reproduced the locations of the contour peaks from ν0, ν−, ν+, and (ν+, νdq+) well (Figure S6). These contour peaks are assigned to the weakly coupled N atom of the NPy3 ligand. The experimental results obtained here do not unambiguously distinguish between whether the central or pyridyl N atom has the greater spin density; however, upon comparison with previously reported hyperfine values for the central 14N, it is likely that the weakly coupled N atom is due to the pyridyl N atom.35 This is supported by the three quadrupole resonance frequencies determined from the HYSCORE experiment being in close agreement with the measured 14N quadrupole resonance transitions and quadrupole coupling constant in different pyridine compounds at 77 K.46 In Zn2+-coordinated pyridine compounds, for instance, the quadrupole coupling constants range from 0.1 to 0.75 MHz. In ring-substituted pyridine derivatives, the quadrupole coupling constants are in the narrow range of 1−1.2 MHz.47 The existence of a nonzero isotropic constant for the interacting 14N of the pyridyl ring, therefore, suggests that the unpaired electron spin density was transferred onto this atom and hence the generated radical was delocalized throughout the entire ligand structure. 1 H Hyperfine. To elucidate complete information regarding the coupling of the electron spin to 1H nuclei, three complementary techniques were used in this study: 1D pulsed ENDOR (Mims and Davies) and 2D HYSCORE. Because polarization of the electron-spin transition is significantly larger than that of the nuclear spin transition, in ENDOR experiments, this polarization can be partly transferred to the nuclear transition to enhance the detection sensitivity, especially for anisotropic hyperfine couplings in a frozen solution. The two 1D pulsed ENDOR experiments used are complementary to each other with the Davies ENDOR optimized for hyperfine couplings 5.0−50 MHz and the Mims ENDOR for hyperfine couplings smaller than 5.0 MHz. From the 2D HYSCORE experiment, information regarding the hyperfine couplings in addition to the isotropic and anisotropic parts of the hyperfine tensor is able to be elucidated. 1 H HYSCORE. The HYSCORE spectrum exhibits wellresolved cross-peaks from 1H nuclei, where the cross-peak was split symmetrically along the antidiagonal, with a peak maximum at (17.3, 12.1) or (12.1, 17.3) MHz [(να, νβ) or (νβ, να)] in the (+, +) quadrant, corresponding to a first-orderestimated hyperfine coupling of ∼5.2 MHz (Figure 5a). Analysis of the cross-ridges from nuclei of I = 1/2 spin (e.g., 1 H, 15N, and 13C) in the ν12 versus ν22 coordinate allows a direct, simultaneous determination of the isotropic aiso and anisotropic T components of the hyperfine coupling.45,47,48 Linear regression of the 1H cross-ridges in the NPy3 spectrum plotted in ν12 versus ν22 coordinates (Figure 5b) was analyzed in Figure S7. Linear regression gives intersection points with the |να ± νβ| = 2νI curve for each cross-peak.44 These points uniquely determine the two principal values aiso and T of the hyperfine tensor. There are two possible assignments to (να⊥, νβ⊥) and (να∥, νβ∥) for each crossing point and, consequently, two solutions, one for each assignment.49 Uncertainty in the assignment of ν1 to να or νβ and, respectively ν2 to νβ or να, allows alternate signs of aiso and T in both solutions (see the footnote of Table 2). Tensors obtained from linear regression analysis are summarized in Tables 2 and S3, respectively. The

Table 2. 1H Hyperfine Constants Calculated from Linear Regression Analysis of the Cross-Ridges Plotted in ν12 versus ν22 Coordinates, Shown in Figures 5c and S7 aHiso (MHz)

T (MHz)

5.0 (±0.4) −7.0 (±0.4)a

2.0 (±0.2) 2.0 (±0.2)

a

Signs of a and T are relative to the general form of two solutions: (±a1, ±T) and (±a2, ∓T) with equal |2a1iso + T| and |2a2iso + T|.

isotropic and anisotropic parts of the hyperfine tensor of the 1H nuclei contributing to the HYSCORE spectrum obtained from linear regression analysis44,47,48 were further used for the numerical simulation using EasySpin.45 For both combinations of aiso and T, the numerical simulations reproduced the exact locations of the cross-ridges, assigned to the coupled protons (Figures 5b and S8). The cross-peak in the (+,+) quadrant arises from weak hyperfine interactions, satisfying a condition |T + 2aiso| < 4νI. If proton hyperfine couplings are smaller than the proton Zeeman frequency, one normally calls them “weakly coupled” protons. Importantly, this result provides evidence that the cross-peak was attributable to protons coupled to the unpaired electron spin and its density delocalization. Nonstructural or simply noncoupled 1H, such as matrix and/or solvent protons, would give rise to the intense contour peak centered at the diagonal point (1νH, 1νH) in the (+,+) quadrant. 1 H ENDOR. The Davies 1H ENDOR spectrum for NPy3 displayed several first-order hyperfine couplings, with 6.5, 3.0, and 1.6 MHz split from the proton Zeeman (Larmor) frequency 1νH ∼ 14.7 MHz because of the presence of the coupled protons in the NPy3 ligand. The system was in the high-field limit (ν > A/2) because the signal was centered at the nuclear frequency and split by the hyperfine value. An additional peak at 6.0 MHz was due to matrix effects from the phosphorus (31P) present in the [(n-C4H9)4N]PF6/ CH3CN electrolyte. The Mims 1H ENDOR spectra recorded with τ = 100, 178, 200, and 250 ns were determined to contain four different hyperfine coupling values for 1H at aiso = 1.6, 3.0, 5.0, and 6.5 MHz centered around 1νH (Figure 6b and the Supporting Information). These hyperfine couplings were assigned to the four chemically distinct environments present in the NPy3 ligand, where 1H in the ortho position gives rise to the largest hyperfine coupling value (6.5 MHz), with 1H furthest from the central N atom giving rise to the smallest coupling value (1.6 MHz), indicating that the radical generated at the triarylamine core was delocalized to the furthest H atom on the pyridyl ring from the triarylamine N atom. This concurs with the large and broad line width of the N splitting seen in the CW EPR spectrum of the radical. Fluorescence Spectroelectrochemistry and Chemical Oxidation. NPy3 has previously been reported to fluoresce light blue in solution upon excitation with a UV lamp (λex = 365 nm).13 Emission spectra of the ligand in both the solution and solid states were obtained upon excitation into the π-to-π* transition of the triarylamine core at 380 nm (26315 cm−1; Supporting Information).13,50,51 The in situ fluorescence spectroelectrochemical experiment was performed to investigate the direct effect of the application of a positive potential to the system (Supporting Information). The experiment was performed in the spectroelectrochemical cell as used for the UV/vis/NIR spectroelectrochemical experiments, where the G


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Figure 6. X-band (∼9.7 GHz) pulsed ENDOR spectra of a frozen solution of NPy3 in the [(n-C4H9)4N]PF6/CH3CN electrolyte at 20 K: (a) Davies 1 H ENDOR spectrum and the corresponding numerical simulation; (b) Mims 1H ENDOR spectra recorded with different τ = 100, 178, 200, 250, and 500 ns. The 1H signals split from the proton Zeeman frequency centered at 1νH = 14.7 MHz, where the asterisk indicates the peak due to 31P in the electrolyte.

ments. The CW EPR spectrum of the framework was spectrally similar to that of the NPy3 ligand as a frozen solution containing many of the same characteristics. The demonstration that the combination of solution and solid state in situ spectroelectrochemical experiments provides a valuable and comprehensive understanding of the material as a function of the redox state is particularly important in the development of materials for electronic swing adsorption and as cathode materials in batteries and in electrocatalysis.5

cell was placed at 90° to the excitation beam in the sample holder of the fluorimeter. NPy3 as a solution in the [(nC4H9)4N]PF6/CH3CN electrolyte exhibited a broad emission peak at 460 nm (λex = 380 nm), which decreased in intensity as a positive potential of 1.5 V was applied and triarylamine was oxidized to its radical-cation state. Acetonitrile was used as the solvent instead of dichloromethane because it is more polar and therefore able to better stabilize the radical cation formed. The trend observed in the spectroelectrochemical experiment, where fluorescence of NPy3 was quenched upon the formation of the triarylamine radical cation, corresponded well with ex situ chemical oxidation of the NPy3 ligand, where fluorescence was quenched upon oxidation (Supporting Information). The [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework retained fluorescence of the ligand (Supporting Information), which was not surprising because diamagnetic d10 Zn2+ quenches fluorescence of the ligand. An emission peak at 570 nm was observed when the sample was irradiated at 400 nm with a relatively large Stokes shift of 170 nm, which was higher than that observed for the ligand (∼50 nm). Also, as found for the NPy3 ligand, the fluorescence of [Zn(NPy3)(NO2)2· xMeOH·xDMF]n exhibited was quenched upon chemical oxidation.

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EXPERIMENTAL PROCEDURES

Distilled and degassed acetonitrile or dichloromethane (dried over CaH2) was used for all electrochemical experiments. N,N-Dimethylformamide (DMF) was dried over activated CaSO4 and then distilled under reduced pressure. Methanol (MeOH) was distilled over Mg/I2. Microanalyses were carried out at the Chemical Analysis Facility, Elemental Analysis Service, in the Department of Chemistry and Biomolecular Science at Macquarie University, Sydney, Australia. The tris[4-(pyridin-4-yl)phenyl]amine (NPy3) ligand was synthesized according to literature procedures.13,15 [Zn(NPy3)(NO2)2·xMeOH·xDMF]n. NPy3 (22.4 mg, 5.00 × 10−5 mol) and Zn(NO3)2·6H2O (42.0 mg, 1.41 × 10−4 mmol) were dissolved in a mixture of DMF (1.0 mL) and MeOH (1.0 mL) and heated at 80 °C for 48 h. A white solid (zinc oxide) was observed to form adhered to the edges of the vial. The solution was filtered while hot and allowed to cool slowly to room temperature, upon which thin yellow needles formed (30 mg, 49%). Elem Anal. Calcd for C132H96N23Zn4O12·7.6DMF: C, 61.87; H, 5.00; N, 14.62. Found: C, 61.68; H, 5.37; N, 14.36. Data: formula C66H48N11O6Zn2, M 1221.89, orthorhombic, space group Pbcn (No. 60), a 12.3866(10) Å, b 27.373(2) Å, c 18.5603(16) Å, V 6293.0(9) Å3, Dc 1.290 g cm−3, Z 4, crystal size 0.15 × 0.12 × 0.1 mm, color yellow, habit block, temperature 150(2) K, λ(Mo Kα) 0.71073 Å, μ(Mo Kα) 0.821 mm−1, Tmin,max (SADABS) 0.76, 0.86, 2θmax 52.58, hkl ranges −15 to +15, −34 to +34, −23 to +23, N 161470, Nind 6504 (Rmerge 0.1463), Nobs 4883 [I > 2σ(I)], Nvar. 397, residuals R1(F) 0.0859, wR2(F2) 0.2625, GOF(all) 1.081, Δρmin,max −1.696, 6.133 e Å−3. CCDC 1473613, 1473614, and 1473615. R1 = ∑||Fo| − |Fc||/∑|Fo| for Fo > 2σ(Fo); wR2 = (∑w(Fo2 − Fc2)2/ ∑(wFc2)2)1/2 all reflections, where w = 1/[σ2(Fo2) + (0.1476P)2 + 21.3790P], where P = (Fo2 + 2Fc2)/3.

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CONCLUSIONS Through the combination of solution-state UV/vis/NIR, EPR, and optical fluorescence in situ spectroelectrochemical techniques, we have unambiguously confirmed formation of the radical cation in the NPy3 ligand and [Zn(NPy3)(NO2)2· xMeOH·xDMF]n framework. The triarylamine radical cation has been characterized in detail through a range of pulsed EPR hyperfine techniques. The radical cation was found to be delocalized through the extended π system because of the nearplanar conformation of NPy3. CW and pulsed EPR experiments revealed that the greatest spin density was located on the central N atom of triarylamine. The incorporation of the ligand into the [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework allowed for the investigation of the ligand in the solid state using in situ UV/vis/NIR and EPR spectroelectrochemical experiH


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Inorganic Chemistry Physical Characterization. General Details. Thermogravimetric analysis (TGA) was performed under a flow of nitrogen (0.1 L min−1) on a TA Instruments Hi-Res thermogravimetric analyzer from 25 to 600 °C at 1 °C min−1. Powder X-ray diffraction (PXRD) data were obtained on a PANalytical X’Pert PRO diffractometer, producing Cu Kα (1.5406 Å) radiation, where the sample was lightly ground prior to analysis. Fourier transform infrared was performed on samples over the range of 4000−400 cm−1 on a Perkin-Elmar Spectrum Two ATR spectrometer with a resolution of 4 cm−1 Crystallography. A yellow blocklike crystal was attached with Exxon Paratone N to a short length of fiber supported on a thin piece of copper wire inserted in a copper mounting pin. The crystal was quenched in a cold nitrogen gas stream from an Oxford Cryosystems cryostream. An APEXII FR591 diffractometer employing mirror monochromated Mo Kα radiation generated from a rotating anode was used for data collection. The cell constants were obtained from a least-squares refinement against 9933 reflections located between 2θ = 5.69 and 49.11°. Data were collected at 150(2) K with ω scans to 2θ = 52.58°. Data integration and reduction were undertaken with SAINT and XPREP,52 and subsequent computations were carried out with the WinGX graphical user interface.53 The structure was solved in the space group Pnma (No. 62) by direct methods with SIR9754,55 and extended and refined with SHELXL-2014/7.56 An empirical absorption correction determined with SADABS57,58 was applied to the data. The non-H atoms in the asymmetric unit were modeled with anisotropic displacement parameters. A riding atom model with group displacement parameters was used for the H atoms. A remaining large residual electron density near Zn2 may be due to disorder of the Zn atom, which exists as a low-occupancy disorder component. This possibility has been demonstrated in an alternate model named “ZnNPy3_Znpartial”. Solid-State UV/vis/NIR Spectroscopy. UV/vis/NIR spectra were obtained on the samples at room temperature using a CARY5000 spectrophotometer equipped with a Harrick Praying Mantis accessory over the wavenumber range 5000−40000 cm−1. BaSO4 was used to acquire the baseline spectrum. Spectra are reported as the Kubelka− Munk transform, where F(R) = (1 − R)2/2R (R is the diffuse reflectance of the sample compared to BaSO4). Solid-State Electrochemistry. Solid-state electrochemical measurements were performed using a Bioanalytical Systems electrochemical analyzer. Argon was bubbled through solutions of 0.1 M [(nC4H9)4N]PF6 dissolved in distilled CH3CN. The cyclic voltammograms were recorded using a glassy carbon working electrode (1.5 mm diameter), a platinum wire auxiliary electrode, and an silver wire quasireference electrode. The framework sample was mounted on the glassy carbon working electrode by dip coating the surface of the glassy carbon working electrode into a paste made of the ground powder sample in CH3CN. CH3CN was allowed to evaporate in air to yield a thin film of the framework on the electrode surface. Ferrocene was added as an internal standard upon completion of each experiment. All potentials are quoted in volts versus Fc+/Fc. Solid-State Spectroelectrochemistry (Vis/NIR). In the solid state, the diffuse-reflectance spectra of the electrogenerated species were collected in situ in a 0.1 M [(n-C4H9)4N]PF6/CH3CN electrolyte over the range 5000−25000 cm−1 using a Harrick Omni Diff Probe attachment and a custom-built solid-state spectroelectrochemical cell.10 The cell consisted of a platinum wire counter electrode and a silver wire quasi-reference electrode. The solid sample was immobilized onto a 0.1-mm-thick indium−tin oxide (ITO)-coated quartz slide (which acted as the working electrode) using a thin strip of Teflon tape. The applied potential (from −2.0 to +2.0 V) was controlled using an eDAQ potentiostat. Continuous scans of the sample were taken, and the potential increased gradually until a change in the spectrum was observed. Solution-State Spectroelectrochemistry (EPR). The procedure and cell setup used were those as previously described.59 A three-electrode assembly based on simple narrow wires (A−M Systems) as electrodes, where Teflon-coated platinum (0.20 and 0.13 mm coated and uncoated diameters, respectively) and silver (0.18 and 0.13 mm coated and uncoated diameters, respectively) wires were used for the

working and quasi-reference electrodes, respectively, and a naked platinum wire (0.125 mm) was used as the counter electrode. The bottom 1 cm of each Teflon-coated wire was stripped (using an Eraser International Ltd., RT2S fine wire stripper). The working electrode was positioned lowest such that the redox product of interest was generated at the bottom of the tube and well-separated from the counter electrode. The naked platinum wire counter electrode ensures a greater surface area than the working electrode, while the Teflon coating on the working and reference electrodes prevents shortcircuiting. The electrodes were soldered to a narrow three-core microphone wire. The cell used was made by flame-sealing the tip of a glass pipet. The potential was controlled with a portable μAutolab II potentiostat, and the EPR spectra were obtained using an EMX Micro X-band EPR spectrometer with a 1.0 T electromagnet. The operating microwave frequency at 20 K (9.794538 GHz) was different from the frequency used at room temperature (9.875069 GHz) because of the size of the cavity. Solid-State Spectroelectrochemistry (EPR). The same cell setup as that described for solution-state spectroelectrochemistry was used for the solid-state experiments. The sample of interest was wrapped in a small piece of platinum mesh (∼5 mm × 3 mm) lengthwise and twisted to ensure the sample remained immobilized. The exposed end of the working electrode was carefully wrapped in a spiral shape around the platinum mesh. A small piece of platinum mesh (∼5 mm × 4 mm) was rolled up lengthwise and attached in a fashion similar to that of the counter electrode to ensure that the surface area of the counter electrode was larger than that of the working electrode. Pulsed EPR Experiments. The X-band pulsed EPR measurements were performed on a Bruker ElexSys E580 spectrometer at 20 K. Standard dielectric ring Bruker EPR cavities (ER4118X-MD5 and ER4118X-MD4) were used and equipped with an Oxford CF 935 helium-flow cryostat. The 2D ESEEM spectra, so-called hyperfine sublevel correlation spectra (HYSCORE) Hoe86,60 were recorded by employing the sequence π/2−τ−π/2−t1−π−t2−π/2−τ−echo with microwave pulses of length π/2 = 16 ns and π/2 = 32 ns, τ = 136 ns, starting times t1,2 = 200 ns, and time increments Δt1,2 = 16 ns. The intensity of the inverted echo following the fourth pulse is measured with t2 and t1 varied and τ held constant. Unwanted features from the experimental echo envelopes were removed by using a four-step phase cycle Gem90.61 In both dimensions, 256 data points were collected. The relaxation decay was subtracted by baseline corrections (fitting by polynomials of 3−6°) in both time domains, subsequently applying apodization (Hamming window) and zero-filling to 1024 data points in both dimensions. After 2D fast Fourier transformation, absolute value spectra were calculated. Analysis of the cross-ridges in ν12 versus ν22 coordinates allowed for the simultaneous determination of the isotropic and anisotropic components of the hyperfine matrix.47,48 Davies ENDOR experiments were performed using the pulse sequence π−RF−π/2−τ−π−τ−echo. A radio-frequency (RF) pulse of 47 μs was generated by the Bruker “DICE” system and amplified by a 60 dB gain ENI A-500 RF amplifier. Mims ENDOR experiments were performed using the pulse sequence π/2−π/2−RF−π/2−τ−echo. Solution-State Spectroelectrochemistry (Fluorescence). The Optically Semi-Transparent Thin-Layer Electrosynthetic (OSTLE) cell used for the solution-state UV/vis/NIR spectroelectrochemical experiment, with a path length of 0.65 mm, was adapted for use in a fluorimeter by placing the OSTLE cell perpendicular to the excitation and emission windows. Solutions for the spectroelectrochemial experiment contained a 0.1 M [(n-C4H9)4N]PF6/CH3CN supporting electrolyte and ca. 1 μM of the compound. Appropriate potentials were applied by using an eDAQ e-corder 410 potentiostat, and the current was carefully monitored throughout the electrolysis. The electrogenerated species were obtained in situ, and their emission spectra were recorded at a scan rate of 100 nm min−1 at regular intervals throughout the electrolysis. I


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(16) Leong, C. F.; Faust, T. B.; Turner, P.; Usov, P. M.; Kepert, C. J.; Babarao, R.; Thornton, A. W.; D’Alessandro, D. M. Dalton Trans. 2013, 42, 9831−9839. (17) Leong, C. F.; Chan, B.; Faust, T. B.; Turner, P.; D’Alessandro, D. M. Inorg. Chem. 2013, 52, 14246−14252. (18) Leong, C. F.; Chan, B.; Faust, T. B.; D’Alessandro, D. M. Chem. Sci. 2014, 5, 4724−4728. (19) Hua, C.; Turner, P.; D’Alessandro, D. M. Dalton Trans. 2015, 44, 15297−15303. (20) Hua, C.; D’Alessandro, D. M. Supramol. Chem. 2015, 27, 792− 797. (21) Hua, C.; Abrahams, B. F.; D’Alessandro, D. M. Cryst. Growth Des. 2016, 16, 1149−1155. (22) Lambert, C.; Nöll, G. J. Am. Chem. Soc. 1999, 121, 8434−8442. (23) Amthor, S.; Noller, B.; Lambert, C. Chem. Phys. 2005, 316, 141−152. (24) Heckmann, A.; Lambert, C. Angew. Chem., Int. Ed. 2012, 51, 326−392. (25) (a) Hua, C.; Chan, B.; Rawal, A.; Tuna, F.; Collison, D.; Hook, J. M.; D’Alessandro, D. M. J. Mater. Chem. C 2016, 4, 2535. (b) Cheon, Y. E.; Suh, M. P. Angew. Chem., Int. Ed. 2009, 48, 2899− 2903. (26) Thelakkat, M. Macromol. Mater. Eng. 2002, 287, 442−461. (27) Wu, Z.; Xing, K.; Luo, C.; Liu, Y.; Yang, Y.; Gan, Q.; Zhu, M.; Jiang, C.; Cao, Y.; Zhu, W. Chem. Lett. 2006, 35, 538−539. (28) Flamigni, L.; Ventura, B.; Baranoff, E.; Collin, J.-P.; Sauvage, J.P. Eur. J. Inorg. Chem. 2007, 2007, 5189−5198. (29) Fang, Y.; Hu, S.; Meng, Y.; Peng, J.; Wang, B. Inorg. Chim. Acta 2009, 362, 4985−4990. (30) Yen, H.-J.; Lin, H.-Y.; Liou, G.-S. Chem. Mater. 2011, 23, 1874− 1882. (31) Wang, B.; Wang, Y.; Hua, J.; Jiang, Y.; Huang, J.; Qian, S.; Tian, H. Chem. - Eur. J. 2011, 17, 2647−2655. (32) Yen, H.-J.; Liou, G.-S. Polym. Chem. 2012, 3, 255−264. (33) Polit, W.; Exner, T.; Wuttke, E.; Winter, R. F. BioInorg. React. Mech. 2012, 8, 85−105. (34) Choi, J.; Nguyen, H. M.; Yoon, S.; Kim, N.; Oh, J.-W.; Kim, F. S. Mol. Cryst. Liq. Cryst. 2014, 600, 22−27. (35) Kattnig, D. R.; Mladenova, B.; Grampp, G.; Kaiser, C.; Heckmann, A.; Lambert, C. J. Phys. Chem. C 2009, 113, 2983−2995. (36) Goodgame, D. M. L.; Hitchman, M. A.; Marsham, D. F. J. Chem. Soc. A 1970, 1933−1935. (37) Lambert, C.; Gaschler, W.; Schmalzlin, E.; Meerholz, K.; Brauchle, C. J. Chem. Soc., Perkin Trans. 2 1999, 577−588. (38) Spek, A. L. J. Appl. Crystallogr. 2003, 36, 7. (39) Yuan Chiu, K.; Xiang Su, T.; Hong Li, J.; Lin, T.-H.; Liou, G.-S.; Cheng, S.-H. J. Electroanal. Chem. 2005, 575, 95−101. (40) Sergei, A.; Dikanov, Y. T. Electron Spin Echo Envelope Modulation (ESEEM); CRC Press: Boca Raton, FL, 1992; p 432. (41) Dikanov, S. A.; Tsvetkov, Y. D.; Bowman, M. K.; Astashkin, A. V. Chem. Phys. Lett. 1982, 90, 149−153. (42) Flanagan, H. L.; Singel, D. J. J. Chem. Phys. 1987, 87, 5606− 5616. (43) Tyryshkin, A. M.; Dikanov, S. A.; Reijerse, E. J.; Burgard, C.; Hüttermann, J. J. Am. Chem. Soc. 1999, 121, 3396−3406. (44) Lin, M. T.; Baldansuren, A.; Hart, R.; Samoilova, R. I.; Narasimhulu, K. V.; Yap, L. L.; Choi, S. K.; O’Malley, P. J.; Gennis, R. B.; Dikanov, S. A. Biochemistry 2012, 51, 3827−3838. (45) Stoll, S.; Schweiger, A. J. Magn. Reson. 2006, 178, 42−55. (46) Hsieh, Y.-N.; Rubenacker, G. V.; Cheng, C. P.; Brown, T. L. J. Am. Chem. Soc. 1977, 99, 1384−1389. (47) Dikanov, S. A.; Tyryshkin, A. M.; Bowman, M. K. J. Magn. Reson. 2000, 144, 228−242. (48) Dikanov, S. A.; Bowman, M. K. J. Magn. Reson., Ser. A 1995, 116, 125−128. (49) Morton, J. R.; Preston, K. F. J. Magn. Reson. 1978, 30, 577−582. (50) Zhang, M.-D.; Di, C.-M.; Qin, L.; Yao, X.-Q.; Li, Y.-Z.; Guo, Z.J.; Zheng, H.-G. Cryst. Growth Des. 2012, 12, 3957−3963.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00981. Synthetic details of the ligand, crystallographic table, electrochemistry, TGA, UV/vis/NIR spectra, pulsed EPR experimental analysis details, IR, PXRD, and UV/vis and fluorescence spectroelectrochemistry for the NPy3 ligand and [Zn(NPy3)(NO2)2·xMeOH·xDMF]n framework (PDF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: +44 (0)161 275 1012. *E-mail: [email protected]. Tel: +61 (2) 9351 3777. Fax: +61 (2) 9351 3329. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Alistair Fielding and the EPSRC UK National EPR Research Facility and Service at the University of Manchester for support with EPR measurements and Dr. Peter Turner at the University of Sydney for helpful advice regarding the crystallographic structure determination of the [Zn2(NPy3)2(NO2)2·xMeOH]n framework. We gratefully acknowledge support from the Australian Research Council.

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REFERENCES

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