Solvent-Independent Electrode Potentials of Solids Undergoing

Article pubs.acs.org/JPCC

Solvent-Independent Electrode Potentials of Solids Undergoing Insertion Electrochemical Reactions: Part II. Experimental Data for Alkynyl−diphosphine Dinuclear Au(I) Complexes Undergoing Electron Exchange Coupled to Anion Exchange Antonio Doménech-Carbó,*,† Igor O. Koshevoy,‡ Noemí Montoya,§ Tapani A. Pakkanen,‡ and María Teresa Doménech-Carbó∥ †

Departament de Química Analítica and §Departament de Química Inorgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain ‡ Department of Chemistry, University of Eastern Finland, FI-80101, Joensuu, Finland ∥ IRP, Universitat Politècnica de València, Camí de Vera s/ns, 46022 València, Spain ABSTRACT: A method is presented to obtain solvent-independent redox potential systems using solid-state electrochemistry of alkynyl−diphosphine dinuclear Au(I) complexes (AuC2R)2PPh2C6H4PPh2 (L1, R = Fc; L2, R = C6H4Fc) containing ferrocenyl units. These compounds exhibit a well-defined, essentially reversible solid-state oxidation in contact with different electrolytes based on ferrocenyl-centered oxidation processes involving anion insertion. Midpeak potentials appear to be essentially solvent-independent upon referring it to the bis(η-biphenyl)chromium(I)/bis(biphenyl)chromium(0) couple. Theoretical modeling of diffusion processes allows us to combine voltammetric and chronoamperometric data to determine equilibrium potentials that are strictly solvent-independent. Data for water, MeOH, EtOH, MeCN, DMS, DMF, and NM are provided.

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INTRODUCTION The problem of the determination of an universal, solventindependent scale of standard redox potentials, first underlined by Bjerrum and Larsson in 1927,1 is a subject of continuous interest because of its importance for obtaining thermochemical quantities.2−6 In aqueous media, experimental values of electrochemical reduction potentials are usually measured relative to the universally accepted standard hydrogen electrode (SHE), to which the value of exactly 0 V has been assigned by convention. Unfortunately, there are no universally accepted reference electrodes for work in solvents other than water. To establish a universal scale for electrode potentials, it is required that the liquid junction potentials, Ejunc, which arise at the liquid-phase boundaries, can be rendered negligible or be estimated reliably in some way. Known solutions to this problem involve the use of extrathermodynamic assumptions that can be grouped mainly into: (i) the liquid junction potentials are negligible when large ions (typically, picrate (Et4Npic) cells)7 are used in the salt bridge so that they have similar electrochemical mobilities and (low) solvation Gibbs energies in many solvents;6,7 (ii) the solvation Gibbs energy of a reference salt composed of a quasi-spherical cation and a quasi-spherical anion of about the same size can be divided equally, tetraphenylarsonium tetraphenylborate (AsPh4BPh4, TATB)8 or tetraphenylphosphonium tetraphenylborate (Ph4PBPh4, TPTB)9 being recommended as reference © 2012 American Chemical Society

salts; and (iii) to use a certain electrochemical couple whose electrode potential is assumed to be solvent-independent, as previously commented, provided that several operational conditions are accomplished.10 This last approach is possibly the most used, with the IUPAC recommending that either of the redox couples ferricenium ion/ferrocene (Fc+/Fc) or bis(ηbiphenyl)chromium(I)/bis(biphenyl)chromium(0) (BBCr+/ BBCr) be used as reference redox systems.11,12 The validity of this approach requires that the difference between the Gibbs free energies of solvation of the oxidized and reduced forms of the reference redox couple was the same for all solvents, a relationship that obviously does not necessarily apply. Here a different approach to solventindependent redox systems is reported based on the voltammetry of immobilized particles (VIMP) methodology, a solid-state technique developed by Scholz et al.13,14 that has been previously applied to calculate individual Gibbs energies of anion15,16 and cation17 transfer between two miscible solvents using electrodes modified with Prussian blue17 and alkynyl−diphosphine dinuclear Au(I) complexes and heterometallic Au(I)−Cu(I) cluster complexes containing ferrocenyl units.15,16 Received: September 10, 2012 Published: November 13, 2012 25984

dx.doi.org/10.1021/jp3089676 | J. Phys. Chem. C 2012, 116, 25984−25992

The Journal of Physical Chemistry C

Article

Voltammetry of microparticles experiments was performed at complex-modified gold (geometrical area 0.018 cm2) and paraffin-impregnated graphite electrodes (PIGEs, geometrical areas of 0.018 and 0.785 cm2) using a CH I660 potentiostat. PIGEs were prepared by impregnated pyrolitic graphite bars in vacuo, as described in literature.13,14 A standard three-electrode arrangement was used with a platinum auxiliary electrode and a AgCl (3 M NaCl)/Ag reference electrode, separated from the bulk solution by a salt bridge. Ferrocene was used as standard in concentration 10−4 M, in separate experiments using the same electrolyte solutions. Electrode modification was performed following reported procedures13,14,29 for studying the electrocatalytic performance of carbon nanotubes: (i) by abrasive transference of few micrograms of the same from a spot of finely distributed material in an agate mortar by pressing the lower end of the graphite electrode on that spot and (ii) by forming a film of PB on platinum electrode by pipeting 10 μL of dispersion (1 mg/mL), previously ultrasonicated by 5 min, of the modifier in ethanol and allowing the solvent to evaporate in air. As a result, a uniform, fine coating of the complex was adhered to the basal electrode. Microparticulate complex deposits were also examined before and after this series of electrochemical runs by means of Jeol JSM 6300 scanning electron microscope operating with a Link-Oxford-Isis X-ray microanalysis system. The analytical conditions were: accelerating voltage 20 kV, beam current 2 × 10−9 A, and working distance 15 mm using a scanning electron microscope operating with X-ray microanalysis system (SEM/ EDX). A Multimode AFM (Digital Instruments VEECO Methodology Group) with a NanoScope IIIa controller and equipped with a J-type scanner (max. scan size of 150 × 150 × 6 um) was used. The topography of the samples was studied in contact mode. An oxide-sharpened silicon nitride probe Olympus, VEECO Methodology Group, model NP-S has been used with a V-shaped cantilever configuration. The spring constant is 0.06 N/m and the tip radius of curvature is 5−40 nm. For electrochemical measurements, the AFM was coupled to a Digital Instruments Universal Bipotentiostat (VEECO Methodology group).

In the presented approach, solvent-independent electrode potentials can be obtained by combining voltammetric and chronoamperometric data, based on previous theoretical modeling.18 This model combined theoretical descriptions of solid-state electrochemical reactions in ion-insertion solids19−25 and partitioning equilibria in redox polymers.26,27 The proposed method requires the insolubility of both the oxidized and reduced forms of the solid in the selected solvents and the suitability of the Nernst equation and the Fick diffusion laws. Two explicit extra-thermodynamic assumptions are taken: (i) there is no accumulation of net charge in the solid complex/ electrolyte boundary and (ii) the structure of the solid and the ion binding to the solid are not affected by the solvent. The proposed approach is applied here to the electrochemically reversible solid-state anion-assisted oxidation of two alkynyl−diphosphine dinuclear Au(I) complexes (L) containing ferrocenyl units in contact with LiClO4 electrolytes. The use of this electrolyte is motivated by the high solubility of this salt in most aqueous and nonaqueous solvents. The alkynyl− diphosphine dinuclear Au(I) complexes (AuC2R)2PPh2C6H4PPh2 (L1, R = Fc; L2, R = C6H4Fc; see Figure 1) were selected because such compounds present the

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Figure 1. Schematic representation of L1 and L2 alkynyl−diphosphine dinuclear Au(I) complexes and cyclic voltammogram at L2 film on Au electrode immersed into aqueous 0.10 M LiClO4. Potential scan rate 50 mV/s.

THEORETICAL MODELING

As already described, the solid-state electrochemical oxidation of L1 and L2 complexes forming microparticulate deposits or continuous-like films on inert graphite, gold, or platinum electrodes can be described on assuming that the redox process initiates at the three-phase electrode/solid particle/electrolyte boundary and propagates through the solid via electron hopping between immobile redox centers and ion migration within the solid,19−25 applicable to the solid-state electrochemistry of ferrocene derivatives.30,31 Analogously to the description of electrochemical processes in redox polymers, studied by Andrieux and Savéant32 and Laviron,33 as far as charge transport under a concentration gradient is concerned, this is formally equivalent to a ion and electron diffusion obeying Fick’s law within the solid.34 The overall anion-assisted oxidation process can be described as:

following combination of properties: (i) crystalline compounds well-characterized from the chemical and structural points of view;28 (ii) reversible electrochemical behavior based on the anion-assisted, ferrocenyl-centered solid state oxidation;15,16 (iii) insolubility in water in most organic solvents and in water−organic solvent mixtures at with relatively high molar fraction of organic solvent; and (iv) neutral character with no presence of potentially mobile ions but ability to incorporate ions via electrochemical oxidation.

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EXPERIMENTAL SECTION Synthesis and characterization of L1, L2 complexes was carried out as previously described.27 Electrochemical measurements were performed at 298 K using L-modified paraffinimpregnated graphite electrodes and gold and platinum electrodes. Nanopure water and MeOH, EtOH, MeCN, DMF, NM, and DMSO (Carlo Erba) were used as solvents.

{L}solid + n(A−)soliution → {Ln +···n A−}solid + ne−

(1)

The oxidation process described by eq 1 can be formally separated into the following processes:18 (i) diffusion of solvated ions from the solution bulk to the particle/electrolyte 25985



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the redox process advances via coupled electron diffusion/ anion diffusion through the solid material so that the A− anions permeate the solid only in the x direction and that there is no discontinuity between the “mother” and “daughter” materials. It will be assumed that the diffusion of anions act as a ratedetermining under our experimental conditions. This implies that the diffusion of electrons is clearly faster than anion diffusion so that coupled electron plus anion diffusion can be approached merely by considering anions diffusion. Here, assuming mass transfer by diffusion in both the electrolyte and the solid film phases, the diffusion problem can be reduced to one-dimension diffusion between two phases. Assuming that the desolvation plus exchange processes described by eqs 2 and 3 can be treated, following Bard et al.,26 as a partitioning equilibrium, characterized by an exchange equilibrium constant, Kpt. Accordingly, the current− time response under the application of a constant potential step sufficiently positive to ensure diffusive control should satisfy:

boundary, (ii) ion desolvation at the solid surface and ingress into the lattice, (iii) reduction of immobile redox centers in the solid, and (iv) ion diffusion through the solid coupled to its association with immobile redox centers. Such processes can be represented as: diffusion

ion transfer

(A −solution)bulk ⎯⎯⎯⎯⎯⎯⎯→ (A −solv )surf ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ {A−)solid + solvent (2) electrontransfer

{L}solid ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ {Ln +}solid + ne−

(3)

binding

{Ln +}solid + n{A−}solid ⎯⎯⎯⎯⎯⎯→ {Ln +···n A−}solid

(4)

{Ln +···n A− + L}solid coupled electron − ion diffusion

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ {L + Ln +···n A−}solid

(5)

Equation 2 represents, conjointly, the exchange or partition process, for which a partition equilibrium constant, Kpt, can be defined. Equation 3 can be viewed as a “pure” solid-state redox couple for which a standard redox potential, EL⊖n+/L, could be attributed. Equation 4 represents the binding equilibrium between the immobile redox centers of the solid (in its oxidized form) and the counterions, in turn represented by a binding equilibrium constant, Kbd. It should be noted that such processes are necessarily coupled by reasons of charge conservation so that their separation is only formal. In equilibrium, the composition of the solid phase is determined by the electrode potential according to the Nernst equation so that adapting the treatment due to Lovric and Scholz et al.20,21 to describe reversible solid-state electrochemistry of ion-insertion solids one can write: Emp(L A/L) = E L⊖n+/L −

i=

(8)

Here S is the exposed area of the solid film and γA− = (DA−solution / DA−solid)1/2, where DA−solution and DA−solid represent the diffusion coefficient of anions in the solution and in the solid, respectively. It will be also assumed that the mobile anions bind to the immobile redox centers, as proposed by Wu et al.26 for protonassisted electrochemistry in redox polymers. If the binding reaction is faster than diffusion in the crystal, then one can assume that chemical equilibrium is established at all points within the solid so that the chronoamperometric current becomes:

(6)

i=

In this equation, EL⊖n+/L represents the standard potential for the redox process described by eq 3, and aA−solution is the activity of the A− ions in the electrolyte bulk. Here it is assumed that the ratio of the thermochemical activities of the oxidized and reduced forms of the solid, aAL and aL, is equal to a unit. This is a reasonable assumption under determined conditions (vide infra).18,35,36 In eq 6, K denotes the equilibrium constant for the reaction: {Ln +}solid + n(A−)solution → {Ln +···n A−}solid

(γA− + K pt)(πt )1/2

⎛ 1 − K pt /γ − ⎞ j A ⎟⎟ ∑ ⎜⎜ 1 + K / γ pt A− ⎠ j=0 ⎝ ∞

× exp[−(j + 1/2)2 δ 2/D A −solid t ]

RT RT ⎛ aLA ⎞ RT ln K − ln⎜ ⎟− nF F ⎝ aL ⎠ F

ln a A −solution

− 2nFSc A −solutionγA−K ptD A1/2 solid

2nFSc A −solutionγAeff− K pt(D Aeff−solid )1/2 (γAeff− + K pt)(πt )1/2 ⎛ 1 − K /γ eff− ⎞ j pt A ⎟ exp[−(j + 1/2)2 δ 2/D Aeff− t ] ∑ ⎜⎜ eff ⎟ solid 1 / + K γ − ⎠ ⎝ pt j=0 A ∞

(9)

Deff A−solidis

where an effective diffusion coefficient, introduced so eff eff 1/2 − that γA− = (DA solution /DA−solid) . This effective diffusion coefficient is given by:

(7)

D Aeff−solid =

This equation can be obtained as the sum of reactions described by eqs 2, 4, and 5 so that K = KbdKnpt. Although the redox potential for the solvent-independent redox couple described by eq 3, EL⊖n+/L, cannot be directly measured separately from K, this last quantity can be estimated from chronoamperometric data on the basis of a suitable model for the involved diffusion processes.18 Let us consider a microparticulate deposit of solid particles containing immobile redox centers in concentration c L homogeneously distributed on the surface of a base electrode in contact with a suitable electrolyte. This system can be described in terms of semiinfinite planar diffusion applied to a particle cylinder attached to a solid electrode.21,26,35,36 In this scheme, the redox process is initiated at the solid/base electrode/electrolyte three-phase junction. It is assumed that

D A −solid 1 + K ptc L[1 + K ptKexc A −solution]

(10)

At relatively long times, a Cottrell-like behavior is predicted, the product it1/2 tending to a limiting value given by: (it 1/2)lim =

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− 2nFSc A −solutionK ptD A1/2 solution

(γAeff− + K pt)π 1/2

(11)

RESULTS AND DISCUSSION Voltammetric Behavior. Figure 1 shows the CV response for a L2 film deposited on Au electrode in contact with aqueous 0.10 M LiClO4. As previously reported,15,16 a well-defined, essentially reversible one-electron couple, as judged by the cathodic-to-anodic peak potential separation (60 mV at low 25986



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sweep rates), is recorded. In successive potential cycles, the peak currents decrease progressively, whereas the peak potentials become negatively shifted until stable values are recorded after three to five cycles. This feature can be associated with the variation in the concentration profile of A− ions in the solid so that the thermodynamic activities of the solid species would be proportional to their molar fractions.35 After four to six potential cycles, however, the voltammetric response becomes essentially unchanged. This situation can be described, following the study of Hermes et al.,36 on Prussian blue-type metal hexacyanoferrates, assuming that the solid forms segregate so that the oxidized solid would appear as inclusions in the reduced one. Here both solid phases would be equally accessible to electrochemical inputs so that their respective thermodynamical activities should be considered as a unit. Notice that, however, the formation of bilayered structures has been reported.37,38 The stationary values of the voltammetric peak potentials were taken for thermochemical calculations. Repeatability tests on a series of five freshly prepared electrodes produced standard deviations in midpeak potentials typically between 2 and 5 mV. Essentially identical peak potential data were obtained for experiments on L-modified PIGEs and L-films on gold and platinum electrodes. In in situ AFM experiments on L deposits in contact with aqueous 0.10 M LiClO4 submitted to repetitive cycling, the potential scan confirmed the solid-state nature of the involved electrochemical processes. As can be seen in Figure 2, acicular crystals of L2 only show minimal surface erosion and no significant morphological changes after 20 successive oxidation/ reduction potential cycles. Similar results were obtained for more prolonged potential cycling as well as for application of a constant potential of +0.50 V during 20−30 min. As can also be seen in Figure 3, similar results were obtained upon examination of the crystal of the complex by SEM, where only minor erosive features in the surface of the crystals appear. Confirming previous results on heterometallic Au(I)−Cu(I) [{Au3Cu2 (C2R)6}Au3(PPh2C6H4PPh2)3](PF6)2 (L3, R = Fc; L4, R = C6H4Fc) complexes,16 if the crystals are submitted to single oxidative steps, then insertion of perchlorate ions occurs, as indicated by SEM/EDX experiments. In agreement with the reversible character attributed to the electrochemical process, Emp versus log(anion concentration) plots were essentially linear in the 10−4 to 10−2 M range, the slope being equal to 59 ± 5 mV. This can be seen in Figure 4 where the variation with the concentration of LiClO4 of the midpeak potential determined from cyclic voltammograms at L1 and L2 films on gold in contact with water and MeOH electrolytes is shown. Deviations from linearity observed at larger anion concentrations can be rationalized as a result of activity effects, as previously described.17 Replacing concentrations by activities using the Davies equation yields essentially linear Emp versus log(anion activity) plots of slope 59 ± 5 mV for all tested electrolytes. As discussed by Bond et al.39,40 for 7,7,8,8-tetracyanoquinodimethane (TCNQ) and tetrathiafulvalene (TTF) solid-state electrochemistry, under these circumstances the midpeak potential in voltammetric experiments can, in principle, be taken as a measure of the equilibrium potential of the system and then used for thermochemical measurements. In cases where L complexes are slowly dissolved by the solvent (MeCN, DMSO), experiments were performed in water−organic solvent mixtures with different molar fractions of that solvent, xorg, as previously described.15−17 Then, the Emp

Figure 2. AFM images for a microparticulate deposit of L2 on a graphite plate immersed into an aqueous 0.10 M LiClO4 solution: (a) before and (b) after 20 potential cycles between +0.05 and +0.75 V versus AgCl/Ag.

at the pure organic solvent can be estimated upon extrapolating the Emp versus xorg curves. Figure 5 shows the corresponding curves for water−MeCN and water−DMSO mixtures, both with 0.10 M LiClO4 concentration. Determination of Diffusion Parameters. Using this approach, the values of the equilibrium constants Kbd and Kpt could be estimated from chronoamperometric data using eq 9 provided that the concentration of immobile redox centers in the solid and the diffusion coefficients for the A− ions in the solution and in the solid are known. To determine such parameters, we performed chronoamperometric experiments at different electrolyte concentrations. Because the diffusion coefficients of anions, DA−solid (in the solid) and DA−solution (in the electrolyte), are unknown and the effective value of the surface area in eq (9) is not exactly known (because it is not necessarily equal to the geometrical surface area of the electrode), the 1/2 SD1/2 A‑solid and SDA−solution factors will be estimated as described in the following. Figure 6a shows the chronoamperometric curve obtained for a L2 film on graphite in contact with 0.10 M LiClO4/water. Interestingly, plotting i versus t−1/2 as a function of time (Figure 6b) tends to a Cottrell-type behavior (i proportional to t−1/2) at 25987



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Figure 5. Emp versus xorg plots for L2 films on graphite immersed into 0.10 M LiClO4 DMSO plus water (squares) and EtOH plus water (solid squares) mixtures. Continuous curves represent the best polynomial fit of experimental data. Form cyclic voltammetric experiments at a potential scan rate of 50 mV/s.

Figure 3. SEM images for a microparticulate deposit of L2 on a graphite plate immersed into an aqueous 0.10 M LiClO4 solution: (a) before and (b) after 20 potential cycles between +0.05 and +0.75 V versus AgCl/Ag.

Figure 6. Chronoamperometry for a L2 film on graphite in contact with 0.10 M LiClO4/water obtained upon application of a potential of +0.55 V versus AgCl/Ag: (a) current/time curve and (b) Cottrell plot of i versus t−1/2.

short times (t < 0.02 s), whereas at relatively long times (t > 0.10 s) a Cottrell-type behavior is again reached. Interestingly, the slope of both the short-time and long-time Cottrell plots (labeled in the following as (CSL)short, (CSL)long, respectively) varied significantly with the electrolyte concentration, as can be seen in Figure 7. As shown in Figure 8, the (CLS)long/ (CSL)short ratio tends to a constant, cA*-independent value that differs from one solvent to another. This behavior can be rationalized on assuming that at short times the diffusion of anions through the particle and the

Figure 4. Variation with the concentration of LiClO4 of the midpeak potential determined from cyclic voltammograms (potential scan rate 50 mV/s) at L1 and L2 films on gold in contact with water and MeOH electrolytes. In all cases a Nernstian behavior (slope of 56 ± 3 mV) was obtained in Emp versus log c plots approaching slopes of 59 ± 3 mV for Emp versus log a plots using the Davies equation for estimating activities. 25988



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between the diffusion of anions through the electrolyte and the solid phases so that the Cottrell-type behavior expected would − − − be given by (cL + cA−solution)Dapp A− = cLDA solid + cA solution DA solution: it 1/2 =

nFS(c L + c A −solution)1/2 (c LD A −solid + c A −solutionnD A −solution)1/2 (π )1/2

(13)

At high electrolyte concentrations (cA−solution ≫ cL); however, this last equation tends to: it 1/2 =

− nFSc A −solutionD A1/2 solution

(π )1/2

(14)

Finally, at relatively long times in the chronoamperometric time scale and high electrolyte concentrations, the binding plus exchange processes described by eqs 2−5 can be considered in equilibrium so that the model leading to eq 9 would be operative. Using Cottrell slopes easily determined from experimental data such as in Figure 5b, eqs 12−14 can be combined to obtain a direct estimate of the diffusion parameters. Using data such as in Figure 7, one can obtain the values of the SD1/2 A−solution 1/2 1/2 − − − and SDA−solid and then γA = (DA solution/DA solid) . Table 1 summarizes the corresponding values obtained from CA experiments in different solvents.

Figure 7. Variation with the LiClO4 concentration of the Cottrell slope at short times (t < 0.02 s) in chronoamperometric experiments for L2 films on graphite in contact with 0.10 M LiClO4 solutions in water (solid squares) and MeOH (squares).

1/2 1/2 Table 1. Values of γA− (= SDA−solution /SDA−solid ) Estimated from Experimental CA Data by Using Equations 12 and 13 and Values of Kbd, Kpt, and K Calculated from the above and the Experimental (CSL)long/(CSL)short Values in CA Experiments at L2 Films on Graphite Immersed into 0.10 M LiClO4 Solutions at 298 Ka

a

long

Figure 8. Variation with the LiClO4 concentration of the (CSL) / (CSL)short ratio in chronoamperometric experiments for L2 films on graphite in contact with 0.10 M LiClO4 solutions in water (solid squares) and MeOH (squares).

it 1/2 =

− + c A −solutionD A1/2 ) solution 1/2

(π )

γA−

Kbd (M−1)

Kpt

K (M−1)

water MeOH EtOH MeCN DMSO DMF NM

280 448 312 352 328 480 392

1.5 1.5 1.5 1.5 1.5 1.5 1.5

5.7 5.1 2.7 3.0 4.2 1.5 11.3

8.6 7.7 4.1 4.5 6.3 2.3 17.0

cL = 4.0 × 10−4 mol/cm3.

To estimate the values of Kpt and Kbd, one can fit experimental current/time CA curves to theoretical ones by inserting the previously determined SD1/2 and SD1/2 terms A A solution solid and inserting different Kpt and Kbd values into eq 9. Figure 9 compares experimental CA data with theoretical data obtained upon inserting different parameter values into eq 9. An excellent agreement was obtained between theory and experiment in all tested cases. The values of Kpt and Kbd can also be calculated from the values of the aforementioned Cottrell slopes at short (CSL)short and long times (CSL)long at high cA−solution values. Combining eqs 11 and 14, one obtains:

electrolyte can be approached by a model of biphasic diffusion. In this situation, two limiting cases can be distinguished following the description of Andrieux et al.41 for redox polymer films: full coupling between the two phases and lack of coupling between phases. The second approach is valid as long as the diffusion front of the diffusing species in solution phase remains within the electrode coating, a condition that typically applies for times shorter than 10−20 ms.42,43 Here one can expect the flux of the diffusing species to be the sum of two independent contributions so that one can write: − nFS(c LD A1/2 solid

solvent

⎛ K ⎞ ⎛ (CSL)short ⎞ pt ⎜ ⎟ ⎟ ⎜ 2 ≈ γ − A ⎜ eff ⎟ K γ + ⎝ (CSL)long ⎠ − ⎝ A pt ⎠

(12)

(15)

Using this approach, for CAs recorded in 0.10 M solutions of LiClO4 in the tested solvents, and taking cL = 0.40 M, different pairs of Kpt and Kbd, values satisfying eq 15 were obtained.

At short times and moderate electrolyte concentrations, one can apply the biphasic diffusion modeling assuming coupling 25989



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Figure 10. Thermochemical cycle for the anion-assisted solid state oxidation of L1 and L2 complexes.

Correlation of ΔG⊖ el values for two given solvents does not cancel the salvation Gibbs energy terms, thus illustrating the fundamental difficulty existing in the definition of a solventindependent redox subsystem. Using the reported model, the redox potential of the nominally solvent-independent couple described by eq 3, EL⊖n+/L, can be calculated from the measured voltammetric midpeak potentials combined with the K (= KptKbd) values estimated from CA data as:

Figure 9. Comparison of experimental (squares) and theoretical (lines) chronoamperometric curves for L2 immersed in 0.091 M LiClO4/water. Theoretical curves from eq 8 inserting cL = 0.40 M, SD1/2 = 1.25 × 10−7 cm3/s1/2, γ = 280, Kbd = 1.5, and Kpt = 5.7. A solid

Because Kbd has to be the same for all solvents, one can select the “best” series of Kpt and Kbd values fitting to eq 14 for the same value of Kbd. The resulting values of K (= KbdKpt) are summarized in Table 2. Using such values and the previously

E L⊖n+/L = Emp(LA/L) +

Table 2. Midpeak and Formal Potential Data Recorded in Cyclic Voltammograms at L2 Films on Gold in Contact with 0.10 M LiClO4 Solutions in Different Solvents at 298 K solvent

Emp(LA/L) vs Fc+/Fc (mV)a

E⊖ Fc+/Fc vs BBCr+/BBCr (mV)b

Emp(LA/L) vs BBCr+/BBCr (mV)c

EL⊖n+/L vs BBCr+/BBCr (mV)d

water MeOH EtOH MeCN DMSO DMF NM

+237 +60 +46 +72a +70a +34a +105a

+970 +1134 +1134 +1119 +1123 +1127 +1112

+1207 +1194 +1180 +1191 +1193 +1161 +1217

+1093 +1083 +1085 +1093 +1087 +1081 +1085

ln a A −solution

(17)

The corresponding values for different solvents are summarized in Table 2. Midpeak potentials, experimentally measured relative to the Fc+/Fc couple, were translated to the BBCr+/ BBCr scale, as recommended by Gritzner and Kuta.11,12 Interestingly, the voltammetric midpeak potentials relative to the BBCr+/BBCr couple could be taken as approximately solvent-independent, with maximum difference of ca. 50 mV. EL⊖n+/L potentials relative to the BBCr+/BBCr couple determined from eq 17 exhibit small differences. As can be seen in Table 3, Table 3. Differences in the E⊖ Ln+/L Potentials (in mV) between Different Pairs of Solvents Relative to: (a) Fc+/Fc Couple (Upper Half-Table) and (b) BBCr+/BBCr Couple (Lower Half-Table)

a

Experimental midpeak potentials extrapolated from voltammetric data in water−solvent mixtures. bData from Kuta and Gritzner.20 c Emp(LA/L) values relative to the BBCr+/BBCr pair. dE⊖ Ln+/L relative to the BBCr+/BBCr pair using eq 17.

water water MeOH EtOH MeCN DMSO DMF NM

estimated diffusive parameters, an excellent agreement between experimental and theoretical curves from eq 9 was obtained, as can be seen in Figure 9. Solvent-Independent Electrode Potentials. Figure 10 shows a thermochemical cycle relating the processes described by eqs 2−7. Here the Gibbs energies associated with the overall electrochemical process, ΔG⊖ el , and the electron-transfer process in the gas phase, ΔG⊖ e , are related to the reticular Gibbs ⊖ energies of the L and LA crystals, ΔG⊖ ret(L) and ΔGret(LA), and + the free energy for anion solvation, ΔG⊖ (M ). Such Gibbs solv energy terms are related by:

0 10b 8b 0b 6b 12b 8b

MeOH a

177 0 −2b −10b −4b 2b −2b

EtOH a

191 14a 0 −8b −2b 4b 0b

MeCN a

165 −12a −26a 0 6b 12b 8b

DMSO a

167 −10a −24a 2a 0 6b 2b

DMF a

203 26a 12a 38a 36a 0 −4b

NT 132a −45a −59a −33a −35a −71a 0

the values of the difference between the E⊖ Ln+/L potentials for different pairs of solvents relative to the BBCr+/BBCr couple are clearly lower than that for such potentials relative to the Fc+/Fc couple. To test the suitability of the proposed reference redox system for providing solvent-independent electrode potentials, we compared the values of the Fc+/Fc couple relative to the BBCr+/BBCr and LA/L couples. As shown in Figure 11, the

⊖ ⊖ ⊖ ΔGel⊖ = ΔGe⊖ − ΔGret (L) + ΔGret (LA) − nΔGsolv (M+)

+ nΣe

RT RT ⎛ aLA ⎞ RT ln K + ln⎜ ⎟+ nF F ⎝ aL ⎠ F

(16) 25990



Article

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Figure 11. Correlation between the formal potential of the Fc+/Fc couple relative to the BBCr+/BBCr and the Ln+/L couples.

representation of E°(Fc+/Fc) relative to LA/L versus E°(Fc+/ Fc) relative to BBCr+/BBCr was linear with slope unit, thus denoting the existence of an unambiguous correlation between both scales.

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CONCLUSIONS Solvent-independent redox potential systems under voltammetric conditions can be approached from solid-state electrochemistry of alkynyl−diphosphine dinuclear Au(I) complexes (AuC2R)2PPh2C6H4PPh2 (L1, R = Fc; L2, R = C6H4Fc) containing ferrocenyl units. These compounds exhibit a welldefined, essentially reversible solid-state oxidation in contact with different electrolytes, based on ferrocenyl-centered oxidation processes involving anion insertion, which appears to satisfy the required conditions of reversibility, anion permeation, and stability. Combining midpeak cyclic voltammetric potentials and chronoamperometric data by means of a diffusion model that incorporates partition and binding equilibria in the solid, electrode potentials appear to be essentially solvent-independent relative to the IUPAC-recommended bis(η-biphenyl)chromium(I)/bis(biphenyl)chromium(0) couple.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support is gratefully acknowledged from the MEC Project CTQ2011-28079-CO3-02, which is also supported with ERDF funds. We wish to thank Profs. Fritz Scholz and Milivoj Lovric for their help in revising the manuscript. This work has been performed by members of the microcluster “Grupo de ́ de bienes culturales y patrimoniales y estudios análisis cientifico de ciencia de la conservación” belonging to the Valencia International Campus of Excellence. We would like to thank to Dr. José Luis Moya López and Mr. Manuel Planes Insausti (Microscopy Service of the Universitat Politècncia de València) for their technical support.

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REFERENCES

(1) Bjerrum, N.; Larsson, E. Z. Phys. Chem. 1927, 127, 358−384. (2) Trasatti, S. Pure Appl. Chem. 1986, 59, 955−966. 25991


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Solvent-Independent Electrode Potentials of Solids Undergoing

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