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Solvent-Independent Electrode Potentials of Solids Undergoing Insertion Electrochemical Reactions: Part III. Experimental Data for Prussian Blue Undergoing Electron Exchange Coupled to Cation Exchange Antonio Doménech-Carbó,*,† Fritz Scholz,‡ and Noemí Montoya§ †

Departament de Química Analítica, Facultat de Química, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain Universität Greifswalwd, Institut für Biochemie, Felix-Hausdorff Straße 4, 17487 Greifswald, Germany § Departament de Química Inorgànica, Facultat de Química, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain ‡

ABSTRACT: Prussian blue-modified electrodes immersed in K+-containing solutions can be used to obtain a solvent-independent redox potential system. On the basis of theoretical modeling of diffusion processes occurring under the conditions of voltammetry of immobilized particles, voltammetric and chronoamperometric data can be combined to obtain solvent-independent electrode potentials for the K+-assisted one-electron reduction of Prussian blue to Berlin white. Data for water, MeOH, EtOH, MeCN, DMS, DMF, and NM are provided.

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INTRODUCTION Defining a scale of standard redox potentials that is independent of the solvent is a well-known demand to correlate electrochemical measurements in different electrolytes and obtain thermochemical quantities.1 To solve this problem there is the need to obtain the liquid junction potentials that build up between two solvents, a problem first formulated by Bjerrum and Larsson.2 Unfortunately, estimates of such liquid junction potentials involve extra-thermodynamic assumptions.3−6 Three main approaches have been used; the first two involve the assumption that liquid junction potentials are negligible when large ions are used in the salt bridge or become compensated when the reference salt is composed of a quasispherical cation and a quasi-spherical anion of about the same size. In the first case, typically, picrate Et4Npic cells,7 the supporting electrolyte ions have similar electrochemical mobilities and low solvation Gibbs energies in different solvents. In the second, typically, tetraphenylarsonium8 or tetraphenylphosphonium9 tetraphenylborates, the solvation Gibbs energies of the cation and the anion are assumed to be equal. A third approach involves the use as a reference of an electrochemical couple whose electrode potential is assumed to be solvent-independent. The proposed couples involve transition-metal complexes or organometallic compounds in two oxidation states for which it is implicitly assumed that there are identical solvation Gibbs free energies in both oxidation states. The IUPAC recommends using either the redox couple ferricenium ion/ferrocene or bis(η-biphenyl)chromium(I)/ bis(biphenyl)chromium(0) as a reference redox system.1,10,11 © XXXX American Chemical Society

The liquid junction potential problem is directly related to the impossibility of obtaining single-ion thermodynamic properties from purely thermodynamic data,12 thus resulting in a circular situation where liquid junction potentials could be determined from solvation Gibbs energies of individual ions or, conversely, such Gibbs energies could be determined if liquid junction potentials are known and, by extension, define a solvent-independent redox potential scale. Most approaches have been proposed to estimate single-ion thermodynamic quantities combining quantum mechanical calculations to describe the solvent portion in the vicinity of the ion with classical continuum modeling to describe the behavior of the solvent in regions relatively far from the ion.13−24 In this context, different electrochemical methods for determining Gibbs free energies of ion transfer between two solvents, based on the aforementioned extrathermodynamic assumptions, have been proposed. These involve the direct polarization of liquid/ liquid interfaces with two adjacent electrolyte-supported immiscible liquids,25 membrane-modified liquid−liquid interfaces,26,27 large surface area,28 micro/nanohole,29−32 and triple−phase boundary measurements at microdroplets immobilized on electrode surfaces.33−37 In a prior work38 the voltammetry of microparticles (VMP) methodology, a solid−state technique developed by Scholz et al.,39,40 was used to theoretically define solvent-independent redox systems based on the ion-assisted electrochemical reduction/oxidation of ion-insertion solids. This approach has Received: September 10, 2012

A

dx.doi.org/10.1021/jp308969j | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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recorded for PB-modified electrodes in contact with KNO3 solutions under our experimental conditions is in agreement with literature data, as can be seen in Figure 1a, where the

been previously applied to determine individual Gibbs energies of transfer of cation41 and anion42,43 between two miscible solvents. Here we present the possibility of defining a solventindependent redox potential scale based on the cation-assisted electrochemical reduction of Prussian blue (KFeIII[FeII(CN)6], PB). The proposed method involves the determination of redox potentials by combining voltammetric and chronoamperometric (CA) measurements on the basis of a theoretical model to describe the diffusion problem in an ion-insertion solid whose oxidized and reduced forms are insoluble.38 The application of this method to define solvent-independent potentials involves two extra-thermodynamic assumptions: (i) there is no accumulation of net charge in the solid complex/ electrolyte boundary region and (ii) the structures of the solid and the ion binding to the solid are not affected by the solvent. These conditions can, in principle, be accomplished by PB, whose ion-insertion electrochemistry has been extensively studied.44−47

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EXPERIMENTAL SECTION Cyclic voltammetric (CV), square-wave voltammetric (SWV), and CA experiments were performed in an electrochemical cell thermostatted at 298 K with 10−4 to 1.0 M aqueous solutions of KNO3, LiClO4, and potassium picrate (KPic) in organic solvents. Nanopure water and MeOH, EtOH, MeCN, DMSO, DMF, and NM (Carlo Erba) were used as solvents. VMP experiments was performed at PB-modified platinum (BAS MF2014, geometrical area 0.018 cm2) and paraffin-impregnated graphite electrodes (PIGEs, geometrical area of 0.031 cm2) using a CH I660 potentiostat. Electrode modification was performed using two different methods: (i) by abrasive transference of a 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−1) 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 adhered to the basal electrode. PIGEs were prepared by impregnated pyrolitic graphite bars in vacuo as described in literature.39,40 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. After electrochemical measurements at PB-modified electrodes, potentials were measured relative to the Fc+/Fc couple by recording CVs at glassy carbon electrode using 10−4 M ferrocene (Merck) as internal potential standard. Potentials relative to the BBCr+/BBCr couple were calculated from the recommended values10,11 of the Fc+/Fc couple relative to the BBCr+/BBCr pair.

Figure 1. CVs for PB films on gold electrode immersed into: (a) 0.05 M KNO3/water and (b) 0.05 M KPic/DMF. Potential scan rate 20 mV s−1.

potential range is restricted to the region where the K+-assisted solid-state reduction process resulting in the formation of Berlin white ({K2FeII[FeII(CN)6]}) occurs. This process can be written as: {KFe III[Fe II(CN)6 ]} + K +solv + e‐ ⇄ {K 2Fe II[Fe II(CN)6 ]} (1)

where { } denotes solid phases. In contact with organic solvents containing KPic as a supporting electrolyte, the voltammetric pattern deviates from reversibility, with cathodic and anodic peak potentials being separated ca. 300 mV, as can be seen in Figure 1b. The peak potential separation increases with increasing scan rate, whereas it decreases with increasing concentration of the supporting electrolyte. Interestingly, the peak potentials become essentially constant after two to three potential cycles. In contact with organic solvents containing LiClO4 as a supporting electrolyte, the voltammetric pattern was essentially the same, the peak potentials being slightly different from those recorded in KPic electrolytes. No differences were found between PIGE’s with abrasively attached PB and PB films on gold and platinum electrodes. Although this response reflects a nonideal voltammetric behavior, it could be in principle used for estimating formal potentials because the midpeak potential remains essentially independent of the potential scan rate. Such midpeak potentials vary linearly with the logarithm of the concentration of K+ with slopes of 55 ± 5 mV/decade (see Figure 2), consistent with a reversible behavior. In fact, different systems exhibiting small deviations from reversibility can be used as potentiometric sensors under voltammetric conditions similar to those used here.48,49 The electrochemical reduction process of a microparticulate deposit of PB on an inert electrode given by eq 1 can be described following VMP literature50−55 by 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 transport within the solid, a situation that can be

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RESULTS AND DISCUSSION PB Voltammetry. In contact with aqueous electrolytes, PB displays a well-defined ion insertion electrochemistry associated with the oxidation of carbon coordinated low-spin Fe(II) ions and the reduction of nitrogen-coordinated high-spin Fe(III) ions. In contact with electrolyte solutions where this compound is not soluble, PB-modified electrodes yield two reversible one−electron couples corresponding to the above processes, which involve, respectively, the expulsion of K+ ions from the crystal lattice and the ingress of metal cations from the supporting electrolyte.44−47 The voltammetric response B



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scribes a binding equilibrium and so a respective equilibrium constant Kbd = (a{K2FeII[FeII(CN)6]})/(a{KFeII[FeII(CN)6]−}aK+solid ) can be defined. It needs to be mentioned that the standard redox potential, E⊖, cannot yet be defined on a strict basis because the activities of the involved species cannot be defined as in solutions but only approximated by concentrations. Under reversibility conditions, the composition of the solid is determined by the electrode potential according to the Nernst equation.51−55 Then, the midpeak potential of the cyclic voltammogram, Emp, obtained for the K+-assisted reduction of PB, is a good approximation of the formal potential E⊖ c ′: ⊖ Emp ≈ Ec⊖′ = E PB +

(6)

Figure 2. Representation of Emp versus log cK+solution for PB-modified electrodes immersed into KNO3/water and KPic/DMF electrolytes. From CVs under conditions such as in Figure 1.

The midpeak potential deviates from the formal potential just by a term involving the diffusions coefficients. This term is frequently very small because the diffusion coefficients of the involved species do not differ too much. The midpeak potential can further deviate from the formal potential if the symmetry coefficient α is not equal to 0.5, which is unlikely in the case of PB. In this equation, E⊖ PB represents the standard potential for the redox process described by eq 4, aK+solid is the activity of the K+ ions in the electrolyte solution, and aPB and aBW are the thermodynamic activities of PB and Berlin white solids. (See the comment above relating to the problems to define these data.) The equilibrium constant of the overall reaction, that is, reaction 1, can be described as follows:38

represented in terms of coupled diffusion of electrons and ions in mutually perpendicular directions. In this context, large peak potential separations obtained in CV of PB-modified electrodes in contact with organic solvents could be attributed to different factors, from deviations from reversibility in the charge-transfer process, appearance of miscibility gaps between the oxidized and reduced forms of the solid, uncompensated ohmic drops and capacitive effects, among others.48,49,56 Miscibility gaps can be excluded in the case of PB because they have never been observed for that compound.44−47 The difference between the voltammetric response in contact with water and organic solvents, however, suggests that kinetic effects associated with the solvation/desolvation of K+ ions could be decisive for explaining such different behavior. Theoretical Approach. The reduction process described by eq 1 can be formally separated into four processes: (i) Diffusion of solvated K+ ions from the solution bulk to the particle/electrolyte boundary, accompanied by ion desolvation and placing of the desolvated ion at the particle surface: K +solv ⇄ K +surf + solvent

K = KbdK ptKET a{K 2FeII[FeII(CN)6 } a K +solid = × a{KFeII[FeII(CN)6 ]‐ }a K +solid a K +solution a{KFeII[FeII(CN)6 ]− } × a{KFeIII[FeII(CN)6 ]}ae− a{K 2FeII[FeII(CN)6 ]} = a{KFeIII[FeII(CN)6 ]}a K +solutionae−

(2)

(3)

(iii) Reduction of Fe(III) centers: {KFe III[Fe II(CN)6 ]} + e‐ ⇄ {KFe II[Fe II(CN)6 ]− }

(7)

The product KbdKpt also stands for a charge-transfer equilibrium, here the transfer of potassium ions: a{K 2FeII[FeII(CN)6 } a K +solid KbdK pt = × a{KFeII[FeII(CN)6 ]− }a K +solid a K +solution a{K 2FeII[FeII(CN)6 ]} = a{KFeII[FeII(CN)6 ]− }a K +solution (8)

(ii) Ingress of K+ ions into the solid, that is, transfer to the bulk of the solid:

K +surf ⇄ {K+}

RT RT ⎛ aPBa K +solid ⎞ ln KbdKex + ln⎜ ⎟ nF nF ⎝ aBW ⎠

(4)

+

(iv) K ion association to compensate the negative charge of the electron:

The values of such constants can be theoretically correlated with CA curves via modeling the diffusion process. The proposed model incorporates the general formulation developed by Andrieux and Savéant57 and Laviron58 to describe charge transport in redox polymers using diffusion Fick’s laws.59 In this formulation, it is assumed that a homogeneous film of PB is deposited on the base, inert electrode so that the electron diffusion through the solid is considerably faster than ion diffusion. It is subsequently assumed that semiinfinite boundary conditions apply so that the diffusion problem can be treated as the diffusion of K+ ions in one direction through two (solution and solid) phases. The proposed model incorporates the consideration of both the exchange reaction and the binding equilibrium in the solid represented, respectively, in terms of the models from Bard et al.62 and Wu et al.63 for redox

{KFe II[Fe II(CN)6 ]− } + K +solid ⇄ {K 2Fe II[Fe II(CN)6 ]} (5)

Of course, reactions 4 and 5 are coupled and proceed simultaneously. Equations 2 and 3 taken together describe the transfer of potassium ions from solution to solid, and the equilibrium can be described by the partition constant, Kpt = (aK+solid )/(aK+solution), similar as in the case of redox polymers57,58 and glass electrodes.59−61. Equation 4 can be taken as a “pure” solidstate redox couple for which, in principle, a standard redox potential, E⊖, can be attributed, or an equilibrium constant KET = (a{KFeII[FeII(CN)6]−})/(a{KFeIII[FeII(CN)6]}ae−). Equation 5 deC



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varies on the electrolyte concentration, as shown in Figure 4. To rationalize this behavior, one can consider that the overall

polymers. Then, solving the diffusion problem leads to the following expression for the CA current obtained upon application of a potential sufficiently negative to ensure diffusion control:38 i=

2nFSc K +solutionK ptDK1/2 +

solution

(γKeff+ + K pt)(πt )1/2

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

× exp[−(j + 1/2)2 δ 2/DKeff+solid t ]

(9)

where S is the surface area of the electrode, cK+solution is the , the concentration of K+ ions in the electrolyte, DK+solid and DK+solution diffusion coefficients of K+ ion through the solid and in the solution, respectively, and δ is the thickness of the layer. In eq eff 1/2 + 9, γeff and: K+ = (DK solution /DK+solid) DKeff+solid =

DK +solid 1 + Kbdc M[1 + KbdK ptc K +solution]

Figure 4. Variation of (CSL)short with the concentration of K+ determined in CA experiments at PB films on gold in contact with KNO3/water and KPic/DMF electrolytes.

(10)

In the above equation, cM denotes the concentration of immobile iron redox centers in the solid. Equation 8 tends, at relatively long times, to a Cottrell-like behavior given by: (it 1/2)lim =

diffusion process is actually depending on the cation diffusion through both the electrolyte and solid film phases. At high electrolyte concentrations and relatively long times, diffusion through the solid film should be rate-determining so that eqs 10 and 11 apply. At short times and low or moderate electrolyte concentrations, one can assume that the aforementioned partitioning and binding equilibria are not established. Under these circumstances, cation diffusion can be described in terms of biphasic diffusion for which two extreme models can be proposed following the description of Andrieux et al.64 for redox polymers. First, it is assumed that full coupling in the cation diffusion between the two phases occurs. Then, cation diffusion would be equivalent to monophasic solution with an apparent diffusion coefficient given by:

2nFSc K +solutionK ptDK1/2 +

solution

(γKeff+ + K pt)π 1/2

(11)

To determine Kpt and Kbd from eqs 9−11, we need to dispose of the values of the surface area and the diffusion coefficients of K+ in the solution and solid phases. This is made difficult, however, by the uncertainty in the S value because of the particulate nature of the solid deposit. For solving this 1/2 problem, the values of SD1/2 K+solid and SDK+solution , which appear in eqs 8−10, were estimated from CA data, as described in the next section. Chronoamperometry of PB. Figure 3 shows it1/2 versus t graphs for CA at PB-film on gold in KPic/DMF. The obtained graphs can be described in terms of two Cottrell-type responses (i proportional to t−1/2) at relatively short (t < 0.02 s) and relatively long (t > 0.10 s) times, respectively, (CSL)short and (CSL)long. The slope of Cottrell i versus t−1/2 plots, (CSL)short,

DKapp + =

c MDK +solid + c K +solutionDK +solution c M + c K +solution

(12)

The CA current/time response being given by: i=

nFS(c M + c K +solution)1/2 (c MDK +solid + c K +solutionDK +solution )1/2 (πt )1/2 (13)

The second extreme model, which would be applicable as long as the diffusion front of the diffusing species in solution phase remains within the solid coating,65,66 assumes that cation diffusion through the solid film and the electrolyte diffusion are entirely decoupled. Now the CA current would be, simply, the sum of the independent contributions of the Cottrell-type diffusion through the electrolyte and the solid coating: i=

+ c K +solutionDK1/2 nFS(c MDK1/2 ) + + solid

(πt )1/2

solution

(14)

Table 1 summarizes the equations used to describe the Cottrell slopes appearing in CA experiments under different conditions. Short/long times and high/low electrolyte concentrations. Consistently, plots of (CSL)short versus cK+solution at low electrolyte concentrations can be fitted to straight lines, as predicted by eq 14 (see Figure 5), whereas at intermediate electrolyte concentrations, linear variations of (CSL)short on

Figure 3. it1/2 versus t graph for CA at PB film on gold immersed into 0.050 M KPic/DMF. Applied potential: −0.25 V versus AgCl/Ag. Dotted lines indicate the regions where Cottrell-type behavior is attained. D



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Table 2. Values of γK+ = (DK+solution/DK+solid )1/2 Estimated from Experimental CA Data by Using eqs 13 and 14 and Values of Kbd, Kpt, and K Calculated from the above and the Experimental (CSL)long/(CSL)short Values in CA Experiments at PB Films on Graphite Immersed in 0.10 M KPic Solutions at 298 Ka

Table 1. Summary of Theoretical Apparent Cottrell Slopes for the Different Chronoamperometric Conditions in This Study “short” times low c

+ Ksolution

nFS(c MDK1/2 + solid

+

c K + DK1/2 ) + solution solution

“long” times 1/2 1/2 nFScM cK+

π 1/2 high cK+solution

nFSc K +

DK1/2 +

solution

π 1/2

solution

DK1/2 +

solution

solution

π 1/2 2nFSc K +

3 −1/2 solvent SD1/2 ) K+solid(cm s

K ptγKeff+ DK1/2 +

solution

water MeOH EtOH MeCN DMSO DMF NM

solution

(γKeff+ + K pt)π 1/2

a

8.0 8.0 8.0 8.0 8.0 8.0 8.0

× × × × × × ×

−8

10 10−8 10−8 10−8 10−8 10−8 10−8

3 −1/2 SD1/2 ) K+solution (cm s

2.7 4.8 4.6 5.5 5.4 5.7 6.0

× × × × × × ×

−6

10 10−6 10−6 10−6 10−6 10−6 10−6

γK+ Kbd (M−1)

Kpt

34 60 58 69 68 71 75

0.21 0.25 0.30 0.38 0.34 0.30 0.51

3 3 3 3 3 3 3

cM = 1.5 × 10−3 mol/cm3.

obtained from CA experiments in different solvents. Using such diffusion parameters, the values of Kpt and Kbd can be calculated from CA curves combining the values of (CSL)short and (CSL)long for high electrolyte concentrations for which, using eq 11, one can take: cK+solution ⎛ K ⎞ ⎛ (CSL)short ⎞ pt ⎜ ⎟ ⎟ ⎜ 2 ≈ γ + K ⎜ eff ⎟ ⎝ (CSL)long ⎠ ⎝ γK+ + K pt ⎠

(15)

Using the above parameters, experimental CA curves can be fitted to theoretical ones predicted by eq 9, as shown in Figure 7. Here experimental data for a 0.40 M KPic solution in DMF are compared with theoretical data, taking cM = 1.50 × 10−3 −6 mol/cm3; SD1/2 cm3 s1/2; γK+ = 71; Kpt = 0.30; K+solution = 5.7 × 10 −1 and Kbd = 3 M . Solvent-Independent Electrode Potentials. Voltammetric and CA data can be combined to obtain solvent-

+ Figure 5. (CSL)short versus cKsolution plots in the region of low K+ concentration determined in CA experiments at PB films on gold in contact with KNO3/water and KPic/DMF electrolytes.

+ c1/2 K+solution , as can be predicted from eq 13, assuming cM > cKsolution , are approached. (See Figure 6.) Combining data from such linear representations, a direct estimate of the diffusion parameters 1/2 1/2 + + + SD1/2 can be K+solution and SDK+solid and then γK = (DKsolution /DKsolid ) obtained. Table 2 summarizes the corresponding values

Figure 7. Comparison of experimental CA data for PB immersed into 0.40 M KPic/DMF with theoretical predictions from eq 9 for selected −6 3 values of δ, taking cM = 1.50 × 10−3 mol/cm3; SD1/2 K+solution = 5.7 × 10 cm 1/2 −1 + s ; γK = 71; Kpt = 0.30; and Kbd = 3 M .

Figure 6. Plots of (CSL)short versus cK1/2+solution in the region of intermediate K+ concentrations determined in CA experiments at PB films on gold in contact with KNO3/water, Kpic/MeOH and KPic/ DMF electrolytes. E



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CONCLUSIONS The potassium cation-assisted reduction of PB to Berlin white permits us to define a solvent-independent redox potential system to be used under voltammetric conditions using the voltammetry of immobilized particles methodology. Application to a diffusive model that accounts for partition and binding equilibria in the solid permits us to estimate solventindependent potentials from CV midpeak potentials and CA data. Such system satisfy the essential criteria theoretically required: high electrochemical reversibility, insolubility of the oxidized, and reduced solid forms and stability under voltammetric conditions.

independent electrode potentials corresponding to the redox couple represented by means of eq 5. Under the aforementioned assumptions, the solvent-independent electrode potential E⊖ PB would be: RT RT ln K − ln a K +solution nF F

⊖ E PB = Emp −

(16)

Table 3 compares the voltammetric midpeak potentials, Emp and the K (= KptKbd) values estimated from CA data for Table 3. Midpeak Potential Data Recorded in Cyclic Voltammograms at PB Films on Gold in Contact with 0.10 M KNO3/Water and 0.10 M KPic/Organic Solvent Solutions at 298 K

a

solvent

Emp vs Fc+/Fc (mV)

+ E⊖ c ′ (Fc /Fc) vs (BBCr+/BBCr) (mV)a

K (M−1

E⊖ PB vs (BBCr+/BBCr) (mV)


−188 −344 −322 −280 −327 −436 −45

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

0.63 0.75 0.90 1.14 1.02 0.26 1.54

+868 +866 +877 +890 +854 +829 +1100

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*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 thank Prof. Milivoj Lovric for his help in revising the manuscript. This work has been performed by ́ members of the microcluster “Grupo de análisis cientifico de bienes culturales y patrimoniales y estudios de ciencia de la conservación” belonging to the Valencia International Campus of Excellence.

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different solvents. The values of Emp and E⊖ PB are referred in this Table to the BBCr+/BBCr couple, which is that recommended by Gritzner and Kuta10,11 as a nearly solvent-independent redox system under voltammetric conditions. As can be seen in Table 3, on the BBCr+/BBCr scale, both the Emp and E⊖ PB values become close, with maximum difference of ca. 50 mV. This suggests that the proposed system could reasonably be taken as a solvent-independent redox system easily used to operationally define a solvent-independent redox system. As can be seen in Table 4, the values of the difference between the E⊖ PB 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.

water

MeOH

EtOH

MeCN

DMSO

DMF

NT

0

156 0

134 −22 0

92 −64 −42 0

139 −17 5 47 0

248 92 114 156 109 0

water

MeOH

EtOH

MeCN

DMSO

DMF

−143 −299 −277 −235 −282 −391 0 NT

0

2 0

−9 −11 0

−22 −24 −13 0

14 12 23 36 0

39 37 48 61 25 0


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Table 4. Differences in the E⊖ PB Potentials (in mV) between Different Pairs of Solvents Relative to: (a) Fc+/Fc Couple and (b) BBCr+/BBCr Couple (a)

AUTHOR INFORMATION

Corresponding Author

Data from Kuta and Gritzner.19

water MeOH EtOH MeCN DMSO DMF NM (b)

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−232 −234 −223 −210 −246 −271 0 F



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