Kinetics of reduction of aqueous hexaammineruthenium(III) ion at Pt and Au microelectrodes: Electrolyte, temperature, and pressure effects

Article abstract of DOI:10.1021/ic400062b

Rate constants k_el obtained by impedance spectroscopy for the reduction of Ru(NH₃)₆³⁺ at polycrystalline Pt and Au ultramicroelectrodes depend strongly on the identity and concentration of the anion present in t

Full text of DOI:10.1021/ic400062b

Article
pubs.acs.org/IC
Kinetics of Reduction of Aqueous Hexaammineruthenium(III) Ion at
Pt and Au Microelectrodes: Electrolyte, Temperature, and Pressure
Effects
Vijendran Vijaikanth,† Guangchun Li, and Thomas W. Swaddle*
Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4
S
* Supporting Information
ABSTRACT: Rate constants kel obtained by impedance spectroscopy for
3+
the reduction of Ru(NH3)6 at polycrystalline Pt and Au ultramicroelectr-
odes depend strongly on the identity and concentration of the anion present
−
−
in the order CF3SO3 < Cl− < ClO4 , but not on the cation of the
supporting electrolyte (Na+, K+, H+). For Cl− as the sole anion present, kel is
directly proportional to the total [Cl−], such that kel would be zero if Cl−
were hypothetically absent, indicating that Cl− is directly involved in
3+/2+
−
mediation of the Ru(NH3)6
electron transfer. For CF3SO3 as the sole
−
counterion, the dependence of kel on the total [CF3SO3 ] is not linear,
possibly because blocking of the available electrode surface becomes
⧧
dominant at high triflate concentrations. Volumes of activation ΔVel for
reduction of Ru(NH3)63+ at an electrode in presence of Cl− or CF3SO3− are
much more negative than predictions based on theory (Swaddle, T. W.
Chem. Rev. 2005, 105, 2573) that has been successful with other electron transfer reactions but which does not take into account
⧧
the involvement of the anions in the activation process. The strongly negative ΔVel values probably reflect solvation increases
peculiar to activation processes of RuIII/II am(m)ine complexes, possibly together with promotion of desorption of surface-
−
3+
blocking Cl− or CF3SO3 from electrodes by applied pressure. Frumkin corrections for Ru(NH3)6 within the diffuse double
⧧
layer would make ΔVel even more negative than is observed, although the corrections would be small. The strongly negative
⧧
3+
ΔVel values are inconsistent with reduction of Ru(NH3)6 in direct contact with the metallic electrode surface, which would
entail substantial dehydration of both the electrode and Ru(NH3)63+. Reduction of Ru(NH3)63+ can be regarded as taking place
in hard contact with adsorbed water at the outer Helmholtz plane.
−RT(∂ ln kel/∂P)T) for an electrode reaction that is likely to be
INTRODUCTION
■
close to fully adiabatic. Only aqueous systems are considered,
Research in our laboratory in recent years has focused on
mechanistic insights provided by the effects of hydrostatic
pressure on the rates of heterogeneous (electrode) and
homogeneous electron transfer reactions of transition-metal
complexes in solution.1,2 Electrode reaction rates, however, are
notoriously susceptible to the influence of the nature of the
electrode surface. Although electron transfer at metal electrodes
is traditionally viewed as adiabatic, we have suggested1 that in
many cases this sensitivity to the state of the surface probably
reflects nonadiabatic electron transfer (i.e., coupling between
the electronic wave functions in the reactant and the electrode
is weak relative to thermal energies3), so that the electrode
reaction rate becomes strongly distance dependent and
consequently sensitive to adsorbed substances, oxides layers,
and so forth on the electrode surface. The standard techniques
of electrode kinetics at conventional electrodes used heretofore
in variable-pressure studies, notably ac voltammetry (ACV), are
limited to moderately slow reactions having standard rate
constant kel less than about 0.3 cm s−1, the slowness of which
may indicate substantial departure from adiabaticity. We have
⧧
since solvent dynamics can determine ΔVel for electrode
processes in nonaqueous media.1
The question of the extent of nonadiabaticity in electrode
reactions is controversial. The reduction of quinones at graphite
electrodes is the subject of a current debate4,5 in which
Compton et al.4 favor a nonadiabatic interpretation. For
reductions of other organic solutes at electrodes in nonaqueous
solvents, Savea
́
nt6 has derived a variant of the classical Marcus−
Hush relationship which allows description of the passage from
nonadiabatic to limiting adiabatic electron transfer. In a similar
vein, Compton et al.7,8 have estimated the degree of adiabaticity
and the changeover between nonadiabatic and limiting
adiabatic behavior for electroreduction of 3-nitrophenolate
and 1-nitropentane at Hg microhemispheres in organic
solvents, using an asymmetric version of Marcus−Hush theory
to interpret the pre-exponential factor in the temperature
dependence of kel. For reductions of aqueous inorganic solutes
at solid metal electrodes, it is typically assumed that the rate
therefore sought information on the pressure dependence of kel
Received: January 10, 2013
Published: February 19, 2013
⧧
(conveniently expressed as the volume of activation ΔVel
=
© 2013 American Chemical Society
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constant should be substantially independent of the nature of
the metalin the present study, Au vs Ptif the reaction is
fully adiabatic;9 for a nonadiabatic process, kel would depend on
the density ρF of electronic states at the Fermi level of the
electrode as well as on the electrode-reactant distance. Gosavi
and Marcus,10 however, point out that kel can also be
approximately the same at Pt and Au for a nonadiabatic
reaction if a large ρF, as is typical for d bands as in Pt, is offset
by the weaker coupling of d bands to the reactant relative to s
bands as in Au. Thus, even if kel for a particular reaction is
approximately the same at Au and Pt electrodes, the reaction is
not necessarily adiabatic. As far as the variable-pressure studies
reported here are concerned, nonadiabaticity will affect kel but
EXPERIMENTAL SECTION
■
Fabrication of Ultramicroelectrodes (UMEs). Gold (⌀ 12.7 μm,
99.9%; ⌀ 25 μm, 99.95%) and Pt (⌀ 25 μm, 99.95%; ⌀ 10 μm,
99.95%) wires were obtained from Alfa Aesar. The wires were soldered
to Cu connecting wire and then sealed in soft glass tubes by melting
the latter cautiously in a Bunsen flame. The other end was closed with
an insulating epoxy resin. Then the uniform microelectrode surface
was exposed by grinding the tip with fine sandpaper (1500 grade)
followed by polishing in a suspension of 0.05 μm alumina. For the high
pressure work, the Au (⌀ 25 μm) and Pt (⌀ 25 μm) electrodes were
constructed from polypropylene micropipet tips by melting the latter
cautiously with an ethanol flame. The ends of the micropipet tips were
then cut off squarely to expose a disk UME. The remainder of the tip
was trimmed down and glued to the electrode holder with an
insulating epoxy resin. The integrity of the UME disks and seals as
checked with an optical microscope. The UME faces were polished
with an aqueous suspension of 0.05 mm alumina, sonicated briefly in a
K2S2O8/H2SO4 bath to remove any traces of oxidizable matter, then
sonicated for 2 min in deionized water. Final cleaning to eliminate any
contaminants (e.g., a surface oxide layer) that might interfere with the
electrochemical measurements was carried out at the start of each
experiment by cycling the potential up to 16 times over the working
range (typically −500 to +200 mV vs AgCl/Ag) at 20 mV s−1 until the
11,12
⧧
probably not ΔVel .
As remarked originally by Gennett and Weaver,13 the low-
3+/2+
spin/low-spin (t2g5/t2g6) Ru(NH3)6
electron transfer
reaction, in which the Ru−N bond length difference between
the effectively substitution-inert reactants (4.0 pm)14 and
consequently the internal reorganization energy are very small,
is likely to be a fast, “well-behaved”, adiabatic reaction. The
3+/2+
Ru(NH3)6
couple has therefore come to be widely
regarded as an electrochemical “reference reaction”, whether
the electrode material be metallic,13,15−23 metallic with
adsorbed monolayers,20,24−36 pyrolytic graphite,37−41 glassy
carbon,42 or boron-doped diamond.43,44 For all these electro-
cyclic voltammogram (CV) showed a constant limiting current Ilim
.
These measurements of Ilim gave values of the diffusion coefficient D of
3+
Ru(NH3)6
D = Ilim/4FrC
(1)
des, it emerges that the Ru(NH3)63+/2+ couple is free of most of
3−/4−
(where C is the concentration of Ru(NH3)63+, F is the Faraday
constant, and r is the radius of the UME disk) in reasonable agreement
with those in the literature; as noted below, however, Ilim measured
from a CV depends on the identity and concentration of the
supporting electrolyte and comparisons can only be made where these
are the same. For example, for UMEs made from Au or Pt wire of
diameter 2r = 25.0 μm (according to the wire manufacturer), Ilim for
5.0 mmol L−1 [Ru(NH3)6]Cl3 in 0.1 mol L−1 KCl at 25 °C was 23−24
nA, corresponding to D = 9.5 × 10−6 cm2 s−1; literature values of D for
Ru(NH3)63+ for these conditions range from 6.4 × 10−6 cm2 s−1 to 9.4
× 10−6 cm2 s−1.19,49−52 These observations, together with the
consistency of the kinetic results between different experiments as
described below, indicate that the potential cycling procedure did not
have adverse effects on the electrochemical measurements.
Materials. Deionized water was further purified to ≥18.0 MΩ cm
by passage through a Barnstead E-Pure train. [Ru(NH3)6]Cl3 (Strem
Chemicals, 99%), triflic acid (Sigma Aldrich, 98%), hydrochloric acid
(Merck), perchloric acid (Baker), NaCl (Fisher Certified) and KCl
(Fisher Certified) were used as received, and KCF3SO3 was either
prepared as previously described53 or purchased from Alfa Aesar and
recrystallized from methanol. [Ru(NH3)6](CF3SO3)3 was prepared
from aqueous [Ru(NH3)6]Cl3 by removal of Cl− with AgCF3SO3,
followed by precipitation and recrystallization of [Ru(NH3)6]-
(CF3SO3)3 from aqueous CF3SO3H, as described by Lavallee et
al.;54 the purity of the colorless needles was established by multiple
CHN microanalyses (calc.: C, 5.54; H, 2.79; N, 12.92; found: C, 5.67;
H, 2.84; N, 12.86%) and by the molar absorbance of aqueous solutions
(460 10 L mol−1 cm−1 at 275 nm54).
Electrochemical Measurements. CV and variable-frequency ac
impedance measurements were made with either a thermostatted
conventional three-electrode cell or the high-pressure three-electrode
Teflon cell previously described,53 using a Model CHI650C
electrochemical workstation with a Model CHI200 picoamp booster
and Faraday cage (CH Instruments, Austin, TX); backup measure-
ments using a Model CHI650B workstation gave identical results. The
reference electrode was Ag/AgCl/KCl (satd. aq. at 25 °C, or, for
experiments at variable P or T, 4.0 mol L−1, i.e., just below
saturation55), freshly prepared before each day’s series of measure-
ments by anodic electrolysis of a silver wire in 4.0 mol L−1 KCl
solution at 0.7 V vs Ag/AgCl/KCl(satd) for 20 min. The working
electrode was a Pt or Au UME, and the counter electrode a Pt wire
the aberrations associated with the Fe(CN)6
cou-
ple,1,24,39−44 traditionally used as a reference system in
electrode kinetics. For metallic electrodes, the reported
3+/2+
Ru(NH3)6
electron transfer rates are very fast, albeit
somewhat scattered for reasons discussed below, and in most
cases appear to be roughly independent of the metal of the
electrode, consistent with substantially adiabatic election
transfer.9 Velmurugan et al.,45 however, found somewhat
3+
higher rates of reduction of Ru(NH3)6 at Pt than at Au
disk nanoelectrodes in various electrolyte solutions, and
suggested some degree of nonadiabaticity, so this remains an
open question.
Successful measurements of the high kel values for the
3+/2+
Ru(NH3)6
electrode reaction were made by Gennett and
Weaver13 using ac voltammetry at a dropping Hg electrode, and
were soon followed by those of Iwasita et al.15,16 using various
ring electrodes in turbulent pipe flow. In many of the early
reports, however, it is unclear whether the uncompensated
resistance of the solutions had been adequately allowed for in
deriving kel values.46 For convenient adaptation to high pressure
3+/2+
experiments, we chose to study the Ru(NH3)6
electrode
kinetics by ac impedance measurements at Pt and Au
ultramicroelectrodes, as used by Muzikar
their studies of this system in dilute HClO4 media at 25 °C.
Oxidizing anions such as perchlorate and nitrate, however, are
́
̌
and Fawcett22,23 in
usually avoided in Ru ammine chemistry because of the risk of
oxidation of Ru(NH3)63+ and especially Ru(NH3)6
;
47,48 this is
2+
́ ̌
unlikely to have been significant in the work of Muzikar and
Fawcett because of the evidently short time-scales of their
−
experiments, the moderate concentrations of ClO4 , and the
merely transient presence of Ru(NH3)62+. In our study, the
variable-pressure and -temperature experiments extended over
several hours, and therefore only chloride and trifluorometha-
nesulfonate (triflate) media and Ru(NH3)63+ salts were used in
them; no attempt was made to isolate solid [Ru(NH3)6]-
(ClO4)3 as it is of limited solubility24 and is potentially
explosive.
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where Rct is the charge transfer resistance.22,23,58 Extrapolation
of Zf′ to infinite frequency gives Rct, from which the standard
rate constant kel for the electrode reaction can be calculated
from eq 3, in which n is the number of electrons transferred per
mol (here, n = 1), a is the area of the UME disk, C is the bulk
concentration of the electroactive species, and the other
symbols have their usual meaning in the SI.
(typically ⌀ 0.5 mm, ∼1 cm long). Experiments at ambient pressure
were conducted with the cell either in the CHI Faraday cage or
completely enclosed in grounded Al foil, whereas for the high pressure
experiments it was sufficient simply to ground the pressure vessel; in
all cases, the external connectors were sheathed in grounded Al foil.
The pressure vessel and pressure train have been described
elsewhere;53 the pressure transmitting fluid was mixed hexanes,
separated from the hydraulic oil of the manual pump and intensifier by
a vessel with a free piston. All variable-pressure experiments were run
at 25.0 0.1 °C, which was maintained with externally thermostatted
water circulating through the pressure vessel jacket and measured
inside the pressure vessel before and after the pressure cycle. For
experiments at variable temperature and 0.1 MPa, a glass cell
incorporating a jacket for circulating water from the external
thermostat was used, and temperatures within the sample were
measured ( 0.1 °C) with a calibrated thermistor encased in an inert
plastic.
kel = RT/n2F2aCRct
(4)
If a UME is performing correctly, the CV should be a tight
sigmoidal trace rather than the “duck” shape familiar from
measurements with conventional electrodes. This was checked
as a prelude to each impedance measurement, as exemplified
for a series of supporting-electrolyte concentrations by Figure 2
in which it may be seen that the ideal sigmoidal shape is more
closely approached the higher the concentration of supporting
electrolyte (i.e., the faster the electrode reaction, see below).
Values of the transfer coefficient α were calculated from eq 5, in
which Emax is the potential of maximum real admittance Y′ (cf.
Figure 3) and E1/2 is the CV half-wave potential; in all cases,
All solutions contained 5.0 mmol L−1 [Ru(NH3)6]Cl3 or [Ru-
(NH3)6](CF3SO3)3 and were purged with Ar for 30 min before the
experiments. For measurements at ambient pressure, an Ar
atmosphere was maintained. Spectrophometric measurements at 275
nm showed that [Ru(NH3)6](CF3SO3)3 solutions underwent no
significant decomposition at near-ambient temperatures over at least
24 h. Measurements of the cell impedance were made using the
supplied CHI software by applying an ac signal of amplitude 10 mV
and frequency f within the range 0.96−96 kHz (depending on reaction
rate being measured) superimposed on a dc signal that was swept
́ ̌
|Emax − E1/2| ≤ 5 mV, whence α = 0.50 0.05 (cf. Muzikar and
Fawcett22). For example, for [Ru(NH3)6]Cl3 reduction on a 25
μm Au UME in 0.1 mol L−1 KCl at 25 °C, Emax = −0.134 V and
E1/2 = −0.135 V, giving α = 0.51.
typically over 250−350 mV on each side of the formal potential of the
3+/2+
Ru(NH3)6
couple (∼ −130 mV vs Ag/AgCl/KCl(satd)). Scan
Emax = E1/2 + (RT/F) ln[α/(1 − α)]
(5)
rates were normally 10 mV s−1.
If the CV was satisfactory, impedance measurements were
then made as a function of the dc potential at selected
frequencies. The frequencies typed in differed slightly from the
work-station’s actual operating frequencies f, which were
recorded and converted to angular frequencies ω = 2πf.
Whereas the uncompensated resistance can be corrected for by
direct subtraction from the real impedance, correction for the
double-layer capacitance Cdl requires conversion to admittances
Yf (reciprocals of Zf). Typical real and imaginary admittances
Yf′ and Yf″ are plotted in Figure 3, which also illustrates the
importance of correcting for Ru, at least in Yf″. The absence of
substantial distortions and baseline noise in admittance vs
potential plots such as Figure 3 indicated that instrumental and
other artifacts that may occur at high frequencies59 were
negligible.
RESULTS
■
In the following, the usual assumption56 is made that the
diffusion coefficients of Ru(NH3)63+ and Ru(NH3)62+ are close
enough to be taken as approximately the same, as literature data
affirm.16,21,57
Electrode and Electrolyte Effects. Figure 1 shows a
simplified equivalent (Randles) circuit relating the overall
In accordance with eqs 2 and 3, Zf′ and Zf″ for a given
experiment were plotted together against ω−1/2 (a Randles
plot),58 as shown in Figure 4 for an experiment with 12 data
points spanning a wide frequency range (0.962−46.3 kHz). A
result was accepted only if, within the experimental uncertainty,
the Zf′ and Zf″ plots were linear, their slopes s were the same,
and Zf″ extrapolated to zero at infinite frequency (ω−1/2 = 0),
confirming the absence of instrumental distortions at high
frequencies. The intercept of the Zf′ plot then gave Rct, from
which the rate constant kel could be calculated from eq 4; in
practice, however, errors in the impedances Zf′ and Zf″ tended
to be similar, and averaged values of (Zf′ − Zf″) were therefore
used in place of Rct, giving a modest improvement in the
standard error. For example, least-squares regression of the Zf″
data of Figure 4 gave a slope s of 6.87 0.09 MΩ rad1/2 s−1/2
Figure 1. Simplified equivalent circuit for an electrochemical cell with
UME working electrode.
impedance of an electrochemical cell to the faradaic impedance
Zf, the Warburg (diffusional) impedance ZW, the uncompen-
sated solution resistance Ru, and the double-layer capacitance
Cdl. The Warburg impedance can be neglected at the ac
frequencies used in our experiments.58 Before making an
impedance measurement, the uncompensated resistance Ru was
measured and automatic correction for it was implemented
using the CHI software.
The impedance Zf can be resolved using the CHI software
into real (Zf′) and imaginary (Zf″) components, each of which
should be a linear function of ω−1/2, where ω = 2πf, with slope s
for a simple electron transfer process:
and intercept −0.57
0.54 kΩ (r2 = 0.9982); thus, the
intercept is negligible on the impedance scale, as eq 3 requires,
and the lower straight line in Figure 4 is therefore plotted with
the intercept set to zero. For Zf′, regression gave a slope s =
Zf′ = Rct + sω−1/2
(2)
7.01
0.13 MΩ rad1/2 s−1/2, which is not statistically
Zf″ = sω−1/2
(3)
distinguishable from that for Zf″, as required by eqs 2 and 3,
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Figure 2. Cyclic voltammograms of the reduction of 5.0 mmol L−1 [Ru(NH3)6](CF3SO3)3 at a Pt disk (⌀ 10 μm) at 25.0 °C; scan rate = 10 mV s−1.
Concentration of KCF3SO3 supporting electrolyte (mol L−1) = 0 (black), 0.05 (red), 0.10 (green), 0.15 (blue), and 0.20 (gray).
Figure 3. Real (Y′) and imaginary (Y″) admittances as a function of potential vs Ag/AgCl for reduction of [Ru(NH3)6]Cl3 (5.0 mmol L−1) at a Pt
disk (⌀ 25 μm) in 0.1 mol L−1 KCl at 30 °C and f = 3205 Hz. Blue, Yf′ uncorrected for uncompensated resistance Ru; black, corrected Yf′; green,
uncorrected Yf″; red, corrected Yf″. Scan rate 10 mV s−1.
and an intercept Rct = 17.9
average (Zf′ − Zf″) of 19.1
calculate kel. In practice, good Randles plots and acceptable
values of kel could usually be obtained with as few as 4−5
choices of f. Again, the consistency of the data at the highest
frequencies with the rest of the plot affirmed correct
instrumental function.59
Table 1 lists standard electrode reaction rate constants kel
derived from Randles plots in which the Zf′ and Zf″ lines were
parallel, the Zf″ plot extrapolated to zero at ω−1/2 = 0, and the
data scatter was acceptable, all within the experimental
uncertainty. The calculation of kel from eq 4 required values
of the effective areas a of the microelectrode disks; these could
0.8 kΩ (r2 = 0.9966), cf. an
0.4 kΩ which was used to
be determined either approximately from the manufacturer’s
wire diameters or more precisely from the limiting currents Ilim
of CVs of either Ru(NH3)6 or Fe(CN)6 solutions:
3+
3−
a = π(Ilim/4nFDC)2
(6)
where D is the diffusion coefficient of Ru(NH3)6 19,22,49−52 or
Fe(CN)63− (7.63 × 10−6 cm2 s−1).60 Values of a from eq 6 were
slightly greater than calculated from the geometrical cross-
section of the wire (e.g., in a typical experiment with Au and Pt
UMEs made from wire of diameter 25.0 μm, the areas
measured according to eq 6 corresponded to ⌀ 26.0 and 29.7
μm, respectively); these discrepancies are attributable to
microscopic roughness of the UME surfaces.61 For the
3+
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Pressure Effects. The results reported in this section all
3+
refer to reductions of Ru(NH3)6 at UMEs of diameter 25.0
μm, as UMEs of smaller diameters proved to be too fragile to
give reproducible measurements at variable pressure. Figure 6
shows the pressure dependences of the half-wave potential
(E1/2, from the midpoints of CVs run before each set of
impedance measurements at a given pressure P) and of the
corresponding standard rate constant kel for a typical
[Ru(NH3)6](CF3SO3)3 electrode reaction, in this case
reduction at a gold UME in 0.10 mol L−1 KCF3SO3 at 25.0
°C. Both plots are linear within experimental uncertainties. It
was important to show that the measurements taken with
increasing pressure (filled symbols) were consistent with those
subsequently taken with decreasing pressure (hollow sym-
bols)that is, that no time-dependent changes such as
decomposition of the Ru complexes occurred over the several
hours’ duration of the experiment.62 For the lower plot in
Figure 6, E1/2 = (−0.196 0.002) − (2.49 0.16) × 10−4P,
from which the volume of reaction ΔVel = −F(∂E1/2/∂P)T cm3
mol−1 for the Ru(NH3)6 reduction half-cell relative to Ag/
3+
AgCl is 24.0 1.6 cm3. The UME-CV method, however, is not
well suited to precise measurements of the small changes in
Figure 4. Randles plot for the reduction of [Ru(NH3)6](CF3SO3)3
(5.0 mmol L−1) in aqueous KCF3SO3 (0.20 mol L−1) at a gold disk
electrode (⌀ 25 μm) at 25.0 °C. Red data: real impedance Zf′. Green
data: imaginary impedance Zf″. Average uncompensated resistance was
7.59 0.08 kΩ.
E
1/2, and ΔVel values obtained in this way ranged from 20.3
1.6 cm3 mol−1 for reduction of [Ru(NH3)6](CF3SO3)3 in 0.10
mol L−1 KCF3SO3 at a Pt UME to about 25 cm3 mol−1 for
[Ru(NH3)6]Cl3 in 0.1 mol L−1 KCl at Au and Pt UMEs. These
results are nevertheless consistent with the definitive ΔVel
measurements of Tregloan and co-workers63−65 for reduction
3+
of Ru(NH3)6 made at conventional electrodes (20.2
0.4
purposes of this study, however, relative rather than absolute
values of kel are required in assessing electrolyte, pressure, and
temperature effects, and geometrical values of a based on the
wire diameters given by the manufacturers were used in
calculating the kel data of Table 1, which is common practice in
UME studies; possible contamination of the UMEs in
measuring Ilim prior to an experiment was thereby avoided.
The uncertainties cited in Table 1 represent the goodness of fit
to eqs 1 and 2 rather than absolute accuracy of kel; nevertheless,
reasonable agreement may be noted between kel values
obtained for given conditions but with different personnel
and sources of chemicals and materials. Agreement with
literature values of kel,13,15−23 where conditions were
comparable, was also satisfactory, given the difficulties in
obtaining reproducible kel for fast electrode reactions and the
lack of clarity in some earlier publications (e.g., Iwasita et
al.15,16) as to whether appropriate corrections (e.g., for
cm3 mol−1 in 0.1 mol L−1 KNO3 at Au, and 19.7 0.6 cm3
mol−1 in 0.1 mol L−1 NaClO4 at Hg/Au, relative to Ag/AgCl).
The pressure dependence of ln kel was linear, within the
experimental uncertainty, in all cases studied; in other words,
the volume of activation ΔVel⧧ was effectively constant over the
200 MPa pressure range. For [Ru(NH3)6](CF3SO3)3 in 0.10
mol L−1 KCF3SO3 at a gold UME (upper frame of Figure 6), ln
kel = (−1.999 0.030) + (6.15 0.30) × 10−3P for P in MPa,
whence ΔVel = −15.3
0.7 cm3 mol−1 for 0.10 mol L−1
⧧
⧧
KCF3SO3 at Au; for the same system at a Pt UME, ΔVel
=
−15.9 1.1 cm3 mol−1. For reduction of [Ru(NH3)6]Cl3 (5.0
⧧
mmol L−1) in 0.10 mol L−1 KCl, ΔVel = −12.3
1.0 and
−12.3
0.6 cm3 mol−1 at 25 μm Au and Pt UMEs,
⧧
respectively. Thus, ΔVel is independent of the UME metal
but shows some significant dependence on the nature of the
anion of the supporting electrolyte.
⧧
Measurements of ΔVel for perchlorate media at variable
uncompensated resistance, important for rapid electrochemical
50) had been applied. Table 1
3+/2+
pressure were impractical, as the rate constants, already fast at
ambient pressure, would become too fast for accurate
measurement at increased pressures. The possibility of
reactions such as Ru(NH3)6
shows that the main influences on kel are supporting electrolyte
identity and concentration, and the UME diameter; the identity
of the polycrystalline UME metal (Pt vs Au) has little effect.
Temperature Dependence of kel. The temperature
dependence of kel for [Ru(NH3)6](CF3SO3)3 in 0.1 mol L−1
KCF3SO3 at a Pt UME is shown in Figure 5 as an Arrhenius
plot (ln kel = ln A − Ea/RT) for which the activation energy Ea
= 18.8 1.1 kJ mol−1 and A = 4.3 × 102 cm s−1. Thus, the
temperature sensitivity of kel is quite low. Use of Eyring
enthalpies ΔHel⧧ (= Ea − RT) and entropies ΔSel⧧ of activation
−
oxidation of the Ru complexes by ClO4 over the time-scale
of a pressure cycle was also a concern.
DISCUSSION
■
Cyclic Voltammetry. The maxima |Ilim| of the (negative)
CV currents for reduction of Ru(NH3)6 were markedly
3+
dependent on the concentrations of the supporting electrolyte,
as shown for example in Figure 2. This reflects a substantial
contribution from the migration current,66 which is negative for
the reduction of a cation at an electrode but tends to zero as the
concentration of the supporting electrolyte (and hence the
solution conductivity) is increased. Thus, as shown in Figure 2,
the observed |Ilim| for the reduction of [Ru(NH3)6](CF3SO3)3
was largest when no supporting electrolyte was present, but
⧧
was avoided, as ΔSel values as normally calculated depend on
̈
the units of the rate constants, and naive comparison with other
entropy parameters could be misleading. For the reduction of
[Ru(NH3)6]Cl3 in 0.1 mol L−1 KCl at a gold UME (⌀ 25 μm),
5.3−29.1 °C, Ea was found to be 24.8
(Supporting Information, Figure S1).
1.3 kJ mol−1
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3+
Table 1. Dependence of Standard Rate Constants kel for the Reduction of Aqueous Ru(NH3)6 at Polycrystalline Au and Pt
a
UMEs on UME Disk Diameter and Supporting Electrolyte Concentration
X in [Ru(NH3)6]X3
Cl
electrolyte, mol L−1
none
Au 25 μm
Pt 25 μm
Au 12.7 μm
Pt 10 μm
0.089 0.001
KCl, 0.05
0.234 0.005
0.66 0.01
b
0.71 0.01
0.08
0.10
1.78 0.03
2.20 0.05
0.54 0.01
0.52 0.01
c
c
0.62 0.03
0.43 0.01
0.49 0.03
b
,c
0.15
0.20
0.88 0.03
1.05 0.01
b
1.16 0.17
HCl, 0.02
0.05
0.063 0.001
0.29 0.01
0.62 0.01
0.26 0.01
0.65 0.01
1.84 0.13
0.10
NaCl, 0.10
0.66 0.01
0.28 0.01
1.86 0.06
b,c
KO3SCF3, 0.10
0.38 0.01
0.29 0.02
0.98 0.02
0.27 0.01
b,c
HClO4, 0.02
0.05
0.21 0.01
0.84 0.01
CF3SO3
none
0.088 0.001
0.21 0.01
KO3SCF3, 0.05
0.21 0.01
0.39 0.01
0.18 0.01
0.38 0.01
0.21 0.01
0.46 0.01
0.68 0.01
0.97 0.01
1.16 0.01
0.10
0.15
0.20
0.57 0.01
0.53 0.01
0.85 0.02
0.33 0.01
HClO4, 0.02
0.05
0.95 0.03
a
b
25.0 °C, 0.1 MPa; [Ru(NH3)63+] = 5.0 mmol L−1. Uncertainties reflect standard errors in Rct or average (Zf′ − Zf″). Measurements by G.L.; all
c
others by V.V. Extrapolated to 0.1 MPa from high pressure kinetic measurements.
ideal tight sigmoid more closely in presence of ≥0.1 mol L−1
supporting electrolyte, which also gave higher rate constants
(Table 1) and generally better fits to eqs 2 and 3.
Measurements of kel at variable temperature and pressure
were therefore conducted using 0.1 mol L−1 KCl or KCF3SO3
as supporting electrolyte.
Factors Affecting the Rate Constants. The following
observations emerge from Table 1.
(1) Although one special advantage of UMEs is that they can
yield kinetic data in absence of a supporting electrolyte, values
of kel for [Ru(NH3)6]X3 without an added electrolyte are
presented only for X = Cl and CF3SO3 at a 25 μm gold UME;
for measurements on other systems without a supporting
electrolyte, the data quality criteria given above were not met.
(2) For a given anion X, kel is about the same at
polycrystalline Au and Pt UMEs of the same diameter
compare, for example, data for 0.10 mol L−1 added KCl, or for
0.10 mol L−1 KCF3SO3, at 25 μm UMEs. Muzikar
́ ̌
and
Figure 5. Temperature dependence of kel for reduction of [Ru-
(NH3)6](CF3SO3)3 in aqueous 0.1 mol L−1 KCF3SO3 at a Pt UME (⌀
25 μm).
Fawcett23 found that, for reduction of Ru(NH3)6 at single-
crystal Au UMEs, kel at Au(111) was significantly larger than at
Au(100), which may account in part for the difficulty in
obtaining reproducible kel values between polycrystalline UMEs
but also diminishes the effectiveness of an apparent lack of
dependence of kel on the identity of the metal of the electrode
3+
decreased with increasing concentrations of added KCF3SO3
(cf. the reduction of Tl(aq)+ at a mercury-on-silver UME in aq.
LiClO467). Moreover, the shape of the CVs approached the
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Mirkin gives kel = 2.6 cm s−1). For our purposes of determining
electrolyte, pressure, and temperature effects, however,
comparison of apparent values of kel at disk UMEs of a
common diameter was sufficient.
(4) The strong accelerating effect of supporting electrolytes
on kel is a function of the electrolyte concentration but is due
specifically to the anion. Thus, for supporting electrolytes MX
at 0.1 mol L−1, kel was essentially the same for M = K, Na, and
H when X was Cl. For different X, however, kel increased in the
sequence CF3SO3 < Cl ≪ ClO4. For reduction of [Ru-
(NH3)6]Cl3 at a gold electrode (⌀ 25 μm) at 25.0 °C (the most
extensive data set), kel was a linear function of [Cl−]
(Supporting Information, Figure S2), and a least-squares
regression of the data of Table 1 gave kel/cm s−1 = (−0.02
0.05) + (5.11
0.34)[Cl−]total, where [Cl−]total includes Cl−
from both KCl (if present) and [Ru(NH3)6]Cl3; the fact that
the intercept is zero within the error limit implies that the
reduction reaction rate would be negligibly small in the
hypothetical case in which no chloride was present. Thus, for
the system with chloride as the only anion present, the
electrode reaction mechanism intimately involves the anion,
even in absence of the supporting electrolyte. The limited data
for the triflate-only system at 25 and 10 μm disks are better
represented by curves passing through the origin; for the 10 μm
Pt disk, an empirical quadratic fit with R2 = 0.9994 extrapolated
to hypothetical zero triflate with kel = 0.050 0.020 cm s−1
0
(Supporting Information, Figure S3), from which case it can
again be inferred that the Ru(NH3)63+/2+ electrode reaction rate
would be very small in the hypothetical absence of the anion.
(5) Instrumental limitations set the upper limit of kel
obtainable at about 2 cm s−1, and accordingly no data for
[MX] > 0.20 mol L−1 are listed in Table 1. For the same reason,
kel values for reduction of [Ru(NH3)6−]X3 (X = Cl or CF3SO3)
in HClO4 are listed only for [ClO4 ] up to 0.05 mol L−1,
beyond which the reaction rates were too high to measure with
the desired accuracy. The standard rate constants at a gold
UME of diameter 12.7 μm in 0.02 mol L−1 HClO4 are
Figure 6. Pressure dependences of the half-wave potential E1/2 relative
to Ag/AgCl (lower frame), and the standard rate constant kel (upper
frame), for reduction of [Ru(NH3)6](CF3SO3)3 (5.0 mmol L−1) in
0.10 mol L−1 KCF3SO3 at a gold UME (⌀ 25 μm) at 25.0 °C; pH ≈ 5.
Filled symbols: increasing pressure. Open symbols: decreasing
pressure.
somewhat lower than that reported by Muzikar
́ ̌
and Fawcett22
as a criterion of adiabaticity. With this reservation, and noting
the argument of Gosavi and Marcus10 discussed in the
(0.54 cm s−1) for the same system (X presumably was Cl) at a
polycrystalline gold UME of diameter 12.5 μm (6.25 μm
radiusapparently misprinted as diameter in Table 2 of ref
22).
3+
Introduction, the reduction of Ru(NH3)6 at Au and Pt
UMEs can be taken to be either essentially adiabatic or at least
not strongly nonadiabaticour data do not distinguish
definitively between these two possibilities. In any event, the
practical issue is that the metal of the electrode (Au vs Pt) has
no bearing on the interpretation of the measurements reported
here.
3+/2+
The direct proportionality of kel for the Ru(NH3)6
cation−cation electron transfer reaction at Au or Pt UMEs in
all-chloride systems to the total anion (chloride) concentration,
independently of the accompanying alkali-metal or H cations,
recalls (reversed charge-type notwithstanding) that of both kel
(3) The apparent values of kel increase substantially on going
from an electrode diameter of 25 μm to 12.7 and then to 10
μm. Although the upper limit of disk diameter for true UME
behavior, with convergent radial diffusion of the electroactive
species to the disk, is usually taken to be ∼50 μm (i.e., radius 25
μm),61 it is possible that a contribution from planar diffusion of
Ru(NH3)63+ may have persisted in the disks of larger diameter,
resulting in the observation of reaction rates slower than the
“true” value. The slightly broadened shapes of some of the CVs
in Figure 2 are consistent with this interpretation.68 Indeed,
Sun and Mirkin69 found that the reduction of [Ru(NH3)6]Cl3
in 0.5 mol L−1 KCl at Pt nanoelectrodes of radii 282−14.7 nm
gave kel values that increased from ∼14 to ∼19 cm s−1 over that
range of radii (mean kel = 17.0 0.9 cm s−1), so that it would
appear that the electrode disk radius effect continues below the
UME size range (extrapolation of our data for a Pt UME of
diameter 25 μm to the KCl concentration used by Sun and
and the corresponding homogeneous self-exchange rate
5−/6−
constant kex for the AlW12O40
anion−anion electron
transfer reaction on the cation (various alkali metal ions)
concentration, independently of the accompanying anions.53
For AlW12O405−/6−, it was shown53 that the variable relevant to
the cation-specific catalysis was simply the concentration of the
cation, and not Debye−Huckel, Gouy−Chapman, ion-pairing,
̈
or other medium effects. Specific alkali-metal ion catalysis of
other anion−anion electrode and self-exchange reactions such
as PW12O403−/4−, CoW12O405−/6−, Mo(CN)83−/4−, W-
(CN)83−/4−, and Os(CN)6
while for the Fe(CN)6
has also been described,70−72
homogeneous self-exchange
3−/4−
3−/4−
reaction alkali-metal cation catalyzed pathways are completely
dominant unless the alkali-metal cations are sequestered with
crypt-2.2.2 or 18-crown-6 to expose the very slow direct
exchange of Fe(CN)63− with Fe(CN)6
.
62 Measurement of kex
4−
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Inorganic Chemistry
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3+/2+
for the Ru(NH3)6
self-exchange73−75 is technically
kel vs [Cl−] plot of Supporting Information, Figure S2, while
challenging (kex = 3.2 × 103 L mol−1 s−1 at 25 °C in 0.1 mol
L−1 CF3SO3H74), but a linear dependence of kex for that
reaction on chloride concentration has been reported, although
a definitive separation of a specific Cl− catalysis from ionic
still less surface would be blocked by the very weakly adsorbed
−
ClO4 (in our experiments with perchlorate media, however,
either Cl− or CF3SO3 was also present to the extent of 15.0
−
−
mmol L−1). For CF3SO3 , an approach to saturated blocking at
strength effects could not be made.75 In this connection, we
3+/2+
high [triflate] even at the Ru(NH3)6
formal potential of
3+/2+
+0.07 V vs NHE could give the curve of Supporting
note that, for the homogeneous Ru(en)3
self-exchange
Information, Figure S3. Thus, anions could affect the
reaction (en = 1,2-diaminoethane), kex is some 20-fold higher in
chloride than in comparable triflate media,76 so that the Cl−
catalysis effect found in this study may reflect a specific affinity
of Cl− for Ru am(m)ine complexes. To summarize, the
3+/2+
Ru(NH3)6
exchange rate in two opposing ways
retardation through partial electrode surface blockage (more
so with triflate), and acceleration through an essential
3+/2+
−
dominant counterion (Cl− and CF3SO3 ) catalysis of the
involvement in the Ru(NH3)6
electron transfer process
3+/2+
(particularly with chloride, which may interact in a specific way
with the Ru complexes).
Ru(NH3)6
electrode reaction reported here, and possibly
also Cl− catalysis of the homogeneous Ru(NH3)6
self-
3+/2+
exchange,75 have precedents in the counterion catalysis of the
electrode and homogeneous self-exchange electron transfer
kinetics of several anion−anion couples.
Temperature Effects on the Electrode Reaction Rate.
The primary purpose in estimating the temperature depend-
ences of kel in various environments was the empirical one of
assessing the relevance of measurements at 25 °C to the
broader near-ambient range. The observed Arrhenius activation
energies Ea are small, as expected in view of the very small
In interpreting the role of CF3SO3 , Cl−, and ClO4 in
−
−
3+/2+
promoting the Ru(NH3)6
electrode reaction, the tendency
of these anions to adsorb on the Au and Pt electrode surfaces
should be considered. For the Cl−-catalyzed electrode reaction,
the direct proportionality of kel to [Cl−] suggests that any such
adsorption is far from saturation over the concentration ranges
used in our experiments, whatever the kinetic role of Cl− might
be. The specific adsorption of Cl− on Pt77−82 and Au81,83−85 is
known to be well advanced at potentials on the order of +0.8 V
3+
change in Ru−N bond lengths on going from Ru(NH3)6 to
Ru(NH3)6 (+4.0 0.4 pm91) with a correspondingly small
2+
Marcus internal reorganization energy (4 2 kJ mol−192 for the
homogeneous electron transfer reaction and hence 2
1 kJ
mol−1 for the electrode reaction1). Values of Ea ranged from 19
kJ mol−1 for the triflate salt in 0.1 mol L−1 KCF3SO3 at a Pt
UME to 25 kJ mol−1 for [Ru(NH3)6]Cl3 in 0.1 mol L−1 KCl at
a gold UME. These activation energies cannot, however, be
simply interpreted in terms of electron transfer dynamics unless
it can be shown that the double layer does not change with
temperature. This will not be the case if the analysis of the
preceding paragraph is applicable, since, as noted above,
vs NHE, but only incipient at the formal potential of the
3+/2+
Ru(NH3)6
electrode reaction (∼ −0.13 V vs Ag/AgCl-
(satd. KCl), ∼ +0.07 V vs NHE; the potential sweeps in our
impedance measurements, however, extended 250−350 mV on
either side of this). The adsorption of ClO4− on Pt or Au in this
potential range is generally considered negligible (most of the
Cl− adsorption studies cited here involved background
perchlorate), although specific adsorption of perchlorate does
0
literature values of ΔHads are substantially negative for both
CF3SO3− and Cl−, meaning that the degree of anion adsorption
would be reduced as the temperature is increased. As only a
minor fraction of the electrode surface would be blocked by
occur at high potentials (>1 V).86,87 For our study, CF3SO3
−
was chosen as an alternative to perchlorate for reasons given in
the Introduction, on the assumption that triflate would behave
similarly to perchlorate with respect to adsorption on Au and Pt
electrode surfaces. Indeed, Lipkowski, Burgess, and co-workers
either CF3SO3 or Cl− at the formal potential of the
−
3+/2+
Ru(NH3)6
couple, the correction of Ea for this effect, if
real, would not be large.
have reported88 that CF3SO3 adsorbs only very weakly at a
−
Pressure Effects on the Electrode Reaction Rate. It is
⧧
possible to predict a value of ΔVel for a simple electrode
positively charged Au electrode surface, and experimental data
⧧
reaction from the analogous parameter ΔVex for the
supplied privately by Lipkowski and Burgess confirm this
−
corresponding homogeneous self-exchange reaction using the
relation
(although coadsorption of CF3SO3 with a cationic surfactant
on Au was noted89). Bockris et al.,90 however, found that
adsorption of aqueous CF3SO3− was extensive on a Pt electrode
1
2
⧧
⧧
at 0.8 V vs NHE (ΔHads = −44 kJ mol−1 and ΔSads = −97 J
K−1 mol−1; cf. −30 kJ mol−1 and −80 J K−1 mol−1, respectively,
for Cl− on Pt82), and was substantial even at −0.05 V, with the
consequence that an adsorption-free reference potential could
not be reached before H2 evolution set in. It is possible that
adsorption of triflate is important on Pt but not on Au.
0
0
ΔV
≈
ΔV
el
ex
(7)
derived from Marcus theory,1 but the numerous reported
experimental difficulties73−75 effectively precluded a direct
⧧
3+/2+
determination of ΔVex for the Ru(NH3)6
self-exchange
reaction in homogeneous solution. A procedure described
elsewhere1 that works well for simple electron transfers in
However, since the data of Table 1 show that kel for the
⧧
3+/2+
aqueous solutions allows the calculation of a theoretical ΔVex
for a homogeneous self-exchange reaction
Ru(NH3)6
electrode reaction at both Au and Pt increased
in the sequence CF3SO3− < Cl− < ClO4 , it may be conjectured
that partial blockage of the electrode surface by specific
adsorption of these ions occurred and decreased in this order
−
⧧
ΔV ⧧(theor) = ΔV ⧧ + ΔVOS⧧ + ΔVCOUL⧧ + ΔVDH
ex
IS
if the results of Bockris et al.90 are applicable at the formal
(8)
3+/2+
potential of the Ru(NH3)6
couple on Au and Pt UMEs,
where IS, OS, COUL, and DH refer respectively to the
contributions of the pressure-dependences of the inner-sphere
reorganization, outer-sphere (solvational) reorganization, Cou-
then the bulky triflate ion could be particularly effective in
blocking a substantial fraction of the electrode surface. The
anion-free surface would then carry the anion-modulated
electron transfer reaction. Only a small fraction of the electrode
surface would be blocked by chemisorbed Cl−, giving the linear
lombic work terms, and activity coefficient (Debye−Huckel)
̈
⧧
corrections. For Ru(NH3)63+/2+, ΔVIS will be negligible (the
corresponding reorganization energy is only 4 2 kJ mol−192).
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Inorganic Chemistry
If r1 and r2 are the radii of Ru(NH3)6 and Ru(NH3)6
respectively, z1 and z2 are the charge numbers, σ is the
separation between these ions at the moment of electron
transfer (presumed = r1 + r2), ε and n are the relative
permittivity (dielectric constant) and refractive index of the
Article
3+
2+
,
declines by 27% from 0 to 200 MPa at 25 °C. This decline
would reduce any catalysis due to ion pairing, leading to less
⧧
⧧
negative values of ΔVex and ΔVel than otherwise expected.
The same factors that favor breakup of ion pairs by increasing
pressure will also promote desorption of anions from electrode
surfaces. For example, molecular dynamics calculations95 show
that chloride ion is “contact adsorbed” on a Pt electrode and
solvated locally by adsorbed water, which implies that Cl−(aq)
is partially desolvated on adsorption and also displaces some
existing adsorbed waterboth of which processes will be
solvent, A and B are the Debye−Huckel parameters at
̈
atmospheric pressure, a is the DH contact distance (effectively
̊
r1 plus the anion radius), I is the ionic strength, and β is the
isothermal compressibility of the solvent, then
ΔVOS⧧ = (N e2/16πε0)[(2r )−1 + (2r2)−1 − σ−1]
disfavored by increasing pressure. Consequently, if, as
A
1
−
[∂(n−2 − ε−1)/∂P]T
suggested above, the catalytic efficacy sequence CF3SO3
<
(9)
Cl− ≪ ClO4 reflects in part decreasing electrode surface
−
blockage, increasing pressure will be particularly effective in
ΔVCOUL⧧ = [N z1z2e2/4πε0σ](∂ε−1/∂P)T
−
accelerating the Ru(NH3)63+/2+ electrode reaction for CF3SO3
(10)
A
as the anion (most negative ΔVel , −16 cm3 mol−1), less so for
⧧
ΔVDH⧧ = [RTz1z2AI1/2/(1 + BåI1/2)2][(∂ln ε/∂P)T
(3 + 2BåI1/2) − β]
Cl− (ΔVel = −12 cm3 mol−1), and least for ClO4 which is
⧧
−
⧧
presumably not specifically adsorbed (ΔVel was not
(11)
−
measurable for ClO4 ). Against this interpretation are the
uncertainty in the article by Bockris et al.90 regarding the extent
If the effective radii of Ru(NH3)63+, Ru(NH3)62+, Cl−, and
−
−
of adsorption of CF3SO3 on Pt at potentials near 0.0 V vs
CF3SO3 are taken to be 340, 344, 181, and 340 pm,
NHE, and the report by Lipkowski et al.88 that adsorption on
Au is negligible at such potentials; this topic deserves to be
revisited. In any event, since the anions are evidently intimately
involved in the electron transfer process itself, the predictions
of the simple Marcus-based theory (eqs 6−11) are not
respectively, then, for 25 °C and I = 0.12 mol L−1 as in our
variable-pressure experiments and the midrange pressure of 100
MPa, ΔVOS⧧ (−8.9 cm3 mol−1) is seen to be dominant because
⧧
ΔVDH (+2.7 cm3 mol−1 for triflate, +2.8 cm3 mol−1 for Cl−)
and ΔVCOUL (−4.2 cm3 mol−1) effectively cancel, giving
⧧
⧧
ΔVex⧧(theor) = −10.3 cm3 mol−1 for Cl− as counteranion and
applicable to ΔVel .
−10.4 cm3 mol−1 for CF3SO3 . If, as suggested by Muzikar
́
̌
and
−
An alternative interpretation of the unexpectedly strongly
negative ΔVel⧧ for Ru(NH3)63+/2+ electrode reaction notes that,
for the comparable RuN6 couple Ru(en)33+/2+, the measured
Fawcett,23 the effective charge on Ru(NH3)63+ is only about +1,
⧧
⧧
ΔVDH and ΔVCOUL will be +0.9 and −1.4 cm3 mol−1,
respectively, and their net contribution will be within the
experimental uncertainty, with ΔVex⧧(theor) = −9.4 cm3 mol−1
⧧
⧧
ΔVel and ΔVex are also more negative than expected from
theory, being respectively −7.5 0.3 (at glassy C in 0.4 mol
and ΔVel (theor) = −4.7 cm3 mol−1.
⧧
L
−1 KCl or CF3COONa) and −15.1 1.7 cm3 mol−1 (from the
⧧
⧧
3+/2+
Marcus cross-relationencouragingly, ΔVel = 0.5ΔVex as
predicted),76 suggesting that the departure from theoretical
expectations has origins peculiar to Ru am(m)ine chemistry;
For a simple Ru(NH3)6
electrode reaction, then, the
⧧
expectation is that ΔVel (theor) (averaged over the 200 MPa
pressure range) should be 0.5ΔVex⧧(theor) or about −5 cm3
⧧
3+/2+
mol−1, which is well within the range of observed ΔVel values
⧧
the fact that ΔVel is more negative for the Ru(NH3)6
3+/2+
couple than for Ru(en)3
may reflect the cation size
for electrode reactions of metal ion complexes that do not
difference (eqs 6−11).1 Since the free energy barrier for RuIII/II
electron transfer is almost entirely due to solvent reorganiza-
tion, it may be inferred that a strong increase in specific
solvation, over and above the Born-continuum solvent effects
invoked in basic Marcus theory, occurs in electron transfer in
RuIII/II am(m)ine couples and makes strongly negative
involve large spin-state changes.1 The observed values of ΔVel
⧧
for Ru(NH3)63+/2+, however, were −12 1 cm3 mol−1 for 0.1
mol L−1 KCl and −16
1 cm3 mol−1 for 0.1 mol L−1
⧧
KCF3SO3, which are the most negative ΔVel recorded to
date for electrode reactions of transition-metal complexes in
⧧
water. The only couples for which ΔVel has been found to
contributions to ΔVel and ΔVex⧧. Indeed, specific interactions
⧧
approach these values are Co(en)33+/2+, Co(bpy)33+/2+, and
Co(phen)33+/2+ (bpy = 2,2′-bipyridyl, phen = 1,10-phenanthro-
line),1 for which large distortions due to electronic spin state
changes accompany the electron transfer process; such
3+
between Ru(NH3)6 and the surrounding water molecules in
aqueous solution are evident in 1H2O and H217O NMR
spectra,96 and theoretical calculations indicate that electron
transfer to polar solvents such as water affects the metal-to-
ligand charge transfer bands of ruthenium(II) ammines.97
Strong solvent dependences of the optical spectra of complexes
3+/2+
distortions are not expected to occur in the Ru(NH3)6
couple, in which both members are in low-spin 4d5/4d6
electronic configurations.
In fact, we have shown above that the Ru(NH3)6
3+
3+/2+
containing the Ru(NH3)5 group confirm that H-bonding of
the ammine protons to polar solvent molecules is extensive,
probably resulting in mixing of solvent character into the dπ
orbitals of Ru.98−100 The intervalence electron transfer band
due to weakly coupled RuII and RuIII in (NH3)5RuII(μ-
electrode reaction is not simple, being specifically catalyzed
⧧
by anions, and that ΔVel is distinctly more negative for
CF3SO3 than for Cl−. Ion pairing of Ru(NH3)6 with the
anion present might be invoked to explain the catalysis, and
indeed Waysbort et al.93 gave evidence for about 30% pairing of
Ru(NH3)63+ with Cl− in 0.1 mol L−1 aqueous chloride at 25 °C.
−
3+
L)RuIII(NH3)5 (L = 2,6-dithiaspiro[3.3]heptane) in D2O
5+
exhibits a large red shift with rising pressure, rather than the
expected blue shift, and this is attributable to pressure-
enhanced hydrogen bonding of the ammine ligands to the
solvent.101 In electron transfer between Ru ammines and
cytochrome c, either in Ru-modified cyt c or between
Ru(NH3)5(ligand)3+/2+ and cyt cII/III, the volume changes are
⧧
The strongly negative ΔVel , however, is not attributable to ion
pairing because increasing pressure works against ion pairing by
increasing the relative permittivity ε and also favoring hydration
of the separated ionsfor example, the ion pair formation
constant for {Ru(NH3)63+,Cl−}, calculated as per Fuoss,94
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dominated by large solvational effects at the Ru ammine
centers.102 In retrospect, even the puzzling strongly negative
volumes of activation found for the aquation of Ru(NH3)5Cl2+
and its reverse could be understood in terms of solvation
increases specific to activation processes in RuIII am-
mines.103,104 In short, there is ample precedent for specific
hydrational interactions involving RuIII and RuII ammine
complexes.
CONCLUSIONS
■
Neither the rate constant kel nor the volume of activation
ΔVel(obsd)⧧ for the reduction of Ru(NH3)63+ at a polycrystalline
metallic UME depend significantly upon the identity of the
metal, be it Au or Pt. According to traditional views,3,45 this is
consistent with substantially full adiabaticity for the electron
transfer process, but, as originally pointed out by Gosavi and
Marcus,10 it does not preclude a modest level of non-
adiabaticity. The question of the extent of nonadiabatic
character is better pursued through adaptations of Marcus
⧧
There remains the possibility that the strongly negative ΔVel
3+
for the Ru(NH3)6 reduction at an electrode reflects pressure
effects on the electrical double layer. Experience with
theory as proposed by Savea
́
nt6 and Compton;7,8 for the
purposes of this study, the essential observation is that the
kinetic parameters for reduction of Ru(NH3)6 are independ-
supporting electrolyte (KCl) concentration effects on the
3−/4−
kinetics of the Fe(CN)6
electrode reaction (Table 2),
3+
ent of the choice of electrode material, Au vs Pt, within the
experimental uncertainty. The apparent kel does, however,
increase as the area of the UME decreases.
⧧
a
3−/4−
Table 2. Dependence of kel and ΔVel for the Fe(CN)6
Electrode Reaction at a Pt Electrode
3+
[KCl]/mol L−1
kel/cm s−1 at 25 °C, P = 0.1 MPa
ΔVel⧧/cm3 mol−1
Values of kel for the reduction of Ru(NH3)6 depend
strongly on the identity and concentration of the anion present
0.06
0.20
0.50
0.017
0.047
0.072
12.0 1.8
10.4 1.4
11.9 1.3
in the order CF3SO3− < Cl− < ClO4 , but not upon the cation
−
of the supporting electrolyte (Na+, K+, H+). For Cl− as the
counterion of both Ru(NH3)63+ and the supporting electrolyte,
kel is directly proportional to the total Cl− concentration, such
that kel would be zero, within the experimental uncertainty, if
Cl− were hypothetically absent. This result echoes (with charge
reversal) the dependences of both kel and kex for many anion−
anion electron transfer reactions on total cation concentrations,
a
Data from Table 5 of ref 1.
⧧
however, has been that ΔVel is independent of the
concentration of a particular supporting electrolyte within the
and suggests that Cl− is directly involved in mediation of the
0.9 cm3 mol−1)
⧧
experimental error (average ΔVel = 11.4
3+/2+
even though kel is strongly dependent on it (actually on [K+]).
The implication is that, for Fe(CN)63−/4− at least, the reactants
are in hard (i.e., effectively incompressible) contact with either
the electrode surface or an inert adsorbed layer at the outer
Ru(NH3)6
electron transfer. For triflate as the sole
−
counterion, the dependence of kel on the total [CF3SO3 ] is
not linear, possibly because the blocking of the available
electrode surface becomes dominant at high triflate concen-
trations. In experiments with a perchlorate as the supporting
electrolyte, 15 mmol L−1 chloride or triflate was also present as
the counterion of Ru(NH3)63+ because of risks in preparing its
perchlorate salt, so that interpretation of the results was less
⧧
Helmholtz plane (OHP) and hence ΔVel is insensitive to
double-layer effects. It is reasonable to expect the same to hold
for the Ru(NH3)6
3+/2+
couple which, although of the opposite
charge-type, shows a similar dependence of kel on the total
counterion concentration.
clear-cut except that ClO4− was nevertheless associated with the
fastest Ru(NH3)6
pressure experiments were conducted with ClO4 because the
already fast reaction became too fast for accurate measurement
at elevated pressures, and besides the likelihood that ClO4
3+/2+
electrode reaction rates. No variable-
Finally, we may consider briefly how ΔVel⧧ might be affected
if Ru(NH3)63+ were not in hard contact with the electrode or at
the OHP but were moving freely within the diffuse double layer
when reduction occurs. A Frumkin correction105 to be applied
−
−
would oxidize the Ru complexes over the longer time-scale of a
pressure cycle is well recognized.47,48 A more orthodox
explanation of the accelerating effect of added electrolytes
might be the collapsing of the diffuse double layer by the
supporting electrolyte, but it is evident that the relevant factor
is the total concentration of the specific anion rather than of the
supporting electrolyte.
⧧
to the observed volume of activation ΔVel(obsd) may be
estimated as outlined in the Supporting Information; the
concept of the Frumkin correction has recently been
discredited,106 but it serves to give an indication of the sign
and order of magnitude of the effect. The key results are that
⧧
the Frumkin correction to ΔVel(obsd) is zero at distance x = 0
(i.e., at hard contact of Ru(NH3)6 with an adsorbed layer at
the OHP) and at distances greater than about 8 nm, but at
3+
⧧
3+
The observed ΔVel values for reduction of Ru(NH3)6 at
an electrode in presence of 0.115 mol L−1 Cl− or CF3SO3− are
much more negative than predicted by a theory that has been
successfully applied to other electrode reactions1 but which is
not directly applicable in this case because of the specific
involvement of the anions in promoting the electron transfer
intermediate distances the correction is always negativethat is,
⧧
it cannot explain the already strongly negative values of ΔVel .
For a reasonable φ value of ∼100 mV, and with the effective z
set at +1,23 the greatest correction would be only about −1 cm3
mol−1 near x = 1.0 nm which is quite far out in terms of
electron transfer probability. It may therefore be safely inferred
⧧
process. The strongly negative values of ΔVel probably reflect
solvation increases peculiar to activation processes in reactions
of RuIII/II am(m)ine complexes. These solvation effects may be
amplified by involvement of the anion in the activation process.
⧧
that ΔVel , unlike kel, is insensitive to double-layer effects (cf.
Table 2), and that electron transfer may be treated as occurring
with Ru(NH3)6 either in contact at the OHP or close to it.
3+
⧧
A further anion-specific contribution to ΔVel may be the
promotion of desorption of surface-blocking Cl− or especially
Direct contact with the electrode, however, would result in
expulsion of adsorbed water molecules and partial dehydration
−
CF3SO3 from electrodes by applied pressure. Increase of the
of Ru(NH3)63+, both of which would tend to make ΔVel(obsd)
⧧
available electrode surface area through pressure-induced
desorption of specifically adsorbed anions could also explain
less negative than predicted.
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the fact that ΔVel⧧ is about 4 cm3 mol−1 more negative for the
triflate system than for the chloride, if indeed the bulky
CF3SO3− ion is more strongly adsorbed than Cl− on Au and Pt
at the Ru(NH3)63+/2+ formal potential as reported by Bockris et
al.90a point that merits reinvestigation. Frumkin corrections
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although the corrections would be small. Conversely, the
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⧧
strongly negative ΔVel values are inconsistent with reduction
3+
of Ru(NH3)6 in direct contact with the metallic electrode
surface, which would entail substantial dehydration of both the
3+
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⧧
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water at the OHP or close to it.
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ASSOCIATED CONTENT
■
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̈
S
* Supporting Information
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dependences of kel on [Cl−] and [CF3SO3 ]; pressure
−
dependence of the Frumkin correction. This material is
available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
*Phone: 403-220-5358. Fax: 403-289-9488. E-mail: swaddle@
ucalgary.ca.
(32) Jun, Y. Y.; Beng, K. S. Electrochem. Commun. 2004, 6, 87.
(33) Degafa, T. H.; Schon, P.; Bongard, D.; Walder, L. J. Electroanal.
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(35) Cohen-Atiya, M.; Nelson, A.; Mandler, D. J. Electroanal. Chem.
2006, 593, 227.
Present Address
†Karunya University, Karunya Nagar, Coimbatore, Tamilnadu,
India 641114.
Notes
(36) Kiani, A.; Alpuche-Aviles, M. A.; Eggers, P. K.; Jones, M.;
Gooding, J. J.; Paddon-Row, M. N.; Bard, A. J. Langmuir 2008, 24,
2841.
The authors declare no competing financial interest.
(37) Chen, P.; Fryling, M. A.; McCreery, R. L. Anal. Chem. 1995, 67,
3115.
ACKNOWLEDGMENTS
■
We thank Profs. J. Lipkowski (University of Guelph) and I. J.
Burgess (University of Saskatchewan) for discussions and
provision of their unpublished data relating to triflate
adsorption on Au electrodes, and the Natural Sciences and
Engineering Research Council of Canada for financial support.
(38) Chen, P.; McCreery, R. L. Anal. Chem. 1996, 68, 3958.
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