Microelectrochemical measurements of electron transfer rates at the interface between two immiscible electrolyte solutions: Potential dependence of the ferro/ferricyanide-7,7,8,8-tetracyanoquinodimethane (TCNQ)/TCNQ?- system

Article abstract of DOI:10.1039/b108882c

The reduction of 7,7,8,8-tetracyanoquinodimethane (TCNQ) in 1,2-dichloromethane (DCE) and nitrobenzene (NB), by aqueous ferrocyanide, and the back reaction were studied by scanning electrochemical microscopy. The effect of galvanic potential at the interface between two immiscible electrolyte solutions (ITIES) on electron transfer (ET) rates, with different electrolyte concentrations in the organic phase was evaluated. The ET rate constants for the forward and back reaction depended strongly on the interfacial potential drop, with an apparent ET coefficient close to 0.5. TCNQ^?- was confined to DCE, but transferred from NB to water under certain experimental conditions, which could complicate kinetic analysis. The ET kinetics for the water/DCE system were analyzed further using Marcus theory. Close to zero driving force, the rate constants for the forward and back reaction were similar and in good agreement with predictions from Marcus theory with a sharp liquid/liquid interface. At equilibrium (when the forward and back ET rate constants were equal), the sharp boundary model for the ITIES predicted a bimolecular rate constant close to that measured experimentally.

Full text of DOI:10.1039/b108882c

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Microelectrochemical measurements of electron transfer rates at the
interface between two immiscible electrolyte solutions:
Potential dependence of the ferro/ferricyanide-7,7,8,8-
ꢀ
ꢁ
tetracyanoquinodimethane (TCNQ)/TCNQ system
Jie Zhang and Patrick R. Unwin*
Department of Chemistry, University of Warwick, Coventry, UK CV4 7AL.
E-mail: P.R.Unwin@warwick.ac.uk
Received 1st October 2001, Accepted 9th April 2002
First published as an Advance Article on the web 4th July 2002
The reduction of 7,7,8,8-tetracyanoquinodimethane (TCNQ) in both 1,2-dichloroethane (DCE) and
nitrobenzene (NB), by aqueous ferrocyanide, and the back reaction have been studied by scanning
electrochemical microscopy (SECM) and microelectrochemical measurements at expanding droplets
(MEMED). The main focus has been to elucidate the effect of galvanic potential at the interface between two
immiscible electrolyte solutions (ITIES) on electron transfer (ET) rates, with different electrolyte concentrations
in the organic phase. SECM studies show that the ET rate constants for both the forward and back reaction
depend strongly on the interfacial potential drop, with an apparent ET coefficient close to 0.5. MEMED
ꢀ
ꢁ
demonstrates that TCNQ is confined to DCE, but transfers from NB to water under certain experimental
conditions, which could complicate kinetic analysis. The ET kinetics for the water/DCE system have been
analysed further using Marcus theory. Close to zero driving force, the rate constants for the forward and back
reaction are found to be similar and in good agreement with predictions from Marcus theory with a sharp
liquid/liquid interface. The results suggest that Butler–Volmer kinetics describe ET at the ITIES when the
driving force is low and the ionic strength in both the aqueous and organic phases is relatively high.
The potential dependence of ET processes at the ITIES has
Introduction
also been established by conventional four-electrode voltam-
metric studies8,9 and photocurrent measurements.7,10,11,12 In
the latter case, Girault and co-workers recently studied the het-
erogeneous quenching of water-soluble zinc tetrakis(carboxy-
phenyl) porphyrin (ZnTPPC) by ferrocene and diferro-
cenylethane in DCE. An a value of 0.32 was measured in the
region close to the potential of zero charge.10 The same group
also studied the photoinduced ET process between aqueous
ZnTPPC and a wide range of organic quenchers. It was found
that the Gibbs energy of activation for the charge transfer pro-
cess was affected by the galvanic potential difference.11 For
photoinduced ET between aqueous neutral ion-pairs and the
neutral electron donors decamethylferrocene (DMFc) and
TCNQ in DCE, an a value of 0.5 was estimated.12
Understanding the potential-dependence of rates of electron
transfer (ET) across the interface between two immiscible elec-
trolyte solutions (ITIES) is currently an area of considerable
research activity. Several techniques have recently been applied
to a number of redox systems, but with quite different results
and conclusions.1–16
In previous scanning electrochemical microscopy (SECM)
measurements of the reaction rate between cationic
5,10,15,20-tetraphenyl-21H,23H-porphine zinc (ZnPor+) in
benzene or benzonitrile and various aqueous reductants,1,2
a
Butler–Volmer trend was observed at low driving force,1
together with behaviour consistent with Marcus theory over
a wide range of driving force.1b,2,3 The reduction of the neutral
species, 7,7,8,8-tetracyanoquinodimethane (TCNQ), in 1,2-
has
There have been several recent reports of the potential-inde-
pendence of ET rates at ITIES.13,16 The observations derived
from a thin layer method were attributed to the formation of
precursor complexes within the interfacial region, as the rate-
determining step, which would be little influenced by the driv-
ing force for the subsequent, faster, ET step.13 Some of the sys-
tems studied showed behaviour contrary to Butler–Volmer
kinetics,13 as supported by SECM data.14 However, a number
of results from the thin layer method may also be complicated
by uncompensated diffusional limitations.6,15
4ꢁ
dichloroethane (DCE) by electrogenerated Fe(CN)6
been studied extensively with both SECM and microelectro-
chemical measurements at expanding droplets (MEMED).4
The measured ET rates showed a strong dependence on the
interfacial potential drop with an ET coefficient (a) in the
range 0.4–0.7, with a relatively high ionic strength in both
the water and DCE phases. The kinetics of the reverse reaction
were also reported recently in a preliminary communication;5
Butler–Volmer behaviour was observed, with a bimolecular
rate constant of 0.06 cm sꢁ1 Mꢁ1 at zero driving force. Similar
characteristics for this redox system were also reported inde-
pendently by Ding et al.3 and Shi and Anson.6 However, an
earlier spectroelectrochemical study suggested that the poten-
tial-dependence of the reduction of TCNQ by aqueous ferro-
cyanide did not show a pure Butler–Volmer trend.7
Liu and Mirkin16 studied the ET reaction between aqueous
redox species (e.g. Ru(CN)63ꢁ) and neutral organic species
(e.g. ZnPor) using SECM, with the potential drop across the
ꢁ
ITIES established with ClO4 salts in each phase. The mea-
sured ET rate constants were found to be independent of the
interfacial potential drop, but dependent on the driving force
3820
Phys. Chem. Chem. Phys., 2002, 4, 3820–3827
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DOI: 10.1039/b108882c

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contributed by the aqueous redox species. It was concluded
that this result agreed with Schmickler’s recent model for ET
at the ITIES.17 It was further suggested that the a value
obtained in previous studies1a may have been compromised
by interfacial concentration effects.17,18
Following our previous study on the one-electron reduction
4ꢁ 4,5
, we further
ꢀ
ꢁ
of TCNQ to TCNQ by aqueous Fe(CN)6
investigate this reaction and the back reaction (oxidation of
ꢀ
ꢁ
TCNQ by ferricyanide) over a much wider range of condi-
tions. In addition to DCE, used as the organic solvent pre-
viously, we also investigate the ET reaction with
nitrobenzene (NB) as the organic solvent. The processes of
interest can be represented as,
ð1Þ
where kf and kb are the effective bimolecular rate constants for
4ꢁ
the oxidation of Fe(CN)6 (reduction of TCNQ) and reduc-
ꢀ
tion of Fe(CN)6 (oxidation of TCNQ ꢁ), respectively.
TCNQ was selected for study because it has been widely
used for investigations of ET at ITIES, particularly with tech-
niques employing externally polarised ITIES.7,8,19 Moreover,
as highlighted above, recent studies3–6 confirm that TCNQ/
Fe(CN)6 is a suitable system for investigating the factors
affecting ET reactions at ITIES. The potential drop across
the ITIES was varied by using ClO4 as a common potential
3ꢁ
Fig. 1 Schematic of the application of SECM in the measurement of
ET reactions at the aqueous/organic interface when the organic solu-
tion forms the top phase.
4ꢁ
ꢁ
The heterogeneous rate constants for the reverse reaction
determining ion in the two phases. A specific interest in this
paper was to determine kf and kb close to zero driving force,
and to carefully investigate the possibility of facilitated ion
transfer processes which may complicate the measured ET
kinetics and potential-dependent behaviour.
ꢀ
3ꢁ
ꢁ
between Fe(CN)6 and TCNQ were measured by SECM,
using a method similar to that proposed by Mirkin and co-
workers.22 The aqueous phase was held at the tip of a glass
tube positioned through the base of the cell (Fig. 1). The bot-
3ꢁ
tom aqueous phase contained either 10 or 20 mM Fe(CN)6
,
0.1 M NaCl and 0.01–1.0 M NaClO4 , while the organic phase
(top) contained 1 mM TCNQ, and either 0.1 or 0.01 M THAP.
In this configuration, the tip UME was positioned in the
organic phase and used to locally generate TCNQꢀꢁ by the dif-
fusion-limited reduction of TCNQ.
Experimental section
Chemicals
Potassium hexacyanoferrate (A.R.), NaCl (A.R.) (both from
Fisons), sodium hexacyanoferrate(II) decahydrate (Strem),
TCNQ (98%, Lancaster), tetra-n-hexylammonium perchlorate
(THAP, crystalline, Alfa), NaClO4ꢂxH2O (A.R.), NB (99+%)
and DCE (HPLC grade) (all from Sigma-Aldrich) were used
as received. All aqueous solutions were prepared from Milli-
Q reagent water (Millipore Corp.).
The basic apparatus used for SECM has been described
previously.4,5,20,21 Approach curves were obtained by translat-
ing the tip towards the ITIES and recording the steady-state
current as a function of d (the distance between the tip and
the ITIES). When the tip attained the distance closest
approach to the ITIES, there was either a plateau in cur-
rent–distance characteristics (for the case of the UME in the
aqueous phase) or sudden change in current (for the case of
the UME in the organic phase). Typically, a 25 mm diameter
tip could be approached to a distance of ca. 1–2 mm from
the ITIES (UME in the aqueous phase) or 2–3 mm (UME in
the organic phase). To determine this distance precisely,
negative feedback experiments were always run without any
redox-active species in the bottom phase and data analysed
with negative feedback theory similar to that of Kwak and
Bard.23
In MEMED, concentration profiles of both reactant and
product were determined. To measure the concentration pro-
file of aqueous Fe(CN)64ꢁ, an organic drop containing 10
mM TCNQ and 0.01 M THAP was grown into an aqueous
receptor phase containing 1 mM Fe(CN)64ꢁ, 0.1 M NaCl
and 0.01–0.25 M NaClO4 , from a capillary with an internal
diameter of about 200 mm. The concentration profiles of
TCNQ and TCNQꢀꢁ in the organic receptor phase, were mea-
sured by growing water droplets containing 50 mM
Fe(CN)64ꢁ, 0.1 M NaCl and 0.01–0.25 M NaClO4 , into the
organic phase containing 1 mM TCNQ and 0.01 M THAP.
Amperometeric detection was used, which involved recording
the current for the species of interest in the receptor phase,
as the drop grew towards the tip.
Apparatus and procedures
Electrochemical measurements were made under controlled
a two-electrode
ambient conditions (23 ꢃ 0.5 ꢄC) using
arrangement. Either a saturated calomel electrode (SCE) or sil-
ver quasi-reference electrode (AgQRE) served as the reference
electrode, and a glass-coated Pt ultramicroelectrode (UME,
either 2 or 25 mm diameter) functioned as the working elec-
trode tip. The UME had a defined RG value of 10 for SECM
measurements which employed a 25 mm diameter tip, and 4 for
MEMED measurements which utilised the 2 mm diameter
probe. RG ¼ rs/a, where rs is the overall radius of the tip
end (electrode plus insulating sheath) and a is the electrode
radius. The electrodes were fabricated and polished as
described previously.20
To measure the heterogeneous rate constants for the reac-
tion between Fe(CN)64ꢁ and TCNQ using SECM, a flat inter-
face was established in a conventional cell,20,21 between an
aqueous (top) phase and an organic (bottom) phase. The aqu-
eous phase contained 1 mM Fe(CN)63ꢁ, 0.1 M NaCl and 0.01–
0.25 M NaClO4 , while the organic phase contained 10 mM
TCNQ and either 0.1 M or 0.01 M THAP. The tip, in the aqu-
3ꢁ
4ꢁ
In contrast to SECM, the small size of the tip used for
MEMED meant that the electrode was a non-invasive probe
eous phase, was used to reduce Fe(CN)6 to Fe(CN)6 at a
diffusion-controlled rate.
Phys. Chem. Chem. Phys., 2002, 4, 3820–3827
3821

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Fig. 3 Dependence of the half-wave potential for tꢁhe reversible first
reduction of TCNQ in either DCE or NB on [ClO4 ]w , with 0.01 M
THAP in the DCE phase (c), and either 0.1 M THAP (K ) or 0.01
M THAP (N) in the NB phase.
Results and discussion
Potential drop across the ITIES
Fig. 2 Schematic of MEMED.
The relative values of the potential drop across the liquid/
liquid interface were obtained by adopting the procedure advo-
cated by Bard and co-workers.1a Steady-state linear sweep vol-
tammograms for the first reduction of TCNQ at a 25 mm
diameter microdisc electrode in each of the organic phases,
were measured with respect to an SCE positioned in a contact-
of the concentration boundary layer that developed adjacent
to expanding droplets.24 Fig. 2 shows a schematic of MEMED
for the situation where organic droplets were grown into the
aqueous receptor phase. For this particular case, the droplets
were formed from a capillary placed above the electrode,
because DCE is more dense than water. An inverted arrange-
ment was used when aqueous droplets were grown into an
organic receptor phase. A method for obtaining the time-
dependent droplet concentration profile, from the UME
response, has been outlined fully elsewhere.25
ing aqueous phase. The reversible half-wave potential (E1/2
)
was derived from the voltammograms.
The dependence of E1/2 on [ClO4ꢁ]w , deduced from these
measurements, with [THAP]o fixed at defined values, is shown
in Fig. 3. The slopes (ca. 59 mV per decade) of the straight lines
agree well with the predictions of eqn. (2). Moreover, the
potential shifts by ca. 60 mV when [THAP]o in the NB phase
changes by an order of magnitude from 0.01 M to 0.1 M, again
consistent with eqn. (2). Although the ionic strength of the
aqueous phase changes in these measurements, the activity
coefficients of the various aqueous ions are fairly insensitive
to the ionic strength for these experiments and those that fol-
low.4
ClO4ꢁ was the only ion common to both phases in all of the
experiments. The electroneutrality of the two phases was main-
tained by the transfer of this common ion when the ET reac-
tion occurred at the ITIES. The ratio of the bulk activities of
ꢁ
ClO4 in the aqueous and organic phases, determined the
interfacial potential drop. At standard temperature and pres-
sure, and assuming appropriate experimental conditions where
the activity coefficients of ClO4 in the aqueous and DCE
phases are maintained constant, within the concentration
range of interest, the following equation should hold:1–5
ꢁ
Potential-dependence of ET rates for the forward and back
reactions: SECM measurements
Previous SECM studies have suggested Butler–Volmer charac-
teristics for the ITIES at low driving force.1–5 In this case, kf
and kb can be written in terms of the driving force for the
reaction, w,
0
½ClOꢁ4 ꢅw
½ClOꢁ4 ꢅo
Dowf ¼ Dwo fo ꢁ 0:059 log10
ð2Þ
ꢀ
ꢁ
where Dow f ¼ fo ꢁ fw is the Galvani potential (V) established
across the interface; fo is the potential of the organic phase
and fw is the aqueous phase potential. The formal transfer
anFw
RT
kf ¼ ko exp
ð4Þ
ð5Þ
ꢀ
ꢁ
ꢁ
ꢁbnFw
potential for ClO4 is given by
kb ¼ ko exp
RT
0
gw
10 go
Dowfo ¼ Dowfo ꢁ 0:059 log
ð3Þ
where ko is the standard rate constant at zero driving force, a
and b are the ET coefficients for the forward and reverse reac-
tions, respectively, F is Faraday’s constant, n is the number of
electrons transferred per redox event, R is the gas constant and
T is temperature. The driving force is defined in terms of the
forward reaction by:
where Dowfo is standard transfer potential for ClO4ꢁ, gw and go
are the activity coefficients of ClO4 in water and the organic
ꢁ
phase, respectively.
Diffꢁu1sion coefficients of 1.05 ꢆ 10ꢁ5 cm2 sꢁ1 and 1.2 ꢆ 10ꢁ5
cm2
s
(in DCE), and 4.8 ꢆ 10ꢁ6 cm2ꢀ sꢁ1 and 5.5 ꢆ 10ꢁ6
w ¼ DEo0 þ Dowf
ð6Þ
cm2 sꢁ1 (in NB) for TCNQ and TCNQ ꢁ, respectively, were
measured using both double potential step chronoamperome-
try14,21b,c and steady-state linear sweep voltammetry.1,4
where DEo ¼ Eo
ꢀꢁ ꢁ Eo
3ꢁ/4ꢁ , is the difference in
the formal potentials of the redox couples in the organic and
0
0
0
0
TCNQo
Fe(CN)6
3822
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aqueous phases, versus a common reference electrode in one
phase.26,27
To accurately determine the driving force, the difference in
ꢀ
3ꢁ/4ꢁ
the formal potentials of TCNQo/ ꢁ and Fe(CN)6
was
measured with respect to SCE in the aqueous phase.1 Because
ꢀ
the diffusion coefficients of TCNQ and TCNQꢁ are similar, as
defined earlier, the measured reversible half-wave potential of
o
28
0
TCNQ reduction was used as E . Since the measured E1/2
for the ferro–ferricyanide couple may depend on the solution
and electrode conditions,29 the formal potential was obtained
from measurements of the equilibrium, open-circuit potential
over the range of conditions used in the kinetic studies.
The analysis that follows considers eqns. (4) and (5) in the
following form:
anFw
lnð10ÞRT
bnFw
lnð10ÞRT
log10 kf ¼ log10 ko þ
log10 kb ¼ log10 ko ꢁ
ð7Þ
ð8Þ
Investigations of the potential-dependence of ET rate con-
stants, for the reaction between TCNQ and Fe(CN)6 and
4ꢁ
ꢀ
ꢁ
3ꢁ
the back reaction between TCNQ and Fe(CN)6 are devel-
opments of recent preliminary work.5 Typical new results are
shown in Figs. 4–6. In each case, the driving force was varied
by changing the concentration of ClO4ꢁ in the aqueous phase,
with fixed [THAP]o . SECM approach curves have been fitted
to the optimal rate constant using a numerical model described
in full previously.2
The results in Figs. 4–6 demonstrate that the ET rate con-
stant depends strongly on the interfacial potential drop across
the ITIES. With 0.01 M THAP in DCE, an a value of
0.44 ꢃ 0.03 and a b value of 0.53 ꢃ 0.01 were obtained (Fig.
4). For comparison in a recent communication,5 we obtained
a ¼ 0.56 ꢃ 0.04 and b ¼ 0.58 ꢃ 0.02 for the aqueous/DCE
system with 0.1 M THAP in DCE. When NB was used as
the organic solvent, an a value of 0.54 ꢃ 0.04 and a b value
of 0.50 ꢃ 0.05 were obtained in the presence of 0.1 M THAP
(Fig. 5) and a b value of 0.53 ꢃ 0.03 was obtained for the
reverse reaction in the presence of 0.01 M THAP (Fig. 6).
The rate of the forward reaction under these latter conditions
was rather low and the reaction could barely be observed by
SECM.
Fig. 4 Dependence of ET rate constants on driving force for the aqu-
eous/DCE system. (a) SECM approach curves (ferricyanide reduction)
for the forward reaction with 10 mM TCNQ and 0.01 M THAP in the
DCE phase. From top to bottom, the first four solid experimental
]
Potential-dependence of ET rates for the forward reaction and
observation of facilitated ion transfer using MEMED
ꢁ
curves are for the following aqueous conditions: [ClO4
¼ 0.01,
w
0.025, 0.1 and 0.25 M (1 mM Fe(CN)63ꢁ and 0.1 M NaCl). The corre-
sponding dashed theoretical curves,2 top to bottom, are for kf ¼ 0.15,
To confirm the measured ET kinetics and determine whether
there were any complications from facilitated ion transfer,
MEMED was used to determine the rate constants for the for-
0.1, 0.04 and 0.025 cm sꢁ1
M
ꢁ1. The lowest solid experimental curve
was obtained in the absence of TCNQ in the DCE phase and the cor-
responding dashed curve is the theory for negative feedback.23 (b)
SECM approach curves (TCNQ reduction) for the reverse reaction
with 1 mM TCNQ and 0.01 M THAP in the DCE phase. From top
to bottom, the first five solid experimental curves are for
4ꢁ
ward reaction. Concentration profiles of Fe(CN)6 in the
aqueous receptor phase, together with those for TCNQ and
ꢀ
ꢁ
TCNQ in the organic receptor phase were recorded accord-
ing to the procedures described above. Typical results for the
aqueous/DCE and aqueous/NB systems are shown in Figs.
7 and 8.
ꢁ
3ꢁ
[ClO4
0.1 M NaCl) in the aqueous phase. The corresponding dashed theore-
]
¼ 1.0, 0.25, 0.1, 0.025 and 0.01 M (10 mM Fe(CN)6 and
w
tical curves, top to bottom, are for kb ¼ 1.0, 0.3, 0.15, 0.06 and 0.03 cm
sꢁ1
M
ꢁ1. The lowest solid experimental curve was obtained in the
3ꢁ
The results in Fig. 7 clearly indicate that the same bimolecu-
lar rate constants were measured for the water/DCE system
whichever of the three species was detected. This illustrates
absence of Fe(CN)6 in the aqueous phase and the corresponding
dashed curve is the theory for negative feedback. (c) Tafel plot of data
in (a, K) and (b, N), constructed using eqns. (7) and (8).
ꢀ
ꢁ
that there are no complications from coupled TCNQ trans-
fer from DCE to water in the potential range of interest. More-
over, the measured rate constants derived from MEMED
studies are comparable to those from SECM (Fig. 4). In con-
trast, while the concentration profile of TCNQ for the aqu-
eous/NB system matches well to an ET rate constant,
by transfer across the interface. This is confirmed by the clear
deviation between the experimental profile of Fe(CN)64ꢁ (Fig.
8(b)) and that predicted based on the rate constant obtained
from the TCNQ profile (Fig. 8(a)). The peak-shaped concen-
tration profile, which is higher than the theoretical simulation,
suggests that an additional electroactive species diffuses from
the surface of the droplet into the aqueous phase, as
ꢀ
ꢁ
kf ¼ 0.04 cm sꢁ1 Mꢁ1 (Fig. 8(a)), the corresponding TCNQ
concentrations are significantly lower than expected, based on
the TCNQ profile. This suggests that TCNQꢀꢁ is lost, possibly
Phys. Chem. Chem. Phys., 2002, 4, 3820–3827
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Fig. 6 Dependence of the reverse ET rate constants on driving force
for the aqueous/NB system. (a) SECM approach curves (TCNQ
reduction) obtained with 1 mM TCNQ and 0.01 M THAP in the
NB phase. From top to bottom, the first four solid experimental curves
ꢁ
are for [ClO4
0.1 M NaCl) in the aqueous phase. The corresponding dashed theore-
]
¼ 0.25, 0.1, 0.025 and 0.01 M (20 mM Fe(CN)63ꢁ and
w
tical curves, top to bottom, are for kb ¼ 0.3, 0.18, 0.08 and 0.04 cm sꢁ1
M
ꢁ1. The lowest solid experimental curve was obtained in the absence
3ꢁ
of Fe(CN)6 in the aqueous phase and the corresponding dashed
curve is the theory for negative feedback. (b) Tafel plot (eqn. (8)) of
data in a.
Analysis of ET rate constants using Marcus theory
Fig. 5 Dependence of ET rate constants on driving force for the aqu-
eous/NB system. (a) SECM approach curves (ferricyanide reduction)
for the forward reaction with 10 mM TCNQ and 0.1 M THAP in
We have observed that the rate constants depend strongly on
interfacial potential drop, consistent with some previous
SECM studies,1–5 which suggested that Marcus theory30 can
be applied to ET at the ITIES. Since ET at the aqueous/NB
interface may be complicated by the transfer of TCNQꢀꢁ, we
focus on the results for ET in the aqueous/DCE system.
Marcus theory for ET at the ITIES considers the liquid/
liquid interface as either a sharp boundary or a region which
is several molecular layers thick.30 Molecular dynamics simula-
tions of the water/DCE system show a picture of the interface
which is molecularly sharp on the shortest timescales, with fin-
ger-like distortions due to one solvent penetrating the other.
the NB phase. From top to bottom, the first four solid experimental
curves are for the following aqueous conditions: [ClO4
ꢁ
]
¼ 0.01,
w
0.025, 0.1 and 0.25 M (1 mM Fe(CN)63ꢁ and 0.1 M NaCl) in the aqu-
eous phase. The corresponding dashed theoretical curves, top to bot-
tom, are for kf ¼ 0.18, 0.1, 0.035 and 0.02 cm sꢁ1
M
ꢁ1. The lowest
solid experimental curve was obtained in the absence of TCNQ in
NB and the corresponding dashed curve is the theory for negative feed-
back. (b) SECM approach curves (TCNQ reduction) for the reverse
reaction with 1 mM TCNQ and 0.1 M THAP in NB. Fromꢁtop to bot-
tom, the first four solid experimental curves are for [ClO4
]
¼ 0.25,
w
0.1, 0.025 and 0.01 M (20 mM Fe(CN)63ꢁ and 0.1 M NaCl) in the aqu-
eous phase. The corresponding dashed theoretical curves, top to bot-
tom, are for kb ¼ 0.09, 0.05, 0.018 and 0.012 cm sꢁ1
M
ꢁ1. The
lowest solid experimental curve was obtained in the absence of
˚
These distortions extend up to 8 A on a timescale of a few
nanoseconds.31,32 Over a longer timescale the result is a surface
roughness of the same scale, with a change from the bulk of
one phase to the other occurring over a distance of ca. 8–10
3ꢁ
Fe(CN)6 in the aqueous phase and the corresponding dashed curve
is the theory for negative feedback. (c) Tafel plot of data in (a, K) and
(b, N), constructed using eqns. (7) and (8).
33,34
˚
A, as observed experimentally.
The dependence of the ET rate constant on the driving force
has a similar form for the two Marcus models.30d For the case
where the interface is sharp and cannot be crossed by the reac-
tants, the bimolecular electron transfer rate constant, k012
(units m4 sꢁ1) is given by:
4ꢁ
Fe(CN)6 is consumed siꢀmultaneously. This is most likely to
ꢁ
be the ꢀtransfer of TCNQ from NB to the aqueous phase.
ꢁ
TCNQ 4ꢁcould either react with Fe(CN)63ꢁ, generating
Fe(CN)6 or be directly detected by oxidation at the UME
tip.
¼
k012 ¼ 2pða1 þ a2ÞDr3kn expðꢁDG =RTÞ
ð9Þ
3824
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Fig. 8 MEMED concentration profiles (solid curves) for the aqu-
eous/NB system. (a) 1 mM TCNQ and 0.01 M THAP in the NB recep-
tor phase, with 50 mM Fe(CN)64ꢁ, 0.1 M NaCl and 0.01 M NaClO4 in
the aqueous droplet phase. (b) 1 mM Fe(CN)64ꢁ, 0.1 M NaCl and 0.01
M NaClO4 in the aqueous receptor phase, with 10 mM TCNQ and
0.01 M THAP in the NB droplet phase. Drop time and final drop radii
were 6.3 s and 0.5 mm, respectively. The dashed theoretical curves are
concentration profiles for each species with kf ¼ 0.04 cm sꢁ1 Mꢁ1
.
rate, usually denoted by bꢁ1 in the literature,35 with a typical
˚
value of 1 A. The parameter k is the Landau–Zener trans-
mission coefficient and n is a typical frequency of molecular
motion. It is usual to consider kn ꢇ 1013 sꢁ1
.
Fig. 7 MEMED concentration profiles (solid curves) for the aqu-
eous/DCE system. (a) TCNQ concentration profiles obtained with 1
mM TCNQ and 0.01 M THAP in the DCE receptor phase, 50 mM
Fe(CN)64ꢁ, 0.1 M NaCl and (from top to bottom) 0.25 (i), 0.1 (ii),
0.025 (iii) and 0.01 M (iv) NaClO4 in the aqueous droplet phase. Drop
time and final drop radii were 6.3 s and 0.5 mm, respectively. Corre-
sponding dashed theoretical curves, from top to bottom, are for
¼
For the case of work term corrected rate constants,30 DG
for the sharp boundary model is given by:
2
¼
DG ¼ ðl=4Þð1 þ DGo0=lÞ
ð11Þ
where DGo ¼ ꢁFw, is the formal Gibbs energy for the one-
electron transfer process and l is the reorganisation energy.
It is convenient to define the equilibrium potential as the
situation when the forward and reverse bimolecular rate con-
stants are equal. This is seen to be close to w ¼ 0 on the plots
in Fig. 4(c) and 5(c), but does not correspond exactly because
no account has been taken of the work terms on the driving
force. While it is possible to estimate work terms in infinitely
dilute solution, it is much more difficult for strong electrolyte
solutions,30 as employed in these studies. However, the work
terms are relatively minor in infinitely dilute solution and will
decrease further in electrolyte solution,36 which serves to mini-
mise electrostatic contributions and also decreases the effective
charge density on highly charged moieties, such as ferro–ferri-
cyanide, through ion pairing. We thus estimate that these
terms will amount to only a few kJ molꢁ1 for this system,
which is the order of the displacement from w ¼ 0 of the poten-
tial where kf ¼ kb .
0
ꢀ
ꢁ
M
ꢁ1. (b) TCNQ concentration
kf ¼ 0.03, 0.05, 0.1 and 0.16 cm sꢁ1
profiles obtained with (from bottom to top) 0.25 (i), 0.1 (ii), 0.025 (iii)
and 0.01 M (iv) NaClO4 in the aqueous droplet phase and other para-
meters already cited in (a). Corresponding dashed theoretical curves,
from bottom to top, are for kf ¼ 0.03, 0.05, 0.1 and 0.16 cm sꢁ1
4ꢁ
ꢁ1. (c) Fe(CN)6
concentration profiles obtained with 10 mM
M
TCNQ and 0.01 M THAP in the DCE droplet phase, 1 mM
Fe(CN)64ꢁ, 0.1 M NaCl and (from top to bottom) 0.25, 0.1, 0.025
or 0.01 M NaClO4 in the aqueous receptor phase and other parameters
as for (a). Corresponding dashed theoretical curves, from top to bot-
tom, are for kf ¼ 0.03, 0.05, 0.1 and 0.16 cm sꢁ1 Mꢁ1
.
For an interface that is several molecular layers deep, of thick-
ness, L, the expression for the corresponding rate constant,
denoted by k00 is:
12
2
¼
k00 ¼ 4pða1 þ a2Þ DrknL expðꢁDG =RTÞ
ð10Þ
12
In eqns. (9) and (10), a1 and a2 are the radii of the reactants,
Dr describes the distance dependence of the electron transfer
In eqn. (11), the reorganisation energy is defined by
l ¼ lo + li , where lo and li are the outer and inner sphere
Phys. Chem. Chem. Phys., 2002, 4, 3820–3827
3825

View Article Online
reorganisation energies, respectively. li is 39.7 kJ molꢁ1 for
Fe(CN)6
phase,5 we have re-analysed earlier data by carefully measuring
the formal potential over the range of conditions of interest.4
The results of this analysis show that the a value is not sig-
nificantly influenced by ionic strength in the aqueous phase
within the range of interest (a ¼ 0.43 ꢃ 0.04 when
[THAP]o ¼ 0.1 M and a ¼ 0.34 ꢃ 0.02 when [THAP]o ¼ 0.01
M). Rather, the apparent decrease in the rate constant
observed with increasing ionic strength in the aqueous phase
is due to a decrease in the driving force for the reaction from
the effect of ionic strength on the formal potential for the
ferro–ferricyanide couple, which was originally approximated
as invariant with ionic strength. Similar effects are seen with
Li2SO4 as the aqueous supporting electrolyte. In this case,
ꢀ
3ꢁ/4ꢁ
and 10 kJ molꢁ1 for the TCNQ0/ ꢁ couple.8 li
for bimolecular ET can be approximated using the mean value
of li of the two redox couples, while lo is given by,30b
ꢀ
ꢁ
ꢀ
ꢁ
2
2
NAðDeÞ
8pa1eo
1
1
D1s
NAðDeÞ
8pa2eo
1
1
D2s
lo ¼
ꢁ
þ
ꢁ
Do1p
Do2p
!
2
NAðDeÞ
Do2p ꢁ Do1p
Ds2 ꢁ Ds1
ꢂ
ꢃ
ꢃ
ꢂ
ꢃ
ꢃ
ꢁ
ꢁ
ꢁ
ꢁ
Do1p Do2p þ Do1p
Ds1 Ds2 þ Ds1
16pd1eo
ꢀ
!
Do1p ꢁ Do2p
Ds1 ꢁ Ds2
2
NAðDeÞ
16pd2eo
ꢂ
ꢂ
ꢁ
Do2p Do2p þ Do1p
Ds2 Ds2 þ Ds1
ꢁ
2
a ¼ 0.70 ꢃ 0.07 (with [THAP]o ¼ 0.10 M and [Li2SO4]w
¼
NAðDeÞ
2pRdeo
1
1
ꢁ
ð12Þ
Do1p þ Do2p
0.10 M), which is similar to a ¼ 0.66 ꢃ 0.06 (with [THAP]o ¼
0.1 M and [Li2SO4]w ¼ 0.50 M) and a ¼ 0.50 ꢃ 0.02 (with
[THAP]o ¼ 0.01 M and [Li2SO4]w ¼ 0.50 M). These results
suggest that concentration effects7,17,18 at the aqueous side of
the interface are unimportant, consistent with the earlier work
of Girault and co-workers.7
Ds1 þ Ds2
where Do1p and Do2p are the optical dielectric constants of the
two phases (1.78 for water and 2.09 for DCE), eo is the permit-
tivity of free space, Ds1 and D2s are the static dielectric constants
of the two solvents (78.4 for water and 10 for DCE) and De is
the charge transferred. The parameters d1 and d2 are the dis-
tances from the two reactants to the interface and we approx-
imate these distances by the radii of the two reactants.
Rd ꢇ d1 + d2 is the characteristic distance separating the two
reactants and NA is Avogadro’s number. Considering
Summary and conclusions
Both SECM and MEMED have been used to investigate the
effect of galvanic potential on the ET rate constant for the
reaction between TCNQ and Fe(CN)64ꢁ, and the reverse pro-
cess. A wide range of conditions have been considered, cover-
ing two organic solvents and different organic electrolyte
concentrations. ET coefficients close to 0.5 have been deter-
mined for all of the conditions explored.
˚
a1 ꢇ a2 ꢇ 4 A, the outer sphere reorganisation energy amounts
to ca. 80 kJ molꢁ1, so the overall reorganisation energy is 105
kJ molꢁ1
.
The bimolecular rate constant at the equilibrium potential
based on the sharp boundary model is thus readily calculated
as k012 ¼ 0.08 cm sꢁ1 Mꢁ1 (converting units for comparison
with experiment). Given the approximations involved in some
of the parameters for the calculations, this result is in close
agreement with the experimentally measured values of 0.08
cm sꢁ1 Mꢁ1 (Fig. 4(c)) and 0.04 cm sꢁ1 Mꢁ1 (Fig. 5(c)) when
the forward and back bimolecular rate constants are equal. To
apply the thicker layer model we shall assume that lo in the
layer is given by eqn. (12). As pointed out by Marcus,30d there
are various elaborations on this model that could be consid-
Although SECM approach curves for ET in the aqueous/
NB system fit well to theory, MEMED has highlighted that
ꢀ
ꢁ
TCNQ transfers from NB to the aqueous phase under the
defined experimental conditions. This result illustrates the uti-
lity of MEMED as a sensitive probe of coupled IT processes
during ET at the ITIES.
Experimental data for the aqueous/DCE system have been
analysed further using Marcus theory. At equilibrium (when
the forward and back ET rate constants are equal), the sharp
boundary model for the ITIES predicts a bimolecular rate con-
stant close to that measured experimentally. Consistency with
this model is a reason why a Butler/Volmer kinetic formalism
describes ET at the ITIES when the supporting electrolyte con-
centration in both phases is relatively high. Analysis of earlier
experimental results,4,5 has established that concentration
effects7,17 at the aqueous side of the ITIES are unimportant.
˚
ered. With L ¼ 8 A, a much larger equilibrium bimolecular
rate constant of k00 ¼ 10 cm sꢁ1 Mꢁ1 results. For both calcu-
12
¼
lations, work term contributions to DG have been neglected,
but this is reasonable because this would amount to no more
than a few percent compared to the reorganisation energy.
This comparison of the experimentally measured rate con-
stants at zero standard free energy with theory indicates that
the model in which the ITIES is sharp at the molecular level
appears to be most appropriate. Consistency with this model
is one of the reasons why Butler–Volmer kinetics are observed,
particularly when the supporting electrolyte concentration in
both phases is relatively high. On the other hand it is impor-
tant to point out that more sophisticated analysis with the
thicker layer model could yield results closer to those found
experimentally.
Acknowledgements
We thank the EPSRC for support of this work. JZ thanks the
ORS scheme, the University of Warwick and Avecia for scho-
larships. Helpful discussions with Dr. John Atherton (Avecia,
Huddersfield) are much appreciated.
Brief comment on the effect of aqueous ionic strength on the ET
reaction
In our previous study,4 we observed that the apparent ET rate
constant decreased when the ionic strength in the aqueous
phase increased by addition of an indifferent electrolyte and
attributed this to a ‘salting out effect’.4 Similar experimental
results were also obtained later by Bard and co-workers.3
The latter study suggested that the effect of ionic strength on
the ET kinetics could be due to several factors, e.g. double
layer effects, specific or nonspecific adsorption, partitioning
of the ions, coupled ET-ion transfer (IT), IT–IT coupling as
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