Scanning electrochemical microscopy: Kinetics of chemical reactions following electron-transfer measured with the substrate-generation-tip-collection mode

Article abstract of DOI:10.1039/a707984b

The substrate-generation-tip-collection (SG-TC) mode of the scanning electrochemical microscope (SECM) is used as a new approach to investigate the kinetics of EC processes. Under the conditions of interest, a species O is generated at a macroscopic substrate (generator) electrode, with potential-step control, through the diffusion-limited electrolysis of a solution species R (E step). As O diffuses away from the generator, it undergoes a first order chemical reaction in solution (C step). A fraction of O is collected by electrolysis back to R at an externally biased ultramicroelectrode (UME), positioned directly over the substrate. This promotes the diffusional feedback of R to the substrate. Theory for the problem, relating the time-dependent tip current response to the rate constant for the C step and the tip-substrate electrode separation is developed numerically. Results of the calculations illustrate how the characteristic features of the tip current transients: peak current, peak time and post-half-peak time, depend on the kinetics of the C step and the inter-electrode separation. It is shown that both the kinetics and tip-substrate separation can be determined independently from a single transient by simply measuring the peak current and peak time. The theoretical results are validated experimentally through model studies of the oxidative deamination of N,N,-dimethyl-p-phenylenediamine (DMPPD) in aqueous solution at high pH. The effective second-order rate constant for the deamination step is in excellent agreement with values measured by alternative methods.

Full text of DOI:10.1039/a707984b

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Scanning electrochemical microscopy
Kinetics of chemical reactions following electron-transfer measured with the
substrate-generation–tip-collection mode
Rachel D. Martin and Patrick. R. Unwin¤
Department of Chemistry, University of W arwick, Coventry, UK CV 4 7AL
The substrate-generationÈtip-collection (SGÈTC) mode of the scanning electrochemical microscope (SECM) is used as a new
approach to investigate the kinetics of EC processes. Under the conditions of interest, a species O is generated at a macroscopic
substrate (generator) electrode, with potential-step control, through the di†usion-limited electrolysis of a solution species R (E
step). As O di†uses away from the generator, it undergoes a Ðrst order chemical reaction in solution (C step). A fraction of O is
collected by electrolysis back to R at an externally biased ultramicroelectrode (UME), positioned directly over the substrate. This
promotes the di†usional feedback of R to the substrate. Theory for the problem, relating the time-dependent tip current response
to the rate constant for the C step and the tipÈsubstrate electrode separation is developed numerically. Results of the calculations
illustrate how the characteristic features of the tip current transients: peak current, peak time and post-half-peak time, depend on
the kinetics of the C step and the inter-electrode separation. It is shown that both the kinetics and tipÈsubstrate separation can be
determined independently from a single transient by simply measuring the peak current and peak time. The theoretical results are
validated experimentally through model studies of the oxidative deamination of N,N,-dimethyl-p-phenylenediamine (DMPPD) in
aqueous solution at high pH. The e†ective second-order rate constant for the deamination step is in excellent agreement with
values measured by alternative methods.
In addition to the well documented use of SECM1,2 as a
probe of interfacial kinetics,3 a number of papers have demon-
strated that SECM is a powerful device for measuring the
solution kinetics of chemically unstable electrogenerated
species.4h6 Processes studied by SECM include chemical reac-
tions following electron transfer, such as Ðrst order EC4,7 and
instances where this may interfere with the reaction of inter-
est.8
The SGÈTC mode is an alternative, but less used, approach
for investigating homogeneous kinetics.12h14 This mode was
introduced by Engstrom and co-workers12,13 in a conÐgu-
ration where an amperometric tip UME served to collect both
stable and transient species generated at a larger electrode. In
these studies, a semi-quantitative theoretical model for the col-
lector electrode response was developed, with the neglect of
feedback e†ects, and used to estimate the kinetics of the
follow-up chemical reaction.13
second-order EC 5,8,9 mechanisms, and chemical reactions
2i
sandwiched between two one-electron transfer steps as in the
ECE-DISP1 framework.6
The investigation of electrode processes involving coupled
homogeneous kinetics with SECM has largely been based on
the feedback mode,2,4h9 or closely related tip-generationÈ
substrate-collection (TGÈSC) mode.5,6,8h10 With these
approaches, the tip UME, positioned directly over a larger
collector electrode, is held at a potential to electrogenerate the
species of interest from a solution precursor at a di†usion-
controlled rate. A competition is then established between the
di†usion of the electrogenerated species to the collector elec-
trode, maintained at a potential to promote the regeneration
and feedback of the initial precursor, and the solution kinetics.
By measuring the tip feedback current or tip and substrate
currents as a function of tipÈsubstrate separation (which
governs the inter-electrode di†usion time), the kinetics of the
solution process can be determined with high precision over a
wide dynamic range.4h9
It has been suggested that theoretical modelling of the
SGÈTC mode with amperometric electrodes would prove diffi-
cult because of feedback e†ects and the complex interaction of
the di†usion layers on the two electrodes.3a However, we have
recently demonstrated that, for a simple redox couple, the tip
UME response can readily be described taking account of
these processes.15 In combination with feedback measure-
ments,16 the SGÈTC mode was shown to be a simple, but
powerful, approach for identifying subtle di†erences in the dif-
fusion coefficients of the reduced and oxidised forms of a
redox couple, without prior knowledge of the sizes of the elec-
trodes or their separation.15,16 In this paper we extend the
SGÈTC model to electrode processes involving irreversible fol-
lowing chemical reactions, of the Ðrst-order EC type, and
demonstrate that the transient response of the tip UME
allows the solution kinetics and inter-electrode separation to
be determined independently, negating the need for a distance
calibrant or sophisticated positioning apparatus for this type
of SECM measurement.
These approaches require that the separation between the
tip and substrate is well deÐned and variable. This parameter
can be obtained by ensuring that the two electrodes are
aligned with sufficient precision that they can be approached
to contact, and then withdrawn a known distance (the method
employed for the studies in this paper). Alternatively, the tipÈ
substrate separation can be obtained by measurement of the
solution resistance,11 although this approach has not been
widely used. The most common method for determining the
inter-electrode separation (employed for all studies of homo-
geneous kinetics hitherto), is to use an internal mediator as a
calibrant of the tipÈsubstrate separation, but there are
Under the conditions of interest, the SGÈTC mode involves
the di†usion-controlled electrogeneration of a species, e.g. O,
at a macroscopic substrate electrode from a solution species,
e.g. R.
Substrate reaction:
R [ ne~ ] O
(I)
Species O di†uses away from the substrate and is intercepted
by a tip (collector) UME, where it undergoes di†usion-
controlled reduction back to R.
¤ E-mail: P.R.Unwin=warwick.ac.uk
J. Chem. Soc., Faraday T rans., 1998, 94(6), 753È759
753

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Initially the solution contains only species R at a bulk con-
Tip reaction:
O ] ne~ ] R
(II)
centration, c* , and hence the initial condition within the tipÈ
R
substrate domain is:
During transport from the substrate to the tip, O may also
decompose in a Ðrst-order irreversible chemical process, with
a rate constant k , to form a product, P, which is electro-
0 O z O d, 0 O r O r
glass
;
c \ c* , c \ 0
(3)
R
R
O
c
inactive at the potentials of interest.
where d is the distance between tip and substrate electrodes
and r deÐnes the position of the radial edge of the tip.
kc
glass
At time t \ 0, the potential of the substrate electrode is
stepped to a value for the di†usion-controlled oxidation of R
[eqn. (I)], while the tip UME is held at a potential to promote
the reverse reaction at a di†usion-controlled rate [eqn. (II)].
There is assumed to be no reaction of either R or O on the
insulating glass sheath surrounding the tip UME and no
radial Ñux of species at the cylindrical axis of symmetry. Since
the UME tip (including the insulating sheath) is smaller than
Solution reaction:
O ÈÈÈ P
(III)
A theoretical model for the above processes in the SECM
geometry is developed using the alternating direction implicit
Ðnite di†erence method (ADIFDM),17,18 which has found
widespread application for solving earlier SECM prob-
lems.4h6,15,16,19h21 The theoretical predictions are veriÐed
experimentally with studies on the oxidative deamination of
DMPPD in aqueous basic solution, which may be considered
as a model EC process:4,22h24
the macroscopic substrate electrode, and RG \ r /a [ 10
glass
for UMEs employed practically and considered theoretically
in SECM,4h6,15,16,19h21,25 it is reasonable to assume planar
di†usion of O and R normal to the substrate electrode at the
edge of the tipÈsubstrate domain.15 The boundary conditions
are therefore as follows:
Lc
Lz
Lc
Lz
R
O
z \ d, 0 O r O r
glass
;
c \ 0, D
\ [D
(4)
(5)
(6)
(7)
(8)
R
R
O
Lc
Lz
Lc
Lz
O
R
z \ 0, 0 O r O a;
z \ 0, a O r O r
0 \ z \ d, r \ r
c \ 0, D
\ [D
O
O
R
Lc
Lz
Lc
Lz
O
R
;
;
D
D
\ D
\ D
\ 0
\ 0
glass
glass
O
O
R
R
Lc
Lr
Lc
Lr
O
R
where eqn. (IV) and (V) represent the E step and C step,
respectively.
Lc
Lr
Lc
O
R
\ 0
0 \ z \ d, r \ 0;
D
\ D
O
R
Lr
Theory
The problem was cast into dimensionless form, in order to
obtain general solutions, by introducing the following terms:
For the electrode and solution reactions deÐned by eqn. (I)È
(III), the time-dependent di†usion equations for species R and
O in the axisymmetric SECM geometry (Fig. 1) are:
R \ r/a
Z \ z/a
(9)
(10)
(11)
(12)
(13)
(14)
Lc
Lt
C
L2c
Lr2
1 Lc
r Lr
L2c
Lz2
D
R
R
R
R
\ D
]
]
(1)
(2)
R
q \ tD /a2
R
Lc
Lt
C
L2c
1 Lc
r Lr
L2c
D
C \ c /c*
(i \ R or O)
O
O
O
O
\ D
]
]
[ k c
i
i R
O
c O
Lr2
Lz2
c \ D /D
O
R
where r and z are the coordinates in the radial and normal
directions starting at the electrode surface, D and c are the
di†usion coefficients and concentrations of species i (R or O),
and t is time.
K \ k a2/D
c
R
i
i
Since R is the only electroactive species in bulk solution, it
is most convenient to normalise the UME collector current,
i , for the SGÈTC mode15 with respect to the steady-state
c
current for the oxidation of R at the tip when it is placed at a
large distance from the substrate,26
i
\ 4nFaD c*
(15)
=
R R
where F is FaradayÏs constant, to give:
P1(LC /LZ)
i /i \ c(n/2)
R LR
(16)
c =
O
Z/0
0
It is worth emphasising that this choice of normalisation is
necessarily di†erent to that for feedback16,25 and other SECM
modes,19h21 for which the tip reaction is the same in bulk
solution and close to the target interface.
The problem was solved numerically using the ADIFDM,
for which general details are given elsewhere.4h6,15,16,19h21
Programs were written in FORTRAN and run on either the
University of Warwick central UNIX system or a local
Hewlett-Packard 735 workstation.
Fig. 1 Schematic diagram of the substrate-generationÈtip-collection
(SGÈTC) mode of SECM for an EC process. The coordinate system
for the SECM geometry is also shown. Note that this diagram is not
to scale: typically r
B 10a; d O a.
glass
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
754

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feedback occurs at longer times decreases with increasing rate
constant, causing the rapid decay in the current and the
appearance of the peak at shorter times.
Theoretical results and discussion
The normalised currentÈtime response of the tip UME
depends primarily on the tipÈsubstrate separation, K and c.
To limit the length of this paper, comprehensive theoretical
results are presented for the case of c \ 1, which both rep-
resents the most general case and was appropriate to the
experimental system of interest (vide infra).
At the larger tipÈsubstrate separations [Fig. 2(b)] the di†u-
sion time for the substrate-generated species to reach the tip
increases. Consequently, for a given value of K, the peak
current occurs at a longer time than for the closer tipÈ
substrate separation [Fig. 2(a)]. Moreover, as found for
feedback2,4h8 and TGÈSC5,6,8 measurements, the current
response becomes less sensitive to solution kinetics, the
greater the spacing between the tip and substrate. For the
SGÈTC mode in the present application, the e†ect of increas-
ing the inter-electrode spacing is to decrease the peak current
for a given value of K. These issues are illustrated further in
Fig. 3, which shows transients for K \ 10 at a range of values
of log(d/a) between [1.0 and [0.5. It is clear that the closer
the tipÈsubstrate separation, the larger the peak current, but
the shorter the peak time. From an experimental viewpoint,
close tipÈsubstrate separations lead to high sensitivity in terms
of tip current, but it is also evident that the tip response has
to be measured with the highest temporal resolution in this
situation.
The characteristic features of the tip current transients in
Fig. 2 and 3 are the peak current, peak time and post-half-
peak time. Comprehensive contour plots illustrating how
these features depend on the tipÈsubstrate separation and K
are given in Fig. 4. The magnitude of the normalised peak
current [Fig. 4(a)] increases as both K and the value of d/a are
decreased. In contrast, the peak time increases as the value of
d/a is increased and K is decreased [Fig. 4(b)]. In principle,
this contrasting variation in the peak current and peak time
with K and d/a should allow both to be determined from a
single transient measurement. The post-half-peak time has a
yet di†erent dependence on d/a and K, by increasing as K
decreases while showing only a minimal dependence on the
inter-electrode separation [Fig. 4(c)].
Calculated tip chronoamperometric characteristics for a
range of values of the normalised rate constant, at two tipÈ
substrate separations, log(d/a) \ [0.7 and [0.2 (typical of
relatively small and large separations) are shown in Fig. 2(a)
and (b), respectively. In the absence of following chemical
reactions (K \ 0), the tip current rises, after an initial lag
period, from zero to a steady-state value. The magnitude of
the steady-state current and the rise time depend on the tipÈ
substrate separation, as discussed in detail elsewhere.15 In
brief, the closer the tip and substrate, the shorter the inter-
electrode di†usion time. Consequently, in this limiting situ-
ation, the more rapid the current rise the sooner a steady state
is established. At steady-state, the concentration gradients
normal to the UME are steeper the closer the inter-electrode
spacing, resulting in an increasingly enhanced current with
decreasing electrode separation.
In contrast, for Ðnite values of K, the current does not reach
a steady state, rather it rises to a peak value and then
decreases at longer times. The value of both K, and the tipÈ
substrate separation, have a marked e†ect on the overall
shape of the tip current transient and the magnitude of the
peak current. For a given tipÈsubstrate separation, the larger
the value of K, the smaller the peak current, the shorter the
time to reach the peak, and the steeper the decay curve follow-
ing the peak. This is expected, since increasing the rate of the
following chemical reaction decreases the fraction of
substrate-generated O that initially reaches the tip in the Ðrst
pass, thereby decreasing the peak current. The extent to which
The implications of the above analysis are that it should be
possible to measure following chemical reaction rates via the
SGÈTC mode without any prior knowledge of the tipÈ
substrate separation. From a practical viewpoint, this opens
up the possibility of making such measurements with very
basic positioning apparatus. The range of measurable rate
constants will largely be governed by the timescale on which
tip currents can be recorded. For example, towards the fast
kinetic limit, a normalised peak current in excess of unity is
predicted for log K \ 2.5, with tipÈsubstrate separations
closer than log(d/a) \ [0.8. The normalised time at which the
peak occurs is, however, smaller than 0.01. For a tip UME
with a radius of 10 lm and a typical di†usion coefficient of
10~5 cm2 s~1, these Ðgures relate to a rate constant in excess
of 3000 s~1 and a corresponding peak time less than 10~3 s.
Under the experimental conditions of this study, with a large
Fig. 2 E†ect of K on the chronoamperometric characteristics for an
EC process in the SGÈTC mode at tipÈsubstrate separations of (a)
log(d/a) \ [0.7 and (b) log(d/a) \ [0.2. Normalised current data are
plotted as a function of normalised time, q. The dashed lines (i) show
the behaviour for K \ 0, while the solid lines are for log K values of:
(ii) [0.5; (iii) 0.0; (iv) 0.5; (v) 1.0 and (vi) 1.5.
Fig. 3 E†ect of tipÈsubstrate separation on the SGÈTC tip collector
chronoamperometric response. The theoretical data relate to K \ 10,
with a range of deÐned log(d/a) values.
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755

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epoxy resin (Delta Resins, Stockport, UK), and then ground
to expose the Pt surface. Both the substrate and the tip elec-
trode were polished with a succession (25, 14, 6 and 1 lm) of
Ðner diamond lapping compounds (Buehler Ltd, Coventry,
UK) on nylon pads (Buehler) and Ðnally using 0.05 lm
alumina (Buehler). A platinum gauze was used as a counter-
electrode and a silver wire served as a quasi-reference elec-
trode (AgQRE).
The position of the UME tip was controlled by mounting it
on a model 461 manual xÈyÈz stage (Newport Corp.). The
z-axis was controlled by a di†erential micrometer (model
DM-13, Newport Corp.) and the x and y axes by Ðne adjust-
ment screws (Model AJS-05, Newport Corp.). The spatial
resolution attainable with the micrometer was quoted as 0.07
lm, but the device was used to measure the tip position to the
nearest 0.25 lm (half of one division on the Vernier scale).
The cell comprised a fully detachable TeÑon base, a cylin-
drical glass body and a TeÑon lid. The base contained a hole
in the centre that could securely accommodate the Pt sub-
strate electrode, such that the surfaces of the substrate and tip
electrodes were parallel. The stages and cell were mounted on
a Newport CSD series breadboard which provided adequate
vibration isolation.
Experiments involved placing the tip UME in contact with
the substrate electrode and then withdrawing the tip a set dis-
tance from the substrate. There was e†ectively no positional
o†set with the set-up described. As found by other workers,14
the alignment between the tip and the substrate was sufficient-
ly precise that when the two electrodes were placed together,
electrical contact was made, as veriÐed by the passage of a
large anodic current with the substrate externally unbiased
and the tip at a potential of 0.40 V vs. AgQRE to e†ect the
oxidation of DMPPD.
Materials
DMPPD (Aldrich, Gillingham, UK) solutions (4 ] 10~3 mol
dm~3) were prepared from a thoroughly deaerated 4 ] 10~2
mol dm~3 stock solution immediately prior to each experi-
ment using Milli-Q reagent water (Millipore Corp.), with 1.0
mol dm~3 potassium chloride (Fisons, AR grade) as a sup-
porting electrolyte and 0.25 mol dm~3 dipotassium hydrogen
phosphate (Fisons) as a bu†er. The pH of the bu†er was
adjusted to the desired level with 1.0 mol dm~3 sodium
hydroxide solution (Fisons).
Fig. 4 Theoretical contour plots showing the variation of (a) peak
current, (b) peak time and (c) post-half-peak time, with tipÈsubstrate
separation and normalised rate constant. The labels on the contours
are either values of the normalised current ratio (a) or normalised
time [(b) and (c)].
Prior to all experiments, solutions were thoroughly deaer-
ated with argon, for a period of ca. 20 min. During experi-
ments, Ar was passed over the surface of the solution under
study. All measurements were made at 25 ^ 1 ¡C.
substrate electrode and conventional bipotentiostat, these
parameters probably characterise the upper limit of rate con-
stants that may be determined with the technique, since at
shorter times there may be coupling between the substrate
and tip responses.1 By employing smaller substrate electrodes,
it might be possible to push the SGÈTC measurements to
higher rate constants, comparable to those of ca. 104 s~1
attainable with the feedback mode.4
Experimental results and discussion
The theoretical model assumes that the electrolysis of the
solution precursor at the generator electrode is a simple
di†usion-limited process, without any heterogeneous kinetic
complications. Initial experiments were performed to demon-
strate that this was the case for DMPPD oxidation in
aqueous solution at pH 7.65, where the following chemical
step [eqn. (V)] is negligible.4 These measurements were impor-
tant since, although previous SECM feedback measurements
have demonstrated that stable di†usion-limited currents are
maintained for up to 15 min,4 provided that the concentration
of DMPPD is low and the solution is thoroughly deaerated,
there are also reports of Ðlming of the electrode surface in
studies carried out with conventional electrodes.23
Experimental
Apparatus and instrumentation
Experiments were carried out in a four-electrode arrangement
using an Oxford Electrodes (UK) bipotentiostat, which was
modiÐed in house to include an option which allowed currents
to be measured with gains of 10~6È10~9 A V~1, as well as the
conventional 10~3È10~6 A V~1 range. Chronoamperometric
characteristics were acquired directly on a NIC310 (Nicolet)
digital storage oscilloscope with disk storage facilities.
A 25 lm diameter Pt disk UME, characterised by RG \ 10,
Potential-step chronoamperometric experiments were
carried out by stepping the potential of the macroscopic gen-
erator electrode from 0.0 V, where there were no Faradaic
processes to a value of 0.50 V, well into the limiting-current
region, where the oxidation of DMPPD was driven at a
and prepared as described previously,15,16,19 was used as the
tip electrode. The substrate electrode was
a platinum
(Goodfellow Metals, Cambridge, UK) square of area, A \ 4
mm2, with a contact wire attached, potted Ñat in a cylinder of
756
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from 0.0 to 0.5 V to e†ect the di†usion-controlled oxidation of
DMPPD, with the substrate potential maintained at 0.0 V to
drive the reverse process at di†usion control. For the SGÈTC
measurements, the applied potentials were interchanged. The
steady-state responses are seen to be very close at long times,
yielding a value of c \ 0.98 (^0.02). This indicates that the
di†usion coefficients of the reduced and oxidised forms of
DMPPD are very close, and may be considered to be e†ec-
tively equal, within experimental error.
Fig. 7 shows the SGÈTC tip collector transients, recorded as
described above, at several other tipÈsubstrate separations, at
pH 7.65. Also shown are the corresponding theoretical predic-
tions for the case of K \ 0, for each of the inter-electrode
separations of interest. The experimental characteristics are
consistent with the predictions above [Fig. 2(a) and (b)]
showing clearly that the product of the electrode reaction
[eqn. (IV)] is e†ectively stable on the timescale of SECM mea-
surements at the deÐned pH.
Fig. 5 Substrate (generator) electrode chronoamperometric response
for the oxidation of DMPPD (ÈÈÈ). The best Ðt of the experimen-
tal data to the behaviour predicted by eqn. (17), with D \ 7.2 ] 10~6
cm2 s~1 is also shown (É É É).
A selection of typical tip current responses are shown in
Fig. 8 for the oxidation of DMPPD at the substrate electrode
and collection of the generator product [eqn. (IV)] at the tip,
with the solution at three higher pH values (10.94, 11.36 and
11.54) to promote the deamination process [eqn. (V)]. The
potentials applied to the substrate and tip electrodes were as
deÐned above for SGÈTC measurements. The shapes of the tip
transients are consistent with the theoretical predictions for an
EC process, with the collector current initially rising to a peak
value and then decaying at longer times. The best Ðts of the
model to each of the transients are also shown for comparison
with experiment. In each case, the inter-electrode separation
and di†usion coefficient of DMPPD was known and thus the
di†usion-controlled rate. Current transients were found to
agree well with the Cottrell equation27
nFAD1@2c*
n1@2t1@2
i \
(17)
s
on a timescale of 0.5 ms and longer. In eqn. (17), c* is the bulk
concentration of DMPPD, i is the substrate electrode current
s
and the other terms have been deÐned earlier. Eqn. (17)
applied to experimental data obtained both without and with
a tip located close (within micrometre distances) to the sub-
strate electrode. Fig. 5 shows a typical chronoamperogram,
plotted according to eqn. (17), for the generator electrode in a
pH 7.65 solution with the UME tip positioned 5 lm above,
and held at a potential of 0.0 V so as to collect the product of
the substrate electrode reaction. The data yield a di†usion
coefficient of 7.2(^0.1) ] 10~6 cm2 s~1 which is in good
agreement with previously published results.4
The tip collector currents are sensitive to the ratio of di†u-
sion coefficients of the reduced and oxidised forms of the
couple, c. Recent work from this group has demonstrated that
SGÈTC and feedback measurements in combination, represent
a simple approach for determining this parameter. In particu-
lar, for a chemically stable couple, the ratio of the steady-state
rate constant, k , was the only variable in the Ðtting pro-
c
cedure. There is seen to be reasonable agreement between
experiment and theory. Moreover, the transients at di†erent
pH yield a consistent rate constant for the deamination step,
with values of k of 8.8 s~1 [(a), pH 10.94], 23 s~1 [(b), pH
c
11.36] and 33 s~1 [(c) pH 11.54]. For comparative purposes,
approximating the measured activity by concentration of
OH~, these values yield a second-order rate constant, k \
2
k /[OH~] \ 1.0(^0.1) ] 104 mol~1 dm3 s~1, in good agree-
c
ment with previously published results for this system (with
the same approximation) obtained with the SECM feedback
mode.4
tip feedback current, i , and collector current, at close inter-
f
electrode separations reveals c directly:15
It is useful, Ðnally, to examine practically the precision with
which the SGÈTC methodology can determine both the rate
constant and inter-electrode separation. Fig. 9 shows the sets
of inter-electrode spacings and rate constants derived from the
peak currents and peak times of the transients in Fig. 8. The
intersection of the two contours on each plot yields the fol-
c \ i /i
(18)
c f
without prior knowledge of the tipÈsubstrate separation. Fig.
6 shows the feedback and SGÈTC tip collector chrono-
amperometric responses at a tipÈsubstrate separation of 5.0
lm. This distance was inferred, in this case, from the steady-
state feedback current which is c-independent.16,25 Feedback
measurements were made by stepping the tip UME potential
lowing values of d and k : (a) 2.7 lm and 9.2 s~1 (pH 10.94);
c
(b) 1.9 lm and 30 s~1 (pH 11.36) and (c) 2.6 lm and 37 s~1
Fig. 6 (a) Feedback and (b) SGÈTC tip collector chrono-
amperometric responses for DMPPD oxidation at pH 7.65 with a
Ðxed tipÈsubstrate separation of 5.0 lm. The transients reach similar
steady-state values indicating that the ratio of di†usion coefficients (c)
of the electrode reactant and product is close to unity [eqn. (18)].
Fig. 7 Tip (collector) electrode chronoamperometric responses for
the oxidation of DMPPD (ÈÈÈ) at pH 7.65 in the SGÈTC mode,
with tipÈsubstrate separations of (i) 1.25, (ii) 2.25 and (iii) 3.25 lm. The
corresponding theoretical responses for these distances with K \ 0 are
shown for comparison (É É É).
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
757

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Fig. 8 Tip (collector) electrode chronoamperometric responses for
the oxidation of DMPPD (ÈÈÈ) under the following conditions: (a)
pH 10.94, d \ 2.75 lm; (b) pH 11.36, d \ 2.0 lm; (c) pH 11.54, d \ 2.5
lm. The experimental data have been Ðtted to theory (É É É) using the
Fig. 9 Contours showing the sets of values of log(d/a) and log K
derived from measurements of the peak current and peak time from
the transients in Fig. 8. Data relate to the measurements at pH: (a)
10.94, (b) 11.36 and (c) 11.54.
value of D cited in the text and k : (a) 8.8; (b) 23; (c) 33 s~1.
c
(pH 11.54). The values of inter-electrode separation are close
to those expected, while the rate constants are in good agree-
ment with those used in Ðtting the full tip transients (see the
caption to Fig. 8). The set of rate constants derived from
The upper limit to the rate constants measurable with the
technique is close to that of the feedback mode4 and could
surpass it with improvements in the electrochemical instru-
mentation employed. From a practical viewpoint, the tech-
nique is unlikely to match the TGÈSC mode operating with
two closely spaced UMEs.5,6 The latter approach does,
however, require high-precision positioning capabilities of the
tip and collector electrodes in all three spatial coordinates.
The SGÈTC methodology could readily be extended to other
classes of coupled chemical processes, such as second-order
following chemical reactions, sandwiched solution processes
(as in the ECEÈDISP scheme) or parallel (catalytic) solution
reactions.
surface Ðtting the peak currents and times yields k \ 1.15
2
(^0.15) ] 104 mol~1 dm3 s~1. The results of this exercise
thus clearly show that the rate constants for following chemi-
cal reactions and inter-electrode separations can be deter-
mined with good precision and accuracy from the
measurement of the peak current and peak time from tip col-
lector transient measurements in the SGÈTC mode.
Conclusions
We thank the EPSRC for a studentship for R. D. M. Helpful
discussions on this work with Dr Julie Macpherson
(University of Warwick) are much appreciated.
The Ðrst theoretical model for the SGÈTC mode with EC pro-
cesses has been developed and shown to be in excellent agree-
ment with experimental measurements on the oxidation of
DMPPD in aqueous solution at high pH. The theory
advances an earlier model12 by taking full account of feedback
e†ects which are shown to be important. If the inter-electrode
separation is known, the SGÈTC mode can be used to
measure following chemical reaction rates by Ðtting the full tip
current transient response, with the homogeneous rate con-
stant as the only variable. Alternatively, both the rate con-
stant and inter-electrode separation can be determined with
high precision by simply measuring the peak current and peak
time in a single transient. This latter approach negates the
need for sophisticated positioning apparatus for SECM mea-
surements of this type.
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