fast scan linear sweep voltammetry at a high-speed wall-tube electrode
TRANSCRIPT
Fast scan linear sweep voltammetry at a high-speed wall-tubeelectrode
Neil V. Rees, Oleksiy V. Klymenko, Barry A. Coles, Richard G. Compton *
Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, UK
Received 20 January 2003; received in revised form 5 May 2003; accepted 16 May 2003
Journal of Electroanalytical Chemistry 557 (2003) 99�/107
www.elsevier.com/locate/jelechem
Abstract
The application of fast-scan linear sweep voltammetry methods to a high-speed wall-tube electrode (HWTE) is reported.
Experiments are reported for the oxidation of N,N,N ?,N ?-tetramethyl-p -phenylenediamine (TMPD) in propylene carbonate
solution containing 0.10 M tetrabutylammonium perchlorate for a 24 mm radius platinum microdisk electrode housed within the
HWTE using a range of scan rates from 200 to 3000 V s�1 and average flow jet velocities from 0.24 to 9.4 m s�1 (corresponding to
volume flow rates of 0.003�/0.12 cm3 s�1, and centre-line jet velocities from 0.5 to 18.9 m s�1). Linear sweep voltammograms
(LSVs) are analysed for a simple electron transfer under high volume flow rates, by curve fitting. Analysis of the transient LSVs
yielded values for k0, a , and Ef0 for TMPD of (5.99/2.4)�/10�2 cm s�1, 0.469/0.08 and 0.2179/0.019 V (vs. Ag), respectively. This is
in good agreement with independent experiments conducted using the high-speed channel electrode which yielded the results: k0�/
(6.39/0.4)�/10�2 cm s�1, a�/ 0.529/0.01, and Ef0�/ 0.2349/0.005 V (vs. Ag). The range of applicability of this method for
measuring k0 was also investigated and compared with existing channel electrode techniques.
# 2003 Elsevier B.V. All rights reserved.
Keywords: Fast scan linear sweep voltammetry; Wall-tube electrode; Heterogeneous rate constant; Oxidation; N,N,N ?,N ?-tetramethyl-p -
phenylenediamine; Simulation
1. Introduction
The impinging-jet electrode is a specific type of
hydrodynamic electrode where a jet of electrolyte is
propelled from a nozzle through a filled chamber
(usually of the same electrolyte composition) to strike
an electrode situated directly opposite the nozzle. The
hydrodynamics of this arrangement under laminar
conditions are believed to consist of two different flow
regimes in the vicinity of the electrode. Directly below
the jet, where the flow is axial, there is a stagnant region,
which extends a distance of approximately 1�/3 nozzle
diameters across the flat surface [1,2]. Outside of this
stagnant region is the wall-jet region where the radial
velocity begins to decay [3]. In the limiting case where
the electrode is entirely within the stagnant region (i.e.,
the nozzle diameter is greater than that of the electrode),
the electrode is uniformly accessible and termed a wall-
tube electrode (WTE) [4]. Where the electrode is larger
than the nozzle, and extends into the wall-jet region, it is
termed a wall-jet electrode (WJE) [5]. Both limiting cases
are illustrated in Fig. 1.
The WTE and WJE have been the subject of much
investigation in terms of their hydrodynamics and
applications to mechanistic and analytical work [6].
The WTE has been further developed by Unwin and co-
workers utilising microelectrodes to develop a microjet
electrode [7]. This has been shown to be effective for
investigating electron transfer kinetics [8], coupled
solution reactions [9], and flow analysis [10]; and a
model has recently been developed to approximate the
mass transport within it [11�/13].
In this article we describe a miniaturised WTE for use
in a pressurised system previously reported for channel
electrode use [14]. This high-speed WTE (‘HWTE’) has
been designed to operate at high volume flow rates
achievable using the pressurised system, to measure fast
* Corresponding author. Tel.: �/44-1865-275-413; fax: �/44-1865-
275-410.
E-mail address: [email protected] (R.G.
Compton).
0022-0728/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0022-0728(03)00352-8
electrochemical kinetics (Fig. 2). In this article we report
the application of fast-scan linear sweep voltammetry to
investigate the heterogeneous electron transfer rate for
the oxidation of N,N,N ?,N ?-tetramethyl-p -phenylene-
diamine (TMPD) in propylene carbonate (PC), together
with high-speed channel electrode experiments [15] to
confirm the kinetic measurements. TMPD has pre-
viously been reported to have a standard heterogeneous
electron transfer rate constant, k0, of 1.5�/10�2 cm s�1
in PC at 293 K [16].To date, the use of WTEs to measure fast hetero-
geneous electron transfer rates has been confined to the
measurement of steady-state voltammograms [7], which
have been analysed using the quarter-potentials method
of Mirkin and Bard [17] assuming uniform accessibility.
As this method is unsuitable for analysis of transient
voltammograms, and has been reported to incur a
relatively large error in the value of the transfer
coefficient, a [7], we have investigated other possible
means of analysing the voltammetry obtained.
In the case of transient linear-sweep voltammograms,we consider the measurement of both peak currents and
peak potentials as a possible means of extracting values
of k0 and a . We also present a method of fitting the
entire voltammogram curve, thereby using all available
voltammetric information, and finding the values of
these kinetic parameters that provide a ‘best-fit’ to the
experimental data.
2. Theory
2.1. Wall-tube experiments
We consider a simple electron transfer reaction at theWTE surface (written as an oxidation):
A�e�?kf
kb
B (1)
where both A and B are kinetically stable on the
timescale of the experiment, and the bulk solution
contains only A before it enters the flow-cell. Theforward and reverse rate constants are given by But-
ler�/Volmer theory:
kf �k0e(1�a)F
RT(E�E0
f); kb�k0e
�aF
RT(E�E0
f)
(2)
where k0 (cm s�1) is the standard electrochemical rate
constant for heterogeneous electron transfer, Ef0 is the
formal potential of the A/B redox couple, a is the
transfer coefficient, and R , T , and F have their usual
significance.
The uniform accessibility property of the WTE (Fig.3) [4,18] allows us to solve the convective-diffusion
equations only in the z direction [18] where the solution
velocity is proportional to z2:
vz��Cz2 (3)
The constant C is given by [19],
Fig. 1. The two limiting forms of the impinging-jet electrode geometry.
Fig. 2. Schematic diagram showing the HWTE (not to scale). Fig. 3. Streamlines and geometry of a WTE.
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107100
C�0:52
�Vf
r3T
�3=2�rT
zT
�0:162
n�1=2 (4)
where Vf is the volume flow rate (cm3 s�1), n is the
kinematic viscosity (cm2 s�1), rT is the nozzle radius
(cm), and zT is the nozzle-electrode separation (cm).
The time-dependent convective-diffusion equationdescribing mass transport of species A to the electrode is
@a
@t�D
@2a
@z2�Cz2 @a
@z(5)
where a�/[A]/[A]bulk.
The boundary condition at the electrode correspond-
ing to Butler�/Volmer kinetics is
D@a
@z jz�0
� (kfa�kbb)z�0 (6)
where kf and kb are given by Eq. (2), and the
concentration tends to its bulk value with increasing
distance from the electrode:
ajz0��1 (7)
The mathematical model Eq. (5) to Eq. (7) was solved
using the finite element technique in Ref. [19].The simulation procedure developed in Ref. [19] for
linear sweep voltammetry was used to generate theore-
tical current�/voltage curves for subsequent comparison
with the experimental ones.
In order to ‘extract’ the values of k0, a and Ef0 from
the experimental voltammograms we used the least
squares method which consists of minimisation of the
following functional:
MSAD(k0; a; E0f )
�1
M
XM
k�1
(Iexp(Ek)�Ith(k0; a; E0f ; Ek))2 (8)
where Iexp(Ek) is the experimental current corresponding
to the potential Ek , Ith(k0, a , Ef0, Ek) is the theoretically
predicted value of the current at Ek , and M is the
number of experimental data points. The values of a , k0
and Ef0 were then found by minimisation of MSAD Eq.
(8) using the modified Newton’s method [15]. The main
iterative formula of the modified Newton’s method of
minimisation of a function f of a vector argument x is
x(k�1)� x(k)�gk[H (k)]�19f (k) (9)
where k is the iteration index, H(k ) is the Hessian matrix
(the matrix of second partial derivatives) of f evaluatedat the point x(k); 9f(k ) is the gradient of f at the same
point, and gk is an adjustable coefficient. All derivatives
were calculated using finite-difference approximations.
2.2. High-speed channel electrode experiments
The methodology used for the simultaneous fitting of
values of k0, a , and Ef0 from the experimental voltam-
mograms has been described in detail elsewhere [15].
3. Experimental
3.1. Reagents
Chemical reagents used were TMPD (Aldrich, 98%),
tetrabutylammonium perchlorate (TBAP) (Fluka Puriss
electrochemical grade, �/99%), and PC (Fluka, purum,
]/99%). These were of the highest grade available and
were used without further purification. Ultra-pure water
was used for cleaning (UHQ grade) and had a resistivity
of not less than 18 MV cm (Elga, High Wycombe,Bucks, UK). All solutions contained 0.10 M TBAP and
were thoroughly degassed with argon (Pureshield Ar-
gon, BOC Gases Ltd, UK). All experiments were
conducted at a temperature of 2929/1 K.
3.2. Instrumentation
The HWTE consists of a platinum microdisk elec-
trode embedded in a miniaturised wall-tube cell con-
nected within the pressurized apparatus described
previously [14]. Fig. 2 shows a schematic representation
of the electrode assembly. High volume flow rates areachieved by pressurizing the chamber containing the
solution and electrode assembly up to 1.5 atm. The
solution flows through the nozzle of the specially
designed wall-tube cell and out to the exit, which is at
ambient atmospheric pressure. The range of volume
flow rates available to the HWTE is determined by the
choice of chamber pressure and also by the solution
viscosity. For example in the present case of PC, volumeflow rates of up to 0.12 cm3 s�1 can be achieved
(corresponding to average flow linear jet speeds ap-
proaching 9.4 m s�1, with centre-line jet velocities of up
to 18.9 m s�1), whereas with acetonitrile the volume
flow rate can reach 0.25 cm3 s�1 (average flow linear jet
speeds of up to 19.8 m s�1, and centre-line jet velocities
of up to 39.5 m s�1).
In considering the solution flow, it is informative toconsider the Reynolds number, Re, given by Ref. [4]
Re�dU
n(10)
where d is the nozzle diameter, n is the kinematic
viscosity, and U is the mean solution velocity. In thepresent case with PC as solvent, the Reynolds number
has a maximum value of 570, which is within the regime
(Re B/2000) where flow has been shown to be laminar
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107 101
[4]. Use of less viscous solvents in the HWTE can easily
result in Reynolds numbers in excess of 2000: the details
of the hydrodynamics of these solvents in the HWTE
will be examined in a following publication.
The high-speed channel electrode (shown schemati-
cally in Fig. 4) and pressurized apparatus have been
described previously [14,15]. Extremely high flow rates
across a microband electrode are achieved by pressuriz-
ing the reaction chamber up to 1.5 atm. The solution
flows through the specially designed flow-cell (with
width, d�/ 0.2 cm and height, 2h�/108 mm) and out
through one of three capillaries of varying internal bore
size, out to the exit which is at ambient atmospheric
pressure. In this way, volume flow rates of 1.85 cm3 s�1
can be achieved with PC, corresponding to linear flow
speeds at the electrode approaching 14 m s�1. The
electrode employed in this work was a Pt microband
with length 12.5 mm and width 0.10 cm.
The ‘fast scan’ potentiostat used was built in-house
and has a scan rate of up to 3�/104 V s�1 and was used
with minimum filtering. This potentiostat is similar to
that described and utilised by Amatore et al. [20�/22]
and is capable of achieving ohmic drop compensation
by means of an internal positive feedback circuit. The
potential was applied with a TTi TG1304 programmable
function generator (Thurlby Thandar Instruments Ltd,
Huntingdon, Cambs, UK) and the current recorded
with a Tektronix TDS 3032 oscilloscope (300 MHz
band-pass, 2.5 GS s�1). Computer programs were
written in FORTRAN 77 and run on a Pentium IV 2
GHz PC, which was also used for data analysis.
3.3. Wall-tube cell and electrodes
The wall-tube cell was constructed from Kel-F (BSL
Ltd, Kidlington, Oxon, UK) and precision bore Pyrex†
tube (Jencons plc, Leighton Buzzard, Beds, UK), and is
shown schematically in Fig. 2. The body of the chamber
is formed from a Pyrex† tube of outer diameter 12.5
mm, wall thickness 1.5 mm, and length 22 mm. The
lead-in tube and nozzle (with nozzle diameter, rT�/127
mm) are formed from hand-drawn Pyrex† and sealed
into a Kel-F plug to form one end to the chamber as
shown in Fig. 2. The microdisk electrode was sealed intoanother Kel-F plug (with an exit hole bored into it) to
complete the cell. A silicone sealant (‘Aquaria Sealant’,
Dow Corning Ltd, Byfleet, Surrey, UK) was used to
ensure a seal between the glass and Kel-F. The Kel-F
plugs were machined to an airtight fit to the inner
diameter of the Pyrex† chamber body, such that the
separation of the nozzle outlet and electrode surface was
approximately 300 mm. Finally, the cell was sheathed ina silicone rubber tube to complete the seal on the cell.
The microdisk electrode was constructed by sealing
platinum wire (�/99.95%, Goodfellow Cambridge Ltd,
Huntingdon, Cambs., UK) into capillary soda glass as
described in the literature [23], and its radius (r1) was
determined to be 24 mm according to reported methods
[24]. The microband electrode was fabricated according
to a previously reported method [14,15].The working electrode was polished in between
experiments using alumina lapping compounds (BDH)
of decreasing size from 3 mm down to 0.25 mm on glass
and soft lapping pads (Kemet Ltd, UK). The polished
electrode was cleaned with ultra pure water and then
immersed in approximately 30% nitric acid and stored
under ultra pure water between each use.
The counter electrode was a smooth, bright platinumwire coil, and a silver wire (99.95%, Johnson Matthey
plc, London, UK) was used as a pseudo-reference
electrode.
4. Results
4.1. Discrimination limits of the curve fitting method
In order to determine the range of k0 which can be
measured experimentally using linear sweep voltamme-
try in the HWTE cell we performed a series of
simulations using the finite element program outlined
above.
We simulated a series of current�/voltage responses
with different values of k0, for fixed values of scan rate,
Vf, D , and v . The resulting voltammograms were thenplotted on the same graph for comparison. It was noted
that at high values of k0, the gradients of the rising part
of the voltammograms converged to a reversible limit.Fig. 4. Schematic diagram of a channel electrode.
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107102
Similarly, at lower values of k0, the gradients of the
rising part of the waves converged to an irreversible
limit. It is necessary to determine the lower limit of k0 in
particular since there is a danger that the fitting
procedure could yield an erroneous result. This is
because the waveshape does not change below a limiting
value of k0, but is shifted to higher potentials (for
oxidation) which will lead to overestimated values of Ef0.
Fig. 5(a) illustrates these two limiting cases. In order to
show the change in the gradients, the waves have been
shifted to coincide at the foot of the wave. Therefore the
abscissa has not been labelled with numerical values, as
these may be different for each voltammogram.
In order to determine the upper and lower measurable
limits of k0, we differentiated the voltammograms for
the range of k0. For each one the highest gradient was
used, corresponding to the point of inflexion of the
rising part of the wave (as shown in Fig. 5(b), where the
abscissa is as in Fig. 5(a)). Next, the difference between
the maximum gradients of reversible and irreversible
limits was measured and the experimental tolerance was
assumed to be 7.5% of this gradient range. Voltammo-
grams were simulated to obtain the minimum and
maximum measurable values of k0, having gradients
7.5% higher than the irreversible limit, and 7.5% less
than the reversible limit respectively. It was found that
the two limits were dependent on the scan rate, and so it
was necessary to find these limits for a range of scan
rates. To do this, we investigated the general current�/
voltage response to the normalised scan rate s and the
normalised heterogeneous rate constant Khet [19], given
by
s�1:546Fv
RTD�1=3 r3
T
Vf
�zT
rT
�0:108
n1=3 (11)
and
Khet�1:602k0D�2=3
�r3
T
Vf
�1=2�zT
rT
�0:054
n1=6 (12)
By considering the variation in voltammetry with
respect to these normalised parameters, a general result
can be obtained independent of the experimental
geometry, solvent viscosity and flow rate. Using theprocedure described above, the upper and lower limits
of Khet were found for a range of s and plotted in Fig. 6.
The lower curve was then fitted with a function, which
gave the following empirical relationship for it
f (s)�0:1559 ln[1�expf3:151(log10 s�0:3643)g]
�0:7721 (13)
For all values of s , it was found that the separation ofthe upper and lower curves was approximately 1.8,
which lead to the following bounds for Khet:
f (s)5 log10 Khet5 f (s)�1:8 (14)
This result is valid for any experimental parameters
which fit in the range of s investigated.
4.2. Steady-state voltammetry of TMPD at the high-
speed channel electrode
We first consider the use of the high-speed channel
electrode to obtain steady-state voltammograms in
Fig. 5. (a) Simulated voltammograms simulated for a range of k0
values, (b) Differential plot of (a), with a�/0.5, D�/10�6 cm2 s�1, v�/
3000 V s�1 and Vf�/0.01 cm3 s�1. Fig. 6. Upper and lower measurable limits of Khet as a function of s .
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107 103
order to measure the heterogeneous rate constant for the
first oxidation wave of TMPD in PC.
A solution containing 6.5 mM TMPD and 0.1 M
TBAP in PC was introduced into the pressure chamberof the apparatus and an initial pressure set. A linear
sweep voltammogram was then recorded at a scan rate
of 0.32 V s�1, which yielded a steady-state response [25]
enabling a limiting current to be measured for the first
oxidation wave. This was repeated at a range of
chamber pressures from 10 to 150 kPa to obtain a
range of volume flow rates (from 0.03 to 1.85 cm3 s�1).
Fig. 7 shows a plot of measured limiting currents againstVf
1/3 according to the Levich equation for channel
electrodes [26]:
ILim�0:925nFw[A]bulk(xeD)2=3(h2d)�1=3V1=3
f (15)
where n , F , D , and [A]bulk have their usual meaning, Vf
is the volume flow rate, and the other terms represent
the geometry of the channel cell and electrode as shown
in Fig. 4. The gradient of this plot can be used to obtain
a value for the diffusion coefficient of TMPD by
application of Eq. (15) as (3.19/0.1)�/10�6 cm2 s�1.Next, the current responses for each voltammogram
were normalized by division by the respective limiting
current and plotted against potential to produce a
‘normalized voltammogram’. These data were then
input into the computer program described previously
for the analysis of steady-state voltammetry [15], and
optimum values of k0, Ef0 and a were obtained
simultaneously. For convenience we display these dataas two separate three-dimensional contour plots. Fig. 8
shows the surface generated by the program as k0 and a
vary independently, and Fig. 9 shows the analogous
surface for the variation of k0 and Ef0. By repeating this
analysis for each data point, we arrive at a value for k0
of (6.39/0.4)�/10�2 cm s�1, a�/0.529/0.01 and Ef0�/
0.2349/0.005 V vs. Ag (quoted as mean9/S.D.). This
compares with a literature value of k0 which has beenreported to be 1.5�/10�2 cm s�1 at 293 K [16].
4.3. Steady-state voltammetry at the HWTE
We next consider the use of the HWTE to obtain
steady-state voltammograms in order to measure diffu-
sion coefficient of TMPD in PC.
A solution containing 6.5 mM TMPD and 0.1 M
TBAP in PC was introduced into the pressure chamber
of the apparatus and an initial pressure set. A linear
sweep voltammogram was then recorded at a scan rate
of 0.5 V s�1, which yielded a steady-state response [25]
enabling a limiting current to be measured for the first
oxidation wave. This was repeated at a range of
chamber pressures to obtain a range of volume flow
rates (from 0.003 to 0.12 cm3 s�1). Fig. 10 shows a plot
of measured limiting currents against Vf1/2 according to
the equation for wall-tube cells [4,18]:Fig. 7. Plot of Ilim vs. Vf
1/3 for 6.5 mM TMPD/0.10 M TBAP in PC
(R2�/0.999).
Fig. 8. Contour plot showing variation in MSAD with k0 and a for
TMPD measured at Vf�/1.75 cm3 s�1, showing a minimum at k0�/
0.063 cm s�1 and a�/0.51.
Fig. 9. Contour plot showing variation in MSAD with k0 and Ef0 for
TMPD measured at Vf�/1.75 cm3 s�1, showing a minimum at k0�/
0.063 cm s�1 and Ef0�/0.236 V (vs. Ag).
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107104
Ilim�0:6244nFp[A]bulkD2=3r21n
�1=6
�Vf
r3T
�1=2�rT
zT
�0:054
(16)
where n , F , D , and [A]bulk have their usual meaning, Vf
is the volume flow rate, n is the solvent kinematic
viscosity, and the other terms represent the geometry of
the channel cell and electrode as shown in Fig. 2. The
diffusion coefficient calculated from the gradient of Fig.
10 using Eq. (16) was found to be 3.1�/10�6 cm2 s�1, in
excellent agreement with that measured above with thechannel electrode.
4.4. Fast linear sweep voltammetry at the HWTE
A solution of 2.86 mM TMPD and 0.10 M TBAP in
PC was placed into the pressure chamber of the
apparatus and the pressure set and capillary selected in
order to achieve the required solution flow rate. A linear
sweep voltammogram was then measured at this flowrate at a scan rate of 200 V s�1 and a transient response
was obtained. Further linear sweep voltammograms
were then recorded over a range of scan rates from
200 to 7000 V s�1 whilst the solution was flowing at
volume flow rates ranging from 0.003 to 0.12 cm3 s�1.
Each recorded voltammogram was averaged a minimum
of 16 times, and negative potentials applied between
scans as a precaution to inhibit electrode passivation. Atno time was any experimental evidence of electrode
passivation or fouling observed.
Next, the voltammograms were amended by the
subtraction of capacitative currents [26], which was
achieved by subtracting the best-fit (least squares) line
through the non-faradaic signal, since the scan was of
sufficient width to enable the non-faradaic response to
become established before the faradaic signal com-menced. A combination of the use of a potentiostat
capable of on-line correction for ohmic drop, and the
low current generated by a microelectrode within the
HWTE made adjustment for ohmic distortion unneces-
sary [27].
The current vs. potential data for the voltammogram
was then input into the computer program describedabove, and optimum values of k0, a , and Ef
0 were
obtained simultaneously by the least squares method.
The simulations were made using parameters set accord-
ing to the experimental geometry, and the flow rate
used. The value used for the diffusion coefficient was
3.1�/10�6 cm2 s�1 as reported above. For convenience
we display this data as two separate contour plots. Fig.
11 shows the surface generated by the program as k0 andEf
0 vary independently, and clearly illustrates the sensi-
tivity of MSAD to the value of Ef0. Fig. 12 shows the
analogous surface for the variation of k0 and a . This
was repeated for over 15 separate voltammograms
corresponding to different scan rates and volume flow
rates. The results obtained were as follows: k0�/(5.99/
2.4)�/10�2 cm s�1, a�/0.469/0.08, and Ef0�/0.2179/
0.019 V (vs. Ag).In all cases these best-fit parameters were used to
simulate a theoretical voltammogram and this was
compared to the experimental result. Fig. 13 shows a
selection of such plots, showing the excellent agreement
observed in all cases.
5. Conclusion
The results obtained for k0 and a using fast-scan
linear sweep voltammetry in the HWTE have been
shown to be in agreement with those measured using
the high-speed channel electrode to record steady-state
voltammetry.
The HWTE has been shown to be an effective method
of measuring a heterogeneous rate constant for TMPD
in PC of k0�/(5.99/2.4)�/10�2 cm s�1. Simulationsindicate that the HWTE may be capable of measuring
Fig. 10. Plot of Ilim vs. Vf1/2 for 6.5 mM TMPD/0.10 M TBAP in PC
(R2�/0.988).
Fig. 11. Contour plot showing variation in MSAD with k0 and Ef0 for
TMPD measured at v�/1920 V s�1 and Vf�/0.065 cm3 s�1, showing a
minimum at k0�/0.051 cm s�1 and Ef0�/0.207 V (vs. Ag).
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107 105
electron transfer rates up to 5 cm s�1. In this regard, it
compares with the high-speed channel electrode,
although the latter has already been used to measure
rates in excess of 3 cm s�1 [29], and is predicted to be
able to reach rates of approximately 10 cm s�1 [15,28].
In terms of practical use, however, the channel
electrode is preferred. First, the hydrodynamics of
channel electrodes have been studied for some years
and are well understood, whereas a comprehensive
model has only recently been proposed for the WTE
and this indicated the existence of unexpected vortices
within improperly designed cell chambers [11�/13].
Second, the impact of the jet on the electrode surface
causes efficient outgassing of the solution forming many
tiny bubbles and possibly compromising the hydrody-
namics causing noise on the voltammograms. Finally,
the assembly and operation of the HWTE is not as
straightforward as with a channel electrode. Alignment
of the jet with the electrode is difficult, and the intra-
chamber pressures caused by the jet places high
demands on the chamber seals. The need for tight seals
also means that the microdisk electrodes cannot be
routinely replaced in the Kel-F blocks making up the
HWTE cell, as each Kel-F plug needs to be machined to
a precise fit with the electrode. This contrasts with the
channel electrode, where a seal is maintained by a
silicone gasket, which allows facile interchange of
electrodes with the flowcell [14]. The channel electrode
is therefore recommended over the HWTE for fast
kinetic measurements for ease of use.
Last we note that the work reported in this article has
utilised the viscous (2.53 cp at 298 K) solvent PC; less
viscous solvents, notably water and especially acetoni-
trile may lead to Reynolds numbers sufficiently large
that the laminar/turbulent threshold may be approached
or exceeded. We return to this, and related hydrody-
namic issues, in a subsequent article.
Fig. 12. Contour plot showing variation in MSAD with k0 and a for
TMPD measured at v�/1920 V s�1 and Vf�/0.065 cm3 s�1, showing a
minimum at k0�/0.051 cm s�1 and a�/0.41.
Fig. 13. Comparison of experimental (*/) and theoretical (k) current�/voltage curves, based on the best-fit parameters obtained, for a selection of
typical voltammograms recorded for a solution of 2.86 mM TMPD/0.10 M TBAP in PC. v�/240 V s�1, Vf�/0.003 cm3 s�1, v�/480 V s�1, Vf�/
0.012 cm3 s�1; v�/1920 V s�1, Vf�/0.065 cm3 s�1, and v�/2880 V s�1, Vf�/0.030 cm3 s�1.
N.V. Rees et al. / Journal of Electroanalytical Chemistry 557 (2003) 99�/107106
Acknowledgements
We appreciate the generosity of Professor C. Amatore
in making available to us the designs for the fast-scanpotentiostat apparatus developed in their laboratory.
We thank EPSRC for a studentship for NVR and the
Clarendon Fund of Oxford University for partial
funding for OVK.
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