Direct rotating ring-disk measurement of the sodium borohydride diffusion coefficient in sodium hydroxide solutions

Article abstract of DOI:10.1016/j.electacta.2009.03.019

This paper presents the experimental determination of the diffusion coefficient of borohydride anion and solution kinematic viscosity for a large panel of NaOH + NaBH₄ electrolytic solutions relevant for use as anolyte in Direct Borohydride Fue

Full text of DOI:10.1016/j.electacta.2009.03.019

Electrochimica Acta 54 (2009) 4426–4435
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Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Direct rotating ring-disk measurement of the sodium borohydride diffusion
coefficient in sodium hydroxide solutions
M. Chateneta,∗, M.B. Molina-Conchaa, N. El-Kissib, G. Parroura, J.-P. Diarda
a Laboratoire d’Electrochimie et de Physico-chimie des Matériaux et des Interfaces, LEPMI, UMR 5631 CNRS/Grenoble-INP/UJF, 1130 rue de la piscine, BP75,
38402 Saint Martin d’Hères Cedex, France
b Laboratoire de Rhéologie, UMR 5520 CNRS/Grenoble-INP/UJF, 1301 rue de la piscine, 38041 Grenoble Cedex 9, France
a r t i c l e i n f o
a b s t r a c t
Article history:
This paper presents the experimental determination of the diffusion coefficient of borohydride anion and
solution kinematic viscosity for a large panel of NaOH + NaBH4 electrolytic solutions relevant for use as
anolyte in Direct Borohydride Fuel Cells (DBFC). The diffusion coefficients have been measured by the
transit-time technique on gold rotating ring-disk electrodes, and verified using other classical techniques
reported in the literature, namely the Levich method and Electrochemical Impedance Spectroscopy on a
gold RDE, or chronoamperometry at a gold microdisk. The agreement between these methods is gener-
ally good. The diffusion coefficients measured from the RRDE technique are however ca. twice larger than
those previously reported in the literature (e.g. ca. 3 × 10−5 cm2 s−1 in 1 M NaOH + 0.01 M NaBH4 at 25 ◦C in
the present study vs. ca. 1.6 × 10−5 cm2 s−1 in 1 M NaOH + 0.02 M NaBH4 at 30 ◦C in the literature, as mea-
sured by chronoamperometry at a gold microsphere), which is thoroughly discussed. Our measurements
using chronoamperometry at a gold microdisk showed that such technique can yield diffusion coefficient
values below what expected. The origin of such finding is explained in the frame of the formation of both
a film of boron-oxide(s) at the surface of the (static) gold microdisk and the generation of H2 bubbles at
the electrode surface (as a result of the heterogeneous hydrolysis at Au), which alter the access to the elec-
trode surface and thus prevents efficient measurements. Such film formation and H2 bubbles generation
is not so much of an issue for rotating electrodes thanks to the convection of electrolyte which sweeps
the electrode surface. In addition, should such film be present, the transit-time determination technique
on a RRDE displays the advantage of not being very sensible to its presence: the parameter measured is
the time taken by a perturbation generated the disk to reach the ring trough a distance several orders of
magnitude bigger than the film thickness, thus minimizing its effect.
Received 29 November 2008
Received in revised form 2 March 2009
Accepted 7 March 2009
Available online 20 March 2009
Keywords:
Direct Borohydride Fuel Cell
Borohydride diffusion coefficient
Rotating ring-disk electrode
Sodium hydroxide
Kinematic viscosity
© 2009 Elsevier Ltd. All rights reserved.
1. Introduction
ing current density, ilim, obtained on a rotating disk electrode (RDE),
the electroactive species concentration, C, and diffusion coefficient,
Starting with the pioneering work of Amendola et al. [1–4], sev-
eral research groups focused on DBFC research and development
[5–11]. However, most of the aforementioned studies deal with the
DBFC testing, and very few focus on the basics of the borohydride
oxidation reaction (BOR). Among the important parameters to be
known to evaluate efficient BOR electrocatalyst, is the number of
electrons n involved in the reaction. In theory, n = 8 (see Eq. (1)),
itself yielding the faradic efficiency of the conversion.
D, the solution kinematic viscosity, ꢀ and the revolution rate of the
RDE, ˝.
1/2
ilim = 0.620 nFD2/3Cꢀ−1/6
˝
(2)
One drawback of this simple technique is that it implicitly
requires that C, D and ꢀ are known for the studied electrolyte
solution. Unfortunately, only C is a priori known with preci-
sion. Although it is possible to stabilize the NaBH4 solutions for
pH beyond 12 [12], practical biases may perturb this theoretical
assertion, since NaBH4 spontaneously hydrolyses on a variety of
materials, e.g. Pt [6,13–15] and Ni [16]. From this prospect, using a
counter electrode/current collector made of any material yielding
to heterogeneous hydrolysis to perform measurements of the boro-
hydride oxidation reaction does not appear wise. However, such
choice is sometimes found in the literature, e.g. with a cell con-
taining a Pt counter-electrode [17,18] or Ni current collector [19].
−
BH4− + 8 OH− → BO2 + 6H2O + 8e− (E0=1.24 V vs. NHE)
(1)
n may be determined using the well-known Levich equation (Eq.
(2)). It gives a relationship between the diffusion-convection limit-
∗
Corresponding author. Tel.: +33 476 826 588; fax: +33 476 826 777.
E-mail address: Marian.Chatenet@phelma.grenoble-inp.fr (M. Chatenet).
0013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2009.03.019

M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
4427
Fig. 1. Cyclic voltammetry at the gold disk of the RRDE in (A) supporting electrolyte (1 M NaOH at 25 ◦C) for ˝ = 0 and in (B) 0.1 M NaOH + 10−3 M NaBH4 at 25 ◦C for several
revolution rates (˝) of the RDE. Geometric surface = 0.124 cm2.
Studies dealing with the mass-transport parameters evaluation of
the potential anolyte solutions (usually NaBH4–NaOH) are scarce
[20]. Only a few papers focus on the tetrahydroborate anion dif-
fusion coefficient determination [14,17,21,22], while the solutions
viscosity is hardly ever measured. Despite their interest, the studies
mentioned above seem insufficient because they do not inves-
tigate a wide range of solution composition and/or temperature
(apart from reference [17]). They also provide a large uncertainty
for the diffusion coefficient values (ca. between 0.66 × 10−5 cm2 s−1
and 10−4 cm2 s−1 according to the experimental conditions inves-
tigated). They nevertheless reveal a strong effect of both the
working electrode was a rotating ring-disk RRDE Pt-Pt (Tacussel
EAD Pt/Pt + analogic monitor Asservitex 4000®) baring a thin Au
deposit on both the disk and ring. The Au deposit was made in
potentiostatic conditions, using a phosphate buffer solution (pH
7.5) of KAu(CN)2 (10 gAu L
−1, Pelidag®) at 50 ◦C. A first deposit
was made for 900 s at −0.560 V vs. NHE, completed for 150 s at
−0.510 V vs. NHE so as to obtain a smooth and dense deposit. The
deposit thickness is between 0.5 and 0.6 ␮m, both for the ring
and disk, which should (i) be sufficiently thick to yield complete
coverage of the Pt substrate and (ii) sufficiently thin to prevent any
hydrodynamic bias when the RRDE is in rotation (see Section 3.2).
Fig. 1 indeed reveals that the deposit is completely covering the Pt
surface of both the disk and ring electrodes.
The revolution rate of the RRDE was calibrated using a numerical
oscilloscope at 399 rpm 1% per loop of the potentiometer (com-
pared to 400 rpm per loop according to Tacussel). The cell was
connected to a numeric potentiostat (Bio-Logic VMP2Z®) in the
Bistat configuration and controlled via the EC-Lab® (version 9.32)
software.
In order to double-check our diffusivity measurements, we used
a PINE AFE7R8AuAu RRDE tip connected to a MSR Electrode Rotator.
The results obtained with this apparel fall within the error bars of
those monitored with the gold-coated Pt-Pt RRDE from Tacussel.
We also used a gold microdisk (UltraMicroElectrode, UME) and
a 2 mm-diameter gold RDE tip for additional chronoamperome-
try and Electrochemical Impedance Spectroscopy or hydrodynamic
cyclic voltammetry measurements, respectively. The diameter of
the gold UME (AuME60, Radiometer Analytical) was checked by
optical microscopy to be 62 1 ␮m.
temperature and ionic strength of the solution on DBH − values [17].
4
From this short literature review, it appears wise to complete
the knowledge about the influence of the solution composition
and temperature on the borohydride mass-transport parameters
in sodium hydroxide solutions. In that frame, the present paper
describes on the one hand the experimental determination of the
kinematic viscosities for electrolyte solutions relevant to DBFC
and BOR studies. On the other hand we measured the tetrahy-
droborate diffusion coefficient using a direct rotating ring-disk
electrode (RRDE) technique, which requires neither the knowledge
of the number of electrons, nor of the concentration in borohy-
dride species: only the solution kinematic viscosity and geometric
parameters of the RRDE are necessary. We will compare this tech-
nique of measurement with others widely used in the literature,
and will show why we think it is the best suited for the particular
case of the tetrahydroborate anion.
2. Experimental
For each series of measurements, the cell was regulated at 10, 25
or 40 1 ◦C and permanently maintained under argon atmosphere
(Messer 4N5) to eliminate traces of dissolved oxygen. Prior to each
experiment, the cell and working electrodes were cleaned in con-
centrated H2SO4–H2O2 mixture and then rinsed thoroughly with
ultrapure water.
2.1. Apparatus and solutions
The electrolytic solutions (0.1 to 4 M NaOH + 10−3 to 1 M NaBH4)
were prepared using high purity sodium hydroxide (Prolabo,
Normapur®) and sodium borohydride salts (Merck Suprapur®)
dissolved in ultrapure water (18.2 Mꢁ cm − 3 ppb COT, Millipore
Elix + Gradient). In order to prevent any borohydride hydrolysis
upon preparation of the solutions, they were always prepared by
dissolving the appropriate amount of NaBH4 salt into an already
prepared NaOH solution at the relevant concentration.
The electrochemical measurements were attempted in
double compartment electrochemical cell made of Pyrex® glass.
The counter-electrode was gold plate, separated from the
working/reference electrode compartment, so as to prevent any
hindrance from the (usually hydrogen) bubbles generation at
the counter electrode (usually, the cathode when BOR proceeds
at the working electrode). An Hg–HgO (1 M NaOH) reference
electrode was used, but all the potentials are expressed on the
Normal Hydrogen Electrode (NHE) scale. In most experiments, the
2.2. Viscosity measurements
The kinematic viscosity of each sodium hydroxide + sodium
borohydride electrolyte solution was measured on a Ubbelohde
micro-viscosimeter (Schott-Gerräte GmbH) baring a capillary tube
(538.10, Schott) at 16, 25 and 40 ◦C. The system does not enable
operation below 16 ◦C for viscous solutions like concentrated
sodium hydroxide. However, the kinematic viscosity values at 10 ◦C
were extrapolated from an exponential fit of the experimental
data obtained at 16, 25 and 40 ◦C. The viscosity measurement
consists of the determination of the time for a solution to flow
through the capillary tube. As the system only stabilizes after
several repetitions of solution flow into the capillary tube, each
a
a

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M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
Table 1
Kinematic viscosities measured for the various sodium hydroxide + sodium borohydride solutions. Each value noted * was extrapolated at 10 ◦C or interpolated at 20 ◦C from
the exponential fit based on the experimental values measured at 16, 25 and 40 ◦C for the considered electrolyte solution. The values noted # were calculated from reference
[34]. The values noted @ were calculated for T = 20 ◦C from reference [35].
[NaOH], M
[BH4−], M
ꢀ, cm2 s−1
10 ◦
C
16 ◦
C
20 ◦
C
25 ◦
C
40 ◦
C
10−1
–
0.0157 *
0.0134 #
0.0146 *
0.0155 *
0.0149 *
0.0168 *
0.0156 #
0.0166 *
0.0171 *
0.0183 *
0.025 *
0.0132 0.0004
0.0114 #
0.0118*
0.0104 0.0003
0.0090 #
0.0075 0.0002
0.0066 #
0.0096 @
10−1
10−1
10−1
1
10−3
10−2
10−1
–
0.0125 0.0001
0.0123 0.0001
0.0126 0.0006
0.014 0.001
–
0.014 0.004
0.0147 0.0005
0.016 0.002
0.022 0.009
0.0101 0.0001
0.0102 0.0001
0.010 0.007
0.0118 0.0007
0.0110 #
0.0114 0.0001
0.0131 0.0004
0.0128 0.0006
0.018 0.001
0.0224 #
0.0075 0.0001
0.0075 0.0005
0.0075 0.0002
0.009 0.004
0.0081 #
0.0084 0.0001
0.0088 0.0004
0.0094 0.0009
0.013 0.001
0.0154 #
0.0130 *
0.0121 @
1
1
1
4
10−2
10−1
1
–
0.0200 *
0.0219 @
0.0326 #
0.0391 *
4
1
0.032 0.003
0.024 0.002
0.017 0.002
measurement was reproduced about 15 times overall: for each
electrolytic solution, the experimental kinematic viscosity values
displayed in Table 1 is the average of the last four/five successive
measurements of the flow time, and the Hagenbach-Couette
kinetic energy correction was taken into account. The uncertainty
in the flow time measurement is estimated to be 0.01 s. This little
value leads to a relative standard uncertainty of less than 0.01%
in the viscosity measurement and can therefore be neglected. The
experimental reproducibility of the flow rate at each temperature
and composition was between 0.01 and 0.5%.
2.3.2. Verification of the DBH − measurements using the Levich
criteria, Electrochemical Impedance Spectroscopy, or
chronoamperometry at UME
4
For each experiment, the tetrahydroborate diffusion coefficient
determined directly using the RRDE technique was compared to
values determined using several classical methods.
The first is based on the Levich criteria (Eq. (2)). For that purpose,
hydrodynamic linear sweep voltammetries were plotted for an Au
RDE at several revolutions rates, as detailed in reference [28]. From
the slope of the (ilim vs. ˝1/2) plots, we calculated the “unknown
parameter”. The calculation was made in a circular way so as to
determine n, assuming DBH − and [NaBH4] are known with pre-
4
cision (the former from RRDE, the latter assuming the hydrolysis
and borohydride depletion was small in the course of the experi-
2.3. Electrochemical measurements
ment) or DBH − assuming n = 8 on gold, which is generally admitted
[21,29,30]. We will discuss such assertion below.
2.3.1. Determination of the “transit-time” using the RRDE
4
The direct rotating ring-disk electrode technique consists of
measuring the so-called “transit-time” for a perturbation applied
at the disk to reach the ring of the RRDE. For that purpose, a
potential step is first applied on the ring from the open-circuit
potential to a potential where the electroactive species is con-
sumed entirely at the ring|solution interface. For example, this
consists of reducing Fe(CN)63− or oxidizing BH4− at the correspond-
ing diffusion-convection plateau of a hydrodynamic CV (Fig. 2A).
Then, after the ring current has reached its steady-state value in
the considered conditions (which is attained within a few seconds),
the same potential step is applied at the disk. The induced lack of
electroactive species created at the disk, reaches the ring after a so-
called transit-time, ts (s), related to the electrode rotational speed,
˝ (rpm), the diffusivity of the electroactive species, D (cm2 s−1) and
the solution kinematic viscosity, ꢀ (cm2 s−1), by Eq. (3) [23–27]:
Electrochemical Impedance Spectroscopy was also used to
determine DBH − . For that purpose, we used the frequency at the
4
apex of the low-frequency loop1 of the Nyquist diagrams to deter-
mine the borohydride anions diffusion coefficient, thanks to Eq. (5)
[31,32]:
fc = 0.102Sc−1/3(1.22 + 2 × 10−5Sc)˝
(5)
where Sc = ꢀ/D is the Schmidt number. We point out that this
method neither requires the knowledge of [NaBH4] nor n, as
described in reference [33].
Finally, additional Cottrell-like chronoamperometry measure-
ments have been performed on a 62 ␮m diameter gold UME using
the technique developed by Denuault et al. [21] for a gold microdisk
andlateroptimizedby Wangetal. fora goldmicrosphere[17]. Inthis
technique, the current monitored upon a potential step (of NaBH4
oxidation for example) is composed of a steady-state component
and a transient one (see Eq. (1) in [17]). The diffusion coefficient of
the reacting species can presumably be extracted directly from Eq.
(6):
ꢀ ꢁ
1/3
ꢀ
−1
ts = K
˝
(3)
D
K only depends on the electrode dimensions. For an ideal RRDE,
with absolutely concentric ring and disk electrodes and perfectly
smooth surface, K (s rpm) is given by Eq. (4) [27]:
r2A2
D =
S2
(6)
ꢂ
where r is the radius of the gold UME (respectively micro-
sphere) and A and S the intercept and slope of the Cottrell line
respectively.
The great advantage of the technique (a detailed description of
which can be found in references [17,21]) is that it does neither
ꢀ
ꢂ
ꢃꢁ
2/3
r2
r1
K = 43.1 log
(4)
where r1 and r2 are respectively the inner radius of the ring and
(outer) radius of the disk. K is worth 5.174 and 4.674 for the Tacussel
and PINE RRDE tips, respectively. The (ts vs. K˝−1) plot results in
a straight line crossing the origin, the slope of which allows the
diffusion coefficient determination (Fig. 2B).
1
The low-frequency loop is mainly related to the mass-transport (diffusion-
convection in the present case) of the tetrahydroborate species.

M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
4429
Fig. 2. (A) example of determination of the transit-time ts for ˝ = 400 rpm and (B) (ts vs. K˝−1) plot enabling Fe(CN)6
diffusion coefficient determination in 0.1 M
3−
KNO3 + 10−2 M K3Fe(CN)6 solution at 25 ◦C.
require the knowledge of the concentration of the reacting species
(C), nor that of the viscosity of the solution (ꢀ).
2500 rpm), slightly below the theoretical value Nth = 0.229 (cal-
culated on the basis of the real dimensions of the RRDE [36]:
r1 = rdisk = 1.99 mm, r2 = rin-ring = 2.19 mm, r3 = rout-ring = 2.39 mm, as
measured from optical microscopy). Such slight (ca. 12%) devia-
tion is classical for RRDE [18], especially upon the presence of a
thin film (here the Au deposit) at its surface [37]; it attests that the
gold deposit is sufficiently thin not to perturb the rotating ring-disk
measurements. Finally, the conjunction of this observation and the
previous one reveals that the Tacussel RRDE can be considered as a
quasi-perfect Au–Au RRDE.
3. Results
3.1. Measurement of the viscosity for the (NaOH + NaBH4)
solutions
Table 1 displays the experimental (at 16, 25 and 40 ◦C) and cal-
culated (10 and 20 ◦C) values of the kinematic viscosities for the
investigated solutions. A quick sight at Table 1 reveals that the pres-
ence of sodium borohydride generally increases the viscosity of the
sodium hydroxide solution; one exception is the 1 M NaOH + 1 mM
NaBH4 solution, but the very small difference falls within the accu-
racy of the measurements. When the ratio [NaOH]/[NaBH4] is below
10, the presence of sodium borohydride non-negligibly increases
the kinematic viscosity of the solution. On the contrary, the impact
of borohydride remains very small when [NaOH]/[NaBH4] > 10,
experimental condition which is widely adopted in the litera-
ture. Therefore, in the following sections, we will assume that
the kinematic viscosities for the 1 M NaOH + 10−3 M NaBH4, 4 M
NaOH + 10−3 M NaBH4 and 4 M NaOH + 10−2 M NaBH4 electrolyte
solutions can be chosen equal to those for the 1 M NaOH and 4 M
NaOH solutions respectively (at the relevant temperatures).
We also point out that the kinematic viscosity values we mea-
sured for the supporting electrolyte solutions fall reasonably close
to those calculated from literature [34,35], which validates our mea-
surements.
3.3. Calibration of the RRDE technique
The method of direct determination of the diffusion coeffi-
cient by the RRDE technique was first attempted for a 10−2 M
K3Fe(CN)6 + 10−1 M KNO3 solution at 25 ◦C. Fig. 2A presents an
example of transit-time (ts) measurement; ts, the origin of which
is taken at t = 5 s (the time at which the disk is brought to cathodic
potential), is measured graphically from the intercept of the base
steady ring current and the fast attenuate ring current line. Such
ts determination is then repeated for 6 different revolution rates
of the RRDE, each sequence of 6 revolution rates being repeated
3 times so as to yield an average ts value for each revolution rate.
3−
Then, one can determine the diffusion coefficient of the Fe(CN)6
species in the solution from the slopes of the well-defined (ts vs.
K˝−1) lines (Fig. 2B). Based on 3 replicate experiments, we find
in average: DFe(CN)
= 7.8 × 10−6 8 × 10−7 cm2 s−1. This value
3−
6
reasonably agrees with the admitted value in pure water diluted
(8.96 × 10−6 cm2 s−1 at 25 ◦C [35]), which validates the method.
The slight difference can originate from the viscosity differences
between pure water and 0.1 M KNO3.
3.2. Characterization of the Au–Au RRDE
The electrochemical response of the Tacussel Au–Au RRDE was
checked both in supporting and borohydride-containing sodium
hydroxide solutions. In supporting electrolyte, the shape of the CV
obtained on the Au disk is classical for gold (Fig. 1A). In particular,
no evidence of hydrogen adsorption/desorption on Pt is monitored
on Fig. 1A. It corresponds to that obtained on the PINE Au–Au RRDE
tip, the Au RDE tip and the gold UME (not shown for brevity). The
same statement can be made from the hydrodynamic CV of Fig. 1B,
relative to sodium borohydride oxidation on the disk electrode of
the Tacussel Au–Au RRDE [18,28,33] in diluted sodium hydroxide:
the onset of the BOR is ca. −0.5 V vs. NHE, far above −0.8 V vs. NHE,
which should be the BOR onset for a Pt electrode (Fig. 1B). Therefore,
from Fig. 1, we can attest that the gold deposit onto the platinum
ring and disk of the Tacussel RRDE is completely covering the Pt
surfaces.
An error analysis of the measurement, based on the calculations
developed in references [23,26] can be obtained from Eq. (7):
ꢃD
D
3ꢃK
K
ꢃꢀ
ꢀ
3ꢃ˝
˝
3ꢃts
ts
=
+
+
+
(7)
Assuming
ꢃK/K = 0.5%,
ꢃꢀ/ꢀ = 0.5%,
ꢃ˝/˝ = 1%,
ꢃts/ts = 5%, the diffusion coefficient error ꢃD/D reaches 20%,
which is reasonable (uncertainties of ca. 20% are for example
admitted for diffusion coefficients measured in pure water [38]).
Such error also matches the experimental reproducibility of our
measurements (see Table 2).
3.4. RRDE measurements of the diffusion coefficient of the
tetrahydroborate anion in sodium hydroxide solutions
The collection efficiency (N) of the Tacussel Au–Au RRDE
was first measured in a 10−2 M K3Fe(CN)6 + 10−1 M KNO3 solu-
tion (not shown for brevity). We found a value of Nexp = 0.202
(averaged from experiments performed at 400, 900, 1600 and
The transit-time determination technique was used for 0.1, 1
and 4 M sodium hydroxide solutions containing 10−3, 10−2, 10−1
and 1 M of sodium borohydride. However, only the measurements
performed with 10−3 and 10−2 M NaBH4 proved successful. Indeed,

4430
M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
Fig. 3. (A) example current transient measured at the ring of the Tacussel Au–Au RRDE during the oxidation of tetrahydroborate anion at 40 ◦C and (B) corresponding (ts vs.
K˝−1) plots.
4 M NaOH + 10−2 M NaBH4 solution at 40 ◦C, the overall average is
DBH − = 2.24 × 10−5 6 × 10−7 cm2 s−1, in perfect agreement with
the 4value extracted from Fig. 3B. It can however be noted that in
some cases (e.g. the data points at 10 ◦C on Fig. 3C) the measurement
dispersion is slightly higher, which can originate from the intrinsic
experimental “noise” of the borohydride oxidation reaction, already
noticed in reference [33].
transit-time measurements require that the ring and disk elec-
trodes of the RRDE are successively brought from ocp to the
potential region of mass-transport limited current (as for the
chronoamperometric and Levich techniques). Unfortunately, the
limiting plateau of the BOR cannot be reached above 10−2 M NaBH4
in solution, as for example shown in reference [39] and confirmed
in the present stu−dy. Therefore, we only investigated the diffusion
coefficient of BH4 in sodium hydroxide solutions containing 10−3
and 10−2 M NaBH4. In that frame, the experiments were achieved at
3 temperatures, 10, 25 and 40 ◦C, and repeated 3 times for increasing
or decreasing revolution rates between 400 and 2400 rpm (see the
Fig. 4A–C presents the variation of the DBH − values as a function
4
of the temperature for the various electrolyte compositions inves-
tigated in the present paper. For all compositions, the (DBH − vs. T)
4
plot roughly follows an exponential behavior.
example of Fig. 3A). Each replicate gives a DBH − value, as extracted
from the slope of the (ts vs. K˝−1) plot (Fig. 3B). An average value
These DBH − values can be used to build a Stokes–Einstein plot.
4
4
For that purpose, the dynamic viscosity ꢄ for each electrolyte solu-
tion investigated was recalculated from the kinematic viscosity
values of Table 1 and the absolute densities of the solution as
calculated using the results from reference [34]. The results from
of the diffusion coefficient was calculated from the 3 replicates: in
the case of Fig. 3B, it gives DBH − = 2.24 × 10−5 8 × 10−7 cm2 s−1
.
Such data points are then plot4ted on (DBH − vs. T) graphs (Fig. 4).
4
Fig. 4D show the (DBH − ꢄ/T vs. T) plot is approximately constant, as
Each of such experiment was reproduced at least 3 times for
all electrolyte solutions, yielding the average diffusion coefficient
values and uncertainties presented in Table 2. In the example of the
4
expected.
3.5. Measurement of DBH − by other relevant techniques
4
Table 2
3.5.1. Using the Levich criteria for limiting currents at a gold RDE
Tetrahydroborate diffusion coefficients determined in various electrolyte solutions
at various temperature using the transit-time RRDE technique. Each DBH − value is
We have plotted CV in hydrodynamic conditions for the BOR
4
averaged on the diffusion coefficient values obtained for least 3 different experi-
ments (performed 3 different days), each of these being themselves averaged on
on a gold RDE so as to evaluate DBH − value using Eq. (2). Such
4
measurements yield values close but generally inferior to those
obtained from the RRDE technique. For the particular case of Fig. 1,
assuming n = 8 one obtains from the limiting plateaus and the Levich
*
a set of 3 replicates (the same day). The values marked by were calculated at
20 ◦C from the exponential regressions of the plots (DBH − − T) plots obtained in
4
the corresponding electrolyte solutions (see the example of Fig. 3). n values were
formula (Eq. (2)), DBH − ≈ 2.9 × 10−5 cm2 s−1, in reasonable agree-
determined using the DBH − values determined from RRDE and the Levich equation
4
4
for the corresponding hydrodynamic CV in relevant experimental conditions.
ment with the corresponding value for 0.1 M NaOH + 1 mM NaBH4
at 25 ◦C (3.5 × 10−5 cm2 s−1, see Table 2). However, we noted that
the currents monitored at the limiting plateaus were non-negligibly
varying with the time of experiment, especially at low revolution
rate of the RDE (Fig. 5A). We point out that the kinetic region also
severely varies with the “history” of the electrode (number of cycles,
duration of the experiments, cleaning procedure, etc., as revealed
on Fig. 5A and B), but any discussion regarding such features is
beyond the point of the present paper. Let we also point out that
the impact of the electrode “history” is obviously very difficult to
monitor, hardly controlled and impossible to forecast, since the
boron-oxidation products film formation onto/expulsion from the
gold RRDE is a quite random phenomenon.
[NaOH], M
0.1
[BH4−], M
0.001
T, ◦
C
ꢀ, cm2 s−1
DBH − , 10−5 cm2 s−1
n
4
10
25
40
20
0.0146
0.0101
0.0075
2.78 0.29
3.50 0.35
4.49 0.67
3.15 *
5.1
5.3
4.8
1
1
4
4
0.001
0.01
10
25
40
20
0.0168
0.0118
0.009
2.26 0.41
2.59 0.68
3.71 0.53
2.30 *
5.8
6.6
6.1
10
25
40
20
0.0166
0.0114
0.0084
1.62 0.54
3.01 0.42
3.63 0.44
2.26 *
7.6
5.8
5.5
Therefore, given that in addition (i) the tetrahydroborate con-
centration value may decrease in the course of the experiment
(following borohydride hydrolysis more than consumption due to
the faradaic reaction) and (ii) n value is required for the calculation2,
0.001
0.01
10
25
40
20
0.025
0.018
0.013
1.41 0.29
1.73 0.19
2.31 0.23
1.64 *
5.3
6.0
6.0
10
25
40
20
0.025
0.018
0.013
0.74 0.33
1.28 0.22
2.21 0.057
1.03*
6.4
5.4
5.8
2
n is a priori an unknown parameter, but usually one chooses n = 8 for gold.
Such choice may be discussed, since some experimental findings tend to show that

M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
4431
Fig. 4. (DBH − vs. T) plot presenting the average DBH − values determined at 10, 25 and 40 ◦C for the various electrolyte compositions investigated; (A) 0.1 M NaOH, (B) 1 M
4
4
NaOH and (C) 4 M NaOH. (D) Stokes–Einstein plot showing the variation of DBH − ꢄ/T as a function of the solution temperature.
4
Fig. 5. (A) Hydrodynamic CV (vb = 5 mV s−1, ˝ = 2500 rpm; [NaBH4] = 10−3 M) for the BOR on gold RDE obtained right after immersion of the gold RDE in the solution following
electrode polishing and cleaning (black) or after several BOR cycles following the introduction of the RDE in the electrolyte solution (grey); (B) variation of the hydrodynamic
CV (vb = 5 mV s−1, ˝ = 1600 rpm; [NaBH4] = 10−3 M) for the BOR on gold RDE during 11 cycles; [NaOH] = 0.1 M, T = 20 ◦C.
DBH − determination from the Levich method might suffer high
inaccuracy.
film at the surface of the RDE, which render n measurements from
the Levich criteria less straightforward and easy than theoretically
expected. In addition, our latest experiments using on-line Mass
Spectrometry (MS) coupled to electrochemistry showed that n is
close but strictly inferior to 8 for BOR on gold, as revealed by the
non-negligible detection of H2 over the whole BOR potential range
[40]. This finding precisely goes in line with the conclusions from
Krishnan et al.: gold may not be a faradaic efficient BOR electro-
catalyst [18], but instead would generate some by-products like H2.
These MS measurements also pointed towards n variation with the
solution composition/temperature, in agreement with the values
from Table 2.
4
We also used the hydrodynamic CV to−calculate the number
of electrons supposedly exchanged per BH4 anion at the limiting
plateau. These n values were calculated using the diffusion coeffi-
cient determined from RRDE. The last column in Table 2 shows that
the n values are non-negligibly inferior to the expected 8 electrons
per BH4− anion. We also note high dispersion in the measurements
(4.8 < n < 7.6), in agreement with literature data: n values from ca.
4.5 [19] to 8 [17,39,41,42] are reported in the literature. Such disper-
sion probably originates from the intrinsic irreproducibility of ilim
measurement due to the possible existence of some boron-oxide
3.5.2. Using EIS at a gold RDE
−
gold also favors BH4 heterogeneous hydrolysis yielding H2 generation (see refer-
EIS experiments have been performed for the BOR on a gold
RDE in 0.1 M NaOH–10−3 M NaBH4 at 20 ◦C (Fig. 6). Using Eq. (5)
for the characteristic frequency of the low-frequency loop (related
to the mass-transport of the tetrahydroborate anion by diffusion-
ence [18]). As gold is inactive with respect to Hydrogen Oxidation Reaction, such
generated H2 is presumably “lost” by bubbles evolution (without generating elec-
trons at the electrode) and consequently, the BOR on gold can fundamentally not be
−
considered as a perfect 8-electron reaction per BH4 species (see also [40]).

4432
M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
Fig. 6. EIS spectra recorded during BOR on gold in 1 M NaOH + 1 mM NaBH4 at 20 ◦C at various potentials using the SPEIS procedure in EC-Lab® (˝ = 2500 rpm). Epp = 50 mV,
5 points per decade of frequency, frequency sweep from 200 kHz to 0.1 Hz. Graphs parametered in Hz.
convection), we obtain DBH − ≈ 2.8 × 10−5 cm2 s−1, as averaged for
electrode upon operation) by opposition to the (rotating) RDE and
RRDE. Fig. 7E obtained for a static RRDE indeed shows much larger
signal variation in that case, compared to the rotating RRDE.
4
4 revolution rates of the gold RDE. This value, the complete deter-
mination of which is described in reference [33], agrees with that
obtained from the RRDE technique in the same experimental condi-
tions (3.15 × 10−5 cm2 s−1, see Table 2). However, it is wise to point
out that the EIS determination of the borohydride diffusion coeffi-
cient is (i) not as straightforward as the RRDE measurement of the
transit-time and (ii) more subjected to experimental uncertainty
(the electrical “noise” monitored during BOR experiments renders
the EIS acquisition difficult, as detailed in reference[33]). This is par-
ticularly true for sodium borohydride concentrations above 1 mM.
4. Discussion
The diffusion coefficient values obtained by the RRDE transit-
time determination technique are usually close but superior to
those determined from the Levich criteria, EIS and chronoam-
perometry on a gold UME, at least when this latter technique
is achieved on a “pristine” gold UME (right after introduction in
the electrochemical cell, without any preceding BOR experiment).
However our DBH − values are consistently higher by ca. 50% than
most values prese4nted in the literature in corresponding electrolyte
solutions (Table 3). We point out that the more recent values (of
references [17,21]) were all obtained using the chronoamperomet-
ric method at gold UME (microdisk or microsphere), which may
undergo severe biases, as discussed below.
3.5.3. Using chronoamperometry and cyclic voltammetry at a
gold UME
The case of the chronoamperometry on a gold UME appears
more complex. While the application of Eq. (6) to the Cot-
trell line obtained right after immersion of the gold UME
in the solution (red trace labeled “initial” on Fig. 7A) gives
The error bars and experimental uncertainty of the RRDE tech-
nique, which is around 20% (see Sections 3.3 and 3.4), cannot
account for such differences. Let we point out that such error bar
DBH − = 2.85 × 10−5 cm2 s−1 in reasonable agreement with that
4
obtained from RRDE (3.01 × 10−5 cm2 s−1, see Table 2), we obtained
much weaker DBH − values after CV cycles between −1 V vs. NHE
4
and 0.3 V vs. NHE (DBH − = 1.31 × 10−5 cm2 s−1 after
1 cycle
at 5 mV s−1 and DBH − =40.93 × 10−5 cm2 s−1 after 20 cycles at
Table 3
Examples of DBH
−
values reported in the literature for sodium hydrox-
4
4
*
20 mV s−1) or after fixed polarization of the gold UME at the
ide + borohydride electrolytic solutions. The value noted with was recalculated
using n = 8.
limiting plateau (DBH − = 0.89 × 10−5 cm2 s−1 after 20 min 0.2 V
4
Reference [NaOH], M [NaBH4], M
T, ◦
C
DBH − , cm2 s−1 Method of
vs. NHE). Fig. 7B also shows that the current at the limiting plateau
dramatically decreases upon cycling the (fixed) gold UME from
ocp to the gold-oxide formation. Once again, it is beyond the point
of the present paper to discuss the modification of the kinetic
region of such voltammograms, even if it clearly shows that the
state of surface of the gold electrode unambiguously changed upon
potential cycling in this potential window. Such modification of
the (normally quasi-steady-state) signal was neither observed
so severely during hydrodynamic CV in rotating disk electrode
configuration (Figs. 1B, 5 and 7D) nor on Cottrell experiments
performed for a RRDE maintained in rotation during the “ageing”
potential cycles/hold (Fig. 7D). This may be related to the fact that
the gold UME is fixed (no electrolyte convection flux sweeps the
4
determination
[17]
0.5
0.02
30
1.88 × 10−5
Chrono-I on Au
␮-sphere
1
4
2
2
2
0.02
0.02
0.02
0.02
0.02
30
30
20
25
40
1.62 × 10−5
9.50 × 10−5
1.09 × 10−5
1.25 × 10−5
1.62 × 10−5
[21]
1
0.02
20
1.7 × 10−5
Chrono-I on Au
␮-disk
Polarography
Polarography
[14]
[22]
0.11
0.01
0.01
0.002
Not precised 25
Not precised 25
25
2.1 × 10−5
10−4
3 × 10−5*

M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
4433
Fig. 7. (A) Cottrell lines relative to a potential step from open circuit to 0.2 V vs. NHE for a “pristine” electrode (right after immersion in the solution) or electrodes after
various sequence of operation (the CV cycles were plotted from −1 V vs. NHE to 0.3 V vs. NHE) and (B) 1st, 2nd, 10th and 20th CV cycle for BOR applied on a gold UME (62 ␮m
diameter) in 1 M NaOH + 10 mM NaBH4 at 25 ◦C; all the CV were acquired at 20 mV s−1. (C) and (D), (E) correspond to (A) and (B) respectively for the Au disk of the Au–Au
RRDE.
and uncertainty are totally acceptable for kinetic values like dif-
fusion coefficients, as previously noted in literature [38], and in
particular for the case of oxygen [24–26]. Possible explanations to
account for the differences between our diffusion coefficient values
and those from the literature are discussed below.
unit time is greater as a result of the higher current. The effect
is even more severe when the electrode is repeatedly cycled up
to the gold-oxide formation region and static, as it is the case for
the gold UME (see Fig. 7B). It suggests that the diffusion of the
electroactive species to the electrode becomes hindered after oper-
ation in the potential range of the BOR. Such findings agree with
those from Atwan et al. [42], who monitored gold deactivation
upon potential hold in the region of the mass-transport limited
plateaus of the BOR. The gradual coverage of the electrode sur-
face by insoluble species upon BOR has also been reported by
Gervasio et al. [43], and is consistent with the ability of boron-
oxides to “polymerize” [44–46], as we recently detected from in
situ FTIR measurements3 during BOR on gold [47]. This is partic-
ularly the case for boric acid, which is known to polymerize in
First of all, our RDE, RRDE and UME results suggest that the
electrode surface may be altered in the course of the BOR exper-
iments. Chatenet et al. [28] and Liu et al. [19] both mentioned the
formation of an oxide “film” at the electrode surface upon BOR
on electrode materials prone to surface oxidation (respectively Ag
and Ni or Pd). In the present case of a gold working electrode
(presumably not prone to quantitative oxidation in the potential
window surveyed), a film of borohydride oxidation products is also
formed, especially upon operation at the limiting plateau of the
−
BOR (i.e. at maximum BH4 conversion rate) and for little revo-
lution speeds of the RDE. In that latter case, the voltammogram
quickly becomes “noisy”, especially for the highest borohydride
concentrations for which the amount of boron-oxide formed per
3
We emphasize the fact that we performed such FTIR measurements on a static
gold electrode, in absence of hydrodynamic convection, like for and UME.

4434
M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
aqueous solution at concentrations above 25 mM and above pH 7
[48].
trode used (at the exclusion of any other parameters), is
hindered by the possible (and uncontrolled) formation of a
boron-oxide gel (or film) at the electrode surface, as well as
Another explanation is linked to the formation of H2 bubbles
at the electrode s−urface as a result of the possible heterogeneous
hydrolysis of BH4 on gold, which has been put into evidence by
Krishnan et al. using RRDE measurements [18] and Chatenet et
al. by on-line Mass Spectrometry [40]. Such bubbles likely remain
attached to the surface of static electrodes (e.g. the gold UME), thus
partially masking their surface and participating to the decrease of
the signal observed on Fig. 7B and E. We emphasize that such phe-
nomenon is especially likely for the Au UME since (i) it is fixed, thus
not prone to evacuate such bubbles, and (ii) its surface is small and
thus easily obstructed by bubbles.
Therefore, it is likely that the measurements performed by Den-
uault et al. [21] and Wang et al. [17] were distorted by the existence
of either a boron-oxide film onto their gold microelectrode, which
readily forms upon potential cycling/holding in the region of the
BOR limiting plateaus −(Fig. 7), or to the presence of H2 bubbles
formed due to the BH4 heterogeneous hydrolysis at the gold sur-
face. It is wise to note that the values they measured roughly
correspond to that we obtained when the chronoamperometry
was performed for a gold UME which had been cycled once from
−1 V vs. NHE to 0.3 V vs. NHE (see Fig. 7A and Section 3.5.3). In
addition, these authors used rather high borohydride concentra-
tion (0.02 M), which in the natural diffusion conditions employed
for chronoamperometry experiments favors fast boron-oxide for-
mation at the vicinity of the electrode surface. In that frame, the
absence of convection necessary for their calculation becomes an
issue for the borohydride diffusion coefficient determination (it
however works fine for other systems, not hindered by any fast
precipitate/film/bubbles formation at the electrode, e.g. using fer-
rocyanide [21]). As a consequence, should a fraction of the electrode
be “covered” by such oxygenated boron species (e.g. H3BO3, NaBO2
or boron-oxide “polymers” or “oligomers”) or H2 bubbles and thus
−
H2 bubbles due to heterogeneous hydrolysis of BH4 [18,40],
as soon as BOR experiments are undertaken. The main draw-
back of this technique is thus that it is only acceptable in the
case of NaBH4 when “pristine” UME (or microsphere) are used,
which is hardly controllable: no one can guaranty that all the
electrode surface is accessible at any time of the measurement,
since the measurement itself, at the limiting plateau of the BOR,
produces boron oxide species and H2 bubbles. Boron oxides are
prone to “polymerize” at the UME surface and thus gradually
prevent access to the species in solution and modify the value
of the true (accessible) geometric surface of the electrode. The
effect is even sharper in the absence of electrolyte convection
(by essence on UME, but also by calculation requirements in the
chronoamperometric technique [17,21]): the boron-oxide film
formation which inevitably occurs onto the electrode surface
in the course of the BOR (as detected from in situ FTIR mea-
surements on gold [47]) cannot be in situ mechanically expelled
during the measurements on static UME.
Conversely, the “transit-time” technique using a RRDE does not
suffer such important drawbacks. It is fast, does only require the
knowledge of the solution viscosity (easily measured, see Section
3.1) and has the dual advantages of (i) proceed in hydrodynamic
conditions while (ii) consist of the transient measurement for a
perturbation generated at the disk to reach the ring. Point (i) pre-
vents (or at least slows down) both the boron-oxide film formation
in the time frame of the experiments, which is little in the present
technique (a few min. overall, but only a few 10 s in BOR conditions,
the remaining duration being at ocp) and the H2 bubbles accumula-
tion at the electrode surface. Should a film/bubbles nevertheless be
present at the ring and/or disk electrodes (partially covering them),
point (ii) guaranties that the implication would be small: the values
measured consist of the time to cross the disk-ring distance, i.e. in
the solution on a distance which is orders of magnitude larger than
the boron-oxide film thickness (should it be present) and a “free”
fraction of the disk/ring is enough for the perturbation generated at
the disk to be detected at the ring (the transit-time determination
is possible even with a partially obstructed ring surface: it does not
require the (free) surface area of the ring to be known with preci-
sion at the time of the measurement, since the transit-time is not a
function of the ring area, but only of the disk-ring distance).
In addition, we point out that the DBH − values determined by
polarography were systematically higher 4than the others reported
in the literature (measured by chronoamperometry at static gold
microelectrodes), and thus in better agreement with our values (at
least when DBH − from reference [22] is recalculated for n = 8). As for
the RRDE trans4it-time technique, we believe the dropping mercury
electrode, which is in situ regenerated in polarography, does not get
covered by any boron-oxide film in the course of the experiment.
Thus one can discard the bias related to the formation of boron-
oxide film at the dropping electrode surface especially hindering
the measurements at static UME.
geometrically inaccessible to the free solution, the measured DBH
−
may be underestimated, for two reasons. Firstly, the measureme4nt
is strictly proportional to the geometric area of electrode [17,21],
the value of which would likely decrease in the time frame of the
experiment if a film of boron-oxide or H2 bubbles are formed at
the electrode surface. Secondly, the presence of such film/bubbles
could also hinder BH4− species mass-transport (diffusion) down to
the electrode surface (across the film). Both biases would result in
the measurement of an apparent diffusion coefficient smaller than
in the absence of boron-oxide film/bubbles.
In the light of these results, the technique which appears the
most suited for the tetrahydroborate anion is the “transit-time”
technique using a RRDE, for several reasons.
(1) The Levich (or Koutecki-Levich) method indeed appear hin-
dered by (i) its slowness (several slow-scan CV are required) and
the fact that the viscosity of the solution ꢀ, the number of elec-
trons n and the concentration of the electroactive species C are
required. These three parameters, although possibly accessed
by additional/separated measurements, may all suffer non-
negligible uncertainty, thus maximizing the experimental error
of the diffusion coefficient determination. Moreover, the (long)
time spent at the limiting plateaus favor boron-oxide precipi-
tation at the electrode surface.
(2) The EIS method is numerically lying on simplifying hypothe-
ses (for example the frequency at the apex, 4.2 Hz on Fig. 6,
is only an estimate) and hindered by the difficulty to monitor
reproducible EIS spectra, even for rather diluted NaOH + NaBH4
solutions [33].
Finally, the higher DBH − values determined by RRDE than those
4
previously available in the literature provide a relevant explanation
to the several n values above 8 reported in some studies of the BOR
(Table 4). It is clear that n values above 8 cannot be explained from
a thermodynamic point of view (see Eq. (1)). The likely explanation
for finding n values above 8 is that the authors of the papers used
DBH − values which were actually much weaker than the practi-
4
cal values in the considered electrolytic solution determined in the
present study. Considering an erroneous value of the solution vis-
cosity (most publications consider no change between the viscosity
of the supporting electrolyte and that of the NaBH4-containing solu-
(3) Finally, the chronoamperometry on a static UME (or micro-
sphere), although very attractive because it is fast and only
requires the knowledge of the precise dimensions of the elec-

M. Chatenet et al. / Electrochimica Acta 54 (2009) 4426–4435
4435
Table 4
Examples of n values above 8 reported in the literature for sodium hydroxide + borohydride electrolytic solutions.
Reference
[NaOH], M
[NaBH4], M
T, ◦
C
DBH
−
n
Method of
4
determination
[39]
[42]
2.5
2
0.27
0.3
25
25
1.68 × 10−5
4–9.7
12
Levich
Levich
Not precised
tion, although we measured non-negligible differences, see Section
3.1) may also induce a non-negligible bias.
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−
(as a result of some extent of BH4 heterogeneous hydrolysis on
gold) at the surface of the static gold microdisk. The presence of
such film/bubbles decreases the accessible geometric surface of the
electrode and hinders reactant access to the electrode. Thus, effi-
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4
relevant anolyte compositions of DBFC, in the range 0.1–4 M NaOH,
10−3 to 10−2 M NaBH4 at temperature of 10, 20, 25 and 40 ◦C.
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This work was supported by the “Cluster Energie” of Région
Rhône-Alpes (France). M.C. thanks Eric Chainet for the gold depo-
sition at the Pt-Pt RRDE.