R. Wibowo et al. / Chemical Physics Letters 492 (2010) 276–280
277
4 2
Fig. 1. The structure of [C mpyrr][NTf ].
+
potential of the Fc/Fc redox couple (careful calculated after taking
into account the discrepancies in diffusion coefficients between the
two species, as described previously [7]) was set as 0 V.
2.2. Simulation conditions
The mathematical simulation model has been described [13]
and applied [5–7,14,15] previously. Briefly, the model assumes a
one electron transfer mechanism for the deposition and stripping
of bulk alkali metal (M) on the electrode surface (Eq. (1)). Both
the deposition and stripping processes are assumed to follow But-
ler–Volmer kinetics (Eqs. (2) and (3)).
Fig. 2. The cyclic voltammograms recorded for a 0.1 M solution of the relevant
metal–[NTf
2 4 2
] salt in [C mpyrr][NTf ] at a 50 lm diameter Ni electrode. Scan
ꢀ
1
rate = 10 mV s
.
k
a
þ
þ eꢀ ꢀ MðsÞ
M
ð1Þ
ð2Þ
ð3Þ
ðsolÞ
k
d
ꢀ
ꢁ
Ni, followed by the rapid deposition of metal-on-metal. The local
concentration of the metal ion is therefore depleted, and in the
0
ꢀ
a
RT
F
0
k
k
a
d
¼ k exp
ðE ꢀ E Þ
f
+
+
+
ꢀð1 ꢀ
ꢁ
case of Li , Na and K this leads to a characteristic peak shape cor-
responding to a mass transport controlled region [16]. All scans
also possess characteristic nucleation loops (where backward and
forward currents cross over), as on the reverse scan Group I metal
is still being deposited on Group I metal at potentials positive to
that required for the initial nucleation of the metal on Ni. In the
0
ꢂ
a
RT
ÞF
0
f
¼ k ½Mꢁ exp
ðE ꢀ E Þ
0
ꢀ1
where k is the surface process rate constant (units of cm s ) for
+
0
the M /M couple,
a
is the transfer coefficient and Ef is the formal
potential. [M]* is the standard concentration equal to
+
+
ꢀ3
ꢀ3
ꢀ1
ꢀ1
case of Rb and Cs , the reduction potentials for these metals were
1
ꢃ 10 mol cm . R is the ideal gas constant (8.314 J K mol ),
+
+
+
ꢀ1
significantly more negative than that of Li , Na and K , such that
nucleation occurred only a few millivolts prior the reduction pro-
F is the Faraday constant (96 485 C mol ) and T is the absolute
temperature in K.
4 2
cess of [C mpyrr][NTf ]. Therefore the scan had to be reversed
Fick’s second law is assumed to be followed for the diffusion
process of species M approaching and escaping the electrode sur-
+
shortly after nucleation, and a considerable amount of metal was
instead deposited on the reverse scan (direction of the scan indi-
cated by arrows in the figure).
face. The surface coverage of M on the electrode,
M
C , is dependant
+
upon the rate of deposition and stripping. Deposition is M concen-
tration dependant; therefore the concentration gradient had to be
solved using a series of partial differential equations, as described
The charge passed under the reduction process can be used to
quantify the amount of alkali metal reduced at the electrode sur-
face. Assuming the metal is deposited as layers with the same geo-
metric area as that of the Ni microelectrode, the reduction charge
calculated for the bulk reduction peak in the voltammograms in
Fig. 2 indicates that approximately 63, 96, 34, 33 and 68 layers of
Li, Na, K, Rb and Cs were deposited, demonstrating that all systems
deposit bulk metal on the Ni electrode. All systems also display
sharp oxidation peaks which correspond to the stripping off of me-
tal from the electrode surface. Therefore, the CV response after the
bulk deposition peak and prior to the bulk stripping peak (e.g.
where the CV crosses over the x-axis, corresponding to zero net
current being passed) corresponds to the system behaving as an
previously [13]. The maximum distance simulated is set to be
pffiffiffiffiffi
6
Dt from the electrode surface, where D is the diffusion coeffi-
cient of M and t is time. It is considered that there is no concentra-
tion gradient beyond that distance. The rate of stripping is
+
assumed to be independent of
M
C .
After the system of equations has been solved, the current, I,
was calculated using the following equation:
Z
r
d
@C
Li
I ¼ ꢀ2
pF
rdr:
ð4Þ
@
t
0
+
+
M/M interface, as opposed to Ni/M . The response of the system
in this region is therefore a feature of the fundamental parameters
3
. Results and discussion
+
of the M/M couple in the IL. The CVs were simulated as described
3
.1. Voltammetric results
below in order to quantify the parameters.
Fig. 2 displays a comparison of CVs for all five Group I alkali
metals, recorded for 0.1 M of the relevant metals–[NTf ]-salt dis-
2
3.2. Simulation results
ꢀ
1
solved in [C
4 2
mpyrr][NTf ] and recorded at 10 mV s
at a Ni
microelectrode.
The details of the simulation were explained briefly in Section 2.
Full details of the development of the simulation model [13], as
well as its application to experimental results have been previously
demonstrated [5–7,14,15]. The simulation model was applied to
the K/K , Rb/Rb and Cs/Cs systems in order to extract the funda-
mental electrochemical parameters of the couples. Figs. 3–5 dis-
play overlays of the experimental results as well as best fits for
Underpotential deposition (UPD) processes [5–7] were ob-
served for all five Group I metals in the region of ꢀ2 to ꢀ3 V, and
+
can be observed most clearly in Fig. 2 for Li . Relatively sharp
+
+
+
reduction profiles were observed for all metals at potentials more
negative than ꢀ3 V, consistent with an overpotential being re-
quired for the initial nucleation of the Group I metal to occur on