Impact of accompanying hydrogen generation on metal nanotube electrodeposition

Article abstract of DOI:10.1149/1.3365038

Ni is electrodeposited into polycarbonate porous membrane templates at various cathodic potentials and bulk solution pH values. The membrane pore diameters are 200 nm. Transmission electron microscope observations reveal that the electrodeposited Ni nanostructures are nanowires but occasionally nanotubes. The nanotube wall thicknesses vary from 10 to 70 nm. Nanotubes with thinner walls are deposited under more acidic and less noble conditions. The numerical model for pH values at the cathode surface in the template is developed. Calculated pH values at the cathode surface are lower in the template than those at a vertical planar cathode. The current efficiency of Ni is measured by inductively coupled plasma emission spectrometry. As the predicted by the pH calculations, the current efficiency of Ni is lower for a porous template than for a vertical planar cathode. The observed nanotube walls become thinner as the current efficiency decreases. Thus, it is deduced that accompanying H ₂ evolutions promote nanotube growth in the pores. Finally, the pH values in the template are more than 1 to 2 times smaller than at the vertical planar cathode surface.

Full text of DOI:10.1149/1.3365038

Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D357
0013-4651/2010/157͑6͒/D357/13/$28.00 © The Electrochemical Society
Impact of Accompanying Hydrogen Generation on Metal
Nanotube Electrodeposition
c, ,z
Munekazu Motoyama,a, Yasuhiro Fukunaka,
Yukio H. Ogata,d, and
*
*
*
Friedrich B. Prinza,b,
*
aDepartment of Mechanical Engineering and bMaterials Science and Engineering, Stanford University,
Stanford, California 94305, USA
cGraduate School of Energy Science, Kyoto University, Kyoto 606-8501, Japan
dInstitute of Advanced Energy, Kyoto University, Kyoto 611-0011, Japan
Ni is electrodeposited into polycarbonate porous membrane templates at various cathodic potentials and bulk solution pH values.
The membrane pore diameters are 200 nm. Transmission electron microscope observations reveal that the electrodeposited Ni
nanostructures are nanowires but occasionally nanotubes. The nanotube wall thicknesses vary from 10 to 70 nm. Nanotubes with
thinner walls are deposited under more acidic and less noble conditions. The numerical model for pH values at the cathode surface
in the template is developed. Calculated pH values at the cathode surface are lower in the template than those at a vertical planar
cathode. The current efficiency of Ni is measured by inductively coupled plasma emission spectrometry. As the predicted by the
pH calculations, the current efficiency of Ni is lower for a porous template than for a vertical planar cathode. The observed
nanotube walls become thinner as the current efficiency decreases. Thus, it is deduced that accompanying H2 evolutions promote
nanotube growth in the pores. Finally, the pH values in the template are more than 1 to 2 times smaller than at the vertical planar
cathode surface.
© 2010 The Electrochemical Society. ͓DOI: 10.1149/1.3365038͔ All rights reserved.
Manuscript submitted June 22, 2009; revised manuscript received February 22, 2010. Published May 3, 2010.
Electrochemical deposition in porous, thin-film-like polycarbon-
ate membranes and anodized alumina films, as a technique to pro-
duce one-dimensional ͑1D͒ inorganic nanostructures such as metal-
lic nanowires and nanotubes, has attracted a great deal of interest.1-9
Many authors have investigated the physical properties and crystal-
lographic characterization of the produced nanostructures with sci-
entific interest and with a goal of applying them to various func-
tional nanodevices, such as magnetic recording media,1-4 energy
conversion electrodes,5,6 and chemical sensors.7-9 Occasional obser-
vations of hollow tube growth in the templates have interested sev-
eral authors.10-17 In comparison to metallic nanowires, metallic
nanotubes exhibit higher surface-to-volume ratios.18,19 The possibil-
ity of nanotubes serving as channels for molecular selection and
delivery20 and the capability toward realizing unique magnetic con-
figurations unattainable in magnetic wires21 make metallic nano-
tubes attractive for a wide range of future applications. However, it
is still unclear as to what exactly occurs during the electrodeposition
process of nanotubes in the finite-sized pores enclosed by polymer
or ceramic walls.
Various growth models have been suggested. Tourillon et al. re-
ported that Fe and Co nanotubes were deposited by a pulsed poten-
tiostatic method.10,11 In a polycarbonate membrane, they observed
that scheduling cycles of a short plating time followed by a long off
time produced nanotubes. They consider that the surface carbonate
groups of membrane walls induce complexation with metal ions.
Hence, metallic adatom layers form on the surfaces, and the elec-
trodeposition on the adatom layers subsequently increases the tube
wall thicknesses. Metal nanotubes were successfully produced by
chemically modifying the template walls to catalyze metal deposi-
tion on the wall surfaces.22-24
tube growth has not yet been found, although improved insights
promise better strategies in designing and building next-generation
nanostructures.
Fukunaka et al. investigated the effects of cathodic potential and
electrolyte pH on Ni nanostructures electrodeposited in polycarbon-
ate templates.15 They reported that when the cathodic potential was
more positive or the electrolyte pH was lower, the deposited struc-
tures tended to form hollow tubes. Moreover, the tube wall thick-
nesses varied from 10 to 70 nm, with an outer diameter of 200 nm,
depending on the cathodic potential and pH. Tube wall thicknesses
that are controllable over a wide range of internal radii may offer
interesting scientific opportunities. Ni plays catalytic roles in various
͑electro͒chemical processes such as the anode reaction of a solid
oxide fuel cell,25,26 hydrogen production by methane
decomposition,27 and growth of carbon nanotubes.28 Moreover, the
range of applications is further broadened by the fact that metal
nanotubes may be deposited from many different materials.
Fukunaka et al. presumed that the hollow core of a Ni nanotube
is associated with a H2 nanobubble because a lower pH electrolyte
produces more significant H2 generation.29,30 In their model, an
electrochemically growing nanotube traps a nucleated H2 bubble in
the center of the end. The bubble neither escapes nor disappears
because H2 gas molecules are continuously generated at the periph-
eral edge of the tube during the deposition and diffuse to the larger
H2 bubble in the core before nucleating multiple bubbles there.
However, the inner pressures of the nanobubble were so high
͑Young–Laplace equation͒ that the gas solubility in the solution was
increased at the front face of the bubble ͑Henry’s law͒. The balance
between the absorption and dissolution rates of the H2 molecules
stabilized the H2 gas/aqueous electrolyte interface of the
nanobubble. The inner diameter of the nanotubes is determined by
the size of a bubble present in the center. The literature also pointed
out the critical role of H2 evolution in nanotube growth.16,17 To
understand the electrodeposition process of the nanotubes, measure-
ments of H2 evolution rates are indispensable.
However, Tourillon et al.’s model was not sufficient to explain
the electrodeposition processes of nanotubes under various condi-
tions encountered in the subsequent literature. Continuous constant
currents12-14 and potentials15-17 can also grow Au, Cu, Fe, Co, and
Ni nanotubes in polycarbonate membranes and anodized alumina
films. Moreover, electrolyte compositions,15-17 cathode geometry at
the template bottom,12,16 and the kind of organic additive used14 are
also critical. Hence, a clear understanding of electrochemical nano-
Our study aims to measure the current efficiency of Ni elec-
trodeposition in polycarbonate membrane templates by inductively
coupled plasma ͑ICP͒ emission spectrometry. We use the calculation
model to estimate the ionic species concentration at the cathode
surface in the nanoporous template. The calculated results show that
the pH value at the cathode surface in the template is much lower
when compared to a vertical planar cathode. From the results of a
vertical planar cathode, the measured current efficiency of Ni is
*
Electrochemical Society Active Member.
z E-mail: fukunaka@energy.kyoto-u.ac.jp
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D358
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
Figure 1. SEM image of a polycarbonate-track-etched membrane surface
after sputter deposition of a 30 nm thick Pt–Pd alloy layer. The nominal
diameter of the pores is 200 nm. Scale bar: 1 ␮m.
Figure 2. ͑Color online͒ Top: Current I vs time t curve for electrodeposition
of Cu into the polycarbonate template at E = −0.4 V. Cu nanowires grow
through the pores and form a capping layer on top of the template. The inset
illustrations show the respective growth stages of the nanowires in the tem-
plate. Bottom: SEM image of Cu nanowire arrays detached from the Pt–Pd
cathode layer after the polycarbonate template was removed. The Cu islands
on top were created after the nanowires reached the template top surface.
Scale bar: 2 ␮m.
lower than expected in the template, as indicated by the calculations.
Therefore, it is understood that Ni nanotube growth is accompanied
by H2 evolution.
Experimental
A polycarbonate-track-etched membrane ͑Toyo Roshi Kaisha
Ltd., Japan͒ was used as a template for the growth of metal nano-
structures. The nominal values of the pore diameter, membrane
desired electrochemical reaction based on Faraday’s law.33 The cur-
rent efficiency of electrodeposition can be obtained by measuring
the weight gain because the side product, H2 gas,30,33,34 does not
produce any weight gain. In this study, the mass of the deposited
metal was analyzed by ICP emission spectrometry. ␩ can be calcu-
lated as follows
thickness, and pore density were 200 nm, 10 ␮m, and
3
ϫ 108 cm−2, respectively. A Pt–Pd alloy layer, with a thickness of
roughly 30 nm, was sputtered on one face of the membrane to serve
as the cathode. Figure 1 shows a scanning electron microscope
͑SEM͒ image of the Pt–Pd surface sputter-deposited on a polycar-
bonate nanoporous membrane. As can be seen, the pores still show
unclosed mouths.31 The electrochemical cell was found by Mo-
toyama et al.31,32 and was designed to press the membrane from
underneath with a flat Pt sheet to attain good electronic contact with
the Pt–Pd cathode and to prevent electrolyte leakage from the bot-
tom. This Pt sheet was connected to a potentiostat.
ime
m/M
Q/zF
␩ =
dt ϫ 100 =
ϫ 100
͓1͔
͵
ime + iH
2
where ime and iH are the partial current densities of the metal, either
Cu or Ni, and H22, respectively, m is the mass of deposited metal ͑g͒,
M
is the metal atomic weight ͑Cu: 63.5 g mol−1
;
Ni:
The electrolyte solutions for Cu and Ni electrodeposition were
0.60 mol L−1 CuSO4, 5 ϫ 10−3 mol L−1 H2SO4, and a mixture of
0.97 mol L−1 NiSO4, 0.19 mol L−1 NiCl2, and 0.62 mol L−1
H3BO3.30 The deposition was conducted under potentiostatic condi-
tions at room temperature. The pH of the Cu plating solution was
1.7. The pH of the Ni solution was regulated down to 3.0, 2.5, 2.0,
and 1.5 from the original value of 3.4 by adding sulfuric acid. A 0.5
mm diameter Cu wire of and a 1 mm diameter Ni wire were used as
reference electrodes in the respective solutions. The lateral surfaces
of these wires were polymer-insulated. Cu and Ni reference elec-
trodes in the above electrolytes showed potentials close to the re-
spective equilibrium potentials of the Cu2+/Cu and Ni2+/Ni couples:
+0.33 V ͑0.60 M ͓Cu2+͔͒ and Ϫ0.23 V ͑1.16 M ͓Ni2+͔͒ vs the
standard hydrogen electrode ͑SHE͒. In either Cu or Ni deposition, E
represents a potential applied with respect to the corresponding ref-
erence electrode. Cu and Ni sheets were used as counter electrodes
for Cu and Ni electrodeposition, respectively. Metal electrodeposi-
tion was conducted within a geometric area of 0.0314 cm2 of the
membrane ͑2 mm in diameter containing 9.4 ϫ 106 nanopores͒ de-
fined by a perforated acrylic resin plate.
58.7 g mol−1͒, Q is the electrical charge passed ͑C͒, z is the va-
lency, and F is Faraday’s constant ͑9.65 ϫ 104 C mol−1͒.
Figure 2 shows the current transient during Cu deposition into
the template at E = −0.4 V and an SEM image of electrodeposited
Cu nanowire arrays after removing polycarbonate in a dichlo-
romethane solvent. As described in a previous work,31,32 the current
transient curve is classified into four stages: ͑I͒ nucleation on the
bottom, ͑II͒ steady growth in the pores, ͑III͒ lateral extension of the
metal film on the membrane surface after filling the pores, and ͑IV͒
steady growth of a thin film on the membrane ͑not presented in Fig.
2͒. The electrolysis was manually stopped immediately after the
deposition current began to sharply increase in the beginning of the
third stage ͑t = 276 in Fig. 2͒. This moment corresponded to the
growth of nanowires reaching the membrane surface, extending the
electrode surface area outside the template, thereby increasing the
deposition current. If the circuit was kept closed, the deposition
current would have increased, indicated by the broken line. The
specimen shown in the SEM image in Fig. 2 was produced by the
deposition until the beginning of stage III. Therefore, several Cu
islands formed on top.
Current efficiency measurement
.— Current efficiency, ␩ ͑%͒, is
defined as the percentage of the current used for carrying out a
After electrolysis, the bottom Pt sheet and the template mem-
brane containing the deposited metal were kept separately in dis-
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Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D359
Figure 3. Schematic illustration of the as-
sumed H+ or Ni2+ concentration profile
from the cathode surface toward the an-
ode. The hemispherical diffusion zones
coalesce each other over the template sur-
face to form the 2D diffusion layer.
tilled water for more than 30 min, and this treatment was repeated.
After carefully rinsing with ethanol, the sample and the Pt sheet
were dried. Subsequently, they were separately kept in 10 vol %
HNO3 solutions, with a total volume of 50 mL each at 313 K for
more than 24 h. A strong HNO3 solution leached out Cu or Ni
embedded in the membrane. The brown or black color, which
stemmed from an embedded metal, disappeared within a few hours,
giving the region the same appearance as where there was no elec-
trodeposition of the metal. After the solutions cooled down to room
temperature, each volume was again adjusted to 50 mL by adding
distilled water. Finally, metal concentrations in the HNO3 solutions
were measured by an ICP emission spectrometer ͑ICAP-575II,
Nippon-Jarrel-Ash, Tokyo, Japan͒. By summing the concentrations
of metal ions that leached out of the template and from the Pt sheet,
the total mass m in Eq. 1 is calculated.
rapidly dissolved into the electrolyte, whereby a bubble was sup-
posed to disappear immediately.38 The nucleation of a H2 bubble
may possibly occur outside the template if the concentration of the
dissolved H2 gas molecules that diffuses outward from the pores
exceeds the critical concentration of the supersaturation. If H2 gas
bubbles form outside the template, they microscopically promote the
hydrodynamic velocities of natural convection along the template
surface due to buoyancy forces ͑Appendix A͒. However, the H2
partial current per unit geometric area of the template did not exceed
4 mA cm−2 in this study. As reported,39 this range of H2 partial
current density was negligible for the mass-transfer rate. Hence, H2
gas evolution was not taken into consideration for the ionic mass-
transfer rate in this study.
The ionic diffusion layer in a stagnant aqueous electrolyte usu-
ally grows 1 order of magnitude greater than 10 ␮m from vertical
electrode surfaces.40 As the template thickness was 10 ␮m, the typi-
cal time scale for the boundary layer thickness to reach out of the
pores was supposed to be L2/D Ϸ 0.1 s compared to deposition
periods of the orders of 102 or 103 s, which depend on the cathodic
potential ͑L is the pore length and D is the ionic diffusion coeffi-
cient͒. Therefore, the diffusion layer hemispherically developed
from all pore openings distributed over the template surface imme-
diately after starting the electrolysis. They coalesced each other,
resulting in a planar diffusion layer with a thickness of ␦ toward the
anode.17,41
Surface pH calculation.— This study presumes the following
four approximations to simplify the surface pH calculations:
1. All species diffuse through the pores with the same diffusion
coefficients and transference numbers as in the bulk solutions.
2. H2 gas evolution does not affect the ionic mass-transfer rate.
3. Growth of nanowires or nanotubes is negligibly slow com-
pared with the development of a concentration boundary layer out-
side the template.
4. Natural convection occurs only outside the template.
Figure 3 schematically shows the supposed concentration profile
of cationic species, i.e., H+ and Ni2+, from the cathode surface to-
ward the anode located distant enough from the template. The x-axis
is defined in the normal direction to the template plane. The distance
Regarding the first assumption above, 200 nm diameter seems
too large for electric double layers on the template walls to signifi-
cantly influence the ionic diffusion transports in such concentrated
electrolyte solutions ͑Ͼ1 M͒, according to the literature.35,36 Al-
though ionic diffusion coefficients in the template pores have to be
determined in a reliable way in the future, understanding how the
surface concentration differs based only on the geometric difference
of the template with fixed diffusion coefficients is significant as a
preliminary calculation of this study.
from the cathode surface to the opening mouths ͑L ͒ decreases,
Ј
whereas nanowires or nanotubes grow. ip and ib in Fig. 3 are current
densities parallel to the x-axis through the pores and across the pla-
nar diffusion layer developed outside the template, respectively. Cs
is the cathode surface concentration, Cm is the mouth concentration,
and Cb is the bulk concentration. A more precise analysis can be
addressed with the moving boundary condition applied to the cath-
ode surface to describe a transient diffusion. However, this study
measures the current efficiencies averaged over the filling periods.
Hence, a precise calculation based on a transient diffusion analysis
with a moving boundary does not necessarily meet the concept of
the time-averaged current efficiency. In this study, the chemical spe-
cies concentration at the ends of nanowires or nanotubes is calcu-
lated, assuming the steady-state diffusion profile, which would be
achieved with a constant length of nanowires or nanotubes.
No H2 bubble was assumed between the cathode surface ͑nano-
wire or nanotube ends͒ and the mouths of the pores. This was be-
cause the membrane walls were made hydrophilic ͓with poly͑vi-
nylpyrrolidone͔͒ by the manufacturer, whereby the nucleation of H2
bubbles in a pore was difficult. The curvature radius of the bubble
must be small if it is present in a pore. The bubble inner pressure
was considered by the Young–Laplace equation ͑pin − pout = 2␥/r,
where pin and pout are the inner and outer pressures of a bubble,
respectively, and ␥ is the interfacial energy͒. For instance, the inner
pressure became 14 atm larger than the outer pressure with ␥ =
The cross-sectional fraction of pores in the template can be de-
37
ϳ 0.07 N m−1 and r = 100 nm. Hence, H2 gas molecules were
scribed by 1 − exp͑−Np␲rp2͒, where Np and rp are the number den-
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D360
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
1.0
0.8
0.6
0.4
0.2
0
1st
2nd
3rd
0
200
400
600
800
1000
Distance / nm
Figure 4. ͑Color online͒ Cumulative probabilities for pores to encounter the
nth ͑n = 1, 2, 3͒ nearest neighbors as a function of distance in the 2D ar-
rangements of the template pores. The solid and dotted lines indicate the
observed results and the ideal Poisson distribution, respectively.
sity of the pores ͑3 ϫ 108 cm−2͒ and the pore radius, respectively.
Because the pore locations randomly distribute, the Poisson distri-
bution should be applicable.42-45 Figure 4 shows the respective prob-
abilities to encounter the first, second, and third nearest neighbors.
376 pores in an area of 106 ␮m2 were examined by SEM ͑number
density = 3.5 ϫ 108 cm−2͒. The dotted lines indicate the ideal Pois-
son distribution expressed by the following equation45
Figure 5. Concentration profile in the vicinity of a mouth. Cm is the inter-
Ј
cept at the template surface of the linear 2D diffusion profile. Ionic mass
fluxes outside the template converge into the pores through the coalescing
3D diffusion zones. Equation B-2 draws a broken line.
2͑␲Np͒nr2nn−1
exp͑␲r2nNp͒͑n − 1͒!
dPn
the hemispherical diffusion fields from the perfectly linear profile is
evident within a distance of ϳ0.5 ␮m from the template surface
͑Fig. 5͒.
=
͓2͔
drn
where Pn and rn are the encounter probability and distance to the nth
nearest neighbors, respectively. Eventually, the Poisson distribution
is a good approximation of the template pore arrangement in Fig. 4.
The steady-state ionic mass-transfer rates of the inside ͑ip/zF͒ and
the outside ͑ib/zF͒ of the template must be balanced as follows
The concentration profile developed from the template surface
toward the anode is virtually the same as the one developed from the
vertical planar cathode surface toward an anode during electrodepo-
sition with a current density of ib, except for the microscopic three-
dimensional ͑3D͒ concentration distribution close to the surface.
This is because reactive species are consumed at a constant rate into
the pores, as exactly seen on a planar cathode surface having a
constant current density. Konishi et al. already demonstrated that
natural convection outside the template needs to be taken into
consideration.31 Hence, Eq. 5 is supposed to give a reasonable value
of the diffusion layer thickness of ␦ measured from the template
surface as long as the concentration profile near the template surface
ib
ip =
͓3͔
1 − exp͑− Np␲r2p͒
The ionic mass flux across an isoconcentration surface decreases
from ip/zF to ib/zF, with the distance in the x-direction from the
opening mouths to the planar diffusion region. By entirely integrat-
ing the ionic mass flux across a plane parallel to the template surface
47-49
can be approximated by Fig. 3
from the template surface ͑x = L ͒ to the boundary with the bulk
Ј
Shy = 0.628Raءy1/5
͓5͔
͓6͔
concentration region ͑x = L + ␦͒, one can obtain the following
Ј
equation ͑Appendix B͒
ibNi͑1 − tء͒y
Shy =
␦
−1
Cb − Cm
dR
1 − exp͓− Np␲͑R + rp͒ ͔
Ј
= ͑Cb − Cm͒
͓4͔
͵
zFDNi⌰
ͭ
2
ͮ
␦
0
g␣ibNi͑1 − tء͒y4
where Cm is the template surface concentration defined by extrapo-
lating the linear concentration profile in the planar diffusion region
to the template surface, and R ͑cm͒ is the diffusion field radius from
the mouths. The pore diameter actually slightly increases in the
middle like a spindle shape, as seen in Fig. 2 and also in the
literature.32,46 Thus, the actual pore volume is increased by a factor
of 1.4 based on the shape profile analysis of electron micrographs.
Therefore, the rp value is modified to be 1.18 ϫ 102 nm corre-
sponding to a 1.4-fold volumetric increase from the nominal volume
of a pore. Hence, the pore-cross-sectional fraction is 0.12͓=1
Ј
Raءy =
͓7͔
zF␯D2Ni
where Shy is the Sherwood number, Raءy is the modified Rayleigh
number,49 tء is the transference number of metal ions, y is the ver-
tical distance from the lower edge of the template ͑cm͒, ⌰ is the
b
m
Ј
difference of CNi from CNi ͑mol cm−3͒, g is the gravitational
2+
2+
acceleration ͑9.8 ϫ 102 cm s−2͒, ␣ is the densification coefficient
for Ni2+ ions ͑cm3 mol−1͒, and ␯ is the kinematic viscosity of the
electrolyte ͑cm2 s−1͒. The Sherwood number represents the ratio of
convective to diffusive mass-transfer rates. The Rayleigh number
represents the ratio of the natural convection mass-transfer rate due
to the buoyancy forces to the product of ionic and momentum dif-
fusion coefficients, which means the convective or diffusive mass-
transfer rate. Previous work49 has proved Eq. 5 using vertical planar
− exp͑−Np␲r2p͔͒.
Regardless of current density, only the template geometrical
characters, Np and rp, and the spatial arrangement of pores deter-
mine where the hemispherical diffusion fields disappear to shift to a
planar field. The deviation of the concentration profile considering
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Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D361
+ 5H2O͒ are also considered.30,52 Boric acid hardly dissociates in
the pH range dealt within this study.30 To simplify the calculations,
the catalytic role of boric ion complexes for Ni deposition, which
were pointed out in the literature,53,54 is not taken into consideration
Table I. Numerical values of Ni2+ ions used for the calculations.30
D ͑cm2 s−1
͒
6.9 ϫ 10−6
0.4
tء
␯ ͑cm2 s−1
͒
1.5 ϫ 10−2
1.23 ϫ 102
␣ ͑cm3 mol−1
͒
−
CH BO CH
+
2
3
KH1
=
= 10−9.21 ͑mol L−1
͒
͓12͔
͓13͔
͓14͔
CH BO
3
3
electrodes under low current density conditions. Finally, the diffu-
sion layer thicknesses of Ni2+ and H+ ions measured from the tem-
plate surface are expressed as
−
CHB O CH
+
4
7
KH2
=
= 10−6.54 ͑mol−2 L2͒
4
͑CH BO
͒
3
3
2FDNi2+
⌰
2
2−
7
␦
2+
=
͓8͔
CB O ͑CH
+
͒
Ni
ibNi
4
KH3
=
= 10−15.55 ͑mol−1 L͒
4
͑CH BO
͒
3
3
␦
+
= ␴ء␦Ni2+
H
͓9͔
We neglect the presence of NiOH+ ions and instead consider
ء
1
4
where ␴ is the diffusion layer thickness ratio of H+ ions to Ni2+
55
4+
4+
−
Ni4͑OH͒ ions Ni4͑OH4͒ = Ni2+ + OH
͓
͔
4
39,50,51
ء
ions, and ␴ of 1.3 was applied in this study.
As mentioned
above, the linear profile is not applicable to the concentration distri-
bution within a range of approximately 0.5 ␮m from the template
surface. However, the calculated diffusion layer thicknesses of ␦
were always close to 100 ␮m. Hence, using Eq. 5 is acceptable.
Table I summarizes the physical properties of Ni2+ ions used for the
calculations.
CNi2+KW
KN1
=
= 10−7.17 ͑mol7/4 L−7/4
+
͒
͓15͔
4+
4
͑CNi ͑OH͒
͒
1/4CH
4
Finally, 1D steady-state diffusion equations to calculate Cm of H+
and Ni2+ ions can be written as follows30,56
iHb
−
4
4+
ץ CHSO
ץ CNi ͑OH͒
4
4
ץ CH BO
ץ CH
+
ץ COH
−
2
3
3
−
4
4+
4
ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ
= DH
+
− DOH
−
+ DHSO
+ nDH BO
− 4DNi ͑OH͒
͓16͔
͓17͔
3
3
4
F
ץ x
ץ x
ץ x
ץ x
ץ x
x=L
x=L
x=L
x=L
x=L
Ј
Ј
Ј
Ј
Ј
ibNi͑1 − t͒
2F
4+
4
ץ CNi ͑OH͒
ץ CNi2+
4
4+
ͯ ͯ ͯ ͯ
= DNi2+
+ 4DNi ͑OH͒
4
4
ץ x
ץ x
x=L
x=L
Ј
Ј
The pH at a given position of x is assumed to be calculated by
the local equilibrium of dissociation reactions releasing H+ and OH−
ions. The water autoprotolysis constant is
where n is
−
−
2−
7
ץ CH BO
ץ CHB O
ץ CB O
2
4
4
3
7
n = −
+
+ 2
͓18͔
ͩ
ͪ
ץ CH BO
ץ CH BO
ץ CH BO
3 3
3
3
3
3
Equations 16 and 17 can be rewritten by integration over the con-
centration boundary layer thickness as follows
iHb
CbH − CmH
+
+
b
m
͑CbH − CmH ͒ − D
−
KW
+ DHSO ͑CHSO − CHSO ͒ + D
͑Cb
− CmH BO ͒ + D
͑Cb
H BO
3
− CmHB O
͒
2
ء
−
4
␦
= DH
+
−
4
−
4
−
3
−
3
−
7
−
7
+
+
+
OH
H BO
3
H
CbH+Cm
H BO
HB O
3
3
2
2
4
4
F
+
H
+ 2DH BO ͑Cb
− CmB O ͒ − 4D
͑CNi ͑OH͒ − CNi ͑OH͒
͒
͓19͔
͓20͔
b
m
4+
4
2−
7
2−
7
4+
4
4+
4
Ni ͑OH͒
B O
3
3
4
4
4
4
4
ibNi͑1 − t͒
2F
b
m
ء
= DNi2+͑CbNi − CNmi ͒ + 4D
͑CNi ͑OH͒ − CNi ͑OH͒
͒
4+
4
␦
4+
4+
4
2+
2+
2+
Ni ͑OH͒
Ni
4
4
4
4
where we define ␦ء as
␦ء =
KW = CH
+
COH
−
= 10−14 ͑mol2 L−2
͒
͓10͔
␦
It is assumed that neutral H2SO4 molecules are not present in an
electrolyte due to perfect dissociation. Both HSO−4 and SO42− are
taken into consideration
dR
1 − exp͓− Np␲͑R + rp͒ ͔
͓21͔
͵
2
0
2−
4
CSO CH
+
where ␦ء represents the total diffusion path length, taking the non-
linear diffusion in close vicinity of the template surface into consid-
eration ͑see Eq. 4͒. The optimum Cm values obtained from Eq. 19
and 20 were then substituted as the boundary conditions into the
following equations, which describe the diffusions through the pores
KS1
=
= 10−1.92 ͑mol L−1
͒
͓11͔
−
4
CHSO
Three dissociation reactions of boric acid ͑H3BO3 = H2BO3 + H+,
4H3BO3 = HB4O−7 + H+ + 5H2O, and 4H3BO3 = B4O27− + 2H+
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D362
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
iHp
−
4+
4
ץ CHSO
ץ CNi ͑OH͒
4
ץ CH BO
3
ץ CH
+
ץ COH
−
2
4
3
−
4
4+
4
ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ ͯ
= DH
+
− DOH
−
+ DHSO
+ nDH BO
− 4DNi ͑OH͒
͓22͔
3
3
4
F
ץ x
ץ x
ץ x
ץ x
ץ x
x=0
x=0
x=0
x=0
x=0
rent efficiency of Cu deposition can be expected.59,60 Before the Ni
current efficiency measurements, we examined whether the Cu cur-
rent efficiency obtained by the present procedure reached 100% or
not to ensure the subsequent discussion of Ni current efficiency.
ipNi
4+
ץ CNi ͑OH͒
ץ CNi2+
4
4
4+
4
ͯ ͯ ͯ ͯ
= DNi2+
+ 4DNi ͑OH͒
͓23͔
4
2F
ץ x
ץ x
x=0
x=0
Likewise, Eq. 22 and 23 are rewritten as
iHp
CmH − CsH
+
+
m
s
2 L = D
+
͑CmH − CsH ͒ − D
−
KW
+ DHSO ͑CHSO − CHSO ͒ + D
͑Cm
− CsH BO ͒ + D
͑Cm
H BO
3
− CsHB O
͒
−
4
Ј
−
4
−
4
−
3
−
3
−
7
−
7
+
+
H
OH
H BO
3
CmH+Cs
H BO
HB O
3
3
2
2
4
4
F
+
H
m
s
+ 2DH BO ͑Cm
− CsB O ͒ − 4D
͑CNi ͑OH͒ − CNi ͑OH͒
͒
͓24͔
͓25͔
4+
4
2−
7
2−
7
4+
4
4+
4
Ni ͑OH͒
B O
3
3
4
4
4
4
4
ipNi͑1 − t͒
2F
m
s
L = D 2+͑CmNi − CNs i ͒ + 4D
͑CNi ͑OH͒ − CNi ͑OH͒
͒
4+
4
Ј
4+
4+
4
2+
2+
Ni
Ni ͑OH͒
4
4
4
4
The total numbers of sulfur and boron atoms were kept invariable at
x = 0, L , and ␦
Two potentials, E = −0.25 and Ϫ0.40 V, were tested. When E
was lowered from Ϫ0.25 to Ϫ0.40 V, the deposition current in-
creased by a factor slightly greater than 2, and the filling period was
shortened by half. Figure 6a and b shows the mass frequency distri-
butions of Cu nanowires electrodeposited at E = −0.25 and Ϫ0.40
V, respectively. Ten samples were analyzed at each potential. The
mean values ͑␮͒ of 40 ␮g ͑E = −0.25 V͒ and 41 ␮g ͑E =
−0.40 V͒ were almost the same. The standard deviations ͑␴͒ were
3.7 and 8.9 ␮g, respectively. The detected mass of Cu deposited on
the bottom Pt sheet was always less than 5% ͑Ͻ ϳ 2 ␮g͒ of the
mass detected from the template. This mass value was less than the
+
Ј
H
CHSO + CSO = CS ͑mol L−1
͒
͓26͔
−
4
2−
4
CH BO + CH BO + 4CHB O + 4CB O = 0.62 ͑mol L−1
͒
−
3
−
7
2−
4
7
3
3
2
4
͓27͔
CS are 2 ϫ 10−2, 5 ϫ 10−3, 1 ϫ 10−3, 3 ϫ 10−4, and 0 at pH 1.5,
2.0, 2.5, 3.0, and 3.4, respectively. The following mass balance
equation for Ni atoms was also considered at x = ␦Ni2+
CNb i + 4CbNi ͑OH͒ = 1.16 ͑mol L−1
͒
͓28͔
4+
4
2+
4
Table II shows the diffusion coefficients of the chemical species.
Table II. Diffusion coefficients used for the calculations.
The optimum CsH value of Eq. 24 and 25 gives the pH value at the
+
cathode surface in the template.
Diffusion coefficient
Species
͑cm2 s−1
͒
Reference
Results and Discussion
H+
5.0 ϫ 10−5
1.0 ϫ 10−5
1.1 ϫ 10−5
1.1 ϫ 10−5
4.3 ϫ 10−6
57
57
56
58
55
.— The Cu2+/Cu couple has a
Measurement method evaluation
OH−
more positive equilibrium potential ͑E0 = +0.33 V vs SHE, 0.60 M
͓Cu2+͔͒ than the hydrogen couple ͑H+/H2͒. Hence, near 100% cur-
HSO−4
H3BO3
Ni4͑OH͒
4+
4
Figure 6. m frequency distributions of Cu
deposited at ͑a͒ E = −0.25 V and ͑b͒ E
= −0.4 V ͑N: sample number; ␮: mean;
␴: standard deviation͒.
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Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D363
Figure 7. ␩ frequency distributions ob-
tained from the Cu deposition at ͑a͒ E =
−0.25 V and ͑b͒ E = −0.4 V ͑N: sample
number; ␮: mean; ␴: standard deviation͒.
Figure 9 shows the variations in pHs with pHb 1.5 as a function
of H2 partial current density with various distances from the cathode
standard deviation. Therefore, the extra Cu deposition on the bottom
Pt sheet did not damage the concept of measuring current efficiency
achieved by Cu deposition into the porous template.
surface to the mouths ͑L ͒. The pH5 values of a vertical planar
Ј
The nominal values of the pore diameter and pore density are
200 nm and 3 ϫ 108 cm−2, respectively. Hence, the mass of Cu
completely filling in the pores of the template with a geometric area
cathode are also shown. The concentration gradient near the tem-
plate surface ͑ץC/ץx at L Յ x Յ L + ␦͒ is one-tenth of that for a
Ј
Ј
vertical planar cathode because 1 − exp͑−Np␲r2p͒ is equal to 0.1
͑see the inset of Fig. 9͒. The diffusion layer thicknesses are not so
different as the concentration gradients are because of Eq. 5-8 ͑␦
ϰ i−1/5͒. Consequently, pHm is maintained much lower than pHs of a
vertical planar cathode with the same H2 partial current density at
of 0.0314 cm2 is 27 ␮g, with a bulk Cu density of 8.96 g cm−3
.
As mentioned above, the actual pore volume is approximately 1.4
times larger than the perfect columnar shape having a nominal di-
ameter of 200 nm. As a result, 27 ϫ 1.4 = 38 ␮g agrees with the
above mean values of the measured data. This agreement supports
the soundness of the present measurement technique for current ef-
ficiency.
the cathode. As L increases, pHs in the template increases while
Ј
approaching a vertical planar cathode because the diffusion path
from the opening mouths to the cathode surface becomes longer. If
Figure 7a and b shows the distributions of the measured current
efficiency, ␩. It ranged from 88.2 to 100% at E = −0.25 V and from
89.9 to 102% at E = −0.40 V. The average efficiencies were 92.5%
͑E = −0.25 V͒ and 95.9% ͑E = −0.40 V͒ with almost the same
standard deviations of 4.0%. The measured efficiencies were slightly
lower than 100%. The reason that the Cu deposition had a current
efficiency less than 100% needs further investigation. However, the
positive facts of ␩ near 100% and a narrow distribution ͑4.0% stan-
dard deviation͒ encouraged us to measure Ni current efficiency with
the present technique. We postulate that the Ni current efficiency,
presented below, is sufficiently reliable.
L
becomes greater than the diffusion layer thickness of a vertical
Ј
planar cathode ͑Ͼ ϳ 100 ␮m͒, pHs in the template becomes higher
than pHs of a vertical planar cathode in the calculation.
Figure 10 shows the variations in pHs with pHb 1.5 as a function
of H2 partial current density with various pore-cross-sectional-
fraction values, 1 − exp͑−Np␲r2p͒. With the same H2 partial current
density at the cathode, a larger proton flux is needed toward the
7.0
3.0
pHb 1.5
6.0
5.0
4.0
3.0
2.0
1.0
3.4
2.5
2.0
Calculated pH value in template.— Figure 8 shows variations in
the cathode surface pH ͑pHs͒ in a porous template as a function of
H2 partial current density, calculated with various bulk pH values
͑pHb͒. The calculation parameters were N ␲r2 = 0.1, L = 1 ␮m,
Ј
p
p
pHs
pHm
and ipNi = 10 mA cm−2. A dotted line indicates the pH values at the
opening mouths ͑pHm͒ for each pHb value. In any case, the cathode
surface pH value suddenly shows a steep increase from the bulk
value to more than 6 at a particular current density. This is the
typical behavior of a cathode surface pH as a function of H2 partial
current density.30,56 Because L is only 1 ␮m, the cathode surface is
Ј
not distant from the mouths. Hence, pHs is always close to pHm,
except for the current density region where it increases steeply. As
pHb becomes higher, smaller H2 partial current densities cause a
steep increase in pHs. However, H2 partial current densities greater
than 10–30 mA cm−2 are impractical for Ni electrodeposition. Ad-
ditionally, the third assumption listed above also becomes unreason-
able. Hence, practically, pHs hardly increases when pHb is 1.5 or 2,
as shown in Fig. 8. The decrease in the Ni2+ concentration at the
cathode surface in the template from the bulk concentration was
ϳ3% of the bulk in the calculations of this figure.
0
0.05
0.10
0.15
0.20
0.25
0.30
Hydrogen Partial Current Density / A cm-2
Figure 8. Local pH variations with different bulk solution pH values ͑pHb
1.5, 2.0, 2.5, 3.0, and 3.4͒ as a function of H2 partial current density. pHb
corresponds to pH values at a H2 partial current density of zero. The dotted
and solid lines indicate pH values at the mouths ͑pHm͒ and the cathode
surface ͑pHs͒, respectively. The calculation parameters for this figure are
N ␲r2 = 0.1, L = 1 ␮m, and ip = 10 mA cm−2
.
Ј
p
p
Ni
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D364
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
7.0
6.0
5.0
4.0
3.0
2.0
1.0
Table III. Summary of Ni nanostructures deposited at various
potentials and pH. Meanings of the superscripts (A) and (B) are
explained in the text.
Planar
50 µm
10 µm
L'=1 µm
E
Tube wall thickness
͑V͒
pH
Structure
͑nm͒
pHs
pHm
Ϫ0.7
Ϫ0.7
Ϫ0.7
Ϫ0.8
Ϫ0.9
Ϫ1.0
Ϫ1.0
Ϫ1.0
Ϫ1.0
Ϫ1.0
Ϫ1.0
1.5
3.4
5.5
3.4
3.4
1.5
2.0
2.5
3.0
3.4
5.5
Tube/wire
Tube/wire
Tube/wire
Wire
20–30
20–50
50–70
—
—
10
20–30
—
—
—
—
͑B͒
C
͑B͒
L'
͑B͒
Wire
͑A͒
Tube/wire
Tube/wire
Wire
Wire
Wire
x
͑A͒
0
͑A͒
0
0.05
0.10
0.15
0.20
0.25
0.30
͑A͒
͑A͒,͑B͒
Hydrogen Partial Current Density / A cm-2
Wire
Figure 9. ͑Color online͒ Local pH variations with different L values as a
Ј
function of H2 partial current density. The dotted line indicates pHm. The
solid lines indicate pHs for nanoporous templates and a vertical planar cath-
ode. The calculation parameters for this figure are Np␲r2p = 0.1, pHb 1.5, and
ipNi = 10 mA cm−2. The inset figure shows the concentration profiles for the
porous-template deposition ͑higher concentration profile͒ and planar-cathode
deposition ͑lower concentration profile͒ with the same current density at the
cathode surfaces ͑x = 0͒.
template with a greater pore-cross-sectional fraction ͑see the inset of
Fig. 10͒. With the same ipH , iHb becomes greater with increasing
2
Np␲r2p ͑Eq. 3͒. The pHm and pH2s values approach a vertical planar
cathode, as 1 − exp͑−Np␲r2p͒ increases toward 1.
In summary, the pH at the cathode surface in the template is
lower when compared to a vertical planar cathode unless L is
Ј
longer than the diffusion layer thickness for a vertical planar cath-
ode. Additionally, the smaller the pore-cross-sectional fraction, the
harder it is for the cathode surface pH to increase.
7.0
Npπrp2 = 0.1
Planar
2
0.5
Ni nanostructure morphologies.— The morphologies of the
electrodeposited Ni nanostructures were examined for several con-
ditions. As shown in Fig. 11a, Ni began to grow and form hollow
tube structures because the template had unclosed mouths at the
bottom61 ͑see Fig. 1͒. Subsequently, Ni grew toward the core and
quickly formed solid wires leaving the initial hollow structure be-
hind ͑Fig. 11b͒.
6.0
5.0
4.0
3.0
2.0
1.0
pHs
pHm
However, as the solution pH value was sequentially decreased
from 3.4 to 3.0, 2.5, 2.0, and 1.5 with a constant potential of Ϫ1.0 V,
some of the nanostructures began to show entirely uniform hollow
nanotubes. Moreover, the cathode potential was also critical. As the
cathode potential became more positive with constant pH 3.4 or 5.5,
some nanotubes grew longer at E = −0.7 V. The results of the
transmission electron microscope ͑TEM͒ observations are summa-
rized in Fig. 11c-i and Table III. The tube walls became as thin as 10
nm at E = −1.0 V and pH 1.5 ͑Fig. 11e͒, whereas they increased to
70 nm at E = −0.7 V and pH 5.5 ͑Fig. 11d and h͒. Grain morpholo-
gies were also different depending on the tube wall thickness. Grain
sizes became greater up to 30–50 nm at E = −0.7 V and pH 3.4
͑Fig. 11g͒, but the tube walls with 50–70 nm in thickness deposited
at pH 5.5 did not show large grains ͑Fig. 11d and h͒. The tube walls
were conformally deposited on the template walls ͑Fig. 11f͒. TEM
exhibits the presence of the hollow interiors by clear contrast with
the tube walls, and hence nanowires appear to be dark totally ͑Fig.
C
2
Npπrp
x
0
0
0.05
0.10
0.15
0.20
0.25
0.30
Hydrogen Partial Current Density / A cm-2
Figure 10. ͑Color online͒ Local pH variations with different Np␲r2p values as
a function of H2 partial current density. The dotted line indicates pHm. The
solid lines indicate pHs for nanoporous templates and a vertical planar cath-
ode. The calculation parameters for this figure are L = 1 ␮m, pHb 1.5, and
Ј
ipNi = 10 mA cm−2. The pore-cross-sectional fractions with Np␲r2p = 0.1,
0.5, and 2 correspond to 0.095, 0.39, and 0.86, respectively. The inset figure
shows two different concentration profiles for the porous-template deposition
with the same current density at the cathode surfaces ͑x = 0͒. The top profile
has a smaller Np␲r2p value than the lower profile.
Figure 11. ͑a͒ SEM image of an initially
grown Ni hollow structure on the Pt–Pd
cathode. The template was removed by
dichloromethane solution ͑E = −1.0 V,
pH 3.4͒. ͓͑b͒-͑i͔͒ TEM images of various
Ni nanostructures. ͑b͒ Nanowires with
hollow sections introduced in the initial
stage of the deposition ͑E = −1.0 V, pH
3.4͒. ͓͑c͒ and ͑g͔͒ Nanotubes deposited at
E = −0.7 V, pH 3.4; ͓͑d͒ and ͑h͔͒ E =
−0.7 V, pH 5.5; ͑e͒ E = −1.0 V, pH 1.5;
and ͑f͒ E = −1.0 V, pH 2.0. ͑i͒ Nano-
wires deposited at E = −1.0 V, pH 3.0.
All scale bars: 200 nm.
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Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D365
1.5 ͑E = −1.0 V͒ is lower than that of a vertical planar cathode in
Fig. 13A. Figure 13B also indicates that current efficiency at E =
−0.7 V, where nanotubes are deposited, is much lower compared to
a vertical planar cathode. Hence, Fig. 13A and B suggests that the
nanotube deposition starts to occur as the ratio of the Ni deposition
rate to the H2 evolution rate decreases.
Additionally, the current efficiency is measured at E = −0.7 V
and pH 1.5. The average current efficiency is as low as 25% ͑Fig.
13C͒, and it has a large standard deviation, suggesting significant
fluctuations in the balance between Ni deposition and H2 gas evo-
lution. Nanotubes with 20 nm thick walls were deposited under this
condition ͑see Table III͒.
Fukunaka et al. discussed the possible physical model of nano-
tube growth.15 The membrane walls are so hydrophilic that if nucle-
ated, a H2 bubble prefers to have contact areas with the inner walls
of a Ni nanotube. The inner pressure of a 100 nm diameter bubble is
10–20 atm higher than the outer pressure.38 When the H2 evolution
rate is continuously balanced with the dissolution rate at the front
face of a H2 bubble trapped in the center at the end of a nanotube,
the bubble does not disappear and maintains the hollow core during
the deposition. Dissolved H2 gas molecules diffuse outward from
the pores, and macroscopic gas bubbles start to nucleate outside the
pores if the dissolved H2 concentration out of the membrane exceeds
the critical concentration of the supersaturation. However, there are
still questions that need investigation. For instance, why are bubble
sizes uniform in every pore where a nanotube grows? What is the
effect of nickel hydride on nanotube growth? How does the interfa-
cial energy between Ni and polycarbonate play a role in the depo-
sition process? The present study does not answer these questions
but quantitatively shows that the current efficiency drops when
nanotubes are electrodeposited as compared to nanowires.
Figure 12. ͑Color online͒ E–pH diagram with contours of the nanotube wall
thickness. Values in each shaded domain indicate the corresponding range of
tube wall thicknesses. The potential E is measured with respect to a Ni
reference electrode used. The arrows of ͑A͒ and ͑B͒ in the diagram indicate
directions where tube-to-wire transitions occur with a constant potential of
Ϫ1.0 V and a constant pH of 3.4, respectively. The dotted line with a slope
−1
of Ϫ0.059 V ͑pH unit͒ is parallel to the H+/H2 equilibrium potential line.
11i͒. The tube-to-wire transition identified along with ͑A͒, the pH
variation from 1.5 to 3.4 at a constant potential of Ϫ1.0 V, and ͑B͒,
the potential variation from Ϫ0.7 to Ϫ1.0 V at constant pH 3.4 is
focused on in this work.
Calculated cathode surface pH.— Partial current density of Ni
Figure 12 shows the distribution of the nanotube wall thickness
as a function of pH and potential. Blank circles indicate conditions
where experiments and morphological observations were conducted,
as listed in Table III. The wall thickness variations between plots
were linearly interpolated, and the positions having the same values
were connected with straight contour lines. A nanotube wall thick-
ness of 100 nm was assigned to the region where only nanowires
were deposited. Extensive experiments on Ni electrodeposition
made it possible to draw the interpolation or contour lines corre-
sponding to the various nanotube wall thicknesses in the diagram.
Figure 12 indicates that a transition from the nanotube to the nano-
wire occurs in the direction toward the more acidic or less noble
corner. The domain for the nanotube deposition is definable as a
function of the pH and potential. The H+/H2 equilibrium potential
in the template can be written as follows
zF␳L
ipNi
=
͓29͔
MtP
where ␳ is the mass density of Ni ͑8.90 g cm−3͒ and tp is a filling
period ͑s͒ from t = 0 until the time when the deposition current
starts to sharply increase, as presented in Fig. 2. This equation cal-
culates ipNi independently of the pore diameter, which deviates from
the nominal value of 200 nm. The membrane thickness is, however,
quite close to 10 ␮m ͑see Fig. 2͒. Transient information is lost
when using Eq. 29, but the current efficiencies measured in this
work are averaged over the filling periods. Hence, it is reasonable to
estimate the partial current density of Ni based on Eq. 29 rather than
a recorded current divided by the total pore cross-sectional area
−1
line ͓slope: Ϫ0.059 V ͑pH unit͒ ͔ roughly forms a right angle with
based on the nominal values. The H2 partial current density, ipH , is
given by ipNi͑100/␩ − 1͒.
the contours in this figure. This may suggest that nanotube walls
become thinner when the overpotential for Ni deposition decreases,
whereas that for H2 evolution remains constant. The nanotube walls
gradually become thicker through transition path ͑A͒, whereas tran-
sition ͑B͒ shows a sudden increase from Ϫ0.7 to Ϫ0.8 V.
2
Figure 14A and B shows partial current densities of Ni and H2.
The Ni partial current density increases from 75 to more than
100 mA cm−2 by increasing the pH ͑Fig. 14A͒. However, the H2
partial current density decreases with pH. The ipH shows as large as
Measured current efficiency.— In the above calculations, the pH
at the cathode surface in the template is lower than that at the ver-
tical planar cathode surface. Hence, the current efficiency is ex-
pected to be lower when carrying out Ni electrodeposition in the
nanoporous template compared to a vertical planar cathode. Figure
13 shows measured current efficiencies ␩ as functions ͑A͒ of the pH
at a constant potential of Ϫ1.0 V and ͑B͒ of the potential at constant
pH 3.4. Three samples were analyzed for each condition. The results
show that ␩ is approximately 75% at pH 1.5 ͑E = −1.0 V͒ and
increases with pH, resulting in almost 100% at pH greater than 2.0
͑Fig. 13A͒. In Fig. 13B, the measured efficiency shows approxi-
mately 85% at E = −0.7 V and linearly increases to almost 100% at
E = −1.0 V.
2
30 mA cm−2 at pH 1.5 where nanotubes with the thinnest walls are
deposited. As the H2 partial current density increases, the Ni depo-
sition rate becomes smaller even at the same potential of Ϫ1.0 V.
The Ni partial current density increases as the potential becomes
more negative ͑Fig. 14B͒, but the results from the vertical planar
cathode are much larger than expected, especially at E = −0.7 and
Ϫ0.8 V. The H2 partial current density also tends to increase as the
potential becomes more negative toward Ϫ1.0 V. Hence, the Ni
deposition rate is smaller when nanotubes are deposited compared to
a vertical planar cathode. The slope of the Ni partial current density,
with respect to the potential, is clearly steeper than that of the H2
partial current density.
Current efficiencies obtained with a vertical planar cathode ͑size:
1 ϫ 1 cm͒ are also expressed with cross marks as reference
values.30 Current efficiency during the nanotube deposition at pH
Figure 15 shows the local pH values in the templates during the
Ni electrodeposition, calculated with L = 5 ␮m, assuming the
Ј
cathode surface is in the middle of the pores. When the bulk solution
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D366
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
100
80
60
40
20
0
η
Nanowires/
Nanotubes
Nanowires/
Nanowires
Nanowires
-0.9
Nanotubes
1.0
1.5
2.0
2.5
3.0
3.5
4.0
-0.6
-0.7
-0.8
-1.0
-1.1
pH
E / V
Figure 13. Variations in Ni current effi-
ciencies as functions of ͑A͒ pH at a con-
stant potential of Ϫ1.0 V, ͑B͒ potential at a
constant pH of 3.4, and ͑C͒ potential at a
constant pH of 1.5. ͑–᭺–͒ nanoporous
template and ͑--ϫ--͒ vertical planar
cathode.30
(A)
(B)
100
80
60
40
20
0
η
Nanowires/Nanotubes
-0.8 -0.9
-0.6
-0.7
-1.0
-1.1
E / V
(C)
pH is smaller than 3.0 ͑pHb Յ 3.0͒, the pH values at the mouths and
the cathode surface hardly increase from pHb ͑Fig. 15A͒. pHs finally
rose to approximately 5 at pHb 3.4. Figure 15B also shows that the
pHs values in the templates were 1 to 2 lower when compared to a
vertical planar cathode. At E = −0.7 V and pH 1.5 ͑plot not
shown͒, the pHs in the template was almost 1.5 compared to 2–3 for
a vertical planar cathode. These results may explain why H2 evolu-
tion occurs more significantly in the template than on a vertical
planar cathode as shown in Fig. 13. Moreover, pHs tended to be
lower when the nanotubes were deposited in tube-to-wire transition
paths ͑A͒ and ͑B͒.
Fig. 12, that the tube wall thickness decreases as the dotted line is
traced in the positive direction is still observed in Fig. 16. When the
␩ and tube wall thickness distributions are compared, the directions
for them to decrease are roughly consistent in the diagram. This
result clearly shows that H2 evolutions promote nanotube growth.
However, the tube wall thickness variation does not follow the ␩
contours toward the more acidic and less noble corner where the
thinnest wall tubes were observed. This may indicate the complexity
in the deposition process of the nanotubes. The absolute H2 evolu-
tion rate seems also critical for the nanotubes to determine the tube
wall thickness.
Figure 16 shows an E–pH diagram reorganized with the calcu-
lated pHs values. The respective distributions of the measured cur-
rent efficiency and tube wall thickness, which are linearly interpo-
lated, are superimposed in the diagram. As already discussed in Fig.
12, tracing a line parallel to the H+/H2 equilibrium potential in the
positive direction means that the overpotential for Ni electrodeposi-
tion decreases while keeping that for H2 evolution constant. Hence,
it is comprehensible that the ␩ monotonically decreases toward the
more acidic and noble corner along the dotted line in Fig. 16. The
tube wall thickness distribution in Fig. 16 is not significantly differ-
ent from Fig. 12 because pHs hardly increases from the original bulk
values except for that at pHb 3.4. Therefore, the trend, observed in
We showed a clear correlation between the nanotube deposition
and H2 evolution. As predicted by the calculations, the measured
current efficiency in the nanoporous template was lower than a ver-
tical planar cathode. We observed an interesting trend that nanotubes
with thinner walls were electrodeposited as the current efficiency
decreased. The Ni deposition rate was slightly smaller when nano-
tubes grew compared to nanowires. From the calculated results, the
pH values in the template were more than 1 to 2 times smaller than
at the vertical planar cathode surface. The assumptions used for the
calculation need to be more severely examined in the future. We
emphasize that the reactive species concentrations at the cathode
surface in the template tend to be higher than that of a macroscopic
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Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
D367
Figure 14. Ni and H2 partial current den-
sities as functions of ͑A͒ pH at a constant
potential of −1.0 V and ͑B͒ potential at a
constant pH of 3.4. ͑–᭺–͒ nanoporous
template and ͑--ϫ--͒ vertical planar
cathode.30
planar cathode. This understanding is suspected to also be important
in the electrodeposition of Ni–Fe nanowires.56,62,63
planar cathode surface. TEM observed the morphologies of Ni nano-
structures deposited into the template. Nanotubes with thinner walls
were deposited under more acidic and less noble conditions. ICP
spectrometry also allowed the determination of the current effi-
ciency of Ni electrodeposition. The calculations indicated that the
pH was lower at the cathode surface in the template than at the
vertical planar cathode surface. The measured current efficiency was
lower in the template compared to a previous work that employed a
Conclusions
We have investigated H2 evolution rates at the cathode surface
during Ni electrodeposition in polycarbonate membrane templates
with pore diameters of 200 nm under various pH and potential con-
ditions. The calculation model of the pH value at the cathode surface
in the template was presented. The calculations revealed that the
cathode surface pH was lower in the template than at the vertical
7.0
6.0
5.0
pHs
pHs
pHm
pHm
4.0
3.0
2.0
1.0
pHb
pHb
Nanowires/
Nanotubes
Nanowires/
Nanotubes
Nanowires
3.0
Nanowires
1.0
2.0
4.0
-0.6 -0.7 -0.8 -0.9 -1.0 -1.1
pHb
E / V
(A)
(B)
Figure 16. ͑Color online͒ Contours of ͑top͒ the measured current efficiency
and ͑bottom͒ observed tube wall thickness in the E–pHs diagram. The po-
tential E is measured with respect to a Ni reference electrode used. Values in
each shaded domain indicate the corresponding range of current efficiency or
tube wall thickness. The dotted lines are the same line with a slope of
Ϫ0.059 V ͑pH unit͒−1. Only the region where the cathode surface pH was
calculated is shaded.
Figure 15. The calculated local pH values as functions of ͑A͒ pH at a
constant potential of −1.0 V and ͑B͒ potential at a constant pH of 3.4. ͑b͒
pHs: pH at the cathode surface, which is assumed to be 5 ␮m recessed from
the mouths in these calculations; ͑᭺͒ pHm: pH at the mouths; and ͑--ϫ--͒
vertical planar cathode.30 The pHb indicates the bulk pH with a broken line.
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D368
Journal of The Electrochemical Society, 157 ͑6͒ D357-D369 ͑2010͒
t
time s
vertical planar cathode, as expected by the calculations. Moreover,
the current efficiency tended to be lower when nanotubes with thin-
ner walls were electrodeposited. Therefore, we concluded that sig-
nificant H2 evolution sustained electrochemical growth of Ni nano-
tubes in the template.
tp period from the beginning to the end of the second stage in depo-
sition current transient, s
transference number of Ni2+ ions
valence number of ions
tء
z
Greek
Acknowledgment
densification coefficient, cm3 mol−1
2D diffusion layer thickness of species i measured from the tem-
plate surface, cm
␣
Part of this work was supported by the 21st Century Center of
Excellence ͑COE͒ Program and the Ministry of Education, Science
and Culture ͑grant-in-aid for Exploration Research no. 15360402͒.
We thank Professor R. Hagiwara, Professor T. Sakka, Professor S.
Kikuchi, and Professor K. Sumiyama for helpful discussions and
Professor T. Kuzuya for assistance with the TEM observations and
M. Hamura for assistance with the ICP measurements.
␦
i
␩
⌰
current efficiency, %
b
m
Ј
difference of CNi from CNi2+, mol cm−3
2+
␮
␯
mean value, g, %
kinematic viscosity, cm2 s−1
mass density of Ni, 8.90 g cm−3
standard deviation, g, %
␳
␴
ء
ratio of diffusion layer thickness of H+ ions to that of Ni2+ ions
␴
Waseda University assisted in meeting the publication costs of this ar-
ticle.
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