A novel electrochemical sensor for formaldehyde based on palladium nanowire arrays electrode in alkaline media

Article abstract of DOI:10.1016/j.electacta.2012.02.050

A novel electrochemical sensor for the detection of formaldehyde based on palladium (Pd) nanowire (NW) arrays was developed. The Pd NW arrays were obtained via the direct electrodeposition of Pd on a glassy carbon electrode within the pores of an anodized aluminum oxide membrane. The electrocatalytic activity of the Pd NW arrays electrode for formaldehyde detection in alkaline media was then investigated via a series of electrochemical measurements; the results show the very high catalytic activity of the electrode. The formaldehyde oxidation on the Pd NW arrays electrode at +0.03 V, which is more negative than that in previous report. The experimental data further reveal that the electrooxidation of formaldehyde inhibits the formation of the poisonous intermediate, carbon monoxide. The proposed sensor has high sensitivity and fast response to formaldehyde, and the oxidation current has a linear relationship with the formaldehyde concentration in the 2 μM to 1 mM range (R = 0.9982). The detection limit was 0.5 μM (S/N = 3). The sensor has high sensitivity and good selectivity.

Full text of DOI:10.1016/j.electacta.2012.02.050

Electrochimica Acta 68 (2012) 172–177
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Electrochimica Acta
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A novel electrochemical sensor for formaldehyde based on palladium nanowire
arrays electrode in alkaline media
Yan Zhanga, Min Zhangb, Zhiquan Caib, Meiqiong Chenb, Faliang Chengb,∗
a Department of Chemistry, Anhui University, Hefei 230039, China
b Center of biosensor research, Dongguan University of Technology, Dongguan, Guangdong 523106, China
a r t i c l e i n f o
a b s t r a c t
Article history:
A novel electrochemical sensor for the detection of formaldehyde based on palladium (Pd) nanowire (NW)
arrays was developed. The Pd NW arrays were obtained via the direct electrodeposition of Pd on a glassy
carbon electrode within the pores of an anodized aluminum oxide membrane. The electrocatalytic activity
of the Pd NW arrays electrode for formaldehyde detection in alkaline media was then investigated via a
series of electrochemical measurements; the results show the very high catalytic activity of the electrode.
The formaldehyde oxidation on the Pd NW arrays electrode at +0.03 V, which is more negative than
that in previous report. The experimental data further reveal that the electrooxidation of formaldehyde
inhibits the formation of the poisonous intermediate, carbon monoxide. The proposed sensor has high
sensitivity and fast response to formaldehyde, and the oxidation current has a linear relationship with
the formaldehyde concentration in the 2 ␮M to 1 mM range (R = 0.9982). The detection limit was 0.5 ␮M
(S/N = 3). The sensor has high sensitivity and good selectivity.
Received 19 September 2011
Received in revised form 14 February 2012
Accepted 15 February 2012
Available online 25 February 2012
Keywords:
Pd nanowire (Pd NW) arrays
Formaldehyde
Sensor
© 2012 Elsevier Ltd. All rights reserved.
1. Introduction
methods include spectrophotometry [7], gas chromatography [8],
high-performance liquid chromatography [9], and the use of sen-
Formaldehyde is an important chemical widely applied in the
manufacture of building materials and numerous household prod-
ucts [1–4]. It is found in foods (e.g., fruits, vegetables, and meat),
beverages (e.g., beer and juices), and human biological fluids [5,6].
Recently, a new risk factor associated with formaldehyde and the
process of ozonation has been revealed. Ozonation is a process used
in potable water pretreatment involving the disinfection of water
by removing iron and manganese, thereby eliminating unpleasant
flavors and odors. Several kinds of toxic and mutagenic aldehydes
(mostly formaldehyde) are generated as a result of the reaction of
ozone with traces of humus [2,5].
Formaldehyde is found in more than 2000 products, to which
many industrial workers are exposed on a daily basis. Chronic
exposure to this chemical via ingestion leads to adverse gastroin-
testinal effects. Hence, the United States Environmental Protection
Agency has set the daily intake of formaldehyde to 0.2 mg/kg body
weight [6]. The International Agency for Research on Cancer has
also classified formaldehyde as a human carcinogen [6]. These
factors underscore the need for rapid, sensitive methods for the
monitoring of trace concentrations of formaldehyde.
sors [2]. Compared with spectral and chromatographic analysis,
sensors are low cost, simple, sensitive, and present operation.
Sensors for the determination of formaldehyde concentration
have been widely researched. Herschkovitz et al. [10] reported
a novel formaldehyde detection method based on the coupling
of a biosensor measuring device and a flow-injection system,
using the enzyme formaldehyde dehydrogenase and a chemically
modified Os(bpy)2-poly(vinylpyridine) (POs-EA) screen-printed
electrode. The as-produced sensor is low cost and has high selec-
tivity, long-term stability, and simplicity of design and operation.
Zhou et al. [13] introduced the electrodeposition of a nanostruc-
tured platinum–palladium (Pt–Pd) alloy in a Nafion film-coated
glassy carbon electrode (GCE). The proposed alloy sensor not only
possesses a broad linear range, good reproducibility, and high
sensitivity, but also exhibits a synergistic effect that minimizes poi-
son formation. Compared with biosensors, electrochemical sensors
have a lower detection limit and a wider linear range. However,
they have lower sensitivity and selectivity and a longer response
time.
In recent years, electrochemical sensors have been widely
applied in the determination of formaldehyde concentration
[10–13]. Amperometric sensors in the potentiostatic mode using
noble metals as electrode nanomaterials are also used for formalde-
hyde detection [3,14]. Metal nanomaterials have high effective
surface areas and extraordinary electron-transport properties.
Their use as electrochemical interfaces provides a rapid current
Various analytical methods that determine formaldehyde in air,
food, water, and wood have been reported. The most common
∗
Corresponding author. Fax: +86 769 22605545.
E-mail address: chengfl@dgut.edu.cn (F.L. Cheng).
0013-4686/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2012.02.050

Y. Zhang et al. / Electrochimica Acta 68 (2012) 172–177
173
Fig. 1. (A) Typical SEM images of AAO template; (B) facet-section of Pd NW arrays.
response and high-detection sensitivity. Consequently, the elec-
2.2. Apparatuses
tron transfer between the electrode and the probe molecules is
accelerated [15].
The electrochemical experiments were performed on a PAR-
STAT 2273 electrochemical workstation (Princeton, USA) at 25 ◦C.
A standard three-electrode system was used during the experi-
ment. Pt and Ag/AgCl (saturated KCl) electrodes were used as the
counter and reference electrodes, respectively. Scanning electron
microscopy (SEM) analyses were performed using a Hitachi S-5200.
Energy-dispersive X-ray spectroscopy (EDX) was conducted on an
Oxford ISIS-300 EDX system.
Pt and Pd nanomaterials have high catalytic activities in the elec-
trooxidation of small organic molecules. They are used as catalysts
in many chemical reactions, such as alcohol oxidation reactions in
fuel cells [16–18], electroanalytical processes [19,20], and sensor
reactions [21–23]. The precious metal Pt [20,24,25] has been com-
monly used as the anode material in formaldehyde electrochemical
sensors. However, poisonous chemisorbed species have been gen-
erated on Pt and Pt-based catalysts during the electrooxidation of
formaldehyde. Pd is considered a substitute for Pt because of its
equally high catalytic activity, lower cost, and reduced generation
of poisonous substances [26,27].
Nanomaterials (nanoparticles, nanotubes, nanowires, and so
on) are fabricated via a variety of preparative strategies [28–34].
The analytical applications of nanoparticles have been extensively
explored for quite some time. However, studies related to the
application of nanowires have been scarce. With the continu-
ous advancements in nanotechnology, nanowires are attracting
increased attention and interest because of their higher active sur-
face areas compared with nanoparticles [35,36]. Therefore, the
exploration of new applications for metal nanowires is a wor-
thy endeavor. In the current paper, Pd nanowire (NW) arrays
were prepared via anodized aluminum oxide (AAO) template
electrodeposition. The as-prepared Pd NW arrays were used as
enhanced electrochemical sensing electrodes for the measure-
ment of formaldehyde. The experimental data reveal that the
modified electrode has a very high catalytic activity for formalde-
hyde and effectively minimizes the formation of poisonous
intermediates.
2.3. Preparation of the AAO templates
Porous AAO templates were fabricated via a two-step anodiza-
tion process in our laboratory [37,38]. Prior to anodization,
high-purity aluminum foils (99.999%) were annealed in a vacuum
at 500 ◦C for 4 h and were degreased in acetone. Anodization was
performed in a 0.3 M H2CO4 solution for 2 h. The alumina layer
was removed using a mixture of H3PO4 (6 wt%) and chromic acid
(1.8 wt%). The aluminum foil was reoxidized under the same con-
ditions for 6 h. The AAO template was etched in a saturated SnCl4
solution to remove the remaining aluminum. The AAO template
was again treated with 5 wt% H3PO4 at 25 ◦C for 30 min to remove
the barrier layer on the other side of the aluminum foil.
2.4. Preparation of Pd NW arrays electrode
The Pd NW arrays were prepared via an AAO template elec-
trodeposition method, as described in our previous work [23,39].
A GCE was polished and thoroughly cleaned, and a piece of the
as-prepared AAO template was attached to the polished surface
of the GCE. Electrodeposition was performed in an aqueous solu-
tion containing Pd(NH3)4Cl2 + NH4Cl. The pH value of the solution
was adjusted to 8 using NH3·H2O. The Pd NW arrays electrode was
prepared at −0.7 V, finally dipped in a 2 M NaOH solution for 1 h
to completely remove the AAO, and washed with distilled water
several times.
2. Experimental
2.1. Materials and reagents
High-purity aluminum foils (99.999%), formaldehyde (36–38%),
acetone (99.5%), SnCl4·5H2O, phosphoric acid (H3PO4, 85%), and
chromic trioxide (99%) were purchased from the Guangzhou
Chemical Reagents Company (Guangzhou, China). K3Fe(CN)6
and K4Fe(CN)6 were obtained from Sigma–Aldrich (USA).
Pd(NH3)4Cl2 + NH4Cl was obtained from the Hong Kong Yuhua
Noble Metal Chemical Engineering Electroplating Company (Hong
Kong, China). All chemicals were analytical reagent grade, and all
solutions were prepared using double-distilled water.
3. Results and discussion
3.1. Characterization
Fig. 1A shows a typical SEM image of the prepared AAO template,
which exhibited pore arrays that were nearly aligned. The porous
alumina structure consisted of cylindrical hexagonal cells with an

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Y. Zhang et al. / Electrochimica Acta 68 (2012) 172–177
Fig. 4. CVs of 5 mM formaldehyde in 0.1 M KOH solution at bare electrode in the
absence and presence of formaldehyde (a and b), respectively; at Pd NW arrays
electrode in the absence and presence of formaldehyde (c and d), respectively. Scan
rate: 100 mV/s.
Fig. 2. Energy-dispersive X-ray spectroscopy (EDX) of Pd NW arrays.
clearly had a lower electron-transfer resistance than the bare GCE,
average diameter of approximately 50 nm. The interface distance
of each central pore was approximately 50 nm. Fig. 1B shows the
typical SEM images of the Pd NW arrays, where the AAO template
was completely dissolved. A large amount of Pd NW arrays was
assembled in the AAO template. The straw shape of the Pd NW
arrays exhibited a good orientation, which was perpendicular to
the surface of the substrate. The diameters of the Pd NW arrays
were approximately 50 nm, retaining the size and nearly cylindrical
shape of the AAO template pores. Fig. 2 shows the EDX results of
the Pd NW arrays. The major peaks correspond to Pd, showing that
the AAO template was removed after treatment in the KOH solution
and that the Pd NW arrays were indeed fabricated.
The impedance spectra of the bare GCE and the Pd NW arrays
electrode a 5 mM Fe(CN)63−/4− + 0.1 M KCl solution are shown
in Fig. 3(a) and (b), respectively; the frequency of the open-
circuit potential varied from 0.1 Hz to 100 kHz. Electrochemical
impedance spectroscopy (EIS) is an effective method of determin-
ing the interfacial properties of a modified electrode. It is often used
to elucidate the chemical transformations and processes associated
with conductive supports [40,41]. EIS curves consist of semicircular
and linear parts. At high frequencies, the semicircular part corre-
sponds to the electron-transfer limited process, and its diameter is
equal to the electron-transfer resistance. This resistance controls
the electron-transfer kinetics of the redox probe at the electrode
interface [41,42]. In the present study, the Pd NW arrays electrode
implying that the Pd NW arrays play an important role in providing
3−/4−
the conducting bridges for the charge transfer of Fe(CN)6
.
3.2. Electrochemistry of the sensor
The cyclic voltammetry (CV) curves of formaldehyde oxidation
on the bare GCE and the Pd NW arrays electrode are shown in Fig. 4.
Fig. 4(a) and (c) show the CV of the bare and Pd NW arrays electrode
in a 0.1 M KOH solution. The background current on the Pd NW
arrays electrode (Fig. 4(c)) was much higher than that on the bare
electrode, probably because of the larger surface area of the Pd NW
arrays electrode [26,43]. Pd oxides were generated for the positive
scan, and a sharp reduction in the current peak at approximately
−0.35 V for the reverse scan was due to the reduction of the Pd
oxides formed during the positive potential sweep.
After the addition of 5 mM formaldehyde to the 0.1 M KOH solu-
tion, no current peak appeared for the bare GCE (Fig. 4(b)). This
finding indicates that the bare GCE had no electrocatalytic activ-
ity toward formaldehyde oxidation. The CV curve of formaldehyde
oxidation on the Pd NW arrays electrode is shown in Fig. 4(d).
The oxidation was characterized by two well-defined current peaks
on the positive and reverse scans. An oxidation peak observed at
approximately +0.05 V corresponds to the oxidation of formalde-
hyde on the Pd NW arrays electrode. Another oxidation current
peak found at approximately −0.3 V is ascribed to the further anodic
oxidation of the intermediates formed during the positive potential
scan. Compared with previous reports (Table 1), the peak potential
(+0.05 V) for the oxidation of formaldehyde in the current study is
much lower, indicating that the sensor has superior electrocatalytic
activity for formaldehyde.
The CV curves for formaldehyde oxidation on the Pd
nanoparticle-modified and Pd NW arrays electrode are shown in
Fig. 5(a) and (b), respectively. The oxidation peak current was 45 ␮A
at +0.05 V on the Pd nanoparticle-modified electrode and 157 ␮A
at +0.05 V on the Pd NW arrays electrode. The oxidation current
on the NW arrays electrode is three times higher than that on the
nanoparticle-modified electrode, indicating that the Pd NW arrays
electrode have higher activity than the nanoparticle-modified one
for formaldehyde oxidation in alkaline media. A similar report for
the comparison of the oxidation peak currents on Pd nanoparticles
and Pd nanowires was found for the oxidation of formic acid [45].
In the current work, the superior activity may be related to the fast
electronic conduction and good orientation of the perpendicular
array structure.
Fig. 3. EIS of bare GCE (a) and Pd NW arrays electrode (b) in a 0.1 M KCl containing
5 mM Fe(CN)63−/4−. Applied frequency was from 0.1 Hz to 100 kHz.

Y. Zhang et al. / Electrochimica Acta 68 (2012) 172–177
175
Table 1
Comparison of the working potential, linear range, detection limit, correlation coefficient of our sensor with other electrochemical sensors from the previous methods.
Electrode fabrication
Detection potential
Linearity range
20–100 mM
Detection limit
–
R
Ref.
Pd NP/CILE/GCE
Pt–SnO2/sol–gel/GCE
Pd NP/TiO2/GCE
Pt–Pd NP/Nafion/GCE
Pt NP/PANI/MWNCS/GCE
Pd NW/GCE
0.15 V
0.6 V
−0.4 V
0.57 V
0.3 V
[26]
[44]
[43]
[13]
[24]
0–17.7 mM
15 ␮M
3 ␮M
0.046 ppM
0.5 ␮M
10 ␮M to 1 mM
1 ppM to 1 mM
2 ␮M to 1 mM
0.9983
0.999
0.9982
0.05 V
Our work
Fig. 5. CVs of 5 mM formaldehyde in 0.1 M KOH solution at Pd nanoparticle-
modified electrode (a) and Pd NW arrays electrode (b). Scan rate: 100 mV/s.
Fig. 6. Chronoamperometry of the Pd NW arrays electrode in a solution of 5 mM
HCHO + 0.1 M KOH. The electrode potentials were +0.05 V (a), 0.00 V (b) and +0.3 V
(c), respectively.
The oxidation mechanism of small organic molecules on Pt–Pd-
based catalysts follows a dual pathway [46–49]. According to
Safavi et al. [26], formaldehyde is oxidized to CO2 via two paral-
lel pathways (Scheme 1). One is the indirect electrooxidation of
formaldehyde via the formation of a chemisorbed CO intermediate,
whereas the other is a direct electrooxidation via the formation of
active adsorbed intermediates. The presence of oxidation peaks in
the forward and reverse scans indicates that formaldehyde oxida-
tion followed a dual pathway. The poisonous intermediate COads
requires a higher electrode potential to be further oxidized into
CO2. However, the oxidation of formaldehyde on the Pd NW arrays
electrode had a lower potential. Hence, the electrochemical oxi-
dation of formaldehyde probably occurred mainly via the direct
pathway.
Chronoamperometry was used to further examine the electro-
catalytic activity of the formaldehyde sensor at different electrode
potentials (Fig. 6). Fig. 4 shows that the oxidation of formalde-
hyde on the Pd NW arrays electrode occurred at low potential
regions. Therefore, the applied potentials of +0.05, 0.00, and +0.30 V
(Fig. 6(a)–(c)) were chosen for the determination of the formalde-
hyde concentration. We can see that the current decays quickly to
a steady-state value. The oxidation current at +0.05 V was the high-
est compared with those at 0.00 and +0.30 V. Hence, the operating
potential of +0.03 V was chosen for the formaldehyde sensor.
The kinetics of formaldehyde oxidation was also investigated.
Fig. 7 shows the CVs of the proposed sensor in the 5 mM formalde-
hyde + 0.1 M KOH solution. The scan rate was increased from
10 mV/s to 300 mV/s. The anodic peak current for the positive
scan was linearly proportional to the square root of the scan rate
(R = 0.9934), indicating that the electrode process was controlled
via diffusion.
3.3. Amperometric detection of formaldehyde
The typical current–time plot of the sensor with successive
injection of 0.01 M formaldehyde is given in Fig. 8A. The work-
ing potential was set at +0.05 V, where the amperometric response
reached the maximum value (Fig. 4). The sensor rapidly responded
and reached a steady state within 5 s after the formaldehyde was
added into solution (as insert in Fig. 8A), demonstrating that the
sensor had a high sensitivity to formaldehyde. The fast response
time and high sensitivity can also be ascribed to the well-defined
Fig. 7. CVs of 5 mM formaldehyde in 0.1 M KOH solution on the Pd NW arrays elec-
trode with different scan rates: 10, 20, 40, 60, 80,100, 150, 200, 250, 300 mV/s (inset:
the relation of the anodic peak current for the positive scan with square root of scan
rate).
Scheme 1. Schematic representation of formaldehyde oxidation.

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Y. Zhang et al. / Electrochimica Acta 68 (2012) 172–177
Fig. 10. Amperometric response of Pd NW arrays electrode to (a) 5 mM formalde-
hyde, (b) 5 mM acetaldehyde, (c) 5 mM ethanol and (d) 5 mM 1-propanol in 0.1 M
KOH solution. The applied potential is +0.05 V.
Fig. 8. (A) Current–time response of the electrochemical sensor for successive addi-
tion of 0.01 M formaldehyde in N2-saturated 0.1 M KOH. The applied potential is
+0.05 V (inset: amplification of part with low formaldehyde concentrations). (B)
Calibration curve of steady-state current vs. the concentration of formaldehyde in
N2-saturated 0.1 M KOH. The applied potential is +0.05 V.
the interfering species was investigated by measuring the amper-
ometric response to the successive addition the same volume of
5 mM formaldehyde (a), 5 mM acetaldehyde (b), 5 mM ethanol (c),
and 5 mM 1-propanol (d) at the +0.05 V potential (Fig. 10). No obvi-
ous current changes were observed when acetaldehyde, ethanol,
and 1-propanol were added. However, a fast current response
occurred after the addition of formaldehyde. These results indi-
cate that acetaldehyde, ethanol, and 1-propanol showed almost no
interference to formaldehyde detection.
surface area. Fig. 8B shows the calibration curve of the ampero-
metric response. A good linear relationship was realized within the
formaldehyde concentration range of 2 ␮M to 1 mM, with a corre-
lation coefficient of 0.9982. The detection limit for formaldehyde
was estimated at 0.5 ␮M, at a signal-to-noise ratio of 3.
The analytical performance of the prepared sensor was com-
pared with those of other chemosensors (Table 1) and biosensors
(Table 2). Through comparison and analysis, we the proposed sen-
sor was shown to exhibit good performance in terms of a low
oxidation potential, a wide linear range, and good sensitivity, which
may be the result of the fast electronic conduction and good orien-
tation of the perpendicular arrays structure.
3.5. Reproducibility and stability of the sensor
The relative standard deviation (RSD) of the sensor response
to 5 mM formaldehyde was 1.1% for 20 successive measure-
ments, indicating good repeatability. The reproducibility was
evaluated from the response of 10 electrodes fabricated under the
same conditions to 5 mM formaldehyde. The RSD obtained was
7.8%.
3.4. Sensor selectivity
Long-term stability is an important parameter in evaluating the
performance of a sensor. The stability of the formaldehyde sensor
was determined using CV by measuring the decrease in the voltam-
metric peak current during potential cycling. The response of the
electrodes to 30 cycles in the potential range of −0.7 to 0.7 V is
shown in Fig. 11. The peaks on the first scans are higher than those
on the subsequent scans. However, starting from the third scan, the
catalytic activity of the Pd NW arrays electrode only slightly var-
ied. The catalytic current was reduced to 80.15% after 30 tests. The
electrode was kept at 4 ◦C in a refrigerator. Afterward, the catalytic
Interferences from electroactive compounds such as acetalde-
hyde, ethanol, and 1-propanol, among others, can cause problems
in the accurate determination of formaldehyde. The CVs for the Pd
NW arrays electrode in the presence of 5 mM formaldehyde, 5 mM
acetaldehyde, 5 mM ethanol, and 5 mM 1-propanol are shown in
Fig. 9(a)–(d), respectively. The sharp current peak at approximately
+0.05 V in Fig. 9(a) corresponds to the oxidation current peak of
formaldehyde. The selectivity of the formaldehyde sensor against
Fig. 9. CVs for Pd NW arrays electrode in (a) 5 mM formaldehyde + 0.1 M KOH,
(b) 5 mM acetaldehyde + 0.1 M KOH, (c) 5 mM ethanol + 0.1 M KOH and (d) 5 mM
1-propanol + 0.1 M KOH. Scan rate: 100 mV/s.
Fig. 11. CVs of formaldehyde oxidation on the Pd NW arrays electrode in 0.1 M KOH
solution containing 5 mM formaldehyde. Scan rate: 100 mV/s.

Y. Zhang et al. / Electrochimica Acta 68 (2012) 172–177
177
Table 2
Comparison of the linear range, detection limit, sensitivity of our sensor with other biosensors from the previous methods.
Linearity range
Detection limit
Sensitivity
Ref.
Bio-functionalized Si/SiO2/Si3N4
FDH-ECH-Sepharose (in solution)
FDH-ECH-Sepharose (in air)
Pd NW/GCE
10 ␮M to 25 mM
10 ␮M to 0.1 mM
0.05–2 ppm
10 ␮M
5 ␮M
50 ppb
0.5 ␮M
31 mA M−1 cm−2
0.24 ␮S/␮M
[2]
[50]
[50]
20 ␮S/ppm
2 ␮M to 1 mM
1.36 mA M−1 cm−2
Our work
current retained 90.7% of the initial value after 7 d. The signal cur-
rent also retained more than 85% of its initial value after 2 months.
The decreased current values may be attributed to the generation
of poisonous organic compounds as well as to the consumption of
formaldehyde.
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219.
4. Conclusions
Pd NW arrays were successfully prepared via a template-
synthesis method by direct electrodeposition. The procedure
represents a promising route for the synthesis of other materials
with well-defined structures. Compared with Pd nanoparticles, the
Pd NW arrays exhibited a higher catalytic activity for formaldehyde
detection. The mechanism of formaldehyde oxidation on the Pd NW
arrays electrode was also investigated. The result shows that the
fabricated sensor can effectively minimize the formation of poi-
sonous intermediates. Furthermore, the fabricated formaldehyde
sensor effectively detected formaldehyde in the presence of inter-
ferences such as acetaldehyde, ethanol, and 1-propanol. Overall,
the sensor has potential applications in practical analyses.
Acknowledgments
This work was supported by the National Natural Science Foun-
dation of China (No. 20975020), the Natural Science Foundations
of Guangdong Province (No. 10151170003000000), Technology
Project of Guangdong Province (No. 2009B030802001) and Tech-
nology Project of Dongguan (No. 201010824000005).
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