Selective conversion of lactic acid into acrylic acid over hydroxyapatite catalysts

Article abstract of DOI:10.1016/j.catcom.2014.01.009

Lactic acid conversion into acrylic acid was carried out over Ca-HAP catalysts at 623 K. Stoichiometric Ca-HAP catalyst gave a high acrylic acid yield of about 60 C-%. Furthermore, non-stoichiometric calcium deficient Ca-HAP catalysts containing the specific amounts of sodium ions, which were prepared under hydrothermal conditions, exhibited remarkably high acrylic acid yields of about 80 C-%. In contrast, non-stoichiometric Ca-HAP catalysts with vacancy sites and Ca-HAP catalysts with excess amounts of sodium species showed relatively low acrylic acid yields and high selectivities into acetaldehyde and 2,3-pentanedione.

Full text of DOI:10.1016/j.catcom.2014.01.009

Catalysis Communications 48 (2014) 5–10
Contents lists available at ScienceDirect
Catalysis Communications
journal homepage: www.elsevier.com/locate/catcom
Short Communication
Selective conversion of lactic acid into acrylic acid over
hydroxyapatite catalysts
Yumiko Matsuura, Ayumu Onda, Kazumichi Yanagisawa
Research Laboratory of Hydrothermal Chemistry, Faculty of Science, Kochi University, 2-17-47 Asakurahonmachi, Kochi 780-8073, Japan
a r t i c l e i n f o
a b s t r a c t
Article history:
Lactic acid conversion into acrylic acid was carried out over Ca-HAP catalysts at 623 K. Stoichiometric Ca-HAP cat-
alyst gave a high acrylic acid yield of about 60 C-%. Furthermore, non-stoichiometric calcium deficient Ca-HAP
catalysts containing the specific amounts of sodium ions, which were prepared under hydrothermal conditions,
exhibited remarkably high acrylic acid yields of about 80 C-%. In contrast, non-stoichiometric Ca-HAP catalysts
with vacancy sites and Ca-HAP catalysts with excess amounts of sodium species showed relatively low acrylic
acid yields and high selectivities into acetaldehyde and 2,3-pentanedione.
Received 27 September 2013
Received in revised form 15 December 2013
Accepted 10 January 2014
Available online 19 January 2014
Keywords:
©
2014 Elsevier B.V. All rights reserved.
Hydroxyapatite
Acrylic acid
Lactic acid
Dehydration
1
. Introduction
those over the previously reported catalysts [22]. And, Ghantani et al.
also reported about the advantages of Ca-HAP catalysts for the acrylic
acid production from lactic acid [23]. So, in the present study, we pro-
pose that Ca-HAP catalysts with moderate Ca/P atomic ratios and specif-
ic amount of sodium ions in their structure show the highly selective
conversion of lactic acid into acrylic acid.
Acrylic acid is widely used as a principal raw feedstock for functional
materials, such as water absorbent polymer. At present, acrylic acid is
mainly produced by the two-step partial oxidation of propylene derived
from fossil resources in the petrochemical industry. Meanwhile, the
shortage of petroleum and the prevalence of global warming have driv-
en researchers to find new processes for acrylic acid production from
sustainable raw materials. Recently, biomass resources have been
attracting attention as an alternative to fossil resources [1]. Lactic acid
is one of a number of commodity chemicals produced from renewable
biomass resources [2]. Acrylic acid can be formed by a simple dehy-
dration of lactic acid, through the elimination of one water molecule
2. Experimental
2.1. Catalysis preparation
Ca-HAP_NaOH catalysts were prepared by a hydrothermal method
using sodium hydroxide as an alkaline source. An aqueous solution con-
taining calcium nitrate was added into an aqueous solution containing
phosphoric acid and sodium hydroxide, and then, the resultant suspen-
sion was treated under hydrothermal conditions at 383 K for 14 h and
washed with distilled water. Ca-HAP_NH3 catalysts were prepared by
almost the same procedure as the Ca-HAP_NaOH catalysts, except for
using ammonia aqueous solution as an alkali source. NaOH/Ca-HAP
(1.68)_NH3 catalyst was prepared by the impregnation method using
[
3]. Some researchers have reported about the dehydration of lactic
acid to acrylic acid under supercritical water [4–6] and gas phase
7–12] at 573–673 K. In most of those reports, catalysts with both
[
acid and basic sites, such as modified NaY zeolite catalysts, were
used. However, the acrylic acid yields were not sufficient and were
limited by side reactions as shown in Scheme 1 [13].
Calcium phosphate hydroxyapatite (Ca-HAP) catalysts have a high
thermal stability and affinity for organic compounds. The stoichiometric
2
Ca-HAP (1.67)_NH3. HAP-300 (Taihei Chemical), SiO (CaRiACT G-6,
form of Ca-HAP catalyst is Ca10(PO
4
)
6
(OH)
2
with the Ca/P atomic ratio
Fuji Silysia) and MgO (JRC-MGO-4 500A, The Catalyst Society of Japan)
were also used. All catalysts were pelletized and crushed to the desired
size and pretreated at 773 K for 3 h under Ar.
equal to 1.67. Ca-HAP catalysts have structural flexibility, and calcium
ions and phosphate ions in its structure can be replaced by various
kinds of cations and anions [14,15]. The substitution of component
ions resulted in a change in the acid–base or bifunctional catalytic prop-
erties of Ca-HAP catalysts [16–19]. Moreover, the acid–base catalytic
properties of Ca-HAP catalysts differed according to its Ca/P atomic
ratio, ranging from 1.5 to 1.67 [20,21].
2.2. Characterization
The X-ray powder diffraction (XRD) measurements of the samples
were carried out on a Rigaku Ultima IV with Cu Kα radiation at 40 kV
and 20 mA. The chemical composition was determined by inductively
couple of plasma (ICP) spectroscopy with ICPE-9000 (Shimadzu). ICP
Recently, we reported that Ca-HAP catalysts showed a higher acrylic
acid yield in the conversion of lactic acid and a longer catalyst age than
1566-7367/$ – see front matter © 2014 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.catcom.2014.01.009

6
Y. Matsuura et al. / Catalysis Communications 48 (2014) 5–10
2.3. Dehydration of lactic acid
The typical catalytic conversions of lactic acid to acrylic acid were
carried in a fixed-bed continuous-flow reactor under atmospheric
pressure. Before reaction, the pelletized catalysts (0.2–1.0 g) were
pretreated at 773 K for 3 h in Ar flow and cooled to 623 K. 38 wt.% lactic
−
1
acid aqueous solution (1.2 mL h ) was introduced into the reactor by a
−
1
microsyringe pump with 40 mL min
of Ar gas. The products were
condensed in an ice–water trap. The collected liquid products were an-
alyzed on a GC-FID (Shimadzu GC14B) with a Stabilwax-DA column.
And, after the dilutions of the collected liquid products with distilled
water into 50 mL, they were analyzed using an HPLC (HITACHI LC-
2000 with UV detector) with a Shodex KC811 column, and a total organ-
ic carbon analyzer (TOC2000, Shimadzu). The gas product of acetalde-
hyde was determined by on-line GC-TCD (Shimadzu GC8A) with a
Gaskuropack 54. CO and CO were non-quantitatively analyzed by on-
2
line GC-TCD. The lactic acid conversion and product yield were calculat-
ed based on the following equations:
Lactic acid conversion ð%Þ ¼ ð1–mol of unreacted lactic acid=mol of
introduced lactic acidÞ ꢀ 100
Product yieldðC‐%Þ ¼ ðC mol of product=C mol of introduced lactic
acidÞ ꢀ 100:
Scheme 1. Main conversion pathways of lactic acid in the gas phase reaction [13].
The mass balance (C-%) was estimated to be a sum of TOC (C-%) and
vaporized acetaldehyde yield (C-%). The reproducibility errors of lactic
acid conversions, product yields, and mass balances were less than ± 4%.
measurement error for Ca/P atomic ratio was ± 0.015. The BET specific
surface areas of the samples were determined by N adsorption using a
BELSORP-max instrument. The acid–base properties were evaluated by
NH -TPD and CO -TPD. After the pretreatment at 773 K, the sample was
exposed under the gas mixture (20 kPa) of 10% CO /He or 10% NH /He
at 353 K for 0.5 h and evacuated under vacuum at 353 K. Then, the tem-
perature was raised from 353 K to 773 K at a ramp rate of 5 ºC/min. CO
m/e = 44) or NH (m/e = 15) was detected by quadrupole mass
spectrometery (ANELVA, M-201QA-TDM). The acid and basic surface
densities were estimated from the peak areas of TPD profiles from 360
to 700 K, using the specific surface areas of samples and the pulse
calibrations.
2
3. Results and discussion
3
2
2
3
Fig. 1 shows XRD patterns of the prepared Ca-HAP catalysts and
HAP-300. All XRD patterns were assigned to Ca10(PO ) (OH) phase
4 6 2
2
(PDF#9-0432) with single phase. Table 1 shows chemical compositions
determined by ICP analysis, the Ca/P atomic ratios are also shown in pa-
renthesis in catalyst names and the alkali sources are noted at the tails of
the names. The bulk atomic ratios were controlled by Ca/P atomic ratios
of mother solutions. In the cases of Ca-HAP_NaOH catalysts, the Ca/P
atomic ratios were 1.55 and 1.61 which were significantly less than
(
3
Fig. 1. XRD patterns of (a) HAP-300 and as-synthesized Ca-HAP catalysts using (a) ammonia and (b) NaOH as alkali source.

Y. Matsuura et al. / Catalysis Communications 48 (2014) 5–10
7
Table 1
Characteristic properties of Ca-HAP catalysts.
Catalysts
Ca/P (atomic ratio)
(Ca + Na)/P (atomic ratio)
Na (wt.%)
Density (μmol m−2)
Acid sites
Basic sites
Ca-HAP (1.61)_NH3
Ca-HAP (1.67)_NH3
Ca-HAP (1.55)_NaOH
Ca-HAP (1.61)_NaOH
NaOH/CaHAP (1.68)_NH3
HAP-300
1.61
1.67
1.55
1.61
1.68
1.66
1.61
1.67
1.65
1.66
1.76
1.66
0.0
0.0
1.4
0.6
1.2
0.0
0.107
0.113
0.047
0.023
0.002
0.156
0.020
0.059
0.045
0.065
0.050
0.042
+
the stoichiometric ratio equal to 1.67, but the specific amounts of sodi-
um ions were detected. The (Ca + Na)/P atomic ratios were 1.65 and
compensating interstitial H ions was energetically favorable, and that
+
the H ion is attached to the OH group to form an H
Based on this first principle calculation investigation, the Ca-HAP_NaOH
catalysts could be expressed as Ca10 − nNa (PO (OH)2 − n(H O)
And, to correct the electrical imbalance resulting from substitution of
ions by Na ions, equivalent amounts of H ions to Na ions
might also be contained in the Ca-HAP catalysts.
2
O group [27].
1
.66 which were close to the stoichiometric ratio. The Ca/P atomic ratios
of Ca-HAP (1.67)_NH3 and HAP-300 were close to the stoichiometric
ratio, but Ca-HAP (1.61)_NH3 had a non-stoichiometric Ca/P atomic
ratio. In addition, NaOH/Ca-HAP (1.68)_NH3 had 1.2 wt.% of sodium
ions and almost the same Ca/P atomic ratio as that of the Ca-HAP
n
)
4 6
2
n
.
2
+
+
+
+
Ca
(
1.67)_NH3 support.
The TPD profiles in Fig. 3 were normalized by surface area. In the
Next, in order to check the existence of vacancy sites in the apatite
2
CO -TPD, the Ca-HAP catalysts showed two peaks around 420 and
structure, the Ca-HAP catalysts were heated at 1273 K and measured
by XRD [24,25]. As shown in Fig. 2, the structures of HAP-300 and Ca-
HAP (1.67)_NH3 catalysts remained unchanged, which indicated that
HAP-300 and Ca-HAP (1.67)_NH3 catalysts had the apatite structure
without vacancy sites. In contrast, Ca-HAP (1.61)_NH3 catalyst was
500 K. The NaOH/Ca-HAP (1.68)_NaOH catalyst showed three peaks
around 400 K, 500 K and 730 k, which indicated that it had relatively
strong basic sites. As shown in Table 1, densities of total basic sites
increased in the following order:
Ca‐HAP ð1:61Þ NH3 bHAP−300 bCa‐HAP ð1:55Þ
ꢁNaOH
decomposed to β-TCP (PDF#9-0169) and Ca10(PO
)
4 6
(OH)
2
phases by
ꢁ
the calcination treatment, which suggested that Ca-HAP (1.61)_NH3 cat-
+
bNaOH=Ca‐HAP ð1:68Þ
ꢁNH3b
alyst had calcium-deficient vacancy-sites. It may gain H ions or lose
−
OH ions to maintain charge balance [26].
Ca‐HAP ð1:67Þ NH3 bCa‐HAP ð1:61Þ
ꢁNaOH:
ꢁ
On the other hand, the Ca-HAP_NaOH catalysts also had low Ca/P
atomic ratios, however they remained almost unchanged during
the calcination at 1273 K although a very small unknown peak was
observed in Ca-HAP (1.55)_NaOH catalyst only after the calcination.
These results importantly indicated that most of the calcium-
deficient sites in the structures of Ca-HAP_NaOH catalysts were occu-
3
As shown in Fig. 3(b), all Ca-HAP catalysts showed a NH desorption
peak around 420 K although Ca-HAP (1.61)_NH3 catalyst showed a rela-
tively broad peak. As shown in Table 1, densities of total acid sites in-
creased in the following order:
+
pied by some elements. Because the ion radius of Na ion is close to
2
+
that of Ca ions and in the Ca-HAP_NaOH catalysts there were almost
NaOH=Ca‐HAP ð1:68Þ NH3bCa‐HAP ð1:61Þ
ꢁNaOH
+
2+
ꢁ
the same amounts of Na ions as those of the deficient Ca
ions,
+
Na ions might occupy the calcium-deficient vacancy-sites in the
bCa‐HAP ð1:55Þ NaOHbCa‐HAP ð1:61Þ
;
ꢁ
ꢁNH3
Ca-HAP_NaOH catalyst. Matsunaga and Murata reported that the
2
+
+
substitution of Ca
ions in Ca-HAP by Na ions with charge-
Ca‐HAPð1:67ÞꢁNH3bHAP‐300:
Fig. 2. XRD patterns of HAP-300 and Ca-HAP catalysts after heating at 1273 K for 3 h.

8
Y. Matsuura et al. / Catalysis Communications 48 (2014) 5–10
2 3
Fig. 3. (a) CO -TPD and (b) NH -TPD profiles of the prepared Ca-HAP catalysts.
And, in terms of density balances of acid and basic sites, Ca-HAP_NaOH
(Fig. S1), but the values of mass balances were about 93 C-% and the
color of Ca-HAP_NH3 and HAP-300 catalysts turned to black during reac-
tions. Probably, the loss of mass balances would be due to formations of
catalysts had a more basic surface character than Ca-HAP_NH3 catalysts,
and Ca-HAP (1.61)_NH3 catalyst had a more acidic surface character than
Ca-HAP (1.67)_NH3 catalyst.
2
carbonaceous compounds and CO and CO . On the other hand, Ca-
According to Table 1, in the cases of both Ca-HAP_NH3 catalyst and
Ca-HAP_NaOH catalyst, the lower Ca/P atomic ratios resulted in the less
basic site densities and the more acidic surface characters in acid–base
balance. And, in the case of Ca-HAP catalysts with similar Ca/P atomic
ratios, the more Na contents resulted in the less acid site densities and
the more basic surface characters in acid–base balance. These results
suggested that the surface characters in acid–base balance can be con-
trolled by changing Ca/P ratios and Na contents in Ca-HAP catalysts. In
addition, Ca-HAP (1.61)_NH3 catalyst showed more acidic surface char-
acter than Ca-HAP (1.67)_NH3 catalyst and Ca-HAP (1.61)_NaOH catalyst,
which would be due to vacancy sites in Ca-HAP (1.61)_NH3 catalyst.
Table 2 shows the conversions of lactic acid and the product yields
over various catalysts. Using the MgO catalyst, the conversion of lactic
acid continuously decreased with time on stream (Fig. S1), and the
acrylic acid yield remained low, independently of the conversion. The
deactivation and the low selectivity might be due to the strong interac-
tions between the surface basic nature of MgO catalyst and lactic acid.
HAP_NaOH catalysts had relatively low catalyst activities, however, Ca-
HAP (1.61)_NaOH and Ca-HAP (1.55)_NaOH catalysts showed remarkably
high acrylic acid yields of 60 C-% and 78 C-%, respectively. The catalytic
activities remained almost unchanged during time on stream for 6 h
(Fig. S1), and the values of mass balances were higher than 98 C-%. For
stability test of the HAP catalyst, the lactic acid conversion was carried
out over Ca-HAP (1.55)_NaOH catalyst for 50 h at 773 K. As shown in
Fig. 5, the conversion of lactic acid was gradually decreased from 97%
to 91% during 50 h of time on stream. Ca-HAP (1.55)_NaOH catalyst
remained almost unchanged during the catalytic performance.
In contrast, NaOH/Ca-HAP (1.68)_NH3 catalyst exhibited a high yield
of 2,3-pentanedione of 29 C-% almost equal to that of acrylic acid, as re-
ported for NaOH/SiO catalyst [6]. And, the catalytic activity remained
2
almost unchanged during time on stream for 6 h (Fig. S1). These results
+
suggested that Na ions importantly affected the product selectivity in
the lactic acid conversion and the presence of sodium ions in the apatite
structure on the extra-surface seemed to enhance the acrylic acid yield.
As shown in Fig. 1, five types of our prepared Ca-HAP catalysts were
similar in crystallinity, but the commercially available HAP-300 catalyst
had the relatively low crystallinity. Therefore, the differences between
catalytic properties of our prepared Ca-HAP catalysts would not be
due to their crystallinity but probably due to their compositions and
surface properties. In contrast, one of the reasons why HAP-300 catalyst
showed a significantly lower acrylic acid yield and a higher acetalde-
hyde yield than Ca-HAP (1.67)_NH3 catalyst may be the relatively low
crystallinity of HAP-300 catalyst.
2 5 2
The P O /SiO catalyst mainly produced acetaldehyde. Acetaldehyde
was formed by acidic catalysis through the decarbonylation or decar-
boxylation of lactic acid as shown in Scheme 1 [13].
As shown in Fig. 4, the Ca-HAP catalysts retained the apatite struc-
ture as a single phase during the catalytic conversions. All of Ca-HAP cat-
2
−1
alysts had similar specific surface areas in the range of 57–68 m g
except for the NaOH/Ca-HAP (1.68)_NH3 catalyst. Ca-HAP (1.61)_NH3 cat-
alyst with vacancy sites showed significantly lower acrylic acid yield
and higher acetaldehyde yield than those of stoichiometric Ca-HAP
(
1.67)_NH3 catalyst, which may indicate that the acidity from vacancy
Although the acrylic acid yields of the Ca-HAP catalysts depended on
the contact time as shown in Fig. 6, Ca-HAP (1.55)_NaOH catalyst exhib-
ited both the highest yield of 83 C-% and the highest selectivity of
87 C-% among the tested catalysts, and this yield is the highest seen in
published studies about acrylic acid production from lactic acid yet.
sites accelerated the acetaldehyde formation preferentially. And, the
catalytic activity and selectivity of Ca-HAP_NH3 catalysts were similar
to those of commercially available HAP-300 catalyst. The catalytic activ-
ities remained almost unchanged during time on stream for 6 h
Table 2
a
Catalytic conversion of lactic acid. .
Catalyst
S.S.A. (m2 g−1
)
Conversion (%)
Yield (C-%)
Acrylic acid
Propionic acid
Acetaldehyde
2,3-Pentane dione
Acetol
Others
bP
MgO
HAP-300
Ca-HAP (1.67)_NH3
Ca-HAP (1.61)_NH3
Ca-HAP (1.61)_NaOH
Ca-HAP (1.55)_NaOH
NaOH/Ca-HAP(1.68)_NH3
O
/SiO
167
141
57
61
68
62
62
10
91
24
100
92
100
83
90
0.5
0.6
47
53
46
60
78
32
1.6
4.4
8.2
4.0
2.6
3.7
0.6
9.0
59
3.7
29
24
30
12
6.0
6.7
0.2
0.2
1.2
1.1
0.9
1.1
0.4
29
0.0
1.6
0.0
0.0
0.0
1.5
0.3
0.0
30
14
14
10
21
4.2
4.2
7.8
2
5
2
84
aReaction conditions: reaction temperature = 623 K, 38 wt.% lactic acid aqueous solution = 1.2 mL h−1, Ar flow = 40 mL min−1, time on stream = 6 h, and catalysts = 1.0 g ( 0.2 g).
b

Y. Matsuura et al. / Catalysis Communications 48 (2014) 5–10
9
Fig. 4. XRD patterns of Ca-HAP catalysts after the catalytic conversions of lactic acid.
The increase of W/F values from 250 decreased the acrylic acid yield,
which was due to unknown products. Probably, condensations might
have easily occurred in the lactic acid conversion at such high W/F
conditions.
According to Tables 1 and 2, the effects of Ca/P atomic ratios and Na
contents on the acrylic acid yield in the lactic acid conversion were not
simple. On the other hand, the order of the ratio of acid site density to
basic site density was as follows,
yields required the catalyst with surface property that is just as well bal-
anced in acidity and basicity.
From these results, we concluded that Ca-HAP catalysts had both
acid and basic properties, which might be important for the selective
dehydration of lactic acid into acrylic acid. The acetaldehyde formation
in the lactic acid conversion was preferentially accelerated by relatively
2 5 2
acidic catalysts, such as, P O /SiO with acid-site islands and Ca-
HAP_NH3 and commercially available HAP-300 catalysts with relatively
acidic surface properties showed about 30 C-% of the acetaldehyde
yields, whereas the 2,3-pentanedione formation was accelerated by rel-
atively strong basic catalysts, such as NaOH/Ca-HAP (1.68)_NH3 catalysts
with base-site islands. On the other hand, Ca-HAP (1.55)_NaOH catalyst
had weaker basic properties than NaOH/Ca-HAP (1.68)_NH3 catalyst
and less acid-site density than stoichiometric Ca-HAP (1.67)_NH3 cata-
lyst, which might be caused by the inhabitation of 2,3-pentanedione
and acetaldehyde formations and the remarkably high selectivity into
acrylic acid. According to TPD experiments, Ca-HAP (1.55)_NaOH catalyst
showed almost the same density of basic sites as that of acid sites. From
these results, one of the reasons why Ca-HAP (1.55)_NaOH catalyst
showed the highest acrylic acid yield can be that it has less acid-
site islands to produce acetaldehyde, less basic-site islands to pro-
duce 2,3-pentanedione, and more acid–base pair sites which might
be effective in the selective dehydration than those of the other Ca-
HAP catalysts. In our future study, we would like to clarify that.
NaOH=Ca‐HAP ð1:68Þ NH3 f32gbCa‐HAP ð1:61Þ NaOH f60gbCa‐HAP
ꢁ
ꢁ
ð1:55Þ NaOH f78gbCa‐HAPð1:67Þ NH3 f53gbHAP‐300
ꢁ
ꢁ
ð1:61Þ NH3 f46g:
ꢁ
The {values} in brackets were acrylic acid yields (C-%) shown in
Table 2. The acrylic acid yields were correlated to the ratios of acid-
site density to basic-site density. Ca-HAP (1.55)_NaOH catalyst showed
the middle of surface properties in acidity and basicity and the highest
acrylic acid yield, and other Ca-HAP catalysts closer to Ca-HAP
(
1.55)_NaOH catalyst in surface acid–base properties showed higher
acrylic acid yields. This correlation indicated that the high acrylic acid
100
80
60
40
20
0
Ca-HAP (1.55)_NaOH
Ca-HAP (1.67)_NH3
Ca-HAP (1.61)_NaOH
NaOH/Ca-HAP(1.68)_NH3
0
50
100
150
200
250
300
350
W/F (h gcat mol LA-1)
Fig. 5. The catalyst stability over Ca-HAP(1.55)_NaOH. Reaction conditions: reaction tem-
−
1
perature = 623 K, 38 wt.% lactic acid aqueous solution = 1.2 mL h , Ar flow =
1
4
0 mL min− , and catalysts = 1.0 g.
Fig. 6. Changes in acrylic acid yields against W/F over Ca-HAP catalysts at 623 K.

10
Y. Matsuura et al. / Catalysis Communications 48 (2014) 5–10
[
[
[
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Ca-HAP catalysts containing Na ions replacing deficient Ca ions exhib-
ited remarkably high acrylic acid yield. In contrast, non-stoichiometric
Ca-HAP catalysts without replacement of Na ions and Ca-HAP catalysts
with excess amounts of sodium species enhanced the selectivities into ac-
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+
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Acknowledgments
We would like to acknowledge the support of Sangi Co. Ltd., Tokyo.
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