Direct perfluorination of an acid-sensitive glycol ether as precursor for perfluoro(2-(Methoxymethoxy)ethyl vinyl ether)

Article abstract of DOI:10.1080/00397911.2010.532578

A four-step approach to perfluoro(2-(methoxymethoxy)ethyl vinyl ether) 5 from an acid-sensitive glycol ether 3 by liquid-phase direct fluorination (DF) has been described. The perfluoro precursor was achieved by control of the gradient increase of temperature (- 20°C to 15° C) and addition of sodium fluoride. Improved workup with benzyl alcohol provided a convenient method for purification and a practical means for tracing the progress of fluorination. Taylor & Francis Group, LLC.

Full text of DOI:10.1080/00397911.2010.532578

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Direct Perfluorination of an Acid-
Sensitive Glycol Ether as Precursor for
Perfluoro(2-(methoxymethoxy)ethyl
Vinyl Ether)
Hongle Liu a , Xusong Pan a , Lihua Yuan a , Shuliang Zou a , Peishen
Li a , Wei Wang a , Youzhou He a , Wen Feng a , Xiaoyong Yang b , Kai
Luo b & Yong Wu b
a Key Laboratory for Radiation Physics and Technology of Ministry of
Education, College of Chemistry, Nuclear Institute of Science and
Technology, Sichuan University , Chengdu , China
b Zhong Lan Chenguang Research Institute of Chemical Industry ,
Chengdu , China
Accepted author version posted online: 30 Aug 2011.Published
online: 16 Dec 2011.
To cite this article: Hongle Liu , Xusong Pan , Lihua Yuan , Shuliang Zou , Peishen Li , Wei Wang ,
Youzhou He , Wen Feng , Xiaoyong Yang , Kai Luo & Yong Wu (2012) Direct Perfluorination of an Acid-
Sensitive Glycol Ether as Precursor for Perfluoro(2-(methoxymethoxy)ethyl Vinyl Ether), Synthetic
Communications: An International Journal for Rapid Communication of Synthetic Organic Chemistry,
42:7, 959-966, DOI: 10.1080/00397911.2010.532578
To link to this article: http://dx.doi.org/10.1080/00397911.2010.532578
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Synthetic Communications1, 42: 959–966, 2012
Copyright # Taylor & Francis Group, LLC
ISSN: 0039-7911 print=1532-2432 online
DOI: 10.1080/00397911.2010.532578
DIRECT PERFLUORINATION OF AN ACID-SENSITIVE
GLYCOL ETHER AS PRECURSOR FOR
PERFLUORO(2-(METHOXYMETHOXY)ETHYL
VINYL ETHER)
Hongle Liu,1 Xusong Pan,1 Lihua Yuan,1 Shuliang Zou,1
Peishen Li,1 Wei Wang,1 Youzhou He,1 Wen Feng,1
Xiaoyong Yang,2 Kai Luo,2 and Yong Wu2
1Key Laboratory for Radiation Physics and Technology of Ministry of
Education, College of Chemistry, Nuclear Institute of Science and
Technology, Sichuan University, Chengdu, China
2Zhong Lan Chenguang Research Institute of Chemical Industry,
Chengdu, China
GRAPHICAL ABSTRACT
Abstract A four-step approach to perfluoro(2-(methoxymethoxy)ethyl vinyl ether) 5 from
an acid-sensitive glycol ether 3 by liquid-phase direct fluorination (DF) has been described.
The perfluoro precursor was achieved by control of the gradient increase of temperature
(ꢀ20 ꢁC to 15 ꢁC) and addition of sodium fluoride. Improved workup with benzyl alcohol
provided a convenient method for purification and a practical means for tracing the progress
of fluorination.
Keywords Acid-sensitive glycol ether; fluorination; perfluoro-vinyl ether
INTRODUCTION
Perfluorocarbon vinyl ethers are important compounds for use as monomers
for preparing lubricants,[1] fluoroelastomers[2,3] and other thermally and chemically
resistant materials especially in medical and electronic applications.[4] Various stra-
tegies have been developed for the synthesis of perfluorinated compounds, including
Received April 23, 2010.
Address correspondence to Wen Feng, Sichuan University, Chengdu 610064, China. E-mail:
wfeng9510@scu.edu.cn and Xiaoyong Yang, Zhong Lan Chenguang Research Institute of Chemical
Industry, Ren Min South Road, Chengdu 610041, China. E-mail: yangxy@sina.com
959

960
H. LIU ET AL.
the use of perfluorinated acyl fluoride RfCOF and hexafluoropropylene oxide,[5]
utilization of perfluoroalkyl-hypofluorites RfOF as intermediates,[6] and application
of the bis(fluoroxy)difluoromethane (BDM) chemistry starting from CF2(OF)2.[7]
One of the most commonly applied processes to prepare perfluorovinyl ethers
involves synthesis of a hydrocarbon precursor, fluorination, conversion of the per-
fluorinated intermediate to its carboxylic acid metal salt (or acyl fluoride), and pyrol-
ysis[8] to its perfluorovinyl ether. The fluorinated starting materials used in the
synthetic approaches were usually prepared by either direct fluorination (DF)[9] or
electrochemical fluorinaton (ECF). Among the documented perfluorocarbon vinyl
=
ethers RfOCF CF2(Rf ¼ perfluoroalkyl, perfluoroaromatic, or derivative moiety con-
taining ether linkage),[5–8,10–13] the compound with the formula of CF3O(CF2O)n-Rf-
=
OCF CF2 (Rf ¼ perfluoroalkyl) is more intriguing because of the high density of
ether linkages (the lower C=O ratio) embedded along the molecule chain and absence
of branches. For example, fluoroelastomers with a lower Tg could be prepared from
polymerization of this monomer.[1]
Although a perfluorinated acyl fluoride containing one 2-alkoxy propionate
moiety, such as CF3OCF2OCF2CF2OCF(CF3)COF, could be pyrolyzed to afford
the perfluorovinyl ether, the preparation of the acyl fluoride precursor involved
photo-oxidation of perfluoroolefins, such as tetrafluoroethylene or hexafluropro-
pene,[13,14] or electrochemical fluorination of the hydrocarbon carboxylic acid ana-
logs. The potential danger and handling of intermediates in the reaction,[15] as
well as transportation of a huge amount of perfluo-olefins such as tetrafluoroethy-
lene, made the process somewhat cumbersome and impractical in some regions for
large-scale production. In spite of the new approaches,[6,7] a simple and improved
process is still in demand for preparing these perfluorovinyl ethers.
The difficulty in directly fluorinating vinyl ethers containing the CH3OCH2O-
(MOM) group is the high sensitivity of the MOM group in the reaction environment.
Herein we report the successful direct fluorination of the acid-sensitive glycol ether 3
in gas–liquid (F2=Freon 113) media with gradient increase of temperature for prepar-
ing the precursor of perfluoro(2-(methoxymethoxy)ethyl vinyl ether) 5.
RESULTS AND DISCUSSION
The monoprotected glycol 1 was readily prepared according to the reported pro-
cedure.[16] Reaction of 1 with hexafluoropropylene oxide (HFPO) in the presence of
NaF proceeded smoothly to the ester 2 in 70% yield. Transesterification efficiently con-
verted 2 into the partially fluorinated methly ester 3 in good yield (90%) with metal
alkoxide or metal salt of alcohol, such as NaOH or MeONa. Preferably the use of
MeONa could facilitate the reaction and bring the reaction to completion in a shorter
time (<8 h) compared to NaOH (ca. 20 h). Conversion of 2 to 3 in step b (Scheme 1) is
worthwhile for more cost-effective fluorination in the next step. Fluorination of 3 in
1,1,2-trichloro-1,2,2-trifluoroethane (Freon 113) was performed using fluorine diluted
with nitrogen (10%). Although the use of this fluorinated solvent is regulated because
of enviromental concerns, we temporarily utilize it on a laboratory scale for con-
venience because it is still much more cheaply available than other fluorinated solvents.
Compounds bearing MOM groups are known to be sensitive to acid and sub-
ject to fast decomposition in strongly acidic media.[17] However, the decomposition

PERFLUORINATION OF ACID-SENSITIVE GLYCOL ETHER
961
Scheme 1. Reagents and conditions: (a) NaF (1.1 equiv), 20 ꢁC; (b) MeOH, MeONa, reflux, 20 h; (c) F2,
Freon113, flow rate: 200 ml=min; (d) (i) MeOH, (ii) benzyl alcohol; (e) KOH, H2O, MeOH; and (f) K2CO3,
220–250 ꢁC.
may be slowed down at lower temperature. Thus, fluorination of the starting
material 3 with F2 was first performed at 0 ꢁC under a flow of 10% F2 for a period
of time and then subject to quenching with MeOH. Our first few attempts failed to
obtain any detectable methyl ester of product 4b (entry 1, in Table 1) because of
serious breakdown. Instead, low-boiling-point species (<50 ꢁC) appeared as the
major product. As temperature was lowered to ꢀ20 ꢁC, together with intermittent
addition of NaF to absorb the released HF,[18] the loss due to decomposition from
Table 1. Effect of temperature, reaction time, and NaF on fluorination of 3
(0.1 mol)
Entry
Temperature (ꢁC)
Time (h)
NaF (mol)
Yield (%)a
1
2
0
0–5
20
20
40
60
20
40
60
20
40
60
1.3
1.0
1.3
1.5
1.3
1.5
1.0
1.5
1.0
1.3
n.d.
1.5
3
0–5
0–5
3.0
2.2
4
5
ꢀ10 to 10
ꢀ10 to 10
ꢀ10 to 10
ꢀ20 to 15
ꢀ20 to 15
ꢀ20 to 15
10.5
11.7
9.6
6
7
8
19.4
19.8
19.9
9
10
aYield was based on methyl ester 4b obtained from addition of methanol to
4a and determined by the distilled fraction. Identity of each fraction was con-
firmed by 1H NMR characterization.

962
H. LIU ET AL.
deprotection of MOM groups was considerably reduced, but the conversion to
fluorinated species was very poor.
Inspired by the Exfluor–Lagow’s process for fluorination of selected hydro-
carbon compounds wherein both temperature and fluorine concentration are gradu-
ally increased,[19] we probed the gradient increase of reaction temperature, but
maintained the F2 concentration (10%) at a flow rate of 200 mL=min. The effect
of temperature, sodium fluoride and reaction time on the yield of product was exam-
ined, and the results are summarized in Table 1.
Among the three temperature ranges, 0 to 5 ꢁC, ꢀ10 to 10 ꢁC, and ꢀ20 to 15 ꢁC,
the fluorination starting from ꢀ20 ꢁC demonstrated a great improvement in yield (ca.
20%, entries 8–10). At the higher temperature range of 0 to 5 ꢁC, the conversion of 3
was remarkably poor (entries 2–4). When the temperature was set to ꢀ10 to 10 ꢁC, a
mixture consisting of partially fluorinated products and side products was obtained,
leading to a yield of less than 10% (entries 5–7). It should be noted that a tempera-
ture greater than 5 ꢁC was necessary in the last stage of the reaction to reach per-
fluorination. However, we observed a considerable decrease in yield if the
temperature was more than 25 ꢁC at a later stage of the reaction. Longer reaction
time exerted little effect on the yield (entries 8–10) at ꢀ20 to 15 ꢁC. Addition of ben-
zene at 5 to 15 ꢁC had no marked effect upon the reaction, which was supposed to be
effective in generating a great concentration of fluorine radicals.[20] The presence of
excess NaF and intermittent addition to the system was critical for the amelioration
of yield and diminution of decomposition of MOM groups in 3. Although addition
of more NaF could alleviate the decomposition, a 1:1.3 ratio was found to be appro-
priate, considering the efficient stirring in the reactor.
It was well known that the replacement of hydrogen atoms adjacent to the car-
bon atoms by fluorine atoms increases the C-C bond strength and makes the mol-
ecule more stable. Therefore, the acid-sensitive MOM group becomes more stable
when part of the hydrogens was replaced by fluorine atoms with progress of the
fluorination. This was realized by careful control of the gradient increase of tempera-
ture starting from low temperature and providing surroundings that are favorable to
the stability of the intermediates. The greatest loss in the fluorination process that
occurs at the start of the reaction was minimized when the substrate has very few
fluorine atoms.[21] Thus, the desired product 4b was successfully obtained in ca.
20% yield under the optimized condition (ꢀ20 to 15 ꢁC, 1.3 mol NaF, and 40 h).
The formation of compound 4b was revealed by 1H NMR, providing only one
signal at 3.98 ppm. This is further substantiated with 19F NMR spectrum. The result
from atmospheric pressure chemical ionization–mass spectrometry (APCI-MS,
negtive mode) afforded a signal at 424.91, which is in good agreement with the
calculated value of 424.97.
Because the perfluorinated product 4a is unstable in moisture,[22] it is difficult
to trace the perfluorination directly. Usually, the reaction was monitored by the for-
mation of 4b via quenching 4a with methanol. Nevertheless, the overlapping of the
signal from methyl ester of 4b with that of methanol around 3.98 ppm would hinder
the accurate assignment and mislead the analysis. We found an efficient means to
1
detect the formation of 4a by converting 4a to 4c with benzyl alcohol. In the H
NMR spectrum of 4c, there are two signals at 7.40 ppm (multiplet) and 5.38 ppm
(singlet) in CDCl3, which are quite distinct from other signals. Moreover, the benzyl

PERFLUORINATION OF ACID-SENSITIVE GLYCOL ETHER
963
alcohol could be readily removed by either distillation or filtering through a pad of
silica gel, rendering the purification of its corresponding benzyl ester simple and
straightforward. It is noteworthy that an increased yield (32%) was achieved when
benzyl alcohol was used to quench the reaction. The difference in fluorination
between the methyl ester and the benzyl ester was ascribed to the loss during the
purification process. Further improvement is possible if a combination of such fac-
tors as temperature range, F2 concentration, and solvents are thoroughly taken into
account. Thus, benzyl alcohol could be utilized not only as a more convenient indi-
cator for the progress of the reaction by displaying the two characteristic signals, but
also as a purification method for the perfluorinated mixture.
The chemical shift in 19F NMR was in full accord with the structure of 4c com-
pared to that of 4b. Furthermore, the result from high-resolution mass spectroscopy
(HRMS, ESI, negative mode) disclosed a signal at 501.0008 (calc. 501.0008), which
unambiguously proved the formation of the perfluorinated precursor (4c).
In conclusion, the liquid-phase direct fluorination of an acid-sensitive partially
fluorinated glycol ether 3 for perfluoro(2-(methoxymethoxy) ethyl vinyl ether 5 was
achieved in four steps. The key fluorinated precursor 4b was obtained in ca. 20%
yield under the optimized condition with the gradient change of temperature
(ꢀ20 to 15 ꢁC) and intermittent addition of NaF. Benzyl alcohol derivative 4c was
useful both as an indicator for tracing the progress of fluorination and as a con-
venient precursor for purification. We expect that this method may also be appli-
cable to the synthesis of other partially fluorinated esters intolerable to strong
acidic media.
EXPERIMENTAL
Ethylene glycol, anhydrous methanol, and potassium bicarbonate are commer-
cially available substances. Benzyl alcohol was dried over Na2SO4 before use. NaF
was dried in vacuum at 250 ꢁC. Boiling points were measured by distillation. The
NMR spectra were recorded on a Bruker ACF 400 spectrometer (tetramethylsilane
1
as internal standard for H, and trichlorofluoromethane for 19F). 19F NMR spectra
were observed at 376 MHz with fluorotrichloromethane as standard. HRMS were
obtained on a Jeol SX-102A coupled to HP-5890 with a 60-m capillary column
(J&W DB-1 or DB-1301). Elemental fluorine was provided by Zhong Lan
Chenguang Research Institute of Chemical Industry, China. Elemental fluorine is
a highly toxic and corrosive gas and may explode when it meets organics in the vapor
phase. Extreme care must be taken when handling it! The hydrogen fluoride (bp
19.5 ꢁC) evolved during the reaction is also highly corrosive and must be absorbed
by a base, such as NaOH. The fluorination was carried out in low-temperature cir-
culating baths purchased from Chengdu Jinniu Refrigeration Co., China, with etha-
nol as cooling agent, and the temperature was determined by a digital thermometer.
2-(Methoxymethoxy)ethanol (1)
Compound 1 was prepared according to the reported procedure.[16] The chemi-
1
cal shift of this compound in H NMR spectrum is in agreement with the reported
values.

964
H. LIU ET AL.
10-Fluoro-10-(trifluoromethyl)-2,4,7,8,11,14,16-
heptaoxaheptadecane (2)
2-(Methoxymethoxy)ethanol (1) 120 g (1.13mol) and NaF 71g (1.70mol) were
added to a 250-mL, two-necked flask equipped with a condenser linked to a cold trap.
While stirring at room temperature, hexafluoropropylene oxide (HFPO) was bubbled
via one neck into the reaction mixture. The reaction was monitored by gas chromato-
graphy (GC) and was completed when the product reached a constant percentage. The
mixture was washed with water, ethyl acetate, dried over Na2SO4, and distilled to afford
product 2 (135g, 0.40mol) in a yield of 72.4%. Bp 80ꢁC=0.2 kPa. 1H NMR (400 MHz,
CDCl3) d (ppm): 3.37 (s, 6H, CH3O–), 3.76 (t, J ¼ 4.8 Hz, 2H, ꢀCH2CH2OCF–), 3.81
(t, J ¼ 4.8 Hz, 2H, ꢀCOOCH2CH2O–), 3.93–4.02 (m, 2H, ꢀCH2CH2OCF–), 4.51 (t,
J ¼ 4.8 Hz, 2H, ꢀCOOCH2CH2O–), 4.64 (s, 2H, ꢀOCH2OCH3), 4.65 (s, 2H,
CH3OCH2O–). HRMS (ESIþ) 361.0866 (M þ Naþ); calculated: 361.0886.
5-Fluoro-5-(trifluoromethyl)-2,3,6,9,11-pentaoxadodecanemethyl (3)
Methanol 710 mL (17.8 mol) and CH3ONa 5.78 g (0.107 mol) were added to a
2-L, two-necked, round-bottomed flask, and the mixture was stirred at room tem-
perature until the base was dissolved. The ester 2 (300 g, 0.89 mol) was added, and
the mixture was refluxed for 48 h. The solvent was removed, and the resulting slurry
was washed with water and extracted with ethyl acetate. After drying over Na2SO4,
the solvent was removed and distilled under reduced pressure to provide the com-
pound 3 (224 g, 0.85 mol) in a yield of 95%. Bp 75 ꢁC=1.0 kPa. 1H NMR
(400 MHz, CDCl3) d (ppm): 3.37 (s, 3H, CH3OCH2O–), 3.760 (t, J ¼ 4.8 Hz, 2H,
ꢀOCH2CH2O–), 3.89–4.02 (m, 2H, ꢀOCH2CH2O–), 3.941 (s, 3H, ꢀCOOCH3),
4.653 (s, 2H, ꢀOCH2O–). 19F NMR (376 MHz, CDCl3) d (ppm): ꢀ81.24 (d,
J ¼ 3.76 Hz, 3F, ꢀCF3), ꢀ131.88 [q, J ¼ 3.76 Hz, 1F, ꢀCF(CF3)–]. HRMS (ESIþ)
287.0505 (MþNaþ); calculated: 287.0519.
2-(2-(Difluoro(trifluoromethoxy)methoxy)-1,1,2,2-
tetrafluoroethoxy)-2,3,3,3-tetrafluoropropanoate (4b)
R113 500 mL, NaF 44 g (1.24 mol), and compound 3 (25 g, 0.095 mol) were
charged into a 1-L autoclave made of stainless steel equipped with a condenser.
The mixture was stirred and cooled down to ꢀ20 ꢁC. At the gas outlet of the auto-
clave, the condenser was maintained at ꢀ20 ꢁC. Nitrogen gas was blown into the sys-
tem for 1 h, and then fluorine gas diluted to 10% with nitrogen gas was blown into
the mixture at a flow rate of 200 mL=min at atmospheric pressure. The temperature
was raised gradiently from ꢀ20 to 15 ꢁC at intervals of 5 ꢁC and maintained at each
temperature for ca. 5 h, while NaF was added portionwise and intermittently. Then,
nitrogen gas was supplied for 1.5 h to remove residual F2 and volatile materials, fol-
lowed by the addition of methanol (150 mL). Workup by removal of the solvents,
neutralization with Na2CO3, drying over Na2SO4, and fine distillation (bp 56 ꢁC=
0.5 kPa) afforded the methyl ester 4b (10.1 g) in a yield of 25%. 1H NMR
(400 MHz, CDCl3) d (ppm): 3.97 (s, 3H, ꢀCOOCH3). 19F NMR (376 MHz, CDCl3)
d (ppm): ꢀ53.75 (d, J ¼ 30.1 Hz, 2 F, ꢀOCF2O–), ꢀ56.94 (d, J ¼ 18.8 Hz, 3F,

PERFLUORINATION OF ACID-SENSITIVE GLYCOL ETHER
965
CF3O–), ꢀ81.91 [d, J ¼ 3.76 Hz, 3F, ꢀCF(CF3)–], ꢀ84.40 (dd, J ¼ 127.8 Hz, J ¼
18.8 Hz, 2 F, ꢀOCF2CF2O–), ꢀ90.14 (d, J ¼ 18.8 Hz, 2 F, ꢀOCF2CF2O–),
ꢀ131.63 to ꢀ131.67) [m, 1 F, ꢀCF(CF3)–]. APCI-MS (negtive mode) spectrum at
424.91 (M-H)ꢀ, calculated: 424.97.
Benzyl 2-(2-(Difluoro(trifluoromethoxy)methoxy)-1,1,2,2-
tetrafluoroethoxy)-2,3,3,3-tetrafluoropropanoate (4c)
The direct fluorination of compound 3 was carried out in the same manner as
before except for the addition of 51.3 g (0.475 mol) of benzyl alcohol, and 15.2 g of
1
the desired product 4c was obtained in a yield of 32%. Bp 78 ꢁC=0.5 kPa. H NMR
(400 MHz, CDCl3) d (ppm): 7.39 (s, 5H, C6H5–), 5.38 (t, 2H, ꢀCH2O–). 19F NMR
(376 MHz,CDCl3) d (ppm): ꢀ53.75 (d, J ¼ 30.1 Hz, 2 F, ꢀOCF2O–), ꢀ56.94 (d,
J ¼ 18.8 Hz, 3F, CF3O–), ꢀ81.91 [d, J ¼ 3.76 Hz, 3F, ꢀCF(CF3)–], ꢀ84.40 (dd,
J ¼ 127.8, 18.8 Hz, 2 F, ꢀOCF2CF2O–), ꢀ90.14 (d, J ¼ 18.8 Hz, 2 F, ꢀOCF2CF2O–),
ꢀ131.63 to ꢀ131.67 [m, 1 F, ꢀCF(CF3)–]. HRMS (APCIþ): 503.0164 (M þ H)þ,
calculated: 503.0164.
1-(2-(Difluoro(trifluoromethoxy)methoxy)-1,1,2,2-
tetrafluoroethoxy)-1,2,2-trifluoroethene (5)
A 1-L, three-necked, round-bottomed flask was charged with compound 4b
(35 g, 0.082 mol), potassium hydroxide 5.6 g (82%, 0.082 mol) dissolved in water
(0.5 mL), and methanol (40 mL). The mixture was stirred under reflux for 8 h. Evap-
oration of methanol and evacuation of water provided a potassium salt, which was
then mixed thoroughly with potassium carbonate 1.23 g (9 mmol) and sand. After dry-
ing at 90 ꢁC in vacuum until a constant weight was reached, the mixture was heated to
about 220 ꢁC in a tubular reactor. The pyrolysis afforded a distillate with a boiling
point of 60 ꢁC. The distillate was washed with water and dried with anhydrous sodium
sulfate to give the title compound 5 (17.1 g, 0.049 mol) in a yield of 60%. Bp 61–63 ꢁC.
1H NMR (400 MHz, CDCl3): no signal. 19F NMR (376 MHz, CDCl3) d (ppm): ꢀ53.7
(s, 2 F, ꢀOCF2O–), ꢀ57.25 to ꢀ58.64 (m, 3F, CF3O–), ꢀ83.37 to ꢀ84.82 (m, 2 F,
ꢀOCF2CF2O–), ꢀ87.56 to ꢀ88.95 (m, 2 F, ꢀOCF2CF2O–), ꢀ135.28 (d, J ¼ 3.76 Hz,
Hz, 1 F, ꢀCF¼CF2), ꢀ140.85 to ꢀ141.97 (m, 1 F, ꢀCF¼CF2), ꢀ143.16 to ꢀ145.35
(m, 1 F, ꢀCF¼CF2). APCI-MS spectrum 346.17, calculated: 346.96 (M-H).
ACKNOWLEDGMENTS
The authors thank Chenguang Research Foundation and the Analytical and
Testing Center of Sichuan University for NMR analysis. Thanks are also extended
to Guowei Yang and Fumin Hu for helpful discussions.
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