Simultaneous determination of titanium, zirconium, and hafnium in

Fukumoto, Katsuo. Murata, and Shigero. Ikeda. Anal. Chem. , 1984, 56 (6), pp 929–932. DOI: 10.1021/ac00270a017. Publication Date: May 1984. ACS Lega...
1 downloads 0 Views 520KB Size
Anal. Chem. 1984, 56, 929-932

scattered light photoacoustic signal (noise). It is evident that the practicability of photoacoustic detection for atmospheric monitoring rests on whether sufficient selectivity can be attained without sacrificing the sensitivity, dynamic range, or ease and rapidity of measurement which are embodied in the results presented here.

ACKNOWLEDGMENT The authors gratefully acknowledge the enthusiastic efforts of William Burke who constructed the photoacoustic cells for these experiments.

Registry No. Acetaldehyde, 75-07-0. LITERATURE CITED (1) Kreuzer, L. 8.; Kenyon, N. D.; Patel, C. K. N. Science 1972, 777, 347-349. (2) Patel, C. K. N.; Keri, R. J. Appl. Phys. Len. 1977, 30, 578-579. (3) Fried. A.; Berg, W. W. Opt. Lett. 1983, 8 , 160-162. (4) Poizat, 0.; Atkinson, G. H. Anal. Chem. 1982, 54, 1485-1489. (5) Patel, C. K. N.; Tam, A. C. Rev. Mod. F i ~ y s .1981, 53, 517-550. (6) Reddy, K. V.; Heller, D. F.; Berry. J. J. J . Chem. Phys. 1982, 76, 2814-2837. (7) West, G. A.; Siebert, D. R.; Barren, J. J. J . Appl. Phys. 1980, 51, 2823-2628. (8) Slebert, D. R.; West, G. A.; Barren, J. J. Appl. Opt. 1980, 79, 53-60. (9) Reddy, K. V. MB9-1, Second International Topical Meeting on PhotoaCoustic Spectroscopy, Berkeky, CA, 1981. (10) Rosengren, L. G. Appl. Opt. 1975, 74, 1960-1976. (11) Cakert, J. 0.; Pttts, J. N. “Photochemistry”; Wiley: New York, 1966. (12) Gandini, A.; Hackett, P. A. Chem. Phys. Len. 1977, 52, 107-111.

929

Leugers, M. A,; Atkinson, G. H., University of Arizona, unpublished r e suits, 1983. Gill, R. J.; Atkinson, 0. H. Chem. Phys. Len. 1979, 64, 426-430. Swarin, S. J.; Llparl. F. “Determination of Formaldehyde and other Aldehydes by Hgh Performance Liquid Chromatography with Fluorescence Detection”; General Motors: Warren, MI, General Motors Research Publication, GMR-3831/ENV 103. Selims, S. J. Ctwomatogr. 1977, 736,271-277. Kwata, K.; Uebori, M.; Yamasaki, Y. J . Chromatcgr. Sci. 1979, 77, 264-268. Katz, M.. Ed. “Methods of Air Sampling and Analysis” 2nd ed.; Air Pollution Control Assoclation Intersociety Committee: 1977. Smith, R. A.; Drummond, I. Analyst (London) 1979, 704, 875-877. “Procedures for Determlning Exbust carbonyls as 2,dDinitrophenyC hydrazones”; Final Report in CY 1966 Under Coordinating Research Council, Air PoYution Research Advisory Committee Project No. CAPE11-68, Fuels Combustion Research Project, Bartiesville Petroleum R e search Center, Bureau of Mines, U S . Department of the Interior, 1969; National Technical Information Service Assession No. PB 200 883. Papa, L. J.; Twner, L. P. J. Chromatcgr. Sci. 1972, 70, 744-747. Papa, L. J.; Turner, L. P. J. Chromatogr. Scl. 1972, 70, 747-150. Grosjean, 0. Envlron, Scl. Techno/. 1982, 76, 254-260. Fung, K.; Swanson, R. D.;Orosjean, D.74th Annual Meeting of the Ak Pollution Control Association: Philadelphia, PA, 1981; Paper No. 8147.1. “Interlaboratory Comparison Study of Methods for Measuring Formaldehyde and Other Aldehydes in Ambient Air”; Final Report Prepared Under Project No. CAPA-17-80; Coordinating Research Council: Atlanta, GA, 1981; National Technical Information Service Assession No. PB 82224486.

RECEIVED for review June 13,1983. Accepted January 6,1984. The Coordinating Research Council is gratefully acknowledged for financial support of this work.

Simultaneous Determination of Titanium, Zirconium, and Hafnium in Aqueous Solution by Phosphorus-3 1 Nuclear Magnetic Resonance Spectrometry Takao Fukumoto,* Katsuo Murata, and Shigero Ikeda Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka, 560, Japan

I n acMk solutlon, the group 4A elements form ternary heteropoly complexes wlth molybdophosphate, e.g., molybdoManophosphate, molybdozlrconophosphate, and molybdohafnophosphate. Each ternary heteropoly molybdate glves a different phsinkal shift In Its 31PNMR spectra, respectively, and Its relqtke peak area Increases wRh lncreaslng metal Ion concentratbn. Shrultaneous detennlnatlon of these elements was found to be possible wlthln accuracles of 1 to 5 % and detectlonllmlts for TI, Zr, and Hf were 20, 40, and 60 ppm, respctlv*, under the proposed experimental condition. The small amounts of these ternary heteropoly molybdates In aqueous solutlon are extracted quantltatlvely wlth cyclohexanone. l h e optlmum acldny for extractlon was found to be In the pH range between 1.5 and 2.5 and Its recovery In cycloheiahone was more than 95 %,

As part of an extensive investigation of ternary heteropoly molybdates, the authors have studied the formation, reaction, and equilibrium state in solution by the use of Raman spectrometry ( I ) , IR spectrometry (21,and UV spectrophotometry (3). In this paper report the apalysig of ternary heteropoly molybdates containing the group 4A elements by using NMR spectrdmetry and the solvent extraction of these compounds with cyclohexanone. 0003-2700/84/035&0929$01.50/0

There is an exceptional similarity in chemical properties between zirconium and hafnium ions since the atomic and ionic radii of hafnium are very close to those of zirconium. Their chemical separation remained a challenge to analytical chemists for many years. Elaborate works have been devoted to this field (4). They were mainly spectrophotometric analysis including tedious ion exchange (5) or solvent extraction techniques (6) or a simultaneous analysis by X-ray fluorescence spectrometry (7). Recently, ICP emission spectrochemical analysis has been introduced to enable the simultaneous analysis of microamounts of the elements (8). The authors found significant differences in the 31PNMR spectra of ternary heteropoly molybdate compounds of these elements. The NMR spectra showed different chemical shifts depending upon the kinds of the group 4A elements involved. Therefore, under appropriate circumstances the 31PNMR technique can give us informatiqn on the ternary heteropoly molybdates in solution and can provide the simultaneous determination of the group 4A elements. By the use of 31P NMR, detection limits for Ti, Zr, and Hf were 20,40, and 60 ppm, respectively, for 2 h of data acquisition including all procedures under the pr6posed experimental condition. In addition, the separation of ternary heteropoly molybdate of the group 4A elements from aqueous solution by immiscible organic solvents was investigated. Binary heteropoly complexes, in contrast to ternary heteropoly molybdates, were 0 1984 American Chemical Socpty

930

ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984

virtually extracted with many oxygenated solvents. On the other hand, Veitsman has used the formation of ternary heteropoly molybdates for the spectrophotometric determination of the group 4A elements, based on the enhancement of the yellow color in aqueous solution (9, IO). In oxygenated solvents, cyclohexanone and propylene carbonate, selectively extract ternary heteropoly molybdates and they give recoveries of more than 95% when the molar ratio (CMo/Cp)is above 11.

EXPERIMENTAL SECTION NMR Measurements. 31PNMR spectra were measured with 10-mm tubes by using both Bruker WM-360WB and JEOL JNM-FX2OO spectrometers operating at 145.805and 80.74 MHz, respectively. Measurements were made at ambient temperature, ca. 25 "C. An external 2H lock (D20)was employed and proton decoupling was not used. Spectra were obtained by Fourier transform FID with a 45" pulse and repetition time of 3.0 s, and they were accumulated for 2000-3000 times. A 0.05 M (1aminoethylidene)bis(phosphonic acid) aqueous solution was used as an external standard in the 31PNMR spectra. The chemical shift of external standard signal is at +14.01 ppm relative to that of 85% H3P04(downfield from &PO,). Preparation of Ternary Heteropoly Molybdates. All solutions were prepared with reagent grade chemicals. A stock solution of sodium molybdate (0.5 M) was prepared by dissolving about 121.0g of Na2Mo04*2H20 in water and diluting to 1L with water. This solution was standardized by the oxine method (11). A stock solution of potassium dihydrogen phosphate (0.1 M) was obtained by dissolving precisely 13.609g (dried overnight at 110 "C) in 1 L of water. In addition, 0.1 M stock solutions of groups 4A elements, Ti(IV), Zr(IV), and Hf(1V) were prepared by dissolving Ti metal, ZrOC12.8H20,and HfOCl2-8Hz0into 1 M HC1 solutions,respectively. This is because titanium, zirconium, and hafnium tend to form hydrolyzed polymeric species at lower acidities with higher metal concentration. These solutions were standardized by gravimetric determination with cupferron (12). Test solutions for extraction were prepared by proper dilution M, while for NMR of these stock solutions, Cp = 1.0 X M. Aqueous solutions with various measurements, Cp = 1.0 X P:Me:Mo ratios and pH values were prepared by mixing these stock solutions. For example, each aliquot of phosphate and molybdate was first mixed and 3 mL of concentrated nitric acid was added to it, and the solution developed a yellow color. Metallic ion was slowly added in the solution with vigorous stirring, and water and 5 N nitric acid were used to adjust the acidity of this solution to the adequate value. Solvent Extraction. In order to investigate the availability of organic solvent for the extraction of ternary heteropoly molybdates of group 4A elements, a large number of trial runs were undertaken. The solvents examined were butyl alcohol, methyl isobutyl ketone, ethyl acetate, cyclohexane, cyclohexanol, cyclohexanone, chloroform, propylene carbonate, etc. Among these, cyclohexanone and propylene carbonate were found to extract ternary heteropoly molybdates very efficiently. Therefore, cyclohexanone was used to study the solvent extraction of ternary complexes. A centrifuge tube with stopper, 3 cm in diameter and 50 mL in volume, was used as a separatory funnel for extraction. The shaking for extraction was carried out with an autoshaker operating at 200 strokes m i d . A mixed solution of equal volumes of cyclohexanone and ternary heteropoly molybdate aqueous solution was equilibrated at 25 "C by shaking the mixture for 20 min and then allowing it to stand for 5 min for phase separation. Both phases were completely separated by centrifugation. After the extraction, the aqueous phase was separated out immediately and spectrophotometric determination of the group 4A metal ion in the aqueous phase with Arsenazo I11 (13)was done to measure the distribution ratios. Spectrophotometric measurements were made with a UVID EC-500 spectrophotometer (Nihon Bunko) at 665 nm using 1-cm silica cells. RESULTS AND DISCUSSION NMR Measurements. Figure 1 shows the 31P NMR spectra of the acidic mixed solutions of phosphate, molybdate,

t

(a )

-15

-16

-17

PPM

CHEMICAL SHlFT

Figure 1. 31PNMR spectra of the KH,PO,-Ti(IV)-Na,MoO, aqueous system, C, = 1.0 X IO-, M, CMo= 2.0 X lo-' M (pH 0.5-0.6): (a) C,, = 0;(b) C,, = 6.7 X M; (C) CTi = 3.3 X M; (d) CTi = 5.0 x 10-3 M.

Table I. 31PChemical Shifts of Heteropoly Molybdates in Aqueous Solution chemical shift,a compound s/PPm H,PThMo,, 0,,(5-x)-16.24 HiPZrMo ,YO4;( 5-x)-16.88 H,PTiMo ,1040(5-x)- -16.98 -17.23 H,PHfMo,,O ( 5 - x ) H , P M ~,,o,, ( jo_x)-17.33 a Relative to (1-aminoethylidene)bis(phosphonic acid). Positive values of 6 represent a resonance at lower field than that of the standard.

and Ti(1V). When Ti(1V) is absent, the spectrum (Figure la) exhibits two peaks: a peak at lower field, near -15.24 ppm, that is rather broad and the other a t -17.33 ppm that is very sharp. The latter is assigned to be due to the phosphorus in 12-molybdophosphate produced by reacting with molybdate and the former is due to 11-molybdophosphate in equilibrium state in solution. The addition of Ti(1V) brings about a new peak at -16.98 ppm and its relative peak area is increased with the increase of Ti(1V) concentration. The group 4A elements have been found to react with 12-molybdophosphate to produce ternary heteropoly molybdate anions and Raman measurements, and elementary analysis revealed the composition of these complexes to be P:Me:Mo = 1:1:11(1). These facts lead to the assignment of the peak at -16.98 ppm to 31P resonance in molybdotitanophosphate, HxPTiMo11040(6-X)-. Similar behavior was observed for Zr(IV) and Hf(IV) with each possessing a characteristic chemical shift. Table I gives values of the chemical shift of 12-molybdophosphate and ternary heteropoly molybdates which are expressed as 6 values in parts-per-million. These 31PNMR peaks of ternary heteropoly molybdates were found to be downfield by about 0.10-0.45 ppm from that of 12-molybdophosphate. The observed downfield shift indicates a deshielding effect on the 31Patom. This can be explained speculatively by the rearrangement of electron density distribution in the Keggin-like structure of ternary heteropoly molybdates. The substitution of one molybdenum atom by the group 4A elements in the Keggin structure results in the decrease in symmetry and then leads to the decrease of shielding around the 31Patom. The reason

ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984

931

Table 11. Determination of Ti(IV), Zr(IV), and Hf(1V) in Aqueous Solution of Ternary Heteropoly Molybdates by 31PNMR H,PZ~MO,,O,,(~-~)-H,PT~MO,,O,,(~-~) H,PHfMo ,,04,(J CMea calcd sample 1 obsd (pH 0.56) C M ~calcd sample 2 obsd (pH 0.54) C M ~calcd sample 3 obsd (pH 0.49) a Metal ion concentration ( M).

1.25 1.30 2.40 2.38 1.50 1.51

1.25 1.22 2.00 2.01 2.00 1.92

1.10 1.11 1.30 1.31 3.00 2.93

Table 111. Recovery of Molybdozirconophosphate Extracted by Various Solvents solvent % recovery" solvent cyclohexanone propylene carbonate acetyl acetone methyl n-propyl ketone acetop he none methyl ethyl ketone methyl isobutyl ketone isoamyl alcohol n-butyl alcohol methyl tert-butyl ketone nitromethane nitrobenzene

99.1 f 0.5 97.8 t 0.6 86.9 f 0.5 74.0 f 0.6 67.5 f 0.7 40.9 f 0.3 40.8 f 0.7 34.6 f 0.7 22.1 i 0.5 16.6 * 0.8 6.2 ?: 0.6 6.0 f 0.4

" Data are average and average deviation of three replicates. cM0= 4.8 x 10-3 M, PH 1.0). for the difference in the chemical shift of each ternary heteropoly molybdate, however, cannot be understood at present. Mixing of equimolar amounts of 12-molybdophosphate and metal ion in the solution gives a single peak whose position is assigned to the ternary heteropoly molybdate. This peak was observed to be dependent on metal ion concentration. Determination of relaxation time, T1, was not stoichiometrically carried out, but each relative peak area was given very close value over a repetition time of 2.0 s. In addition, no other peak was observed by the measurement with repetition time of 10.0 s and by the data acquisition with that of 3.0 s overnight. The results obtained from the 31PNMR spectra indicate the absence of any ternary heteropoly molybdates other than the 1:1:11anion in the solution. In aqueous solution the following two reactions are in equilibrium, and ternary heteropoly molybdate is found with the fairly larger equilibrium constant of eq 2 than that of eq 1. The ternary hete-

% recovery

4.7 f 0.4 3.9 f 0.5 3.4 f 0.6 1.0 t 0.6 1 . O f 0.8

ethyl acetate chloroform carbon tetrachloride cyclohexane benzonitrile ethyl n-butyl ketone isoamyl acetate diethyl ether diisopropyl ether n-caproic acid n-butyl acetate Not detected

-b

-

-

(Sample: Cp = Czr = 4.0 x

I

-1 5

,

I

-16

,

/

-17

,

M,

l

PPM

CHEMICAL SHIFT

Flgure 2. 31P NMR spectrum of ternary heteropoly molybdates in aqueous solution (pH 0.49): Cp = 1.0 X M, , C = 2.0 X 10-1 M, cT,= 2.0 x 10-3 M, cZr= 3.0 x 10-3 M, c,,, = 1.5 x 10-3 M.

hafnophosphate, and 12-molybdophosphate,from lower field. The relative peak area was also observed to depend on the metal ion concentration. The simultaneous determination of group 4A elements in aqueous solution was carried out at various Ti:Zr:Hf molar ratios. Some of these results are shown + Zr02+ e ( P Z ~ M O ~ ~ O ~(2) ~ ) ~ - in Table I1 and give a good reproducibility within experimental error of h5%. Under existing conditions the limitation of the ropoly molybdate anion, which is remarkably more hydrophilic applicability of this method is that the total metal ion conthan the 12-molybdophosphate anion, becomes more stable centration must be equal to or less than of phosphate in in acidic solution. This is also implied by the fact that the aqueous solution. If excessive metal ion is present, it is ultraviolet spectra of ternary heteropoly molybdate in aqueous gradually precipitated by hydrolysis and the ternary heterosolution show a characteristic absorption maximum at 302 nm poly molybdate decomposes. Further work is proceeding on which is obscure in the corresponding 12-molybdophosphate. this aspect in order to extend the applicability of this method. The presence of this absorption band is associated with the 31P NMR spectra of the solution containing 12-molybdorigid formation of the ternary complex in a liquid medium. phosphate and Th(1V) were also measured in similar manner In addition, Figure 1 induces the prediction that relative as above and gave a new peak which is assigned to molybpeak area of 31PNMR may give a linear relationship with dothorophosphate, at -16.24 ppm (Table I). Ti(1V) concentration. Each ternary heteropoly molybdate The high stability of ternary heteropoly molybdate in solution, in practice, yielded linear calibration curves over the aqueous solution observed by 31PNMR is mainly due to the range 5 X M to 1x 10" M. The concentration of metal higher solvency of water. This induced the prediction of ions can be estimated from these results within the standard difficulty in the extraction of these complexes from aqueous deviation of 5 % . Figure 2 shows the 31PNMR spectrum of solution. But it might be possible to separate ternary heteTi(IV), Zr(IV), and Hf(1V) coexisting in solution. Five peaks ropoly molybdates from aqueous solution if solvents with are observed in Figure 2 and these are identified by each rather high basicity are used. specific chemical shift value as 11-molybdophosphate, molSolvent Extraction. In general, oxygenated solvents are ybdozirconophosphate, molybdotitanophosphate, molybdothe best extractants for heteropoly complexes (14). However,

032

ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984

'I

I

1-

L

L

N

n .

8'

(3

3

9

10

11

12

13 14 15 16 17

cM0/10-4 0-

Flgure 4. Dependence of distribution ratios on molybdate concentration (C,= C , = 1.0 X lo4 M, pH 1.9-2.1): (a) CM = Czr (0); (b) C , = c,, (0). b

-11

M

1

2

3 PH

Flgure 3. Dependence of dlstributlon ratios on pH value (C, = C = 1.0 X io4 M): (a) , C = 1.1 X lo3 M (0); (b) C, = 1.2 X los M (A);(c) c, = 1.5 x 10-3 M (0).

solvent extraction of ternary heteropoly molybdates formed in aqueous solution was found to be selectively extracted with cyclohexanone and propylene carbonate, compared with other oxygenated solvents. This result is shown in Table 111. We have investigated the extractability of ternary heteropoly molybdates with cyclohexanone, one of the more basic solvents. In preliminary experiments each shaking time of 10,15,20, 30, and 60 min gives the same distribution ratio within experimental error. In addition, to ensure that equilibrium was attained to give a valid value for distribution ratio, two sets of samples were shaken overnight. It was found that 20 min of shaking time was enough for equilibration in all cases. For optimum extraction of ternary heteropoly molybdate, the variation of distribution ratio was determined with various pH values. Figure 3 shows the distribution ratio vs. pH values at various molybdate concentrations. These data show that ternary heteropoly molybdates are only formed within the limited pH range of 1.5-2.5. These ternary heteropoly molybdates are unstable in the strong acidic medium and many molybdenum species are needed to produce the complex quantitatively. In this series of experiments, molar ratios (CMo/Cp)were preserved from 9 to 16 in the aqueous medium of pH 1.5-2.5. Lower pH induced the decomposition of the compound, while at higher pH, group 4A metal ion was precipitated by hydrolysis. To ensure the extraction of metal ion quantitatively, the back-extraction with basic aqueous solution was carried out. Ternary heteropoly molybdate is decomposed when the organic phase is contacted with a basic aqueous solution; the group 4A metal ion is transferred into the aqueous phase. Spectrophotometric determination of that was done as above. However, cyclohexanone dissolved in aqueous phase accelerated the degradation of Arsenazo 111 reagent. The color was stable up to 5 h, so that measurement must be made within this period. In addition, to ensure that uncomplexed group 4A metal ions are not extracted with various organic solvents, preliminary experiments were also carried out as above. The distribution ratio was measured at an initial phosphate concentration (Cp) of 1.0 x lo4 M in aqueous solution for all systems. The average values from three to five runs in each system are plotted in Figure 4. Keeping other factors con-

stant, the molybdate concentration was varied from 9.0 x lo4 to 1.6 x M. Figure 4 shows that the distribution ratio approaches almost to a constant limiting value, the molar ratio (C,,/Cp) at the intercept of the extrapolation of two lines being 11. This result indicated that the ternary heteropoly molybdate has the composition of PMe:Mo = 1:1:11 and has a greater formation constant. Distribution ratios ( D M J were calculated from following equation: DMe

=

(cP-Me-Mo)org/(cMe)aq

+ (CP-Ms-Mo)aq

(3)

where is free metal ion concentration and (Cp-MeMo) is the ternary heteropoly molybdate concentration, respectively. These values are log Dzr= 25.0 and log DHf= 15.5 (pH 2.0, Cp CMe = 1.0 X M). If an excess of 12-molybdophosphate should be present, the two distribution ratios would become greater. No evidence for the effect of acidic species was found and a one-step extraction was found to be sufficient in this work.

ACKNOWLEDGMENT The authors wish to express their thanks to Jun Iyoda of Government Industrial Research Institute, Osaka, and Yuji Kobayashi of Institute for Protein Research, Osaka University, for their help with NMR measurements. Registry No. 12379-13-4; ( P T ~ M O ~ ~ O ~ ~ ) ~ - , 87785-37-3;(PZrMo,,O,O)", 87785-40-8;(PHfMo1,04,J5-,8778543-1; Ti, 1440-32-6; Hf, 7440-58-6; Zr, 7440-67-7.

LITERATURE CITED (1) Murata, K.; Ikeda, S. Anal. Chim. Acta 1883, 151, 29-38. (2) Murata, K.; Ikeda. S. Anal. Chim. Acta 1870, 51, 489-495. (3) Murata, K.; Yokoyama, Y., Ikeda, S. Anal. Chim. Acta 1868, 48, 349-356. (4) Mukherji, Ani1 K. "Analytical Chemistry of Zirconium and Hafnium"; Pergamon Press: Oxford, 1970; pp 100, 128. (5) Strelow, F. W. E.; Bothema, C. J. C. Anal. Chem. 1967, 39, 595-599. (6) Cerral, E.; Testa, C. Anal. Chim. Acta 1862, 26, 204-211. (7) Goshl, Y. Adv. X-ray Anal. 1868, I f . 518. (8) Nakamura, Y.; Noto, Y. Bunsekl Kagaku 1962, 31, 413-416. (9) Veitsman, R. M. Zavod. Lab. 1858, 25, 408. (10) Veitsman, R. M. Zavod. Lab. 1960, 26, 927. (11) Furman, N. H., Ed. "Standard Method of Chemical Analysis", 6th ed.; Van Nostrand New York, 1982; Vol 1. (12) Elvlng; Philip J.; Olson, Edward C. Anal. Chem. 1855, 27, 1817-1820. (13) Kammorl, 0.; Taguchi, I.; Komlya, R. Bunseki Kegaku 1885, 74, 249-252. (14) Keggln, J , K. Prac. R. Soc.London, Ser. A 1934, 144.

RECEIVED for review June 27, 1983. Accepted January 30, 1984. The present work was partially supported by a Grant-in-Aid for Scientific Research (No. 57540331) from the Ministry of Education, Science and Culture, Japan.