Nitroform in Various Solvents1aJJ - American Chemical Society

Publiccdion costs assisted by the Lockheed P a b Alto Research Laboratory. Q4SOd (Received June $9, 1970). Proton exchange rates were determined for ...
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STRUCTURE OF KITROFORM IN VARIOUS SOLVENTS

499

Nitroform in Various Solvents1aJJ

y €3. P. Marshall," F. G. Borgardt, Paul Noble, Jr., and N. S. Bhacca Lockhed Palo Alto Research Laboratory, Palo Alto, California Q4SOd (Received J u n e $9, 1970) Publiccdion costs assisted by the Lockheed P a b Alto Research Laboratory

Proton exchange rates were determined for nitroform in D,0-D2S04 solvent up to an analytical mole fraction of 1)20 = 0.5. The proton exchange rate for an analytical mole fraction of 0.159 of DzO in D2SO4-D2Ois given by log k (see-I) = 9.38 - 19,200/2.303RT (AS+at 55" is -17 eu) for the temperature range of 40-70'. Further, the log of the rate constants was found to be proportional to the analytical mole fraction of D20 in ISzS04. il, mechanism for the proton exchange reaction is proposed. Proton chemical shlfts for nitroform, l,l-dinitroethane, and 1,l-dinitropropane were determined in a series of solvents. The chemical shift of nitroform ranges from 6 (ppm) of 7.40 in CC14 to d (ppm) of 9.18 in acetone; in the latter solvent, complex lormation occurs with a K,, = 10 (-37') (concentration in mole fraction). Rapid proton exchange occurs hetween water, methanol, and 12 N HCl and nitroform. Proton chemical shifts of 1,l-dinitroethane and 3 1-dinitropropane for the C-1 proton are shifted downfield by -0.7 (ppm) in changing solvent from CCl, t o acetone. Small shifts (-0.04 ppm) downfield were observed for the C-2 protons. Coupling constants were determined for the various protons in the dinitroalkanes and found to be independent of the solvent system.

Introduction For some time, this laboratory has been involved in studies of the synthesis, reactions, physical properties, and structure of the polynitroallranes. As part of these studies, an nm;c investigation was carried out to obtain an insight into the structure, H-bonding, complex formation, and proton exchange rates for several polynitroallranes. Previous studies hmve shown nitroform to have some of the propeiptjes of strong protic acids, also t o occur as a colorless to inl ensely yellow substance depending upon the nature of the solvent, and t o undergo addition reactions with a,p-unsaturated carbonyl compounds in which either @-. or O--alkylation can occur. This paper is concerned nith defining the structure of nitroform and other 1,l-dinitroalkane species in various solvent systems.

Experimental S e d h Matevials. Nitroform (HKF) was prepared by a modificatjon of the procedure2used in the course of preparation of trinitroethanol. Tetranitromethane was titrated with alcoholic KOH to give KC(NO&, which upon acidificatjon with HG1 yielded an aqueous slurry. Extraction of this slurry with CCb, followed by drying and evaporation, yielded reasonably pure HNF. Final purification of the IINP just before use was achieved by fractional sublj malcioii . The polyizitcaaikanes, 1,l-dinitroethane and 1 , l dinitropropane, were prepared by the method of Schechter and Kaplari. These materials were purified by fractiona,l distillation a t reduced pressure. The purity was 99+% as indicated by gas-phase chromotography. The dioxane-nitroform complex, C,H802.

2HC(X02)3, was prepared as previously described by Shechter and Cates.4 Solvents. The acetone, acetonitrile, and carbon tetrachloride were commercial spectral grade solvents. Acetone-& (purchased from Varian) was used as received. Aiethanol was dried by a procedure described by Wiberg.6 Trifluoracetic acid, commercial grade (Peninsular Chemical Co., Gainesville, Fla.), was purified by distillation. Deuterated acetic acid (C€13COOD) was prepared by reaction of purified CHsCOCI with DzO followed by fractional distillation. Proton magnetic resonance spectra showed the presence of only a trace of CH3COOH. Deuteriosulfuric acid was prepared in an all-glass vacuum system. Purified SO, was slowly distilled into D20until a slight excess of SOawas attained. Then the D2S04was distilled into a glass container for storage. The proton magnetic resonance spectra of the D804 showed the presence of only a trace of HDSOI. Solutions of various analytical mole fractionG of (1) (a) This work has been carried out as part of the Lockheed Independent Research Program: (b) portions of this paper were presented before the Division of Physical Chemistry at the 153rd National AMeeting of the American Chemical Society, Miami, Fla., April 1967. (2) F. G. Borgardt, A . K. Seeler, and 1'. Noble, Jr., J . Org, Chem., 31, 2806 (1968).

(3) R. B. Kaplan and H. Shechter, J. A m e r . C'hem. Soc., 83, 3535 (1961). (4) H. Shechter and R.L. Cates, Jr., J. O r g . Chem., 26, $1 (1961). (5) K. Wiberg, "Laboratory Techniques in Organic Chemistry," McGraw-Hill, New York, N. Y., 1960. (6) Throughout this paper analytical mole fraction (X)refers to the composition of the solvent in terms of the original amount of reagents employed for its preparation; thus for DzO, XD,O= moles of DzO/(moles of DzO moles of DzSO~).No attempts are made to calculate actual mole fractions of various species after equilibration or complex formation has occurred.

+

T h e Journal of Physical Chemistry, VoE. '76, No. 4%1571

H. P. MARSHALL, F. G. BORGARDT, P. NOBLE,JR.,AND N.

500

S.BIIACCA

DzO(XD,o)with the D2S04were prepared gravimetrically. The composition of the D2S04 solutions at several X D , O was checked by titration with standard base and was found t o be within 0.2% of the calculated X D ,values. ~ All proton spectra were determined at 60 Mc/sec using a Va,riaJn14-60 spectrometer equipped with a variable temperitlure probe. Tetramethylsilane was used as an internal stanclard unless otherwise indicated. Ultraviolet spectra of the H N F in various solvents were determined with a Cary-14 spectrophotometer. Results and Discnuision The chemical shifts of H N F were determined in Uz0-D2SCT4solvent a t various mole fractions of DzO (XDzD).Thwe data are summarized in Table I and plotted in Figure 1. The chemical shift of H N F increased from 8.18 ppm to 8.60 ppm as the XD,o was increased from -0 to 0.5. The chemical shifts of the HDSO, were essentially the same for the pure solvent as in the presence of ihe HNF. The absorption peaks for the HNF and HD804 were very sharp up to an XD,ON 0.5 with a single peak observable for X D ~> O0.5. _ I I _ -

Table I : Chemical Shift of H N F in DzO-D&~O~" hnalytical mole fraction of mater,

xu10

0.00:72b*d 0 143 0.191 0.298 0.370 0.430 0 472 0.487" 0.49L 0.493 0,495 0.49'7 0,498 0.49!) 0.598 0.659 0.718 0.749

Chemical shift--------

7 -

GHNB, Ppm

GHDSOa,

8.18 8.27 8.28 8.33 8.42 8.42 8.61" 8.58" 8.60" 8.60' 8.60" 8 I58"

11.18 11.15 11.70 11.98 12.09 12.13 12.13 12.12 12.05 12.07 12.13 12.13 12.09 12.11 11.72 11.34 10.85 10.45

ppm

8.60'

'

a TM6 wed as an exteriial standard. All solutions were prepared on a might basis; concentration of solutions at several D2f504were checked by titrations with standard base. BHNF signal observed only at spectrum amplitude of 80. I n the absence of I-IPJF, the chemical shift for the pure solvent was 11.24. ' I n the absence of HNF, the chemical shift for the pure solvent was 12 16.

The proton exc'hange rates of H N F in D20-DzS04 were determmcd as a function of XD,O. The rate constants, kl, were calculated using a first-order rate expression for which the concentration of HNF was asThe Journal of Physical Chemistry, VoE. 76, No. 4, 1971

L

o

I

I

I

0.1

0.2

0.3

1

I

0.5

0.4

__i

1

0.6

I

I

0.7

0.8

0.'

XOsO

Figure 1. Chemical shift of HNF and HDSO4 in D20-D2SOa as a function of analytical mole fraction of D20.

sumed to be proportional to the line intensity of the proton resonance peak of the HNF. The same values of rate constants were obtained, within experimental error, when the areas of the proton resonance peaks were used to estimate the H N F concentrations. The kinetic data are given in Table 11. At an XD,Oof 0.159, the proton exchange rates were determined as a function of temperature and gave for the energy of activation, LE', 19.2 kcal/mol and for the entropy of activation, AS', - 17 eu at 5.5'. The exchange rate is relatively slow and increases as XD,Ois increased. A forty-fold increase in k l was observed as XD*O was increased from 0.159 to 0.468. The proton exchange reaction occurring between H N F and the D20-D2S04 solvent is probably a bimolecular reaction involving H N F and D20. Thus the rate of disappearance of HWF may be expressed by --d(HKF)/dt

k2(aasp)(aD2o)

(1)

where IC2 is the bimolecular rate constant and a H N F and UD,O are the activities of H X F and D20, respectively. The ICI'S reported in Table I1 were obtained by eq 2, namely

kl(BNF) (2) Strictly speaking, the rates should have been computed using the activities of HXF as given by -d(HNF)/dt

-d(HSF)/dt

=

=

ki(aai;vr?) = ~I(HNF)(YHSF)(3)

being the activity coefficient for nitroform. The activity of HNF is assumed to be proportional to its concentration, which implies that Y H N F is a constant during the course of a kinetic run. This is a reasonable assumption since the total Concentration of nitroform species (sum of the concentration of nitroform and deuterionitroform) during a run is constant. Thus eq 1-3 can be combined giving ery 4. YHNF

STRUCTURE OF WITRCIFORM IN VAR,IOUS SOLVENTS

501

Table 11: Kinetic Data for HNF Proton Exchange in DzO-DzS04 hfQlE

Run

fraotion

T dmpeiriture, ‘C

of D20,

XDzo

11 10

0.159 0,159 0.150 0.159 0.159 0.159 0.260 0.260 0.365 0.365 0.468 0.468 0.468

1 2 12 13

3 4 5 6 7 8 9 Average error in k’s.

a

7 -

First-order rate constant-------h,sec-1 (% errorla 76

9.58 X I .os x 4.48 x 4.08 x 1.39 X 1.61 X 1.34 x 1.13 X 4.45 x 5.97 x 1.87 X 1.60 X 1.68 X

10-4 10-4 10-4

10-3

5 5

(12) (16) (3) (3) (3) (6) (2)

22 13 9 10 6 11 6 4

(5) 10-3 (7) 10-3 (4) (7) (4) (9)

8 8 9

Initial canon oE H N F (e of HNF)/ (g of DaO-DrSOa) aolvent

0.0967 0.0702 0.0806 0.1151 0 0836 0.0801 0.0506 0.0502 0.0576 0.0533 0.0536 0.0460 0,0561

AE 1,

AS?,

kcal/mol

@U

19.2

- 17

I

Xrimber of points used in determining each ICl.

The uD2O in the I&Q--D,SO, was assumed to be the same as the activity of water (a,) in HZO-WsS04 at the same concentration. The assumption that a, = u D 2 0 is quite vdid since it has been shown that the acidity functiors of IIO arid DOare very similar.’ The a, (molar uniis) were computed from the data of Giauque;* for the dmsities of D20-D2S04, the values of the densities of Xi20-H2S04were used.9 The value of k2 computed for this reaction is 14 1. molw1 sec-’ (Table 111).

+products (sa)

Table I11 : Calculated Second-Order Rate Constants for Proton Exchange of H N F in D J ~ O ~ C Dat ~ O55’ k 2 , 1. mol -1

I?, XDzO

0.259 0.260 0.365 0.468

g/CCa

1.84

1.83 1 82 1.78

sec-1’

4.28 X l o b 4 1 . 2 4 x 10-3 5.21 X 1.72 X

sec -1

.wo

2.38 X l o F 5 9 . 5 3 x 10-5 3.78 X 1.41 X lo-*

16 13 14 12

-

Av

14

Denqity of H2O-H2S04 soliltions at same X H ~ O as X’D~O. Data calculated from ref 16 (molal units). a

’ Average value from duplicate xiins, Table IV. _s_l

The reaction appears to represent a monotonic function of the solvent composition; i . e . , the rate of reaction is related directly to thc activity of water in the concentrated acid. lo The reaction can be envisioned to be proceeding as indicated in eq ;i,n.here the species in the brackets is the activated complex.

In either case, 5a or 5b, ion-pair formation could occur followed by collapse to the deuterated species. Also, the HD20+ could leave the vicinity of the nitroform anion followed by reaction with the DzO-DzSOa solvent. Further information bearing on the structurc of the nitroform species was obtained by determining the uv spectra of HXF in H20-H2SOi. The pertinent data are summarized in Table IV. No significant change in the uv spectra was observed (7) E. Hogfeldt and J. Biegeleison, J . Amer. Chem. Soc., 82, 15

(1960). (8) W. F. Giauque, E . W. Hornung, J. E. Kunzler, and T. 1%. Rubin, ibid., 8 2 , 62 (1960). (9) “Handbook of Ghemistry and Physics,” 45th ed, The Chemical Rubber Publishing Co., Cleveland, Ohio, 1963. (10) J . Leffler and E. Grunwald, “Rates and Equilibrium of Organic Reactions,” Wiley, New York, N. Y., 1963. The Journal of PhysicaE Chemistrg, Vol. 7’6,N o . 4 , 1971

H. P. nfARSHALL, F. G. BORGARDT, P. XOBLE, JR.,AND b;T. 8. BHACCA

502 I

Table IV : U1i raviolet Absorption Bands for HNF in Various Solvents Concn of NNF, mol/l. X 10'

Absorbance, A

Xmnx

11.06 6.95 5.79 6.32 5.69 7.68 8.61 6.59 0.0335 3.77 2.62 2.84 2.76 4.21 2.83

(mnx

278 276 278 277 280 276 277 270-280" 350 290-310" 341 275(s)* 350 280 281(~)~ 351

0.832 0.595 0.424 0.517 0.097 0.202 0.650 (0.57) 0.22 1.818 0.54 0.30 2.08 0.42 0.31

75 86 73 81. 17 26 75 (86) '9,000 480 206 105 754

looc

110 16, OOOd

= 110 In isooctane; V. N. Slovetskii, V. A. Shlyapochnikov, K. K . a Broad band. * 8houlder. Reported A,, = 280 and Babievskii, and 6. S.Kovikov, Izv. Akad. Nauk SSSR, Otd. Khim. Mauk, 1709 (1960). Approximate value: we found some variation of x,*, TA ith concentration; HNF is unstable in aqueous solvents; M. Kamlet, private communication.

Table V : Solvent Effect on Chemical Shifts of Polynitroalkane Protons

7.40 7.40 7.83 8.2 8.35 8.68 Exchange* 9.1Re

7.82(7.70)'

2.16(6.6)d

6.14(7.0)d

6.55

2.22

6.35

2.59

1.15

6.60

2.13

6.47

2.52

1.07

6.80 6.95

2.11 2.19

6.66 6.81

2.55 2.59

1.12 1.14

8.34 Exchangeb

2.55(7.5)d

I . 15 (7.5y

6.19(6.6)d

8.62

'

a Concentration oE polynitroalkanes about 10%. HNF exchanges rapidly in water, 12 N HC1, and slowly irr concentrated D2SOa. Concentration about 5%; no shift of CHZproton of dioxane occurs on changing the concentration. No observable change of J with solven change. e I n acetone-&, 6 Is 9.23.

c

as the XHZ0 was wricd from -0 to 1.0. A decrease of O the range of 0.55 the c5xtinction coeificient for X H ~ in and 0.7'9 and a Ehift of, , ,X toviard the visible as XHzo approached a value of 1.0 were noted. These spectra of HNE' in 1120-H2SOa solutions (similar spectra would be obtained for HNF in D20-D,S04 system) lead one to conclude that the preponderance of the HIC-F is in the stale with H bonded directly to carbon. This would indicate that a reaction scheme shown by eq 5%is the favored reaction path for the proton exchange procces. The data indicate the exchange in the N20-H2S04iiysteni is a specific base (HzOor D20) catalyzed reaction. Further insight into the behavior and structure of HNF was obtained in the determination of the proton resonance spectra in a series of solvents. Also, proton resonance slwcira for several other polynitro comThe Journal of Physirai' Chemastry, Val. 76, N o .

4,1971

pounds were determined. The chemical shifts derived from these spectra arc given in Table Q with some coupling constants for the polynitroalkane compounds. In Figure 2 the chemical shift of nitroform in CCl, and in acetone is plotted as a function of the analytical mole fraction of HKF. I n CGld, the proton resonance is shifted upfield essentially linearly to a value of -7.25 ppm as XHNF approaches zero. The upfield shift probably results from a lowering of the dielectric constant of the medium in going from X H N F of 1.0 to 0. In acetone, the proton resonance of the HKF is shifted downfield by -1.4 ppm as the X H N F is varied from 1.0 to 0. The chemical shift of the proton resonance of the H N F is probably associated with complex formation between HKF and acetone by hydrogen bondingll with rapid exchange occurring between the complex and the 'lfree" HNF. The equilibrium con-

STRUCTURE OF NITROFORM IN VARIOUS SOLVENTS

3

0.1

0.’

0.4

0.3

0.5

0.6

0.7

0.8

0.9

sented by structure I would be resonance stabilized as is apparent from the number of resonant structures possible for this complex. This structure is compatible with the observed uv spectra of HKF in acetone (see of HXF in acetone is shifted Table IV): The A, toward the visible and emax is larger than that observed for HNF in nonhydrogen bonding solvents such as CCl4 and hexane. This structure is also strongly favored based on the proposed structures for the activated complex for the proton exchange reaction between HNF and DzO-DzS04. Another possibility is the formation of a compound as indicated by structure I1

1.0

NO2 CH3

X~~~

Figure 2. Chemical shift of nitroforni in CCh and acetone as EL function of analytical inole fraction of HNF.

stant for complex formation between acetone and HNF (eq 6) was cttlculated as 10 (concentration in mole fraction) at, 37”. CH3COCH3 3. HNF

CH3COCH3.HXF

(6)

The procedure, described in the literature,12 gave for the chemical shift of the complex a value of 9.36 ppm. The proton absorption peak due t o the HNF-HNF. acetone complex was vary sharp over almost the entire range of concentration. Some line broadening of the signal was obscrved (st XHNFof 0.0987. The chemical shifts of the acetone methyl protons varied from 2.06 to 2.24 ppm (extrapolated values) linearly as X H N F mas increased from 0 to 1.0, with no proton excliange occurring between N F and CH3 group in acetone as indicated by na change in the ‘Pine intensity of CHD, absorption whenever acetone-& was used as the solvent. Some self-association of the HNF may take place, but probably is very small. Equilibria such as shown in eq 7 ale certainly plmsible and would account for the

0 2 (NOZ)&H

/I z?(XO,) sC--H* *O-N-CH 1

(KOz)2 (7)

slight line broadening that was observed as well as the difference in Chemical shift between the neat liquid and its solutiorts in CC1,. (Differences between the viscosity of the neat liquid and the CC14 solution are not responsible for the observed line broadening.) The structure of the complex between HNF and acetone may be repreaented by structure I 0I

I

0-

503

fi-

6-

wherein the proton of HNF is still strongly bound to the NN (nitrofarm anion) group. The complex repre-

I I

OnN-C---C-OH

I 1

(11)

NO2 CHI

as a result of the Henry reaction.13 Several arguments against structure HI for the HNFacetone complex are as follows. (a) Hall14 was not able to prepare 2,2,2-trinitr0-1,l-dimethylethanol (11); however its existence in acetone solution could be argued. (b) Compound 11 would be expected to be a strong acid even in acetone and exist mostly as the individual ions, part of the driving force for ionization being obtained from steric interactions of the methyl groups with the nitro groups. The pK’s in NzO14of 2,2,2-trinitroethanol and 2,2,2-trinitro-E-methyI-ethanol are 6.1 and 3.6, respectively. Substitution of another methyl group would further increase the acid strength by several orders of magnitude yielding highly acidic solution which should promote proton exchange between HNF and acetone-&. This ‘vi‘asnot observed. (c) Also, the uv spectra are more compatible with structure I than I1 (see Table IV). In other solvents (data in Table V) rhe proton resonance of the HKF is shifted to lower fields as compared to the neat solution; the noticeable exceptions are the upfield shifts observed in F3CCOOH and in CCI, (discussed above) and for the rapid proton exchange occurring in CH30H. We believe that the downfield shifts are due to complex formation through hydrogen bonding as discussed for the behavior of HXF in acetone. In CH3COOD and in trifluoroacetic acid t i ~ osharp absorption peaks are observed in each caw, indicating that proton exchange between these solvents and the HNF, if it is taking place, does so slowly. In trifluoroacetic acid the proton resonance due to the HXF is observed at 7.40 ppm, i.e., upfield of that for the neat solution. The upfield shift is probably not due to a lowering of the dielectric constant of the medium (for (11) A . Loewenstein and Y .Margaht, J . Phys. Chpnz., 69,4152 (1965). (12) The NMR-EPR staff of Varian Associates, “KMR and EPR

Spectroscopy,” Pergamon Press, New York, N Y . (13) For a resume of the Henry reaction, see F. Noble, Jr , F. 6. Borgardt, and W. L. Reed, Chem. Rev., 64, 19 (1964). (14) T. N. Hall, Tetrahedron, 19 (l), 115 (1963) I

The Journal of Physical Chemistry, Vol. 7 6 , S o . 4 , 1971

H. P. MARSHALL, F. G. BORGARDT, P. NOBLE,JR., AND N. S. BHACCA

504

CF3COOH, the dielectric constant16 is 43 at 25"), but probably is due to the lower basicity of the solvent, trifluoroacetic acid, compared to the other solvents. Tlie effect of various solvents on the chemical shifts of the protons in llhe other polynitro compounds and the molecular complex, dioxane .2HNF, were studied and the findings are summarized in Table V. Good agreement WAS obtained with the data of HoffmanlGfor studies carried out in the same solvent systems. The chemical shift of dinitroethane and dinitropropane are similar in character to those observed for HNE' in the same solvents, the notable exception being that no rapid exchange occurred in methanol. The resonance absorption peaks were very pronounced m5th no noticeable line broadening. The coupling constants for the various protons of the two dinitro compounds were found to remain constant with change of solvent. The chemical shift of HNF was found to be essentially independent of temperature in acetic acid (CH&OOD) and in acetonitrile, as is evident from the data presented in 'Fable 1'1, The change in chemical shift was only 0.05 :tnd 0.1 ppm for a temperature change of 45" in acetic acid and acetonitrile, respectively. Slow proton exchangc takea place between the acetic acid and the HNF sinl:e the spectra showed two sharp resonance peaks at 3'7"- one for the H X F and the other due to the

38 60 70 80 BOO 110

-----Chemical CHsCOOD

HNF NF-

+ H20

+ H30+

NF- -f- HaO+

---3~

different

HNF 4-HzO

(8%) (8b)

followed by the reverse reaction, eq 8b. In carboxylic acid solvents (weak base) the acid dissociation proceeds as shown in eq 9a HNF

+ RCOOH' +

RCOz+H'HNF-

RCOz IH'HNF- (ion pair)

(9a)

+ RCOOH

(9b)

different -3

proton

H'NF

CHaCN

probably proceeding through an ion pair, followed by collapse of the ion pair to starting materials. Steps 8a and 9a are probably rate determining. The relative rates of proton exchange of H N F in the various solvents appear to be a function of the specific basicity of the solvent.

8.35 8.32 8.30 8.30

Acknowledgment. The authors are grateful to Professor E. Grunwald for some helpful suggestions in the preparation of this manuscript.

Table VI: Effect of 'L'emperature on Chemical Shift of HKF in Acetic Acid and Acetonitrile Temp, "C

acidic proton of acetic acid. Increased line broadening of the HNF resonance absorption was observed with increased temperature. A few further comments must be made relative to the behavior o€ H N F in various solvents. It has been shown experimentally that the proton exchange between HNF and methanol, water, concentrated HC1, and Dz0-DzS04 for XD,O2 0.5 occurs quite rapidly. On the other hand, slow proton exchange occurs between HNF and CH&OOH, CF,COOH, and I)20-D2S04 for X D ~5 O 0.5. Proton exchange in these solvents is the result of acid dissociation of HNF. In water, a strongly\ basic solvent, the acid dissociation proceeds as sho6n in eq 8a

shift, HNF, ppm------

8.70" 8.62

8.60 8.56 8.53

Same vsluc of ci [ppm) obtained after cooling sample from 110". a

The Journal of Physical Chemistry, Vol. 76, No. 4, 1971

(15) J. H. Simons and K. E. Larentzen, J. Amer. Chem. Soc., 72, 1426 (1950). (16) W. Hoffman, L. Stefanak, T. Urbanski, and M. Witanowsky, {bid.,86, 54 (1964).