1622
ROBERT R. HF!KTZ
that decay labeling not only gives tritiated propane but also tritiated products whose formation required C-C bond rupture. Table V compares L ( X ) p values estimated by different methods. Here, it is essential to specify (T,) because L ( X ) p depends on Since the largest number of experiments were carried out a t (T,) = 2.2 curies, the comparison was made a t this total P-activity. Under thesr experimental
Vol. 66
conditions, accuracy in determinations of L(X)p was sacrificed for good estimates of L(X)d; nevertheless, L ( X ) p values estimated by the different methods agrec reasonably well. Acknowledgment.-Nre express our appreciation to Dr. F. H. Dickey and L. 0. Morgan for their valuable discussion and Mr. E. L. DeWitt and Mr. J. D. Reedy for helping with the experimental work.
7-IRRADIATION OF ISOPROPYLBEXZENE BY ROBERT R. HENTZ Socony Mobil Oil Company, Inc., Research Department, Princeton, N. J . Received Pehruary ,926,1062
Cobalt-60 ?-irradiation of isopropylbenzene has been studied in the liquid phase a t 36 and 145' and in the gas phase over the tem erature range 163-385" a t ressures of 0.5 and 1.0 atm. Maximum G-values are obtained in the gas phase a t 385" antlare as follows (G-values for {quid-phase irradiation a t 36' are in parentheses): isopropylbenzene reacted, 18 ( 1.8); polymer, 9 (1.7); methane, 3.4 (0.090); benzene, 2.8 (0.05); Cs-benzene, 2.3; hydrogen, 2.1 (0.179); Cn-benzene, 1.5 (0.04); propene, 0.56 (0.010); propane, 0.51 (0.011); toluene, 0.5; ethene, 0.23 (0.002); ethane, 0.07 (0.004); and acetylene, 0.05 (0.004). Radiolysis is compared with catalytic and non-catalytic thermal cracking.
This study was undertaken to determine how g. were used in gas-phase irradiations. I n liquid irradiations, of 1-5 g. were uscd. radiation cracking of isopropylbenzene compares weights Gas-phase irradiations were carried out in cylindrical with catalytic and non-catalytic thermal cracking Pyrex cells about 3 cm. in internal diameter, 8-9 cm. in and whether a selective radiation dealkylation to length, and 60 ml. in volume. The cells were equipped with benzene might be obtained with reasonably high a breakoff seal and a tube for filling. The volume of each was determined accurately so that the pressure could be radiation-energy yield (G) in the presence of a cell calculated from temperature and weight of isopropylbcnzene microporous solid which is a good catalyst for the using the ideal gas law. Liquid irradiations were carried out thermal dealkylation. Isopropylbenzene was in cylindrical Pyrex cells about 3 cm. in length and 2 cm. in chosen for study because of the availability for internal diameter, also equipped with a breakoff seal and a for filling. These cells were designed to prevent any comparison of thorough studies on the catalytic and tube appreciable contribution from irradiation of the vapor. A non-catalytic thermal cracking of this compound.'S2 new cell was used in each experiment. The reaction cells were placed in a vertical cylindrical This paper reports on the fiilst phase of this study furnace surrounded by four cobalt-60 cylinders (about 2 kiloin which isopropylbenzene has been irradiated with curies in vertical aluminum tubes at the corners of a cobalt-BO y-rays over a wide range of experimental square.each) Temperatures were measured with thermocouples conditions. A communication to the editor on attached to the cell; in high temperature experiments, the thc 7-irradiation of isopropylbenzene adsorbed on cobalt cylinders were protected from possible ill-effects of heat by passing a stream of air through a manifold on the microporous silica-alumina has been p~blished,~"the bottom of the irradiation unit and up through the slipporting and a complete paper on this second phase of the aluminum tubes. After irradiation the reaction cell was work accompanies this article.3b attached to a high-vacuum line. Total gas products were measured in a modified Saunders-Taylor apparatus4 after Experimental separation from the liquid a t the temperature of an ethyl Chemicals.-A volume of 1170 ml. of Eastman Kodak 1481 isopropylbenzene was distilled on a 100 theoreticalplate column undcr conditions giving 85 plates. A constantboiling middle fraction of 223 ml. was used in all experiments: n 2 0 ~ 1.4913; n% (lit.) 1.4914. Not more than t,wo days prior t o each experiment, 20 ml. of the distilled isopropylbenzene w a ~passed through 10 ml. of Alcoa F-20 alumina in a 60-ml. burcat with a Teflon stopcock at a rate of about 2 ml./min. for rcmoval of isopropylbenzene hydroperoxide.2 Procedures.-Reagent was measured into a weighed bulb which then was reweighed. The bulb was attached to a high-vacuum line on which the isopropylbenzene was transferred into a tube which contained a sodium mirror. The reagent then was dcgassed by rcpeated freezing with liquid nitrogen, pumping, and thawing. The procedure was completed by transfer of the reagent into the reaction cell on the vacuum line and sealing off of the cell. Weighing of the reaction cell before and after filling gave a second weight of reactant and the average was used. Weights of 0.087-0.198 ~-
(1) C. J. Plank and 13. M. Nape, Ind. E w . Chem., 47, 2374 (1955). (2) R. W. Maatman, R. M. Lago, and C. D. Prater, Advan. Cataly818, 9 , 531 (1947). (3) ( a ) R. R. Hents. .I. Phvs. Chem., 66, 1470 (1961); (b) R R Hentz, zhzd , 66, 1625 (1962).
bromide mush, -118". Gas products were analyzed mass spectrometrically . The condensed liquid after irradiation has a yellow color. The liquid was distilled from the reaction cell, after gas removal, into a weighed tube immersed in liquid nitrogen on the vacuum line. The tube, equipped with a breakoff seal, was sealed off and weighed to ohtain the weight of Iiqiud recovered. The distilled liquid was colorless, and on the walls of the reaction cell a yellow deposit was left which appeared t o be a very viscous liquid. The distilled liquid and yellow residue were both analyzed mass spectrometrically except for the liquid product of the liquid-phase radiolysis, which was analyzed chromatographically. The difference between initial weight of isopropylbenzene and weight of liquid recovered gives essentially the weight of yellow residue. G-(Residue\ is based on molecules of isopropylbenzene converted to residue. The weight of liquid recovered with its percentage of isopropylbenzene gkes G( -1sopropylbenzene) and the percentage decomposition. The weights of residue and of isopropylbenzene lost are obtained as small differences. @(Residue', G-( -1sopropylbenzene), and percentage decomposition in experiments two and three in Table I have a reliability of about f10%. At
(4)
K. W. Fsunders and H. A. Taylor. J . Chenh. P h g ~ . ,9, 616
(1941).
Y-ISRRDIATSON OF IAOPHQPYLPEKZENB
Sept., 1962
1623
TABLN X IRRADIATION 71,
"C.
P , atm. G ( Hydrogen)e G (Methane)
G (Acetylene)
103 0.51 0.49 2.08 0.21 .13 .02 .14
233 178 1.10 0.69 0.43 0.70 1.92 1.89 0.15 0.11 .11 .16 .02 .01 .ODd .OSd .00 .08
230 0.47 1.01 2.14 0.18 .14 .01 .loJ
OF
244
1.oa 0.89 2.02 0.18 .ll .03 .lod -13
ISOPROPYCRE~XZWNE 307 387" 385 385b 36G 1 . 0 4 1.01 0.YIi 0.98 1.88 0 . 1 5 2 . 2 3 2.08 0.179 ,090 .13 3 . 5 0 3.37 2.87 0 . 0 5 0 . 0 5 ,004 0.05 0 ,002 .16 0 . 0 1 .24 .23 .07 .07 ,004 .04 .05 0 .58 .56 .O l O d . l 5 .13d 0 . 0 2 .01 .52 .51 .011 .27 18
320 0.97 1.65 2.18 0.10 ,12
36"
148"
0.185 0.203 ,088 .179 ,004 .008 0 .003 0.001 ,003 .015d ,021d ,061 ,015
G (Ethene) G (Ethane) G (Propene) G (Propane) .os .lo G ( -1sopropyl18 1 8 5 5 6 7 7 benzene) 4 4 5 5 3 G (Residue) 9 1.7 P 0.3 0.4 P 1.2 2 . 5 2.8 0.05 G (Benzene) P .6 .6 P P 0.9 1.5 0.04 G (C&enzene)f G ( CG-Benzene)' P P 1.0 2.3 G (Toluene) P .1 .2 P P 0.4 0.5 Thermal blank (dose = 0) with apparent G-values based on the dose that would have been received for the reaction time and sample weight used. * G for radiolytic reaction assuming additivity of thermal and radio1.ytic reactions. 0 Liquid phase irradiations. These values are a little low due to incomplet,eremoval from the liquid. e G is the yield in molecules/ Definitely ethylbenzene in liquid radiolysis and prohably also ethylbenzene in gas radiolyses. 0 Could be di100 e.v. isopropylbenzene or a hexylbenzene. I
lower percentage decompositions these values have only order of magnitude reliability. The li uid recovered contained from 97 to almost 100% isopropy;benzene. Consequently, the G-values given for liquid products are not of high accuracy, but are represented reasonably well by the figures given. Where amount of a product was too small for re resentation by a meaningful number, its presence is noted gy the symbol P. Dosimetry.-Energy absorbed in the gas phase is based on G = 72 for the acetylene dosimeter6 and is corrected for the electron density of isopropylbenzene relative to acetylene. A dose rate of 1.08 X 1 0 2 0 e.v./g./hr. was obtained with the acetylene dosimeter in the experimental geometry. Energy absorbed in the liquid phase is based on G = 2.40 for the ceric sulfate dosimetel.6 and is corrected for the electron density of isopropylbeneene relative to 0.4 M sulfuric acid solution. A dose rate of 0.94 X loeoe.v./g./hr. was obtained with the ceric sulfate dosimeter in the experimental geometry. All doses are corrected for decay of the cobalt-60 source. Energy absorbed is based on the initial weight of isopropylbenzene I n all gas-phase irradiations except those a t 178 and 233", the absorbed dose was within the range 2-5 X 1020 e.v., corresponding to 1-5% decomposition of isopropylbenzene. At 178 and 233' the dose was increased to 13.0 X 1 0 2 0 e.v. to give about 10% decomposition in order to obtain more reliable values of yields for loss, residue, and the liquid products. The G for total gas products is seen to be about 10% smaller a t this higher dose. Doses in the liquid-phase irradiations a t 36 and 145" for which liquid products are not reported were 7.4 and 9.4 X 102' e.v., respectively, corresponding to about 0.6 and 1.1% decomposition. The liquidphase irradiation a t 36" for which liquid products are reported was a t a dose of 12.1 X 102' e.v., corresponding to about 470 decomposition. The slight decrease in gas yields a t this higher 7 0 decomposition is within experimental error in this case.
renes, and possibly acenaphthenes and naphthacenes, benzanthracenes, or chrysenes are all present both bare and subst>ituted. KO dimer of isopropylbenzene wag detected; however, it may be present since the dimer parent peak sensitivity is very low. A prominent mass-224 peak suggests the presence of C9Hll-CsH9. A maximum molecular weight of approximately 740 was recorded with an average of roughly 300-400. The dark yellow color may be attributable to naphthacene and higher polynuclear hydrocarbons. Previous work7-l0 on the yellow residue formed in irradiation of all aromatics also has shown it to consist largely of polymers of the parent compound having an average molecular weight of 395 in the case of toluene and an average molecular weight that increases to a maximum of . 530 with increasing dose in the case of benzene. It is apparent that yirradiation of isopropylbenzene yields a complex array of products. This certainly is not unexpected in view of the literature of hydrocarbon radiation chemistryll and the fact that the mass spectrometric fragmentation pattern of isopropylbenzene shows the formation of about 85 different ions.12 Because of this complexity, it is futile to attempt a detailed discussion of the radiation chemistry of isopropylbenzene in terms of primary ionizations and excitations and subsequent reactions of the ions, excited molecules, and free radicals formed; discussion will be limited to some plausible processes that could be responsiResults and Discussion ble for the more important observations. Introduction.-The results are given in Table I. Gas-Phase.-In the mass spectrum of isopropylIn irradiation of the gas phase, small amounts of benzene the predominant ion is that formed by loss butane, isobutane, butenes, pentenes, and isopen- of a methyl radical. This ion accounts for about tane also were detected. Mass spectrometric 40% of the total ionization. If 25 e.v. be assumed analysis of the yellow residue shows it to consist of a for the average energy required tp form an ion complex mixture with indications of several promi- pair in isopropylbenzene vapor, a G = 1.6 is obnent aromatic systems based on correlations ob(7) R. R. Hentz and M. Burton, J. Am. Chem. SOC.,7 5 , 532 (1951). served with the usual hydrocarbons found in (8) W.N. Patrick and M. Burton, i b d , '76, 2626 (1954). (9) S. Gordon, A. R. Van Dyken, and T. F. Doumani, J. Phye. Chem., petroleum. Phenanthrenes or anthracenes, py62, 20 (1958). ( 5 ) L. M. Dorfman and F. J. Shipko, J. Am. Chem. Soe., 77, 4723 (1955). (6) D. E. Harmer, Nucleonics, 17, No. 10,72 (1959).
(10) A. R. Jones, J. Chem. Phys., 52, 953 (1960). (11) W. H. Hamill, Ann. Rev. Phys. Chem., 11, 87 (1960). (12) Unpublished mass-spectral fragmentation pattern.
1624
ROBERT R, HGXTE
tained for methyl radical production by this process alone. There are several other likely sources of methyl radicals. High-energy radiation produces excitation as well as ionization. Photochemically excited isopropylbenzene in the gas phase yields methyl radicals. l 3 In addition, neutralization of the parent ion and of the predominant ion may result in splitting off of methyl radicals. The benzene ring is a very effective free radical scavenger in the liq~iidphase at room temperature,14 which may preclude methane formation cza methyl radicals. It is reasonable to attribute some methane formation to methyl radicals and molecular elimination reactions (including ionmolecule), but to account for all methane in this way requires an explanation of the temperature dependence of the methane yield in terms of possible molecular elimination processes. Since the activation energy for abstraction of a hydrogen atom from isopropylbenzene should be considerably less than that for abstraction from benzene, it seems more reasonable to attribute some of the methane yield to thermal methyl radical abstraction reactions and to account for the temperature dependence in terms of competition between abstraction and ring-addition reactions. (HardwicklS has presented evidence that for reaction of hydrogen atoms with isopropylbenzene the rateconstant ratio for abstraction relative to ring addition is about 0.05 a t 23".) This argument is given some support by vapor-phase photolysis data at 150-160O and about 0.5 em. pressure.la Ethane is the major gas product, exceeding methane by a factor of about two and hydrogen by a factor of about three. Clearly, all methyl radicals are not being scavenged by addition to the ring and combination is favored over abstraction at the low pressure of the photolysis. Considerations similar to the foregoing would apply to most of the other products formed in the radiolysis. Of the 85 ions in the mass spectrum of isopropylbenzene only 10 have a relative abundance greater than 5 . It is possible, but not particularly enlightening, to account for all products observed in terms of the 10 most abundant ionization processes and plausible secondary reactions of the ions and radicals formed. The increase in yield with increase in temperature of all products except acetylene may be accounted for as in the case of methane; however, a unique explanation is possible for the relatively large rates of increase in benzene, propene, and propane yields (by analogy to the mechanism for catalytic dealkylation which involves proton transfer from the catalyst) in terms of slightly endothermic proton transfers from positive ions in the system to isopropylbenzene with ultimate formation of benzene and a propyl radical (or propene and a hydrogen atom) on neutralization of C9H13+or of C&+ after decomposition of CsH13+. Radiation cracking in the gas phase is similar t o (13) T. J. Sworski, R. R. Hrnte, and M. Burton, J. Am. Chem. Soe., 1998 (1951). (14) J. G. Burr and J. M. Soarborough, J. Phvs. Chem., 64, 1367
la,
(1960). (IS) T. J. Hardwick, %bid.,66, I17 (1962).
Vol. 66
non-catalytic thermal cracking in that hydrogen and methane are major gas products; the ratio of methane to hydrogen varies from 4.2-1.3 as temperature goes from 183-385". This ratio is 0,9 at 385" in non-catalytic thermal cracking as seen in column 8 of Table I and as reported by Plank and r\lTace.l As in catalytic thermal cracking, benzene is a major product of gas-phase radiation cracking; however, propene is not formed in equal amount. Whereas a unimolecular decomposition into benzene and propene is probably the only significant reaction in catalytic thermal cracking, such a decomposition is only one of many possible reactions which may ultimately yield benzene and propene or propane in radiation cracking. Very significant differences between radiation cracking and both catalytic and non-catalytic thermal cracking are seen in the multiplicity of radiolysis products obtained and, particularly, in the formation of a non-volatile, largely polymeric residue as the major product. Liquid.--h twofold increase in pressure has a small effect 011 the gas-phase results (compare columns 4 and 5 of Table I). However, an almost sevenfold decrease in G for total gas occurs in going from irradiation of gas to liquid at about the same temperature (compare columns 1 and 13 of Table I). Significant decreases also occur in G-values of isopropylbenzene reacted and of liquid products. Manion and Burton16have observed a greater than threefold decrease in gas yield in electron irradiation of benzene in going from gas to liquid, but no decrease in the case of cyclohexane. It would appear that marked radiation resistance of aromatics relative to aliphatics may be characteristic only of the condensed state. Additional evidence is found in the G( -CeHe) = 4.23 reported by Huyskens and co-workers17for gas-phase irradiation of benzene as compared to G-(polymer) = 0.77 in liquid-phase irradiation.** The large change in yields with change in phase on irradiation of aromatics is most plausibly attributable t o collisional deactivation processes in the liquid phase. Effects of excitation and ionization are assumed to be spread over many bonds in an aromatic. Consequently, in excited aromatic ions and molecules the time required for sufficient energy to concentrate in a particular bond is long enough that appreciable collisional deactivation can occur in the liquid state. An additional factor in the decreased yields of the liquid state is evident in comparison of the hydrogen and methane yields in columns 1 and 13 of Table I. While G-(HJ decreases by only a factor of 2.5, G-(CHJ decreases by a factor of almost 12; thus hydrogen becomes the predominant gas product in irradiation of the liquid. Yields of all other products possibly derived from larger free radicals are also greatly reduced relative to hydrogen. This effect also has been observed in radiolyses of benzene and cyclohexane.16 These observations are understandable in terms of the Franck-Rabino(16) J. P. Allanionand M. Burton, ibid., 66, 560 (1952). (17) P. Huyskens, P. Clars, and F. Cracco, Bull. SOC. chim. Relges, 68, 88 (1959).
Sept., 196%
IRRADI .ITIOP;
OF
ISOPROPYLBESZENE ADSORBED O N SILICA-ALUM IN^
mitchl8 potrtulate of a cage effect which favors recombination of larger radicals with a resultant de-
1625
gen yield ihan do methyl radicals to the methane yield, The observed general increase in liquid-
The smaller hydrogen atom may
radiolysis rields with increase in temperature and
escape the cage more readily, or hydrogen atoms may contribute much less to the gas-phase hydro-
partioularlg the much greater increase in G-{CHJ relative to G-(H,) is consistent with an increased
crease in yield.
(18) J Franck and E Rabinowtch, Tram Faraday Soc , 50, 120 (1934).
probability
Of
escape from the cage
Or Of
atom abstr,rction from the caging molecules.
IRRADIATION OF ISOPROPYLBENZESE ADSORBED ON MICROPOROUS SILICA-ALUMINA BY ROBERT R. HENTZ Socony Mobil
Oil Company, Inc., Research Pepartment, Pranceton, N . J . Recezved March 16, 1951
Irradiation with cobalt-60 ?-rays of a heterogeneous system consisting of isopropylbeneene and microporous silica-alumina has been studied over the entire range of isopropylbeneene electron fraction, F , and with two solids of different surface &rem. G(benzene) increases markedly relative to yields of all other products as F decreases and passes through a sharp maximum a t very low F ; yields for benzene formation azd isopropylbenzene decomposition are higher in the presence of solid than in the pure li uid a t the same temperature, 36 , even though the radiation is absorbed overwhelmingly in the solid. Characteristic G-v2ues for the major products a t low electron fraction are as follows for F = 0.0068: isopropylbcw e n e reacted, 3.8; benzene, 1.05; hydrogen 0.208; methane, 0.0042. Interpretation of the maximum as due to saturation of sites effective in isopropylbenzene dealkyiation permits a calculation for both solids of effective site concentrations which are in good agreement. The unique behavior of benzene yields and the higher per cent conversion of decomposed isopropylbeneene to benzene suggest that isopropylbenzene is chemisorbed on those sites effective in thermal dealkylation; that radiation produces in the solid electronic excitation of relatively long lifetime a t room temperature; and that this excitation energy is transferred to chemisorbed isopropylbenzene, where it is utilized ( a i t h greater efficiency than in the liquid) for the reaction of dealkylation to which the isopropylbenzene is predisposed on the chemisorption sites. A different mechanism is postulated for hydrogen formation reweighed after each high temperature evacuation, but was allowed to come to room temperature under high vacuum. The desired weight of isopropylbenzene then was introduced isopropylbenzene compares with catalytic and non- as in gas-phase radiolyses, and the cell was sealed off. At catalytic thermal cracking and whether a selective least 2 hr. was allowed for attainment of a homogeneous radiation dealkylation to benzene might be obtained distribution prior t o irradiation. Weights of solid ranged 0.2-40.0 g. and weights of isopropylbenzene from 0.01with reasonably high radiation-energy yield (G) in from 2.0 g. A new cell and fresh reagents were used in each the presence of a microporous solid which is a good experiment, except as noted. catalyst for the thermal dealkylation. A recent Irradiations were conducted in the same apparatus and paper1 on the first phase of this study reports re- in the same manner ag previously described.' After irradiathe cell was attached to the vacuum line, usually after sults on the cobalt-60 y-irradiation of pure iso- tion having stood overnight. The breakoff seal was broken and propylbenzene over a wide range of experimental gas products were removed from the solid in the reaction conditions. A communication to the editor has cell a t r w m temperature by repeated expansion through a been published2 on preliminary results obtained trap a t -118" (eth 1 bromide muah) into the 550 ml. volof a Saunders-?aylor* apparatus, followed by xqeawrein y-irradiation of isopropylbenzene adsorbed on ume ment in a 5.28 ml. volume, until no further gas could be microporous silica-alumina. removed. Liquid products then were removed from the solid by placing liquid nitrogen around the trap and a boiling Experimental water bath around the cell for about 4 hr. Any additional Chemicals.-The aame isopropylbenzene was used as in gas products (usually very little) then were removed before the earlier experiments,l and the same purification proce- isolating the cell by means of a stopcock and again after dures were followed. The microporous silica-alumina (10% stopaook closure by placing ethyl bromide mush around the alumina) beads used were from 2-6 mm. in diameter with a trap containing the recovered liquid, This liquid was transsurface area of 400 m.t/g., ore volume of 0.43 ml./g., and ferred by liquid nitrogen distillation into a weighed bulb on particle density of 1.15 g.&l. The low-surface silica-aluthe vacuum line, ,and the bulb was sealed off and reweighed mina was prepared by steam treatment (20 hr. a t 700") of the to obtain the weight of liquid recovered, When liquid rehigh-surface beads and had the properties: surface area, 169 covery was likely t o be very small, a weighed amount of m.2/g.; pore volume, 0.36 ml./g.; particle density, 1.25 g./ pure 'so ropylbenzene was added to the weighed bulb and ml degassetprior to transfer of the liquid products into the bulb. Procedures.-Prior to use, the silica-alumina was placed Gas products were analyzed mass spectrometrically in a muffle furnace a t 550" for 20-70 hr. and then stored in a and liquid products chromatographically. Except for isodesiccator containing anhydrous magnesium perchlorate. propylcyclohexane, products heavier than isopropylbenzene This procedure resulted in a weight loss of about 7'%. The were not found in sufficient concentration in the recovered desired amount of solid was weighed into a reaction cell of the liquid to warrant routine determination. This may be due type previously used in gas-phase irradiations'; the cell w a ~ partially to limitations of the chromatographic equipment attached to IZ vacuum line and placed in a furnace. The cell used but is more likely a result of inability to remove heavier then was maintained a t about 450" for approximately 22 hr. products from the solid by the technique necessitated. while evacuation proceeded to and was maintained at a presSince the silica-alumina solid used is a catalyst for thersure of lO-i-l0--6 mm. This treatment caused a further weight loss of less than 0.6%; therefore, the solid was not mal dealkylation of isopropylbenzene, it was found neoessary to employ a temperature for liquid product recovery -
This paper reports on the second phase of a study
undertaken to determine how radiation cracking of
.
(1) R.R. Hentz, J. Phys. Chem., 66, 1622 (1962). ( 2 ) R. R . Hentz, z b d , 6 6 , 1470 (1961).
(3) K. W. Saunders and H. A. Taylor, J. Chem. Phus., 9,610 (1941).
