J. J. RUSHA N D 1'.I .
2534
'rAYI,OIt
Rotational Motions in Hexamethylbenzene and Ammonium Perchlorate by Cross Section Measurements with Slow Neutrons'
by J. J. Rush and T. I. Taylor
Xcutron scattwing cross sections for 1ic~xaiiiethylhcnzcIleand aniriioniuni pcmdiloratc have t m i i drtcriiiiricd as a fuiictioii of the iieutroii wave Iciigth and sample tc.tiipc~raturc.. T h e slope Aus 'AX,, of a plot of the scattering cross scctioii pcr hydrogcn atoll1 1's. thc' wave' lerigth of the neutrons ( 5 to 11.5A.) was 9.5 i 0.5 hariis A.-II atom for Iic~xari~ctli~lbct~zcrlc' at rooin tmiprraturc. I " I t i i an cnipirical corrclation of harriers to rotation 1's. Au9jLA,, for a series of atnnioniiini salts and nnc.thyl-substituted conipoiitids, this slop(. iiidictLtcs an avc'rage barrier to rotation of nitthyl groups in hexainc~tliylberizci~~~ of approxitilately 1 kcal.,'niolc. The slope for SH,ClO, decreased from 1 3 barns /.+\.-I1atoiii a t 296°K. to 2.5 barnsl.l.-II atom at 80°K. 'l'hc niagnitudc of the scattering cross section arid thc slope indicates that the hindercd rotational or torsional statcs of the aninmriiuni ions are still significwitly excited a t 8 0 O I i . Cross scctiori nieasureiiimts on hexann~.thylbenzciicas a function of teiiiperaturc. using neutrons with a wave length of about 10 '1. show a siiiall atmipt change a t ahout 1 15"K., in the neighborhood of the A-point trailsition. .lnalysis of the. cross sectiori ciirvc i n this region indicates that the change in cross section is due to a sinal1 cliangr in barrier to rotation rather than to the onset of rotation of the nicthyl groups. This conclusion is corisistent with the results of nuclmr niagiirtic r(wmaiice ~iicasurcmerits.
Introduction The niolccular motions and thermal transttions in hcuatiirthylbcnzcnc havc h e n investigated by a nuriibcr of nivthods including specific heat,*crystal structurcI3-a iiuclmr magtictic r ~ ~ o i i a n c t , 7absorption -~ spectra,lO and contluctancr.ll Total cross sevtion iiieasurenimts with v t ~ yslow neutrons have txcn found uscful for invcstigations of the niotions of aninioiiiutii ions in a series of aninioniiini salts arid of tiicthyl groups in inethvlbc.ii/,(.ties."2 - 1 5 Similar mwmretiients o n hcxanic,thylt,c.rizc~rIcmay cont ributcx further inforniat ion COP cclrning the. behavior of thc rtic3thyl groups at the thrrnial transitions. Coiiipai&xis with aninioniuni salts are useful since the naturci of thc iiiotions of thv ariinioniuin ions havc bcc~nrclasonably w-cll cstahlishcd in a numhcr of cascs For slow neutrons with cwc.rgicis E,, ~3: 9.5 f 0.3 barns/W. for o-xylene and 11.4 f 0.3 barns/a. for toluene, nz-xylene, p-xylene, and mesitylene. Thus, the hindrance to rotation of the methyl groups in hexamethylbenzene appears to be about the same as in o-xylene but significantly greater than that for the nonadjacent methyl groups in the other methylbeyzenes and dimethylacetylene. The slopes in barns/A. per hydrogen atom from previous The Journal of Physical Chemistry
m e a s ~ r e m e n t s ~ on ~ - ~ ammonia, ~ ammonium perchlorate, and a series of ammonium salts are: NH3 (15.5); NH4C104 (13.0); NH4PF6 (12.7); xH41, phase I (11.2); SH4S03F (10.0); (NHJ2Cr207(9.7); (NH& S2OS (9.6); NHJ, phase I1 (6.5); "4N03 (41)~ SH4CNS ( 5 3 ); XH4Br (5.7) ; (KH4)&r04 ( 5 . 5 ); NH&1 (4.8); NH4F (2.8). The barrier to rotation of the ammonium ions in a number of these salts has been evaluated from infrared and nuclear magnetic resonance measurements and a plot of the cross section slopes against the known barriers was used to estimate the barriers from other ammonium ~alts.'~-15 Assuming a similar correlation for methyl groups, as discussed prev i o u ~ l y a, ~slope ~~~ of ~9.5 barnsI8. would indicate a barrier of approximately 1 kcal./mole for the internal rotation of methyl groups in hexamethylbenzene at 296°K. Calculations by Dass from results of nuclear magnetic resonance measurements7 indicate only that the barrier is less than 5.3 kcal./mole. Effect of Temperature. The effect of decreasing the temperature from 296 to 80°K. on the scattering cross section per proton and on the slope for aonimonium perchlorate is shown in Fig. 1 . At X, = 10 A, for example, a,/H decreased from 173.6 to 97.7 barns or an average of 0.35 barn/"K. The scattering cross section at 80°K. still increases significantly with wave length, with a slope of 2.5 f 0.3 barns/8. This indicates that considerable inelastic scattering due to motions of the ammonium ions is still present at this temperature. The decrease in cross section slope by a factor of about five, that is from 13 a t 296°K. to 2.5 a t 80°K., is expected since a decrease in temperature greatly reduces the number of excited rotational or torsional states and thus decreases the cross section for energy-gain scattering. From our previously estimated barrier of -0.2 kcal./mole a t room temperature and the slope a t 8OoK., it can be concluded that the ammonium ions are still undergoing rapid reorientation a t this temperature. This is consistent with nuclear magnetic resonance measurement~,2~ which predict a barrier to rotation of less than 1kcal./mole a t low temperatures. Almost identical cross section results have been obtained for "4PF615 in which the slopes were 12.7 f 0.3 and 2.5 f 0.2 barns/,&. at 296 and 80°K., respectively. Moreover, cross section measurements as a function of temperature for t$is compound, using neutrons with a wave length of 8 A. (0.00128e.v.) showed no transitions involving a marked change in barrier as was (22) K. S. Pitzer, Discussions Faraday Soc., 10, 66 (1961). (23) Unpublished data. (24) R. E. Richards and T. Schaefer, Trans. Faraday Soc., 57, 210 (1961).
ROTATIOKAL R4oTIom
IN
HEXAMETHYLBENZENE
observed for n",I a t about -10'. The similarity in the results for NH,C104 and SHdPFO indicates that their barriers are essentially the same down to a t least 80'K. Methyl groups have rotational masses25close to that for ammonium ions 50 that transitions involving significant changes in barriers to rotation should show similar changes in cross section as a function of temperature. Thermal Transitions in Hexamethylbenxene. A Apoint transition has been observed in hexamethylbenzene a t about l10°K.2 which involves little change in crystal structure. IO A mechanism for this transition, which suggests that the methyl groups begin to rotate near llO°K., has been proposed as an explanation for the results of ultraviolet absorption measurements.'O Nuclear magnetic resonance studies, however, show no significant change in line width near this transition tempeiature,' and recent measurementsSindicate reorientation of methyl groups down to very low temperatures. A second specific heat anomaly occurs a t 135-165°K.2 and this has been associated with the gra,dual decrease in n.m.r. line width over the temperature range 135210'K. resulting from the onset of reorientation of the molecules about their hexagonal axes.' I n Fig. 2, the scattering cross section per hydrogtn atom r,/H for neutrons with a wave length of X, 'v 10 A. is plotted as a function of temperature from 78 to 295O.K.. The small but rather abrupt change of about 4 barns from about 110 to 120°K.26indicates a change in the inelastic scattering near the transition temperature and thus a change in the number of excited states. There is also a change in the variation of cross section with tentperature from about 0.1 barn/OK. to 0.23 barn/"K. above the transition. No marked change in the cross section curve occurs in the temperature range from 135 to 165OK. The change in cross section a t -115OK. probably does not involve significant changes in the rotational motion of the molecule as a whole since its barrier to rotation has been estimated to be about 6 kcal. in the high-temperature phase.8 Furthermore, the rather large "rotational of hydrogen atoms in such a motion would result in only a small contribution to inelastic scattering at low temperatures. Thus it appears that the change in scattering cross section at 115OK. is primarily due to a change in the freedom of rotation of the methyl groups. The fact that the change in cross section centered at about 115OK. is not large and that the cross section continues to decrease below the transition without reaching the bound-atom limit (m, 'v 85 barns) indicates that a significant number of hindered rotational or torsional states are still excited in the low-temperature phase.
2537
I50 f 140
HEXAMETHYLBENZENE XnUlOA
-
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130 -
-:
120
-
110
-
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0
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b"
'O 60
* 60
80
100
120
140
160
180
200
220
240
260
280 3
TEMPERATURE I'K)
Figure 2. X'eutron scattering cross sections per hydrogen atom for hexamethylbenzene as a function of sample temperature. The error bars represent the statistical error6 due to counting.
Thus the increase in barrier from our estimate of kcal./mole above the X-transition is probably not large. Our results indicate, therefore, that the transition at 110OK. involves not the onset of rotation of methyl groups as suggested from studies of absorption spectra,,l0 but rather a small change in barrier a t the transition. This is consistent with the results of n.1ii.r. measurements' which, because of the low barrier to rotation and the sinall change in barrier, show no significant changes in line width a t the transition temperature. The barrier below the transition still appears to be low enough so that fairly rapid reorientation, presumably by tunneling, can occur even at very low temperatures, a s indicated by the n.m.r. result^.^ Differential inelastic scattering measurements with cold neutrons are in progress to determine, if possible, the torsional frequencies of the methyl groups above and below the A-transition. Precise measurements of the total cross section as a function of neutron wave length just above and below the transition would also aid in evaluating the change in barrier to rotation.
Acknowledgments. The authors are indebted to Professor W. W. Havens, Jr., for his support of this work and to Mr. R. Graeser for assitance with the nieasurements and the calculations. (25) T. J. Krieger and M. S.Nelkin, Phys. Rev.,106, 290 (1957) (26) The observed increase in cross section is centered a t about 115'K. compared to the reported transition temperature of 110'K. This difference may be attributable to the uncertainty in the value of the transition temperature (ref. 10) as well as to a possible temperature lag in the polycrystalline sample due to the warm-up procedure used in taking the data.
Volume 68, Number 9
September, 1964
