3688
J . Phys. Chem. 1984, 88, 3688-3696 Calorimeter. The experiments were carried out using an automated calorimeter with a quartz thermometer as the temperature measuring probe.8 The previous design was modified by producing a 30-MHz signal from a harmonic of the IO-MHz master oscillator, and mixing it with the -28-MHz signal from the quartz thermometer. The -2-MHz signal thus produced contains all of the information and is sent to the data synchronizer and paired counters as previously described.8 It is then possible to use LSI counters, and to avoid the difficulties associated with transmitting and counting high frequencies. The computer system also was improved, and new calibration heater timing and power units were con~tructed.~ Equilibration of Trifluoroacetates. Mixtures of the trifluoroacetates which lay on opposite sides of the approximate equilibrium ratio were prepared and added to trifluoroacetic acid containing 0.25 M trifluoroacetic anhydride and 0.5 M methanesulfonic acid. The solutions were placed in N M R tubes and sealed under reduced pressure. They were placed in thermostats at the indicated temperatures (Tables I and VI) and periodically checked by N M R until the spectra were identical. In the case of the heptyl trifluoroacetates, the tubes were opened, diluted with methylene chloride, and the solution was washed with sodium bicarbonate solution until neutral. After drying over magnesium sulfate, the solutions were analyzed by GC using a 35 ft X l/s in. didecyl phthalate column at 90 OC. The response factors were determined with synthetic mixtures having compositions near that at equilibrium. With the pentyl trifluoroacetates, the product composition was determined from the 500-MHz N M R spectra. The protons adjacent to the trifluoroacetoxy group were well separated and the relative areas were determined by integration. An examination of spectra of mixtures of the two trifluoroacetates indicated groups of bands which also could be used for the analysis. The two sets of data gave comparable results.
separated by gas chromatography using a Carbowax column at 70 OC. The trans-2- and -3-heptenes (Chemical Samples Co., 99.8%, 99.9%) were found to contain insignificant amounts of the other isomers. cis-2-Heptene (Chemical Samples Co., 96%) had as its major impurity the 1-isomer, and it was removed by gas chromatography. cis-3-Heptene (Chemical Samples Co., 98%) was found to contain only the other 2- and 3-heptenes. A partial separation was effected by gas chromatography. Analysis was performed with a 25 ft. X l/s in. 10% XF-1150 analytical column. The purified cis-heptenes contained less than 1% of the other isomers, and the enthalpies of reaction are so close that even a 1% impurity would cause less than a 0.1% error in the measured enthalpy. Some of the compounds were obtained in 1-mL ampoules sealed under nitrogen. When freshly opened, the samples were used directly. Later, the contents were purified by gas chromatography to eliminate possible autoxidation products. No difference in enthalpy of reaction was observed. 1-Pentene and trans-2-pentene (Chemical Samples Co., 99.9%, 99.9%) were found to contain negligible amounts of impurities. cis-2-Pentene was obtained from two sources (Chemical Samples Co., 98%; Fluka, 99%) and was found to have several impurities. The second sample contained four impurities, two of which, 1pentene and trans-2-pentene, were present in less than 0.05%. Pentane (0.25 f 0.05%) was a third impurity. The fourth and largest impurity (0.66 f 0.12%) was shown by GC/MS to be an isomeric pentene. It was shown not to be 2-methyl-2-butene by its retention time, and therefore it is presumably 3-methyl-1-butene or 2-methyl-1-butene. The enthalpy of reaction of these compounds will be close to that of cis-2-pentene, and the impurity should cause less than 0.08% error in the observed enthalpy. The experimental result was corrected for the pentane impurity. 2-Heptanol (Chemical Samples Co., 99%) and 4-heptanol (Chemical Samples Co., 99%) were dried by heating to reflux over calcium hydride overnight and then distilling under nitrogen, collecting a center fraction. 3-Heptanol (Chemical Sample Co., 99%) was found by IR to contain a small amount of ketone, and therefore it was treated with a small amount of sodium borohydride until the spectrum showed that the carbonyl band had disappeared. It was then treated as described above. The reaction solvent was prepared as previously described.'
Acknowledgment. This investigation was supported by the Office of Basis Energy Sciences, Department of Energy. (8) Wiberg, K. B.;Squires, R. R. J . Chem. Thermodyn. 1979, 11, 773. (9) The details of the modified calorimetric system may be found in the Ph.D. Thesis of Eric Martin.
Muonium Formation in Vapors Donald J. Arseneau, David M. Garner, Masayoshi Senba, and Donald G. Fleming*+ Department of Chemistry and TRIUMF, University of British Columbia, Vancouver, B.C., Canada, V6T 1Y6 (Received: February 13, 1984)
The fractions of positive muons thermalizing in vapors either as the polarized muonium atom (fM)or in diamagnetic environments cfD) have been measured in water, methanol, hexane, cyclohexane, the chlorinated methanes, and tetramethylsilane, in the pressure range from -0.1 to -2.5 atm. There is a marked difference in every case in comparison with the corresponding fractions (PMand PD) measured in condensed media, with -80% of incident muons forming polarized muonium in the vapor phase compared to -20% in the corresponding condensed phases. CCI4 appears somewhat anomalous in that it shows an unusually small muonium fraction in the vapor (fo fM = 0.5)and an unusually large diamagnetic fraction in the liquid (PD= 1.0). The vapor-phase results can be understood in terms of a charge-exchange/hot atom (ion) model, providing also a likely explanation for observed pressure-dependentfD's in hexane, cyclohexane, and tetramethylsilane at low (C0.5 atm) pressures in terms of termolecular processes, in analogy with some hot tritium studies. The present vapor-phase results indicate that hot atom reactions cannot account for more than about 30% of the much larger diamagnetic fractions seen in condensed phases, strongly suggesting therefore that radiation-induced spur effects play a dominant role in determining thermal muon fractions in condensed media.
-
Introduction Since the earliest experiments in which a spin-polarized beam of positive muons (b+) were stopped in matter, attempts have been made to account for the polarization of the thermalized muon
'1983-1984 John Simon Guggenheim Fellow. 0022-3654/84/2088-3688$01.50/0
ensemble. In 1958, Swanson found that the ensemble polarization depended on the chemical identity of the stopping target.' In the 1960%it was recognized that the chemistry of muonium (Mu fi+e-) played an important role in determining the thermalized (1) R.A. Swanson, Phys. Reu., 112, 580 (1958).
0 1984 American Chemical Society
Muonium Formation in Vapors
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3689
ensemble polarization in condensed media.2 A spin-polarized ensemble of paramagnetic muonium atoms was first directly observed in solid-phase targets in the late 1960s3and in a gas target at about the same time4 but curiously enough not in liquids until about 10 years later, first in waterS and most recently in some organic liquids! Since the mid 1970s, considerable work has been done on the thermal and near-thermal chemistry of m u o n i ~ m , ~ - ’ ~ particularly in gases and liquids, and it has been demonstrated that Mu behaves chemically like an isotope of hydrogen but one with an unprecedented mass ratio of mH/mMu= 9. Despite this effort, though, attempts to account for and explain the ensemble polarization of muons stopped in all three phases of matter remain, in many respects, unsatisfactory. In general, there are two categories of polarized muon ensembles observed in a target: (i) muons in polarized paramagnetic environments (with an ensemble polarization denoted P p ) and (ii) muons in polarized diamagnetic environments (denoted PD). In addition, the target may also contain a depolarized ensemble of muons, often referred to as the “missing” or “lost” fraction (denoted PL) which manifests itself as the difference between the empirically determined polarization of the initial beam and the total polarization of the stopped muon ensemble. The chemical environment of polarized paramagnetic muons is normally unambiguously identified either as chemically free muonium or as various muonic radicals.I6 In most studies, particularly those involving saturated-bond systems, chemically free muonium atoms are the only paramagnetic muon species observed, and hence Pp is normally just identified with free muonium, P,, as is the case in the present experiment. However, the chemical environments of the diamagnetic muon ensemble are not easily identifiable; the possibilities include free p+ ions, p+ molecular ions, or muonium chemically bound in a molecule. In principle, as in N M R studies, these different environments, particularly in condensed media, could be identified by a measurement of their corresponding diamagnetic shifts in an external field, but these are expected to be 5 1 0 ppm,” well outside the sensitivity of most studies in Mu chemistry to date. Finally, the missing fraction may include any or all of the above paramagnetic or diamagnetic species.
(2) A. I. Babaev et al., Sou. Phys.-JETP (Engl. Trawl.),23,583 (1966); I. G. Ivanter and V.P. Smilga, ibid., 34, 1167 (1972), and earlier references contained therein. (3) G. G. Myasishcheva et al., Sou. Phys.-JETP (Engl. Trawl.),26,298 (1968); I. I. Gurevich et al., Phys. Lett. B, 29B, 387 (1969). (4) R. M. Mobley et al., J . Chem. Phys., 44,4354(1966); 47,3074(1967); V. W. Hughes et al., Phys. Reu. A , 1, 595 (1970). (5) P. W. Percival et al., Chem. Phys. Lett., 47, 1 1 (1977);39,333 (1976). (6)Y.Ito et al., Can. J . Chem., 58, 2395 (1980);B. W. Ng et al., ibid., 61,671 (1983);Y. It0 et al., Chem. Phys. Lett., 93,361 (1982);Y.Ito et al., Proceedings of the 3rd Topical International Conference on Muon Spin Rotation, Shimoda, Japan, North-Holland Publishing Co., 1983;Hyperfine Interact., 17-19, 733 (1984). (7) J. H. Brewer, K.M. Crowe, F. N. Gygax, and A. Schenck, “Muon Physics”, Vol. 111, V. W. Hughes and C. S. Wu, Eds., Academic Press, New York, 1975,p 3; D. G. Fleming et al., “Positronium and Muonium Chemistry”, H. J. Ache, Ed., 1979,Adv. Chem. Ser., No. 175, p 279. (8) D. M. Garner, D. G . Fleming, and J. H. Brewer, Chem. Phys. Lett., 55, 163 (1978);D.M. Garner, Ph.D. Thesis, University of British Columbia, 1979 (unpublished). (9) D.C. Walker, Y. C. Jean, and D. G. Fleming, J . Chem. Phys., 72,2902 (1980);70,4534 (1979). (10) D. C. Walker, Hyperfine Interact., 8,329 (1981). (11) P. W. Percival, E. Roduner, and H. Fischer, Chem. Phys., 32, 353 (1978). (12) P. W. Percival, J. Chem. Phys., 72, 2900 (1980); P. W. Percival, Hyperfine Interact., 8,315 (1981). (13) P. W. Percival and H. Fischer, Chem. Phys., 16,89 (1976);P. W. Percival, Radiochim. Acta, 26, 1 (1979). (14) D. C. Walker, J . Phys. Chem., 85, 3960 (1981). (15) P. W. Percival, J. C. Brodovitch, and K.E. Newman, Chem. Phys. Lett., 91,1 (1982); P. W. Percival, Hyperfine Interact., 8,325 (1981). (16) E. Roduner et al., Chem. Phys. Lett., 57, 37 (1978);E. Roduner, “Exotic Atoms ’79,Fundamental Interactions and Structure of Matter”, K. Crowe, J. Duclos, G. Fiorentini, and G. Tovelli, Eds., Plenum Press, New York, 1980, p 379;E.Roduner, Hyperfine Interact., 8, 561 (1981). (17) M. Camani et al., Hyperfine Interact., 6,475 (1979);M. Castro, J. Keller, and A. Schenck, ibid, 6,439 (1979).
Recent muon spin rotation (pSR) studies on the disposition of the muon beam polarization among the three ensembles, P,, PD, and PL,have shown a strong dependence not only on the chemical identity of the target but also on its phase. For example, ref 11 and 14 report PD = 0.62 f 0.01, PM= 0.20 0.01, and PL = 0.18 f 0.01 in liquid water but PD = 0.48 h 0.01, P , = 0.52 0.02, and PL = 0 in ice, while in the present study we find PD = 0.09 f 0.01, PLI= 0.78 f 0.02, and PL = 0.13 f 0.02 in water vapor at 2.5-atm pressure. In the gas phase, however, the lost fraction is understood to be due to dephasing of the muon spin as a result of “singlet” Mu formation in the charge-exchange regime. This effect is inversely proportional to pressure and disappears (PL 0) at only moderately high pressures of a few Thus, it is the (pressure independent) relative fractions fD and fM cfL = 0) in the vapor phase, defined by fD = PD/(P, P M )and fM = 1 fD, that are relevant for comparison with the corresponding “absolute” polarizations measured in condensed media. There has been a lively discussion of the two models that have been put forward to explain the condensed-phase data primarily for water: (1) the “spur” model and its variants9-I2 in which the high-energy muon beam (several MeV) creates a radiolysis track of highly reactive species which, in turn, dominate the chemistry of both muonium and diamagnetic muon formation and (2) the “hot” atom in which muonium is formed in a charge-exchange process, as in the gas with its subsequent epithermal reactions playing a dominant role. The motivation for the present study is to aid in the elucidation of the chemical identity of and the mechanisms leading to P M , PD, and PL by extending, for the first time, the set of muon polarization data to the vapor phase for many of the common solvents that have not been studied in the liquid p h a ~ e : ~ ,water, ~*” methanol, hexane, cyclohexane, the chloromethanes, and tetramethylsilane (Me,Si). There are at least three important reasons for carrying out such vapor-phase studies. (i) As noted above, the origin of the polarization loss in low-pressure gases is well understood in terms of the time spent by the muon undergoing charge exchange with the target gas molecules.’s-20 Thus, the term “missing fraction” is not really applicable to gases and can be assigned a value of zero (Le., fL = 0), unlike the situation in condensed phases. (ii) Although gas-phase targets will also undergo radiolysis by the high-energy muon just as liquids do, the mean free paths in gases at a few atmospheres pressure or less are sufficiently large that the importance of intraspur processes can surely be regarded as negligible (it is germane to note that the range of a 2-MeV p+ in a typical gas at 1-atm pressure is of order 10 cm compared with a few microns in a liquid). Hence, only the hot atom model of Mu or its variants can be expected to have any validity in low-pressure (- 1 atm) gases. (iii) In condensed media one can expect many-body (termolecular) processes to play a more important role than in the gas phase. Hence, it is important to be able to directly compare results obtained in low-pressure gases with those in condensed media. The spur model of Mu formation in liquids is based on an analogous concept developed by Mogenson for e+ thermalization and positronium (Ps = e’e-) formation in matter. Although conceived primarily for condensed media:’ it has also been applied to gases where it is found that radiolysis processes have a negligible effect on Ps formation at low (510 atm) pressures.22 It is worth
*
*
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+
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(18) D.G. Fleming, R. J. Mikula, and D. M. Garner, Phys. Reu. A , 26, 2527 (1982);R. J. Mikula, Ph.D. Thesis, University of British Columbia, 1980 (unpublished); D. G.Fleming, R. J. Mikula, and D. M. Garner, Hyperfine Interact., 8, 307 (1981). (19) R. E. Turner and M. Senba, Phys. Reu. A , 29, 2541 (1984). (20) D. G. Fleming et al., Proceedings of the 3rd Topical International Conference on Muon Spin Rotation, Shimoda, Japan, North-Holland Publishing Co., 1983;Hyperfine Interact., 17-19, 655 (1984);press; D. J. Arseneau, MSc. Thesis, University of British Columbia, 1984 (unpublished). (21) 0.E. Mogensen, “Proceedings of the 6th International Conference on Positron Annihilation”, 1982,Arlington, TX”, P. Coleman, S. Sharma, and L. Diana, Eds., North-Holland Publishing Co., Amsterdam, 1982,p 763;J . Chem. Phys., 60,998 (1974); G . Wikander, Chem. Phys., 38, 1891 (1979).
3690 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
Arseneau et al. OSOatm C C L 4 a t 225gauss
emphasizing though that the e+ and its Ps atom are very poor analogues for p+ and Mu, the latter being much more like the triton, since Mu is also effectively an isotope of h y d r ~ g e n . ~ ~ ~ ~ ~ O,Z ~O ~ 0.15 In this regard it is important to note that hot tritium studies have I been successfully interpreted for years in terms of hot atom c h e m i ~ t r y . ~ ~In- ~particular, ~ measured hot atom yields for abstraction reactions are typically pressure independent and hence the same in gases and liquidsz3whereas for substitution reactions this is often not the case, depending on the gas pressure.z4 In the limit of moderately high pressures then (see later discussion), we expect either the hot atom model to be equally applicable to both the gas and liquid phases or else the mechanisms of the epithermal reactions involved to be quite different in the two phases.
3
Experimental Results The experiments were conducted primarily on the M20 channel of the TRIUMF cyclotron using a surface muon beam. The gas-phase target was positioned between Helmholtz coils which provided an overall magnetic field range of 1-250 G transverse to the muon spin. The aluminum target vessel was maintained at 155 OC and was fitted with a double window of thin Mylar to prevent condensation of vapors on the outer window. Spectroscopic grade CHZCl2,CHC13, CCl,, C H 3 0 H , C6H14, C6HIZ, and Me4Si were distilled over sodium or Pz05,and samples were taken from the middle 1/3 fraction. Water samples were distilled and demineralized. All samples were degassed by at least three freeze-pump-thaw cycles and introduced as vapors into the evacuated target vessel by boiling the corresponding liquids. The effectiveness of these purification procedures and degassing was checked with CCl, for which neat samples were run after 3 freeze-pump-thaw cycles and distilled samples after 10 freezepumpthaw cycles. No difference was observed in the pSR spectra of undistilled samples or with samples treated to more than three freeze-pump-thaw degassing cycles. Experiments were conducted at several target pressures for each sample ranging from 0.2 to 2.5 atm, depending upon the stopping power of the sample. Earlier measurements at only two pressures and in low (-75 G) fields are reported in ref 20. The basic pSR technique has been described in detail in many reference^,^^^*^^,^^^'* and only a brief description is given here. An effectively 100% longitudinally spin-polarized beam of high-energy (-2 MeV) p+ enters the target vessel and thermalizes in a typical gas within about 30 ns (cf. a few picoseconds in a condensed target). As stated in the Introduction, thermalized muons are found in one of three ensembles: (1) a spin-polarized paramagnetic ensemble, free muonium in the present paper, P M , (2) a spinpolarized diamagnetic ensemble, PD,or (3) an unpolarized ensemble, PL. Regardless of its environment, the muon decays (p+ e+v,2J with a mean lifetime of 2.2 ps, emitting a high-energy positron preferrentially along the vector of the muon spin at the instant of decay. In a transverse magnetic field, there is coherent precession of the muon spin in the polarized paramagnetic and diamagnetic ensembles, each of which have characteristic Larmor frequencies (vM = 1.39 MHz G-’ and vD = 13.55 kHz G-’); the unpolarized ensemble, of course, precesses incoherently. Thus, a time differential measurement of the muon decay in a transverse magnetic field will show oscillations characteristic of the polarized ensembles. Typical pSR signals for diamagnetic muon precession in CC14vapor at 380 torr and in HzO vapor at 1900-torr pressure
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(22) F. M. Jacobsen, N. Gee, and G. R. Freeman, ‘Proceedings of the 6th International Conference on Positron Annihilation, 1982, Arlington, TX”, P. Coleman, S. Sharma, and L. Diana, Eds., North-Holland Publishing Co., Amsterdam, 1982, p 92. (23) R. T. K. Baker, M. Silbert, and R. Wolfgang, J . Chem. Phys., 52, 1120 (1970); E. Tachikawa and F. S. Rowland, J. Am. Chem. Soc., 90,4767 (1968); E. K. C. Lee and F. S . Rowland, ibid., 84, 3085 (1962). (24) Y. N. Tang et al., J . Am. Chem. Phys., 79, 2181 (1983); P. Volpe and M. Castiglioni, J . Chem. Soc., Faraday Trans. I , 74, 818 (1978); Y. N. Tang and F. S.Rowland, J . Am. Chem. SOC.,90,574 (1968); E. K. C. Lee and F. S. Rowland, ibid., 85, 897 (1963). (25) L. C. Vaz, University of British Columbia, Department of Chemistry, Internal Report, 1976 (unpublished); F. S.Rowland, “MOlecular Beams and Reaction Kinetics; Hot Atom Chemistry”, Vol. I and 11, Academic Press, New York, 1970, pp 108-138; R. Wolfgang, Prog. React. Kinel., 3, 97 (1965).
0 10
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1
I
I
I
I
1
I
I
I
050
100
150
200
250
300
350
400
TIME in px (20 ns/bin)
Figure 2. As in Figure 1 but for water vapor a t 2.5-atm pressure. Note the much smaller amplitude in comparison with Figure 1.
in a 225-G magnetic field are shown in Figures 1 and 2, respectively. Typical muonium spin rotation (MSR) signals in an 8.5-G magnetic field are shown in Figures 3-5 for methanol vapor at 1600 torr, hexane vapor at 510 torr, and carbon tetrachloride vapor at 380 torr pressure, respectively. These data are fit to the expression
s(t)= A&-‘‘
cos
(UMt
+ $M) + AD cos ( U D t - $D)
(1)
where AM, wM, $M and AD, wD, $D are the initial signal amplitudes, frequencies, and phases for the paramagnetic (Mu) and diamagnetic muon ensembles, respectively. The relaxation rate of the Mu signal in these pure vapors is denoted Xo and is discussed later. At 8.5 G, precession of the diamagnetic signal is so slow that only about l/zcycle is observed over 4 ps. The diamagnetic signal is more readily fit when measured at a higher field, 2100 G, where it looks qualitatively similar to Mu precession (Figures 1 and 2 ) ; at these fields, coherent Mu precession is too fast to be observed and the data is fit to only the second term of eq 1. In practice, two independent sets of data are taken in different histograms (“top” and “bottom” in the present apparatus), with results reported as an average. For gas-phase pSR experiments, a correction must be applied to AD due to the fact that some muons may scatter into the walls of the aluminum target vessel where they contribute to the observed diamagnetic amplitude. A detailed discussion of this effect, which is dependent on the applied magnetic field, and other possible corrections arising from the muon stopping distribution are given in ref 18 and 20. As in those studies, the wall signal correction, Aw, was obtained from various pressures of an Oz/Nz (air) mixture as the target gas. The total diamagnetic signal
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