Addition Kinetics and Spin Exchange in the Gas Phase Reaction of the

J. Phys. Chem. 1996, 100, 6561-6571

6561

Addition Kinetics and Spin Exchange in the Gas Phase Reaction of the Ethyl Radical with Oxygen Herbert Dilger,† Martina Schwager,† Philip L. W. Tregenna-Piggott,‡ and Emil Roduner*,† Physikalisch-Chemisches Institut der UniVersita¨ t Zu¨ rich, Winterthurerstrasse 190, CH-8057 Zu¨ rich, Switzerland

Ivan D. Reid Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland

Donald J. Arseneau, James J. Pan, Masayoshi Senba, Mee Shelley, and Donald G. Fleming TRIUMF and Department of Chemistry, UniVersity of British Columbia, VancouVer, BC, Canada V6T 1Z1 ReceiVed: September 5, 1995; In Final Form: January 23, 1996X

The kinetics of the addition reaction of O2 to the ethyl radical has been investigated as a function of temperature (259-425 K) and pressure (1.5-60 bar) using the muon spin relaxation technique in longitudinal magnetic fields. Within this temperature range at 1.5 bar, the chemical reaction is represented by an Arrhenius rate law with an activation energy of -4.4(4) kJ mol-1 and an apparent frequency factor of 1.3(2) × 10-12 cm3 molecule-1 s-1. The high-pressure limit of the rate constant at 294 K amounts to k∞ch ) 8.7(8) × 10-12 cm3 molecule-1 s-1. Within error, this limit has been reached at 1.5 bar. The rate coefficient for spin exchange, kex ) 2.8(2) × 10-10 cm3 molecule-1 s-1, is collision controlled. The results for kch agree well with experimental literature values, but the temperature dependence is more pronounced than that predicted on the basis of a RRKM extrapolation from low-pressure data. The theoretical basis for the analysis of experimental data is given, and the results are discussed.

1. Introduction Free radicals are important intermediates of pyrolysis and in oxidation and photochemical reactions. In the gas phase, they play a key role in combustion and in the degradation of organic pollutants in the atmosphere. Accurate rate constants are needed for computer modeling of these processes, but the relevant kinetic parameters have often been obtained under much different conditions than those of interest and hence need to be extrapolated to the actual pressures and temperatures. It is therefore necessary to have a detailed understanding of all the elementary steps involved. Although gas phase reaction rate theory has made enormous progress during the past decades, a large number of processes and phenomena are still poorly understood. The availability of accurate experimental data is the basis for further development of theories. In the present context, though a large amount of reliable kinetic data for gas phase radical reactions has been collected in recent years,1 the vast majority of these data relates to reactions of H atoms and of OH radicals with larger organic molecules, which lead to the formation of transient organic free radical intermediates. Far less work has been devoted to the subsequent reactions of these transient organic radicals, which is partly due to the lack of appropriate experimental techniques. The kinetics of one of the most elementary reactions of this nature, that of alkyl radicals (R) with molecular oxygen, has been studied extensively.1-8 Despite this effort there is still significant uncertainty about the kinetics and particularly also about the mechanisms of the elementary steps and their relative * Author to whom correspondence should be addressed. † Present address: Institut fu ¨ r Physikalische Chemie, Universita¨t Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany. ‡ Present address: Department of Physics, Monash University, Wellington Road, Clayton, Victoria 3168, Australia. X Abstract published in AdVance ACS Abstracts, March 15, 1996.

0022-3654/96/20100-6561$12.00/0

importance as a function of temperature and pressure. A common way to express the reaction of R with O2 is as follows: ka

kc

kp

R + O2 {\ } RO* 2 {\} R-HO2H*98R-H + HO2 k b

ksV[M] RO2

(1)

For R ) CH3C˙ H2, at temperatures below 600 K and at modest pressures, formation of the alkylperoxy radical RO2 dominates, and only a small fraction of C2H5O* 2 proceeds on to ethene and HO2.6,7 At high pressures the disappearance of R asymptotically approaches a constant value, the high-pressure limit. At low pressures such that ks[M] , kp and particularly also at temperatures above ca. 700 K, it is dominated by the formation of the alkene, R-H. An extended theoretical investigation of the reaction of CH3C˙ H2 with O2 has been carried out by Wagner et al.,6 in which RRKM theory was used to obtain the pressure and temperature dependencies of the rate constants of all the elementary steps both by extrapolation based on the set of experimental data by Slagle et al.3 and by spectrometric data and ab initio calculations. Molecular parameters and an energy transfer term were adjusted to properly describe the experimental results of Slagle which had been obtained at pressures between 0.5 and 15 Torr and temperatures between 296 and 850 K. It was then expected that the theory would allow reliable extrapolations to all pressures, but the theoretical values disagree with the experimental rate constants obtained at 1 atm of pressure by Munk et al.4 and with the extrapolated high-pressure limit by Plumb and Ryan,2 being higher by a factor of 1.5-2. More significantly perhaps, the theory also shows a much weaker temperature dependence. The origin of the discrepancy is not known. Moderator effects or the different experimental © 1996 American Chemical Society

6562 J. Phys. Chem., Vol. 100, No. 16, 1996 techniques used are possibilities to explain this difference. In recent work reported by Kaiser,7 the rate contants for the formation of C2H4 and for the disappearance of R were investigated for different pressures (50-1500 Torr) and temperatures (260-530 K). The results agree with Wagner’s predictions. Further experimental data for pressures around 1 bar or higher are not available. In the present work we introduce the muon spin relaxation (µSR) technique and explore its potential and its limitations in the field of gas phase radical kinetics. The first rate constants at pressures >1 bar are determined for the title reaction. µSR is a variant of magnetic resonance which, in the present context, uses spin-polarized muons as spin labels. Energetic positive muons, available at the beam ports of suitable accelerators, are stopped in the experimental target. In the present study, ethyl radicals are generated formally by addition of muonium (Mu ≡ µ+e-, chemically a light isotope of hydrogen with a positive muon nucleus9) to the CdC double bond of ethene. This leads to MuCH2C˙ H2 formation with the spin label in the methyl group. The technique will be described in more detail in the Experimental Section. Standard methods of magnetic resonance are not suitable for the investigation of radicals in the gas phase, other than diatomics and simple triatomics,10 since the resonances are numerous and broadened by collisions, which leads to a low signal-to-noise ratio. The muon-substituted ethyl radical was observed in the gas phase for the first time by Roduner and Garner11 and later in Percival et al.12 and by Fleming et al.13 over a much wider range of field and pressure. The kinetics of Mu addition was studied by Garner et al.14 in the high-pressure limit over a range of different temperatures. Since Mu has only one-ninth the mass of H, large primary kinetic isotope effects were observed for this reaction. Only secondary kinetic isotope effects are expected for the reactions of MuCH2C˙ H2 of interest here as long as the C-Mu bond is not affected, and these are expected to be far smaller, if not negligible, in comparison with the more customary primary isotope effects.15 This has been verified for reactions of other Mu-substituted radicals in solution using a related experimental technique.16 A small secondary isotope effect was also reported in a comparative study of Mu addition to C2H4 and C2D4.14 In addition to its utility for the study of chemical reaction kinetics, the µSR technique is sensitive to spin exchange and spin relaxation phenomena as well. In the present case, spin exchange is a consequence of the intermolecular interaction between the unpaired electron of the radical in collisions with the paramagnetic O2 molecule, inducing a spin flip of the muon (or proton) in MuCH2C˙ H2, which leads to relaxation of the µSR signal. Spin exchange is a frequently observed phenomenon in magnetic resonance. It plays an important role in other processes as well, as for example in optical pumping, masers, plasmas, and astrophysics. Spin exchange in the context of µSR was treated first by Nosov and Yakovleva,17 by Mobley et al.,18 by Ivanter and Smilga,19 and by Heming et al.20 More recent treatments have been by Senba,21-23 and by Turner, Snider, and Fleming,24 in which the electron of the paramagnetic collision partner was taken into account explicitly. Senba, using a stochastic formalism, derived relations between the collision rate of the reaction partners and the spin exchange efficiency and has recently extended the theory to collision partners with spins larger than one-half,25 obtaining results which agree with those obtained earlier.24 The treatment by Heming et al.20 also includes the behavior at avoided level-crossing resonances. In addition to electron spin exchange, there is another contribution to muon relaxation in the radical which we here call “intrinsic”. This self-relaxation, driven largely by electron spin rotation interaction,11 also occurs in the absence of a paramagnetic

Dilger et al. reaction partner and hence is not of central interest here. It has been discussed by Fleming et al.13 and analyzed theoretically by Turner and Snider.26 To describe the interaction of the ethyl radical with O2 in the present work, we adopt the analytical formalism developed by Nosov and Yakovleva,17 but we have to introduce as a known empirical parameter the nonnegligible intrinsic relaxation of the muon in the radical in the absence of chemical reaction and of spin exchange. 2. Theory 2.1. Kinetics. The elementary steps in mechanism 1 are conveniently represented by the following processes: ka

R + O2 98 RO* 2 kb

RO*2 98 R + O2 ks

RO*2 + M 98 RO2 + M* kp

RO*2 98 R-H + HO2

(2) (3) (4) (5)

The possible formation of the rearranged intermediate R-HO2H* indicated in reaction 1 has little consequence on the overal kinetics. With the aim of determining ka, the present experiments were carried out over the temperature range 259425 K and for pressures up to 60 bar at room temperature. Since for R ) CH3C˙ H2 below 600 K and for pressures above 1 bar the buildup of R-H + HO2 is slow compared with the other processes,6,7 it is reasonable that ethene product formation (kp, eq 5) can be neglected in the present µSR study as well and that the excited peroxy radical will be mostly stabilized (ks, eq 4) in collisions with a bath gas M. In the present case of RO*2 ) MuCH2CH2O* 2, it would be argued that a kinetic isotope effect could favor the transfer of Mu in the rearrangement reaction, resulting in the formation of MuO2 and C2H4. However, since the apparent activation energy for ethene formation amounts to less than 5 kJ‚mol-1, representing the increased energy in the excited adduct rather than a real energy barrier,7 it is unlikely that zero-point vibrational energies will play an important role. This is a point which could be tested further with RRKM calculations along the lines of those carried out by Wagner et al.6 Furthermore, as will be shown later, even if these rearrangements were facilitated for Mu transfer, this would not affect the measured value of ka. Moreover, the magnetic field dependence of muon relaxation can distinguish MuO2 from Mu-substituted ethene and from MuCH2C˙ H2 and MuCH2CH2O2 as well. This is an important feature of the µSR technique. Under steady state conditions for [RO*2] the rate of loss of the radical is described by

-

ka(kp + ks[M]) d[R] d[RO2] [R][O2] ) kch[R][O2] ) ) dt dt kb + kp + ks[M] (6)

For sufficiently high pressures, as in the present experiments, we expect ks[M] . kp, and thus

kch )

kaks[M] kb + ks[M]

(7)

This is the elementary Lindemann-Hinshelwood expression. In a step beyond it, the strong and weak collision-broadening effects as taken into account in a Troe calculation27 which multiplies the right-hand side of eq 7 by a general broadening

Addition Kinetics and Spin Exchange

J. Phys. Chem., Vol. 100, No. 16, 1996 6563

factor F(ki) given by

log F )

log Fcent 1 + {log(ks[M]/kb)}2

(8)

where Fcent e 1 is represented by a polynomial27 which is fitted to an RRKM calculation. 2.2. Spin Dynamics in the Absence of Chemical Reaction. The parameter of prime interest is kch, but our experimental technique measures the evolution of muon spin polarization and not directly the evolution of the radical concentration. There are four mechanisms which influence the time evolution of the muon spin probe in the radical: muon spin relaxation, electron spin relaxation which is coupled to the muon via the isotropic hyperfine interaction, chemical reaction, and spin exchange. We assume that our system is subject to a magnetic field of sufficient strength that the muon is decoupled from any other magnetic nuclei and that the eigenstates are well separated in energy.28 Under these conditions, well outside any crossings of magnetic energy levels, the system is described adequately as a muonelectron two-spin-1/2 system. With the adoption of the nomenclature of Meier,29 the Hamiltonian for the system in the representation of the Pauli σµ for the muon and the electron, respectively, matrices, b σe and b is given by

1 e e 1 µ µ 1 σ µ‚σ be + pω b - pω b b ‚σ b ‚σ H ˆ ) pωµ0 b 4 2 2

(9)

b µ are the Zeeman frequencies corresponding to where ω b e and ω the external field B B, and ωµ0 represents the isotropic muon electron hyperfine coupling constant. The density matrix describing the system is given by

1 p e‚σ be + ∑pjkσjµσek) bµ + b F ) (1 + b p µ‚σ 4 j,k

(10)

with j, k ) x, y, z. The prefactors to the spin matrices, describing the polarization of the muon, the electron, and the cross polarizations, are defined as

bµ); b p e ) Tr(Fσ be); pjk ) Tr(Fσjµσek) (11) b p µ ) Tr(Fσ Using the equation of motion for the density matrix

dF ) [H ˆ ,F] dt

pi

(12)

and the commutation rules for the Pauli matrices, we obtain a set of 15 coupled differential equations, as described in detail by Meier.29 As perturbations we now add relaxation terms

dpjµ/dt ) ‚‚‚ - λµpjµ

(13)

dpje/dt ) ‚‚‚ - λexpje

(14)

dpjk/dt ) ‚‚‚ - (λex + λµ)pjk

(15)

where λex is introduced phenomenologically for electron relaxation, arising for example from spin exchange, and λµ for muon self-relaxation which originates from sources other than the relaxing electron and thus is not to be confused with the effectively observed relaxation of the muon polarization. Conventionally, the muon decay with τµ-1 ) 0.456 µs-1 is not included in λµ and is treated separately in the analysis of experimental results.

The present experiments have been carried out in a configuration with the external magnetic field along z. We are only interested in the z-component of the muon polarization, pzµ, in which case the system reduces to a set of six coupled equations. These describe the time evolution of the muon spin in an unperturbed muonium atom or in a Mu-substituted radical at sufficiently high fields. The relevant set of coupled equations has been previously studied for the case of chemical reaction and electron relaxation in the absence of intrinsic relaxation (λµ ) 0) by Ivanter and Smilga.19 Written out for λµ * 0 they are

dpzµ ωµ0 ) (pyx - pxy) - λµpzµ dt 2

(16)

ωµ0 dpze ) - (pyx - pxy) - λexpze dt 2

(17)

dpxy ωµ0 µ ) (pz - pze) + ωzµpyy + ωzepxx - (λex + λµ)pxy dt 2

(18)

ωµ0 dpyx ) - (pzµ - pze) - ωzµpxx - ωzepyy - (λex + λµ)pyx (19) dt 2 dpxx ) ωzµpyx - ωzepxy - (λex + λµ)pxx dt

(20)

dpyy ) -ωzµpxy + ωzepyx - (λex + λµ)pyy dt

(21)

Two out of these six equations have the same structure and are therefore combined: addition of eq 20 and eq 21 and subtraction of eq 18 from eq 19 leads to the reduced system

dpzµ ωµ0 ) p - λµpzµ dt 2

(22)

dp) ωµ0 (pze - pzµ) - (ωze + ωzµ)p+ - (λex + λµ)p- (23) dt dp+ ) (ωze + ωzµ)p- - (λex + λµ)p+ dt

(24)

dpze ωµ0 ) - p- - λexpze dt 2

(25)

with p+ ) pxx + pyy and p- ) pyx - pxy. Comprehensive work has been performed for the case of electron relaxation in the absence of chemical reaction.17,19,21,24,26,30 In analogy to the solution previously derived for slow electron relaxation (2λex , ωµ0 ) by Nosov and Yakovleva,17 we obtain for the time dependence of the muon polarization

pzµ(t) )

[(

)]

λex 1 + 2x2 exp λ + t µ 2(1 + x2) 2(1 + x2)

(26)

with x ) B/B0. Here, B0 ) ωµ0 /γe ) 11.83 mT is the isotropic hyperfine coupling constant between the muon and the electron, and γe ) 17.608 × 1010 rad s-1 T-1 is the gyromagnetic constant of the electron. The field-dependent initial amplitude multiplying the exponential function takes the value 1/2 in zero field and approaches unity for B . B0. For λµ ) 0 eq 26 transforms into the well-known solution.17 It should be noted that Mobley

6564 J. Phys. Chem., Vol. 100, No. 16, 1996

Dilger et al. agreeing with the numerical solutions for all electron relaxation rates. However, while at the highest field in the experiment (0.4 T), the condition x . 1 is satisfied, data were also taken at fields down to 0.03 T, which is comparable to the intrinsic field B0. In an earlier estimation32 we derived an upper limit for the ethyl-radical-oxygen collision rate of the order of 108 s-1 for the highest oxygen concentration, which is significantly lower than ωµ0 , so that the conditions of the experiment were generally far from the limit of rapid spin exchange where eq 27 applies. Therefore, and because low fields were also used, eq 26 is entirely satisfactory for analysis of the data. 2.3. Combination of Spin Dynamics and Chemical Reaction. The above equations describe the relaxation in Musubstituted radicals in the absence of chemical reaction. To continue, we assume a general chemical reaction

Figure 1. Numerical solution of the set of differential equations 2225 (dark dots) compared with the analytical approximations for slow electron relaxation (solid line) and fast electron relaxation (dashed line). The calculations are for zero muon relaxation and a magnetic field of 1 T. The electron relaxation rates are 5 × 108 (a), 2 × 109 (b), 1010 (c), 1011 (d), and 1012 s-1 (e).

used a different exponent which contained in place of (1 + x2) its square root.18 For the case of very fast relaxation (2λex . ωµ0 ), the solution, again in close correspondence to the one found by Ivanter and Smilga,19 is

[(

pzµ(t) ) a exp - λµ +

λex 2((λex/ωµ0 )2

)]

+x ) 2

t

λch

A 98 B

(28)

where the reactant A and the product B can both be either paramagnetic or diamagnetic, and λch represents the rate constant of the reaction of first or pseudo first order. The theoretical treatment of muon spin polarization in the presence of chemical reaction has been outlined first by Ivanter and Smilga19 and by Brewer et al.33 Following these treatments, we assume that the muon polarization is transferred intact during the chemical reaction. The appropriate equation

PAB(t) ) pA(t) exp(-λcht) + λch∫0 pB(t - t′)pA(t′) exp(-λcht′) dt′ (29) t

(27)

As long as x . 1, eq 27 is also valid for λex < ωµ0 , because in this case the denominators in the exponents of eq 26 and 27 are very similar. The prefactor a of eq 27, given in full by Smilga,19 goes to unity for very high fields, as is the case in eq 26. Furthermore, very fast spin exchange results in a decoupling of the muon and electron spins and in a decrease of the effective B0, so that in this case, a is close to unity even for low external fields. To test the validity of eq 26 and 27 when λex is similar to ωµ0 , it is necessary to compare them with simulations of the above set of linear differential equations which are valid for the whole range of λex. To this end, we solved eqs 22-25 numerically, using one of the ADAMS algorithms.31 A comparison between the analytical solution for both fast and slow spin exchange and the numerical solution is shown in Figure 1. The magnetic field was set to B ) 1 T, and for ωµ0 , the muon electron hyperfine coupling in the ethyl radical at room temperature (2π × 330 MHz) was used. λµ was set to zero to have a wider range for varying the electron relaxation, though the formulae are of course also valid for λµ * 0. In the slow spin exchange region (upper curves in Figure 1), both analytical solutions agree very well with the numerical calculation. The time dependence of the muon polarization follows an exponential function with a damping which is proportional to the spin exchange rate λex. For λex ) 1011 s-1 we see that the muon depolarization calculated numerically is slower than we expect on the basis of eq 26, but it agrees with eq 27. At an electron relaxation rate of 1012 s-1, we are in the “inverse” region, where the muon depolarization actually decreases with increasing λex. Equation 27 describes this behavior very well; here, as expected, the result of eq 26 markedly disagrees with the exact solution. For the above simulations, a relatively high field of 1 T was chosen to illustrate the behavior of the muon spin for both slow and fast spin exchange. Here, eq 27 gives the better result,

describes the observed total polarization. The first term, decreasing in time, represents the contribution of unreacted A, whereas the second term stands for the increasing B. Substitution into eq 29 of the following expressions of the form of eq 26 for the polarizations of A and B

pA(t) ) aA exp(-λAt)

(30)

pB(t) ) aB exp(-λBt)

(31)

where the index z, signifying the component parallel to the external field, and the superscript for the muon have been dropped, followed by integration leads to the general formula AB B A PAB(t) ) aA[PAB 0 exp(-λ t) + (1 - P0 ) exp(-λ - λch)t] (32)

where

PA,B ) 0

aBλch λA - λB + λch

(33)

and aA,B are the field-dependent prefactors

aA,B )

2 1 + 2xA,B 2 2(1 + xA,B )

(34)

The individual muon spin relaxation terms are

λA,B ) λA,B + 0

λA,B ex 2 2(1 + xA,B )

(35)

is the intrinsic relaxation rate of the muon in the where λA,B 0 absence of a partner for chemical reaction or spin exchange. It contains the muon self-relaxation λµ as introduced in eq 13 but

Addition Kinetics and Spin Exchange

J. Phys. Chem., Vol. 100, No. 16, 1996 6565 of the order of 10-4 compared with that of the ethyl radical. Therefore, the peroxy radical behaves as if it were diamagnetic, and a single exponential results for the relaxation of the muon polarization (eq 36). Taking into account that our reaction is of pseudo first order so that λex ) kex[O2] and λch ) kch[O2], the polarization decays according to

(

λ ) λR0 + kch +

Figure 2. Simulation of the time dependence of the muon polarization (eq 36) for λR ) 1 µs-1 and λch ) 0 (a), 0.5 (b), 1 (c), and 2 µs-1 (d). The product fraction is indicated as P∞RD for b. Note that in the absence of chemical reaction (curve a) the muon polarization goes to zero.

in a more general sense can be described by a set of parameters which are interpreted in terms of specific spin relaxation mechanisms.13,34 Here, λµ is taken as an empirical parameter which in the experiment is determined separately for the actual reaction conditions from the oxygen-free gas mixture, since it depends on the magnetic field, temperature, pressure, and composition of the gas. Equation 32 gives a biexponential decay, which is to be expected when both species are paramagnetic. In this case, the two components are still separable via the magnetic field dependence, as long as the hyperfine coupling constants of A and B are significantly different or if the intrinsic relaxation rates are different. In cases where either A or B is diamagnetic (superscript D), which normally implies xD f ∞, λD f 0, and aD f 1, the situation simplifies further. Thus, for a reaction of a radical R to a diamagnetic product as needed in the present work, eq 32 reduces to

PRD(t) ) aR[P∞RD + (1 - P∞RD) exp(-λR - λch)t] (36) PAB 0 is now interpreted as the total muon polarization at infinite time and written as P∞RD ) λch/(λR + λch), and aR is field dependent as in eq 34. The result of eq 36 is simulated in Figure 2 in the limit x2R . 1, for λR ) 1 µs-1 and various values for λch on the µSR time scale. It is seen that in the absence of chemical reaction (curve a) the muon polarization relaxes to zero, whereas with increasing λch the amplitude of the relaxing component decreases since more and more muons are transferred into the diamagnetic environment. It is important to note that in sufficiently high fields or in the absence of spin exchange the presence of an intrinsic muon relaxation λR0 is essential; in its absence there would be no relaxing component, and chemical reaction giving a diamagnetic product alone does not cause relaxation, so that the muon polarization becomes unobservable by this technique. For the present experimental system, the reaction of the Musubstituted ethyl radical with oxygen, the expected principal product, MuCH2CH2OO˙ , is also a radical. However, this can effectively be treated as a diamagnetic product, since the muon electron hyperfine coupling, calculated using the semiempirical MOPAC package with the AM1 Hamiltonian,35 is found to be 0.11 mT, which is only 1% of the muon electron coupling in the Mu-substituted ethyl radical. Experimental values for protons in comparable peroxy radicals lie in the range of 0.20.7 mT.36 Taking into account the quenching factor of 1/(1 + x2R) and the fact that xR . 1 at the field of interest, the influence of the electron on the muon in the peroxy radical is

kex 2(1 +

)

xR2)

[O2] ) λR0 + k[O2]

(37)

which is the direct basis for the analysis of the experimental data. The quantities of interest, kex and kch, are the bimolecular rate constants for spin exchange and for chemical reaction. We see from eq 37 that due to the inverse quadratic field dependence the effect of spin exchange on the muon relaxation is quenched in high longitudinal fields (x2R . 1), which allows the separation of the two processes. This has been recognized in collisions of Mu with paramagnetic species37 and emerges here as well for Mu-substituted radicals. 3. Experimental Section 3.1. Muon Production and Decay. All experiments were carried out using “surface” muons of 4.1 MeV energy from beams either in the πE3 area of the Paul Scherrer Institute (PSI) in Villigen, Switzerland or in the M13 area of TRIUMF in Vancouver, Canada. To produce polarized muons, a proton beam is accelerated up to an energy of approximately 600 MeV and focused onto a production target, typically graphite. Nuclear reactions result in positive pions, π+. Some of these spin zero particles decay at rest on the surface of the target with a lifetime of 26 ns according to

π+ f µ+ + νµ

(38)

into a positive muon µ+ and a muon neutrino νµ, both spin-1/2 particles. In this parity-violating decay, guaranteed by the essentially zero mass of the neutrino, the helicity of the neutrino is minus one, which means that the direction of the neutrino spin is exactly opposite to its momentum. Due to conservation of spin and momentum, which are both zero for the pion at rest, the muons are also polarized antiparallel to their momentum. If these muons are selected in a very small solid angle, a muon beam with a spin polarization close to 100% is produced. With a mean life of τµ ) 2.2 µs, the muon decays

µ+ f e+ + νjµ + νe

(39)

into a positron and two neutrinos, which is also parity violating. The decay positron is then emitted preferentially along the muon spin, with a probability of emission proportional to the function (1 + a cos θ), where θ is the angle between the muon spin and the direction of the e+ emission. In the experiment, these decay positrons are detected using plastic scintillator counters, as outlined below. The decay “asymmetry” represented by a is typically about 1/3, averaged over all decay energies, and proportional to the polarization of interest. 3.2. Experimental Setup and Gas Handling at PSI. The experimental setup is shown schematically in Figure 3. The reaction vessel is placed in the horizontal bore of a superconducting magnet. The bore has a length of 1 m and is 200 mm in diameter. The magnetic field can be continuously swept between 0 and 5 T. The reaction vessel is a cylinder of 500 mm length and 80 mm diameter. It is surrounded by a copper tube (C), which allows heating and cooling of the gas in the vessel by recirculating a temperature-regulated liquid. Methanol was used up to 290 K, followed by water in the range 290360 K and silicon oil above this.

6566 J. Phys. Chem., Vol. 100, No. 16, 1996

Figure 3. Experimental setup consisting of magnet, reaction vessel with copper tube (C) for temperature regulation, muon detector (M), and positron detectors (F and B). The muons enter from the left, pass through the beam pipe window, the M detector, and the two windows of the thermostat and reaction vessel, and stop in the gas.

To isolate the vessel thermally from the environment, it is placed in a vacuum jacket. The Mylar windows at the end of the vacuum jacket and at the end of the beam line have a thickness of 120 µm. One end of the reaction vessel is equipped with a 25 µm thick titanium foil, through which the incident muons enter the gas. This can hold a pressure of 2 bar at the maximum temperature. Degrader foils are added at the entrance of the reaction vessel to compensate for the lower stopping density of the gas at higher temperature. The reaction vessel is pumped out and filled via a tube with a diameter of 28 mm. The gas was premixed in a 1 L minican. For this, the evacuated minican was first filled with a known amount of oxygen and then topped up with ethene and nitrogen to a defined pressure. Then the gas mixture was let into the reaction vessel up to a pressure of 1 bar. To determine the amount of oxygen, calibrated standard volumes (10 or 50 mL) were used. The oxygen pressure was measured to an accuracy of ca. 2% using a Vacuubrand absolute pressure gauge with an integrated piezoresistive sensor. For all experiments, ethene with a purity, as stated by the supplier, of >99.8% and an oxygen contamination of 99.999%, with an oxygen content of