J. Phys. Chem. 1981, 85,451-454
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Origin of the Residual Polarization in Muon Chemistry Studies of Solvent Mixtures Y. C. Jean, 6. W. Ng, J. H. Brewer, D. G. Flemlng, and D. C. Walker” Departments of Chemistry and Physics and TRIUMF, Unlverslty of British Columbia, Vancouver V6T 1 WS, Canada (Received: Ju& 16, 1980)
When polarized positive muons are stopped in common chemicals, there is always a “residual polarization” due to the fraction of muons which immediately enter diamagnetic states. This fraction varies considerably, being 0.17,0.62, and 1.0 in benzene, cyclohexane, and carbon tetrachloride, respectively. In order to examine the mechanism by which it arises, we studied mixtures of benzene with cyclohexane and carbon tetrachloride. The results indicate that incorporation into diamagnetic species occurs mainly in a one-step intramolecular process, which is consistent with the “hot model”. Competitive secondary reactions are involved to only a limited extent, and the “spur model” is evidently inoperative. The results also suggest that the average energy range over which the hot process occurs is comparable to the energy lost during a thermalizing encounter with a molecule.
Introduction When longitudinally polarized, energetic positive muons (p+) impinge upon a solid or liquid chemical target, they transfer energy to the medium and are themselves thermalized by a complicated sequence of events within a few picoseconds. They emerge from this melange of “end of track” processes incorporated either in diamagnetic molecules, or as free muons, or in paramagnetic species, such as free muonium atoms (p+e-) and muonic radicals.l* This paper is concerned with those muons which appear immediately (within the experimental observation time, Le., ;5W9s) in diamagnetic states (including free p+) in liquid media and which thereby contribute to the amplitude of the coherent “muon spin rotation” (p+SR)signal.I4 It has already been shown for a wide variety of common chemicals that the fraction (PD) of initial muons appearing in diamagnetic species varies from 0.17 (for benzene) to 1.0 (for CC14),with water, saturated hydrocarbons, and aliphatic alcohols all having PDvalues of -0.63 f 0.02.’g3 Attempts to correlate P D with various physical and chemical properties of the liquids have been only partially ~uccessful.~ There seems to be no consistent correlation with one property such as density, dipole moment, polarizability, dielectric constant, and ionization energy or even with the bond energy of the molecule’s weakest bond, though some systematic trends are evident? For instance, PDhas been found to be less than 0.5 only in molecules containing ?r bonds, and the greater the degree of conjugation the smaller is PD, with benzene as the lower extreme. Also, the more extensive the substitution of H atoms in organic compounds by halogens, the higher is PD, with CC14 being an example of the upper extreme. The experimental parameters observable in a w+SR experiment is the muon asymmetry, a measure of the residual polarization of the incident p+ at the time of observation. Hence PDis taken as the observed muon asymmetry in the liquid of interest divided by the asymmetry found under identical conditions in CC14. This is a convenient method (1) J. H. Brewer, K. M. Crowe, F. N. Gygax, and A. Schenck in “Muon Physics”, V. W. Hughes and C. W. Wu, Eds., Academic Press, New York, Vol. 111, 1975, p 3. (2) J. H. Brewer and K. M. Crowe, Annu. Reu. Nucl. Sci. 28, 239 (1978). (3) D. G. Fleming, D. M. Garner, L. C. Vaz, D. C. Walker, J. H. Brewer, and K. M. Crowe, Adu. Chern. Ser. No. 175, 279 (1979). (4) (a) P. W. Percival, E. Roduner, and H. Fischer, Chern. Phys., 32, 353 (1978); (b) P. W. Percival, E. Roduner, and H. Fischer Adu. Chern. Ser., No. 175, 335 (1979). (5) P. W. Percival, H. Fischer, M. Camani, F. N. Gygax, W. Ruegg, A. Schenck, H. Schilling, and H. Graf, Chern. Phys. Lett., 39, 333 (1976). (6) E. Roduner, P. W. Percival, D. G. Fleming. J. Hochmann. and H. Fischer, Chern. Phys. Lett., 57, 37 (1978).
of normalization of residual polarization data since CCll has invariably been found to give the maximum obtainable asymmetry, equal to that found in aluminum and other meta1s.l Equation 1 defines P D in terms of four compoP D = h + rPrea(R)+ (1 - h - r)P,,,(Mu) (1) nents: h, the “hot diamagnetic fraction”, a nonscavengable, field-independent, direct component; r, the direct component of free radicals formed at t = 0; P,,,(Mu), the residual polarization resulting from the interaction of thermalized muonium atoms (Mu) with solvent or scavenger molecules to place the muon in diamagnetic species at short enough times to contribute to the coherent p+SR signal; and P,(R), the analogue to P,,(Mu) for “hot” free radicals. P,,,(Mu) and P,,,(R) are field dependent, and their magnitudes also depend on the reaction rate constants of Mu and R $ith the solvent or scavenger. For many liquids, including CC14,saturated hydrocarbons, and benzene, as used in this study, it has been shown’s2 by varying the magnetic field or measuring the rate constants directly that the second and third terms in eq 1 are negligible and therefore that P D = h. We are involved here with the origin of h (i-e., P D ) . It was originally so named because it was thought to arise from abstraction or exchange reactions with the solvent by hot (epithermal) p+ or Mu during the final stages of thermalization. This is what has become known as the “hot model” in muonium chemistry.l However, Mogensen postulated a “spur model” for positronium chemistry? in which the positron (e+)reaches thermal energy while still in the neighborhood of reactive free radicals, electrons, and ions generated in spurs in its thermalization track. An analogous spur model has been suggested4to explain the initial distribution of muons between diamagnetic and paramagnetic species simply based on the relative probabilities of reaction or escape of thermalized muons from the reactive species of the terminal spur. Although this spur model does not conform with expectation in certain regards, particularly in water containing intraspur scavengers? it can further be tested in the present study using liquids of low dielectric constant (where p+ should combine with spur electrons much more readily than in a highdielectric medium like water). In an attempt to resolve these issues, we have measured P D in mixtures of benzene with cyclohexane and CC14. Previously methanol ( P D = 0.62) was mixed with benzene (7) 0. E. Mogensen, J. Chern. Phys., 60, 998, (1974). (8)D. C. Walker, Y. C. Jean, and D. G . Fleming, J. Chem. Phys., 70, 4534 (1979); 72, 2902 (1980).
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and CHC1, ( P D = 0.85);1-3 but those results could be misleading because alcohols form nonhomogeneous mixtures with weakly polar liquidsg (the alcohol molecules preferring to aggregate with themselves), and therefore p+ would be successively in fairly large regions consisting predominantly of one component, rather than in true mixtures at the molecular level. However, that study gave results which are in no way contradictory to the conclusions drawn in this paper, though the earlier interpretation’ has been modified by use of volume fractions in later discussion^.^^^ In addition, there is some published work in which reaction rate constants were evaluated from the asymmetry coefficients of concentrated solutions and binary mixtures; lo but none of it seems to be inconsistent with the present work. Experimental Section A beam of 4.1-MeV positive muons from the M20 channel of the TRIUMF cyclotron was used in typical p+SR experiments as previously described in detail., The spin-polarized muons stop in the liquid sample under study, which is held in a transverse magnetic field (70 G); muons in diamagnetic species precess in this field with a characteristic frequency (0.949 MHz at 70 G). These muons decay (I*+ e+, ue, vP) emitting e+ preferentially along the original p+ spin direction, defining a characteristic asymmetry (A) that is extracted from the data by fitting the experimental time histograms to a theoretical expression for the p+SR signal, as described el~ewhere.~J’ When CC4was used as the target material, a value for the maximum asymmetry (A,) was obtained, so that P D is taken as A / A o . Two values of PDare obtained independently in these experiments by the use of two positron detectors (“left” and “right”) for each solution. Mixtures were made by combining measured volumes of the two liquids of reagent-grade quality. There were no corrections necessary for changes in the total volume upon mixing since these were found to be negligible for the cases used. The solvent mixtures were contained in shallow Teflon cells with thin mylar windows at front and back,ll which let the muons in and did not distort the polarization of the emitted positrons. These mixtures were not deoxygenated because this was deemed unnecessary as O2 has been shown to react with thermalized Mu atoms in water with a rate constant of 2.4 X 10’O M-l S-’.’~ Thus M in these solvents) at 1-atm pressure of air ([O,]< there could be only a trivial contribution to the coherent residual polarization by reaction of Mu with O2even if that reaction resulted in the muon being in diamagnetic states (though in fact it may well result in paramagnetic species).12
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N
Results The results are shown in Figure 1as plots of P D against volume fraction for mixtures of carbon tetrachloridebenzene and cyclohexane-benzene. In the former case there is a substantial enhancement in PD due to the presence of a small amount of CC14 in benzene; but oth(9) See, for example: (a) A. N. Fletcher, J. Phys. Chem., 76, 2562 (1972); (b) B. C. Anderson, J. H. Rytting, S. Lindenbaum, and T. Higuchi, ibid., 79, 2340 (1975). (10) (a) A. I. Babaev, M. Ya. Balats, G. G. Myasishcheva, Yu. V.
Obukhov, V. S. Roganov, and V. G. Firsov, Sou. Phys.-JETP (Engl. Transl.), 23,583 (1966); (b) G. G. Myasishcheva, Ya. V. Obukhov, V. S. Roganov, and V. G. Firsov, Khirn. Vys. Energ., 1, 390 (1967). (11) (a) Y. C. Jean, J. H. Brewer, D. G. Fleming, D. M. Garner, R. J. Mikula, L. C. Vaz, and D. C. Walker, Chern. Phys. Lett., 57,293 (1978); (b) Y. C. Jean, J. H. Brewer, D. G. Fleming, and D. C. Walker, ibid., 60, 125 _ - (1_97x1. ~
(12) Y. C. Jean, D. G. Fleming, B. W. Ng, and D. C. Walker, Chern. Phys. Lett., 66: 187 (1979).
Jean et al.
100% B~~~~~~
02
04 06 Volume Fraction
08
IO
Flgure 1. Plots of PDagainst volume fraction of CCI, or cyclohexane in benzene (1) for CCI,-benzene mixtures and (2) for cyclohexanebenzene mixtures: (0)data polnts obtained on the left-hand-side detector; (A)data from the right-hand-side detector; (0)data taken from ref 3. The statistical errors are comparable to the size of the data points. Random errors from other sources are -*lo%. IO
0
0
1
1
02
04
I
06 Composition
1
08
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Flgure 2. Plots of PD against composition expressed on the abscissa
in three different ways. Curves 1-3 refer to CCI,-benzene mixtures and curves 4-6 to cyclohexane-benzene mixtures. Curves 2 and 6 are the volume-fraction plots as in Figure 1; curves 1 and 4 are the mole-fraction plots: curves 3 and 5 are the mass-fraction plots.
erwise PD changes almost linearly with volume fraction. For the cyclohexane-benzene mixture there is very mild curvature at the concentrated cyclohexane end, but otherwise it too is nearly linear. Mixtures of CC14-cyclohexane show a curve of shape similar to that of CCGbenzene; that is, the PDfrom cyclohexane is strongly enhanced in the presence of small amounts of CC14 but is then roughly linear. Data obtained previously for the neat liquids3 are also given in Figure 1. The present benzene data fall within the published range whereas the cyclohexane value is some 8% smaller. It can be argued that volume fraction is the most likely composition function to resolve the issues at stake in these experiments, because it most closely reveals the fraction of time the muon spends in contact with each ingredient during the slowing-down process. However, the basic shapes of these curves are not changed significantly when the data are plotted against mole fraction or against mass fraction. Using just lines connecting the mean values of P D for each mixture, we have presented these three types of plots together for comparison in Figure 2. Discussion The present results do not reveal exactly why CC14and benzene have the largest and smallest values of PD (and h ) known, but they provide some information about the mechanism of formation of the “hot” fraction and certainly
The Journal of Physical Chemistty, Vol. 85, No. 4, 1981 453
Muon Chemistry Studies of Solvent Mixtures
1
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I 1 1
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Figure 3. Comparison of observed data with expectations based on certain mechanisms. Curves 1 and 2 are the plots of Figure 1. Curve 3 is expected on the basis of a “spur model” with CCI, as an intraspur electron scavenger (see text), and curve 4 is expected if benzene protects cyclohexane by energy transfer or sacrificial scavenging (see text).
eliminate various possibilities. Spur Model. It could have been argued that PD= 1in CC14 because all spur electrons would be immediately captured by CC14to give CC&-and then C1- CC13,which are long-lived and therefore available for neutralization with p to give diamagnetic species through reactions such as reaction 2. Because of the low dielectric constant, this p+ + C1- (or CC14-) MuCl (+CCl,) (2) neutralization would occur over considerable distances and therefore up to times when the original spur has virtually dispersed due to of diffusion. (This argument could not be extended to a comparison of H20 with cyclohexane, for instance, in which the P D values are similar but the lifetime of electrons and Coulombic forces governing neutralization are vastly different.) If intraspur reactions, such as reaction 2, are responsible for PD= 1.0 in pure CC14, then they should be nearly equally effective when the spurs are partly composed of benzene molecules too (a spur, even initially, consist of many molecules). In fact CC14,which is known to be an excellent electron scavenger of both solvated and presolvated electrons,13should have allowed reaction 2 to occur with nearly the same efficiency when CC14constituted 50% and less of the medium. The spur model therefore predicts that the CCl,-benzene mixtures should give a very pronounced curve such as that sketched as curve 3 in Figure 3. Curves such as this are found, for instance, for the yield of free ions in the radiolysis of alcohol-alkane mixtures.14 However, in the present study P D was found to change in an almost linear manner over the volume (or mole) fraction range where CC14should dominate. Therefore these results very strongly imply that a “spur model’’ is not appropriate. In fact the curvature favoring CC14which is evident occurs at low CC14 concentrations, as seen in Figure 1 and discussed later. At high CC4 concentrations the faint curvature which is evident is in the opposite sense to that expected to arise from spur processes. Perhaps one could argue that the efficient capturing of spur electrons by C C 4 to give long-lived anions in fact
+
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(13) (a) J. W. Hunt Adu. Radiat. Chem., 5,185 (1976); (b) M. Anbar, Farhataziz, and A. B. Ross, Natl. Stand. Ref. Data. Ser. (US., natl. Bur. Stand.), 51 (1975). (14) See, for example: (a) T. J. Kemp, G . A. Salmon, and P. Wardman in “Pulse Radiolysis”, Academic Press, New York, 1965, p 247; (b) B. J. Brown, N. T. Barker, and D. F. Sangster, Aust. J. Chem., 26,2089 (1973); (c) J. H. Baxendale and E. J. Rasburn, J. Chem. SOC., Faraday Trans. 1, 70,705 (1974).
prevented neutralization of p+ in the spurs, and this would predict P D = 1.0 in CC14on the basis of all muons having no option but to remain as p+ ions. However, if one took this alternative approach, one would still have to reject the spur model because of these results with mixtures, as above. For instance, in 0.50 mole fraction CC14in benzene, there would equally be no neutralization possible and therefore, according to the spur model, all muons would remain as p+ so that P D would have to equal 1.0, contrary to the results. Since the spur model distributes muons between diamagnetic and paramagnetic species on the basis of intraspur processes involving competition between combination, neutralization, and escape, then it seems to be completely at variance with the results in these mixtures when one ingredient (CC14)captures electrons. s-Bond Effect. Since P D for cyclohexane, cyclohexene, 1,6cyclohexadiene, 1,3-cyclohexadiene, and benzene are respectively 0.68,0.47,0.40,0.32, and 0.17,916it is evident that increased unsaturation, particularly when conjugated, leads to substantially reduced values of PD. This could originate by either of at least two possible mechanisms. It may stem from the possibility of epithermal Mu adding across a double bond particularly readily when the s bonding is extensively delocalized. Such reactions would result in muons being incorporated into free radicals. Alternatively, the presence of low-lying delocalized orbitals may accelerate the thermalization process so that muonium atoms emerge rapidly from the epithermal state with greatly reduced probability of having undergone an abstraction or substitution reaction with atoms in the molecules of the medium. Thus the yield of thermalized muonium atoms would be enhanced. In either case, one would expect the delocalized 7~ bonding of benzene to be effective in reducing P D of cyclohexane when mixed with it. That is, one would have expected an intermolecular protection to be shown by benzene in these mixtures, so that a relationship approaching that sketched as curve 4 of Figure 3 would result. This is the shape obtained for the yield of H2in the radiolysis of benzene-cyclohexane mixtures and attributed to “protection” by benzene.16 However, for PD in the present study, no such effect of benzene is found for its mixtures with either CC14or cyclohexane. Instead, at high benzene concentrations the curvature in CC14solutions is in exactly the opposite sense, and for cyclohexane PD changes linearly with composition. There is only rather small curvature at the low benzene concentration end in both solutions, and the 67:33 and 33:67% mixtures of benzene and cyclohexane (Figure 2) have PDvalues somewhat larger than 1,3-~yclohexadieneand cyclohexene, respectively.I6 These results with mixtures tell us about two types of processes which are not involved in forming the hot fraction. First, if intermolecular energy transfer does occur to benzene, it does not occur on a time scale that can alter the hot fraction. Second, there are no important secondary reactions involved in forming the hot fraction which could be inhibited by the presence of an unsaturated molecule capable of scavenging Mu (and thereby reducing PD by forming a paramagnetic muonic species). Intramolecular Hot Process. For the mixtures, where P D changes almost linearly with volume (or mass) fraction, the “hot diamagnetic fraction” must result from a direct (15) (a) V. G. Firsov and V. M. Byakov, Sou. Phys.-JETP (Engl. Transl.), 20,719 (1965); (b) V. G. Firsov, ibid., 21,786 (1965); (c) E. V. Minaichev, G. G . Myasischeva, Yu. V. Obukhov, V. S. Roganov, G. I. Savel’ev, V. P. Smilga, and V. G. Firsov, ibid., 66, 1926 (1974). (16) J. P. Manion and M. Burton, J. Phys. Chem., 56, 560 (1952).
J. Phys. Chem. 1981, 85,454-458
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(one step) event, involving abstraction, substitution, or final deexcitation by direct interaction with one molecule. It means that there are no competitive primary processes involved and that the hot Mu* did not have a chance to discriminate between the two types of molecules present in a mixture. The processes must be purely intramolecular, with no chance for “sacrificial” or “spongelike” protection of one compound by the other. Let us suppose that the primary interaction of hot muonium atoms (or hot muons, since the products cannot be identified) with solvents SI or S2 leads, via an activated complex, to products D or P. These are either diamagnetic (D) or paramagnetic (P) species including muonium atoms (which are not observable in these experiments). This scheme is represented by process 3 or 4, where u is an effective cross Mu*
+ S1
a3
+
Mu* is in contact with only one molecule during the time period available: either it undergoes a hot reaction with that molecule or its energy is degraded below the level where it can react efficiently. This picture is tantamount to an upgraded “hot model”. If the deactivation took much longer than the time for Mu* to pass one molecule, and if u3 and u4 were significantly different, then the PDvs. composition plot would approach the shape of either curve 3 or 4 of Figure 3, since complete dominance by one component would set in. Instead, the major influence of one solvent on another is seen at low CC14concentrations in benzene and in cyclohexane. From Figure 1it can be noted that 17.5% CC14 increases PD by -0.23, equal to -30% of the overall change in PD in going from neat benzene to neat CC1& (In cyclohexane the increase in PDis also -0.2, but there it is -50% of the difference between the solvents). This suggests that CC14 reacts efficiently with a portion ( 30% in benzene and -50% in cyclohexane) of the species containing muons which in the neat liquid would have yielded paramagnetic states in the form of either free Mu atoms or free radicals. It thereby converts some of the paramagnetic species to diamagnetic molecules such as MuC1, CC13Mu, or even C6H6MuC1. The major point is, however, that the limited extent of the scavenging found, even with excess CC4, indicates that CC14 is reacting after P and D are formed, not with [MUS*]. The relative magnitudes of KD and KP in the reaction scheme above (shown for eq 3 only) will dictate the size of PD and will depend on the actual composition and chemical characteristics of the particular solvent. For CCl, KD evidently dominates, whereas for benzene K~ is some 6-fold larger than KD. In general, abstraction reactions will lead to diamagnetic products and addition reactions to paramagnetic species.
[MuS1*] -% D KP
N
-P (3) MU* + Sz
04 -*
MUS^*]
-+
D’ P’ (4)
section for formation of the activated complex and K is a partial width (in the sense of a Breit-Wigner resonance with several exit channels).” The plot of PD(totalfraction of D + D’) against volume (or mole or mass) fraction will be linear only when the cross sections for epithermal reactions u3 and u4 are equal at all energies. It is rather unlikely that u3 and u4 will even peak at the same energy for each of these three molecules, much less that the efficiency ( K P / ( K D + KP)) for muonium thermalization without reaction will be the same for each. Therefore we conclude that the energy range involved must be comparable to the energy lost per encounter with a solvent molecule. Thus (17) A. M. Brodskii and A. Ya. Temkin, Khim. Vys. Energ., 1,4 (1967).
Acknowledgment. We are grateful to D. M. Garner for his help with some unexpected experimental difficulties and to NSERC of Canada for financial support.
Diffusion- and Activation-Controlled Reactions of Muonium in Aqueous Solutions B. W. Ng, Y. C. Jean, Y. Ito, T. Suzukl, J. H. Brewer, D. G. Flemlng, and D. C. Walker” Chemistry Department, Physics Department and TRIUMF, University of British Columbia, Vancouver, British Columbia V6T 1 Y6, Canada (Received: July 23, 1980)
The temperature dependence of five types of reactions of muonium atoms in aqueous solution have been measured between 2 and 92 “C by the muonium spin rotation (MSR) technique. Results show that for an electron-transfer reduction with Mn04-, for an addition to a bonds in maleic acid, and for a spin-conversion reaction with Ni2+, the rate constants are all diffusion limited. An activation energy for diffusion of 17.5 kJ mol-’ was found, while the A factors varied somewhat in the range 1013M-’ s-’. For these diffusion-controlledreactions there was no kinetic isotope effect when compared with H atoms, so the diffusion coefficient, even for these very small light species, is mass independent. For the abstraction reaction with formate ions, on the other hand, there is a large kinetic isotope effect and the rate constant is activation controlled. The reaction between muonium and NOB-was also studied and tends to exhibit a curved Arrhenius plot even over this short temperature range. Such curvature is consistent with either a contribution from quantum mechanical tunneling or alternative reaction paths.
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Introduction High-energy positive muons dissipate their kinetic energy in a target material by ionization and excitation, and the appear in One Of states. Three of these have been identified 8s muons in diamagnetic states’, as free muonium atoms,’ or, recently, 0022-3654/81/2085-0454501 .OO/O
as muonic free radicak2 This paper is concerned only with muonium, the neutral atom formed when a muon (1) (a) V. W. Hughes, Annu. Reu. Nucl. Sci., 16, 445 (1966); (b)V. I. Goldanskii and V. G. Firsov, Annu. Reu. Phys. Chern., 22,209(1971); (c) J. H.Brewer and K. M. Crowe, Annu. Reu. Nucl. Part. Sci., 28, 239 (1978).
0 1981 American Chemical Society
