Positronium and Muonium Chemistry - ACS Publications - American

14 Radiation Chemistry and Reaction Kinetics of Muonium i n Liquids

Downloaded by UNIV OF CINCINNATI on June 3, 2016 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0175.ch014

PAUL W. PERCIVAL, EMIL RODUNER, and HANNS FISCHER Physical Chemistry Institute, University of Zürich, 8001 Zürich, Switzerland

The muonium chemistry research performed at the Swiss Institute for Nuclear Research is reviewed. Muonium has been detected in water and other liquids, and rate constants for reactions in aqueous solutions were determined. Com parison with hydrogen atom data reveals marked isotope effects, and these are discussed in terms of transition state theory. Relaxation of the muonium signal in ice below 160 Κ is consistent with slowing of the translational diffusion of muonium atoms. The distribution of muon polarization be tween muonium and muon-substituted diamagnetic mole cules has been investigated in water, ice, and aqueous nitrate solutions. It is suggested that muonium or the free muon itself interacts with transient radicals produced in the ter minal spur of the muon track.

he background and underlying principles of muonium ( M u ) chemistry have been dealt w i t h i n a preceding paper ( I ), as has the experimen tal technique, known as /A SR. Therefore, except for the brief notes i n the next paragraph, this chapter is confined to the description and discussion of experimental results. These stem from work carried out at the Swill Institute for Nuclear Research ( S I N ) . T h e S I N muon channel supplies a continuous high-energy (10-60 M e V ) beam of longitudinally spinpolarized muons. T h e facility is, therefore, w e l l suited to the study of dense target materials as opposed to the "Arizona M o d e " beam at T R I U M F ( J ), which is ideal for gas-phase studies. Accordingly, w e have investigated the liquid-phase chemistry of M u , w i t h the main effort centered on water and aqueous solutions. l

A

+

0-8412-0417-9/79/33-175-335$05.25/l © 1979 American Chemical Society Ache; Positronium and Muonium Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1979.


336

POSITRONIUM A N D M U O N I U M CHEMISTRY

In general the spin polarization of positive muons that are stopped in an experimental sample can give rise to two precession signals, w h i c h are observable by / S R . ( A third type of precession signal has been detected since the Montreal symposium. It arises i n certain organic liquids and is attributed to muonic free radicals (2).) The first, present i n a l l but a few substances, is the simple nuclear Larmor precession of the muon (13.55 k H z / G ) . It arises from bare muons or muons incorpo rated in diamagnetic molecules, and we refer to it here as the diamagnetic signal. The second signal comes from muons that have combined w i t h an electron to form M u ( M u s / e " ) , M u signals have been observed only i n a limited number of substances. Their nature is described below. Diamagnetic and M u signals are characterized by their frequencies, phases, amplitudes, and decay rates. I n samples of chemical interest the frequencies are determined by the external field only and thus merely serve to identify the signals. Similarly, except i n a few cases, the phases are of no interest. The amplitudes are very important, however, since they lead to determination of the fractions of initial muon polarization carried over into the different muonic species. W e label the M u and diamagnetic polarizations P and P , respectively. The rates of decay also contain valuable information since they are determined by spin relaxa tion and chemical reaction rates. M

D

Muonium in Liquids The allowed transitions between the energy levels of a M u atom i n a field transverse to the initial muon polarization give rise to four precession frequencies. Two of these are too high to be detected under normal conditions (the typical resolution of /* SR assemblies is 1 nsec). A t very low field (^ 10 G ) the two observable frequencies are degenerate and take the value 1.4 M H z / G . A t higher fields a splitting is evident, and this gives rise to a beat pattern i n the precession signal. This is shown clearly i n Figure 1, which shows the M u precession signal for a sample of quartz i n a transverse field of 101 G . Although M u has been identified i n both gas (3,4,5,6,7) and solid (8,9,10,11,12) phases for more than a decade, it escaped detection i n liquids until our first experiments at S I N i n 1975 (13). Weak precession signals were observed i n the Fourier transforms of μ SR. histograms accumulated for a sample of water at a number of different fields. A n a l ysis of the splitting of the observed frequencies supported assignment of the signals to M u atoms that exhibited a muon-electron hyperfine fre quency consistent with the vacuum value (4463 M H z ) . A more recent example of M u precession, as evident i n the Fourier transform of a /* SR histogram, is shown in Figure 2. Figure 3 displays a time spectrum +

+

Ache; Positronium and Muonium Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

14.

PERCIVAL E T A L . .3,

•

•

•

•

337

Muonium in Liquids •

•

•

•

1

.2

- J

•

r

0

.02

• — • — • — • — • — • — • — • — • — • — • — • — • — • — •

M

.06

.08

.10

Time


Figure 1.

.12

.U

.16

1

.18

.20

με

Mu precession in quartz at 101 G

showing the degenerate M u precession arising i n water at about 4 G applied field. The constant amplitude of the signal demonstrates lack of chemical reaction or spin relaxation on the microsecond time scale. The M u signal i n water accounts for 2 0 % of the initial muon polarization (only half of which is actually detectable at the observable frequencies ). This is clearly one reason why its detection came so much later than for solids and gases, where up to 100% of the initial muon polarization occurs i n M u . A second pitfall is the presence of dissolved oxygen i n undegassed liquid samples. Oxygen is expected to both undergo fast chemical reaction with M u and to cause rapid spin relaxation v i a Heisenberg spin exchange.

Freq. 80 Figure 2.

120

160

200 MHZ

Fourier transform showing splitting of the Mu precession frequencies in water at 30 G



338

POSITRONIUM AND M U O N I U M CHEMISTRY

-.2

.2

.6

10 Time

Figure 3.

U

με

Mu precession in water at about 4 G

Since its detection i n water, M u has also been observed i n methanol, ethanol, diethyl ether, and dioxane (14). Water, as a l l other liquids so far studied, also exhibits a diamagnetic precession signal; more than 6 0 % of the initial muon polarization manifests itself i n this way. However, the sum of diamagnetic and M u polarizations, P and P , is significantly less than unity. This also applies for methanol and ethanol (see Table I ) . The problem of the missing fraction of polarization is discussed later. D

Table I.

Muon Polarizations in Pure Substances

Sample

T?

H 0 , liquid H 0 , ice (Τ > 160K) D 0 , liquid D 0 , ice (Τ > 160K) CH OH

0.622 ± 0.006 0.480 ± 0.004 0.57 ± 0.03 0.393 ± 0.005 0.61 ± 0 . 0 1 0.51 ± 0 . 0 2 0.59 ± 0.03 0.990 ± 0.007

2

2

2

3

CD3OD

C H OH Aluminum, granular β

P

a

D

2

2

M

5

0.196 0.52 0.18 0.63 0.19 0.31 0.20

± 0.003 ± 0.02 ±0.01 ± 0.01 ±0.02 ±0.05 ±0.04 —

Relative to P = 1.0 for CC1 . D

a

M

4


14.

Muonium in Liquids

PERCIVAL E T A L .

339


Muonium Kinetics in Aqueous Solution Since M u is long lived in pure water ( on the microsecond time scale dictated by the muon lifetime, 2.2 /^sec), it is possible to study its rates of reaction w i t h dissolved substrates by simply following the rates of disappearance of the precession signal (15). The interest i n such a study lies in the comparison of M u rate constants with those of the hydrogen atom. The magnitude and direction of the measured kinetic isotope effects provide useful tests of chemical reaction theories. M u kinetics has thus become a major part of our research program, w i t h about 20 rate constants determined to date. Experimental Method and Results. The experimental method is entirely analogous to that described by Fleming et al. ( J , 16,17) for their gas-phase kinetic measurements. Experiments were always performed at low magnetic field, so that the /* SR histogram was given by (16) +

S =

Ν

{Β

+

e

[1

t/T

4

M

e"

i / 7

+

Α

Ό

2 M cos

e 2* t/T

(ω £

+

Μ

cos

(

φ )

] }

Μ

W D

i

+

φ)

+

Ό

(D

where Ν is a normalization factor, Β is the background (usually < 0.01), and τ is the muon lifetime. A , ω , and φ represent the asymmetry ( i.e., the amplitude),, frequency, and phase of the diamagnetic signal and A , ω , and σ are the aspmmetry, frequency, and phase of M u . I n addition, the decays of the muon and M u precession signals are charac terized by effective relaxation times T D and Γ Μ· Relaxation of the diamagnetic signal is negligible i n nonparamagnetic aqueous solutions (15). The M u decay rate λ = T is given by D

M

Μ

Ό

Ώ

Μ

2

2 M

λ —λ(ο)

2

_ 1

(2)

+fc[X]

where k[X] is the rate of the pseudo first-order reaction w i t h substrate X , and λ ( ο ) is the decay rate i n pure water. During an experiment 10 muons at most are stopped in a few milliliters of solution, so there is a negligible change i n the concentration of X . M u precession signals for three concentrations of fumaric acid are shown i n Figure 4 together with the best fits to Equation 1. The increase in λ with solute concentration is clearly visible; extracted values are plotted in Figure 5. The straight line is the least-squares fit of the data to Equation 2, and its slope gives the rate constant, k = 1.4 X l O ^ M " sec" . In the same way rate constants have been determined for reactions w i t h a variety of substances i n aqueous solution. The results are gathered in Table II, where they are compared with literature values for hydrogen atom reactions. W e have determined further that k < 2 χ 1 0 M sec" for H , N a , and CI" since there was no visible M u decay in 5 M solutions of H C 1 and N a C l . Similarly k < 1 χ 1 0 A i sec" for C10 ~ was deduced from the lack of decay i n 0.1M HC1Ô . 8

1

1

5

+

+

7

_1

1

4

4


_ 1

1

340



2 10 M

12 Time

Figure 4.

16

20

με

Mu precession signals in aqueous solu tions of fumaric acid

r~

1

2

10 sec 6

1

10

12

W' M 5

Figure 5. Mu decay rates at different concentrations of fumaric acid. The rate constant is given by the slope of the least-squares line.


14.

PERCIVAL E T A L . Table II.

Comparison of Rate Constants for Muonium and Hydrogen Atoms in Aqueous Solution kir (M-'sec )

J^L k

k (M-'sec ) Mu

1


341

Muonium in Liquids

1

Hydrogen abstraction methanol ethanol 2-propanol 2-butanol formate ion

2.5 2.1 6.8 1.3 1.24

Χ Χ Χ Χ Χ

Bromine abstraction bromoacetic acid ( p H 1) 2- bromopropionic acid ( p H 1) 3- bromopropionic acid ( p H 1)

2.6 9.5 1.7

Χ 10 Χ 10 Χ 10

6 9 1.1

Χ Χ χ Χ

10 10 10 10 10

6 7 7 8 8

8 8

8

< 3 < 3 ~ 7 1.1 7.8

Χ Χ Χ Χ Χ

Mu

10 10 10 10 10

1.5 Χ 10 4.0 Χ 10 ~ 3 Χ 10

4 5 5 6 6

> 83 > 70 100 118 16

9 9

8

0.17 0.24 0.6

Hydrogen addition to olefins maleic acid ( p H 1) fumaric acid ( p H 1) ascorbic acid ( p H 1) dihydroxyfumaric acid ( p H 1 )

9

10 10 10 10

8 8 8 7

1.1 1.4 1.8 4.5

Χ χ Χ Χ

10 10 10 10

10 10 9 7

0.06 0.06 0.06 2

Diffusion-controlled reactions Mn0 Ag

2.4 Χ 10 1.15 X 1 0

4

+

10

1 0

2.5 Χ ΙΟ 1.6 X 1 0

10

1 0

1 0.7

Further reactions acetone ( p H 1) HO' N0 -

2.8 1.5 9

3

Χ 10 Χ 10 Χ 10

6 7 6

8.7 Χ 10 1.7 Χ 10 1.5 Χ 10

7 7 9

0.03 1 0.006

Discussion. The substrates i n Table II are grouped according to type of reaction with hydrogen (18,19). The M u reactions are assumed to be analogous and are: hydrogen atom abstraction R H + Mu-»R- + M u H ;

(3)

R B r + M u -> R - + M u B r ;

(4)

bromine abstraction

addition to olefinic double bonds C=C

+Mu-»Mu—C—C-;


(5)

342

POSITRONIUM A N D M U O N I U M C H E M I S T R Y

fast oxidation at or close to the diffusion-controlled limit Mn0 " + M u -» u + Mn0 "

(6)

Ag + M u ^ ^ + Ag°;

(7)

+

4

4

2

and +

and the miscellaneous reactions ( C H ) C O + M u -> ( C H ) C 0 M u

(8)

O H ' + M u -> M u O H + e "

(9)

3

2

3

2


aq

N 0 - + M u ^ MuO" + N 0 . 3

(10)

2

The (assumed) diffusion-controlled reactions show little or no kinetic isotope effect. This is i n accord with the nearness of the M u and hydrogen atomic radii, which is expected to lead to close similarity i n diffusion constants and reaction radii. Almost a l l other reactions show marked isotope effects; hydrogen abstraction is lower for M u while bromine abstraction and addition to an olefinic bond are faster. Transition state theory states that the rate constant for the reaction A + Β - » products

(11)

is given by ,

^

RT

(

Ε

\

where Γ is a transmission factor (including the effect of tunneling), Q , Q , and Q ^ a r e the molecular partition coefficients of the reactants and the transition state (excluding the vibration equivalent to translation along the reaction coordinate), and Ε is the activation energy for the reaction—i.e., the difference between the ground state electronic and vibrational energies of transition state and reactants: A

B

Ε =

Ε

—

—

(13)

ΕΒ·

W h e n this theory is applied to the hydrogen atom abstraction as i n Equation 3, the predicted isotope effect becomes

k

M

—

Γ

Μ

' Q

N

' Q*MX

^

{

^

P

B

T

RT

X

^

f

}


(

1

4

)

14.

PERCIVAL E T A L .

343

Muonium in Liquids

Table III. Comparison of Experimental Isotope Effects with BEBO Calculated Values for the Fourth Factor in Equation 14 Substrate Methanol Ethanol 2-Propanol 2-Butanol Formate

W k *

BEBO

> 83 > 70 ~ 100 118 16

103 73 37 37 8

where the difference i n activation energies ( E — E M ) has been factored into its vibrational and electronic parts. The first factor on the right of Equation 14 is 1 if tunneling is unimportant and otherwise favors the reaction of M u . A ratio of translational partition functions comes next; its value is 1/27 i n the gas phase and presumably is somewhere between this value and 1 for liquids. The total partition functions for the transition state should be very similar at room temperature, so that the third factor is not much different from 1. The fourth factor arises from the difference in vibrational zero-point energy i n the transition states; it is the only factor that can have a value much greater than 1. Finally, the electronic activation energies are equal within the Born-Oppenheimer approximation, thus predicting a value of 1 for the last factor. I n reality it should be a little less. Since hydrogen atom abstraction is slower for M u than for hydrogen, the fourth factor of Equation 14 must be of overriding dominance. To estimate its magnitude, bond lengths and force constants for the transition states were estimated by the bond energy-bond order method ( B E B O ) (20), assuming the usual linear structure M u · · · H · · · R and treating R as a single heavy atom. Table III lists the predicted values of the dominant factor of Equation 14 and compares them with the experimental isotope effects. The predictions clearly account for the approximate magnitude of the isotope effects and demonstrate that tunneling i n particular must play only a minor role i n the hydrogen abstraction reaction at room temperature. The remaining reactions i n Table II have not been subjected to theoretical analysis, but we suspect that tunneling w i l l be found to be important. This is thought to be the case for hydrogen addition to olefins (21).


H

H0 2

and D 0 Ices 2

Experimental Results. T h e M u precession signal i n H 0 and D 0 ices is much stronger than i n the corresponding liquids. This is partly the result of a smaller diamagnetic fraction i n the ices (see Table I ) but 2


2

344


also because a l l the initial muon polarization is accounted for—i.e., there is no missing fraction, as is the case for liquid H 0 and D 0 . Examples of the diamagnetic and M u signals i n ice are i n Figure 6. The initial amplitudes of the two signals lead to values of P and P , and the results are plotted as a function of temperature i n Figures 7 and 8 for H 0 and D 0 ices, respectively. The dashed lines drawn through the points are intended as guides only and are based on the more precise P values. The M u polarization, plotted as 1 - P , is scattered about the dotted lines, confirming the absence of a missing fraction over the whole ice temperature range. P and P are essentially constant between the melting point and 160 K , but below this temperature P seems to grow at the expense of P . Relaxation rates T M and T were also determined, assuming exponential decay kinetics. Values of T of approximately 0.12 χ 10 sec' were found for H 0 above 160 K , with an increase to 0.23 Χ 10 sec" at 98 K . Diamagnetic relaxation i n D 0 ice above 160 Κ was negli gible (

Positronium and Muonium Chemistry - ACS Publications - American

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