Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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150 Charged Particle and Photon Interactions with Matter

for the electron mobility measurements inradiation chemistry studies. Carbon disulde, CS

, has

a high electron afnity. Therefore, it was expected that the electron mobility in CS

should not be

high. In the initial experiments, a small mobility of electrons was obtained, as expected (Gee and

Freeman, 1989: 5399). However, very high Ps formation yields were obtained in CS

. The CS

con-

centration dependence on Ps formation was measured in many nonpolar liquids, as shown in Figure

7.12 (Jansen and Mogensen, 1977: 75). Ps formation was inhibited by the addition of a small amount

of CS

, as observed for many other electron scavengers. However, Ps formation enhancement was

observed at higher concentration. The only reasonable explanation for this phenomenon is the high

electron mobility at higher concentration of CS

. It was completely opposite of the results obtained

by the electron mobility measurement; it was then measured again, and high electron mobility was

nally

obtained (Gee and Freeman, 1989: 5399).

7.6.3 electron therMalization in water

Jonah tried to investigate the electron thermalization in water by pulse radiolysis experiments (Jonah

and Chernovitz, 1990: 935). The decay curves of the absorption of hydrated electrons in water were

measured as a function of the concentration of heavy water, as shown in Figure 7.13. The heavy

water concentration dependence of decay rates of hydrated electrons shows a linear relation with

the concentration of water with two Ds, as indicated in Figure 7.14. Therefore, it was mentioned that

O and HOD showed similar effects on the electron thermalization.

Ps formation is caused by free or quasi-free electrons, as mentioned in Section 7.6.1. Ps forma-

tion probability will increase with the decreasing distance of electron–positron pairs, because the

competitive phenomenon of Ps formation is the hydration in water. Therefore, Ps formation will be

capable of providing some information regarding the thermalization distance. Figure 7.15 shows

that Ps formation yields showed linear dependence on the concentration of D, and not on the water

0.2

0.5

–1

)

0.5 1 2

1/C

–1

)

5 10 20

Figure 7.11 Plot of 1/C

−1

) for the scavengers versus the Ps inhibition constant, k

−1

). (Reprinted

from

Duplatre, G. and Jonah, C.D., Radiat. Phys. Chem., 24(5/6), 557, 1985. With permission.)

Positron Annihilation in Radiation Chemistry 151

Intensity (%)

0.25 0.50

Volume fraction

TMS

Neopentane

Isooctane

n-Hexane

n-Tetradecane

0.75 1.0

Figure 7.12 Intensity, I

, of the long-lived component versus volume fraction of carbon disulde. (Reprinted

from Jansen, P. and Mogensen, O.E., Chem. Phys., 25, 75, 1977. With permission.)

1.0

0.9

Fraction of initial OD

0.8

0 1 2

Time (ns)

a, b

Figure 7.13 Decay of the hydrated electron at 600nm in different mixtures of H

O and D

O: (a) 100 mol%

O, (b) 60 mol% H

O, (c) 50mol% H

O, (d) 40mol% H

O, (e) 20 mol% H

O, and (f) 0mol% H

O. (Reproduced

from

Jonah, C.D. and Chernovitz, A.C., Can. J. Phys., 68, 935, 1990.)

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4

Fraction of water molecules with two Ds

Change in amount of decay

0.6 0.8

1.0

Figure 7.14 Change in the amount of decay at 3.4ns versus fraction of D

O molecules in the solution.

(Reprinted

from Jonah, C.D. and Chernovitz, A.C., Can. J. Phys., 68, 935, 1990. With

permission.)

152 Charged Particle and Photon Interactions with Matter

molecules with two Ds (Hirade, 1995: 675). This shows that the thermalization distance is larger

heavy water. However, it does not show that H

O and HOD have the same effect on the thermal-

ization distance. Crowell et al. indicated that the diffusion coefcients of reactive species in D

inuenced the reactions of the hydrated electrons, and that the electron thermalization distance in

O did not need to be greater than that in H

O (Crowell and Bartels, 1996: 17713). Further studies

are

needed to understand the thermalization of electrons in water.

7.6.4 electric field effect (blob Model of ps forMation)

The application of external electric elds can quench Ps formation, as shown in Figure 7.16 (Stepanov

et al., 2005: 054205). Stepanov explained the electric eld dependence on Ps formation using the

modied spur model, that is, the blob model. He introduced the distribution of excess electrons and

positrons in the terminal spur of the positron track, because the number of species in the terminal

spur is large. Probably, there are more than 20–30 excess electrons. He employed the method of

Debye screening of the positron in the terminal spur. He then divided these positrans into two

positron species. One of these is thermalized in the excess electron blob, and the other is out of that

blob, as indicated in Figure 7.17 (Stepanov et al., 2005: 054205). In the blob, there are many excess

0 20 40

Concentration of D (%)

o-Ps intensity (%)

60 80

100

Figure 7.15 D concentration dependence on o-Ps intensity.

Chlorinated polyethylene

–(CH

2–x

)–

x = 0

x = 0.031

x = 0.055

x = 0.096

x = 0.209

100% EVA

60% EVA

24% EVA

(b)

(a)

10 20 30 40

D (kV/cm)

50 60 70

Pure

polyethylene

(0% EVA)

10 20

D (kV/cm)

, %

30 40

Figure 7.16 o-Ps intensity versus electric eld in chlorinated polyethylene as indicated in (a) and polyethy-

lene (PE) and ethylene vinyl acetate copolymer (EVA) as indicated (b). Lines are ts obtained by the model

explained in the text. (Reprinted from Stepanov, S.V. et al., Phys. Rev. B, 72, 054205, 2005. With permission.)

Positron Annihilation in Radiation Chemistry 153

electrons and the external electric eld is not effective. Stepanov succeeded in explaining many

experimental results using the blob model, as shown in Figure 7.16 (Stepanov et al., 2005: 054205).

7.6.5 Slow ps forMation in SpurS (young-age broadening effectS)

A very interesting attempt has been made to clarify the Ps formation mechanism. The Stuttgart

group produced many experimental results with the use of AMOC. They showed that there exists

young-age broadening on S(t) in many materials (Stoll et al., 1995: 17). One example of S(t) without

the young-age broadening is shown as lled circles in Figure 7.18 (Komuro et al., 2007: 330). At

the positron age of zero, large S(t) appeared. It was caused by the p-Ps intrinsic annihilation. One

of the S(t) observed by the Stuttgart group is shown in Figure 7.19 (Stoll et al., 1995: 17). At very

young ages, smaller S(t) appeared. Smaller S(t) means that the energy distribution is broader. This

is the reason why it is called “young-age broadening.” They interpreted that young-age broadening

out

–

blob

Effective potential well for e

Figure 7.17 Spatial distribution of the positron density at the Ps formation stage in the presence of an exter-

nal electric eld, E. e

is the density of the positrons bounded within the blob and not perturbed by E. The

other part, e

out

, is biased by the eld. (Reprinted from Stepanov, S.V. et al., Phys. Rev. B, 72, 054205, 2005.)

0.6

0.55

0.5

0.45

0 0.5 1

Positron age t (ns)

S parameter

1.5 2 2.5 3

Figure 7.18 S(t) curves for a synthetic fused quartz. The solid lines were simulated by assuming that Ps is

formed at the time of positron injection. Open circles were measured under no electric elds, and lled circles

were measured under an electric eld of 48kV/cm. (Reprint from Komuro, Y. et al., Radiat. Phys. Chem., 76,

330,

2007. With permission.)

154 Charged Particle and Photon Interactions with Matter

was caused by the incompletely thermalized p-Ps (Stoll et al., 1995: 17). They also claimed that it is

possible to observe the process of Ps thermalization by young-age broadening. On the other hand,

Komuro interpreted that young-age broadening is caused by the slow Ps formation in the terminal

spur. For the electron–positron pair that acquires a larger initial distance after the thermalization,

formation time is slower. If there is slow Ps formation, the fraction of annihilation from the free

positron is large near the positron age of zero; therefore, young-age broadening appears. Komuro

applied a weak external electric eld to test the model. The young-age broadening, if caused by slow

Ps formation, will disappear because a weak external electric eld will affect the slow Ps forma-

tion. She used very pure fused quartz to observe the young-age broadening. The measured S(t) is

shown in Figure 7.18 (Komuro et al., 2007: 330). Open circles showed probably the rst young-age

broadening except for the results form the Stuttgart group. Although the effect was very small, the

external electric eld quenched the young-age broadening as the lled circles indicated (Komuro

al., 2007: 330).

The

slow Ps formation reactions were obtained for ionic liquids. The result for N,N,N-trimethyl-

N-propylammonium bis(triuoromethanesulfonyl)imide (TMPA-TFSI) is shown in Figure 7.20

(Hirade, 2009b: 232). The solid line indicates the S(t) curve assuming Ps formation at the positron

age of zero. The dashed line indicates the S(t) curve with an electron solvation time of about 30ps. It

is a clear indication of the long lifetime of free or quasi-free electrons in ionic liquids, as indicated

Katoh (Katoh et al., 2007: 4770).

7.6.6 ps forMation with trapped electronS

As explained in Section 7.5, the large and slow enhancements of Ps formation at low temperatures

are caused by the accumulation of long-lived shallowly localized electrons, such as trapped elec-

trons, by the irradiation of injected positrons. The most famous experimental result was observed

for branched polyethylene by Kindle, as shown in Figure 7.21, in 1987 (Kindle 1987: 707). As

explained in Section 7.5, some people believed that it was a special phenomenon for polymers.

However, the details of the mechanism of the slow enhancement of Ps formation were explained by

the accumulation of trapped electrons in 1998, and it was not a special phenomenon for polymers

(Hirade et al., 1998: 89; 2000: 465; Wang et al., 1998: 4654). Indeed the slow enhancement of Ps

formation in cyclohexane at low temperatures had been measured by Eldrup in 1980 (Eldrup et al.,

1980: 175). This was the rst experimental result that showed a slow Ps enhancement caused by the

accumulation of trapped electrons, as indicated in Figure 7.22 (Hirade, 2003: 375).

0.62

Fused quartz

0.60

0.58

0.56

0.54

0.52

0.50

0.48

0.0 0.5 1.0 1.5

Positron age (ns)

parameter

2.0 2.5 3.0 3.5 4.0

Figure 7.19 Annihilation γ-rays line-shape parameter, S

, measured at room temperature for fused quartz.

(Reprinted

from Stoll, H. et al., Appl. Surf. Sci., 85, 17, 1995. With permission.)

Positron Annihilation in Radiation Chemistry 155

0.54

0.53

0.52

0.51

0.5

0.49

0 0.5

Positron age (ns)

S(t)

1 1.5

Figure 7.20 S(t) curve for N,N,N-trimethyl-N-propylammonium TMPA-TFSI. Solid lines are obtained

by an assumption that Ps forms at the positron age = 0. Dashed lines are obtained by slow reactions in ionic

liquids.

(Reprinted from Hirade, T., Mater. Sci. Forum, 607, 232, 2009b. With permission.)

I (%)

–200 –150 –100 –50 0

T (°C)

Figure 7.21 The relative intensities obtained by fourth-component analysis as a function of temperature.

indicates the relative intensity of o-Ps. Open triangles were measured with faster cooling rates than open

circles. Filled circles were measured with xed temperatures. (Reproduced from Kindl, P. and Reiter, G.,

Phys. Status Soldii

(a), 104, 707, 1987. With permission.)

156 Charged Particle and Photon Interactions with Matter

Some experiments exhibited Ps formation by trapped electrons. At rst, the visible light effect

was used. In this case, the Ps formation was inhibited immediately, because the visible light

quenched the trapped electrons. This effect was tested by Hirade at rst, and subsequently many

other investigators obtained the same effect in many materials, as shown in Figure 7.23 (Hirade

etal.,

2000: 465). It is obtained by the use of

Co γ-irradiation.

–160 –140 –120 –100

Temperature (°C)

Intensity (%)

–80 –60 –40 –20 0

Figure 7.22 o-Ps intensity, I′

, as a function of temperature. The dotted line indicates the isothermal

measurement.

(Reproduced from Eldrup, M. et al., Faraday Discuss. Chem. Soc., 69, 175, 1980.)

0 5

Dose (kGy)

(%)

10 15

Figure 7.23 Absorbed dose dependence of the intensity of the longest-lifetime component, I

, in PE (■, in

darkness; □, under visible light) and PMMA6N (●, in darkness; ○, under visible light) at 77K. (Reprinted from

Hirade, T.

et al., Radiat. Phys. Chem., 58, 465, 2000. With permission.)

Positron Annihilation in Radiation Chemistry 157

The trapped electron density dependence of Ps formation enhancement was also measured by

Hirade, as shown in Figure 7.24 (Hirade et al., 2000: 465). A combination of EPR and PAL mea-

surements gives linear relations in polyethylene (PE) and polymethyl methacrylate (PMMA). This is

the only result of measuring the Ps formation enhancements caused by the irradiation of

Co γ-rays.

Ps formed by the spur process and that formed by trapped electrons could be separated by observ-

ing the formation time. The Ps formation by the spur process occurred within about 1ps, and that by

trapped electrons was delayed because positron diffusion was needed. p-Ps annihilation gives a nar-

rower distribution of the annihilation γ-ray, as explained in Section 7.4.2, and a fast annihilation life-

time of 125ps. The S(t) curve observed for PE at 20K is indicated in Figure 7.25 (Hirade et al., 2007:

3714). While a simple decrement of S(t) was observed for PE with no trapped electrons, the S(t) curve

of the Ps formation by trapped electrons showed increment at rst. This means that there exists the

0 1 2 3

Density (spins/g)/10

(a)

o-Ps intensity (%)

4 5 6

0 1 2

Density (spins/g)/10

(b)

o-Ps intensity (%)

Figure 7.24 Relation between trapped electron density and intensity of the longest-lifetime component,

, at 77 K, (a) in PE and (b) in PMMA6N. (Reprinted from Hirade, T., et al., Radiat. Phys. Chem., 58, 465,

2000. Withpermission.)

0.54

0.52

0.5

0.48

0.46

0.44

0 1

Positron age (ns)

S(t)

2 3 4

Figure 7.25 Positron age dependence of the S parameter. The open circles were measured in darkness,

and the lled circles were measured under visible light. Solid lines are obtained by the least square ts by

considering the positron localization. (From Hirade, T., Radiat. Phys. Chem., 76, 84, 2007. With permission.)

158 Charged Particle and Photon Interactions with Matter

delayed Ps formation by trapped electrons. The solid line in Figure 7.25 shows the tted curve taking

positron trapping into consideration. It is impossible to t the S(t) curve without positron trapping.

The competitive phenomenon of Ps formation with trapped electrons, that is, positron trapping, was

successfully observed and the positron trapping rate could be obtained (Hirade et al., 2007: 3714).

There are several methods for the detection of trapped electrons or anions formed at low temper-

atures. EPR, light absorption, and glow curve measurements are often applied in radiation chemis-

try, and now the positron annihilation method can be used. The binding energy of trapped electrons

is usually 0.5–3eV, and the Ps binding energy is 6.8eV in vacuum and probably 4–5eV in materials.

Therefore, just by placing a positron in the materials, Ps can form, by picking off the trapped elec-

trons. This means that positrons have two chances of Ps formation. The rst chance is given by the

spur reactions, and the positrons that escape from Ps formation by the spur process have the next

chance

of Ps formation with trapped electrons.

The

observation of trapped electrons by the positron methods yields some advantages. The

injected positrons induce irradiation and act as a probe. Continuous irradiation takes place during

measurement. Some interesting measurements are possible, for example, the measurement of the

apparent activation energies of local motions. The Arrhenius plots can give the apparent activation

energies, for which the isothermal decay rates should be measured at several temperatures. This

means that several samples should be prepared. However, the apparent activation energies can also

be obtained just by measuring PAL at several temperatures, because continuous irradiation exists

during measurements and the measured values are under the equilibrium condition of thermal decay

and formation that takes place through positron irradiation. The formation rate is constant; therefore,

Ps formation yields under the equilibrium condition at several temperatures can give the Arrhenius

plots, through which the apparent activation energies can be obtained (Hirade, 2003: 375).

The saturated density of trapped electrons in PE is much lower than that in PMMA, as shown in

Figure 7.24. However, Ps formation yields by the accumulation of trapped electrons are almost the

same for both of these (Hirade et al., 1998: 89). This means that the positron diffusion length in PE

larger than that in PMMA.

the other hand, the saturation of trapped electron density is controlled by the electron diffu-

sion length. A larger diffusion length gives larger probability of electron–cation recombination, and

so the saturated density becomes small. For example, a smaller diffusion length of electrons at lower

temperatures gives higher density, because the positron mobility in PE is lower at lower tempera-

tures (Brusa et al., 1995: 447). If the temperature dependence of diffusion lengths for electrons and

positrons

are similar, Ps formation yields will have very small temperature dependence.

interesting experiment was conducted. At a certain low temperature, PAL was measured

until the Ps formation yield saturated in a long-chain alkane. After a long time of saturation, the

temperature was elevated and measured. The density of trapped electrons was not changed imme-

diately, but the diffusion lengths of positrons and electrons had to be changed, as these are larger

at higher temperatures. The density saturated at lower temperature, and then Ps formed at higher

temperature. The Ps yields should be larger than the saturated value at that temperature. This phe-

nomenon

was successfully revealed by Zgardzinska (Zgardzinska et al., 2007: 309).

7.6.7 reactionS of o-ps with Spur SpecieS

The fourth-lifetime components in pure benzene (Consolati et al., 1991: 7739), the scintillator

NE104 (Consolati et al., 1992: 131), and a 1M solution of 2,5-diphenyloxazole (PPO) in toluene

(Consolati et al., 1992: 131) have been measured by Consolati et al., who showed that the fourth

component is quite possibly caused by a Ps state due to the use of three-gamma measurements.

The lifetime spectra of many liquids showed the fourth-lifetime components, as shown in Table 7.2

(Mogensen, 1995: 73). These fourth lifetimes are shorter than the longest lifetimes, and are caused

by the reactions of o-Ps and the spur species (Mogensen and Jacobsen, 1982: 223). The most

important reactions are those of oxidation of o-Ps by cation radicals. Mogensen proposed that

Positron Annihilation in Radiation Chemistry 159

electron scavengers should inhibit the fourth-lifetime component as the o-Ps component could be

inhibited. This effect was measured directly for CCl

/hexane mixtures, as indicated in Figure 7.26

(Hirade and Mogensen, 1993a: 249). The interesting feature of the inhibition of the fourth compo-

nent is that the inhibition parameter, β, is larger than 1. The inhibition of Ps formation is normally

described

by the expression (Levay and Mogensen, 1980: 131; Mogensen and Jacobsen, 1982: 223)

I C

( )

1 α

(7.2)

where

I(C)

(I(0)) is the intensity at concentration C(0)

α and β are tting parameters

The

Equation 7.2 was proposed by Levay and Mogensen (Levay and Mogensen, 1977) by applying

empirical expression using a adjustable parameter β. The parameter β for the inhibition of the fourth

component is 1.2. The β values for 59 different combinations of inhibitors and nonpolar liquids are

found to be β ≤ 1 in all cases (Mogensen, 1995: 122). The reason of this large β is that there exist

0.001 0.01

Concentration (M)

o-Ps intensity (%)

Short-lived o-Ps intensity (%)

0.1 1

Figure 7.26 Intensities of the two o-Ps components in the lifetime spectra versus CCl

concentration in

n-hexane. Open circles indicate the long-lifetime o-Ps, and open squares indicate the short-lifetime o-Ps. The

lines are given by Equation 7.1 with α, β equal to 24 M

−1

, 1.0, and 3.5M

−1

, 1.2, respectively. (Reprinted from

Hirade,

and

Mogensen, O.E., Chem. Phys., 170, 249, 1993a. With permission.)

table 7.2

results

of Four-

term

nalysis

of l

ifetime

pectra

for l

iquids

liquids I

(%) τ

(ns) I

(%) τ

(ns) I

(%) τ

(ns) I

(%) τ

(ns)

Hexane 15.2 0.127 39.8 0.410 6.0 1.7 39.0 4.18

2,2-Dimethylebutane 15.9 0.122 28.8 0.372 8.1 0.8 47.2 4.47

diethylether 15.6 0.155 49.4 0.410 8.4 2.1 26.6 4.60

3-Methylpentane 16.8 0.131 39.1 0.429 5.7 2.03 38.4 4.31

3-Methyloctane 14.9 0.132 41.7 0.407 4.5 1.70 38.9 3.87

2,2-Dimethylpentane 12.8 0.109 37.3 0.373 7.2 1.08 42.8 4.34

2,2-Dimethylhexane 13.6 0.122 46.4 0.430 4.2 1.96 35.8 4.14

Methanol 14.0 0.184 63.1 0.446 6.8 2.3 16.1 4.02

Source: Based on data from Mogensen, O.E., Positron Annihilation in Chemistry, Springer, Berlin,

Germany,

1995, 73.