Further studies of the spur process of positronium formation in mixtures of organic liquids

Chemical Physics 2.5 (1977j 75-86 0 North-Holland Publishing Company

FURTHER

STUDIES OF THE SPUR PROCESS OF POSITRONIUM

FORMATION

IN MIXTURES OF ORGANIC LIQUIDS

P. JANSEN

and O.E. MOGENSEN

Chemistry Department, Research Establishment Risd. Roskilde. Denmark Received 11 February

1977

To test some predictions of the spur model of positroninm (Ps) formation, positron lifetime studies were made of the following binary organic mixtures: (a) carbondisulphide mixtures with n-tetradecane, n-hexane, isooctane, neopentane, and tetramethylsilane (TMS): (b) neopentane mixtures with methanol, ethanol, cyclohexanol, and methylcyclohexane; (c) cis2-buteneltrans-2-butene, and benzene/ethanol. The results were in agreement with the model. A minimum in the Ps yield versus CSz concentration, explained as being caused by electron localization on CSa at low and delocaliiation on several CS2 molecules at higher CS2 concentration, depended on the electron work function Vo of the solvent. This minimum was pronounced (shallow or absent) at high (low) Vo- Salvation of electrons and positrons in alcohol clusters strongly influenced the Ps yield for the neapentane mixtures. The Ps yield was higher in cis- than in tram-2-butene. The Ps formation process in polar liquids is discussed. Experimental facts do not preclude that Ps is also formed by the encounter pair process of fully solvated particles in the positron spur.

1. Introduction

The electron, the positron, and the positronium (Ps) atom are the only light particles, which participate in the normal low energy processes of physics and chemistry. Because of their small masses, quantum mechanical phenomena, such as zero-point motion, tunnelling, and delocalization, are of great importance in the description of their behaviour. At present, the behaviour of the excess electron in nonpolar liquids is an important topic of research in radiation chemistry [ 1,2] _ The properties of the excess electron are strongly correlated to those of the two other light particles in liquids. III this work, which is part of a series of papers on Ps formation [3-g], we shall discuss some new results of Ps yield measurements in mixtures of organic liquids. In a liquid the longest lifetime 73 in a positron lifetime spectrum is ascribed to ortho-Ps pick-off annihilation [9] with the outer electrons of the molecules. The relative intensity 1, of the long lifetime component is i P, where P is the Ps yield (i.e. the probabi!ity of Ps formation), provided that Ps is not involved in chemical reactions before the annihilation [9].

The positron lifetime measurements of the Ps yield described in this work were performed to test some predictions of the spur model of Ps formation [3J, and to obtain new information on excess electron behaviour. In the spur model, Ps is assumed to be formed by a reaction between a positron and an excess electron in the terminal positron spur, which is the transient cluster of reactive species (positron, excess electrons, positive ions, etc.) formed when the positron loses the last of its kinetic energy. Ps formation must compete with electron-ion recombination, with any electron and positron reaction with the molecules of the liquids, and with electron and positron diffusion out of the spur. It is also infiuenced by electron or positron solvation and by other changes in the spur properties- Obviously, the spur process of Ps formation is qualitatively similar to the electron spur processes studied in radiation chemistry [lo-121. However, the positron spur, i.e. the terminal end of the positron track, differs from a typical electron spur in the details. A positron track is more dense (high LET [lo]) than a typical eiectron spur at positron energies below roughly 2 keV. On the other hand, the positron will probably slow down to thermal energies somewhat outside the center of its

76

P. Jansen, 0. E. MogensenjPs formation in mixtures of organic liquids

terminal spur, and hence, the positron spur might effectively (i.e. from a Ps formation point of view) be less dense than a so-called electron “short track” [iO] _ In this paper we shall not discuss the positron spur processes in detail. It is our opinion that the available knowledge about spur and track processes does not allow a very detailed discussion of the fast (see below) spur process of Ps formation. More detailed discussions of the spur model of Ps formation have been given in refs. [3,5,7,8] _It is our opinion that the spur model correctly describes the Ps formation process in condensed matter because of the good agreement between its predictions and experimental facts. Hence, we shall not discuss our results in terms of the older models, the Ore model and the hot Ps reaction model [9,13,14]. In a previous paper [4], Jansen et al. described studies on mixtures of carbondisulphide and n-hexane. An expected minimum was found in the Ps yield at roughly 5 vol.% CS,. It was explained in terms of electron trapping on CSa at low concentrations resulting in a reduction of the Ps yield, while at higher concentrations tunnelling between and delocalization on the CS2 molecules sets in, and the Ps yield increases again. In pure CS,, the Ps yield was higher than in n-hexane. In this paper we discuss Ps yield results for mixtures of CS2 and other nonpolar liquids. We found an expected strong dependence of the Ps yield minimum on the excess electron work function, PO [15-171, for these nonpolar liquids. In the last few years the excess electron behaviour in mixtures of polar and nonpolar liquids has been an important new topic of research in radiation chemistry [ 1,2]. In particular, studies have been made of excess electron solvation in alcohol clusters in hydrocarbons. As discussed in refs. [3,4], the solvation of excess electrons in the positron spur causes a strong decrease in the Ps formation. Such decrease was reported for water dioxane mixtures in ref. [IS] and for pyrrolidine nheptane mixtures in ref. [4J. We shah here discuss some new Ps yield results for methanol, ethanol, cyclohexanol, and methylcyclohexane mixtures with neopentane and for ethanol benzene mixtures. The results will be correlated to recent radiation chemistry data. We shall also describe Ps yield results for mixtures of cis-Zbutene and trans-Zbutene. Besides testing the spur model of Ps formation, the new Ps yield data can be used to predict new radiation chemistry results.

In section 2 the experimental methods are described and the results are presented. A detailed discussion of the results in terms of the spur model and accepted ideas of radiation chemistry is found in section 3, which also gives a brief discussion of the Ps formation in polar liquids. Some concluding remarks and recommendations for new experiments are given in section4.

2. Experiments and results The positron lifetime spectra were measured by means of a conventional fast-slow coincidence system [7,9]. 22Na was used as the positron source. Hence, the positron lifetime was measured by determining the time interval between the detection of a 1.28 MeV photon, that is emitted simultaneously with the emission of a positron; and the detection of a 0.511 MeV annihilation photon [9]. Normally the positron source consisted of 22NaCl between two 7.5 p (1 .l mg/cm2) Capton foils. The lifetime spectrum of the positrons annihilating in the foils [8.5% of the positrons, which gave a curve with lifetimes (relative intensities) 0.39 1 ns (99.6%) and 4.03 ns (O-4%)] was subtracted from the measured spectra before the final analysis. In a few cases (CS2 in hexane and cis- and trans-2-butene mixtures), “zNaC1 between two Ni foils of about 3.7 mg/cm* was used as positron source. In this case, the source correction was roughly 20% [a curve with lifetimes (relative intensities) 0.2 ns (95%) and 2 ns (S%)] _ The prompt curve, fitted by a sum of several gaussians, had a full width at half maximum (fwhm) of roughly 0.39 ns. The lifetime spectra were analyzed by means of POSITRONFIT EXTENDED [ 191 for three lifetimes and intensities. AI1liquids were puriss, p.a. and spectrocgrade. They were used without further purification. All samples were degassed using the freeze-thaw method and afterwards destilled in vacuum into an ampoule containing the positron source. During the recording of the spectra the sample and source were kept io this airtight arnpoule. In table 1 are shown the long lifetime 7s and its relative intensity, I,, in the lifetime spectra for 19 pure liquids. The shortest lifetimes, the middle lifetimes, and their respective relative Intensities are not presented. When three or more lifetimes are present in the spectrum, it is, in our experience, often difficult to get reliable absolute values for the two shortest lifetimes and

P. Jansen, O.E. MogensenfPs fortmtion in midrues of organic iiquids

77

Table 1 Excess electron properties and ortho-Ps parameters for 19 liquids. References: b, secondary electron range (spur size constatlt) [20,21]; p. excess electron mobility [ 17,201; Vo. excess electron work function [IS-171; I,, long lifetime intensity [our work]; 73, long lifetime [OUTwork];& long lifetime intensity 1221., T>, long lifetime [22]. The uncertainties in I, are roughly *0.7% and in 73 roughly r0.05 ns Liquid tetramethylsilane neopentane isooctane cis-butene-2

b (A) (TMS)

_ 21.5 95 74

P

(cmWs.)

v, W)

I;

6)

(ns)

7;

-0.5 1

55

4.75

-

-

-0.35 -0.24 -0.16

52.5 43.5 49

5.15 4.15 4.31

43.8 36.4 -

5.03 4.00 -

42 31 41 41 40 38 36 41 41 45 28 21 22 26 44.5

3.17 3.29 4.25 3.95 3.85 3.43 3.35 3.50 2.91 4.58

35.8 30.5 34.4 35.2 35.3 31.1 29.6 32.6 -

3.10 3.20 4.12 3.94 3.70 3.29 3.24 3.38 -

1.85 3.58 3.50 2.85 2.20

20.3 19.0 20.9 21.2 40.0

2.07 3.94 3.81 2.73 2.08

(-30°C)

53 18 a) 20 a) 22a) -

0.0018 0.0006 0.0003 -_

hydrated solvated sohated solvated -

water methariol ethanol cyclohexanol carbondisulphide

73 m

90

0.029

42 61 70 70 -

(%I

63 7 2.2

-0.14 0.0 1 0.0 1 0.02 0.21 0.08 -

benzene cyclohexane n-pentane n-hexane n-heptane ndodecane n-tetradecane methylcyclohexane decalin tram-butene-2

I3

0.6,O.l 0.35, 0.45 0.14 0.09

a) The b-values for the polar liquids seem to be uncertain; 2-3 times larger values have been used in theoretical

spur diffusion

models [12]. their intensities. In most cases the analyses gave short lifetimes of 100-200 ps and middle lifetimes of 420-500 ps. In all measurements the intensity of the short lifetime was above l/3 of that of the longest lifetime. This fact strongly suggests that the normally used interpretation [9] stating that the shortest lifetime represents p-Ps, the middle lifetime represents free positrons, is not applicable. Hence, although we used the same quality of measurements and computer analyses as is normally used in metal defect work, we were unable to separate three decaying exponentials in a way that allowed an unambiguous interpretation of the shorter lifetimes_ In another work [7] it was shown that fairly reliable, but still rather uncertzin, values of the fitting parameters could be obtained for water in three-term fits, in which the middle lifetime was fared to be equal to the measured free positron lifetime. However, for nearly ail the liquids studied here, no reliable free positron lifetimes are available. On the other hand, the long lifetime is much longer than the other two lifetimes in the liquids studied. Hence, the long lifetime and its intensity are well de-

fined. Since we found no Ps chemical reactions, I3 is the ortho-Ps contribution and, hence, the Ps formation probability, P, is given by P = z13_ In table 1 are also shown the long lifetime, T;, and its intensity, Z;, as determined by Gray et al. [X2] around 1967. The resolution of their lifetime system was roughly 0.9 ns and they used a two-term fit of the

lifetime spectra. Our ~~ values agree remarkably well with their long lifetimes. However, our intensities 1, are generally larger than their corresponding f3 values This correlates well with the fact that the long lifetime intensities found in the literature are much more uncertain than the corresponding long lifetimes. Long lifetime intensities published by other groups also indicate that the Gray et al. 1; values are in general too small.

The measured intensities, I,, of the longlived component in the lifetime spectra of the carbondisulphide mixtures with tetramethylsilane (TMS), neopentane (2,2-dimethylpropane), isooctane (2,2,4-trimethylpentane), rz-hexane, and Iz-tetradecane are shown in fig. 1. The minimum in intensity at roughly 5 vol.%,

P. Jamen, O.E. ~1ogetlsenfF~formation in mittures of organic liquids

NEOPENTANE 0 A

25

0

0

0.25 VOLUME

a

ISOOCTANE HEXANE n - TETRAOECANI

0.02 ODL 0.06 o.Og

0

VOLUME FRACTION

n -

0.50

0.75

1.0

FRACTION

Fig. 1. The intensity, fs, of the longlived component versus volume fraction of carbondisulphide in mixtures of carbondisulphide and various nonpolar liquids. TMS stands for tetramethslsilane. The curves are beat tits to the experimental points. The uncertainties are roughly f 0.7%.

found for the n-hexane case [41, is deeper in the ntetradecane, shallower in the isooctane and the neopentane, and absent in the TMS cases. A broad maximum of Z, is found for isooctane and neopentane at roughly 70 vol.% CSz. In figs. 2 and 3 are shown the intensity of the longlived component for various neopentane mixtures. The figures illustrate the correlation between the f, values and the initial yield of alcohol-solvated electrons reIative to that in pure alcohols as measured by Brandon and Firestone [23] - The methylcyclohexane and cyclohexanol data in fig. 3 show the difference between a mixture of two hydrocarbons and a hydrocarbon-alcohol mixture, where the molecules added to neopentane have roughly the same shape. In figs. 4 and 5 are shown the long lifetime, r3, versus concentration for eight mixtures. We note the almost linear lifetime dependence on the concentration. We have also determined the long lifetime and its intensity in benzene ethanol mixtures at benzene con-

0.1

OB

ALCOHOL

Fig. 2. The intensity, Ia, of the longlived component and the relative initial yield of alcohol-solvated electrons [ 231 versus the volume fraction of alcohol in mixtures of methanol and ethanol in neopentane. The curves are best fits to the experimental points. The uncertainties are roughly 50.7%.

t_L 0

0.1 0.2 0.3 0.L VOLUME FRACTION

1

.

I

08

Fig. 3. The intensity, 13, of the longlived component versus the concentration of cyclohexanol and methylcyclohexane in their mixtures with neopentane. The relative initial yield of cyclohexanol solvated electrons versus the volume fraction of cyclohexanol in the cyclohexanol neopentane mixture [23]. The curves are best -fits to the experimental points. The uncertainties are roughly 50.7%.

79

P. Jansen. O.E. Mogensen/pS formation in mixtures of organic liquids

5.0

CARBONDlSULF’HlOE

MIXTURES

NEOPENTANE

5.0

MIXTURES

1.5 4.5

z i%

LO

c

3 51 c w 3.5 z

w

z

la.0

2 -1

3.5

k 3 3.0

3.0

t

2.5

0.0

0.2

0.L VOLUME

2.0 -

0.0

02

a.& VOLUME

0.6

0.6

10

FRACTION

lifetime.~3, versusthe carbondisulphide volume fraction in the carbondisulphidemixtures with various nonpolar liquids. TMS stands for tetramethylsilane.The curves are best tits to the experimentalpoints. The uncertainties are roughlykO.05 ns. Pig. 4. The long

centrations below 50 vol.%. The long lifetime, r3 = was roughly independent of the mixing ratio, while the intensity decreased slightly from 22% in pure ethanol to roughly 20% at 50 vol.% benzene. The long lifetime intensity in mixtures of cis-2butene and tram-2-butene decreased roughly linearily with the volume fraction of tram-2-butene from 49% in pure cis- to 45% in pure tram-2-butene. The long lifetime increased linearily with the volume fraction of trans-2-butene from 4.3 1 ns in pure cis- to 4.58 ns in pure tram-Zbutene. The uncertainties of the presented results are well illustrated by the case where several independent determinations of roughly the same points are shown in the figures, and by the generally good agreement between our lifetimes and those of Gray et al. [22]. We estimate the uncertainty in the intensity to be 20.7% (absolute %, i.e. in the units shown in the figs. l-3), while the lifetime uncertainty is estimated to be roughly iO.05 ns. 3.5 ns,

0.6

0.8

1.0

FRACTION

pig. 5. The long lifetime,~3, versusthe volume fraction of addedliquids in the neopentane mixtures. The curves are best fits to the experimental to.05 ns. 3.

points. The uncertainties

are roughly

Discussion

Since the primary purpose of this work was to look for several specific effects in the Ps yield to test the spur model of Ps formation, we shall in this section first discuss the Ps yield results and the correlation to radiation chemistry. As mentioned in the introduction, the discussion of the spur processes responsible for Ps formation is necessarily rather qualitative, as the present fairly low ievel of understanding of the fast spur processes does not allow a detailed discussion. The lifetime results are discussed at the end of the section. Table 1 shows the intensity of the longlived component in the lifetime spectra, 13, and three important radiation chemistry quantities: b, the secondary electron range (spur size constant) [20,2 11; p, the excess . electron mobility [17,20]; and PO, the excess electron work function [15-l 71. Because we found no Psquenching in any of the investigated liquids or mixtures, the 13-value is the relative intensity of ortho-Ps formation for all systems. 6, p, and PO have been shown to be mutually correlated, in particular b and p [21]. Table 1 shows clearly that I3 is correlated to b, p, and Vo. In particular, 13 and gare strongly corre-

80

P. Jansen, O.E. MogensenjPs fornation in miknues of organic liquids

lated; a larger /.zcorresponds to a larger Qalue except in a few cases. This correlation seems to be genershy applicable to other systems too: for example, to mixtures of liquids, i.e., other things being equal (see below) 13 increases with increasing p. This 13-~ correlation is mainly empirical and we have no obvious explanation for it. In ref. [3] the idea was discussed that this correlation could be partly explained by the reasonable assumption that the positron mobility is also higher in liquids with higher p-values, which, of course, would make the Ps formation process more competitive in relation to the other spur processes. The recently measured anti-inhibition effect [24] seems to indicate that the positron diffusion constant, and hence its mobility, is indeed much larger than that of normal heavier reactants in benzene and hexane. However, the results of CS2 mixtures discussed below probably cannot be explained in terms of a high positron mobility. They seem to be mainly influenced by changes in the electron properties only. Measurements in the mixtures of cis-2-butene and tram-?_-butene were made in order to study the correlation between I; and ,u. The fact that the mobility in cis-2-butene is much greater than that in trans-2-butene does not seem to have been explained yet [20] _We found roughly the 13-values for the two liquids, as we expected from the correlation to the ~-value. Because Is was found to vary linearly with the volume fraction in the mixtures we expect roughly similar behaviour for the (2s yet unmeasured) electron mobility in the mixtures. The fairly low 13-value for cyclohexane compared to the linear hydrocarbon I;-values might be the result of the very high hole mobility found in cyclohexane [25]. The higher hole mobility means, all other things being equal, that the electron-hole recombination. process is better able to compete with the electronpositron reaction, i.e. a lower Ps yield is expected. Since the electron (positron) mobility is not the only factor influencing the Ps yield, a detailed f3-p correlation is only expected for liquids which molecules have roughly the same properties (e.g. linear hydrocarbons) as Dodelet et al. [21] found for the correlation between y and b. The Ps yield measurements on CSZ mixtures with several nonpolar liquids is a continuation of the measurements of Jansen et al_ [4] _The purpose of the uresent work was to study the influence of the elec-

tron work function PO (see table 1) of the nonpolar liquids on the Ps yield in their CS2 mixtures. Let us fust discuss the CS, hexane mixture results. Apparently, CS, has an electron affiity of roughly 0.98 eV in vacuum [26]. This value may be rather uncertain. By means of pulse radiolysis, Simonsen [27] found that CS, traps electrons in n-hexane. The assumed CST ions (or perhaps C,S, ions) are correlated to an absorption band at 257 nm. This author was able to study this absorption only for CS, concentrations below 5 volp/o in hexane. These facts led us to propose the following explanation of the main features of the Ps yield results. At low CS, concentration, the trapping of electrons on CSZ in the positron spur causes a reduction in the Ps yield, not just because of the trapping itself, but also because of the associated strong decrease in the electron mobility_ Here we refer to the mainly empirical correlation between I, and p, discussed above. As the positron-electron binding energy is 6.8 eV, the positron can always pick off the electron from the CS, ion, where the electron binding energy may be roughly 1.7 eV (taking into account the polarisation energy of the CS, ion). The strength of Ps-inhibition at low CS, concentrations can be estimated in the hexane and tetradecane cases. We may assume that I3(c)/l3(0) = (1 + UC)-], where 13(c) [Is(O)] is the Is-value at a CS, concentration of c M [0 M]. This expression has been shown to fit well the measured Is-values in many cases [7,8] _The low concentration Is-value give u = 1.3 M-l for hexane and tetradecane, while u-values of 20-50 M-l are found for the typical strong Ps-inhibitors e.g. MnOi in water [7] and Ccl, in nonpolar liquids [S]). Hence, CS7 is a fairly weak Ps-inhibitor at low CS, concentration. As the CS7 concentration increases, the average distance between two neighbouring CS2 molecules decreases. At high enough [CS,] , the electrons on the CS, ion begin to tunnel to the nearest CS, molecules. At still higher CSZ concentrations the electrons may be delocalized over several CS, molecules. The degree of tunnelling and delocalization depends, of course, cn the motion of the solvent molecules. The potential seen by the electron is determined by the actual coordinates of the molecules of the liquid, and it changes. along with the changes in the molecular positions due to the thermal motion. The tunnelling and delocalization will increase the mobilities of the electrons trawed

P. Jansen, O.E. Mogensen/Ps formation in mixtures of organic liquids

on the CS2 molecules and hence, the Ps yield will increase too, as discussed above. In pure CS,, the electron is very probably delocalized in a conduction band, that is lower than in hexane. The electron mobility (as yet unmeasured) is probably higher than in hexane, and correspondingly we measure a high Ps yield in CS2. Sambrook and Freeman [28] found an unusual behaviour of CS, in free ion yield and electron range measurements. However, their results indicate that the electron range in CS, is larger than in hexane, which indicate that also the mobility is larger in CS? if use is made of the normal correlation between electron range and mobiiity [21]. The electron binding energy on CS2 in a liquid depends, of course, on the electron work function, Vo, of the liquid. A higher Vu means a stronger binding of the electron on CS2 and a reduction in the penetration of the electron wavefunction outside the CSZ molecule. Hence, an increase in Vn will decrease the degree of electron tunnelling between CS, molecules and the delocalization over several CS2 molecules at a given CS2 concentration. The electron mobility decreases, and we therefore expect a decrease in the Ps yield, all other things being equal. We searched for and found this expected Vu effect, as shown in fig. 1. Clearly, the 13-minimum is deeper in tetradecane (Vu = 0.2 1 eV) than in hexane (Vo = 0.02 eV), and it is much shallower in isooctane (Vo = -0.24 eV) and neopentane (Vo = -0.35 eV) than in hexane. In TMS (Vu = -0.51 eV) no IX-minimum is found. The Ps yield is very little influenced by the presence of CS2 in TMS. The CS, results are strongly correlated to the important, new “anti-inhibition” effect found by Anisimov and Molin [24]. These authors showed that the addition of small amounts of molecules, which bind the electrons weakly (e.g. C6F6, CS2, CO?, and naphtalene), strongly reduces the Ps-inhibition caused by the presence of the well known electron scavengers, Ccl, and C,H,I, in benzene and hexane. The following explanation was proposed [24] _The electron reaction with, for example Ccl,, results in the formation of the Cl- ion, from which the positron cannot pick off the electron (Cl- binds the positron [29]). At a high enough concentration of, for example, CS,, the excess electrons are trapped on CS2 instead of on CC&, and then the positron can pick-off the electron from CS$ and the Ps yield increases strongly again.

81

This explanation of the “anti-inhibition” effect indicates tha: the positron rate constant with CST is much larger than the rate constant of the Ccl, + CS, reaction. This seems, at present, to be the yet best experimental evidence of the expected [3], larger positron diffusion constant compared to the diffusion constant of normal reactants like CS, and CC14 in hydrocarbons. The electrons bound in shallow traps on molecules in nonpolar liquids have recently been studied by radiation chemists (biphenyl [30], CO, [3 I], and other molecules). The change from a mainly trapped electron at low trap concentration to a highly mobile dectron on the traps at high trap concentration is a well known phenomenon in semiconductor physics and in other systems (compare, e.g., to Li/NH, solutions). The CS2 results presented here differ from most other similar results, because in our case mainly one (or perhaps a few) electrons are trapped on the CS-, molecules in a positron spur. The change in the electron mobility on the traps is not due to a many-electron cooperative effect (as e.g., in a Mott transition). To summarize, the Ps yield results for the CS, mixtures with various nonpolar liquids is well accounted for by the above, mainly qualitative, explanation based on the spur model of Ps formation. Several other independent studies of similar phenomena speak in favour of the given explanation. It must be emphasized that our interpretation describes the most important cause of the change in the Ps yields. Of course, secondary effects, such as changes in the spur yields and in spur size, may also somewhat influence the Ps yields. In the previous work [4] the Ps yield in pyrrolidine n-heptane mixtures was determined_ A strong decrease in the Ps yield at roughly 5 vol.% pyrrolidine was ascribed to the-onset electron and positron trapping in hydrogen bondedpyrrolidine clusters, which presumably are only formed at pyrrolidine concentrations above roughly 5 vol.%. A similar strong decrease in the Ps yield in water dioxane mixtures measured by others [18] has been interpreted [3] in terms of trapping in hydrogen-bonded water clusters. We determined the Ps yield in the aLcoho1 neopentane mixtures to study this cluster effect in more detail. Recently Brandon and Firestone [23] studied several alcohol alkane mixtures by pulse radiolysis. They determined the initial yield of alcohol solvated electrons relative to that in the pure alcohols from the solvated electron absorption spectrum, as shown in

of

82

P. Jansen, 0-E. MogensenjPs formation in mixiures of organic liquids

figs. 2 and 3 for neopentane mixtures of methanol, ethanol, and cyclohexanol. Clearly, the solvated eIectrons are present only at alcohol concentrations above a certain minimum concentration. This was interpreted [23] as caused-by electron trapping in alcohol clusters, which only form above rhis minimum concentration. In the case of methanoi we found (fig. 2), as we had expected, that the Ps yield decreased strongly at roughly the same concentrations, at which the soIvated electron appeared. This is interpreted as caused by the effect of electron and positron trapping in the alcohol clusters. We shall below discuss in detail why the trapping decreases the Ps yield. In the ethanol and cyclohexanol cases the Ps yield starts to decrease at a lower alcohol concentration than that at which the solvated electron absorption appears. We interpret this extra (i.e., apart from the decrease due to particle trapping in clusters) decrease in the Ps yield as caused by the reduction in the excess electron mobility as a result of the presence of the alcohol molecules. As mentioned above, a decrease in electron mobility corresponds to a decrease in the Ps yield; roughly speaking a decrease in p by a factor of ten corresponds to a Z-3% (absolute) reduction in 1, (see table I). Apparently, electron mobility has not been measured for our neopentane mixtures. However, Baxendale and Sharpe [32] recently presented mobility results for several alcohol aikane mixtures. n-propanol in nhcxane. cyclohexane, and isooctane caused an appreciable decrease in n at concentrations that were low compared to the concentration at which the solvated electron appears in neopentane. On the other hand, in the methanol isooctane mixtures, p was roughly constant at methanol concentrations below 0.04 M (=0.005 vol. fr.), while it decreased from fi = 7 cm2 Y-f 5-l at 0.04 M to 0.3 cm2 Y-l s-l at 0.06 M. Hence, Baxendale and Sharpe found that the influence of the addition of methanol on electron mobility was quite different from that of propanol addition. This behaviour might be correlated to the difference between the influence on the 13-value of adding methanol and ethanol in our case. By use of the measured decrease in f, we can roughly estimate an expected decrease in ccto be a factor of IO (103) in the ethanol (cyclohexanol) case at the concentrations at which the solvated electron appears. Because ,u is very high for neopentane, these decreases in Mare roughly in agreement with what is expected from the general variation

of & from one liquid to another (see table 1). We also measured the Ps yield in methylcyclohexane neopentane mixtures at low methylcyclohexane concentration to study the influence of the addition of a nonpolar molecule of roughly the same shape as cyclohexanol. As shown in fig. 3, methylcyclohexane causes a much smaller decrease in I3 than cyclohexanol. We expect the decrease in p to be correspondingly smaller in the methylcyclohexane case. As the results presented in figs. 2 and 3 are in agreement with the predictions of the spur model of Ps formation, they constitute an important test of thismodel. It must be emphasized that particle trapping in alcohol clusters (and the influence of electron mobility in the ethanol and cyclohexanol cases) is the primary cause of the decrease in Ps yield in our interpretation. Of course, secondary effects may give additional small effects in the Ps yield (e.g. changes in the spur yields and spur size). It must also be realized that the decrease in the Ps yield is not expected to occur at exactly the alcohol concentration at which the solvated electron yield increases, because the yields measured by Brandon and Firestone refer to nanosecond times while Ps is mainly formed in picosecond times (see also the discussion of polar liquids below). As seen in fig. 2, the Ps yield decreases at a somewhat higher methanol concentration than that at which the solvated electron yield starts to increase. In ref. [4] it was found that proton scavenging in the positron spur increased the Ps yield at low pyrrolidine concentrations. It could be imagined that the reason for the absence of an increase in Ps yield in this work - although we expect proton scavenging by the alcohols to take place - might be that the effect of proton scavenging is balanced by the decrease in Ps yield due to a simultaneous electron mobility decrease, which is much larger in neopentane than in the previously used heptane. Benzene added to alcohols is known to reduce the initial yield of solvated electrons as measured by Ogura and Hamil [33] _We therefore measured the Ps yield in benzene ethanol mixtures for benzene concentrations below 50 vol.%. We found a very small decrease in 1, from 22% in pure ethanol to 20.5% in the 50 vol.% mixture, while the r3-value was independent of the benzene concentration. These I3 results may be explained by referring to a probably weakly bound electron on the benzene molecule in ethanol. The efficiency of the Ps formation process seems not to be

P. Junsetz, O.E. MogensezzlPsfornzution in mirtures of organic liquids

much influenced by the electron trapping in very shallow traps, as illustrated by the CS2-neopentane and CSZ-TMS mixture results discussed above. We shall now discuss the Ps formation process in polar liquids in mare detail. Such a discussion is ap propriate here not just because of our own results, but also because of (a) some uncertainties in the interpretation of Ps yield results for polar liquids found in recent papers, and (b) new developments in radiation chemistry. Since the problems involved are very complicated, we certainly cannot give a very detailed discussion here. Experimental facts [7] indicate that Ps is mainly formed within a period of time that is short compared to the paraPs lifetime of roughly 120 ps in water. The spur reactions of the hydrated electron take about 10 ns in water [ 121. Hence, the Ps formation process is an early (or fast) process to use radiation chemistry terminology. Apparently, this is the case in other polar liquids too. The above mentioned uncertainties in the interpretation of some recent Ps yield results concern the following question: which process(es), out of several possible early (or fast) processes, is (are) responsible for Ps formation? In particular, Byakov and collaborators claim that only the dry (see below) particles form Ps [34]. We (i.e. the Risg group and collaborators) have also stated [7,35] that Ps is probably mainly formed by presolvated particles. In view of recent developments in radiation chemistry, these statements need to be reconsidered. Let us discuss the case of water as an example. By a mode-locked laser technique, Rentzepis et al. [36] found an infrared absorption of electrons in water roughly l-2 ps after the creation of the electron. This absorption deveIoped into the normal hydrated electron (e&) absorption band within 4 ps. Apart from this study, no direct information is available on the electron states in water in times 530 ps after the creation of the electron. The limited knowledge available about the early states of the electron and the early reactions between the electron and other radiation products in the spur, is nearly always deduced from experimental facts obtained after 30-100 ps,or from steady state scavenging experiments. Many models for the early electron processes may explain the available experimental facts; and many electron states have been used in the models (e.g. subexcitation, eib; hot or epithermal, e;; thermal, e;; quasi-free, es; mobile,

83

e,; damp, ed; dry, e&; and hydrated, e: ). A recent review article by Hunt [12] (see also ref.“I-37)) and a glossary of radiation chemistry terminology [2] may help to clarify the uncertainties in concepts, models, and definitions found in the literature. Hunt [l>] discusses in detail several models of the early or fast electron processes in polar liquids. He states: “Most of these modeIs have aspects that esplain some of the results, but each has clear limitations and present difficulties when an attempt is made to fit it to the totality of the observations”. This important statement applies just as well to the Ps yield results available. We refer to the article by Hunt 1121 for the discussions of the various models. Here we can only discuss some aspects of these models that are of importance for the Ps formation process. A light particle (positron or electron), which is slowed down in a polar liquid, could, in principle, attain the foliowing successive low energy states: (a) the epithermal, mainljr free state:(b) the thermal, mainly free state;(c) the state in which the particle is trapped (in e.g. preexisting traps) but not fully solvated, and (d) the final equilibrium, solvated state. The tern1 thermal particle is used here IooseIy to mean a particle with kinetic energy of the order of kT(see [ 11J for a detailed discussion of such particle states). The “dry” particle has been defined by some authors as a particlt in one of the first three states and as a particle in only the first two states by others (see fig_ 1 in [ 121). The different models discussed by Hunt refer to electron reactions in one or several of the four states. Ps formation is a fast process. As any particle in the first two (and partly in the third) states can react very rapidly, it is tempting to state that Ps fomiation takes place 0nIy as long as one of the particles (positron or electron) is in one of these states. and hardly ever if both particles are (trapped or) solvated. This is the hypothesis of dry (and only dry) particle Ps formation, which might be incorrect for the following reasons. The wavefcnction for an electron or positron in the trapped or the equilibrium, solvated state will penetrate outside the trap. Hence, it can react over fairly Iong distances by tunnehing and/or delocahzation effects just l
84

P. Jansen, O.E. MogensenfPs formation in mixtures of organic liquids

with iodide ions [39]. These distances are the effective reaction radii, that must be used to fit the theoretical, diffusion-controlled rate of reaction to the measured rates. In the Ps formation case, where both particles are light, fast reaction is expected to take place over fairly long distances (10-15 a). Czapski and Peled discussed the effect of encounter pair formation in the electron spurs [40]. h encounter pair is two reactants formed within a distance that is smaller than the reaction radius, and which therefore reacts within short times (= l-10 ps). The concentration of excess electrons in the positron spur depends, of course, on the fairly unknown parameters: the size of the spur (see table i) and the number of electrons per spur. It is reasonable to assume that the spur electron concentration is so high that the positron has a great probability of being trapped or solvated within a distance smaller than the reaction radius (= IO-15 a), and of forming Ps in a fast reaction (i.e. within X ICIps). Of course, the trapped, but not yet fully solvated particles may react rapidly over distances longer than the reaction radius of the fully solvated particles, because they are more weakly bound and hence their wavefunctions may penetrate far outside the trap. Experimental facts indicate that a trapped but yet unsolvated electron, which absorbs in the infrared, is present in alcohols and water at the earliest experimentally available times, and that it has a fairly long lifetime until full solvation [ 121. Clearly, a model in which an appreciable (or even the main) part of the Ps formation takes place by the encounter pair effect after both particles are solvated is not in disagreement with current experimental facts. Although we cannot clearly disprove any of the different early reaction models [12] of Ps formation in polar liquids, we shall here speculate a little about what processes seem to be most likely in our opinion. Since the trapped, butyet unsolvated electron state seems to have a fairly long lifetime, and since both the electron and positron are light particIes, we believe that the main part of Ps is formed after the particles have been trapped in the first shallow traps. An appreciable part may be formed from the fully solvated state, and the available experimental facts do not preetude that several percent of the Ps atoms are formed in times of the order of 100 ps. Theoretically, we expect that a small part of ‘he Ps formation takes place

as long as the free positron lives (e 400 ps). We wonder whether this process may be the reason why we have run into difficulties with high-quality three-lifetime fits of the lifetime spectrum for water. Maybe this lifetime spectrum does not consist of three exponentials only but is somewhat distorted because of a small percentage of slow Ps formation. (Of course, all lifetime spectra are also influenced by the finite reaction time of the early Ps formation processes_) We have reached the following conclusion conceming our alcohol neopentane mixture results. In pure neopentane, the electron and maybe also the positron are in the mainly free (delocalized) states, and Ps formation takes place in times comparable to the normal spur reaction times (probably l-10 ps). At sufficiently high alcohol concentrations, the particles get trapped chiefly in prefomled alcohol clusters. The explanation of the Ps yield decrease caused by this trapping is roughly similar to the above discussed for pure polar liquids. It is caused by (a) a reduction in the time in which the particles can react as free and/or partly trapped particles and/or (b) the fact that only electron-positron pairs within a distance smaller than roughly the reaction radius can react rapidly enough. Several early reaction models, including the encounter pair reaction from the fully solvated states, are in agreement with our results and with the experimental facts in general. We shall now shortly discuss the lifetime results for the eight mixtures shown in figs. 4 and 5. The long lifetime, r3, is due to ormoPs pick-off annihilation on the molecules of the mixtures. Hence, it is determined by the overlap of the positron in ortho-Ps with the outer electrons of the molecules. Experimental facts indicate that ortho-Ps is situated in a bubble in a liquid, i.e. Ps digs a hole in a liquid. The detailed structure of this bubble is not known. Several models of the pickoff annihilation rate, Xp, have been proposed. In the normally accepted model, it is assumed that the bubble is empty (except for Ps), and that the size of the bubble is mainly determined by a balance between the inward pressure due to the surface tension and the outward pressure due to the zero-point motion of Ps. This model has been discussed in detail by Tao [41], and it has been modified by Levay et al. [42]. The simple bubble model gives $, = rF1 = k~“, where y is the surface tension and k and v are constants. By use of an empirical correlation, Tao showed that b 0: 6, expect

P. Jansen, 0-E. Mogensen/Ps formation

for a weak dependence on the molar volume Pm. The solubility parameter 6 is given by s2 = (AH, - RT)/V,, the cohesive energy density. In the latest development of the Ps bubble model by Jensen [43] it was shown empirically that a Xn versus 6 plot gave a rather poor correlation. However , h correlates well (except for water) with 6,, the dispersion (van der Waal) part of 6. We shah not here discuss our lifetime results in detail in terms of these models, because we do not know y and the effective 6 D for our mixtures. It is surprising that the curves are nearly linear on figs. 4 and 5. Clearly, the long lifetime is fairly unaffected by the onset of alcohol clustering in the neopentane alcohol mixtures. Altogether, we do not have any obvious explanations of these !ifetime results in terms of the existing models discussed above. However, we have not made a more complete study of the data and the literature on solutions to find explanations.

4. Conclusion The Ps yield measurements discussed in this work were made in order to test specific predictions of the spur model of Ps formation. First, a correlation between the excess electron mobility and the Ps yield was shown to be valid for our new, more reliable Ps yields for pure liquids, including the interesting difference between the Ps yields for cis- and tram-Zbutene. Second, we studied a minimum in the Ps yield versus CS, concentration in CS, mixtures with nonpolar liquids. The depth of this mi&uum was shown to depend on the electron work function, Vu, for nonpolar liquids. At very low vu-values (-0.51 eV for TMS), no minimum was found, while a very deep minimum was found at high Vu values (0.21 eV for tetradecane). We interprete this minimum as caused by trapping of excess electrons in the positron spur on CS2 at rather low CS, concentrations, while tunnelling and delocalization of the electrons result in a higher electron mobility and therefore a greater Ps yield at high concentrations of CS,. Third, the studies of alcohol neopentane mixtures showed a strong decrease in the Ps yield at roughly the methanol concentration at which electron absorption appears in the methanol case. This was interpreted as caused by spur electron and/or positron trapping in

in mixtures of oeanic liquids

85

methanol clusters, which start to form at this concentration. In the ethanol and cyclohexanol cases the Ps yield decreases at concentrations lower than that at which the sohated electron absorption appears. The extra (i.e. apart from the decrease due to particle trapping) decrease was interpreted as caused by rhe reduction in electron mobility, and therefore the Ps yield, due to the presence of the polar molecules. The Ps formation process in polar liquids were discussed in some detail. It was argued that several models of the early electron reaction can explain the available Ps yields. In particular, also the encounter pair reaction of the positron and the electron from the full solvated states is in agreement with the experimental facts. Hence, it is premature to state that only dry particles form Ps. The results presented here are strong arguments in favour of the spur model of Ps formation, which is now fairly well established. Although further tests of the model are very useful, it might now be more fruitful to accept the model and use Ps yield measurements to study radiation chemistry problems. Ps yield measurements seem to be appreciably cheaper and faster than the related radiation chemistry (pulse radiolysis, steady state scavenging, electron mobility, etc.) measurements. We can propose many new experim*nts :c, test our interpretation of the results and to continue the studies. The mobility of the excess electron in the CS2 mixtures with the nonpolar liquids will probably show minima that correlate with the Ps yield roughly like the correlation between the Ps yield and the mobility found in pure liquids. Hence, we expect strong mobility minima in the tetradecane and hexane cases, and a weak or no minimum in the TMS case. The mobility for pure CS, is probably comparable to that of isooctane. Obviously, we also expect the absorption spectra of CS, to be strongly correlated to the Ps yield. As discussed in section 3, the Ps yield results for the neopentane alcohol mixtures might also be used for a qualitative prediction of electron mobility. Our Ps yield studies may be continued by a search for molecules (candidates are CO,, biphenyl, hexafluorobenzene, naphtalene, etc.), that may behave similar to CS, with respect to Ps formation. The results of such studies may be correlated to anti-inhibition results, similar to the results presented in [24], and to electron “attachment-detachment” studies in radiation chemistry [44].

86

P. Jamen, O.E. Mogensen/Ps formation in mixtures of organic

Hence, Ps yield studies might contiibute much to the of some of the basic problems in the more physical branches of radiation chemistry. solution

Acknowledgement The authors are grateful to &I.Eldrup, B. Skytte Jensen, and P. Pagsberg for many stimulating discussions. Also we wish to thank ST. Andersen, N.J. Pedersen, and P. Zeuthen for valuable technical assistance.

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[22] P.R. Gray, C.F. Cook and G.P. Sturm Jr., J. Chem. Phys. 48 (1968) 1145. [23j J.R. Brandon and R.F. Firestone, J. Phys. Chem. 78 (1974) 792. [24] O.A. Anisimov and Yu.N. Molin, Khim. Vys. Energ. 9 (1975) 539 [English translation: High Energy Chem. 9 (1976) 4711. Preprint C31, IV. International Conference on Positron Annihilation, Helsingar. 1976. 1251 J.M. Warman, P.P. Infelta, P. De Haas and A. Hummel, Chem. Phys. Letters43 (1976) 321. [26] K. Kraus, W. Muller-Duysing and H. Neuert, 2. Naturforsch. 16a (1961) 1385. [27] P. Simonsen, private information. [28] T.E. Sambrook and G.R. Freeman, Can. I. Chem. 53 (1975) 2822. [29] O.E. Mogensen and VP. Shantarovich, Chem. Phys. 6 (1974) 100. [30] J.M. Warman, M.P. De Haas, E. Zador and A. Hummel, Chem. Phys. 35 (1975) 383. [31] R.A. Hohoyd, T.E. Gangwer and A.O. Allen,Chem. Phys. Letters 31 (1975) 520. [32] J.H. Baxendaie and P.H.G. Sharpe, Chem. Phys. Letters 41 (1976) 440; J.H. Baxendale, private information. [33] H. Ogura and W.H. HamiU, J. Phys. Chem. 78 (1974) 504. 1341 V.M. Byakov, V.I. Gohianskli and V.P. Shantarovich, Dokl. Acad. Nauk. SSSR 219 (1974) 633 [English translat.: Dokl. Phys. Chem. 219 (1975) 10901; V.M. ByakoviV.1. Grafutin and O.V. Koldaeva, ITEP-36 (1976); V.M. Byakov, V.I. Grafutin, 0-V. Koldaeva, E-V. Minaichev, F.G. Nichiporov, Yu.V. Obykhov and O.P. Stepanova, ITEP-62 (1976); V.L. Bugaenkov, V.M. Byakov, V.I. Grafutiu, 0.V. Koldaeva and E.V. Minaichev, ITEP-154 (1976).

[35] 0-E. Mogensen, preprint RlO, IV. International Conference on Positron Annihilation, Helsingfir, 1976. [36] P.M. Rentzepis, R.P. Jones and J. Jortner, J. Chem. Phys. 59 (1973) 766. [37] K.Y. Lam and J.W. Hunt, Intern. J. Radiat. Phys. Chem. 7 (1975) 317. [38] C.D. Jonah, J.R. MiiIer, E.J. Hart and M.S. Matheson, 5. Phys. Chem. 79 (1975) 2705. [39] O.E. Mogensen and P. Jansen, preprint Gl5, IV. Internationai Conference on Positron Annihilation, Helsingdr, 1976. [40] G. Czapski and E. Peled, J. Phys. Chem. 77 (1973) 893. [41] S.J. Tao, J. Chem. Phys. 56 (1972) 5499. (421 B. Levay, A. Vertes and P. Hautojaxvi. J. Phys. Chem. 77 (1973) 2229. 1431 B. Skytte Jensen, preprint G16, IV. InternationalConferehce on Positron Annihilation, Helsingbr, 1976. [44] R.A. Holroyd, Ber. Bunsen-Gesellschaft 81(1977) 298.