Chemical Physics 48 (1980) 97-104 Q North-Holland Publishing Company
ENHANCEMENT OF POSITRONIUM FORMATION IN SdME NONPOLAR CAUSED BY SCAVENGING OF THE HIGHLY MOBILE POSITIVE HOLES B. L&VAY’
S.J_G. LUND* and 0-E. MOGENSEN**
Chemistry** and Electronicsf DK-4000 Roskilde. Denmark Received 9 November
Positronium
LIQUIDS
Department,
Rise iVati&aI Laborutory,
1979
yields as a function of pyridine concentration
were studied in nine nonpolar solvents. Strong (c 0.3 M) of the positive hole scavenger pyridine were found in those liquids where the hole moves rapidiy (ie. partly delocalized), but not in those where the hole moves slowly. Pyridine acts also as a very weak Ps inhibitor in all systems investigated if its concentration exceeds a certain limit (ZZ0.3 M). The results can be well interpreted within the framework of the spur reaction model of Ps formation
enhancementsin the Ps yields on addition of low concentrations
1. Introduction
During the last few years in the field of positronium (Ps) chemistry the characteristics of the process of Ps formation in liquids have been more and more thoroughly studied [I]. In particular, the correlations between the Ps formation probabilities and the properties of the radiation spurs studied in radiation chemistry, as predicted in the spur model of Ps formation [z], have been studied in some detail. According to the spur model, Ps is formed by a reaction between a mainly thermahzed positron and one of the excess electrons in the terminal positron spur. The Ps formation process competes with other spur reactions, such as electron ion recombination, electron and positron out-diffusion, and electron or positron reactions with sokent molecules or added species. The effect of added species on the Ps yield in a liquid depends on their reactivity towards the components of the t&m&l positron spur, i.e. the’ different reactive intermediates (the positron, electrons, positive ions, radicals, etc.) created by the positron when it Ioses the last amount of its kinetic energy_ * On leave from Departmentof Physical Chemistryand Radiology, E&v& Universityof Budapest,Budapest, Hungary.
The scavenging of an excess electron (or the positron) in the positron spur results in a simple, clear case of inhibition of the Ps formation if the scavenged electron (positron) cannot form Ps in a secondary reaction. In such cases (e.g. Ccl, in hydrocarbons [3] and MnO; in water [4]), the Ps yield can be reduced to half its initial value at a scavenger concentration of 0.01-0.1 M. As the _ positive ions also react with the spur electrons in competition wit@ the positron, an enhancement of the Ps yield is expected on the addition of positive ion scavengers, if the reactivity towards the electron of the product of the scavenging is smaller than that of the unscavenged positive ion. This interpretation was first used by. Jansen et at [S] for explaining the increased Ps yield due to the addition of dioxane, triethylamine or pyrrolidine to n-heptane. Enhancement of the Ps yield on the addition of ammonia to water.was measured [6] before the spur model was proposed, and more recently enhanced Ps formation was observed on the addition of NaOH to water [7]_ Inhibition followed by enhancement of Ps yields probably due to positive hole scavengin& was lately observed _jn aqueous solutions of halides, sulfide and thiocianate [8]_ In all of the above cases thti enhancement of Ps formation o&u+ at fairly high 65oncentrations of .-
98
B. L&ray er al./Ps formation
the positive ion scavengers ( 1 03 M), which probably can be accounted for by reference to the very low mobiIity of the massive moIecuIar ions and of other massive species (e-g_ OH and H30 + in water) reacting with spur electrons_ Recently enhancement in the Ps yield on the addition of a somewhat lower concentration of alcohols to hydrocarbons was reported [9]_ Extremely mobile positive ions (hoIes) were IateIy discovered in certain irradiated liquid hydrocarbons by the radiation chemistry group in Delft [IO-141. According to the spur model the.presence of rapidiy moving holes should affect the Ps formation process. The relatively low Ps yield in cyclohe*dne for instance, was explained by this way [IS]_ The abrupt enhancement of the Ps yield due to the addition of small amounts of pyridine to cyciohexdne [16] was also tenratively accounted for by considering the existence and scavenging of highly mobile positive holes in this liquid [17]_ The main aim of the present work is to carry out systematic experiments on the positive ion scveng ing by pyridine in nonpolar liquids with special regard to those containing extremely mobiIe holes.
in nonpolar liquids
recording of the spectra the sample and source were kept in that airtight ampouleThe different amine type compounds (e.g., ammonia, dimethylaniline etc.) seem to be among the best known positive ion scavengers in nonpolar liquids (see e.g. ref. [12]). We have used pyridine for this purpose, because it has some advantages_ Pyridine is available in high quaIity and is easy to handIe when preparing soIutions. Furthermore, it is expected to be not only a strong positive ion ScdVen$r, but a fairly weak electron scavenger as well. Its rate constant with hydrated electrons is about IO9 M-‘s-’ [19]; hence it might be suitable for studying the kinetics of the combined ion and electron scdvenging-
3. Results Positron lifetime spectra have been recordedafter successive additions of increasing amounts of pyridine to different nonpolar solvents_ In all cases the O-l.2 M concentration range has been studied in detail, but the measurements have normally covered the whole concentration range. The following nine systems have been investigated: n-hexane.
Z Experimental The measurements were carried out with a conventional lifetime spectrometer. including digital stabilization of the spectrum peak position. The time resolution was roughly ChaIXCteriZed by its full width of half maximum being less than 400 ps. The positron source consisted of about 40 FCi Na”CI deposited between two thin (1.1 m&m’) Kapton foils. The lifetime spectrum of the positrons annihilating in the foils (85 %) was subtracted from the measured spectra before the final analysis. The spectra were anal_yzed by means of the POSITRONFIT EXTENDED computer program [IS] for three lifetimes and intensities_ The prompt curve was fitted by a sum of :hree gaussians by use of the newly developed RESOLUTION program. All the liquids were puriss, p-a. or spectroscopic grade and were used without further puriIication_ The wmples were degassed using the freeze-thaw method and afterwards distilled in vacuum into the ampoule containing the positron source_ During the
I
I Ortho-Ps
I Yield
Q
Aceione/Hexone
0
Benzene
x n
Cyclohexane Hexane
Pyridine
c
I
mixture
mixtures
cis-Oecotin
0 Isooctane
Fig. 1. Relative o-Ps yields ve&s concentrations of pyridine or acetone in nonpolar liquids. Filled points are pure liquids.The curves are visual fits. The uncertainties are roughly + 0.6 %_
99;
B. Lhay et al./Ps formation in nonpolar liquidf Table 1 Main parameters extracted.from the measurements. TV,12 and IF were obtained from the lifetime spectra The other parameters were obtained by fitting of the o-Ps intensity EUN~S in figs; 2 snd 3 with eq~. (I) OF(2)): * indicates a fixed parameter System
cyclohexane-D12 cyclohexane trans-de&in cisdecalin cisdecalin + 0.05 M CClr iooctane
n-hexane benzene carbondisulphide pyridine pyridine + 0.05 M CCI, acetone
73b4 (+ 0~05)
G (%I (+ 0.6).
et”(%)
3.32 3.24 2.93 2.75 2.74 4.05 392 3.15 2.12 268 2.58 3.29
40-4
429 42_8 41.8 43.7 28.0 _-
379
362 33.6 17.8 43.1 424 43.0 46.7 143 13.1 17.1
(fO.6)
as a function
of acetone
concentration
&‘J
190 66 49 70 20
_t i f 2 f _
400 34 16 22 3
-
_ -
2,2,44rimethyIpentane (isooctane), benzene, carbondisulphide (CS,), cycIohexane, deuterated cycIohexane (cyclohexane-DlZ), transdecalin, cis-decalin, and cis-decaIin containing 0.05 M CC&. In addition we have studied acetone/hexane mixtures. The Iifetimes (rJ and reIative intensities (I:) ofthe Iongest Iiving (o-Ps) component for the pure liquids are given in table 1. The relative o-Ps yields (Z3) as a function of pyridine concentration for some of the systems investigated are shown in fig. 1 together with the I,-values
a
B
(M-l)
1.5 0.78 0.70 0.58 0.47 1.20 OX9 0.45 0.74
& 0.2 f 0.06 f 0.07 i-’ 0.08 F 0.19 & 0.09 & 0.09 k 0.06 * 0.0s -
-
0.35 * 0.31 + 0.32 -f 0.35 t 0.35* 0.23 & 0.25 + 0.23 * 0.4s _ -
0.01 0.03 0.03 0.01
O-34 2 0.66 2 o.s7 + 0.74 f 1.6 f 0_54 _t 0.53 & 1.03 * 1.09 _t -
0.01 0.01 0.04
0.06 0.10 .0.13 0.09 0.6 0.052 0.08 0.14 0.13
o-Ps yield up to a certain maximum can be observed (fig. 3). In all of the pyridine mixtures investigated pyridine acts as an inhibitor of Ps formation when its concentration exceeds a certain limit. Addition of acetone to hexane increases the Ps yield at low acetone concentrations. We measured
I’ F-
/
50 L
r’ Uncertainty
1
I cs,
1
n iso-octane
D n-Herane 0 Benzene
in
the acetone/hexane mixtures_ The I,-values for the trans-decalin mixtures were very similar to those of the cis-decalin mixtures at concentrations above roughly 2 M. The o-Ps yields versus pyridine concentrations are shown in more detail in figs. 2 and 3. As seen by a simple visual comparison of figs. 2 and 3 the’pyridine mixtures investigated can be divided into two groups. The basic difference between them appears most clearly at low pyridine concentrations (c 0.3 M). In the first group of solvents (i-e, n-hexane, isooctane, benzene and CSd the relative o-Ps yield remains nearly constant or decreases slightly (CS,) in that concentration range (fig. 2) In the other group of systems (i-e_ cyclohexane, cyclohexane-D12, transdecaliu, cis-decalin and cis-decalin + CCI,) an abrupt increase of the
CONCENTRATION
OF PYRIDINE
II.41
Fig. 2. Low concentration results. Relative o-Ps yieids versus pyridineconcentration in nonpolar liquidswhere nd -. fast holes are formed_ The curves are fits acc&&ng to eq. (1) (see text). -The uncertainties are roughly +- O-6 “/,
:
i LIncertainty o Cyctohemne-Dt2 I cyclchexan~
o Pyridine/Hexane
Ortho-Ps
Lifetime
2o Pyridine/lscoctone 0 Pyridiie/CycIohexane-m yridine/Benzene yridiieftrans-Decolin yridiiekis-Decalin
t 0
0.5 tONCENTRATlON
7.0
OF TYRKXNE [Ml
Fig. 3. Low coneentretionresuIts_ ReIativeo-Ps yields versuspyridineconcentrationin nonpolarliquidswhere fastholesare farmed.The curvesare titsaccordingto cq. (2) (seetext).The uncertainties are roughly + 0.6%_ I, = 43.1%. 43.I 75,439 %, 44.272 and 43.6‘;‘, at acetone concentrations of 0.01 M, O-02M, 0.05 M, O-07M and 0.1 M respectively. Fig 1 shows the I, values at higher concentrations, where Ps inhibition is observed_ The o-Ps lifetimes, rs$versus pyridine or acetone concentrations are shown in fig 4.
4. Discussion
Comparing our results with those reported by the mdhtion chemists [IO-143 we shall below draw our main conclusion, viz_ the abrupt enhancement of o-I’s yields in certain liquids due to the addition of small amounts or pyridine can very probably be attributed to the existence and scdvenaina I 5 of extremely mobile solvent positive ions (holes) in those liquids. To reach this conclusion we must show (1) that the o-Ps yields versus concentration behave as expected by use of the proposed explanation and (2) that other explanations are unlikely. Apparently, two modeIs can be invoked to explain the measured Ps enhancements,namely (a) the effect of scavenging of the positive ions and (b) the so-
CONCENTPATION [Ml
The o-PSlifetimesversuspyridineor acetoneconcentrationin nonpolarliquids.The curvesare visual fits. Fig 4.
The uncertainties are rou&ly
f: MS ns.
called antiinhibition effect. Other effects causing Ps enhancements (e.g. the spur shrinking effect caused by added impurities in argon [2]) seem not to be applicable in our eases_ First, let us consider the positive ion scavenging effect. Pyridine is expected to be a good positive ion scavenger_Its ionization potential (IP) is 93 eV compared to IP’s of 9.8,9_61,9.61, 10.18,9.86, 9.24 and 10.08eV for cyclohexane, cis-decalin, transdecalin, n-hexane, isooctane, benzene and CS,, respectively [20]. Hence, apart from the benzene case, the IP of pytidine is lower than that of the used solvents_ We therefore expect pyridine to react with the positive ions by charge transfer_Positive ion scavenging is expected to cause an increase in the PS yield if the product or the scavenging has a lower reactivity towards the excess electrons in the positron spur than that of the initial positive ion. The scavenging of the rapidly moving positive ion
B_ L~%ay et al.fPs formation
(hole) in cyclohexane and in the decalins results in a product which has a diffusion constant and a spatial extension comparable to those of heavy positive ions. Hence, in par&&r the diffusion constanf but also the spatial extension (reaction radius) of the product, are smaller than those of the rapidly moving hole. The reactivity of the product towards the spur electrons is therefore much Iower than that of the fast hole. This explains the measured strong Ps enhancements at low pyridine concentration in the liquids where the positive ion is rapidly moving (fig. 3). In the cases where the positive ions are slow we cannot in advance predict the changes in the Ps yield caused by the scavenging of the positive ion by pyridine. Apparently, information on the properties of the product of such reaction is not available in the literature, and hence we cannot compare the reactivity of the slow positive ions towards the excess electron with that of the product of the scavenging_ Our results (fig_2) show no Ps enhancement on addition of pyridine to those liquids where the positive ion is slowly moving_ Hence, the positive ion and the product of the scavenging have roughly similar reactivity towards the excess electron. In liquids which have similar spur properties (cyclohexane, cis- and trans-decalin, n-hexane, isooctane, and benzene) we therefore expect to get roughly similar Ps yields at pyridine concentrations of about 0.2 M, where apparently the rapidly moving ions are scavenged in cyclohexane and the decalins in agreement with our results (figs. 2 and 3). We can therefore conclude that the scavenging of positive ions by pyridine explains the main features of the Ps yield versus pyridine concentration data at low pyridine concentrations in figs. 2 and 3. The “antiinhibition” [21] (“antirecombination” in pure liquids [22]) effect can in principle also explain the Ps enhancement in the nonpolar liquids studied in this work This effect occurs when excess electrons in the positron spur are trapped on certain electron scavengers, where they are bound in fairly shallow potential wells, and hence probably have spatially somewhat extended wavefunctions. They can easily be picked off these traps by the probably rapidly moving positron to form Ps. In cases where this pick off process is very effective, some of the electrons
b nonpolar liquids
101
which would have recombined with the ions in the pure liquid will form Ps by this secondary reaction on addition of the “shallow trap” electron scavengers resulting in Ps enhancement For example, addition of C,F, causes Ps enhancement in pure n-hexane and reduces strongly the Ps inhibition by Ccl, in Ccl&hexane solutions [22]. Py-ridine reacts with the hydrated electron (k = LO9M-‘s-l) [19]. Pyridine or pyridine clusters might react with the electron in nonpolar liquids too. Hence, we must also consider the possibility that the measured Ps enhancement is caused by the antiinhibition effect. In this context it must be realized that Ps formation probably takes placewithin picoseconds, and hence it might be influenced by phenomena (e.g. relaxation and spatial extension of wavefunctions, [23]), which have not been studied in typical radiation chemistry experiments of a much slower time resolution_ The antiinhibition effect probably occurs mainly because the rapidly moving positron can pick off the trapped electron with a greater efficiency than the slow positive ion. Hence, as the positive ion is much faster in cyclohexane and the decalins than in the other liquids, we expect of course the smallest Ps enhancement in the former. liquids in strong contradiction to the experimental results. We therefore can conclude that the antiinhibition effect cannot explain our results. The positive ions can probably oxidize P.S. In principle, changes in the Ps yields on addition of solutes might be explained in terms of changes in the probability of this reaction_ However. the effect is very probably unimportant because Ps is a slowly moving, neutral specie. We have also studied the effect of the presence of the strong electron scavenger Ccl& on the enhancement and inhibition of Ps formation caused by pyridine (fig. 3). The positron forms a bound state (i.e. not Ps) in a reaction with Cl- [23] which is formed as a result of the electron scavenging by CC14. Comparing the curves obtained for pure cisdecalin and cis-decalin containing 0.05 M Ccl, the following conclusions can be drawn: Although Ccl, at the given concentration reduces the o-Ps yield in cis-decalin by a factor of about two, the absolute enhancement caused by the addition of pyridine remains the same (10 %). Hence the positive ions compete more effectively with the positron for the
102
B. L.&ay et aI./Psformation in nonpolar liquids
remaining electrons not scavenged by CCI& compared to the situation in the pure cis-decalin, probably because the easily scavengable fraction of the electrons in the outer part of the spur is first scavenged on addition of an electron scavenger_ The fact that a higher pyridine concentration is needed to geetthe maximum in the Ps yield in the CCI, solutions compared to pure cis-decalin is also in agreement with this explanation. Similarly, the comparatively higher pyridine concentration needed to cause Ps inhibition in the CCI&is-decalin solution is easily explained 1241. It is worthy of note that Ccl, has only a fairly wedk effect on the o-Ps intensity in pure pyridine (table IL as has also been found in the cases of CSI and C,F6 [22]. Altogether, we can conclude that the measured Ps yields at low pyridine concentration are explained well in terms of the spur model and the existence of a rapidly moving positive ion in some of the liquids. This result also confirms thd previously proposed explanation [IS] of the Iow Ps yield in CycIohexane compared to hexdne. The Ps enhancement by pyridine in the liquids with large positive ion mobilities occurs at Iower concentrations than in most other cases of Ps enhancement_ Ps enhancements caused by addition oTnlcohoIs to hydrocarbons including hexane and cyclohexane have been observed by others and interpreted in terms of positive ion scavenging but without reference to the rapidly moving hole in cyclohexane [9]_ However, as the measurements were made to study mainly the alcohol cluster effects the Iqw concentrations regions were not studied in detail, and hence no cIear differences between the cycIohe.xane and hexane solution can be seen in the data. This comment applies at present alSO for Some measurements on alcohol solutions done at Rise, which however, showed clearly that Ps enhancements nearly as strong as in the pyridine/cycIohexane case are found on addition of certain alcohols to cyclohexane. Ethanol reacts with the positive hole in cy-cIohexane (k = I.4 x LO’I M-’ s-l) [Iz]_ The strongest Ps enhancement measured in a case where the antiinhibition effect is probably the most important cause OFthe enhancement is the naphthalenejrz-hesane solution, which showed a somewhat lower enhancement than in the pyridine/cycIohexane
case c22-J. Naphthalene reacts probably with the positive ions too. The Ps inhibition at higher conamtrations of pyridine appears in all of the nonpolar solvent systems investigated irrespective of whether mobiIe positive holes are formed in them or not As seen in Iigs. 1-3 pyridine apparently acts as a Ps inhibitor in a rather particular way. It becomes effective only I its concentration exceeds a certain limit. Similar observations were reported on the electron scavenging and Ps inhibition caused by different alcohols in nonpolar solvents [15,9]. The effect was interpreted by considering the formation of alcohol clusters. AIcohoI clusters are known as efK%ive traps for spur electrons [25]. A similar interpretation seems to be reasonable in our case too. However, other explanations are possible. For example, we cannot exclude that the positron can pick off the electron from the product of a possible pyridine electron reaction at low concentrations_ At higher
concentrations this product might react with another pyridine molecule resulting in a product from which the positron cannot easily pick off the electron_ These processes can also explain the measured Ps inhibition above = 03 M pyridine. It is interesting that we find a stronger inhibition by pyridine in cyclohexane-D12 than in normal CyCIOhexane.This might indicate that the electron mobility is highest in the deuterated compotmd. To geetmore quantitative information about the combined processes of enhancement and inhibition of Ps formation caused by pyridine in nonpolar solvents, we attempted to fit the measured o-Ps intensity curves by formulae containing parameters characterizing the enhancement and inhibition processes. For liquids not containing mobile positive holes the following formuiae are applied: I, = 1: = constant,
if c d c,;
,.,
ilt = 1$/Z = !$/:I +[G(c - co)]‘}.
if c > co,
‘I’
while for liquids with highly mobile holes: I, =
zp+ (zy
I, = W/Z,
- Z4[1
-
I/(1 + PC)] = rv,
if c G co; if c > cO_
Here p and G are the enhancement and inhibition
(21.
B_LPmy et ai_/Ps fommtion in nonpolar liquids coefficients, respectively (in M-r), a is a dimensionless’fitting parameter, c, is the critical pyridine concentration (in M), c is the pyridine concentration, and I’;” stands for the maximum value of o-Ps yield when only hole scavenging takes place without any inhibition. The results of fitting are shown in table 1. Because of the small changes in the lifetimes (fig. 4) the a-Ps intensities were used without quenching correction. Formula I$/2 is analogous to the one applied by US earlier describing the Ps inhibition in nonpolar liquids [3,26]. Without the CLparameter the fits resulted in very poor z2_ Expression W describes the process of Ps enhancement_ The I’;” parameter was tixed at the maximum value of 0-R intensity measured experimentally_ Because of the very few numbers of experimental points in the concentration range characteristic of the process of enhancement, the fitted values for the enhancement coefficients (B) are fairly uncertain and they could not be compared quantitatively with the available hole mobility data [lO-141. Their order of magnitude (= 60 M-‘) is comparable with similar values of inhibition coefficients which correspond to electron reaction rate constants of the order of lOr3 M-’ S-’ [3,4,24,26-J. In spite of the great uncertainties of the p values, the decreasing effect of the electron scavenger CCI, in cis-decalin is reliably seen. The parameters found for the o-Ps inhibition (cr, a) and ce are much better defined and are in agreement with the conclusions drawn above. It is worthy of note that the correlation found by us earlier between the two fitting parameters for o-Ps inhibition [26] seems to be valid also for pyridine, viz., a - ’ is a linear function of G (fig. 5). a-i=ac+b,wherea=l_4Mandb=0.2_The reciprocal value of the slope of such a straight line was suggested to be used for characterizing the inhibition efhciency of an electron scavenger by a solvent independent number [26]. This value for the pyridine is a -’ = 0.7 M-r, which shows that pyridine acts as a very weak Ps inhibitor in nonpolar liquids. For comparison_ the similar values for ethylbromide and Ccl, are 4.8 and 67 M-t respectively [3,26]. Acetone added to tz-hexane also causes Ps enhancements at low concentration and Ps
103
Fig. 5. I/a versus C_Correlation between the two titting parameters used for describingthe Ps inhibitioncaused by pyridinein nonpolar liquids.(See eqs. (1) and (2) in the text) Data taken from table l_The straight line is a leastsquares tit to the points. inhibition above 03 M. Acetone rapidly scavenges electrons, and the formed anion might react further with other acetone molecules at high enough acetone concentration [19,27]_ However, acetone (IP = 969 eV [20]), can be expected to scavenge the positive ions too. We do not kno*wwhich of the two processes, antiinhibition or positive ion scavenging, is the cause of the Ps enhancement. The Ps inhibition is explained well in terms of electron scavenging stabilized by a secondary reaction between the formed anion and an acetone molecule_ The long lifetimes, r3, shown in fig. 4 are caused by the ortho-Ps pick off annihilation on the molecules of the mixtures_ Ps is situated in a cavity, rrormally called the Psbubble, in a liquid The size of the bubble (radius z 5 A in n-hexane) is determined by the inwards pressure of the surface tension balanced by the outwards pressure caused by the zero-point motion of Ps. Hence, the rX values reflect the overlap of the positron in ortho-Ps with the outer electrons of the molecules of the bubble surface. We shall not discuss the rs values in any detail here. (See ref. [ 1, f 51 for references to recent literature.)
5. Concfusion It can be concluded that the measured Ps formation probabilities in pyridine mixtures with
104
IX Lticav er ui_/Ps~rmafion
nine different nonpolar liquids are well explained in terms of the spur model of Ps formation and the existence of rapidly moving positive ions (holesj in some of the liquids_ Our results show that a fast hole probably exists also in deuteratcd cyclohexane. The present results again demonstrate the decisive role of the spur processes For the Ps formation in liquids and the close correlation between Ps chemistry and rddiation chemistry_
AcknoH-Iedgement B.L. wishes to thank the Chemistry Department OFRise Nationa Laboratory for its hospitality_ The authors are much indebted to A-B. Nielsen and NJ_ Pedersen for vdhmble technical assistance.
Rererences
in nonpolar liquids
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