Primary Trapping and Solvated Electron Yields Part 1. Recombination Kinetics BY F. KIEFFER, J. K L E I N , ~ C. LAPERSONNE-MEYER AND M. MAGAT Part 2. Correlation between G-Value and Neutralization Efficiency BY J. BELLONI, F. BILLIAU, P. CORDIER, J. DELAIRE, M. 0. DELCOURT AND M. MAGAT Laboratoire de Physico-Chimie des Rayonnements, associk au CNRS 9 1405, Orsay, France Received 29th November, 1976 The isothermal decay of luminescence emitted in frozen hydrocarbons as a result of the recombina- tion of trapped electrons with aromatic solute cations has been studied in relation to theoretical models for the primary processes of radiolysis. The kinetics were determined on a time scale extending from -20 to 800 ns, with radiations of different LET. In polar liquids the influence of physical as well as chemical properties of the solvent on the yield G(e,,,) at a given time ( t = 3 ns) has been investigated: in particular, evidence was found of the existence of a correlation between the survival probability of eGlv and the efficiency factor of the eS;,,-cation recombination, which had so far been assumed to be limited only by diffusion.It is generally agreed that the initial distribution of events in condensed matter submitted to ionizing radiation is in no way homogeneous. On the one hand the primary species are initially distributed in spurs and blobs, related of course to the LET, and on the other hand, even in the limiting case of an isolated pair, the spatial distribution is not uniform since the secondary ion and radical, resulting from an ion-molecule reaction, are closely spaced.We were especially interested in the following two problems : a) for how long a time this inhomogeneous spatial distribution reflects itself in the b) in what way this non-uniform ion radical distribution may influence the G(e&) kinetics of consecutive processes such as ion neutralisation, value, measured at a given time. PART 1 : RECOMBINATION KINETICS: LUMINESCENCE AT 77 K O N THE NANOSECOND SCALE The kinetics of neutralization can be conveniently investigated by studying the decay of deferred luminescence at constant temperature (ITL), arising from the recombination of trapped or pretrapped electrons with positive ions of added aromatic compounds, formed by charge transfer from the primary aliphatic ions of the matrix.It was shown earlier' that often the decay kinetics of ITL can be described by a hyperbolic law (1.1) A I(t) = - t Centre de Recherche Nucleaire, Strasbourg, Cronenbourg, France.56 PRIMARY TRAPPING A N D SOLVATED ELECTRON YIELDS where I(?) is the intensity of luminescence at time t and A a constant. In a " hard " glass such as methylcyclohexane (q = 10'' P at 77 K) this law was found to apply over a time range of 9 orders of magnitude from 2 p s to 1 h; in a " softer " glass, 3-methylpentane (q = 10" P at 77 K), this law is valid only for a shorter period, 2 pus to a number of minutes, increasing with solute concentration,' whereas at longer times the decay law becomes3 B ? '' I(?) = - Whenevei. eqn (1.1) applies at 77 K, other experimental results, such as identical decay kinetics at 4 K, or the effect of cooling from 77 to 4 K, are consistent with a tunnelling mechanism for electron-cation re~ombination.'*~ Tunnelling probability depends exponentially on the electron-cation distance. A spatial distribution of electrons and cations, therefore, implies a distribution of tunnelling probabilities.Tachiya and Mozumder5 have shown that this can account for the form of (1.1). On the other hand eqn (1.2) seems to correspond to a thermally activated process. The validity of the same decay law from 2 ps to minutes or hours means that all information about the primary ion-electron distribution in a track is already lost 2 p s after an ionizing pulse lasting 3 ns. In order to obtain such information it was necessary to extend experiments to the nanosecond range, the lower time limit being only determined by the lifetimes of excited states formed directly.Such an extension proved possible with a technique based on coincidence counting of photons, and we thank Prof. Voltz for kindly letting us do this work in his laboratory. EXPERIMENTAL The glassy matrix was methylcyclohexane doped with one of two solutes, bPBD and PTP,* having a short fluorescence lifetime (z 1 ns) and high fluorescence yields. They were used in concentrations 10-5-10-3 mol dm-3. Sources of B or a particles (90Sr90Y and 210Po respectively) of about 1 pCi were either sealed inside the sample or placed in a thin- walled finger protruding into the silica tube containing the sample. Degassing was done by the usual freeze-pump-thaw procedure.The details of the technique have been described previously by Paligoric and Klein6 and Heisel, Fuchs and V01tz.~ The equipment was adapted to the work at liquid nitrogen temperature mainly by the adjunction of a Styrofoam container fitted with two silica light guides between which the sample tube was held in position. Coincidences between two photomultipliers, one of which operated in single photo-electron counting, were analysed by a time-to-amplitude converter and the results were stored in a multichannel analyser. The resolution time was about 5 x s. RESULTS The data, corrected for background noise and the instrument function, show a decay consisting of two components : a) a " rapid " one which is exponential and has the lifetime of solute fluorescence; it i s attributed to excitation transfer from solvent to solute molecules.6 b) a " slow " one, attributed to the electron-cation recombination.Initial results obtained with bPBD seemed to indicate a significant difference between samples irradiated with a- and P-particles respectively.8 However, further experiments have shown that the differences we observed were due in part to poor reproducibility. A study of fluorescence spectra and fluorescence lifetimes of bPBD in methylcyclo- * bPBD = 2-(4-butylphenyl) 5-(4-biphenylyl)l,3,4-oxadiazole. PTP = p-terphenyl.F. KIEFFER, J . KLEIN, C. LAPPERSONNE-MEYER AND M. MAGAT 57 hexane showed a variation with concentration from which we concluded that aggre- gates can be formed in methylcyclohexane glass at concentrations as low as mol dm-3.For this reason we replaced bPBD by PTP, which we found to form aggregates only at concentrations close to Fig. 1 and 2 show the mol dm-3. 100 1000 - I I I 1 I i 1 1 1 I I l l I 1 1 1 , - - - - c - L - - - 10 c - - A - - - + I I I l l I I 1 1 1 I 1 1 1 1 I I I 1 20 60100200 6OOlooO t / n s FIG. l.-ITL decay of p-terphenyl in methylcyclohexane after ionization with a-particles at 77 K. p-Terphenyl concentrations (mol dm-3): A-10-5, B-3 x lo-’, C-10-4, D-3 x For clarity, curves C and D are shifted to the right by one and two decades respectively. slow component of the decay kinetics with 01- and /3-particles respectively. For clarity some of the curves have been displaced by one or two decades. In fact, they all cover the time span 20-800 ns.These curves can be described by the Debye- Edwards equation I(t) cc t - m . (1 -3) For m = 1 this equation is of course identical with (1.1) and is hence valid for t > 2 ,us. TABLE VA VALUES OF rn FOR M and p IRRADIATIONS AS A FUNCTION OF PTP CONCENTRATION /mol dm-3 U P 1.3 (t = 20-55 ns) { l.Os (t > 55 ns) 10-5 1.40 3 x 10-5 1.43 1.28 (t = 20-60 n ~ ) 1.2,, (t > 60 ns) 10-4 1.31 1.3 3 x 10-4 1.34 1.358 PRIMARY TRAPPING AND SOLVATED ELECTRON YIELDS t / n s FIG. 2.-ITL decay of p-terphenyl in methylcyclohexane after ionisation with P-particles at 77 K. p-Terphenyl concentrations (mol dm-3): A-10-5, B-3 x lo-’, C-10P4, D-3 x loP4. For clarity, curves C and D are shifted to the right by one and two decades respectively.Table 1 shows the values of m for the two cases (a and p irradiations) as a function of PTP concentration in the time range from 20 to 800 ns. DISCUSSION In all cases, at the shortest times, the m-values lie between 1.3 and 1.4, these “ high ” values of rn being valid in the case of a particles up to 800 ns (our upper time limit). On the other hand, in the case of j? irradiation at low PTP concentrations, the m-value decreases markedly after some 50-60 ns, while it remains high at higher concentrations. Comparing these results with our previous results at t > 2 ,us, we can say that there exists a significant track effect, the primary charge distribution influencing the decay kinetics up to at least 800 ns in the case of a particles and up to times between 50 and over 800 ns for p particles.However, the effect is just beyond the limits of experi- mental error and does not justify complicated theoretical calculations. It can be stated, however, that it appears in the expected sense: in the case of a j?-particle track, single pair recombinations become predominant well before 800 ns, whereas in the case of a particle tracks multiple recombination possibilities seem to exist for all solute cations. PART 2: CORRELATION BETWEEN G-VALUE AND NEUTRALIZATION EFFICIENCY Since the discovery of the solvated electron in irradiated water, it has appeared possible to describe the primary effects of radiation on condensed matter through theBELLONI, BILLIAU, CORDIER, DELAIRE, DELCOURT AND MAGAT 59 fate of e;,,. Accordingly, the proposed diffusion models calculate a survival prob- ability of eGlV, as a result of its diffusion in the Coulomb field of the cation and its recombination with this counter-ion, in an isolated pair or in multipair spurs. The survival probability depends on the initial spatial distribution and on the physical properties of the liquid, such as viscosity, dielectric properties, etc.However, the models only consider the disappearance of the electron by reaction with the cation, and, moreover, they imply that the neutralization occurs at each encounter. Experimental results concerning the radiolysis of liquid ammonia9 have led us to consider in more detail the reaction efficiency of electron-cation collisions and it appeared possible to explain, at least qualitatively, the rather high yield of eLm by the sluggishness of the neutralization reaction eTm + NH:.The efficiency of neutraliza- tion at each encounter could be accounted for, using a diffusion model, like the one considered by Schwarz:lO the recombination rate constant includes an efficiency factor and an average value of the diffusion velocity in a Coulomb field. However, as in previous radical diffusion models, the displacement of charged species experiences no direction effect. We have now extended our investigations to some other liquids in order to determine the influence of the neutralization probability (reaction efficiency) at each encounter on the G(eilV) value at a given time, and in cases where this efficiency was low, to decide what was the main process of electron disappearance.In order to approach the ideal situation as assumed in models, we have chosen, on the one hand, solvents in which reactions such as eGlv + e;,, and e,,, + solvent do not occur. On the other hand, in order to avoid secondary chemical reactions, specific for each liquid, we have examined the correlation between recombination efficiency and G(eGl,) values observed a few nanoseconds after irradiation. EXPERIMENTAL We used as radiation source a 706 Febetron, delivering 3 ns pulses of 600 keV electrons.11a The standard dose per pulse was 5 x lozo eV dm-3 as determined from the initial absorption of the hydrated electron, taking G(eJ = 3.3 and E(e,g) = 1.3 x lo4 dm3 mol-' cm-' at 600 nm.12 The reaction cells were entirely made of silica with an electron entrance window of 200 xm thickness, withstanding internal pressures up to 10 bar.11b The recombination efficiency f was determined by comparing the experimental and the calculated (diffusion-controlled) rate constants of the reaction between e,,, and the main cation: f = kexp/kdiff.Solutions of the cations were prepared either by addition of a salt (N2H4, 2HC1; n-propylamine, HCl) or by acidification with HCl (case of 1,2-dimethoxy- ethane). Solvated electron yields have been determined indirectly using biphenyl (Ph,) as a scavenger and assuming ~ ~ ~ , , ( P h l ) = 1.21 x lo4 dm3 mol-' cm-'.13 The oscillograms of fig. 3 show the decay of solvated electrons measured at 900 nm in pure solvents : 1,2-dimethoxyethane, n-propylamine and hydrazine.RESULTS (a) 1,2-DIMETHOXYETHANE (DME) Due to the proton affinity of this kind of ether, and the high rate constant of the on-molecule reaction l4 DME+ % DMEH+, (2.1) it can be safely assumed that the initial DME+ cation is very rapidIy replaced by the stable cation DMEH+. These DMEH+ cations can also be produced by addition of HCl to DME, If one now assumes that in the concentration range of 6 x to60 PRIMARY TRAPPING AND SOLVATED ELECTRON YIELDS icl (6) n-propylamine (50 ns div-l); (c) hydrazine (1 ,us div-l). FIG. 3.-Solvated electron decay at A = 900 nm in (a) 1,ZDimethoxyethane (50 ns div-l); 4 x mol dm-3 all these cations are present as isolated ions, one can deduce from the experimental rate of disappearance of solvated electrons a rate constant :15 ke,lv+DMEH+ = 2 x 10" dm3 mol-' s-l.Since however, it is more likely that only a fraction of DMEH+ cations are isolated, this figure for ke.lv+DMEH+ is to be considered as a lower limit of the rate constant at infinite dilution (see discussion), The rate constant for electron scavenging by added biphenyl molecules was found to be kesolv = 1.1 x 10l1 dm3 mol-' s-l. The dependence of G(PhF) on scavenger concentration permits an estimate of the electron yield at a mean reaction half time. We have determined15 a value of G(eGlv) = 0.8 5 0.1 at 3 ns ([Ph,] = 8 x mol dm-3) and deduced the extinction coefficient: E(eElv) = 6000 dm3 mol-1 cm-l at 900 nm. (b) n-PROPYLAMINE In irradiated n-propylamine (PrnNH2) the main cation is PrnNH3+; the recom- bination rate between this cation and the solvated electron was measured.The solvated electron decay rate does not depend on concentration of cations below lo-, mol dm-3. In the range 10-2-10'1 mol dm-3, the experimental rate constant is kPrnNH3+ +esolv = 7 x lo8 dm3 mol-I s-l. The static dielectric constant of Pr"NH, is close to that of 1,ZDME (see table 2). Therefore, assuming that ion pairing and ionic strength effects are the same in the two liquids, the recombination rate constant in PrnNH, is 30 times lower than in 1,2-DME. (1.3 &- 0.1) x lo1' dm3 mol-1 s-l. We also deduce, as above: G(esYlV) = 1.40 & 0.15 at 3 ns and e(eLlV) = 13 000 dm3 mo1-l cm-' at 900 nm. The rate constant for the biphenyl-electron reaction in PrnNH, is: kesolv+Phz - - (C) HYDRAZINE The experimental rate constant kNzH+ +e;lv has been determined earlier16 at infinite dilution as koexp = (5 & 3) x lo7 dm3 mol-l s-l. It is quite low, leading, as inBELLONI, BILLIAU, CORDIER, DELAIRE, DELCOURT AND MAGAT 61 the case of ammonia, to a low value o f f , since kdiff - loll dm3 mol-' s-l.The solvated electron yield at 3 ns is correspondingly rather high: GCe;,,) = 3.4 and has been interpreted as resulting from the slowness of the recombination reaction. As in the case of ammonia again, the main process determining the observed disappearance of eZlv [see fig. 3(c)] has as yet not been established. No pertinent data are available concerning the main radical N2H3' produced at an early stage and its possible reaction with the solvated electron according to N2H4 -+ N2H4+ + e' (2.2) (2.3) (2.4) N2H4+ + N2H4 ----+ N2H5+ + NzH3* N2H3' -k eZlv -+ N2H3.However, the reaction between e & , and N2H5 + would ultimately lead, as in water,17 to a production of M,. We have measured the yields of stable products resulting from the irradiation of pure hydrazine: G(H,) = 1.90; G(N,) = 2.60; G(NH3) = 4.1. These figures are in good agreement with the results of Prosch18 who has also found that G(H2) is but slightly influenced by the presence of CC14, used as electron scavenger. Therefore, inolecular hydrogen does not originate from the N2H5 + neutralization reaction and the disappearance of e,,, must occur through reaction with the radical. (d) AMMONIA For ammonia both the solvated electron yield and the neutralization rate constant are knownlg (table 2).It was also suggested that eLm, poorly reactive towards NH4+, was disappearing by a second order reaction with the main oxidizing radical NH2*. The expected product, amide ion NH,, however, has never been observed at low temperature (-50°C) and is less abundant at room t e m p e r a t ~ r e ~ ~ than expected from the stoichiometry. For this reason, the rate constant of the eZlv + NH2' reaction at -50°C was determined15 from the decay of elm at 650 nm and the correlated increase of NH, at 330 nm (LmaxNH, at -50°C) in metal ammonia solutions, containing stable solvated electrons in excess [4.3 x loe4 mol dm-3 (Na+, e,) compared with 7.5 x lod5 mol dm-3 elm produced by radiolysis at the end of the pulse]. The decay at 650 nm, faster than in pure ammonia, and the increase at 330 nm are correlated pseudo first order processes (fig.4). Due to the respective values of G(NH2) and G(NH), the observed decay depends mainly on the reaction rate of eFm + NHo2. At -5O"C, it was found that ke,-,+NH2 = 3.5 x 1O1O dm3 mo1-I s-l. At the same temperature, the rate-constant of the diffusion controlled reaction would be: kdlff - 4.35 x 10" dm3 rno1-I s-'. The efficiency factor of the reactionf = kexp/kdiff is very close to 1. This result confirms that, in pure ammonia, the decay of e, is also due to reaction with the radical at practically every encounter. Fig. 5 presents the absorption variation at il = 800 and 330 nm for temperatures -50, -20 and 0°C. While at -50°C the decays at both wavelengths are similar, at -20 or 0°C the decay of e&, is faster than at -50°C and at 330 nm one observes the slowing down of the decay, indicating a slight increase super-imposed on the decay and attributed to NH2-.The differences between metal-ammonia solutions and pure solvent in the experi- mental evidence of the NH; formation can only be understood as a result of the different distribution of reacting species. (i) In metal ammonia solutions, solvated electrons are homogeneously distributed and in large excess relatively to NH2 radicals or NHZ ions. Both of these species62 PRIMARY TRAPPING AND SOLVATED ELECTRON YIELDS 0 .I 0.01 0.001 0 0.1 0.2 0.3 t l p s FIG. 4.-Decay of elm absorption at 650 nm in sodium-ammonia solutions: 0-3.2 x mol dm-j x - 4 . 3 x mol dm-3. Initial radiolytic concentration of e&: 0.75 x mol dm-3.Inserts: absorption changes in 3.2 x mol dm-3 Na solution (a) at A = 650 nni; (b) at A = 330 nm. 01 I FIG. 5.-Decay t / p s of absorption at (a) 800 and (6) 330 nm in pure ammonia. -- --- -50°C. ooc, . . . .. I 2O0C,BELLONI, BlLLIAU, CORDIER, DELAIRE, DELCOURT AND MAGAT 63 interact with added e, to give NH, or a loose pair NHZ . . . erm, but the anion NH; disappears after diffusion towards the neutral pair (NHZ . . . e,) with weakened Coulomb attraction. (ii) Conversely, in the pure solvent, where the charges are only those produced by radiation, the solvated electron is strongly attracted by the parent cation (kdiff is high) and, since they are poorly reactive, they diffuse as a pair without disappearing.After encounter of this pair with NH;, the reaction occurs and the NH; produced is then right in the Coulomb field of the very close NHZ. Consequently, the rate deter- mining step is the formation of NH, and its concentration remains low, although at higher temperature it becomes just detectable. This picture is valid as well for non- homogeneous early reactions as for the later homogeneous process NH; + (NH;. . . In fact, we conclude that the same situation is to be expected whenever the recom- bination rate constant is much smaller than the diffusion controlled rate constant while the formation of a geminate pair, e z l v . . . cation, is certainly fast. ea-m). DISCUSSION Table 2 contains data for the solvents presented above as well as for water and alcohols which are well known as regards their respective ezl,-cation and eLl,-radical reactions.Diffusion-controlled rate constants were calculated from Smoluchowski-Debye relations, using for diffusion coefficients D data from the literature and estimates obtained by comparison with similar solvents (see table 2). Experimental rate constants ke;lv+c+ in DME and PrnNH, have been corrected for ion pairing and ionic strength effects to obtain the constant at infinite dilution koexp. Considering that in these solvents the low static dielectric constant favours the forma- tion of triple ions,2o these coexist with the neutral ion pairs at the concentrations used. The conductance of such solutions is usually not lower than one tenth of that at infinite dilution: assuming that the monovalent triple ions have the same reactivity as isolated ions, koexp is -10 times higher than the actual experimental values.Other values are taken from original papers. Qualitative comparisons between solvents of table 2 show that G(e;,,) is higher in Pr"NH, than in 1, 2-DME although dielectric constants and kdiff values are nearly equal. Ammonia may be compared with alcohols, although diffusion coefficients and kdiff values are higher in ammonia; the electron yield is still higher than in alcohols, due to the low efficiency factor f = kexp/kdiff. Finally G(e&) is practically the same in hydrazine as in water, although &N2H4 < cHZ0. This again is probably due to a low value offin hydrazine. In order to improve present theoretical models3' and to explain our experimental data, we tried to take into consideration the fact that every collision does not effectively give rise to neutralization, as was shown by values of theffactor different from unity.We, therefore, solved the Smoluchowski equation using a boundary condition similar to that formulated by some a u t h o r ~ ~ l g ~ ~ in the theoretical treatment of reaction rates in solution. According to these authors the boundary condition expresses the assumption that there exists, near the cation or near the radical associated with the ion, a partially absorbing (or reflecting) boundary on which reaction proceeds by pseudo first order kinetics. In a first approximation, this model supposes that the radical and the cation are located inside a common barrier defined by one reaction radius. In the case of an isolated pair and using an approximation method known asch P TABLE 2-RATE AND DIELECTRIC CONSTANTS AND G(eGI,) VALUES FOR VARIOUS SOLVENTS 1,2-DME n-propylamine n-pro pano ethanol methanol ammonia 25°C h ydrazine water - 50°C 5.5 1 x 10-521 20.1 1.0 x 10-5 33.6 5.3 x 10-5 17 5.5 x 10-4 25 1.7 x 10-4 78 1.4 x 10-4 5 25.1 2.3 x 52 ~~~ 2 x loll l5 2 x 10l2 0.8 f 0.1 * l5 1.40 f 0.15* 1.27.1.77. 2.07. 3.4 & 0.2" l6 2 x 10'2$ 2.2 x 1Olo 22 4.1 x 1O1O 22 6.9 x 1O1O 22 5 x 10" $ 1 x loll (7 1) x 109 (2.5 f 0.2) x 10'' 22 (4.5 f 0.2) x 1O1O 22 (6.8 & 0.6) x 1O1O 22 3.2 x 10724 1.4 x l0l2 2.9 x 1011 3.2 f 0.3 25 1.2 x lo6 l9 (5 5 3) x 107 16 2.2 x 1O'O 27 1.03 x 10" l2 3 x 1O1O 27 2.3 x 1O1O 3.3 l1 3.5 x lolo l5 4.35 X lolo 3.0* 9; 3.2 2 5 ; 3.3 26 ~~~~ * These values were determined relatively to the same G3 ns (e,) value in water and so are self-consistent.f Values of free-ion yield as discussed in the review ref. (29). $ These values were estimated by comparison between solvents of close dielectric constant.BELLONI, B I L L I A U , CORDIER, DELAIRE, DELCOURT A N D MAGAT 65 prescribed diff~sion,~~ our preliminary calculations show that the G-value of the solvated electron at a given time is strongly dependent on a parameter y characterizing the boundary. Fig. 6 shows the typical case of liquid ammonia at -50°C: reaction radius = 5.8 A, mean thermalization lengths = 30 and 45A, diffusion coefficient = 1.5 x lo4 cm2 s-’. Abscissae have been expressed in terms of y, and for convenience they have been converted into second order rate constant k’ according to ref.(32). l.C 2 0 . 5 7 I I I I u 0 12 8 4 0 FIG. 6.4-value (normalised to initial ionization yield Go) versus the parameter y and reactivity k’ at 3 ns and infinite time, for two thermalization lengths (- 45 A, ---- 30 A). G-value at infinite time is calculated with (lower curves) and without (upper curves) electric field. log k‘l dm3mo~-1 It can be seen from fig. 6 that, at a given time, the G-value starts from a total escape when there is no reaction with either the cation or the radical (k’ = 0), that is when there is a total reflectivity of the boundary ( y --+ co) and then decreases with the reactivity k’. It should be noted that the limiting value of G for longest time and for lowest y agrees exactly with that calculated from the Onsager escape pr~bability.~~ This value corresponds to the ultimate probability for the solvated electron to escape radical capture or ion neutralization.Moreover in the presence of a Coulomb field, this limiting G-value is reached for a value of y higher than in the absence of the field. The authors thank Dr. P. Penel for his help and advice concerning the mathematical This work was made possible by grants from the Centre National de la treatment. 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