Feb., 1951
NEGATIVE ION FORMATION BY ELECTRON CAPTURE rn NEUTRAL MOLECULES
mium iodide a t which the transference number would be zero calculated in this way is 0.20 mole/l. A concentration of 0.21 mole/l. is obtained if the second set of constants is used. These values are in as satisfactory agreement with the results of
[CONTRIBUTION FROM
THE
523
Redlich and Longsworth as could be expected in view of the differencein ionic strength. This work was supported by a grant from the Wisconsin Alumni Research Foundation. MADINN,WIS.
RECEIVEDAPRIL8, 1950
DEPARTMENT OF CHEMISTRY OF THE UNIVERSITY O F NOTREDAME]
Elementary Processes in Radiation Chemistry. 11. Negative Ion Formation Electron Capture in Neutral Molecules 1,2,3 BY JOHN L. MAGEEAND MILTONBURTON Ionization processes characteristic of radiation chemistry yield energetic electrons which are ultimately degraded to thermal energies in ionization and collision processes. Although negative ions can be produced without positive-ion formation by impact of energetic electrons on molecules, the yield of such processes is so small that they make practically no contribution t o the over-all picture. Thermal electrons can yield negative ions either in simple capture or in dissociative capture processes. When conditions for negative ion formation are satisfactory, low energy electrons (< I/* ev. in gases, I/, ev. in liquids) disappear almost exclusively in formation of negative ions rather than in neutralization of positive ions. At usual irradiation intensities, common substances which give negative ions by thermal electron capture include oxygen, liquid water, alcohols, alkyl halides and, in general, all compounds in states in which they have low-lying vacant orbitals. For capture of thermal electrons in a dissociative process, the electron affinity of the ion produced must exceed the strength of the bond ruptured. In general, such processes tend t o increase ion-pair yield, but certain clearly described exceptions exist. Radiation chemical syntheses of ozone and of hydrogen peroxide show behavior characteristic of reactions in which the principal neutralization process involves negative oxygen ions. When a negative-ion source (c.g., oxygen or water) is present as impurity in a substance of low ionization potential (c.g., benzene), the principal neutralization reaction in a radiationchemical process involves interaction of the negative ion of the former and of the positive ion of the latter. Resultant characteristic reactions may mask the normal radiation-chemical reaction of the uncontaminated principal constituent. Water vapor captures thermal electrons without dissociation but solvation of the negative ion in liquid water confers large electron affinity and produces a situation conducive t o capture accompanied by dissociation. Resultant anisotropic distribution and high concentration of positive and negative ions may have special consequences, particularly in biological systems.
1. Introduction Free electrons and positive ions are produced when high-energy charged particles pass through matter. The kinds of positive ions and the energy distribution of the free electrons depend primarily upon the nature of the substance and to a lesser extent on the incident particle (i. e., its charge, mass and energy).‘ The complete radiationchemical mechanism, which describes in detail all the chemical reactions resulting from the irradiation, depends upon all ions and radicals produced! One small, but important, possible step in that mechanism is electron capture in the neutral molecule of the irradiated material. If capture is possible, large numbers of negative ions will form in the system, and neutralization will occur principally by positive-negative ion reaction. If capture is not possible in the neutral molecules, the free electrons will be thermalized and eventually recaptured in the positive ions which exist in the system. In this paper we axe considering in a general way negative ion formation by the electron capture mechanism only. We find it convenient to divide the discussion into four parts: (a) electronic states of negative ions; (b) cross section for electron capture as a function of electron energy; (c) energy distribution of free electrons in irradiated (1) Presented at the September 1949 meeting of the American Chemical Society, Atlantic City, N. J.
(2) A contribution from the Radiation Chemistry Project, operated by the University of Notre Dame under Atomic Energy Commission Contract NO. AT(ll-1)-38. (3) Paper I of this series: THIS JOURNAL, ‘78, 1965 (1960). (4) H. A. Bethe. “Handbuch der Physik,” Vol. 24, pt. 1, Julius Springer, Berlin, 1933. ( 5 ) M. Burton, Ann. Rev. Phys. Chcm., I,113 (1950).
systems; (d) probability for capture of such free electrons. These topics are treated in the required detail. A discussion of capture possibilities in real systems with possible radiation chemical effects follows thereafter. In this paper we are not concerned with formation of negative ions in the primary radiation chemical act, e. g. RX -wv+ R + 4-Xeither by the action of the primary charged particle or by action of fast secondary electrons. Our concern is exclusively with negative ion formation by electron capture and the consequences of such a possible process.
2. Electronic States of Molecular Negative Ions 2.1. Negative Ions of Singly Bonded Diatomic Molecules.-Most atoms are able to form negative ions because they have an electron affinity i. e., the reaction A+s--tA-
is exothermic. A few, of course, have zero or negligible affinity. Molecules are more complicated systems. Most of them have stable negative ion forms6; thus, dissociation from the lowest energy state of such ions is always endothermic. It is an important fact that the stable form is not necessarily attainable directly by electron capture (see the case of hydrogen’). Whether or not such attainment is possible depends upon the nature of the potential curves for the negative ion. The purpose of this section is the examination (6) H. S. W. Massey, “Negative Ions,” Cambridge University Press, 1938.
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JOHN
Vol. 7.3
L. AfAGEE AND MILTONBURTON
of the more important features of these potential possibility. The three body reaction (3) is improbable. Therefore, the molecular ion would not curves. The simplest case is Hz-. This system has been be formed to any appreciable extent in an irradidiscussed by the authors3and a detailed calculation ated system. We shall see later that the number using the variational method has been made by of H - ions formed in irradiated hydrogen gas is Hirschfelder.? The two potential curves for Hz-, negligible, so that there is a second reason for the both dissociating into H H-, are easily under- unimportance of Hz- in the radiation chemistry of stood qualitatively in terms of molecular orbitals.6 hydrogen. In general, the potential curves of all other negaIn its ground state the H2 molecule has its two valence electrons in the lowest (bonding) molecular tive ions, including diatomic, will be more compliorbital. When the molecule adds an electron to cated than those of Hz-.The number of electronic form H2-, the added electron can go to the next states and their types will depend upon the molehigher (anti-bonding) orbital. A second electron cular orbital structure of the system. The posiarrangement, which involves only the same two tions of each of the dissociation limits depends upon molecular orbitals, places one electron in the the electron affinity of the fragment concerned. bonding orbital and two electrons in the anti- The calculation of a complete potential curve is a bonding orbital. Clearly the energy for this state complicated matter. No reported attempt has is higher than the first, and this is actually the lowest been made for a system other than Hz-. Probably, most electron capture phenomena inexcited state of the ion. The higher potential energy curve in Fig. 1 represents a curve of this volving single bonds can be understood on the type. Electron capture into it requires the basis of sets of potential curves of the type shown simultaneous excitation of one of the valence in Fig. 1. From data of the types indicated above electrons of the molecule. This capture is an one can draw approximate curves for a given bond. illustration of what is called a dielectronic process, Table I lists some electron affinities, I-, and Table I1 gives some energy data for single bonds. From because two electrons are involved. them, approximate dissociation limits for the ions can be calculated. Some of the few available threshold values for electron capture appear in Table 111. It is probable that deep minima in the potential curves go with high electron affinity for the two atoms, but quantitative relations are not known. In principle, the electron capture crosssection as a function of energy directly gives the potential energy of the ion for a configuration very nearly like the equilibrium configuration of the molecule (cf. the Frank-Condon principle).
+
TABLE I SOME ELECTRON AFFINITIES~ Atom
I - , e.v.
I - , kcal. mole-'
H C
Fig. 1.-Negative
Internuclear separation. ion potential curves for a molecule AB.
The potential energy curves of Fig. 1 demonstrate a case in which it is impossible to reach the negative ion of the molecule directly by electron capture. The Franck-Condon principle requires that the resulting state of that negative ion has energy El to E2, Fig. 1, above its dissociation limit. Thus, the newly formed ion dissociates immediately, The stable state of the negative ion of a molecule such as Hz- can be formed by one of the reactions* 2.1 (1) Hi e +Hz-
+ Hz- + H H + H- + M +HI- + M H-
+ Hz
--f
2.1 (2) 2.1 (3)
Reaction (1) simply cannot occur a t ordinary temperatures. The high activation energy of reaction (2) likewise eliminates it as a significant (7) H. Eyring, J. 0. Hirschfelder and H. S. Taylor, J . Chem. Phys., 4, 479 (1936). (8) T h e symbol Hn' refers to a hydrogen molecule in a highly excited vibrational state.
0,715 16.5 0.69 15.9 x 2.36 54.4 0 2.87 66.2 F 4.15 95.7 c1 3.79 87.4 Br 3.68 84.9 I 3.53 81.4 None of these affinities are experimental measurements. The value for hydrogen is from E. A. Hylleraas, Phyysik, 65 209 (1930). It was calculated by the variational method. All others are given by R. Mulliken, J . Chem. Phys., 2, 782 (1934). They are estimated for the appropriate valence states of the elements for single bonds.
If the bond under consideration is in a molecule more complicated than diatomic, the above remarks are only approximately valid (see section 2.4). 2.2. Negative Ions of Doubly Bonded Diatomic Molecules.-A double bond of great interest in radiation chemistry is that of the oxygen molecule. Bates and Masseyg have examined the available data and have proposed two sets of potential energy curves for the ion each of which may be in agreement with the data. The fact that it (9) D. R. Bates and H. S. IV. Massey, Phil. Trans. Roy. Soc., 288, 269 (1943).
NEGATIVE IONFORMATION BY ELECTRON CAPTURE IN NEUTRAL MOLECULES
Feb., 1951
525
TABLE I1 SINGLE BONDDISSOCIATION ENERGIES IN KCAL.MOLE-’ The quantities listed in the sections are successively: 1. Dissociation energy of bond X Y.O 2. Heat of reaction XY e + X- -I-Y.‘ c +X Y-. 3. Heat of reaction XY Br I 0 c1 Y H C N
+
-
+
+
X
103.2 86.7
H
C ~ H84.3‘ B 68.4
CHa 102’ 85.5 86.1 NHI 104” 87.5 49.6 HzO 114 97.5 47.8
C
N
0
OH 103 36.8 86.5 CHIOH 90.2‘ 24.0 74.3
CHaNHz 79’ 63.1 24.6
102.1 14.7 85.6 CHIC1 73’ 14 57
-
83.0 -1.9 66.5 C b B r 68. 5d -16.4 52.6
CHJ 54. Od -27.4 38.1
N2H4 60’ 6 150 95.6 83.8
117.2 51.0
44
-43
-22 57.08 -30.3 52.1 GHsBr 67d 45.44 -35.3 -39.5 51 Br -32.8 18 49.63 CpH5154’ 41.89 35.55 63.4 38 -37.8 -43.0 -45.8 46.9 I -31.8 -39.5 27 -18.0 0 Values for diatomic molecules were obtained from Gaydon. ref. 19; sources for bonds in pdyatomic molecules are E. T. Butler and indicated. b Calculated with electron affinities of Table I. H. A. Skinner, Natwe, 158, 592 (1946). M. Polanyi, Trans. Faraday Soc., 39, 19 (1943). 0 M. Szwarc, J . Chem. Phys., 17, 505 (1949). Adjusted to agree with CHrH. c1
-
-
TABLE I11 cal c-C single bond of ethane is not quite so deep. The threshold energy for electron capture (;.e., APPROXIMATETHRESHOLD ENERGIES FOR ELECTRON CAPE1 EOof Fig. 1) is expected to be approximately TURE BY GASEOUS MOLECULES‘
-
the same for the two cases. Although such threshold energy is generally sufficient for rupture of a Hzb 5 NO* 0 single bond, it usually does not suffice for a double HzO’ 0 HCl’ 0 bond. 02O 0 Cl,d 0.25 2.3. Negative Ions of Other Multiply Bonded SOZ‘ 0 Brt’ .2 Molecules.-There are no reported studies of cop 2 12’ .2 other multiple bonds. I n general, the values of NHsC 0.25 A discussion of the experimental methods and some of neither E1 - EOnor I- (the electron affinity) are the results are found in H. S. W. Massey, “Negative Ions,” greatly different for different carbon compounds, or Cambridge University Press, 1938. Calculation by for the different radicals. The increase in the CEC Hirschfelder. C N .E. Bradbury, J . Chem. Pkys., 2, 827 bond strength as compared with the C-C bond (1934). V. A. Bailey and R. H. Healey, Phil. Mag., 19, 725 (1935). ‘V. A. Bailey, R. E. B. Makinson and strength consequently makes even less likely the J. M. Somerville, ibid., 24, 177 (1937). R. H. Healey, probability for electron capture in a dissociative ibid., 26, 940 (1938). process in such compounds. 2.4. Negative Ions of Polyatomic Molecules.was impossible for them to obtain a unique set of Very few general statements can be made about curves emphasizes the dearth of information reelectron capture in complex molecules and so we garding ions. shall consider the topic only briefly at this point. The feature of interest of 0 2 - for radiation chem- Almost any motion of the molecule involves the istry is that 0 2 (as one may see from the curves of changing of many interatomic separations. ConBates and Massey) captures electrons without sequently, relatively simple potential curves cannot threshold energy. More mention of this will be be drawn. However, in case one atom has considmade later. Also the reaction erably larger electron affinity than any other, it 0 2 e +0 0would seem that capture resulting in formation of its negative ion and dissociation of one of its bonds occurs for certain electron energies. Another example of a double bond of interest in could be approximately represented by a transition radiation chemistry is the ethylenic bond. Mul- to a curve such as the lowest one in Fig. 1. An extiple bonds, because of their greater strength, tend ample of this is an alkyl halide Rx, which should to be more difficult to dissociate than single capture electrons to form X-. Other examples are bonds. This factor may be important in the inROH + e --3 R + OHsensitivity to ionizing radiation of aromatic comRI+ ORZ- or pounds and compounds containing “resonance” R10R2 f e energy. The potential energy curve for the typiRz f O R Molecule
&(e.v.)
+
Molecule
Eo(e.v.1
+
-E
526
JOHN
L. MAGEEAND MILTONBURTON
I n compounds containing many like atoms (e.g. hydrocarbons) and particularly those having resonance (aromatics), electron capture is not expected to result in the breaking of chemical bonds. One can see this qualitatively by noting that the electron tends to be shared by a number of different atoms and thus the forces tending to change the interatomic distances must act on many bonds. Since there is usually energy enough to break a t most one bond and several bonds are involved, no dissociation is expected. 3. Capture Cross Section Because of the Franck-Condon principle, in order for capture to occur the energy of the electron is restricted within certain limits. In Fig. 1, a schematic set of potential curves for the negative ion states of a single bond is given. The value of G2 for the lowest state of the normal molecule AB is shown with the dotted curve; this gives, of course, the relative probability that the normal molecule will be found with a certain internuclear separation. Thus, it is clear that, if an electron is to be captured into the lowest ion state, its energy must be, for all practical purposes, within the limits El and E*. For capture into the higher state, the electron energy must be approximately between E3 and Ed. It is clear, therefore, that the capture cross section must look qualitatively as indicated in Fig. 2.
VOl. 73
spectrum of energies of electrons ejected by high velocity charged particles. The theory of the process is rather rough but it is usually considered more satisfactory than the limited measurements for obtainment of the energy spectrum. It cannot be said that theory and experiment agree; it is better to say that they do not disagree. Table I V gives the secondary electron spectra for incident electrons of several energies. These spectra do not differ greatly. They have approximately the same form for all high energy particles. A typical spectrum has the following characteristics: (a) Half the electrons ejected have energies less than about 5 ev. (b) The average energy given to an electron is about 70 ev. These two facts indicate that the distribution has a long high-energy “tail.” TABLE IV CALCULATED SPECTRUM O F SECONDARY ELECTRONS FROM PRIMARYELECTRONS OF VARIOUS ENERGIES(FROMREF. 4) The figures in columns 2-5 give the percentages of secondary electrons having energies above the values indicated in column 1. Energy of secondary electron6 ev.
0 3.39 6.77 13.54 27.1 40.6 67.7 135.4
10’
100 66.9 49.0 31.1 17.4 12.1 6.6 2.5
Energy of primary electrons, ev.
10’
104
100
100
64.6 45.1 27.4 14.7 10.0 5.4 3.1
62.9 43.9 26.2 14.0 9.7 5.7 2.6
10’
100 61.1 41.6 23.9 12.2 8.2 4.7 2.2
4.2. Effect of Secondary Electrons.-In an energy region in which an ionization process is possible, its cross section is likely to be much higher than any other cross section. It is therefore rather certain that the most energetic electrons will produce much additional ionization. Those electrons having sufficiently high energy will produce several other electrons, the average spectrum of which in the low energy range (Le., below the cut-off set by the energy of the incident electron 0 E1 - Eo E2 - Eo E4 - Eo will be very similar to that of electrons produced by Ea - Eo the original high energy particle. Energy. 4.3. The Low-energy Free Electron Spectrum. previous considerations have made clear Fig. 2.-Electron capture cross section for the molecule AB -Our that only the relatively low-energy free electrons as a function of energy. can be captured. For estimations of capture Various experimental studies on electron capture probability we need a spectrum of electron have been made.’O-14 The numerical value of the energies in the low-energy region (Le., below the cross section tends to be low. For most cases, a t ionization potential of the substance under study). the maximum, the probability that the electron is By “spectrum” we now mean the distribution of captured in a collision is only about one part in l o a energies which electrons have when they first apor lo4. pear in the low energy region (not necessarily the 4. Free Electrons distribution of energies they have when they are 4.1. The Secondary Electrons Formed Di- first produced). Clearly a theoretical or experirectly by the Incident Particle.-Very few satis- mental spectrum is extremely difficult to obtain. factory measurements have been made on the We make the assumption that this net spectrum is the same as the low-energy portion of that of the (IO) N. E. Bradbury, J . Chem. Phys., 2,827 (1934); N.E. Bradburp primary particle described in section 4.1. Although and H.E. Tatel, ibid., 2, 835 (1934). this is only an assumption, it can be supported by (11) V. A. Bailey and R. H. Healey, Phil. Mag.,19, 725 (1935). (12) V. A. Bailey, R. E. B. Makinson and J. M. Somerville, ibid., semi-quantitative appeals to theory, cf. arguments 24, 177 (1937). by Bethe.I6 (13) R. H. Healey, ibid., 26, 940 (1938). (14) H.D.Hagstrum and J. T. Tate, Phys. Rev., 69, 354 (1941).
(15) H. A. Bethe, Ann. Physik, 6, 325 (1930).
Feb., 1951
NEGATIVE I O N FORMATION BY ELECTRON C A P T U R E IN NEUTRAL MOLECULES
We find that an analytical expression which reproduces the low energy spectrum satisfactorily is
ity electrons are not captured in any significant number. Po = f j ( r P ( c ) d c
where c is the energy, f ( c ) is the fraction of free electrons per unit energy interval, and I is the ionization potential of the molecule of the medium. From the definitions it is clear that the integral of f(e) is unity, Le. J j ( € ) dr = 1
(2)
527
(6)
Some experimental knowledge exists of the quantities h(e) and X(e), which determine P ( B )in , equation (3). For the purpose of orientation we consider a very simple case. W e shall find that in any case there i s but little chance of electron capture in this process and that a n elaborate calculation i s unnecessary. Assume that h(e) differs from zero in the low energy region only between E1 and EZand is a constant in this region. That this situation is approximately true is shown by consideration of the cross sections shown in Fig. 2; each area there shown may be taken as rectangular in shape. We also assume for convenience that X(E) is a constant in this region. With these restrictions we can integrate (4)analytically. For electrons initially having the energy EZor greater P(€)= 1 - p3]”’” &
