Solvated Electrons in Alkaline Methanol
3765
ct~o~ in$Irradiated Concentrated Alkaline Methanol and no1 Mixtures
. K. Pikaev," P. P. Zhestkova, and G. K. Sibirskaya Institute of Physicai Chemistryof Academyof Sciences of the U.S.S.R., Moscow, U.S S. R. (Received Apni 21 1972)
The properties of solvated electrons (e, -) in concentrated alkaline methanol and water-methanol mixtures with emphasis on their optical absorption spectra, decay kinetics, and yields have been studied by the pulse radiolysis method. In methanol a t [CH30Na] 2 3.5 A4 a maximum (Amax) of e,- optical has an inband is shifted slightly to the shorter wavelengths. In alkaline water-methanol mixtures Am, termediate position between pure alkaline methanol and water. In some cases the optical band of e,also has a shoulder a t longer wavelengths, which seems to belong to a particle of the type Me+. * .e,-. The e,- decay in alkaline methanol occurs in a reaction of pseudo-fipt order; in water-methanol mixtures the kinetics of this process is complex. The rate constants k(H f CH30-) in alkaline methanol es-) in water-methanol mixtures have been evaluated. The first rate constant is equal to and 2k(e,-1.2 x 107 M-1 sec-1; the second is dependent on water content in the mixture, increasing from 5109 - 1 sec-1 for 5.5 M methanolic solution of CH30Na to (3-4) X l o 9 M-1 sec-1 for 6 M aqueous solution of NaOH. The values of G(es-)Emax (emax is Lolar extinction coefficient of e,measured. It has been estimated that in alkaline methanol emax is equal to 9.7 X l Q 3 creased with the growth of water content in the mixture, reaching 1.6 X lo4 M - l cm- for 6 M aqueous solution of NaBH.
+
Introduction It is well known (see, e . g . , ref 1 and 2) that upon irradiation of water, alcohols, and water-alcohol mixtures the solvated electron (e5--) is formed as one of the main products of the radiolysis. However, the properties of this particle have been studied mainly in neutral liquids. In alkaline medium the behavior of e$-- can he quite different in comparison with the neutral medium. R e ~ e n t l y i~t . was ~ found that in water in the presence of ions of alkaline metals the solvated electron seems to form particles of type Me+. .e,- (Me' is a cation). In alkaline alcohols and water-alcohol mixtures this effect has not been studied. This is one of the reasons for carrying out the present investigation. Methanol has been chosen because of better solubility of alcoholate and alkali in this alcohol in comparison with other alcohols. Besides, in the case of alcohols it was f o ~ n d that ~ - ~in alkaline medium G(e,-) and the lifetime of e,- are higher than in neutral medium. In particular, in sufficiently concentrated alkaline solutions G(e,--) is equal to the yield of initial ionization of alcoho1.6,s Further, in alkaline methanol the e,- decay is a pseudo-first-order r e a c t l ~ n ~However, ~ ~ ~ ~ . in alkaline water this process i s more complex (see, e.g., ref 9-11). Obviously, it is interesting to study the possible influence of water addition on the yields and stability of e,- in alkaline alcohol. In our work the pulse radiolysis method with optical registration of short-lived species has been used for the investigation of e,- properties.
-
~ x ~ e r i ~Section e n t ~ ~ The linear electron accelerator U.12 was used as a source of pulse-ionizing radiation. The energy of electrons is 5 MeV and pulse duration is 2.3 x 10-6 sec. The measurement of optical absorption of solvated electrons and thle study of decay kinetics of these species were achieved by a means of the pulse radiolysis apparatus.8 Methyl alcohol used was of Chemically Pure grade and contained about 1.5% water. It was purified by refluxing with 2,$-dinitrophenylhydrazinein the presence of sulfuric
-
acid; then it was twice distilled in a nitrogen atmosphere, middle fractions being retained. Triple distilled water was used for a preparation of the mixtures. Sodium metal, KOH, and RbOH were of Chemically Pure grade and were not subjected to any additional purification. Sodium hydroxide was of Chemically Pure grade and was purified by recrystallization. Alkaline methanol and water-methanol mixtures were prepared by the addition of sodium metal in inert atmosphere or by the dissolution of alkali. Before irradiation the solutions were saturated with argon of Especially Pure grade by prolonged bubbling. The solutions were irradiated in quartz cylindrical cells (volume 2 ml) a t room temperature. The dose in solution along the path of analyzing light was determined by means of a 5 x 10-3 M solution of KCNS saturated with oxygen. The values of the molar extinction coefficient of (CIVS)Zat hmax 475 nm and G[(CNS):!-] were taken to be equal to 7 . 3 X l Q 3 M - 1 cm- 12913 and 2.9 radicals/100 eV.12 The charge collected on a platinum wire in solution or on a metal holder of the cell was used as a secondary standard. The doses per pulse were from 2 to 11krads. K. Pikaev, "Sol'vatirovannyi elektron v radiatsionnoi khimii." lzdatel'stvo "Nauka", Moskva, 1969. E. J. Hart and M. Anbar, "The Hydrated Electron," Wiley-lnterscience, New York, N. Y., 1970. C. Gopinathan, E. J. Hart, and K. H. Schmidt, J. Phys. Chem., 74, 4169 (1970). S. A. Kabakchi and V. N. Shubin, /nt. d. Radiar. Phys. Chem., 4, 1 (1972). S. Arai, A. Kira, and I. Imamura, J. Phys, Chem., 74, 2102 (1970). J. W. Fletcher, P. J. Richards, and W. A. Seddon, Can. ,I,Chem.. 48, 1645 (1970). G. K. Sibirskaya and A. K. Pikaev, Khim. Vys. Energ., 4, 472 (1970). A. K. Pikaev, G. K. Sibirskaya, E. M. Shirshov, P. Ya. Glazunov, and V. I. Spitsyn, Dokl. Akad. NaukSSSR, 200, 383 (1971). M.S. Matheson and J. Rabani, J. Phys. Chem.. 69, 1324 (1965). S. Gordon, E. J. Hart, M,S. Matheson. J . Rabani, and J. K,Shomas, Discuss. Faraday Soc., 85, 1375 (1963). W. C. Gottschall and E. J. Hart, J. Phys. Chem., 71, 2101 (1967). G. E. Adams, J. W. Boag, J. Currant, and B, D. Michael, "Pulse Radiolysis." M. Ebert, et a/.. Ed., Academic Press, New York, N. Y., 1965, p 117. J. H. Baxendale, P. L. T. Bevan, and D. A. Stolt, Trans Faraday SOC., 64, 2389 (1968).
(1) A. (2) (3) (4)
(5) (6) (7)
(8) (9) (10) (11) (12)
(13)
The Journal of Physical Chemistry, Vol. 75. No 25, 1972
A. K.
3766
Pikaev, T. P. Zhestkova, and G.K. Sibirskaya
Results a n d Discussion In the case of methanol containing -1.5% water it was possible to study the properties of e,- at concentration of CH30Na up to -5.5 M . It was found that the maximum ),,A(, of the e,- optical band a t [CHsONa] 2 3.5 M is shifted slightly to the shorter wavelengths. In Figure 1 are compared as an example the e,- optical spectra in neutral methanol and methanol containing 5.5 M CH30Na. The , , ,A values of e,- optical absorption bands in methanol a t different concentrations of CH30Na are given in Table IC. Let us note that in neutral methanol A,, = 640 nm. This agrees with previous measurements (see ref 1). Perhaps, as in the case of hydrated electrons (eaq-),I4 the i s due to the decrease of size of “cavities” in shift of A, which the electrons are localized.
h Irn
Figure 2.
Optical absorption spectra of solvated electron in M solution of RbOH in methano! (n = 0 ) , (2) watermethanol mixture of 1 1 composition (by volume) containing 8 M KOH ( n = 0 2 ) , and (3) 16 M aqueous solution of KOH ( n = 0 4) (1) -8
TABLE II: Characteristics of Optical Absorption Spectra of Solvated Electron in Water-Methanol Mixtures Containing 6 M CH30Na and/or NaOHa
y
ad O f [ ,
,
irw
500
,
,
,
500
,
,
?m
, BOO
933
A, nm
Figure 1. Optical absorption spectra of solvated electron in (1) neutral methanol ( n = 0) and (2) methanol containing 5 5 is the M CH30Na ( n = 0 2 ) Here and in Figure 2 and 3 D, optical density of A,, Influence of KOH or CH30Na on Optical Characteristics of Solvated Electron in Irradiated Methanola
TABLE I :
2.7 M CH3QNa 3 MKOH 3.6 M CH30Na
5.5 M CH30Na
640 f 10 640 f 10 640 f 10 630 f 10 610 f 1 0 ’
1.23 f 0.04b 1.30 f 0.04 1.26 f 0.05 1.28 f 0.05 1.35 f 0.05
a W 1 / 2 means half-width of optical absorption band. bLiterature data (M. C. Sauer, S. Arai, and L. M. Dorfman, J . Chem. Phys., 42, 708 (1965); F. S. Dainton, J. P. Keene, T. J. Kemp, G . A. Salmon, and J. Teply, Proc. Chem. Soc., London, 265 (1964)) for neutral methanol are
t h e foliowing: , , ,A
630-650 n m ; W1,p = 1.29 eV.
Besides the e, - maximum, the optical absorption spectrum of irradiated methyl alcohol containing 5.5 M CH3ONa has a shoulder at the longer wavelengths (see Figure 1). In this system it is a t -670-700 nm. This effect is more distinct in -8 M methanolic solution of RbOH and in water-methanol mixture of 1:l (by volume) composition containing 8 M KOH (see Figure 2). In Figure 2 is also shown for a comparison the optical absorption spectrum of irradiated 16 M aqueous solution of KOH. This spectrum is similar to the spectrum which was reported earlier.43’5 The introduction of water into alkaline methanol (the investigation was carried out with the mixtures in which 6 M Na were dissolved) causes the narrowing the e,- band and the shift of A,,, to the longer wavelengths (see Table The JoUrRa/ Of Physical Chemistry, Vol. 76, NO. 25, 1972
Mixture composition, VOI
%
85% CH30H-15% H 2 0 75% CH30H-25% H 2 0 60% CH30H-40% H 2 0 50% CH30H-50% H 2 0 40% CH30H-60% H 2 0 25% CH30H-75% H 2 0 15%CH30H-85% H 2 0 100% H 2 0 b
Amax,
nm
620 f IO
630 ct: 10 640 f 10 650 f 10 660 f 10 665 f 10 670 f 10 675 Z k 10
WI 12. eV
1.26 f 0.04 1.12 f 0.04 1.04 f 0.04
0.98 f 0.04 0.95 0.05 0.95 k 0.04 0.92 f 0.04
*
0.95 f 0.04
a T h e e,- band in t h e mixture of composition of 40% CH30H and 60% H20 containing 9.2 M NaOH has , , ,A 640 nm and W 1 / 2 = 1.03 eV. * Literature data (E. J. Hart and J. W. Boag, J . Amer. Chem. Soc., 84, 4090 (1962); J. P. Keene, Radiat. Res., 22, 1 (1964)) for neutral water are the following: , , ,A 720 nm and W1/2 = 0.92 eV.
11). Similar phenomenon was described earlieri6 for neutral water-methanol mixtures. Because of this effect the overlapping of the e,- maximum and the shoulder under consideration takes place with the increase of water content in the mixture. In particular, the shoulder is not observed in the mixtures in which the concentration of water is equal to 40-60 vol 70.In the spectra o f alkaline mixtures of composition o f 75-85% HzO and 25-15% CH30H (by volume) and in 6 M aqueous solution of NaOH there is a bend in the region 700-750 nm. The optical absorption spectra of alkaline water-methanol mixtures are shown in Figure 3. The maximum and the shoulder (or the second maximum in highly concentrated alkaline solutions) seem to belong to the two different species. By analogy with alkaline aqueous solutions4 it can be supposed that the shoulder (or the second maximum) under consideration is due to the particle of type Me+...e,-. The solvated electron in methanolic solutions of CH3ONa over the whole studied range of concentrations (to (14) M. Anbar and E. J. Hart,J. Phys. Chem., 89, 1244 (1965). (15) S. A. Kabakchi, Khim. Vys. Energ., 5, 180 (1971). (16) S. Arai and M . S. Sauer, J. Chem. Phys., 44, 2297 (1966).
Solvated Electrons in Alkaline Methanol TABLE Ill: Observed Rate Constants k' of e,Alkaline Methanola
Decay in a8
k ' , sec-'
x
Solute
2.7 M CHt30Na 3.0 M CH30Na 3.0 M KOH 3.3 M CH30Na 3.6 M CH30Na
Solute
jo-4
-
k', s e c - l x 10-4
356 9.8
7.0
9.3 8.6
The precisiori of k' measurements is equal to f20%. from ref 8.
a
6.3
3.7 M KOH 4.4 M CH30Na 5.0 M CH30Na 5.5 M CH30Na 7 8 M RbOH
9.8
7.8 7.4
-
ao 04-
302-
6.1 4.0
0-
* Value taken -02
-
-n& -
-5.5 M ) decays during the process of pseudo-first order. The observed rate constants h' of this process are given in Table 111. Usually the e,- decay was monitored at 600 nm. The kinetics was also measured by using the wavelengths 525, 700, and 800 nm, when identical results were obtained. The rate constants are independent of the dose per pulse (it was changed from 2 to 11 krads). From this it follows that the e,-' decay reactions of second order are practically absent. Hence it may be concluded that in alkaline methanol the role of reaction l under studied cone,- i- es- C 2CH3OH--+ H 2
+ 2CH30-
(1)
ditions is negligible. Obviously, the es - disappearance during the process of pseudo-first order is mainly due to the reaction of the solvated electron with methyl alcohol
+ C H 3 0 H + H + CH3O-
e,-
(2)
Earlier8 it was found that the rate constant of the e,decay in alkaline'methanol is independent of the concentration of 'CH3,ONa and KOH over the range of concentrations 0.1-.2 and 0.1-1.5 M. respectively. Under such conditions it is equal to -2 x lo5 sec-I. Fram this it was con8 x l o 3 M - l sec-l. This value is close cluded that kz to the rate constant of the reaction of the solvated electron with ethyl alcohol, which is equal to (7-10) X lo3 M - 1 sec-1,6.8 but i s much higher than the rate constant of the eaq- reaction with water (16 M - I s ~ c - ~ ) From .~? the results of the present work it follows that the rate constant of the e,- decay in more concentrated solutions of CH30Na or KOH is noticeably less than the k 2 value. This effect can be explained by the competition of reactions 3-5 in such solutions.
-
H
+ CH313H-+ Hz C
H
+ cHa0-
---*
H -k C H & - e , - -
CH2OH
(3)
Hz i- C H i 0 -
(4)
iCH30H
(5)
Let us assume that e,- reacts with CH30- ions much slower than with CH:gOH and that h3 = hq. Then h' is approximately equal to
From eq 6 and the experimental dependence of h' values on CH30- concentration the rate constant of reaction 5 can be evaluated. In the calculations it is proposed that the k3 values in methanol and water are identical (in the case of water k 3 i s known and equal to 1.6 X lo6 A4-l sec From this one obtains ks 1.2 X 107 M-1 sec -1.
-
1
-06
A, nm Figure 3. Optical absorption spectra of solvated electron in ( 1 ) 6 M aqueous solution of NaOH (n = 0 ) , water-methanol mixtures (volume per cents) in which 6 M Na was dissolved ( 2 ) 85% H20-15% C H 3 0 H ( n = 0.15), (3) 75% H20-25% C H 3 0 H ( n = 0.3),(4) 60% H20-40% C H 3 0 H ( n = 0.45),(5) 50% H20-50% C H 3 0 H ( n = 0.6), (6) 40% H20-60% C H 3 0 H (n = 0.75), ( 7 ) 25% H2O-75% C H 3 0 H (n = 0.9),(8) 15% H2O-85% C H 3 0 H ( n = 1.05), and (9) 9.2 M solution of NaOH in the mixture of composition 40% CH30H-60% 1-120 ( n = 1.2).
This approximate value is close to the rate constant of similar reaction in water H+OH--ee,,+H20 (7) which equals (1.8-2.3) x lo7 M - I sec-l. 9 ~ 1 7 Another possible reason for the h' decrease in concentrated methanolic solutions of CH30Na is the formation of the particle of type Me'. *e,- and the presence o f equilibrium
-
+
Me+. e,- s Me' e,(8) Such an equilibrium was postulated in the work4 on concentrated alkaline aqueous solutions. However, in our case the Me+ concentration is not so high; because of this the concentration of Me+. e,- is comparatively low, and such particles do not have any noticeable effect on the rate of the e,- decay. This conclusion is confirmed by the identity of the rate of the e,- band disappearance over the range of wavelengths 525-800 nm. The half-life ( t l l z ) of solvated electron in alkaline water-methanol mixtures containing 6 M CH30Na and/or NaOH is d.ependent on the mixture composition. At first t1/2 increases with increasing water content, reaching the maximum value in the mixtures whSch contain 40-60 vol 70 water, then t l / 2 decreases. The values of t l l 2 are shown in Figure 4. The kinetics of e,- decay in alkaline water-methanoi mixtures which were studied is complex. In mixtures containing up to 25 vol % water the observed rate constant of this process is practically independent of the dose per pulse (or on initial optical density DO of solution within the e,- band). At the higher water content siich a depen-
--
(17) E. J. Hart, S. Gordon, and E. M. Fielden, J . Phys. Chem., 70, 150 (1966). (18) P. Neta, R. Fessenden, and R . H. Schuler. J. Phys. Chern., 75, 1654 (1971). The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
A. K. Pikaev, T. P. Zhestkova, and
3768
TABLE I V :
Values
G. K. Sibirskaya
of h ~k,e r f / € ,a n d 2k11for Alkaline Solutionsa ~
Composition of system0
Value of t used at 600 nm,c .M-'crn-'
k l , sec-'
5.5 M solution of CH30Na in C H 3 0 H 85% CH30H-f5% H20-6 M Na 75% CH3QH-25% H 2 0 - 6 M Na 60% CH$3-l-40%H 2 0 - 6 M Na 50% CH3OH-50% H20-6 M Na 40% CW3QH-60% H2O-6 M Na 2 5 % CH30H-75% H 2 0 - 6 M Na 15% CH30H-85% H20-6 M Na
(6.1 f 1.3) X i o 4 (5.7 rt 1.2) x 104 (3.2 f 0.7) X l o 4 (3 rt 2) x 104 (2.9 f 1.5) X i o 4 (1.5rt 1.1) x 104 ( 3 f 2) x 104 ( 1 . 3 4 0.7) X l o 4 (1.5 f 0.6) X l o 4 (5 A 4) x 1 0 4
40% CH30H-.60% H2Q-9.2 M NaOH 6 M solution of NaOH in H 2 0 d
(1.1 rt 0.6) x 105 (8 f 3) x 105 (1.7 f 0.4) x 105 (2.2 A 0.6) x 105 (2.6 f 0.4) X l o 5 (1.0 A 0.4) x 105 (1.2 f 0.2) x 106
Decay was monitored at 600 nm; experimental results were treated by a method of the least squares. in text of the paper. a k e P f for this system includes rate constants of some reactions (see text).
2kl7, M - ' sec-'
-
1.1 x 104 1.1 x 1.3 x 1.4 x 1.4 x 1.3 x 1.4 x
17.2 f 0.7)x 109 (9 f 3) x i d 8 ( 2 . 2 rt: 0.5) x 109 (3.1 0.8)x 109 ( 3 . 6 f 0.8) x 109
io4 104 104 104 104 104
(1.31 0 . 5 )
Volume per cents.
x 109
Choice of e is discussed
-
4s
:
I
I-
40
L, 0
I
20
I
I
40
I
I
60
1
I
a0
I
I
I_i_L_ii
66 0 7 08 09
05
f00
cuntent of d e z , vue. % Figure 4. Half-life ( t l p ) of solvated electron in 5.5 M solution of CH30Na in methanol and water-methanol mixtures in which 6 M Na was dissolved (the composition is given in volume per cent) and 6 M aqueous solution of NaOH. The dose is 2-2.5 krads per pulse; the decay was monitored at 600 n m . dence takes place. In this case the decay curves were treated by the method of normalized concentrations which was used in worklg during the study of the decay kinetics of hydrated electron in irradiated crystalline ice. Under some conditions this method gives the possibility of the determination of rate constant of first- (or pseudo-first) order reaction (e g., rate constant of the e,- reaction with solvent or impurity) and effective rate constant of secondorder reactions. In the case of the e,- decay the determination of such constants is based on the graphical solution of the equation
where hi is the rate constant of first- (or pseudo-first) order reaction, [e,-]o is the initial concentration of eq(z.e , at time t = 0) and h e f f = 2 , = ~ ~ h ~ ( [ x , ] / [ e , -( ]k~, )is the rate constant of second-order reaction of solvated electron with radical x,). Equation 9 i s true if only a small fraction of solvated electrons decays during the pulse. Obviously, DO can be taken instead of [e,-]o. Then
where t is molar extinction coefficient of solvated electron and 1 is optical path length. The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
a4
'-d3'
47
Figure 5. Dependence of v on D o ( A 600 nm) for t h e mixture 2 5 % CH30H-75% H 2 0 (volume per cent) in which 6 M Na was dissolved. In Figure 5 is shown as an example the dependence of v = -d/dt(D/Do)lt=o on DO ( A 600 nm) for the alkaline mixture of composition 25% CH30H and 75% 1420. The calculated values of k.1 and k,tf/c (in the experiments 1 was equal to 2 cm) are given in Table IV. For the alkaline water-methanol mixtures k,t I is, most probably, the rate constant of reaction e,-
+ e,- + 2CH3OH (and/or 2Hz0) Hz
+ 2CH3Q
-
(and/or 2 0 H - )
(11) i.e., heff 2h11. The QH radicals formed from water or the products of their ionic dissociation (0- radical ions) react with methyl alcohol
-
OH (or 0 -)
-
+ CH30H -+HzO (or OH -1 -+ CH20H
(12)
and the resulting radicals are relatively inert toward solvated electrons.2o For the determination of 2 k l l it is necessary to know the t values. The latter were evaluated from the values of G(es-)t (see below). The values of 2hll calculated by such a manner are given in Table IV. From this table it is seen that 2 h l l is increased with the growth of water content in the mixture. Because of relatively high rate constant h' in alkaline methanol it is impossiblc to determine the value of 2 h l l for this system a t the doses used. However, from the data on kinetics of the es- decay in alkaline water(19) T. E. Pernikova, s. A. Kabakchi, V. N. Shubin, and P. / . Dolin, Radiaf. Eff., 5, 133 (1970). (20) M. Anbar and D. Meyerstein, Trans. Faraday Soc., 62, 2121 (1 966).
Solvated Electrons in Alkaline Methanol
3769
methanol mixtures it can be concluded that in methyl alcohol containing 5.5 M CH30Na 2 k l l 5 lo9 M - l sec-l. For the determination of the exact value of this constant it is necessary to use the higher doses per pulse. Obviously, the upper limit of 2kll values for alkaline mixtures of composition 75-85’70 CH30H and 25-15% H2O is the same. E a r l i e F it was estimated that the value of 2hll in weakly alkaline methanol is equal to (6.6 f 4) X 109 M-1 sec-l. The decrease o f 2hll in concentrated alkaline methanol may be due to the increase of viscosity of the system. Alkaline mixture of composition 85% water-l5% methanol-6 M NaOH contains -4 M methanol and more than 40 M water. Therefore it is reasonable to assume that the value of 2 k l l is the same for this mixture and 6 M aqueous solution of NaOH. In water a t pH 10.9-13.3 2hll = (0.9-1.26) r: loxo M - l bec-1.9-11 Our value (-3.6 X lo9 M - l sec-l) is much less. Apparently, this effect is due to the increase of viscosity of concentrated alkaline aqueous solutions. It must be noted that a similar effect was observed earlier22 for the rate constant of recombination of radical ions (CNS)2 - in aqueous solutions of KCNS. In alkaline aqueous solutions in the absence of alcohol the predominant second-order processes of eaq- decay are the reactions 11and 13 eaq - 4- 0 -
+
02-
(13)
In this ease (14)
Dependence of G(es-)cmaxfor solvated electron in methanol on concentration of CH30Na at the dose 5 krads per pulse. Figure 6.
since in our experiments the width of irradiated layer of liquid was less by a factor 1.5-2 than the range of electrons. Taking into account the increase of the density of solutions with the growth of CH30Na concentration it has to give the increase of the dose at equal currents per pulse. In Figure 6 is shown the dependence of G(e,-)tmax on CH30Na concentration a t equal doses per pulse and with the corrections taking into account the e,- decay during the pulse. In these calculations of dose a correction was applied for the difference between the densities of the solutions under consideration and the solution of KCNS which was used in dosimetry. It was taken that the dose is proportional to the density of solution. The corrections for the e,- decay during the pulse were calculated by a means of the equation
Obviously, in alkaline water [O-]o/[eaq-1o = Go-/(& 1.. Geaq-). lit can be taken in the first approximation that this ratio of yields for 6 M aqueous solution of NaOH is equal to the ratio for water a t pH 13. For water a t pH 13 the ratio under consideration is equal to 0.8-0.9.9,23 If we assume further that the value of 211211 is the same both in the mixture of cornposition 85% water-15% CH3OH, in which 6 M Na were dissolved, and in 6 M aqueous solution of NaOH, then k13 1.3 x 1O1O M-I sec-l. In water at pH 13 1213 = 2.2 X1O10 M - I S ~ C - ISimilar . ~ results were obtained by using the method of linear anamorphoses of kinetic curves. From the initial slopes of plots l / D t us. t at doses -10 krads per pulse it was found that keff = 1.4 X 101oM-lsec-l. Hence k 1 3 -1.2 x 1OlOM-lsec-1. The kinetics of disappearance of the optical absorption a t wavelengths corresponding to the maximum of e,band and to the shoulder (or to the second maximum) is the same even in -8 M methanolic solution of RbOH and in. the mixture of c.:omposition of 40% CH3QH-60% H2O (by volume) containing 9.2 M NaOH. However, in other work4 it was found that the kinetics is different in the case o f 14.5 M aquebus solution of KOH. Apparently in the systems which ‘were investigated by us the concentration o f formed particle!$ which are responsible for the additional optical absorprion is relatively low. and they do not affect appreciably the kinetics of e,- decay. The values of G ( e , - ) c , , , is molar extinction coefwere measured for concentrated alfiicient of e,- at),,,A, kaline methanol and water-methanol mixtures. In the case of methanolic solutions of CH30Na the initial optical density a t the maximum of e,- band for the same electron current per pulse increases by -220% in 5.5 M methanolic solution of CH3ONa in comparison with 2.9 M solution. However it is not equivalent to the increase of G(e,-)
-
where D’ is the observed optical density of solution at A,,, immediately after the pulse, DOis the optical density with such a correction, k’ is the observed rate constant of e,decay (sec-I), and is the duration of the pulse. The data on the values of G(es-)tmaxfor water-methano1 mixtures are given in Table V. In calculations of these values the corrections taking into account the difference between the densities of mixtures and the decay of solvated electrons during the pulse were applied. The values of G(es-)tmax were obtained at the doses 2-3 krads per pulse. At such doses the plot In Dt us. t is a straight line. The 12’ values which were found from such plots were used for the calculations of corrections associated with the e, decay during the pulse. From Figure 6 is seen that G(es-)tmaxfor the methanolic solutions of CH30Na does not depend significantly on the concentration of methylate over the concentration range under investigation. Ions CH30-- which are the scavengers of positive ions CH3OH2+
-
C H 3 0 - f CH30H2+
2CH30H
(16)
suppress the process of geminate recombination occurring in “spurp,”5,6,8 e,-
+ CHsOHz+
-
H C CH&H
(17)
It should be noted that CH30H2t is formed from parent (21) J. W. Fletcher and P. J. Richards, Can. J. Chem., 49, 2275 (1971). (22) T. P. Zhestkova, A. K. Pikaev, and V. I . Spitsyn, Doki. Akad. N a u k SSSR,204,1147 (1972). (23) E. M. Fielden and E. J. Hart, Radial. Res.. 32, 564 (1967). The Journal of Physical Chemistry, Voi. 76, No. 25, 1972
A. K. Pikaev, T. P. Zhestkova, and
3770 TABLE V:
G.K. Sibirskaya
Values of G(es-)€max, G(es-), and tmax for e 8 - in Alkaline Water-Methanol Mixturesa
Mixture composition, VOI %
4.2 x 4,4 x 4.6 x 5.1 x 5.0 x 6.0 x 6.3 x
5.5 M CH30Na in C H 3 0 H 85% C H 3 0 H - 1 5 % H2O-6 M Na 75% t%30H-25% H20-6 M Na 60% CH&H-40% H2O-6 M Na 50% CH3oH-50% H z 0 - 6 M Na 40% cH3oH-60% H2O-6 M Na 25% CH30H-75% H2O-6 M Na 15% CH30H-85% H2O-6 M Na 6 M NaOH in W 2 0 40% cH30H-60% H20-9.2 M NaOH a
Precision of G(e,-)ema,
measurements is equal to *IO%.
b
+ CH30H -,CH3OH2+ + CH30
Choice of G(e,-)
(18)
(19)
Therefore a positive “hole” in methanol consists of CH3OH2f and CHzQH or CH30. Because of this the solvated electrons can undergo geminate recombination also with CH30 radicals (CW2QH radicals are relatively inert toward e,-2o) Blr- 4CH3O CH30(20) -+
However, in alkaline solutions the radicals CH30 are transformed into radical ions CH20-
+ CH30-
-+
CH20-
+ CH30H
(21)
According to W O in ~ ethanol P ~ the rate constant of reaction of type 21 is >8 X l o 7 M - I sec-I. The radical ion CH20- should be less reactive toward es- than even the radical CH20N. Besides, it is not excluded that kzo is less than k17. Obviously, at sufficiently high concentrations of CH30- reactions 17 and 20 must be suppressed completely, and G(e,-) has to be equal to the yield of initial ionization of alcohol. Since G(e,-)emax in the concentration range under consideration does not depend on CH30Na concentration, it is reasonable to assume that under such conditions reactions 17 and 20 are suppressed completely. The yield of initial ionization of methyl and ethyl alcohols is equal to 4.3 ions/100 eV.63,25,26From this it follows that the molar extinction coefficient of solvated electron in alkaline methanol is 9.7 x lo3 M - l cm-i. This a ,t, ,A is much less than the,,,X, value 1.7 x lo4 M - l cm-1 for neutral methanol measured earlier in Our value of Amax is confirmed by the following facts. First, recentlyz8 it was found that the molar extinction coefficients of trapped electrons in glassy methanol, ethanol, and 2-propanol a t 77°K are characterized by the relatively low values (-4 x 103 1M-l e m - l a t Arnax. Second, the G(es-ltrnax value for alkaline water-methanol mixtures is increased with the growth of water content in the mixture (see Table V). For 6 M aqueous solution of NaOH G(eaq-)ernaxis equal to 5.6 x l o 4 electrons/100 eV M-1 c m - l . Let us propose that G(e,,-) is the same both in water at p H 13 and in 6 M aqueous solution of NaOH. According to work23 in water at pH 13 G(e,,-) taking into account reaction 7 is equal to 3.6 electrons/100 eV. Then the molar extinction coefficient of hydrated electron a t Amax in 6 M aqueous solution of NaOH is 1.6 X lo4 M - l The Journal of Physical Chemistry, Voi. 76, No. 25, 1972
104 104
104
6.1 X l o 4
CHsOHf -I- CH30H+ CH30H2+ + CHzOH
CH30
104
7.0 x 104 5.8x 104
positive ion C&OH+ by reactions
CH30H-t
4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 3.6 4.3
104 104 104
9.7 x 1.0 x 1.1 x 4.2 x 1.2 x 1.4 x
103 104 104 10A 104
I 04
1.5 X l o 4 1 . 6 x 104 1.6 X l o 4 4.4 x 104
values is discussed in text of the paper.
cm-1, This coefficient for neutral water is equal to (1.61.8) X l o 4 M - 1 cm-1.23329 Let us note that in concentrated alkaline aqueous solutions tniaXhas to be slightly less. From other work14 it follows that e for 15 M aqueous solutions of KOH or NaOH is equal to 90-9370 of the extinction coefficient for neutral water. Since the mixture of composition 85% water-15% CH3OW (by volume) in which 6 M Na were dissolved contains only about 4 M CH30H, it may be taken that tmax for this mixture is the same as for 6 M aqueous solution of NaOH. Then G(e,-) in this mixture is equal to 4.3 electrons/100 eV. Hence, in the mixture under consideration there is the increase of the yield in comparison with 6 M aqueous solution of NaOH. Such an increase can be explained by suppressing reaction 13, which occurs in “spurs,” with methyl alcohol. In this mixture the only process occuring in “spurs” i s the reaction eaq-
+ eaq- + 2HzO +Hz
-t2OH-
(22)
In the case of neutral and slightly alkaline water G H = ~ 0.4-0.45 molecules/100 eV.30 In 6 M aqueous solution of NaOH the role of reaction 22 in “spurs” must be less than in neutral or slightly alkaline water, since in concentrated aqueous solution of alkali the rate constant of reaction 22 is lower. From this it may be concluded that the maximum value of G(e,,-) is within the limits of 4.3-5.2 electrons/100 eV. Let us note that the maximum value of the electron yield for concentrated alkaline and acid aqueous media, which has been r e p 0 r t e d , ~ l . 3is~ equal to 5.0-5.1 electrons/100 eV. In accordance with the described data it may be taken that for alkaline water-methanol mixtures G(e,-- ) is also equal to 4.3 electrons/100 eV. The values of ellid, calculated on this basis are given in Table V. J. W. Fletcher, P. J. Richards, and W. A. Seddon, Can. J , Chem.. 48,3765 (1970) G .R. Freeman, “Actions Chimiques et Biologiques des Radiations,” 14 Serie, M. Haissinsky, Ed., Masson et Cie, Paris, 1969, p 73. S, J. Rzad and J. H. Fendler, J . Chem. Phys., 52, 5395 (1970). M. C. Sauer. S. Arai, and L. M. Dorfman, J. Chem. Phys., 42, 708 (1965). 2. A. Sinitsina and Kh. S. Bagdasar’yan, Khim. Vys. Energ, 5, 140 (1971). J. Rabani, W. A. Mulac, and M. S. Matheson, J. Phys. Chem., 69, 53 (1965). A. 0.Allen, “The Radiation Chemistry of Water and Aqueous Solutions,” Van Nostrand, Princeton, N. J., 1962. G. V. Buxton, F. C. Cattell, F. S. Dainton, T. E. Lantz, and F. P. Sargent, “International Discussion on Progress and Problems in Contemporary Radiation Chemistry,” Vol. 2, J. Teplp. et ai., Ed., Prague, 1971, p 295. E. J. Hart, ref 31, p 326.
Excitons Boidnd to Ionized Impurities Therefore wur experimental data testify that the properties of solvated electrons in strong alkaline methanol and strong alkaline water are different. The main differences aire tile f o l l o ~ n g : the extinction coefficient of e,- in methanol is appreciably less than in water and the recombination of e,- in alkaline water occurs faster than in alkaPine methanol. These differences are gradually removed
3771
with the increase of water content in the water-methanol mixtures.
Acknowledgments. We wish to express our indebtedness to A. Kulakov and A. Konopeshko for careful Linac operation and Dr. P. Glazunov and E. Shirshov for maintenance of electronic equipment.
Excitons Bsun to Ionized Impurities in Inorganic Crystals lkQIllQSS
Laboratoirre de Spectroscopie at d’Optique du Corps Solide.’ lnstitut de Physique, Strasbourg, France (Received April 21, 1972)
Pekeris’ method for helium atom generalized recently by Frost for the three-particle systems has been developed extensively to apply to excitons bound to ionized impurities in inorganic crystals. Haken’s exciton potential, where the dielectric constant between the two particles is a function of the interparticle distance, the optical and static dielectric constants, the electron and hole effective masses me* and mh*, ,respectively, and the longitudinal vibrational frequency of the lattice, has been generalized for the three particles. This potential shows the important effect of the polarizability. A considerable long recursion jrelation of 57 terms has been derived. In exciton-ionized-donor complexes, the binding energy of the system is a function of the mass ratio rne*/mh*. This complex has been studied for real systems such as CMS, ZnO, CuCl, CuBr, CUI, ZnSe, ZnTe, CdTe, S i c 6H, TlCl, and TlBr. The agreement with experiment is better than that obtained by the previous authors where the polarizability has been neglected. The calculations have also been carried out for exciton-ionized acceptor. In this case the results are given in terms of the mass ratio mh*/me*. For known inorganic crystals, this mass ratio is usually high, and consequently it is highly improbable to find such a stable complex for these crystals.
Introduction In inorganic crystals, experimental evidence2 has shown the existence of excitons bound to ionized donors, It is of interest to carry out some exact calculations for these complexes. The method given by Pekeris3 for the helium atom and generalized recently by F r ~ s t for ~ - the ~ threeparticle system has been developed further. Haken’s exciton potential7 in which the effect of the polarizability is included has been used in these calculations. For excitonionized-donor conqdexes the results are given in terms of the mass ratio F = mr*/mh* where me* and mh* are the effective masses of the electron and the hole, respectively. I n the case of the exciton-ionized-acceptor complexes the binding energies are function of the ratio 6, = mh*/me*. Comparison with experiment is also carried out for some real systems.
Farm of the Potentia As described by I4aken,7 the dielectric constant K(i-23) between the hole and the electron of a delocalized exciton iis tl function2 of the distance (i-23) separating the two particles, of their effective masses, of the optical ( K O )and the static (K,)dielectric constants, and of the longitudirial vibrational frequency ( w ) of the lattice. As atomic units in terms of a. certain effective dielectric constant K e r f are usually adopted, the generalized Haken’s poten-
tiaP for any two particles i and J of effective masses mi* and mj* in a crystal can be written in the following form
with
For the complex exciton-ionized donor given in Figure 1, (1) Research group associated with the Centre Nationale de ta Recherche Scientifique (CNRS), France. (2) For full review on the experimental evidence of exciton-ionizeddonor complex, see the references given in S. G. Elkomoss, Phys. Rev. 5,4, 3411 (1971). (3) C. L. Pekeris, Phys. Rev., 112, 1649 (1958). (4) A. A. Frost, J. Chem. Phys., 41,478 (1964). (5) A. A . Frost, M. Inokuti. and J . P. Lowe, J. Chem. Phys., 41, 482 (1964) (6) A. A. Frost, D. K . Harris, and J. D. Scargle, J. Chem. Phys., 41, 489 (1964). (7) H . Haken, Z. Naturforsch. A , 9, 228 (1954); “Halbleiter Probieme,” Vol. I, W. Shottky, Ed. Vieweg, Braunschweig, 1954, p 72: “Halbleiter Probleme,” Vol. II, W. Shottky, Ed., Vieweg, Braunschweig, 1955, p 1; J. Phys. Radium., 17, 826 (1956); J . Chin?. Phys., 55, 643 (1958): J. Phys. Chem. Solids, 8, 166 (1959). ~
The Journal ot Physical Chemistry, Vol. 76, No. 25, 1972
