Trapped Electroiis in Amorphous Solids
3683
rption Spectra of Excess Electrons in Molecular Aggregates. in y-Irradiated Amorphous Solids at 77°K arnasa Shida,” Suehiro Iwata, The Institute of Physical and Chemical Research, Wako-shi, Saitama, Japan
and Tsutomu Watanabe Depsrtmen! of Applied Physics, The University of Tokyo, Tokyo, Japan
(Received U a r c h 10, 1972)
Ptibiization costs assisted by The Institute of Physical and Chemical Research
Absorption spectra of trapped electron have been recorded for the low-temperature matrices of over 40 different molecules and compared with the theoretical spectra derived from a hydrogenic model for the electron. Remarkable agreement between experiment and theory was obtained for almost all the cases. The analysis of the line shape of the observed spectra in terms of the theory provided information concerning the nature of absorption, the binding energy, and the Bohr radius of the electron in the ground state. Some experimental data of interest appearing in the recent literature were also analyzed by the present theory to obtain successful explanations of the observed spectral features.
IntF0dU Cti01Ip It is a striking thing that such an elementary entity as an electron render6 itself sensuous blue color when it is in ammonia OT water. it is natural, therefore, that the previous workers attempted to reproduce theoretically the observed transition energy. l - 4 However, due to the complexity of the system the theoretical treatments were confined within the realm of the assumption that a single Is- to 2p-type transition was mainly responsible for the absorption. Owing to the prominence of the character of the 1s@-type transition for water and ammonia (vide mf-ra) semiquantitative agreements were achieved by the previous theories for the transition energy. However, the characteristically broad and asymmetric absorption line shape has not been W l y accounted for. There has been a longstanding speculation that the broadness and asymmetry are due to the ronfributron of higher Lransitions,1g2 but this has not been rigorously tested because of the difficulty of realistic delineation of the excited electron. Thus, even though one m a y say that “the higher energy levels are only slightly influenced by the form of the potential well a t small distances and can be adequately represented by hydrogen-like states,”I one can not easily estimate, for example, the effective “nuclear charge” felt by the optical electron from the theoretical calculation. In this paper we propose a compromising semiempirical approach based om a hydrogenic model for the excess electron in ~ ~ n d e nmatter ~ e ~ I ~t is found that the proposed theory is applicable t u the trapped electron in y-irradiated frozen matrices of a variety of substances and that pertlnene information of the electronic state is obtained from the comparison between the experimental and the theoretical spectra constructed on the basis of the model. An excess electron in the condensed medium is stabilized by the total p o l ~ r ~ z a t of i o ~the ~ medium which consists of the o ~ j e ~ t ~ t i polarization ona~ of molecules having a permanent dipole moment and the electronic polariza. tion of the rnedrnm molecule. Only the former component
of the polarization provides a persisting potential for the excess electron and the latter follows the motion of the electron self-consistently. This correlation between the excess and the medium electrons prevents derivation of a simple potential energy curve for the excess electron and a segmental description of the energy of the system (excess electron plus medium) is required.’-4 However, since the optical transition energy between the ground (eq 1) and the nth states is related to the total energy of the system relative to a reference energy state 881-44 hvn = En
- El
(1)
one may conceive a n imaginary effective one-electron potential whose eigenenergies are equal to En’s. Obviously, the explicit delineation of such an effective potential is prohibitive. However, if the potential was known, the optical excitation of the excess electron could be treated as a usual potential problem. Schematically, such a potential may be drawn as in solid curves of Figure 1. A reasonable assumption for further steps will be as follows: the ground-state electron confined in a small region may be characterized mainly by the potential at small distances. Conversely, for the excited states the local potential at small distances may not be so influential as quoted above. Then, one may be able to replace the potential curve with a set of approximate potentials as indicated by broken and dotted curves in Figure 1. In this work we employ Coulombic potentials for the approximation. Thus, for the potentials in Figure 1 the approximate curves are represented as -&/r and -Z2/r and so on. Such a truncation of the realistic potential may J. Jortner, J. Chem. Phys., 30, 839 (1959). D. A. Copeland, N. R. Kestner, and J. Jortner. J. Chem. Phys., 53, 1189 (1970). K. Fueki, D. F. Feng, and I. Kevan, J. Phys. Chem.. 74, 1976 (1970). K. Fueki, 5. F. Feng, L. Kevan, and R. E. Ghristoffersen, J. Phys. Chern., 75, 2297 (1971). T. Shida, S. Iwata, and T. Watanabe, lo be sbbmitted for publication
The Joornai of Physical Chemistry, Val. 76, No. 25, 1972
T. Shida, S. lwata, and T. Watanabe
3684
/d=O30
t jAr0.20
A=O.lO
ZdZ, 3 1
ZdZ, =I
ZZ/Zl < 1
Schematic representation of the effective potential for the excess electron. The left ( A ) and the right (C) indicate respectively a potential of a longer and a shorter range than the Coulombic potential at the middle (B). The bottom of the conduction state of the excess electron is taken as the reference energy state. Figure 1.
seem to be too drastic but its justification will be discussed elsewhere.5 Let us assume that the effective charge Zn is related to the actual total energy of the nth electronic state of the system relative to the conduction state4as
En = -Zn2/2n2
(2)
In other words, we regard that the electron in the nth bound state is energetically equivalent to a hydrogenic electron which is in the Coulomb potential of - Z n / r . For the continuum state also we consider a hydrogenic potenZn/Zl tial - Z c / r and, for convenience, call the ratio An and A , E Z,/& the attenuation coefficient. From Figure 1 it is seen that A exceeding unity means that the effective potential in solid curves is of a longer range type than the Coulomb potential and uice uersa. Physically speaking, the medium of polar molecules having a permanent dipole moment will provide a long-range potential whereas in nonpolar molecules the effective potential will quickly tend to zero as indicated by Figure 1C. The main advantage of this hydrogenic model is that one can calculate the transition moment analytically. Assuming, for simplicity, that the coefficient An and A , for all the excited states can be represented by a single value of A , we obtain the following theoretical spectral distribution of the oscillator strength over the whole energy region including the continuum state5
f(Eln) = 283-W(iz2 - l)A5(2 - A)2(n A)2,.-5(~1+
A ) - 2 n - 5 6 ( E- Eln) ='fn6(E - Eln) (3)
df(Eik)/dE =283-nZEA(2 - A ) 2 ( k 2 + A 2 2 2 ) ( 2 2 + P - 5 exp{(-4AZlk) arccot (Z/k)J{l- exp(-27rAZ/k)]-1 (4) which are quite analogous to those for the hydrogenic atom.6 In eq 3 and 4 E is the photon energy and Eln and E l k are the transition energies to the nth bound excited state and to the continuurn state where the ionized electron has the momentum of k.
Ein
=z
Elk
En - EI = ( Z 2 / 2 ) ( 1- A 2 / n 2 ) = EI, - El = 2212 -I- k2/2
(5). (6)
Note that we have dropped the suffix 1from 21. The oscillator strength is further modified by the linebroadening procedure to take into account the statistical fluctuation of the environment of the electron in the condensed mediurn.5 The fluctuation is assumed to obey the Gaussian distribution as The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
Figure 2. Some examples ot the theoretical simulation spectrum. The spectral oscillator strength distribution given by eq 3 and 4 is shown at the bottom of the figure for various values of A. Note that f is dimensionless while d f / d E is given in units of ( Z 2 / 2 ) - ' . The distribution is further line broadened as specified by the value of A l l , to obtain the simulation of the absorption spectrum. For the continuum state the product of d f / d E times AE (in units of Z 2 / 2 ) is regarded as a "line." All the simulation spectra shown in the body of the figure are normalized to the absorption maximum and the energy is given in units of Z 2 / 2 .
df(E)/dE = q Z f n e x p I - 4 E - E I ~ , I R ) ~ I( 7 ) where f n is identical with that in eq 3 for the discrete transitions ( E < Z z / 2 ) and is equal to Idf(E1k)IdE)AEfor the ionization ( E > Z 2 / 2 ) where A E stands for a small energy interval in the continuum state. (Y is related to the half-height width 2A1/2 of the Gaussian distribution as
YZ = exp( - ( Y A I / z ~ ~
(8)
Then, the absorption line shape of the theoretical spectrum (eq 7 ) can be fixed if the values of A , A1/2, and Z are known. Instead of assessing these quantities from the physical consideration we determine them semiempirically; we first construct a set of simulation spectra for a wide range of A and A112 using the "ionization potential," Z2/2, as the unit of energy. From the set of the simulation spectra a best-fit one is searched in comparison with the experimental spectrum. By identifying the observed absorption maximum ibfobsd (in eV) with the peak of the theoretical spectrum at an energy of m ( Z 2 / 2 ) we obtain the value of zz/2in eV as M o b s d / m . Once the values of A , A1/2, and Z are fixed, one can obtain the transition energy for the discrete levels by eq 5, the effective charges Z and AZ, and the Bohr radius of the ground state by rg = I / Z (in atomic units). Some examples of the simulation spectrum are shown in Figure 2 which includes also the spectra before the line broadening. It is seen that as the value of A1/2 increases the structure due to the discrete transitions is smeared out and the band becomes broad and symmetric. For a fixed value of A1/2, the spectrum becomes sharp and symmetric (at the half-heights) as the value of A increases from zero toward unity which is due to the diminution of the contribution from the bound-free transition. It is (6) E. U. Condon and G. H. Shortiey, "The Theory of Atomic Spectra," Cambridge University Press, New York, N . Y . , 1335, p 133; H. A . Bethe and E. E. Saipeter, "Quantum Mechanics 0.1 One- and TwcElectron Atoms," Springer-Verlag, West Berlin, 1357. p 304.
Trapped Electrons in Amorphous Solids
3685
"0
Absorption spectra of et- in paraffins: circles, observed; solid curves, theoretical (cf. entry no. 1-3 in Table I ) . To avoid cornplexity in the figures an obvious abbreviation is made for the chemical formula of the matrix molecule.
_r__l_q___ 2 , ev
1
0
0
"
Figure 3.
noted that although :he absorption ma?imum is roughly at the ionization threshold 2 2 / 2 for all the values of A, the major component of the absorption changes gradually from the bound-free to the 1s-2p-type discrete transition as A increases from zero to unity. In the following sections the spectral data of trapped electrons i n various matrices will be compared with the theoretical spectiurn outlined above. In General Discussion we also compare some experimental data in the literature with the theory. Experimental Section All the samples formed transparent glassy solids at 77°K. Ethers and amines contaminated with stabilizers or decomposed products were purified by contacting them with potassiurn-sodium alloy under vacuum. Aromatic impurities in paraffins were removed by passing through an activated alumina column. The liquid samples were placed in a silica cell of 0.5-2 mm thickness, degassed, frozen a t 77"K, and subjected to y irradiation at 77°K to doses of 5 x 401B t o 5 x 1019 elilg. After the irradiation the sample exhibited an intense absorption due to the trapped electron (abbreviated as et-) in the near-infrared and visible regions which was measured by a Cary 14 RI spectrophotometer. The sample was photobleached partially or totally with light of selected wavelengths (given in the figure caption. The total bleaching left a small residual absorption in the near uv due to unspecified radicals concomitantly produced with the electron. The difference between the absorption immediately after irradiation and the residual absorption was plotted to obtain the net absorption due to et - (open circles in the figures). Similarly, the absorption of partially bleached samples was obtained by subtracting the residual absorption remaining after the subsequent total bleaching. All the observed spectra shown in the figures were normalized to the maximum absorbance.
rbsorption spectra of e+- in ethers. See caption for Fiaure 4. Figure 3 (cf. entry.no. 4-8 in Table I): Experimental Results a n d Individual Discussion
Paraffins. The spectrum of et- in paraffinic glasses has been reported p r e v i o u ~ l y . However, ~.~ the absorption at h > 2 p was not precisely measured because of the background vibrational absorption. We have extended the measurement to the threshold of absorption by using properly thin cells (Figure 3). The curves are drawn by assigning the values of A and A1/2 in Table I to the theoretical spectrum given by eq 7. (In all the figures below open circles represent the observed absorption while the solid curves are theoretical. All the spectral data are compiled in Table I and not all the experimental results will be presented in the figure). With the assigned value of A = 0.2 the observed spectrum should be associated mostly with the bound-free transition (see Figure 2 ) . Hamill proposed that the absorption of et- in 3-methylpentane glasses may consist of the components of a discrete and a bound-free transition of a comparative order of magnitude.9 His argument is based on the anomalous spectral behavior observed for the pulse-radiolyzed 3-methylpentane at low temperatureslO and on the quantum yield of selective photob2eaching.ll However, we consider that the apparent quantum yield may not necessarily be relevant to the discussion on the nature of electronic state of electrons in condensed media because of the possible wavelength-dependent competition between the bleaching (detrapping) and the stabilization (retrapping). As for the cited result o f the low-temperature pulse radiolysis, it is not necessarily convincing in view of more recent reports.12 Ethers. Figure 4 shows the spectra for a series of ali(7) J. B. Gallivan and W . H. Hamill, J. Chern. Phys., 44, 2378 (1966). (8) J. Lin, K . Tsuji, and F. Williams, J. Arner. Chern. Soc., 90, 2766 (1968). (9) W. H. Hamill, J. Chern. Phys., 53, 473 (1970). (10) J. T. Richards and J. K. Thomas, J. Chern. Phys., 53, 218 (1970), (11) D. W. Skellyend W . H. Hamill, J. Chem. Phys., 44, 2891 (1966). (12) N. V. Klassen, H. A. Gillis, and D. C. Walker, J. Chern. Phys., 55, 1979 (1971):
The Journal of Physicai Chemistry, Vol. 76, No. 25, 1972
T. Shida, S. Iwata, and 1.Watanabe
3613 TABLE I:
Observed and Theoretical Spectral Dataa
Entry no.
1
3-Methylpentane
2 Methylcyclohexane 3 3-Methylheptane 4 Methyltetrahydrofuran 5 Ethyl ether 6 Methylal 7 n-Butyl ether 8 Isoamyl ether 9 Diethylenetriarnine 10 lsobutylamine 11 n- I- I soamylamine 12 sec-Butylamine 13 Diisopropylamine 14 Triethyiamine 15 N,N-Dimethylarninopropylamine 16 Methanol 17 Methanolb 18 Ethanol 19 Ethanolb 20 t -Propanolb 21 I-Butanoib 22 2-Butanolb 23 l-Pentanoib 24 Isoamyl alcoholR 25 2-PropanuP 26 Glycerin 27 Ethylene glycol 28 Propylene glycol 29 1,4-ButanedioI 30 1,3-Butanediol 31 2,3-Butanediol 32 Hexylene glyc~l 33 Diethylene glycol 34 Methyl Cellosolveb 35 Ethyl Cellosolweb TetrahydrofurfJryl alcoholb 3 37 n-Propyl Cellosolveb 38 n-Butyl Cellosolve* 39 2- Am~~oe~hanol 40 3-Amino-'I -propanol 41 1-Amino-2-propanol 42 2-(2-Amino-l -ethyiaminoethanol 43
[email protected] 44 Diisopropvlarnim 4- ethanol (1 : 1 ) 45 10 M aqueous KOH 46 10 M aqueous KOHD 47 Single crystal of iceC 48 Methanol 4"Kd 49 Methanol 25"Kd 50 Methanol 51"Kd 51 Methanol 77"Kd 52 Ethanol 53 Ethanol 4'Kd3l
la
Ib
0.700 0.760 0.708 1.030 0.918 1,100 0.825 0.689 1.283 1.290 1.150 1.055 0.825 0.729 0,868 2.390 2.485 2.320 2.360 2.360 2.250 2.290 2.250 2.360 1.930 2.524 2.389 2.290 2.250 2.210 2.213 1.420 2.250 2.160 2.160 2,060 2.160 2.180 1,750 1.600 1.460 1.460 1.240 1.991 2.140 2.300 1.937 2.021 2.157 2.262 2.355 0.818 1.586
0.672 0.845 0.795 0.520 0.51 1 0.624 0.796 0.930 0.842 0.786 0.801 0.583 0.654 0.809 1.048 0.428 0.373 0.607 0.559 0.644 0.666 0.733 0.724 0,775 0.782 0.753 0.590 0.873 0.760 0.841 1.102 1.100 0.795 0.726 0.773 0.898 0.833 0.816 0.777 0.875 1.010 1.075 1.112 0.919 0.434 0.356 0.31 7 0.'721 0.592 0.504 0.455 0.646 1.077
Il a
Ilb
IIC
Illa
Illb
0.20 0.20 0.20
0.10 0.225 0.15
1.300 1.375 1.325
0.537 0.552 0.534
0.201 0.198
2.66 2.63 2.67
0.275 0.25 0.525 0.725 0.40 0.725 0.625 0.30 0.425 0.95 0.96 0.75 0.75 0.65 0.60 0.60 0.55 0.55 0.40 0.45 0.725 0.425 0.65 0.60 0.45 0.40 0.50 0.55 0.475 0.40 0.425 0.375 0.425 0.40 0.35 0.45 0.35 0.40 1.08 1.08 0.85 0.825 0.83 0.83 0.83 0.675 0.60
0.2375 0.175 0.2875 0.2625 0.25 0.1 375 0.1375 0.225 0.2875 0.115 0.105 0.15 0.125 0.15 0.15 0.20 0.20 0.225 0.225 0.20 0.1375 0.2875 0.225 0.25 0.275 0.40 0.25 0.20 0.2375 0.30 0.2875 0.2625 0.2375 0.30 0.40 0.425 0.45 0.35 0.125 0.105 0.070 0.2125 0.145 0.120 0.105 0.1625 0.25
1.325 1.300 1.175 1.025 1.250 0.950 1.000 1.300 1.250 0.800 0.800 0.950 0.925 1.000 1.050 1.075 1.125 1.125 1.225 1.175 0.950 1.250 1.050 1.100 1.225 1.325 1.175 1.1 25
0.623 0.530 1.092 1.258 0.920 1.110 0.825 0.560 0.694 2.987 3.106 2.442 2.551 2.360 2.143 2.130 2.000 2.098 1.575 2.148 2.514 1.832 2.251 2.009 1.806 1.071 1.915 1.920 1.800 1.615 1.728 1.710 1.428 1.255 1.062 1.123 0.870 1.531 3.057 3.285 2.348 2.184 2.465 2.585 2.771 0.818 1.442
0.214 0,197 0.283 0.304 0.259 0.285 0.246 0.203 0.271 0.469 0.477 0.423 0.433 0.416 0.397 0.396 0.383 0.393 0.340 0,397 0.429 0.366 0.406 0.384 0.364 0.280 0.375 0.375 0.363 0.344 0.356 0.354 0.324 0.303 0.279 0.287 0.252 0.335 0.473 0,491 0 415 0.400 0.425 0.435 0.451 0.245 0.325
2.47 2.68 1.86 1.74 2.03 1.85 2.15 2.60 1.95 1.14 1.10 1.25 1.22 1.27 1.33 1.34 1.38 1.34 1.55 1.33 1.23 1.44 1.30 1.37 1.45 1.88 1.41 1.40 1.45 7.53 1.48 1.49 1.63 1.74 1.89 1.84 2.09 1.57 1.11 1.08 1.27 1.32 1.24 1.21 1.17 2.15 1.62
1 .zoo
1.275 1.250 1.275 1.225 1.275 1.375 1.300 1.425 1.300 0.700 0.700 0.825 0.925 0.875 0.875 0.850 1.ooo 1.100
0.198
Iiic
a I iexperimenlal): a, observed absorption maximum in eV ( M o b s d ) : b, relative band width (half-height width v s . Mob&). I I (assigned theoretical spectrum): a, attenuation coefficient ( A ) ; b, line-broadening paramaer in units of Z 2 / 2 AI,^); c, theoretical absorption maximum in units Of Z 2 / 2 ( m ) . 1 1 1 (derived information): a, ground-state energy in eV (Mobad/m zobsd2/2); c, Bohr radius in A (O.%?g/Zobsd). "he sample is partially photobleached. Reference 25. Reference 27. e Curve b of Figure 14. f Curve of Figure 14.
phatic ethers. The structure which gradually fades away with the increase of the paraffinic character of the molecules is e x t r ~ ~ ~ ~compared ~ i n a r with ~ the featureless spec.tra commonly observed for et- in other matrices. From .the set of simulation spectra which covered the range of A = 0.1-1.1 and & / 2 : -- 0.01-0.4 (in units of z2/2) we ?-heJournal of PPtysical Chemistry, Vol. 76, No. 25, 1972
could not find a superposable spectrum except for the n-butyl and isoamyl ethers. The failure of correspondence between the experimental and theoretical spectra could be attributed to one of the two possible reasons below. (I) In the construction of the simulat>ionspectrum we assigned, for simplicity, a single
Trapped Electrons in Amorphous Solids value of A for all the excited states. This may be an oversimplification for some matrices and if we differentiate A according to each electronic state, a better simulation spectrum will he obtained. (2) One of the primary assumptions in the theory is that the electron in the ground state can be approximated by the 1s-type wave function. If the electron interacts with a specific ether bond, the wave function may be distorted from the assumed spherical form and the line shape may be altered accordingly. The proximivy of' A values for n-butyl and isoamyl ethers to those for the paraffins suggests that the general environment of the electron in these higher ethers is similar to that in the paraffins. Amines. The spectra in Figure 5 indicate a rather subtle correlation l)etw+eenthe spectral features and the molecular character. The energy a t the absorption maximum and the band width for the first three primary amines are large compared with the polysubstituted diisopropylamine and triethylamine. sec-Butylamine is the intermediate between the two groups. Also, the spectrum for N , N dimethylamino- n-prop:ylamine seems to be a hybrid of those of triethylamine and the primary amines. Such a correlation has been pointed out previ0us1y.l~From the above result as well as that for alcoholic matrices discussed below i!: may be said that the difference in the functional group of matrix molecule results in the spectral difference and a possible speculation will be made in the next subsection. Monohydrox~,AIcohoIs. Although the spectra of et- in this class of matrix have been observed by many authors,14 the absorption in the near-infrared region has not been carefully measured. As shown in Figure 6, higher alcohols exhibit bumps in this region in addition to the major absorption in the visible. This structure is not of the same nature as that of the spectra for the ethers because the partial bleaching with longer wavelengths ( A >0.7 1) removed the structure ar; shown in Figure 7. Qualitative observations indicate that the infrared band is more easily photobleached than the visible band and that the former is more sensitively removed by electron-scavenging impurities. The dose dependence of the absorption is also different between the infrared and the visible bands, the former being more easily saturated. Because of this complexity we compared the theoretical spectrum only for tnethanol and cthanol which gave no infrared absorption. The comparison was made, however, for all the photobleached samples (Figure 7). The observed difference between the near-infrared and visible bands indicates that there are two types of trap and the shallower ones increase as the alkyl branch becomes larger. It may be speculated that the electrons giving rise to the infrarcd and the visible absorptions are trapped respectively in the regions where the paraffinic and the hydroxyl groups are locally concentrated. Since in suck a higher alcohol as 1-pentanol the bulky alkyl group would prevent the formation of extensive hydrogen network, the eiectron surviving the partial photobleaching will see only dimeric or a t most a few associated hydroxyl groupc. in its vicinity and yet the spectra for the photobleached primar:y alcohols are more or less similar, being in a na.rrow range of 2.2-2.5 eV (Table I). the,,,A, On the other hand, the A,, of the secondary alcohol (2propanol) shift:; remarkably to red as has been observed for the solvated electron in liquid 2-propanol.15 A recent result of pulse radiolysis of 2-propanol a t 77°K indicates
Figure 5. Absorption spectra of et-- in amines. See caDtion for Figure 3 (cf. entry no. 9-1 5 in Table I ) .
Figure 6. Absorption spectra of et- in monohydroxy alcohols. See caption for Figure 3 (cf. entry no. 16 and 18 in Table I ) . Comparison with the theoretical spectrum is made only for methanol and ethanol for the reason stated in the text. I
,
,
,
,
I
I
,
.
,
,
,
1 1 -
Absorption spectra of et- in monohydroxy alcohols after partial photobleaching of t h e irradiated samples. See caption for Figure 3 (cl. e n t r y no. 17-25). A > 0 . 7 p was used for methanol and ethanol and A 3-1 I.( for the rest. Figure 7.
(13) S. Noda, K. Fueki, and 2. Kuri, Chem. Phys. Lett.. 8, 407 (1971). (14) For example, A. Habersbergerova, L. Josirnovic. and J. Teply, Trans. Faraday Soc., 66, 669 (1970) ( 1 5 ) M. C. Sauer, Jr., S. Arai, and L. M . Dorfrnan. J Chem. Phys.. 42, 708 (1965).
The Journal of Physical Chemistry, Vol. 76, No. 2 5 , 1972
T. Shida, S. Iwata. and T. Watanabe
3688
Figure 8. Absorption spectra of e,- in polyhydroxy alcohols. See caption for Figure 3 (ct. entry no. 26-32 in Table I )
that the polar groups are reoriented toward the electron even in the low-temperature glass.16 Referring to these results, it may be conceived that the degree of reorientation is different between the primary and the secondary alcohols owing to the blocking two methyl groups in the latter and that this difference makes the distance between the electron and the polar group of 2-propanol slightly longer which, in turn, causes the spectral red shift. The correlation between the spectrum and the type of the functional group of the amines mentioned above may be similarly explicable. Although the apparent Amax for the primary alcohols are similar as mentioned above, the coefficients A in Table I show a gradual decrease with increasing the size of the alkyl group which implies more contribution of the bound-free transition according to the theory. This is reasonable because the dilution of the matrix with the alkyl group will provide an environment resemblant to the paraffinic matrices where the electron is concluded to suffer mainly the bound-free transition. Table I also shows that the ground-state energy becomes larger (in absolute magnitude) as the primary alcohol becomes smaller which is understandable because for smaller alcohols the stabilization due to the interaction between the electron and the permanent *dipolemoment should increase through the increase of the number of the dipole in the unit volume and through the easier rotation of dipole toward the electron. It is not inconsistent that the Amax remains relatively constant while the ground-state energy increases with the decrease of the molecular size because the reoriented permanent dipole moments remain “frozen” during the optical transition of the electron. Polyhydroxy Alcohols. As shown in Figure 8, et - in the polyhydroxy alcohols did not show the infrared absorption but only a single visible band similar to that observed for the partially bleached monohydroxy alcohols. The result suggests that the phase of the polyhydroxy alcohols is not segregated into the nonpolar and polar regions owing to the abundance of the hydrogen bridges. All the alcohols in Figme 8 except 2,3-butanediol and hexylene glycol have the primary alcoholic group, CH20H. This may be the reason for the spectral similarity between the primary mono- and polyhydroxy alcohols. Ais for the secondary diols, the remarkable red shift for hexylene glycol is similar to that for 2-propanol. However, the shift is not so The Journal of ?hysical Chemistry, Vol. 76,
No. 25. 7972
Absorption spectra of e,- in ether alcohols. See caption for Figure 3 (cf. entry no. 33-38 in Table I ) . Only for diethylene glycol the spectrum immediately after irradiation was compared with the theoretical spectrum. For all the samples the bleaching with >1 p was carried out but t h e result of the comparison with the theoretical spectrum is illustrated only for n-propyl and n-butyl Cellosolves (solid curves for t h e spectra b which are obtained after bleaching with X > 1 p. Spectra c are obtained after subsequent bleaching with 0.6 1.1 > X > 0.4 p ) , The data for the others are listed in Table I . Figure 9.
conspicuous for 2,3-butanediol, and it might be that the vicinal hydroxyl groups accidentally provide a similar environment to the electron as in the primary alcohols. Compared with the monohydroxy alcohols the attenuation coefficients shown in Table I are not so regular. It seems that the presence of the secondary alcohol group in the molecule suppresses the value of A to 0.4-0.45 while the pure primary diols (ethylene glycol and 1.4-butanediol) maintain similar features as the monohydroxy primary alcohols. At present we can only speculate that the inter- and intramolecular hydrogen bridges involving the secondary alcohol group might be responsible for the lower A values. Ether Alcohols. For the partial esters of polyhydroxy alcohols the infrared absorption becomes prominent again as in the cases of higher monohydroxy alcohols (see, e . g . , n-butyl Cellosolve in Figure 9). The infrared absorption manifests a slight structure similarity to the ethers in Figure 4. Thus, it is apparent that in the Cellosolves as in the higher alcohoki the hydrogen bridge between the hydroxyl groups separates the phase into the ethereal and the alcoholic regions to give rise to two types of el - . The absence of the infrared absorption for diethylene glycol in Figure 9 is analogous to the absence of the corresponding absorption in polyhydroxy alcohols. The partial photobleaching with h > I p eliminated the infrared absorption as shown representatively for n-propyl and n-butyl Cellosolves (curves a to b). Successive bleaching with shorter wavelengths (0.4 p < X < 0.6 p) recovered slightly the infrared absorption (curves b to c). Therefore, the electrons trapped in the two different regions seem to go forth and back upon bleaching. Part of the electrons trapped in alcoholic region, however, seems to suffer the photoinduced decomposition~7 KOH
+ e , - 5RO-
C €1
because the recovery of the infrared ahsorption shown in (16) L. Kevan, Chem. Phys. Lett., 11, 140 (1971). (17) T.Shida and W. ti Hamill, J . Amer. Chem. SOL 88. 3689 (1966).
3689
Trapped Electrons in Amorphous Solids
Figure I O . Absorption spectra of e t - in amino alcohols. See caption for Figure 3 (cf. entry no. 39-44 in Table I ) . T h e mixture is 1 : 1 by volume at room temperature. curve c is disproportionately small. The values of A and A 1 / 2 assigned to the spectrum after the first bleaching are close to those for the mono- and polyhydroxy alcohols which indicates that the electrons after the first bleaching are mainly localized in the alcoholic region. The present results of the ether alcohols are consistent with the results of the previous work on the mixtures of methyltetrahydrofuran plus ethanol1* or methanol19 at 77°K which upon irradiation produce two absorption bands characteristic of each component. If the ethereal oxygen was as strong a hydrogen acceptor as the hydroxyl oxygen, the mixtures of the previous work as well as the ether alcohols studied in this work would not be microscopically segregated, so that one would have a single kind of et- as in the polyhydroxy alcohols. Amino Alcoh~ls Contrary to the ether alcohols, the amino alcohols give rise to a single band as shown in Figure 10. Also, a mixture of diisopropylamine and ethanol exhibits only a single band which is an intermediate of the absorption bands of et- in the constituent matrices. In these matrices one can expect four different combinaOH-NH, tions for tlie hydrogen bridges, OH-OH, NH-OH, and NH-NH. If the first pair predominated, the phase of the medium would be segregated into two regions and one might have two distinct absorption bands as in the case of higher alcohols and ether alcohols. The appearance of an intermediate single band suggests that all the combinations participate in the hydrogen network formation so that tlie electron may see a relatively homogeneous medium compared with the higher alcohols. The pairs of 3-amino-1-propanol us. 1-amino-2-propanol and 2-(2-aminoethylamino)ethanolus N-p-hydroxypropylethylenediamine in Figure 10 provide additional examples of the red shift in the matrix having the secondary alcohol group. Aqueous Solution. Figure 11 (upper two spectra) shows the familiar spectrum of et- in the alkaline ice.20 The partial photobleaching makes the spectrum a little sharper and shifts the %max slightly as has been observed previously.2~~22 The sharpening has been taken as an indication of the dispersion of the nature of trap site. In accordance with this interpretation the value of A,,,, a measure of the randomness of trap, decreases slightly upon f,he bleaching (Table I). With the assigned value of A = 1.08 the first excited level should locate near the 2p level of a hydrogenic atom,
4ev
3
1
(single crystal)
1, , , 1.2 1. .9
,
.a
, 2,
.7
.E
,
.5
,
3, .4
,
4ev,
.3P.
Figure 11. Absorption spectra of et- in aqueous systems: upper two, alkaline glassy solid immediately after irradiation and after the subsequent partial photobleaching with % >0.7 p ; bottom, single crystal of ice.25See caption for Figure 3 (cf. entry no. 45-47 in Table I ) .
i.e., about 3" x Z 2 / 2 below the ionization threshold of 2212 (see eq 5 ) . Also, most of the oscillator strength should reside in the first transition, and the contribution of the bound-free transition should be small as has been , ~ the spectra at briefly pointed out by Copeland, et ~ l . (cf. the bottom of Figure 2). This conclusion is in apparent contradiction to the experimental result that the activation spectrum of photoconduction superposes on the optical absorption spectrum over the measured region of 1.9 -3.4 eV.23 However, in a preliminary .experiment on the photobleaching of trapped electron in aqueous alcoholic glasses containing various amounts of potassium hydroxide we found that the efficiency of bleaching increased with the concentration of the salt although the spectral pattern was not much affected by the presence of the additive.24 Since the light used for bleaching corresponded to the absorption due to the 1s-2p type transition, it seems that the 2p electron whether in ice or water-alcohol glasses is released from the trap by some influence of the ionic solute. It is interesting in this context that the result of the study on the single crystal of ice is consistent with the theoretical conclusion above (see bel0w).~5Also, it is interesting that the hydrated electron in water without the .excessive alkaline hydroxide is not apparently photobleachable by the intense laser light.26 (18) L, Shields, J. Phys. Chern., 69, 3186 (1965). (19) K. Sawai and W. H . Harnill, J. Phys. Chem.. 73, 3452 (1969). (20) D. Schulte-Frohlinde and K. Eiben, Z. Naturforsch. A , 17, 445 (1962). (21) B. G. Ershov and A. K. Pikaev, Advan. Chom. Ser.. No. 81, 1 (1968). (22) G. V. Buxton, F. S. Dainton, T,E. Lantz, and F. P. Sargent, Trans. Faraday Soc., 66, 2962 (1970). (23) I. Eisele and L. Kevan, J. Chem. Phys., 53, 1867 (1970). (241 T. Shida and M. Irnamura. u n w b l i s h e d results. (25j K. Kawabata, J. Chem. Phys.: 55, 3672 (1971). (26) G. Kenney-Wallace and D. C. Walker, J . Chem. Phys., 5 5 , 447 (1971).
The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
T. Shida, S.Ivvata, and T. Watanabe
3690
t 1.0
-
L.0.2.
O0.l
I
.
0.3
.
0.4 -%
.
,
05
Figure 12. Plot of the attenuation coefficient A vs. t h e effective charge for the ground state Z. The numbers refer to the entry in Table I .
Absorption spectra of et-- in methanol at various low temperat~res.2~ See caption foi Figure 3 ( c i e n t r y no, 48-51 in Table I ) . Figure 13.
General Discussion Except for the case of ether, the agreement between theory and experiment is satisfactory. One might claim that with two parameters any theory could give as good a result as the present approach. However, the quantities A and b.1,~ are not completely arbitrary and should be subject to some restriction imposed by the physical meaning attached to them: as mentioned above, the attenuation coefficient should tend to zero for the nonpolar matrix such as paraffin and should become larger with the polarity of the matrix molecule. As for A1/2, we expect a higher value for a larger molecule having a n irregular molecular shape. Although we searched a best-fit set of A and A112 purely fmm the graphical matching between the observed and the simulated spectra, the selected values showed some regularity indicative of physical significance. For example, the plot of A against Z shown in Figure 12 demonstrates a relatively smooth sequence of the polarity of the matrix molecule. As will be discussed elsewhere,5 Z also should be subject to a physical restriction of Z 2 5 / 16(1 where ts is the static dielectric constant of the matrix which may be in the range of 2-3 a t 77°K. The Figure 14. Absorption spectra of et- in ethanol at 4”K:i7 a, values of Z ir, Figure 12 are in conformity with this reimmediately after irradiation; b, the component of a photostriction. bleached by light of A 1.2 p ; c, same as a after t h e bleaching. Recently two interesting papers concerning the specDotted curves are e~perimental.~~ Solid curves are theoretical , ~ entry ~ no. 52 and 53 in Table I ) . trum of et - in frozen solids have been p ~ b l i s h e d . ~ ~(cf. Hase, et al., found that the absorption spectrum of et- in We applied our theory to each component and obtained alcohols and ice shows a temperature-dependent change the theoretical spectra in solid curves which are in fair between 4 and 77°K.27 Some of their results are reproagreement with the experimental spectra. Since A112 asduced in Figures 13 and 14 (dotted curves). The spectrum signed to the relaxed trap is still much larger than that for methanolie glasses becomes gradually sharper and for et- in ethanol at 77”K, the component c IS expected to asymmetric as the glass is warmed from 4°K to progressuffer a similar sharpening as shown in Figure 13 when sively higher temperatures (Figure 13). The values of A,/, the temperature is raised toward 77°K. assigned to the observed spectra indicate that the statistiThe second paper of interest concerns the spectrum of cal fluctuation of the environment of the electron is higher et- in single crystals of pure ice (open circles shown at the for lower temperatures. We conjecture that the enhanced bottom of Figure l l ) . 2 5 The simulation curve drawn with rigidity at lower temperatures prevents the reorientation A = 0.85 and A l / z = 0.07 (in units of Z22/2) apparently exof the functional group to the electron and that the elecplains the sharp and partly structured experimental spectron will see a more disordered environment than in the trum. The significantly smaller valne of A1/2, of course, softer matrix. ‘The components of absorption, the dotted curves b and e of Figure 14, have been associated with ( 2 7 ) H Hase, M. Noda, and T. Higashimura, d Ghem Phys , 54, 2975 “~nrelaxed”and “relaxed” traps in the ethanol matrix.27 (1971) The Journal of Physical Chemistry, Yo/. 76, No. 25. 1972
Excess Electrons in Molecular Aggregates implies that the environment of the electron is much more regular in the crystal than in the amorphous glass, The smaller value of A than that for the alkaline ice ( A = 1.08) means less polarity in the crystal which is reasonable because the excessive alkaline hydroxide in the glassy solid would enhance the dielectric constant and lower the rigidity to permit more rotation of water molecule toward the electron. It should be emphasized that Kawabata has found that et- in the crystal is hardly photobleached by
3691
the light corresponding to the absorption on the low-energy side of the spectrum. This result is consistent with our assignment of A = 0.85 which guarantees that the absorption on the low-energy side is mainly due to the 1s-2ptype bound transition.
Acknowledgment. The authors wish to acknowledge the discussions of Dr. M. Imamura and Mr. M. Tachiya.
Electronic Abs rption Spectra of Excess Electrons in Molecular Aggregates.
I I. Solvated Electrons Tadamasa Shida,* Suehiro Iwata, The Inshtute of Physical and Chemical Research Wako-shi Saitama, Japan
and Tsutomu Watanabe Department of Applied Physics, The (lniversity of Tokyo, Tokyo, Japan
(Received March 10, 1972)
Putiiicahon costs assisted by The Institute of Physical and Chemicai Research
Spectra of solvated electrons from various sources have been compiled for analysis in terms of the theory proposed in the preceding paper. The observed absorption line shape has been well reproduced by the theoretical simulation spectrum. In particular, the temperature and the pressure effects on the spectrum of hydrated electron are reasonably accounted for.
Introduction Recent developments in the pulse radiolysis technique have broadened our scope of the solvated electron in liq1~ids.lHowever, the newly observed spectra have not always been fully discussed from the theoretical viewpoint. Since the theory proposed in the preceding paper proved to be successful for the explanation of the optical spectrum of trapped electron in y-irradiated frozen solids,2 we have applied it to the solvated electron in liquids whose spectral data are now abundantly available in the literature. Although the phenomenological agreement with experiments does not prove the uniqueness of the theory, the results in this as well as in the preceding papers should add to the credence of the proposed theory. Discussion on the Individual Spectrum According to the hydrogenic model in the preceding paper, the nature of the medium for the exces5 electron can be characterized by the attenuation coefficient A and the degree of randomness of the trap site A1/2. The values of these quantities are determined semiempirically by superposing the experimental spectrum on the theoretical spectrum which is an envelope of the oscillator strengths for a hydrogenic atom. The effective charge %' for the upper states of the atom is supposed to be properly attenuated as 2' = AZ where 2 is the effective charge assigned to the ground state. By this comparison between the theory and experiment one can deduce the following information an the electronic states: the ground-state energy - Z 2 / 2 relative to a reference energy state, the effective
charge for the ground 5: as well as for the excited states A Z , and the Bohr radius of the ground-state S./Z. In the following we apply the above theoretical analysis to the individual spectrum reported in the literature. Both the theoretical and experimental information will be summarized in Table 1. Paraffins. Gillis, e t al., found for the first time the absorption spectrum of the solvated electron in low-viscosity liquid paraffin^.^ The spectrum observed for liquid propane a t - 185" is reproduced in open circles of Figure 1. A similar pulse-radiolytic experiment by Klassen, e t al., also revealed a similar spectrum for a more rigid paraffinic glass4 (the dotted curve in Figure 1. The original spectrum shown in ref 4 is not corrected for the absorption in the silica cell. The author wishes to thank Dr. Klassen for sending him the corrected spectrum in Figure 1.) The solid curves in Figure 1 are obtained by assigning the values of A and A1/2 in Table I to the theoretical spectrum discussed in the preceding paper.2 Compared with the trapped electron in frozen paraffins2 the values of for the solvated electron in viscous liquids are a little larger which may be attributed to the enhanced thermal fluctuation of the solvents. As in the case of the trapped electron the electronic absorption is mostly associated (1) Ber. Bunsenges. Phys. Chem., 75, 608-714 (1971) (special issue for the excess electron in condensed media.) (2) T. Shida, S. Iwata, arid T. Watanabe, J . Phys. Chem.. 9 6 , 3683 (1972). ( 3 ) H. A. Gillis, I\I. V. Kfassen, G . G . Teather, and K. H , Logan, Chem. Phys. Lett., 10, 481 (1971). (4) N. V. Klassen, H. A. Gillis, and D. C . Walker, J , Chem. Phys., 5 5 , 1979 (1971). The Journal of Physical Chemistry, Vol. 76, No. 25, 1972
