Optical Excitation Energy of Solvated Electrons of gy,. In contrast to the high mobilities of AgX2- and X - in AN, those of acetate and benzoate homoconjugates are much smaller, XO of H2(0Ac)3- = 74 and XO of H(Bz)2- = 45 26 as compared to Xo(OAc-) = 107 and Xo(Bz-) = 62.25 This indicates much stronger solvation of HX2- in AN than of X- or 05' AgXz-. There is a n indication from the data in Table a that values of Kd(Ag(HX)2X) and Kd(AgHX2) ( X - - =: acetate, benzoate) are a t least 100 times larger than the corresponding values of Kd(AgX) in AN. Unfortunately, values of Kd(AgX) could not be deter-
7
mined accurately as the dimerization constants of AgBz and AgOAc are unknown. For this reason Kd(AgAgXz) could not be evaluated. However, on grounds that the charge in the HX2 ion is more delocalized than in X - it is reasonable to expect that the silver homoconjugate salts are more dissociated than the simple silver salts.
Acknowledgment. We thank the National Science Foundation for Grant No. GP-20605 in support of this work.
Solvent Structure Dependence of the Optical Excitation Energy of Solvated Electrons' ;. Freeman Ck?NliSfi'y Department, University of Alberta, Edmonton, Alberta, Canada, T6G 2G2 (Received May 19, 19721 Pubkation costs assisted by the University of Alberta
Interpretation of optical excitation energies of solvated electrons in liquids and solids requires consideration of the solvent structure and the polarizabilities of the solvating groups. The importance of solvent structure is illustrated through the use of the Kirkwood correlation factor g K , which indicates the extent to which molecules align themselves with their neighbors to create short-range order. Values of Emax, the energy at the absorption maximum, for e-solv in water, alcohols, ethers, ammonia, and amines measured over wide ranges of temperature and pressure correlate approximately with € d g K 3 q , where t and d are the (dielectric constant and density of the liquid, respectively, and a p is the polarizability of the polar group in the molecule. A more detailed treatment would consider the anisotropy of ap.
Attempts have been made for several decades to interpret the optical absorption spectra of solvated electrons in terms of properties of the solvent.2 Although most of the early work involved electrons in liquid ammonia, during the past decade experimental and theoretical investigation has been extended lo electrons in water and many other s0lvents.2-~9Kn much of the theoretical work the solvent has been considered to be a dielectric continuum, with the electron occupying a cavity in it. The properties of the solvent that have been used in the interpretation of solvated electron spectra have therefore been those of the bulk solvent, mainly the dielectric constant, but also the surface tension and the pressure differential of the dielectric constant (for electrostriction). "Molecular models" of electron solvation5,7JlJ3 have received less attention and are not completely satisfactory. Most of the models have been able to rationalize a portion of the properties of electrons in a given solvent, but none has explained all of the known optical properties. Neither has any model quantitatively correlated the shift of a given property from solvent to solvent. For example, by comparison with the energy of the absorption maximum Emaxof electrons in water, Emax in ammonia seems too low and that in alcohols seems too high.6,16 T o f a d i t a t e development of the theory, new empirical
correlations should be sought to indicate what new factors are needed in the model calculations. Emaxhas been measured in many polar liquids at 296 f , 3 K (see summary in ref 16), and in several liquids under (1) Supported by the Defence Research Board of Canada. (2) J. Jortner, S. A. Rice, and E. G. Wilson, "Metal-Ammonia Solutions," G. Lepoutre and M. J. Sienko, Ed., W. A. Benjamin, New York, N. Y., 1964, p 222. Most of the earlier work is mentioned in this article. (3) M. J. Blandamer, R. Catterall, L. Shields, arid M, C. R. Symons, J. Chem. SOC.,4357 (1964). (4) M. J. Blandamer, L. Shields, and M, 6. R. Symons, J. Chem. Soc., 3759 (1965). (5) M. Natori and 5 . Watanabe, J. Phys. Soc, Jap., 4, 1573 (1966). (6) G. R. Freeman, Gordon Research Conference on Radiation Chemistry, New Hampton, N. H.. Aug 1966. (7) R. H. Land and D. E. O'Reilly, J. Chem. Phys., 46,4496 (1967). (8) N. F. Mott, Advan. Phys., 16,49 (1967). (9) M. H. Cohen and J. C. Thompson, Advan. Phys., 17,857 (1968). (10) K. Fueki, ,I. Chem. Phys., 49, 765 (1968). (11) K . Iguchi,J. Chem. Phys., 48, 1735 (1968); /bid., 51,3137 (1969). (12) R. Catterall and N. F. Mott, Advan. Phys., '18,665 (1969). 113) D. A. Copeland, N. R. Kestner, and J. Jortner, J. Chem. Phys., 53, 1189 (1970). (14) K. Fueki, D.-F. Feng, and L. Kevan, J. Phys. Chem., 74, 1976 (1970). 115) M. Weissmann and N. V. Cohan. Chem. Phvs. Lett., 7,445 (1970). (16) L. M. Dorfman, F. Y. Jou, and R. Wagernan, Wer. Bunsenges. Phys. Chem., 75,681 (1971). (17) J. Jortner, Wer. Wunsenges. Phys. Chem., 75,696 (1971). (18) S. Rav. Chem. Phvs. Lett.. 11. 573 11971). (19) R. Caiterall, Natuie (London), Phys. Sci.,'229, 10 (197'1)
The Journalof Physical Chemlsfi,y, Vol. 77, No. 1 , 1973
G.R.Freeman TABLE I: Solvated Electron Excitation Energies and Solvent Properties -lll_
P,kbara
Solvent
873 573 473 :369 345 325 302 298
302 298 3 c12 358 320
294 298
298 195 1E13
343 296 298 2118 135 17 3 1 ti5
288 240 203 298 298 298 298 298 208 2913
Emax,eVb
0 0 0 0 0 0 0 1.o
2.1 3.8 6.3 0 0 0 2.8 4.1 0 0 0 0 2.1 5.2 0 0 0 0 0 0 0 0 0 0 0 0 0
0.91 1.05 1.24 1.51 1.57 1.65 1.71 1.79 1.84 1.93 2.0 1.77 1.90 1.95 2.06 2.14 2.20 2.23 1.66 1.80 1.95 2.07 2.12 2.22 2.27 0.73 0.80 0.86 2.17 1.67 1.51 0.59 0.59 0.92 0.65
r
d. 9/cm3
gKc
-5
19.6 34.6 56.3 63.1 69.3 77.5 81.2 85.7 91.o 96.9 23.3 29.0 33.5 40.1 41.6 63.8 69.0 18.4 24.5 28.0 31.5 48.1 56.2 64.5 16.3 21.6 25.3 37.7 19.5 18.3 8.2 4.3 14.2 3.6
(0.74) (0.87) 0.961 0.977 0.987 0.996 1.046 1.077 1.127 1.177 0.729 0.767 0.792 0.916 0.948 0.878 0.888 0.737 0.780 0.894 0.962 0.870 0.892 0.908 0.62 0.68 0.73 1.109 0.804 0.786 0.889 0.714 0.899 0.706
(13) (2.3) 2.4 2.5 2.6 2.7 2.7 2.6 2.6 2.6 2.7 2.8 2.9 2.7 2.7 3.2 3.2 2.8 3.0 2.9 2.8 3.3 3.4 3.4 1.3 1.2 1.1 2.4 3.1 3.1 1.3 1.7 1.3 I .8
01, A3 d
ap,A3 e
1.46
1.46
3.22
3.22
4.92
3.0
2.16
2.16
5.7
5.7 3.0 2.8 3.8 3.8 7.3 4.6
12 54 112 146 182 217 233 239 266 289 111 165 219 237 238 604 672 92 160 176 195 428 571 673 5 5 5
6.7 6.7 7.9 8.7 7.3 9.5
325 136 121 6 6 19 7
denotes 1 bar or the vapor pressure, whichever is greater. Data taken from ref 16 and 20-28. Kirkwood correlation parameter; a vaiue > 1.0 is due to the hindered rotation of a molecule relative to it& neighbors. Molecular polarizability. e Polarizability of the polar group, such as HOCH2-(R).
wide variations of temperaturezo-25 and pressure.24,26-28 A simple plot of Emaxagainst the dielectric constant 6 of the liquid has a positive slope when 6 is varied in a given compound by clianging the temperature or pressure, but the curves for different types oi compounds are stratified (Figure 1A). The difference between E m a x for the alcohols and that fOr water seemed to be roughly explainable in terms of the differences in molecular polarizabilities a, Emax increasing with increasing a, but this argument would have to be reversed to explain the difference between ammonia and water; for a given value of t , E m a x varies in the order CH30H > HzO > NH3, whereas the a values are in the order CHBOH > NH3 > H20 (Table I). In alcohols and in water E m a x increases with decreasing temperature21),2?,23925 and increasing pressure,27928 but the changes in Emaxdo not correlate simply with the changes in t under the two sets of conditions.25-29 It has recently been shown that E m a x in a given liquid correlates empirically with the product c-d, where d is the density, whether c.d is changed by temperature or by pressure.25-29 The density presumably represents the r nfactors in the energy equations, where r is the electron-dipole separation; d a r 3However, . t d does not bring the alcohol and water curves together. The Journal of Physical Chemistry. Vol. 77, No. 1, 1973
One feels intuitively that the liquid structure plays an important role in determining E m a x . Kirkwood's interpretation of the dielectric polarization Moof polar liquids is based upon a molecular lecular rotation in some liquids is severely hindered by dipole-dipole interactions, with the result that orientational correlation exists between neighboring molecules. If neighboring dipoles tend to line up in a parallel fashion the contribution of the individuzl molecular dipoles to the (20) S.Arai and M. C. Sauer, Jr., J. Chem. Phys., 44,2297 (1966). (21) W. C. Gottschall and E. J. Hart, J. Phys. Chem., 71, 2102 (1967). (22) R. K. Ouinn and J. J. Lagowski, J. Phys. Chem., 73,2326 (1969). (23) B. D. Michael, E. J. Hart, and K. H. Schmidt, J. Phys. Chem., 75, 2798 (1971). (24) R. Vogeisgesang and U. Schindewoif, 5er. Bunsenges. Phys. Chem.. 75.651 11971). (25) K. N. Jha; G. Bolion, and 6 .R. Freeman, J. Phys. Chem., 76, 3876 (1972). (26) U. Schindewolf, H. Kohrmann, and E. Lang, Angew. Chem., Int. Ed. Engl., 8,512 (1969). (27) M. G. Robinson, K. N. Jha, and G. R. Freeman, J. Chem. Phys., 55.4933 (1971). (28) R . ' R I Hentz, Farhataziz, and E. M. Hansen, J , Chem. Phys., 55, 4974 (1971). (29) M. G. Robinson, K. N. Jha, G. L. Bolton, and 6.R. Freeman, paper presented to the Chemical Institute of Canada Pulse Radiolysis Symposium, Pinawa, Manitoba, Oct 1971. (30) J. G.Kirkwood, J. Chem. Phys., 7,911 (1939). (31) G. Oster and G. J. Kirkwood, J. Chem. Phys., 11, 175 (1943).
i.
Optical Excitation Energy of Solvated Electrons
9
TABLE II: Correlation between Emax in Glasses at 77 K and Kirkwood QK Values for the Liquid at 298 K _ I I
Emax,
Solvent
0 x
8
E
LRoR
CH3QH CzHsOH n-C4HgOH i-C4H90H i-C3H70H f-C4HgOH a
A-J.---
0
20
40
60
80
2
0
L 16 32
dg;
40
56
72
ap(10-**g)
Figure 1. Plot:) of the energy at t h e optical absorption peak Emax of solvated electrons against properties of the solvent: (A) c is the static dielectric constant; (B) d IS the density, gK is the Kirkwood correlation factor, and ag the polarizability of the polar group of the molecule: 0,water; A , methanol; 0 ,ethanol; 0 , ammonia; e, other compounds listed in Table I . The open points refer to wide ranges of temperature and pressure: 6, -296 K and I bar Values of Emax were taken from ref 16 and 20-28.
dielectric constant is increased. This behavior is gauged by the correiat ion parameter g K in [(e
2.5 2.4
2.5 2.4 2.3
