J. Phys. Chem. 1984, 88, 3702-3709
3702
Localization of Excess Electrons in Dense Polar Vapors Peter Krebs Institut fur Physikalische Chemie and Elektrochemie der Uniuersitat Karlsruhe, 0 - 7 5 0 0 Karlsruhe, Federal Republic of Germany (Received: August 25, 1983; In Final Form: March 1 , 1984)
We discuss electron mobilities in dense sub- and supercritical polar vapors (NH,, H20) as a function of vapor density and temperature. They show a transition from the quasi-free to the localized electron state. The density where the onset of this transition is observed obeys the Ioffe-Regel rule. It can be demonstrated by a variational method of Luttinger that at this density the formation of orientational fluctuations becomes important for electron localization. Photoemission experiments in order to determine the electron injection level in the vapor show that, dependent on the energy of the incident light, injection of electrons into the polar medium occurs not only into the conduction band but also into preexisting trap states. This additional information allows a qualitative discussion of the electron transport process including the involved electron states. With increasing ammonia vapor density the experimentally observed electron mobility shows an anomalous density dependence around the critical density of the vapor. It is concluded that in this density range a further transition occurs: The electron localized in a dense orientational cluster turns into an electron localized in a cavity (solvated electron).
Moreover, the influence of the electric dipole moment D of the polar molecules on the electron localization can be investigated by comparing the results of excess electrons in ammonia vapor ( D = 1.47 D) with those in water vapor ( D = 1.84 D). In order to understand the properties of excess electrons in any disordered material it is necessary to get in addition some information on the electron states since the response of the electrons to any external stimulus in principle depends on the density of states. Therefore, we report on results of photoemission experiments at the phase boundary metal/NH3 (vapor) which give some hints to the distribution of electron states. Finally, we will discuss an anomalous density dependence of the electron mobility in supercritical ammonia around the critical density.
1. Introduction During the past few years much work has been done in order to understand the physics of the motion of excess electrons in nonpolar fluids, especially in rare gas But only very few studies have been conducted on polar media.5-15 Our investigations have focused on the transition from the quasi-free to the localized electron state. These quasi-free or extended states are characterized by large mobilities on the order of 10’ cm2/(V s) and more, in contrast to the localized electron states with small mobilities on the order of cm2/(V s). It is the specific to interaction of the excess electron with the disordered medium which changes the electron state. At low vapor densities the motion of the excess electron in the quasi-free state is determined by scattering due to the electron/molecule interaction potential. Additionally, the electron can be temporarily or permanently captured by density fluctuations in the disordered medium. As the probability for such “localization processes” increases with increasing vapor number density n the electron mobility shows a more or less strong dependence on n. Before beginning our experimental work on electron mobilities in polar vapors it was expected that due to the strong and longrange electron/electric dipole interaction, electron localization should occur at much lower vapor densities compared with nonpolar disordered media at the same temperature. Therefore, it should be easier in polar media to study experimentally this transition from the quasi-free to the localized electron state by mobility measurements in a wide density and temperature range.
2. Survey on the Experimental Results 1 . Electron Mobility in NH3 and HzO Vapor as a Function of Density n and Temperature T. Recently, we measured the drift mobility p of excess electrons in sub- and supercritical ammonia vapor over a wide temperature range (300 5 T 5 460 K) and in the density range 2 X 10l8 < n < 1.6 X cm-3.8,9,15Some of these results are displayed in Figure 1 as a function of NH3 vapor number density n (we have omitted the results for the temperature range 300 IT I380 K15). This figure shows that at very low densities ( n lozo cm-3 a strong decrease of the electron mobility is observed. p passes a minimum of some cm2/(V s) at about nc/2 (n, = 8.31 X loz1cm-3 is the critical density of NH3) and increases again reaching a maximum of about lo-’ cm2/(V s) at n N 2nc. Very striking is the temperature dependence of the mobility at nc/2 in comparison with that at 2 4 . In order to study the reasons which are responsible for the electron localization process the electron mobilities in subcritical water vapor” are plotted for comparison in Figure 1. The drift mobility measurements have been extended now to T = 553 K up to a vapor pressure of about 60 bar ( n N 1 X loz1~ m - ~ The ). mobility of electrons in H 2 0 is much lower than in NH, at the same temperature. Moreover, a strong decrease of the mobility with n is observed in H 2 0 at lower densities than in NH3. In H 2 0 the rate of the mobility decrease with increasing n is much faster than in NH3. With other words, at constant density n the electron mobility in H 2 0 shows a very strong temperature dependence.
(1) W. F. Schmidt in “Electron-Solvent and Anion-Solvent Interactions”, L. Kevan and B. C. Webster, Ed., Elsevier, New York, 1976, and references therein. (2) Colloque Weyl V, J . Phys. Chem., 84, 1065-1298 (1980), and references therein. (3) K. W. Schwarz, Phys. Rev. B, 21, 5125 (1980). (4) N. Gee and G. R. Freeman, J . Chem. Phys., 78, 1951 (1983). (5) C. A. Kraus and W. W. Lucasse, J . A m . Chem. Soc., 43, 749,2529 (1921); 44, 1941 (1922). (6) K. H. Schmidt and W. L. Buck, Science, 151, 70 (1966). (7) L. G. Christophorou and A. A. Christodoulides, J . Phys. B, 2, 71 (1969).
(8) P. Krebs, V. Giraud, and M. Wantschik, Phys. Rev. Lett., 44, 211 (1980). (9) P. Krebs and M. Wantschik, J . Phys. Chem., 84, 1155 (1980). (IO) P. Krebs, Chem. Phys. Lett., 70, 465 (1980). (1 1) V. Giraud and P. Krebs, Chem. Phys. Lett., 86,85 (1 982); V. Giraud, Dissertation Universitat Karlsruhe, 1983. (12) N. Gee and G. R. Freeman, Can. J. Chem., 60, 1034 (1982). (13) L. G. Christophorou, J. G. Carter, and D. V. Maxey, J . Chem. Phys., 76, 2653 (1982). (14) P. Krebs, K. Bukowski, V. Giraud, and M. Heintze, Be?. Bunsenges. Phys. Chem., 86, 879 (1982). (15) P. Krebs and M. Heintze, J . Chem. Phys., 76, 5484 (1982).
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The Journal of Physical Chemistry, Vol. 88, No. 17, 1984
Localization of Excess Electrons
3703
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(16) J. L. Pack, R. E. Voshall, and A. V. Phelps, Phys. Rev., 127, 2084 (1962). (17) L. G. Christophorou and D. Pittman, J . Phys. B, 3, 1252 (1970). (18) G. S. Hurst and J. E. Parks, J . Chem. Phys., 45, 282 (1962). (19) E. S. Sennhauser and D. A. Armstrong, Can. J . Chem., 56, 2337 (1978). (20) B. L. Henson, J . Phys. D.,11, 1405 (1978). (21) A. M. Brodski, Yu. Ya. Gurevich, and V. G. Levich, Phys. Status Solidi, 40, 139 (1970). (22) J. K. Sass and H. Gerischer in "Photoemission and the Electronic Properties of Surfaces", B. Feuerbacher et al. Ed., Wiley-Interscience, New York, 1978, section 16. (23) Yu. Ya. Gurevich, Yu. V. Pleskov, and Z. A. Rotenberg, "Photoelectrochemistry", Plenum, New York, 1980.
states without violating the Franck-Condon p r i n ~ i p l e . ~ ~AsJ ~ a consequence of his arguments it would follow that all photoinjection experiments done so far in polar liquids do not yield the lower edge of the conduction band V,,as predicted by theory, but rather the lower edge of a band of preexisting trap states.22,23,26,27 We have performed extensive measurements at the phase boundary M/NH3 (vapor) at T = 400 K in the vapor bulk density range between 1.7 X 1017 and 1.6 X lo2' cm-314in order to investigate the possible electron states. The observable quantity (24) C . E. Krohn and J. C. Thompson, Phys. Reu. B, 20, 4365 (1979). ( 2 5 ) C. E. Krohn, P. R. Antoniewicz, and J. C. Thompson, Surf. Sci., 101, 241 (1980). (26) R. R. Dogonadze, L. I. Krishtalik, and Yu. V. Pleskov, Electrokhimiya, 10, 507 (1974). (27) K. Itaya, R. E. Malpas, and A. J. Bard, Chem. Phys. Lett., 63, 411 (1979).
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The Journal of Physical Chemistry, Vol. 88, No. 17, 1984
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Krebs approximation of a density-independent eAx is thus confirmed to be reasonable, if we forget for the moment the density difference between liquid ammonia and the bulk vapor at the high-density limit of the present investigation (see section 3.4). It may be suggested that the observed shift (c) - aM= -0.43 eV (at n N 1.7 X 10'' ~ m - which ~ ) we ascriie to eAX is due to the contamination of the stainless steel photocathode surface. Additional photoemission experiments in an evacuated photocell yield a strong shift in the work function to higher energies supporting the value aM= 4.65 f 0.10 eV taken from the literature. In spite of some contamination which cannot be completely excluded in our experimental setup the main contribution to this drop eAx, therefore, is due to a "rigid dipole layer" of NH, molecules on the photocathode surface. This is also supported by preliminary photoemission experiments in low-density saturated water vapor which show likewise two injection bands." It is well-known that the work function of a polycrystalline material depends on the structure of the surface. Therefore, it might be argued that the work functions ayH3(c)and @gH3(t)are characteristic properties of the microscopically inhomogeneous photocathode material. However, the strong density dependencies, which are different for both work functions, demonstrate that both thresholds reflect the properties of the electrons in the vapor a t the phase boundary. For the moment we want to point out only the important experimental result that the energy of the incident light determines which of these bands will be occupied by the electron during the injection process.
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