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Acknowledgment. Professor S. Lipsky and Mr K. Lee are gratefully acknowledged for having made available to us recent results and for helpful comments.
However, from the results obtained in n-hexane these authors suggest that another deactivation path (quantum fleld dn)might occur from the third singlet state of TMPD (below about 218 nm). To take it into account eq 7 and 8 must be rewritten as
References and Notes (1) R. C. Jarnagin, Acc. Chem, Res., 4,420 (1971);S.H. Peterson, M. Yaffe, J. A. Schultz, and R. C. Jarnagin, J . Chem. Phys 63, .1
2625 (1975). (2) R. A. Holroyd and R. L. Russell, J . Phys. Chem., 78,2128 (1974). (3) J. Bullot and M. Gauthier, Can. J . Chem., 55, 1821 (1977). (4) K. Wu and S.Lipsky, J. Chem. Phys., 66,5614 (1977). (5) A. Hummel, Adv. Radiat. Chem., 4, 1 (1974). (6) H. T. Davis and R. G. Brown, Adv. Chem. Phys., 31,329 (1975). (7)J. P. Dodektet,Can. J. Chem.,55,2050 (1977),and references therein; J. P. Dodelet, K. Shinsaka, and G. R. Freeman, Can. J . Chem., 54, 744 (1976),and references therein. (8) L. Onsager, Phys. Rev., 54, 554 (1938). (9) J. Casanovas, R. Grob, D. Bhnc, G. Brunet, and J. Mathieu, J . Chem. Phys., 63, 3673 (1975);J. Casanovas, Thesis, Toulouse, 1975. (10) P. Wong and E. 0.Forster, Can. J. Chem., 55, 1890 (1977). (1 1) J. Bullot, P. Cordw, and M. Gauthii, Chem. phys. Left., 54,77 (1978). (12)J. Bullot, P. Cadi, and M. Gauthii, J. Chem. phys., 69,1374 (4978). (13) J. Buliot, P. C a d i , and M. Gauthii, J. Chem. phys., 69,4908(1978). Equatlon 5 of this paper shoukl read as u(r,E,O) instead of u(r,E,B). (14) M. Gauthier, R. Klein, and I.Tatischeff, unpublished results. (15) The slight + F decrease observed In Me,Si and 2,2,4-trimethylpentane in the absence of an external electric field has been accounted for quantitatively by the production of free electrons by Wu and L i p ~ k y . ~
From ref 4 9 Dcannot be hlgher than 0.05 for A 5210 nm (E,,, 2 5.9 eV). In this wavelength range, our 4: determinations, and hence 9 ip, would thus be underestlmated by -5 % . (16) 6.Brocklehurst, Nature(London), 221, 921 (1969);Chem. Phys. Lett., 28, 357 (1974). (17) Yu A. Berlin, J. Bullot, P. Cordier, and M. Gauthier, Radiat. Phys. Chem., in press. (18) D. M. Pai and R. C. Enck, Phys. Rev. B , 11, 5163 (1975). (19) R. H. Batt, C. L. Braun, and J. F. Hornig. Appl. Opt. Suppi., 3, 20
(1969). (20) R. R. Chance and C. L. Braun, J . Chem. Phys., 64,3573 (1976). (21) L. E. Lyons and K. A. Milne, J . Chem. Phys., 65, 1474 (1976). (22) P. M. Borsenberger and A. I.Ateya, J. Appl. Phys., 48,4035(1978). (23) P. M. Borsenberger, L. E. Contois, and D.C. Hoesterey, J . Chem. Phys., 68,637 (1978). (24)J. Terlecki and J. Fiutak, Int. J. Radiat. Phys. Chem., 4,469 (1972). (25) J. Ortet, These 3e cycle, Toulouse, 1978. (26) G. C. Abell and K. Funabashi, J . Chem. Phys., 58, 1079 (1973). (27) W. F. Schmidt and A. 0. Alien, J . Chem. Phys., 52,2345 (1970). (28)S. Llpsky, private communication.
Symmetry Properties of the Transport Coefficients of Charged Particles in Disordered Materials James K. B a l d Health and Safety Research Division, Oak RMge National Laboratory, Oak Ridge, Tennessee 37830 (Received July 17, 1979) Publication costs assisted by the Oak Ridge National Laboratory
The transport coefficients of a charged particle in an isotropic material are shown to be even functions of the applied electric field. We discuss the limitation which this result and its consequences place upon formulae used to represent these coefficients.
The mobility of charged particles in isotropic materials (gases, liquids, and amorphous solids) is a scalar. If the drift velocity is a nonlinear function of the electric field E , then the mobility p is a function of E also. Because of either charge conjugation or parity invariance,1*2 p must be an even function of E , namely, p ( E ) = p(-E). Thus, if f(E) is a function containing empirical parameters to be fitted to mobility data, we must have p ( E ) = (1/2)[f(E) 4- f(-E)I (1) The function f(E)must be real valued for negative values of its argument. Below, we discuss some examples. The semiempirical formula p ( E ) = p ( 0 ) ( e X E / k ! V 1sinh (eXE/kn (2) has been used to represent the mobility of electrons which proceed through a material by the process of thermally activated h ~ p p i n g .Here, ~ p(0) is the zero field mobility, X the jump distance, e the magnitude of the electron charge, h Boltzmann’s constant, and T is the absolute temperature. This formula can be constructed from eq 1 by letting f(E) = p(O)(eXE/kT)-l exp(eXE/kT). In the case of the drift of He+, Ne+, and Ar’ ions in their parent gases, the mobility goes over smoothly from a value ‘Also adjunct member of the faculty of the Department of Physics, University of Kansas, Lawrence, KS 66045. 0022-3654/80/20841258$0 1 .OO/O
p(0) at zero field to p ( E )
-
at high field. To represent this behavior, Frost suggested the empirical formula P(E) =
d O ) P + a(E/P)l-”z
(3)
where p is the neutral gas pressure and a is an adjustable parameter! This formula is not an even function of E and, as such, is not acceptable. A formula with the proper symmetry which gives the same limiting behavior is P(E) = p(0)[1 + a(E/p)Zl-’/4
(4)
It is not in contradiction with the invariance principles for the mobility to be approximately proportional to E-’/2at high field. Rather, it means that the term c ~ ( E / pis) so ~ much larger than unity in the factor 11+ ~ ( E / p ) ~ ] that -l/~ the experiment is not capable of sensing the complete formula. It is not acceptable to attempt to salvage eq 3 by replacing E by IEl since the resulting formula is not analytic a t E = 0.l Finally, it is to be noted that, when the mobility is field dependent, the longitudinal diffusion coefficient D&E)is Again, because of the invariance principles, we must have D,,(E) = Dll(-E). Acknowledgment. This research was sponsored by the Office of Health and Environmental Research, U.S. Department of Energy, under contract W-7405-eng-26 with 0 1980 American
Chemical Society
J. Phys. Chem. 1980, 84, 1259-1262
Union Carbide Corporation. References aind Notes (1) J. K. Balrd. (J. Chem. Phys., 70, 1575 (1979). (2) I. Carmichael, J. Chem. Phys., 70, 1576 (1979).
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(3) (a) H. Eyring, J . Chem. Phys., 4, 283 (1936); (b) W. F. Schmidt, G. Bakale, and U. Sowada, ;bid., 61, 5275 (1974). (4) L. S. Frost, Phys. Rev., 105, 354 (1957). (5) (a) C. E. Kbts and D. R. Nelson, Bull. Am. Phys. Soc., 15,424 (1970); (b) R. E. Rubson, Aust. J. Phys., 25, 685 (1972).
Photoionization of Solutes and Conduction Band Edge of Solvents. Indole in Water and Alcohols A. Bemas," D. Grand, and E. Amouyal ERA 718, St. 350, Universit6 Paris-Sud, 91405 Orsay, France (Received August 1, 1979)
Publication costs assisted by CNRS
Indole has been photoionized at neutral pW and room temperature in a few transparent solvenk tetramethylsilime (Me4%),water, methanol, and ethanol. Photoconductivity measurements in Me4%solutions and solvated electron scavenging by N20 in all solvents lead to the following results: (la) The electron affinity of the scavenger does not intervene in the relationship giving the solute optical ionization potential IliT (Ib) I1iq = 4.95,4.85,4.60, and 4.35 f 0.1 eV in Me4Si, ethanol, methanol, and water solutions, respectively. (2) The threshold energy and the empirical law describing the relative photoionization yield, 4e-,in the threshold region were found dependent on the solvent. (3) The values of the solvent conduction band edge Vodeduced from the solute Iuqare found to be -1.3, -1.0, and -0.65eV for water, methanol, and ethanol, respectively. (4)An extrapolation of Ibqvs. the alcohol chain length to 1-propanol and 1-butanol leads to VO,pfiH= -0.3 eV and VoBuoH= + 0.03 eV.
Introduction During the past decade, a great deal of experimental and theoretical work has been devoted to the photoionization of impurity atoms or molecules. However, the systems investigated have been mostly liquid and solid rare gases,' hydrocarbon and alcoholic glasses,2and dielectric whereas the studies pertaining to polar liquids have been scarce. Recently aqueous tryptophan (Trp) photoionization was reexamined arid the photodissociation channels were analyzed below aind above 111q.5 Indole (In) photoionization was then inveefigated in liquid tetramethylsilane (Me4Si) and water with particular emphasis on the conduction band edge and energy gap of liquid water.6 Indole was chosen as a solute because it serves as a model compound in Trp photochemistry studies; besides, it is soluble in both polar and nonpolar solvents and a relatively high solvated electron yield, $e- = 0.25,has been reported78upon 265-nm excitation in oxygen-free aqueous solutions at neutral pH and 25 "C. The present study deals with the photoionization of indole in water, methanol, and ethanol at neutral pH and room temperature. Me4& solutions, where both photoconductivity ineasurements and solvated electron scavenging could be performed, have been used to calibrate the aqueous and alcoholic solutions. As is well established, excess electrons injected in fluids not only constitute "microscopic probes" of the dynamical molecular structureg but the knowledge of an impurity ionization potential also allows an indirect determination of a solvent bulk property: that of the fundamental energy Vo of quasi-free e1ectrons.l Such Vo values may in turn be correlated with transport properties'O and the reactivity of the excess electron.11J2 Since Vomeasurements have not been performed, to our knowledge, i n alcoholic fluids, euen a n indirect ap0022-3654/80/2084-1259$01 .OO/O
proach seems of interest. With this objective in mind, we have considered the following in succession: (I) the influence of the solvent on the optical ionization potential of the solute; (11) an empirical law relating the photoionization yield to the exciting light frequency in the threshold energy region; (111)the energy position of the lower edge of the solvent conduction band Voas deduced from the solute photoionization threshold Iliq. Experimental Section Detailed experimental conditions have been described previou~ly.~~~ Indole (Fluka puriss.) was used as supplied. The deaerated solutions were 4 X M. T h e alcohols were doubly distilled under a N2 atmosphere, first over 2,4-dinitrophenylhydrazineand concentrated H2S04and then over a mixture of clean dry magnesium and iodine to remove traces of water. Continuous, monochromatic light illuminations (Ah N 10 nm) were performed with a xenon source (Osram XBO 2500 W)fitted to a Bausch and Lomb monochromator. The light flux measured at 265 nm was of the order of 2 X 1013photons cm" s-l. Scavenging of soluated electrons by N 2 0 was used to evaluate photoionization yields. The measured N2derives onIy from a dissociative electron attachment since N20, in contrast to ionic scavengers such as H+, NO,, ... has been shown not to quench In fluorescence.13 N20 (from Air Liquide) was used at concentrations (4.7 X and 5 X M) such that the competitive reaction e,, - + In could be neglected. %he photoproduced N2,measured by gas chromatopaphy, was corrected for a low and constant residual N2, observable in blank experiments. Photoconductiuity measurements have been performed on degassed In-Me4Si solutions, the applied electric field 0 1980 American Chemical Society
