J . Phys. Chem. 1989, 93. 7977-7978
composition. However, the time-resolved PL decay functions still reflect the appearance of e--h+ pairs at compositions far removed from the initial excitation. The results are shown in Figure 3A,B. The "gated spectra" in Figure 2B demonstrate an increase in the relative intensity at shorter wavelengths corresponding to the appearance of carriers in the deepest regions, Le., toward the bulk. Hence, the observed trends in decay functions for this material are reversed with respect to the oppositely graded CdSe/S material. In particular, the decay functions for the deepest region (620-500 nm) become longer with decreasing wavelength (increasing depth or distance from initial excitation). This trend is observed even though appearance of e--h+ pairs in the CdS region involves transport up a band gap gradient of at least -0.35 eV (assuming significant absorption occurs to the region of roughly CdSo,,Sq,5composition). It appears, therefore, that diffusion down the carrier concentration gradient is sufficient to drive the e--h+ pair transport. In the 620-740-nm region the decays become longer at longer wavelength. This trend presumably reflects both diffusion in the carrier concentration gradient and the band gap gradient. Furthermore, since the band gap increases away from the surface, self-absorption and reemission effects will contribute to longer decays for wavelengths characteristic of the near surface region. Although it is clear that the system is appropriate for studying e--h+ transport, it is not straightforward to map the observed trends into position and time-dependent equations (diffusion and continuity equations) for the number of carriers. Transport in a graded semiconductor has been treated in the special case of doping to eliminate space charge (i.e., internal electric fields).* In this case it can be shown that the diffusion of electrons (and holes) is described by two terms dE i = -D dn Dn (3) dx k T dx where i is the particle current, D the diffusion constant, n the number of particles, x the position, T the temperature, and E the conduction (or valence) band edge energy. The first term is the standard Fick's diffusion, and the second term indicates transport to lower band edge regions. In the current experimental situation, with arbitrary doping profile, it is not clear what effects space charge regions have on carrier dynamics. However, if these effects were extremely important, carriers would probably not reach the deepest regions, since internal electric fields move electrons and holes in opposite directions. The transport mechanisms described by eq 3 yield particle currents in the same direction for both electrons and holes and therefore can account for smooth trends in the characteristic decay times and appearance of carriers in the deep regions. A further complication involves specifying a position-dependent recombination rate that couples continuity equations for the electron and hole populations. Finally, the graded semiconductor system provides an opportunity to study another phenomenon, the effect of local potential (8) Van Ruyven, L. J.; Williams, F. E. Am. J . Phys. 1967, 35, 705.
7977
fluctuations due to S/Se substitution on e--h+ pair dynamics. In a graded semiconductor where the composition changes slowly relative to the lattice spacing, the environment at a given depth can be considered to be that of a homogeneous semiconductor layer with a particular mole fraction x . An understanding of transport properties associated with this composition requires knowledge of the band edge states. In an alloy material the description is complicated by the random substitution of the lattice sites, which does not produce a periodic potential. Further deviations from periodicity arise through geometric constraints imposed by differing lattice constants. Although both CdS and CdSe crystallize in a hexagonal wurtzite structure, CdS has lattice constants a = 4.14 and c = 6.72 A, while CdSe has a = 4.30 and c = 7.01 A. However, if the de Broglie wavelength of carriers is long relative to the potential fluctuations, it has been shown that a valid picture can be obtained when the statistical distribution of unit cells is replaced by an array of average unit cells. The potential associated with this average unit cell then determines the band gap energy. The linear shift in emission maximum for homogeneous samples with a particular x supports this picture of the band edge states. However, time-dependent measurements have established that, for an alloy material such as CdS,Se,-,, trapping in regions of low potential will occur.9 The picture of radiative recombination occurring from band edge states with wavelength corresponding to a given composition is an oversimplification in this case. Since the decay functions include all radiative transitions with a particular energy, they will reflect local fluctuations from a (possibly) broad range of compositions. The resulting form should be highly nonexponential, as observed. Further experiments are in progress to determine the extent of localization, as well as the effect of smoothly varying x, and thus the amount of disorder, with depth. In summary, the graded CdS>e,-, semiconductors provide an interesting system to probe the effects of band gap distortion over a macroscopic distance on the dynamics of excess e--h+ pairs. The luminescence decay functions for systems with both increasing and decreasing band gap reflect diffusion in concentration and band gap gradients as expected, although some features remain unexplained. The overall time scale of the decays is fast (hundreds of picoseconds), indicating transport is competitive with recombination and making quantitative description difficult. The system also looks promising for studying the effects of local potential fluctuations in a partially disordered material, since changes in the composition fraction x correspond to differing degrees of substitutional disorder. Acknowledgment. This work was supported by the Office of Naval Research. We also acknowledge the US.Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, under Contract No. DE-AC03-76SF00098 for some specialized equipment used in these experiments. (9) Gourdon, C.; Lavallard, P.; Permogorov, S.; Reznitsky, A.; Aaviksoo, Y . ;Lippmaa, Y . J . Lumin. 1987, 39, 111.
Reevaluation of the Bond-Dissociation Energies (AH,,,) H-0, H-00-, and H - 0 0
for H-OH, H-OOH, H-00-,
Donald T . Sawyer Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: August 3, 1989)
The thermodynamic redox potentials for H+, HOH, 02,HO;, O;-,'OH, and 0'-,when appropriately combined, provide accurate values for the dissociative bond energies (AHDBE) of H-OH (1 19 kcal), H-OOH (90), H-0' (106), H-0- (1 16), H-OO- (80), and HOO' (59). The latter two values are 21 and 12 kcal greater, respectively,than their long-accepted values. O W ,
The hydrogen-oxygen dissociative bond energies (AH,,,) of H-OH, H-OOH, H-0', H-0-, H-00-, and HOO' are a mea0022-3654/89/2093-7977$01.50/0
sure of the hydrogen atom abstraction reactivity of the HO', 02*-, and '02* radicals, respectively. Values for HOW, *O',0'-, 0 1989 American Chemical Society
7918
The Journal of Physical Chemistry, Vol. 93, No. 24, 1989
Letters
TABLE I: Standard Reduction Potentials for Protons, Water, and Oxygen Species and Dissociative H-O Bond Eneriges (AHDBE) for Several H y d r o g e A y g e n Species
-+ -
redox couple HO' + H+ + eH-OH H+ + eH' '0' + H+ e - + H-O' 0'- HOH + e- -0-H
+
+
A. Reduction Potentials in H 2 0 (Standard States, Unit Molality)' E o , V vs NHE redox couple +2.72 HOH+e--H'+HO-2.10 HO,' + H+ + e H-OOH +2.14 02'-+ HOH + eH-OO'OH +1.77 0, + H+ + eHO,'
--
+ HO-
E o , V vs NHE -2.93 + 1.44 +0.20 +0.12
B. Dissociative Bond Energies -AGBF = [2.72 - (-2.10)]23.1 kcal (eV)-' A H D B E = -AGBF + TA&E = 11 1.3 + 7.8 = -AGaF = 12.14 - (-2.io)i23.i = 97.9 + 7.8 = -AG,, = i1.77 - (-2.93jj23.1 = 108.6 + 7.8 = -AGRF = 11.44 - (-2.10)123.1 = 81.8 + 7.8 = -AGyF = [0.20 - (-2.93)]23.1 = 72.3 + 7.8 = -AGBF = [0.12 - (-2.10)]23.1 = 51.3 + 7.8 =
H-OH H-0' H-0H-OOH H-00' H-00' a
119 106 116 90 80 59
119 ( I ) 102 (8)
References 4-7
these bond energies traditionally are extracted from kinetic data for a given reaction p a t h ~ a y , l -and ~ in the case of polyatomic molecules are usually subject to considerable error. In contrast, the electron-transfer thermodynamic data for H+, HO', HOH, O,, H02', 02'-, *O*, and 0'- in aqueous solutions have been subjected to repeated refinements and are considered to be accurate (see Table Appropriate combination of the electron-transfer half-reactions provides an expression for the free energy of bond formation [-AGBF = nF(AEO),,]. For example, in the case of the H-OH bond, the energetics for the reduction of a proton in the absence and presence of 'OH is given by H+ + e-
-
H'
and *OH + H+
+ e-
-
E o , -2.10 V vs N H E
-
H-OH
(1)
+2.72 V
(2)
(AEo)reac, +4.82 V
(3)
E O ,
Subtraction of eq 1 from eq 2 gives H'
+ *OH
H-OH
which provides a measure of the H-OH bond energy. -AGBF = nF(AEo),,,,
= [4.82][23.1 kcal (eV)-']
= 11 1.3 kcal
(4)
(1) Benson, S . W. J. Chem. Educ. 1965, 42, 502. (2) (a) Kerr, J. A. Chem. Rev. 1966,66,465. (b) Kerr, J. A. In Handbook of Chemistry and Physics, 68th ed.; CRC: Boca Raton, FL, 1987; pp F169-F-184. (3) McMillen, D. F.; Golden, D. M. Annu. Reo. Phys. Chem. 1982, 33, 493. (4) Bard, A. J.; Parsons, R.; Jordan, J. Standard Potentials in Aqueous Solution; Marcel Dekker: New York, 1985. ( 5 ) Parsons, R. Handbook of Electrochemical Constants; Butterworths: London, 1959; pp 69-73. (6) Fee, J. A,; Valentine, J. S.In Superoxide and Superoxide Dismutases; Michelson. A. M.. McCord. J. M.. Fridovich. I.. Eds.; Academic Press: New York, 1977; pp 19-60. (7) Schwarz, H. A,; Dodson, R. W. J . Phys. Chem. 1984,88, 3643.
If the entropy (AS,,,) &.,r reaction is assumed to be 5 e.u. then the dissociative bond energy (AHDBE) at 298 K for the H-OH bond is given by the expression = 111.3
+ 7.8 = 119 kcal
(5)
which is identical with the literature value.* Analogous arguments are used to evaluate the dissociative bond energies (AHDBE) for the H-O', H-0-, H-OOH, H-00-, and H-OO' bonds, which are summarized in Table IB together with their literature values. The agreement between the A H D B E values for the H-OH, H-0', and H-OOH bonds is impressive and confirms that the use of standard-potential data for the evaluation of bond energies is soundly based. The values of 80 kcal for the H-00- bond and 59 kcal for the H-00' bond are significantly larger than those in the literature, but still are in accord with the limited radical character of 02*and *02*. The H - 0 0 ' bond at 59 kcal (rather than 47 kcal) is more consistent with the spontaneous reaction of '02'with Pt-H (AHDBE, 52 f 5 kcal).2v" An analogous approach has been used to evaluate metal-ligand covalent bond energies of metal complexes (MLJ from the differential redox potentials (U" = Eo'.L,L-- Eo'ML3,ML,-) of their ligand-centered electron-transfer processes, with -AGBF = (U0')23.1 kcal.I2 Hence, appropriate combinations of electron-transfer thermodynamic data provide a convenient and accurate means to evaluate covalent-bond energies of many polyatomic molecules. Acknowledgment. This work was supported by the National Science Foundation under Grant CHE-85 16247. (8) Hubert, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure Constants of Diatomic Molecules; Van Nostrand: New York, 1979. (9) Shum, L. G. S.; Benson, S. W. J. Phys. Chem. 1983,87, 3479. (10) Valentine, J. S. In Biochemical and Clinical Aspects of Oxygen; Caughey, W. S., Ed.; Academic Press: New York, 1979; pp 659-677. (11) Barrette, W. C., Jr.; Sawyer, D. T. Anal. Chem. 1984, 56, 653. (12) Richert, S. A,; Tsang, P. K. S.; Sawyer, D. T. Inorg. Chem. 1989,28, 2471.
