4955
J . Phys. Chem. 1984,88, 4955-4959 At higher laser powers, the energy ( E ) per dissociating parent molecule is high, corresponding to a low value of @. It is then essential to limit the summation in ( 5 ) to levels below dissociation. For the temperatures (1500-3000 K) of interest in the present study this affects primarily the vibrational contribution to the partition function. In the rigid rotor-harmonic oscillator approximation6 the partition function factorizes. In the classical limit it is given by Qvib
= Jm&b(E)
exP(-E/kT) d E
(A. 1)
where pvib(E) = E'r'/(S,-l)!IIhvjj i
(-4.2)
sj is the number of vibrational modes of species j , and vij is the frequency of the ith mode (i = 1, ...,sj) in species j . We use the
truncated harmonic oscillator approximation where the upper limit of integration in (A.l) is replaced by the dissociation energy. To evaluate the integral, we write it as ovib E
JDPvidE) exP(-E/kT) d E = Qvib(1 - F)
('4.3)
where F is the Hinshelwood12 fraction
si- 1
C [(D/kT)'/i!]
exp(-D/kT)
(A.4)
i=O
For a given dissociation energy D and a t a given temperature T, the higher sj is the higher the vibrational energy content and hence the higher the fraction F of molecules that have dissociated and are not to be counted. For the special case of a van der Waals bimer we write the vibrational partition function as a product of three terms: two partition functions, one for each monomer, and a partition function for the van der Waals bond. In the latter, si in (A.2) and hence in (A.4) is restricted to a small integer. (Its precise value matters not. We used 6). This is equivalent to counting the predissociative states of the bimers as stable. Had we computed one vibrational partition function for the entire bimer by using (A.3), then at the low value of D (51 eV) for the van der Waals bond the high value 1 at all temperatures of of si for the bimer would lead to F interest. Registry No. Toluene, 108-88-3.
-
(12) C. N. Hinshelwd, Proc. R. SOC.London, Ser. A, 113,230 (1927).
Methyl Orange as a Probe for Photooxidation Reactions of Colloidal TiOp Graham T. Brown and James R. Darwent* Department of Chemistry, Birkbeck College, University of London, London WCl E 7HX. England (Received: April 12, 1984)
Colloids containing TiOz supported by PVA can only sensitize the reduction of Methyl Orange. In contrast unsupported Ti02 colloids catalyze the photooxidation of Methyl Orange and concomitant reduction of 02.H202inhibits oxidation of Methyl Orange in a manner analogous to noncompetitive enzyme inhibition. This suggests the Hz02intercepts a precursor to the species responsible for dye oxidation. A kinetic analysis shows that lo4 M H2O2can intercept 50% of photogenerated h+ before recombination with e-, whereas Methyl Orange reacts with surface radicals, (TiO.)s. Only 1 in 450 photogenerated h+ lead to (TiO.)s and in the absence of H202charge recombination is the major reaction pathway. Cationic surfactants (CTAC) and cationic polymers (Polydmeama and Merquat 100) increase the rate of Methyl Orange oxidation. This results from up to a fivefold increase in surface oxidation compared to charge recombination.
Introduction The interface between an electrolyte and a semiconductor is a unique environment in which to catalyze and control chemical reactions. A potential gradient is formed at a semiconductor/liquid junction.' This electrostatic field can drive mobile holes and electrons to different regions of the semiconductor material and hence provide oxidizing and reducing species. In addition, the surface may function as a conventional heterogeneous catalyst by adsorbing reactants and providing catalytic acid/base groups. Recently, several research groups, including ours, have shown that colloids containing semiconductor particles provide an excellent medium in which to investigate electron transfer reactions across a semiconductor/liquid i n t e r f a ~ e . ~ Using -~ colloidal TiOz (1) Heller, A. Acc. Chem. Res. 1981, 14, 154. (2) Henglein, A. Ber. Bunsenges. Phys. Chem. 1982,86, 241. (3) Duonghong, D.; Ramsden, J.; Gratzel, M. J . Am. Chem. SOC.1982, 104, 2977. (4) Kuczynski, J. P.; Milosavijevic, B. H.; Thomas, J. K. J. Phys. Chem. 1983, 87, 3368. ( 5 ) Rossetti, R.; Brus, L. J. Phys. Chem. 1982, 86, 4470. (6) Moser, J.; Gratzel, M. J. Am. Chem. SOC.1983, 105, 6547.
0022-3654/84/2088-4955$01 .50/0
particles stabilized by polyvinyl alcohol (PVA), we studied the photosensitized reduction of Methyl Orange ((CH3)2NC6H4N= NH4C6S03-Na+).9 In this system, PVA and water are rapidly oxidized by photogenerated holes (h+), so that photogenerated conduction band electrons were effectively trapped on the particles and their subsequent transfer to Methyl Orange was monitored by flash photolysis. Significantly, this work provided quantitative information about the effect of pH on the rate of interfacial electron transfer from TiOz to Methyl Orange and oxygen. We would now like to report further work on colloidal TiOz, but in this case using naked (unsupported) particles and colloids containing cationic surfactants and polyelectrolytes which unlike PVA are not readily oxidized. Consequently, the photogenerated holes can now oxidize probe molecules such as Methyl Orange, so that the colloids behave quite differently from thosd stabilized by PVA. As a result, we were able to investigate the rates of (7) Fox, M. A,; Lindig, B.; Chen, C. C. J. Am. Chem. SOC.1982, 104, 5828. (8) Darwent, J. R. J. Chem. SOC., Faraday Trans. 1, 1984,80, 183. (9) Brown, G. T.; Darwent, J. R . J. Chem. SOC.,Faraday Trans. 1, accepted for publication.
0 1984 American Chemical Society
4956
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
Brown and Darwent
- Absorbance
charge recombination compared to reactions of h+ with adsorbed hydrogen peroxide and surface hydroxyl groups. Also by adding cationic supporting agents we have monitored the effect of surface. charge on these processes. Experimental Section Steady-state irradiations were carried out with an Applied Photophysics clinical irradiator employing a 900-W xenon lamp and monochromater. Solutions (30 mL) were irradiated in an Applied Photophysics Clark membrane oxygen electrode cell, so that both the concentration of 0, and Methyl Orange could be monitored simultaneously.1° Samples (ca. 3 mL) were taken and the UV/visible absorption spectrum was recorded with a Perkin-Elmer 554 spectrophotometer using 1-cm quartz cells. The extinction coefficient taken for unprotonated Methyl Orange was 2.68 X lo4 M-' cm-' and found to be the same in the presence of polymers. Methyl Orange and TiC1, (98.5%) were supplied by BDH (AR grade). CTAC (hexadecyltrimethylammonium chloride) was obtained from Kodak Ltd. Polydmeama and Merquat 100 were gifts from Unilever Research Ltd., the structures of these compounds are as follows:
I I
CI~H~~N(CH~):CI-
CH,CC02CH2CH2N(CH3),Cl-
CTAC
time / min 0
/
0
6b0
4bO
-C H 7 \
CH~-N+-
80
1 -
A (nm)
Polydmeama
,-CH-CHC H
35
-\\\
Figure 1. Photosensitized oxidation of Methyl Orange (TiOz, 5 M; pH 11.2).
X lo4
C H 2 CI-
(CH3)2 Merquat 100
Time (minutes) 0
20
40
60
80
Water was double distilled. The stock TiOz (0.025 M) was made by the method described by Henglein., Laser light scattering showed that the average radius of the particles was 33 nm. The following method was used to produce stable, reproducible colloids of naked and polymer-stabilized TiOZparticles at pH 1 1.2. The required volume of stock TiOz was added to either water or a solution of polymer to give a stable colloid (pH ca. 3). The pH of this solution was then rapidly changed by adding one or two drops of 10 M NaOH solution to bring the pH to ca. 11. Fine adjustment to pH was then made with a 0.1 M NaOH solution. The hydrogen peroxide used was standardized by measuring the absorbance of 13- ( E = 25180 MI cm-I) at 350 nm when a known quantity of H202was added to an acidic solution of KI (1 .O M) and ammonium molybdate (lo4 M).12 Special care of all quartz cells was required when using solutions containing TiOz at high pH, since TiO, is strongly adsorbed onto quartz. Therefore cleaning with fresh chromic acid was carried out prior to each set of experiments. Results and Discussion TiOz particles carry a high surface charge at either end of the pH range. Consequently, colloids can be prepared in the pH range 9-12 or below pH 3, which are stable for several days without requiring any polymer support. It is also worth noting that the sharp absorption edge of the band gap in the UV/visible spectrum is blue shifted by 2-4 nm for low pH solutions compared to high pH solutions. Our previous work on PVA-supported TiOZcolloids demonstrated that above pH 5 Methyl Orange cannot be photoreduced in aerobic s o l ~ t i o n s .Furthermore, ~ photoreduction of Methyl Orange by TiOz leads to the formation of a hydrazine derivative, which absorbs light at 247 nm ( e = 2.1 X lo4 M-' cm-' ). However, when aerobic solutions of naked TiO, ( 5 X lo4 M, pH 11.2) and Methyl Orange ( M) are illuminated with ultraband-gap radiation (250 < X < 380 nm), the absorption due to Methyl (10) Mills, A,; Porter, G . ; Harriman, A. Anal. Chem. 1981, 53, 1254. (11) Klotz, I. M.; Burkland, R. K.; Urquhart, J. M. J. Am. Chem. SOC. 1952, 74, 202. (12) Basset, J. A,; Denney, R. C.; Jeffrey, G . H.; Mendham, J. In 'Vogel's Textbook of Quantitative Inorganic Analysis"; Longman: London, 1978.
Figure 2. Photosensitized oxidation of Methyl Orange and reduction of oxygen (Ti02, 5 X M; pH 11.2; Methyl Orange, 6.0 X M).
Orange is destroyed and a new species detected at ca. 410 nm which also disappeared during irradiation and prevented the development of any clear isobestic point. This is shown in Figure 1, where the sharp absorption below 360 nm is due to the band edge of colloidal TiOz ( 5 X M, pH 11.2). Similar changes in the UV/visible spectrum were observed when Methyl Orange was oxidized thermally by boiling with hydrogen peroxide (pH 11, [H2Oz]= 5.8 X M) over a period of hours and similar spectral changes have been reported when Methyl Orange is oxidized by Br2.13 These results show clearly that Methyl Orange can be photooxidized by naked TiOz particles. Since thermal oxidation of Methyl Orange is a slow reaction even with powerful (13) Laitinen, H. A.; Boyer, K. W. Anal. Chem. 1972, 44, 920.
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 4957
Photooxidation Reactions of T i 0 2
tively charged Methyl Orange is at a comparatively low conM) and electrostatically repelled by centration ((2-20) X the negatively charged TiOz surface, so that it can probably only react with the longer-lived (TiO.)s radical. Hydroxyl radicals (OH.) might be suggested as an alternative to (TiO.)s. Such a species would lead to an identical rate law for dye oxidation; however, surface oxidation of (TiO.)s is likely to be a more facile process than direct oxidation of water. The essential reactions are summarized in the mechanism
21 18 15
12
+ + + -+ + -- + T i 0 2 + hv
9
h+
6
O2
2e-
2h+ MOFigure 3. Effect of H202 concentration on the initial rate of dye oxidation (TiO,, 5 X lo4 M; pH 11.2; [H20,] 0 (0),4.5 X M (a), 8.4 X M (O), and 1.2 X M (0)).
oxidizing agents such as bromine and boiling hydrogen peroxide, this is an indication of the reactivity of photogenerated oxidizing species in Ti02. In a quantitative study, photooxidation of Methyl Orange and reduction of O2 were monitored simultaneously with a Clark membrane polarographic detector.I0 An example of a typical decay profile for naked T i 0 2 is shown in Figure 2. O2reduction obeys first-obey kinetics, whereas dye oxidation shows a more complex behavior, with an initial burst followed by a slower steady decay. When the light was switched off, the concentration of O2 slowly recovered over a period of 2 h to the initial preillumination concentration, but there was no change in the absorption spectrum of Methyl Orange. When the sample was further illuminated 24 h later, dye removal again showed an initial fast burst followed by a steady decay. Since there was no change in the spectrum of Methyl Orange after standing for 24 h, the behavior does not result from inhibition by products from the dye oxidation. Instead, the results suggest that photooxidation of Methyl Orange is inhibited by surface adsorbed peroxide formed by reduction of O2 and oxidation of surface hydroxyl groups.I4 This suggestion was supported experimentally by adding ( 5 X M) concentrations of H202to aerobic samples of Methyl Orange and T i 0 2 at pH 11.2 immediately before irradiation, which led to a comparable reduction in the initial rate of dye oxidation. It has been shown by Boonstra and Mutsaersls that H202is chemisorbed on to TiOz a t low pH to give a surface peroxo complex. The inhibiting effect of H202on the initial rate of dye oxidation was studied over a wide range of Methyl Orange (3.5 X 10*-2.5 X M) and H202(10-5-l.2 X M) concentrations. The results are summarized in Figure 3 which shows a double reciprocal plot of l/(initial rate) against l/[Methyl Orange]. This has two significant features: (1) increasing the concentration of H20zincreases the slope and (2) the intercepts at infinitely high dye concentration also increase with increasing concentration of H202. These observations are identical with those found for noncompetitive inhibition in enzyme kinetics and suggest that H202 is reacting with the precursor to the reactive species responsible f o r Methyl Orange oxidation. In contrast, if both H202and Methyl Orange were oxidized by the same reactive species (e.g., h+) then the double reciprocal plots would have a common intercept (as in competitive inhibition). Alternatively, if H20j,was irreversibly blocking the sites on Ti02 (equivalent to uncompetitive inhibiton) then the reciprocal plots should be parallel with the same slope but different intercepts. This indicates that surface adsorbed H202reacts with photogenerated h+, which is the reactive precursor to surface radicals such as (TiO.)s, whereas the nega~
e-
h+ + e-
heat
I,
(1)
kR[h+]
(2)
(022-)s ko[02] [e-]
h+ (Ti-O-)s (H202)s 0
2
(Ti-O-)s 2H+
+ (TiO.)s
(TiO-) M O 2 ( T i 0 ~ ) ~ (Ti-0-O-Ti)s
(3)
kT[h+] (4) k~[H202][h+] ( 5 )
kDIMO-][(TiO.)s] k,[(TiO.)sl
(6) (7)
In the above scheme I, (mol dm-3 s-l) is the rate of photon absorption by Ti02 in 30 mL of solution. kR (s-l) is the rate constant for recombination of the photogenerated charge carriers (Le., h+ e-). Albery et al. have shown that colloidal Ti02particles behave as n-type semiconductors with a carrier density of l O I 9 cm-3,16 which gives approximately 300 carriers per particle for the TiOz used in these experiments. Recombination of photogenerated h+ e- pairs will occur on a nanosecond time scale." With the light intensity used only one photon is absorbed per particle per millisecond, therefore no significant buildup of minority carriers will occur and the net result is that recombination will always be pseudo-first order for the minority carriers (h'). ko (dm3 mol-' s-l) is the rate constant for electron transfer from TiO, to 02. Extrapolation of our previous result^,^ which were measured in the pH region 1-4, suggests that ko = 3.3 X lo8 dm3 mol-' s-l at pH 11.2, so that ko[O,] = 6 X lo4 s-l for an O2concentration M (equivalent to air saturated). Consequently, there of 2 X should be no concentration effects due to a buildup of e- which is removed by oxygen before the next photon arrives. kT (sd) is the rate constant for oxidation of surface hydroxide (Ti-O-)s by h+ and kH (mol dm-3 s-l) is the rate constant for oxidation of surface adsorbed H202. This constant was calculated for the total concentration of H202added to the solution. The adsorption isotherm is not known at tfiis pH (although it has been measured under acidic conditions), so it is not possible to express the rate in terms of the heterogeneous rate constant. However, our results show that the surface is not saturated with H 2 0 2for the range of concentrations in this study (Figure 4). As a result kH will be directly proportional to the rate constant for the surface reaction. kL (s-l) is the sum of the loss reactions for the surface radicals (TiO-)s excluding the reaction with dye. This will largely result from conproportionation of (TiO.)s to form a surface peroxide (Ti-eO-Ti), since the concentration of particles is low ( M) the process will be intraparticulate with first-order kinetics. Similar first-order behavior has been observed for the disproportionation of B r p on the surface of CTAB micelles.l8 Under continuous illumination on the concentrations of the minority carriers h+ and surface radicals (TiO.)s should satisfy the steady-state approximation and the initial rate (R,) for dye (D) oxidation will be given by the following rate equations: kTrakDIDl
Ro =
(8) ( k+ ~ k~ + ~ H [ H ~ O ~ ] ) ( ~-D I- kL) [D] kH[H2021 r k R + kT)kL kLkHLH2021 -1= - kR + kT RO kTra kTIa kTzakD LD1 kTIakD [Dl (9) Only the initial rates were considered (over 30 s) so that the
+
+
+
~~
(14) Yesodharan, E.; Gratzel, M. Helv. Chim. Acta 1983, 66, 2145. (15) Boonstra, A. H.; Mutsaers, C. A. H. A. J . Phys. Chem. 1975, 79, 1940.
(16) Albery, W. J.; Bartlett, P. N.; Porter, J. D. J . Electrochem. SOC., submitted for publication. (17) Gratzel, M.; Frank, A. J. J . Phys. Chem. 1982, 86, 2964.
4958
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
Brown and Darwent
Intercept ( 10"M-'s)
. +
20
10
[ ~ o ~ y r n e rx ] ~ 00130 Figure 5. Effect of polymer support on the first half-life for Methyl Orange oxidation (CTAC ( O ) , Polydmeama ( 0 ) ,and Merquat ( 0 ) ) .
TABLE I: Effect of Cationic Supports on Oxidation Reactions of Colloidal Ti02 type of particle
naked Merquat Polydmeama CTAC
/
21
re1 kT/kR 1.o 1.9 2.7 5.1
re1 k D / k L 1.o
1.o 1.o 2.6
s-l for 30 mL of solution). Applying Za to eq 10-13 results in the following ratio of rate constants when [H202]= lo4 M and [D] = 10-5 M:
0
2
4
6
8
10
12
[H,O,] (IO' M) Figure 4. Effect of H,02 concentration on the intercepts ( 0 )Ihd slopes (0)from Figure 3.
concentration of photogenerated- peroxides was negligible. Equation 9 predicts that a plot of 1/& against l/[D]o, where [D]o is the initial concentration of Methyl Orange, will show an increasing slope and intercept with increasing [H202],which would explain the results in Figure 3. The resulting slopes and intercepts from this figure are plotted against [H,Oz] in Figure 4, which shows that there is good agreement between eq 9 and the experimental results.
-kH- - 5.8 X
10" (5.6 X 10") dm6 mol-z s
kTza
kR + kT -- 2.7
X
lo7 (2.5 X lo7) dm3 mol-' s
(11)
(3.6 X lo6) dm3 m o l - ' ~
(12)
kTza
k ~ -k 3.3~ X --
(10)
kTzakD
The figures in parentheses were obtained by analyzing all values obtained for l/Ro, 1/[DIo, and [H202]using a multivariate regression analysis to find the coefficients in eq 9. These values are more reliable and have been used in the following discussion. In these experiments solutions were illuminated with a wide range of wavelengths (A > 250 nm) using a Methyl Orange filter solution so that the light absorbed by TiOz was the same for all concentrations of Methyl Orange. The quantum yield was measured by using monochromatic light (A = 3 10 nm) and found to be 5 X so that by oxidizing an equivalent amount of Methyl Orange using the cutoff filter and full output from the xenon lamp over a shorter period of time (30 s as opposed to 180 s), a reliable estimate of Za was obtained (Ia = 1.8 X mol dm-'
kR/kT = 450
(14)
k ~ [ H z O z/]k R = 2.2
(15)
k ~ [ D l / k=~ 1.6
(16)
kH [H202] / k~ = 1000
(17)
Considering the simplicity of the equipment used in these experiments the above results provide a remarkable insight into the photochemistry of colloidal TiOz. When mol dm-3 HzOz is added to the solution, peroxides can intercept more than 2/3 of the photogenerated minority carriers before they recombine with conduction band electrons (reaction 2). Oxidation of surface hydroxyl groups is a much less favorable process, so that only 0.2% of the photogenerated h+ lead to the generation of the surface radical (TiO.)s (reaction 4). This might explain why an additional RuOz catalyst is required to stimulate oxygen evolution from TiOz in water photolysis systems.lg Apparently Methyl Orange oxidation can compete efficiently with loss of (TiO.)s even at dye concentrations as low as lod mol dm-3. However, it cannot compete with charge recombination. In order to be oxidized by ht Methyl Orange must be adsorbed or attracted toward the surface of the colloidal particles. To test this possibility we have prepared colloidal Ti02 particles supported by cationic surfactants and polymers, which will attract the anionic dye toward the semiconductor surface. TiOz Supported by Cationic Surfactants. A major obstacle to oxidation of Methyl Orange at pH 11.2 could be charge repulsion between the anionic dye and TiOz particles, which carry an overall negative charge at high pH. In order to overcome this problem, the surface of TiO, particles was coated with a selection of cationic supports-CTAC, Polydmeama, and Merquat 100. All of these polymers led to a significant increase the rate of dye oxidation. Figure 5 shows the effect of polymer concentration on the reciprocal of the first half-life for Methyl Orange oxidation. All three polymers show an increase in initial rate up to polymer concentrations of 0.003-0.005% (by weight), after which t l l z ~~
(18) Frank, A. J.; Gratzel, M.; Kozak, J. J. J . Am. Chem. SOC.1976, 98, 3317. (19) Borgarello, E.; Kiwi, J.; Pelizzetti, E.; Visca, M.; GrPtzel, M. J. Am. Chem. SOC.1981, 103, 6324.
J . Phys. Chem. 1984, 88, 4959-4963
4959
I/[D],( 10-5M-') Figure 6. Effect of polymer support on the initial rate of dye oxidation and dye concentration (naked Ti02 (0),Merquat (O), Polydmeama (0), and CTAC ( 0 ) ) .
sequently eq 9 is also expected to apply to these solutions. Figure 6 shows a plot of l / R o against l/[D], for the three surfactants and a standard sample of naked Ti02. By comparing the slopes and intercepts of these plots, the relative effect of surfactants on k T / k Rand k D / k Lwere derived and the values are collected in Table I. All these cationic supports lead to an increase in the rate of surface oxidation ( k T )compared to charge recombination ( k R ) . This is most pronounced for CTAC which gives a fivefold enhancement in the yield of surface radicals (TiO.)s. This could result from a decrease in k R or an increase in kT. An increase in kT is less likely, since the cationic supports should repel h+ from the surface and stabilize (TiO-)s relative to (TiO-)s. In contrast k R might be expected to decrease if the cationic surface helps to separate e- and h'. Merquat and Polydmeama have no net effect on the relative rate of reaction of Methyl Orange with (TiO,)s: the ratio kD:kL is the same as for naked particles (Table I). In contrast CTAC also leads to an increase in kD relative to kL. Even in this case, however, the enhanced rate of oxidation is largely due to an increase in kT relative to kR,i.e., a reduction in the rate of charge recombination.
remains reasonably constant. A concentration of 0.003% Merquat provides one cationic group for every two TiOz species. This is sufficient to coat the particles and higher polymer concentrations are expected to have little effect on the surface charge of Ti02. Photooxidation of Methyl Orange by cationic particles shows a behavior similar to that reported above for naked Ti02. Con-
Acknowledgment. This work was supported by SERC and London University Central Research Fund. G.T.B. is grateful to SERC and Unilever Research for a CASE studentship. Registry No. CTAC, 112-02-7; Ti02, 13463-67-7; 02, 7782-44-7; H202,7722-84-1; Methyl Orange, 547-58-0;Polydmeama, 26161-33-1; Merquat 100, 26062-79-3.
15
I 01 0
I
2
3
Temperature Effect on the Decay of H (D) Atoms in the Radiolysis of Solid H,, D,, and HD at 4.2 and 1.9 K. Evidence for Tunneling Migration Tetsuo Miyazaki,* Kwang-Pill Lee, Kenji Fueki, and Akira Takeuchi Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Chikusa-ku, Nagoya 464, Japan (Received: March 22, 1984)
The radiolysis of H,, D2, and HD has been studied at 4.2 and 1.9 K by ESR spectroscopy. Though the amounts of H atoms produced by y-irradiation of solid H2 decrease rapidly upon storage of the irradiated samples at 4.2 and 1.9 K, those of D atoms in the y-irradiated solid D2 decrease very slowly. The fast decay of the H atoms at the two ultralow temperatures cannot be explained by a model of thermally activated diffusion, but by a model of tunneling migration. H atoms repeat a tunneling abstraction reaction with H2 (H,+ H H H,) and migrate through solid Hz to recombine with other H atoms. Theoretical calculation indicates that the rate constant for the H2 + H H + Hz reaction is very large and thus the repetition of the tunneling abstraction reaction may be possible. The slow decay of D atoms in D2 is due to the slow rate of D2 + D D + D2 reaction. H and D atoms are produced in the radiolysis of solid HD. Though the amounts of the H atoms are nearly constant upon storage of the sample at 4.2 and 1.9 K, the D atoms decay fast at these temperatures. The fast decay of the D atoms in HD is due to the HD + D H + Dz reaction which is caused by a quantum mechanical tunneling effect, though the HD + H D + H2 reaction cannot occur at the ultralow temperature because of the endothermic reaction resulting in the slow decay of H atoms in HD. The rate constant for the tunneling reaction of HD D H Dzwas obtained experimentally as 2.3 X cm3mol-' s-l at 4.2 K and 2.1 X cm3mol-' s-' at 1.9 K. The rate constant for the tunneling abstraction reaction has been calculated by use of an unsymmetrical Eckart potential. The calculated rate constants are compared with the experimental values.
-
-
-
-
+
-
+
-
+
Introduction Basic to any theory of elementary chemical reactions is an understanding of the simplest atom-diatomic molecule exchange reaction. A number of experimental and theoretical studies on the reaction of H (or D) with H2 (or D2) in the gas phase have been reported previously.' The previous studies, however, have been undertaken above room temperature. Thus it was difficult to discriminate between the reaction caused by a quantum mechanical tunneling effect and the reaction which proceeds by
passing over a potential energy barrier. In order to clarify the tunneling effect, it is desirable to study the H 2 (Dz) + D (H) reaction at ultralow temperatures, such as 4.2 and 1.9 K. It is known that the isotope effect on a reaction provides information on the tunneling effect. Quite recently the remarkable isotope effect on the formation of D and H atoms in the radiolysis of solid D2-H2 mixtures has been found at 4.2 K;2 the ratio of the rate constant for the H2 D reaction to that for the D2 H reaction exceeds 2 X lo4. The results were explained in terms
(1) Truhlar, D. G.;Wyatt, R. E. Annu. Reo. Phys. Chem. 1976,27, 1; the related papers are cited therein.
(2) Tsuruta, H.; Miyazaki, T.; Fueki, K.; Azuma, N. J . Phys. Chem. 1983, 87, 5422.
0022-3654/84/2088-4959$01.50/0
+
0 1984 American Chemical Society
+
