J. Phys. Chem. 1988, 92, 3959-3960
3959
Absolute Quantum Yield for the Photochemical Activation of Methane by Excited-State Copper Atoms in Solid Methane J. Mark Parnist and Geoffrey A. O h * Lash Miller Chemical Laboratories, University of Toronto, 80 St. George St.. Toronto, Ontario, Canada M5S 1 A1 (Received: November 16, 1987)
A method for evaluation of quantum yields for atom consumption in photochemical reactions of metal atoms with reactive
molecules in solid low-temperature matrices is outlined. The method relies only upon the evaluation of the initial rates of photon absorption and metal atom depletion for a sample in which the initial number of metal atoms is known. Errors due to secondary photolysis in which metal atoms are regenerated are thereby avoided. The quantum yield for the photochemical reaction of zP Cu atoms with methane in a solid methane matrix to form CH,CuH is found to be 0.4 f 0.2.
Introduction As part of the preliminary studies of the Cu/CH, matrix photochemical reaction, Mitchell' established methods for quantifying the initial number of metal atoms per unit area (C,) and the rate of photon absorption per unit area (labs) for a typical matrix sample. He also collected data that allowed the estimation of the quantum yield for the primary photochemical process in the Cu/CH4 reaction, insertion into the C-H bond to form CH3CuH. He obtained a value of 6 = 0.5 f 0.25, using a method involving modeling the decay of Cu atoms over the entire photolysis time to a first-order exponential decay rate law. In this paper, we present a new method for evaluating an absolute quantum yield for loss of metal atoms during photolysis in a chemically reactive matrix. The method uses the initial rate of change in absorbance of the sample dA/dt as a measure of the rate of depletion in number of metal atoms. This approach overcomes an intrinsic complication in systems such as the Cu/CH, reaction, wherein metal atoms are regenerated during the unavoidable secondary photolysis of the primary photoproduct, C H 3 C ~ H . 2 . 3Such regeneration of metal atoms results in an underestimation of the quantum yield which becomes progressively more severe as the concentration of the primary photoproduct increases with respect to that of the metal atoms. Therefore, unless corrections are made for this metal atom regeneration process, an accurate measurement of the rate of loss of metal atoms can only be made at the initial stages of the photochemical reaction. With this consideration in mind, we have reevaluated the quantum yield for the Cu/CH4 reaction using the initial data of Mitchell] and the method for quantum yield evaluation described below. Experimental Section For the sake of clarity, the experimental procedure is briefly outlined here based upon the detailed description of Mitchell.' A conventional matrix isolation apparatus was used in which copper atoms were co-condensed with methane gas on a 12 K NaCl optical window. The cryosurface was masked with a small rectangular aperture which ensured that only a small uniform fraction of the matrix surface was probed during the measurement. Metal atom areal concentrations were established through calibration of the metal atom flux from a tantalum filament wrapped with copper wire by means of a pair of quartz crystal microbalances (QCM) mounted on the cryostatic surface and in the furnace respectively during a typical deposition. Sticking coefficients for the matrix support gas were also evaluated with a cooled QCM placed directly above the cold substrate. This ensured that highly dispersed samples were made such that C H 4 could be considered to be in great excess of Cu ( > l O O O O : l ) . Photon flux was measured by using a pyroelectric radiometer before and after the actual absorbing sample, allowing a meat Present address: Laser Chemistry Group, Division of Chemistry, National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario, Canada K 1 A QR6.
surement of the absorbed photon flux at the beginning of the reaction following correction for geometrical factors. Sample absorbances were measured by peak height from an optical absorbance spectrum of the 2P 2S transition of Cu atoms at about 320 nm. For complete details of the experimental design, refer to ref 1.
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Results and Discussion The efficiency of any photochemical process is normally established through measurement of the chemical quantum yield, 6.This is defined as the ratio of the number of primary chemical reaction events induced through photon absorption divided by the number of photons absorbed by a collection of the photochemically active species. The same value 6 can be evaluated as a ratio of the rates of chemical reaction divided by the rate of photon absorption
where C is the number of absorbing centers per unit area is the absorbed photon flux (photon cm-2 in the sample and labs s-'). In the matrix isolation experiment, it is only possible to accurately evaluate the initial concentration of absorbing atoms. During photolysis, the variation in the sample atomic absorbance is the only convenient measure of the change in concentration of the absorbing species. Therefore, it is necessary to express eq 1 as a change in absorbance with photolysis time. The relationship between absorbance and concentration is the well-known BeerLambert law A = ax[X]I
(2)
where ax is the sample extinction coefficient, [XI is the volume concentration of the absorbing species, and I is the sample thickness. This expression may also be cast as a relationship between absorbance and the number of species X per unit area A = (Y~C
(3)
such that dC/dt = (1 / a X )dA/dt
(4)
Substitution of eq 4 into eq 1 yields
CP
= (1/ai)(-dA/dt)/labs
= (cO/AO)(-dA/dt)/zabs
(5)
where C, and A, are respectively the number of absorbing species per unit area and the sample atomic absorbance at the beginning of the reaction. (1) Mitchell, S. A. Ph.D. Thesis, University of Toronto, 1982. (2) Parnis, J. M.; Mitchell, S. A,; Garcia-Prieto, J.; Ozin, G. A. J . Am. Chem. SOC.1985, 107, 8169. Parnis, J. M. Ph.D. Thesis, University of Toronto, 1987. (3) Parnis, J. M.; Ozin, G. A,, submitted for publication in J . Phys. Chem.
0 1988 American Chemical Society
Parnis and Ozin
3960 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988
4 = (7.0 X 10l5atoms/(cm2.AU)) 10
Cu/CH,q
(4.0 X
i
0.8 W
V
5
0.6
0, $
04
m u
0,2
0
0
1
2
3 min
PHOTOLYS,S TIME
Figure 1. Graphical representation of sample absorbance versus photolysis time for Cu atoms in solid methane during 320-nm photolysis. Data were obtained from the unpublished work of Mitchell (ref 1).
The use of the Beer-Lambert law in studies of matrix-isolated species involves an approximation due to the immobility of the absorbing species in the solid matrix. The distribution of metal atoms in the solid is likely to be spatially uniform before photolysis. However, loss of metal atoms during photolysis will occur to a somewhat greater extent on the side of the matrix facing the lamp, such that a small concentration gradient should develop across the depth of the sample. Therefore, the Beer-Lambert law becomes invalid soon after the photolysis begins. This effect is most severe for samples of very high absorbance, A > 1. In practice, the deviation from “Beer-Lambert” behavior in samples of lower absorbance is not expected to be great, especially when measurements are made close to the beginning of the photolysis. Note also that a similar assumption was successfully used in the theoretical simulation of the growth and decay behavior of Cu atoms, CH3 radicals, and CH3CuH in a previous ESR study of the Cu/CH, system.2 Evaluation of the quantum yield for loss of atoms involves measuring the initial number of atoms per unit area, C,, the initial sample absorbance, Ao, as well as the rate of photon absorption, Iabs, and the rate of change in absorbance, dA/dt, at any time during the photolysis. In the special case where secondary reactions occur in which metal atoms are regenerated, dA/dt must be evaluated at the beginning of the reaction, as discussed above. Using this approach and data obtained by Mitchell’ for values of C,,A,, and Iabs at t = 0, as well as dA/dt obtained from a new plot of Mitchell’s original data for the change in the absorbance of Cu atoms with photolysis time (Figure l), the following value for 4 is obtained:
AU/s)/(7.0
4 = 0.4
X X
1013 photons/(cm2.s))
& 0.2 atoms/photon
where AU = absorbance units. This value should be seen as a lower limit for the quantum yield since the true value of dA/dt at t = 0 is only approximately determined with the data given in Figure 1. Our experience is that the true form of the decay curve is a smoothly varying function which resembles exponential decay. Therefore, the initial value of dA/dt is likely to be slightly greater than that given here and the quantum yield correspondingly higher. The error in the measurement is estimated from the reported error in the values of Zabs (30%) and C, (20%).] The experimental details for determination of these error values are given in ref 1 . The quantum yield obtained here applies to the observed rate of depletion of the Cu atom absorbance. The implication is made that this depletion is due exclusively to chemical reaction and therefore the value obtained is a chemical quantum yield. This is only true if no other processes contribute to the loss of atomic absorbance. There are two major processes that could invalidate this assumption. The first is photoaggregation, in which Cuz and other higher clusters are formed. The second is site interconversion in which the atom is placed in a spectroscopically distinct site such that it is effectively removed from the population of potentially reactive atoms. Both these processes could contribute to the loss of Cu atoms without leading to products. In a detailed study of the Cu/CH, matrix photochemical system,2no evidence was found for either of these processes. It is admitted that a change in extinction coefficient on the order of 100/1 could conceivably have made the change in the dimer or secondary site absorbance undetectable. However, such a change seems unreasonably extreme, since Ozin4 as well as Mitchell and Ozins have established that the extinction coefficients of Cu and Cu2 in argon matrices as well as Ag and Ag, in argon and krypton matrices are approximately the same. It is expected that this is the case for Cu and Cu2 in methane as well. Therefore, these processes are not considered to be important routes for Cu atom loss in methane, and the absolute quantum yield obtained here is believed to reflect the efficiency of the photochemical reaction of Cu atoms with methane at 12 K. Acknowledgment. The generous financial assistance of the Natural Scieflces and Engineering Research Council of Canada’s Operating and Strategic Grants Programmes is deeply appreciated. J.M.P. thanks NSERC for a postgraduate scholarship. Valuable technical and scientific discussions with Dr. Steven Mitchell are also acknowledged. Registry No. CH,CuH, 88778-41-0; Cu, 7440-50-8; CHI, 74-82-8. (4) Ozin, G. A. Appl. Specirosc. 1976, 30, 573. (5) Mitchell, S. A.; Ozin, G. A. J . Am. Chem. SOC.1978, 100, 6776; J . Phys. Chem. 1984,88, 1425.
