4912
J. Phys. Chem. 1992, 96,4912-4917
References and Notes
(13) Beaman, R. A.; Nelson, T.; Richards, D. S.; Setser, D. W. J. Phys.
(1) Coombe, R. D.; Pritt, A. T., Jr. Chem. Phys. Lett. 1978, 58, 606. (2) Pritt, A. T., Jr.; Patel, D.; Coombe, R. D. Int. J. Chem. Kinet.1984, 16 ~. 911.. ._, (3) Habdas, J.; Wategaonkar, S.; Setser, D. W. J. Phys. Chem. 1987,91, 451. (4) David, S. J.; Coombe, R. D. J. Phys. Chem. 1985, 89, 5206. ( 5 ) Henshaw, T. L.; MacDonald, M.A,; Stedman, D. H.; Coombe, R. D. J . Phys. Chem. 1987, 91, 2838. (6) Henshaw, T. L.; McElwee, D.; Stedman, D. H.; Coombe, R. D. J. Phys. Chem. 1988, 92,4606. (7) Henshaw, T. L.; Ongstad, A. P.; Lawconnell, R. I. J . Phys. Chem. 1990, 94, 3602. ( 8 ) Piper, L. G.; Krech, R. H.; Taylor, R. L. J. Chem. Phys. 1979, 7 1 , 2099. (9) May, D. J.; Coombe, R. D. J. Chem. Phys. 1989, 93, 520. (IO) Coombe, R. D. Chemical Production of Excited NF. Final Report for US. Air Force Contract No. AFWL-F29601-79-C-0016, 1982. (1 1) Jourdain, J. L.; LeBras, G.; Poulet, G.; Combourieu, J. Combust. Flame 1979, 34, 13. (12) David, S. J.; Coombe, R. D. J. Phys. Chem. 1986, 90, 3260.
1987y919 6090.
(14) Marinelli, W. Private communication. (15) Douglas, A. E.; Jones, W. E. Can. J. Phys. 1965, 43, 2216. (16) Ganguli, P. S.; Kaufman, M. Chem. Phys. Lett. 1974, 25, 221. (17) Habdas. J.: Setser. D. W. J. Phvs. Chem. 1989. 93. 229. (18) Du, K. W.;’ Setser,‘ D. W. J. Phis. Chem. 1990; 94,’ 2425. (19) Appelman, E. H.; Clyne, M. A. A. J. Chem. SOC.,Faraday Trans. I 1975, 71, 2072. (20) Bauich, D. L.; Cox, R. A,; Crutzen, P. J.; Hampson, R. F., Jr.; Ken, J. A.; Troe, J.; Watson, R. T. J. Phys. Chem. Ref. Data 1982, 1 1 , 327. (21) Yamasaki, K.; Fueno, T.; Kajimoto, 0. Chem. Phys. Lett. 1983, 94, 425. (22) Quinones, E.; Habdas, J.; Setser, D. W. J . Phys. Chem. 1987, 91, 5155. (23) Coombe, R. D. Chemical Generation of Nitrogen Metastables. Final Report for US. Air Force Contract No. AFWL-F29601-84-C-0094. (24) Du, K. Y.; Setser, D. W. J. Phys. Chem. 1991, 95, 4728. (25) Liu, X.Ph.D. Dissertation, Department of Chemistry, University of Denver, 1989.
Infrared Multiphoton Decomposition of Highly Excited tert-Butyl-d, Bromide B. M. Toselli,f Glenn A. McRae,* M. Ivanco, and Robert D. McAlpinet AECL Research, Chalk River, Ontario, Canada KOJ 1JO (Received: December 30, 1991; In Final Form: March 3, 1992)
The infrared multiphoton decomposition (IR MPD) of tert-butyl-d, bromide as a function of pressure and fluence is reported. The major decomposition route was molecular elimination of DBr in accord with earlier pyrolysis studies. Evidence for a second channel comprising Br and tert-butyl radicals was found at high fluence or high pressure. The pressure dependence of this second channel suggests that through energy pooling collisions the molecules can reach an otherwise inaccessible channel. The effect of added gases (02, N2,He, Ar, DBr, and 2-methylpropene-d8)on the MPD is presented. This study is a further indication of the utility of a new method of analysis of MPD experiments.
Introduction Over the past 20 years, the phenomenon of multiphoton dissociation (MPD) has generated intense interest partly because multiphoton absorption (MPA) is a good technique for inducing ground-state unimolecular reactions. Moreover, the MPD process was viewed as a potentially important technique for isotopic enrichment, and the intriguing possibility of bond-selective photochemistry was also aggressively pursued. Bond selectivity was found to be an elusive goal which was achieved only in certain very special circumstances. Furthermore, the analysis of MPA and MPD experiments proved to be difficult with many confusing and interacting parameter ambig~ities.’-~ Recently, a new method of analysis of MPD experimental results was developedO4This analysis explicitly takes into account the dependence of MPD on the partial pressures of the gases being irradiated. Virtually all MPD experiments involve the exposure of a “target” gas to several hundred, or thousand, laser pulses in order that a measurable quantity of product can be obtained. This new analysis, unlike previous ones, takes into account the pulsetepulse variations in decomposition probability caused by changes in reactant and product pressures during the course of the experiment. Previous studies generally contained one of two incorrect assumptions. First, the decomposition probability was implicitly assumed equal for all pulses, and therefore pressure independent. ‘Present address: INFIQC, Departamento de Fisicoquimica, Universidad Nacional de Cbrdoba, Sucursal 16, C.C. 16. 5016, Cbrdoba, Argentina. ‘Present address: Research Grants Directorate, Natural Sciences and Engineering Research Council, 200 Kent St., Ottawa, Ontario, Canada K1A 1H5.
0022-3654/92/2096-4912$03.00/0
This assumption was often inconsistent with the pressure dependences reported in the very same papers. It has since been established that the pressure independence of the decomposition probability is not a good assumption.e’’ The other error contained in many previous studies was that a rate equation could be assumed in which “pulse number” is treated as a differentiable quantity analogous to “time” for conventional kinetic rate equations. Making an equivalence between “pulse number” and time has some intuitive appeal. For example, a plot of reagent depletion, or product appearance, versus pulse number, looks qualitatively like an equivalent plot versus time in a standard kinetics experiment. But pulse number is not a true independent variable. The dependent variable, product appearance for instance, depends on the time between laser pulses. In many instances, product formation occurs because of energy pooling that happens after the laser pulse is over.4-6JoTreating “pulse number” as a differentiable quantity, analogous to time, implies that there is no distinction between a multipulse MPD experiment and a “continuous-wave” experiment. This is clearly not true in systems where there is a pressure dependence. In this new scheme, the single-pulse decomposition probability of a target gas molecule isf(&a,b), where the laser fluence is q5 (=2E/rrw2and E is the radiant energy and r, is the focused Gaussian beam waist), a is the reactant partial pressure, and b is the decomposition product partial pressure. This is expanded as a power series in a and b: f(+,a,b) = i=]j=o C~hij(+)ai-’b’
(1)
The model parameters are determined from a fit of the target and product gas partial pressures, as a function of the number of laser
Published 1992 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4913
Decomposition of tert-Butyl-d9 Bromide
5
pulses, to a decomposition probability dependent formula; for instance, where N,,, is the number of molecules remaining after m pulses,
The product partial pressure will be proportional to No - N,,,. There will be a proportionality constant for each product gas, or mixture of gases, which is labeled by S ,, and is equal to the channel ratio multiplied by the stoichiometry. The value of this parametrization scheme is that different pressure dependences can be distinguished by simply determining the magnitude and sign of the h,j parameters; this was not possible with the earlier methods. In addition, many of the previous comparisons between theory and experiment should be reviewed, in the context of this new analysis, because they are predicated on an incorrect formulation for the experimental decomposition probability-the equations used to link theory with experiment in the vast majority of MPD papers are incorrect. Traditionally,mechanisms are inferred from pressuredependent decomposition. The parameters of the current model have been successfully associated with various collisionless and collisional processes. For example, a true collisionless unimolecular decomposition would be characterized by hlo. In this instance, the molecule is pumped to a sufficiently high excitation level, by direct absorption, that its decomposition lifetime is shorter than the time for collisional deactivation and pressureindependent decomposition ensues. However, collisional processes can give rise to pressure-independent decomposition and hlo is also consistent with a thermal reaction cooled by adiabatic expan~ion.6*~,~ Cooling by this mechanism occurs at higher pressures and is essentially independent of pressure so that the yield scales with the amount of photon-absorbing reagent; the gases cook until they cool by expanding. The higher order parameters are associated with collisional processes. The hm contribution to the decomposition of the target gas, A, is thought to require an energy-pooling collision of the sort, A* + A* A** + A followed by the decomposition of the more highly excited A**. For the h l l collision sequence, an A in the above sequence would be replaced with a B to denote the buffer gas. These sorts of collisions will be more or less efficient at transferring energy, depending on the molecules colliding and on whether they are vibrationally hot or cold. Furthermore, these effects should be reflected by the relative magnitudes and by the signs of the determined model parameters.
-
Experimental Section Details of the experimental setup were similar to those of previous ~tudies.~J-' Briefly, the laser, operating in the TEMm multilongitudinal mode was tuned to the 9P(20) line of W02 (1050 cm-l). The pulse was of approximately 150-11s duration, with no discernible tail. The laser beam was focused with a 93.7-cm BaF2 lens into a l0cm-long cylindical glass cell (radius 1.1 cm) fitted with NaCl windows and placed with the center of the cell at the focal point (Gaussian beam waist r, = 0.94 f 0.08 mm) . The ferr-butyl-dg bromide ((CD3),CBr;t-BuBr-d,) (99.3%) and the additional deuterated compounds used in this study were obtained from MSD Isotopes and were used after several freeze-pumpthaw cycles. Initial pressures were measured with an MKS Baratron capacitance manometer. Reactant and product partial-pressure analyses were done with a Bomem DA3.02 infrared spectrometer. Authentic samples were used to construct calibration curves from which partial pressures were obtained. The uncertainties associated with the quoted partial pressures are the sum of two terms; first, a minimum detectable signal derived from a consideration of the infrared spectrum signal-to-noise, and, second, a constant percent error to account for the variability in defining the baseline for the absorption area measurement. The partial-pressure uncertainties were thus f(0.03 5%) kPa for f-BuBr-d,, and f(0.07 + 8%) kPa for the product 2-methylpropened, (TMP-d,). Product analysis were also done qualita-
+
"
"
"
"
'
"
"
"
"
'
'
"
'
"
"
"
'
9 = 8.1 J/ cm* :
$ = 4.3 J/ cm2 4c
i O b ' ' "500'
'
ldod
"
lsbo.
'
2doo ' ' 2 5 6 0
"3ok ' ' 1 x)
Number of pulses $ = 2.9 J/ cm2
h
d Y V
3
OO
4000
8000
12000
1 m
2oooo
Number of pulses Figure 1. Pressure dependence of the MPD of t-BuBr-d9at several fluences. The apparent solid lines represent the pressures calculated using the model and the parameters of Table I. tively with a Hewlett Packard Model 5995 gas chromatograph mass spectrometer (GCMS), fitted with a 30-m GS-Q wide bore capillary column, 0.5 mm i.d., from J & W Scientific.
Results and Discussion The target, neat t-BuBr-d,, and product, TMP-d8, partial pressures as a function of numbers of pulses and fluence are presented as data points in Figures 1 and 2. The apparent solid lines are calculated from the best-fit parameters of Table I. In the fits, each datum was weighted by the inverse square of the experimental uncertainty, defined in the preceding section. The experiments presented in this study can be characterized by one of three fluences. We have chosen to label this as the fluence at the center of a Gaussian beam focused at the center of the evacuated reaction cell. Of course, the effect of fluence from the molecular point of view must be integrated over the length and radial extent of the reaction cell. This is not possible with the present data due to the limited range of fluences so that, in
4914 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
Toselli et al.
TABLE I: Model Parameters Determined" fluence, J/cm2
hlo x lo5
h2, X lo6 (t-BuBr-d9)
h l l X lo6 (TMP-d8, DBr)
8.7 4.3 2.9
228 (7) 47.5 (29) 3.0 (5)
2.66 (51) 1.84 (35) 0.321 (53)
-4.75 (40) -3.25 (39) -1.04 (13)
hlol x
hlol x
106
(TMP-d,)
106
(oxygen) -5.40 (36)
hIo2x 109
hlo, x io6
(OXYgen) 7.09 (74)
(helium) -4.09 (37)
-1.90 (20)
"The units of the h parameters are kPa-' of the appropriate gas, except for hIo2which has units of kPa-2 and hlo which has no units. The numbers in parentheses are the standard deviations in units of least significant figure. For the high fluence an S parameter was determined to be 0.97 (2) in the absence of oxygen or helium. When oxygen or helium was added, and for the other fluences, S was fixed at 1 .
h20
h
hl 1
5i
w h*O
W
t-C4D9
+
Br
Radical channel Eo= 280 kJ/mol
h, 1 h10 4 hl0
w
Molecular channel
hl0
+(Jlcmz)
Number of pulses
8.7
1
$ = 4.3 J/ cm2
4
zm
2.5
2
I?
a $
=i:
m
2
1.5 1
0.5 500
0'
1000
1500
2000
2500
3000
3500
Number of pulses
n
I
$ = 2.9 J/ cm21
W
this experiment, fluence is best used in a relative sense: low, intermediate, and high. A schematic representation of the MPD of t-BuBr-d, is outlined in Figure 3. There are two decomposition routes available at these energies: a low-lying molecular channel, which has been observed in low-temperature pyrolysis,12and a higher energy radical route, observed here for the first time. At high fluence the energy gathered by the molecule, through photon absorption, is sufficient
DBr
( TMP-d8 )
Ep = 183 kJlmol
2.9
4.3
t-C4D9Br
(CD3)$CD2+
+
hv
(t-BuBr-dg )
Figure 3. Schematic summary of the important processes leading to MPD of r-BuBr-d,. The activation energies are from ref 13.
to enable the decomposition rate to exceed the cooling rates of diffusion-limited collisional deactivation or adiabatic expansion. The decomposition is essentially via an hlo mechanism with relatively minor contributionsfrom collisional self-activation,h20, or from collisional deactivation with the buffer, hll. The energy is also sufficient to overcome the barrier to the high-energy radical channel. Products from both channels have been observed with the lower energy channel preferred in 97 (*2)% of the MPD (since the stoichiometry ratio of these reactions is 1:1, the Sgas constant listed in Table I represents the channel ratio). At intermediate fluences the excitation level, and hence the decomposition rate, is less, so that the effect of collisions becomes more dramatic; h20as well as hll processes oocur as larger fractions of the total decomposition. At low pressures only products from the low-lying molecular channel were observed. As the pressure was increased, to the level where an h20coefficient was required to fit the pulse-dependent changes in target and product partial pressures, products associated with the higher energy radical channel appeared in the GCMS analysis. This is indicative of an h20process, where molecules with insufficient energy gathered through photon absorption acquire more energy through energy-pooling collisions. This is also consistent with time-resolved studies of the MPD of chloroform which showed that collisional events, well after the laser pulse, could be responsible for a substantial pooling of vibrational energy.6 At the lower fluence the unimolecular lifetime is even longer and hence the effect of collisions greater still. This is demonstrated by a larger relative contribution of pressure-dependent to pressure-independent processes. For this lower fluence, higher pressures did not produce any products from the higher energy channel, indicating that collisional energy pooling is, in this instance, not sufficient to overcome the barrier of the radical channel. In these experiments, collisions between excited target molecules lead to energy pooling, increased decomposition, and higher energy channels. Collisions between excited target and product gases are also important and in this study always lead to deactivation of the target molecule. This is evident from the negative signs of the hll parameters in Table I. This is at first surprising as the product TMP-d, absorbs at the same frequency used to decompose the target gas. It was expected that the product gas would be vibrationally hot and be able to transfer this energy to the target
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4915
Decomposition of tert-Butyl-d9 Bromide
4 1
1.2
I
i
+ = 8.7 J/cm2
I 1
1.33 kPaoft-BuBr-dg c2.44 kPaofTMP-d8
0.8
r(
h
/
1
$i a"
0.6 0.4
I
0.2 1 0
500
1000
1500
2000
2500
3000
3500
Numbct 01 pul\cr
0
Figure 4. Result of addition of one of the molecular decomposition products, TMP-d,; the decomposition is lowered. The lower curve corresponds to neat r-BuBr-d,. The parameters that produce the best fit curves, for this irradiation at 4.3 J/cmZ, are listed in Table I.
gas through energy-pooling collisions, yielding a positive hll. This was the explanation for the positive hll in the MPD of chloroform4 and conversely, when the products did not absorb and were deemed vibrationally cold, the explanation for negative hl values in other In this instance, apparently the product is only vibrationally warm and the net result of collisions is to deactivate (moderately) the target. This can be seen graphically in Figure 4. For the intermediate fluence, 2.4 W a of product gas (TMP-dJ was added to 1.3 Wa of the target gas and the mixture irradiated. The decomposition of this mixture clearly is less than that of the corresponding neat sample supporting the contention that, even though it is warm, the product TMP-d6 deactivates the target. a The best fit curve through the data points of the mixture is produced with an additional term in eq 1. This term, linear in the pressure of added TMP-d8, has as a coefficient the hlol value in Table I. The magnitude of this parameter for collisional deactivation by TMP-d6 alone is about half of the hll parameter for deactivation by TMP-d6plus DBr. This suggests that the two products in the molecular elimination channel, TMP-d6and DBr, are equally responsible for collisional deactivation. This is surprisiig since polyatomia are generally believed to be more efficient at collisional deactivation than diatomics;13however, as discussed later, it is consistent with TMP-d, being vibrationally warm. As a cautionary note, the deactivating effectiveness of DBr may be underestimated since its partial pressure is probably lower than expected from stoichiometry. The pressure of an aliquot of DBr, introduced into the reaction cell, was found to decrease with time presumably because it was sticking to the vessel walls. Collisional deactivation was investigated further with the addition of oxygen to the reaction cell. Initially, oxygen was added to scmnge the radical products from the higher energy ~hanne1.I~ The expected reactions were15 (CD3)3C'
02
-
(CD3)3C02'
DBr
+
(CD3)3C02D Br' (3)
Under high fluence conditions, the products associated with the radical channel disappeared with the addition of oxygen but no new species were found in their place. This, coupled with the fact that large pressures of oxygen were found to lower the decomposition probability of t-BuBr-d, (Figure 5). suggested that oxygen was not acting as a radical scavenger but instead was collisionally deactivating the MPD. This conclusion was supported by experiments with added nitrogen that showed identical behavior. To fit the oxygen data required two new terms, dependent o n the partial pressure of 02,to be incorporated into the expression for the decomposition probability, eq 1. These terms are distinguished by the parameters hlol and hIo2which are the coefficients of the pressure of oxygen to the first and second power, respectively. The parameters obtained from the fits are in Table I and the best fit calculated partial pressures, as a function of the number of pulses, are represented by the curves in Figure 5 (only a few out of the 160 data taken at oxygen pressures in the range of 1.3-8.0kPa are shown). The S parameter was not required to fit the de-
500
1500
1000
2000
2500
Number of Pulses Figure 5. MPD of t-BuBr-d9, deactivated with the addition of oxygen. The parameters that produce the best fit curves are listed in Table I. 1.6
1.4 1.2
1
1
4i
+ = 8.7 J/cmz
A
i
s
0.2 0.4 ! :\
!;;o
\
(Wa);
, nohelium,
oo "0
"""
500
'
loo0 '
'
1500 '
"
'
2000
'
2500
Number of pulses Figure 6. MPD of r-BuBr-d9, deactivated with the addition of helium. The parameters that produce the best fit curves are listed in Table I.
composition data when oxygen was added. This indicates that only the lower energy channel is active, which is consistent with the disappearance of the products associated with the radical channel upon addition of small amounts of oxygen. In fact, the high-energy radical channel disappeared with the addition of only 0.1 kPa of O2 or N2 and decreased by about one-half with the addition of the same amount of argon. In another series of experiments, helium was added to the t-BuBr-d, in the reaction cell and irradiated at the high fluence. As with oxygen, the result of adding helium was to decrease the decomposition. In order to account for the helium deactivation, another hlol term was added to the decomposition probability, eq 1. The determined parameter is again in Table I and the results of the fit, for representative data points, can be seen graphically in Figure 6. As with oxygen, the addition of helium eliminated the higher energy radical channel so that an S parameter was not required to fit the helium data. The result of irradiating t-BuBr-d, at high fluence in the presence of the buffer gases, TMP-d8/DBr as a mixture, O2(N2), and He is that they all deactivate the decomposition to about the same extent. This is inferred from the signs and the relative magnitudes of the hll-likeparameters. At first this is surprising because it is generally accepted that the efficiency of collisional vibrational deactivation, and hence, we suggest, the magnitude of the hll-like parameters, should decrease as the colliding gas changes from polyatomic to diatomic to monoatomic. This is because vibrational to vibrational (V-V) energy transfer is more efficient than vibrational to translational (V-T) transfer,16and because polyatomia are generally more efficient at V-V collisional deactivation than diat0mi~s.l~ This similarity in the effectiveness of the different buffer gases in deactivating the decomposition of t-BuBr-d, is likely accidental. TMP-d6, which should be the most efficient at deactivating the target molecule, through V-V exchange, is itself warm. Hence, it is not as good at deactivation
4916 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
as cold TMD-d8 would be. This is evident at the intermediate fluence where the deactivating ability of TMP-d, is comparable to DBr. Oxygen and nitrogen are not expected to be greatly different as collisional partners; in this instance, there are apparently no resonance exchanges. Helium cannot, of course, deactivate the target molecule through V-V exchange, but it has a large thermal conductivity'' which makes up for this deficiency.@ During the course of this study it was discovered that freezing the decomposition products at liquid nitrogen temperatures and then allowing them to warm up resulted in the TMP-d8 and the DBr recombining to form the starting gas, 1-BuBr-d,. This suggested the possibility that a room temperature reverse reaction could be affecting the analysis. This was tested by mixing HBr and TMP-d, in the reaction cell. The cell was irradiated at high fluence for 1600 pulses to mimic experimental conditions. Infrared spectra showed no evidence of t-BuBr-d8-h suggesting that the back reaction is not important under these experimental conditions. Throughout this work the GCMS was used to identify the reaction products. At low fluences, the analysis of the reaction products with the gas chromatograph showed two peaks that were identified by their mass spectrum as TMP-d, and t-BuBr-d,. The other product, DBr, was not observed with the GCMS; however, it was seen with the infrared spectrometer. At the intermediate fluence and high pressure, or at high fluence and all pressures, a third peak in the gas chromatograph appeared soon after the peak for t-BuBr-d,. This peak showed a similar mass spectrum to that of t-BuBr-d,. This product was identified as (CD,),CDCD2Br (i-BuBr-d,) by comparing the mass spectra of the deuterated molecules with the protiated species.I9 The peak at a mass to charge ratio (m/e) of 43 was found to be a reliable indicator of i-BuBr-h,. This corresponds to the loss of CH,Br from the parent leaving the CH3CHCH3radical. The product i-BuBr-d, was identified by the analogous peak at a m/e ratio of 50. This product was only observed at intermediate fluences and high pressures, or at high fluences. At high fluence it was accompanied by a channel ratio for the lower energy molecular channel of 97 (*2)% suggesting this product is from another source. This product was identified with the radical MPD channel and the following reactions are proposed:20v21
+ + + + -
(CD,),CBr (CD3),C' (CD3),CDCD3
(CD3),C* + Br'
(4)
+
(5)
DBr
(CD3)3CD Br'
Br'
Br'
(CD3)2CDCD2' Br,
(CD3),CDCD2'
Br'
+ DBr
Br,
(CD3)2CDCD2Br+Br'
(6) (7)
(8)
A brownish tinge consistent with the production of bromine gas was observed which supports reaction 7. The bromine gas can react directly with t-BuBr-d, to give another route to i-BuBr-d,.,' Another source of (CD3)3CDis through collisions of two (CD3)3C. radicals. This can result in combination and a radical dimer that should have a very low vapor pressure, or, the transfer of a deuterium from one radical to the other-disproportionation-that gives an olefin (TMP-d8) and (CD3)3CD.22 If disproportionation was happening to any great extent then the channel ratio for the molecular elimination would be overestimated, by a few percent, because TMP-d8 would be produced in both decompositionroutes. Although the association of the hij parameters with collisional processes has proven helpful in the understanding of the MPD process, it is important to remember that there are many processes which will contribute to a pressure dependence and caution must be stressed when trying to interpret the hij parameters. As an example, to fit the MPD data when oxygen was added as a buffer gas required a linear and a quadratic term, in oxygen partial pressure, to be incorporated into the formula for the decomposition probability; the coefficients of these terms were hlol and /alo2, respectively (Table I). The coefficient of the linear term was negative, which is consistent with deactivation of the decomposing target gas by an effective collision with oxygen. The coefficient
Toselli et al.
of the quadratic term was positive. Generally, positive pressure-dependent coefficients are interpreted in terms of energypooling collisions as a precursor to decomposition. It is not reasonable to suggest that the first collision with oxygen could be deactivating and then to suggest that a second collision would activate the target. Instead, the positive hImparameter is indicative of saturation at high pressures; at low pressures the deactivation is dependent on the pressure, while at high pressures the deactivation becomes pressure independent. It is expected that higher-order corrections will oscillate in sign because the deactivation due to oxygen will asymptotically approach total deactivation. The series expansion in oxygen partial pressures, in this instance, could, perhaps better, be replaced with a "falloff" expression. Conclusions The MPD of t-BuBr-d, under the current experimental conditions proceeds via two channels: a low-energy molecular channel, and a high-energy radical route. At an intermediate fluence the high-energy channel is only accessible with the aid of energypooling collisions that raise the energy of the decomposing molecule to a higher level than simple photon absorption. The energy difference between these two channels is large enough, *lo0 kJ/mol (see Figure 3), to allow for speculation that collisional processes may involve the exchange of very large amounts of energy between excited molecules. The pressure and fluence dependence of the MPD of t-BuBr-d, has been examined and the results were analyzed with a new method for multipulse experiments. This method is very successful in that an extensive data set, including target, product, and added buffer gases as a function of pulse number, can be fitted with a small number of parameters. The parametrization of the MPD data by a pressure-dependent power series is more than just convenient; the h, coefficients contain information about decomposition rates and collisional energy transfer mechanisms. Acknowledgment. We thank J. W. Goodale for technical assistance and R. B. (Bob) Back for helpful discussions. Bob Back, recently retired from the National Research Council of Canada, died suddenly on December 19, 1991. He was a great scientist, teacher, and friend. He will be truly missed. Registry No. TMP-d,, 20762-54-3; f-C,D9Br, 42310-83-8; (CD3)+2, 76913-33-2; DBr, 13536-59-9; Br, 10097-32-2; 02,7782-44-7; N,, 7727-37-9; He, 7440-59-7; Ar, 7440-37-1.
References and Notes (1) Letokhov, V. S.Nonlinear Loser Chemistry; Springer-Verlag: Berlin, 1983. (2) Letokhov, V. S.;Moore, C. B. Chemical and Biochemical Applications of Losers; Moore, C. B., Ed.; Academic: New York, 1977; Vol. 3. (3) Lupo, D. W.; Quack, M. Chem. Rev. 1987, 87, 181. (4) McRae, G. A,; Yamashita, A. B.; Goodale, J. W. J. Chem. Phys. 1990, 92, 5991. ( 5 ) McRae, G. A.; Evans, D. K.; G d a l e , J. W. J. Chem. Phys. 1990,93, 1689. (6) Ivanco, M.; McRae, G. A.; Back, R. A.; G d a l e , J. W.; Lee, P. E. Decomposition of Highly Vibrationally Excited CDC13. J . Chem. Phys., in press. (7) McRae, G. A,; Lee, P. E.; McAlpine, R. D. J . Phys. Chem. 1991, 95, 9332. (8) McRae, G. A.; Ivanw, M.; Lee, P. E.; G d a l e , J. W. Proceedings of the International Symposium on Isotope Separation and Chemical Exchange Uranium Enrichment, Tokyo, Ocr 2+Nw 1,1990, Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology: 0-okayama, Meguroku, Tokyo 152, 1990. (9) McRae, G. A.; Ivanw, M.; Back, R. A. Chem. Phys. Lett. 1991,185, 95. (10) McRae, G. A.; Ivanco, M.; Evans, D. K.; McAlpine, R. D. Proceedings of the 14th International Conference on Coherent and Nonlinear Optics, Sr. Petersburg, Russia; World Publishers: Singapore, 1991. (1 1) Ivanco, M.; McRae, G. A.; Lee, P. E.; Grice, D. High Isotopic Selectivity in the Infrared Multiphoton Decomposition of 1 ,I ,I-Trichloroethane. To be published. (12) Brown, T. C.; King, K. D.; Gilbert, R. G. Int. J . Chem. Kinet. 1988, 20, 549. (13) Yardley, J. T. Introduction to Molecular Energy Transfec Academic: New York, 1980. (14) Calvert, J. G.; Pitts, J. N . Photochemistry; Wiley: New York, 1966. (15) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1976.
4917
J. Phys. Chem. 1992, 96,4917-4924 (16) Oref, I.; Tardy, D. C. Chem. Reu. 1990, 30, 1407. (17) Yaws, C. L. Physical Properties; McGraw-Hill: New York, 1978. (18) Bayley, R. T.; Cruickshank, F. R.; hgh, D.; Guthrie, R.; Johnstone, W.; Mayer, J.; Middleton, K. J . Chem. Phys. 1982, 77, 3453. (19) McLafferty, F. W. Anal. Chem. 1962, 34, 2.
(20) Morrison, R. T.; Boyd, R. N. Organic Chemistry; Allyn and Bacon: Boston, 1973. (21) Seakins, P. W.; Pilling, M. J. J . Phys. Chem. 1991, 95, 9874. (22) Bethune, D. S.;Lankard, J. R.; Sorokin, P. P.; Shell-Sorokin, A. J.; Plecenik, R.M.; Avouris, Ph. J . Chem. Phys. 1981, 75, 2231.
Scannlng Electrochemical Microscopy. 16. Study of Second-Order Homogeneous Chemical Reactions via the Feedback and Generation/Collection Modes Feimeng Zhou, Patrick R. Unwin; and Allen J. Bard* Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712 (Received: January 2, 1992; In Final Form: March 6, 1992)
The application of the scanningelectrochemicalmicroscope feedback and generation/collection (G/C) modes in the measurement of second-order homogeneous reactions of electrogenerated species (Le., the ErCzimechanism) is considered, with particular emphasis on dimerization. Two G/C modes are assessed: (i) tip generation/substrate collection (TG/SC) and (ii) substrate generation/tip collection (SG/TC). The TG/SC mode is shown to be preferable for kinetic studies in terms of the higher collection efficiencies attainable under steady-state conditions. A numerical treatment of the feedback and TG/SC problem, which relates the tip (feedback) and substrate (collection) currents to the tip-substrate separation, the electrode radii, and dimerization rate constant, is developed, and an extensive set of calculated steady-state feedback and collection characteristics is presented that allow construction of appropriate working curves. The theoretical results suggest that fast dimerization rate constants, up to 4 X lo8 M-I s-l (defined in terms of the rate of loss of the monomer), should be accessible to measurement in the steady-state TG/SC mode. The application of the proposed methodology is demonstrated through studies of the reductive coupling of both dimethyl fumarate (DF) and fumaronitrile (FN) in N,N-dimethylformamide. Good agreement between theory and experiment is displayed over a wide range of concentrations, yielding mean values for the dimerization rate constants of 170 M-l s-l (DF) and 2.0 X lo5 M-' s-l (FN).
Introduction Recent papers have demonstrated that the feedback mode of the scanning electrochemical microscopeLJ(SECM) is useful in studying the kinetics and mechanisms of reactions associated with electrode processe~,~-~ in addition to the surface imaging and fabrication capabilities of the device2 Experimental studies have been conducted, and theoretical treatments developed, for both irreversible and quasi-reversible heterogeneous electron-transfer processes3v4 and first-order homogeneous chemical reactions following the electron-transfer reaction.s The SECM configuration has been shown to be particularly attractive for studying fast kinetics because of the high rates of mass transfer attainable a t close tipsubstrate separations (down to fractions of a micrometer). The aim of this paper is to extend the application of the SECM, as a device for electrochemical kinetics investigations, by addressing theoretically and experimentally the application of both the feedback and generation/collection (G/C) modes in the study of second-order homogeneous chemical reactions following reversible electron transfer, Le., the ErCZimechanism.6 Particular attention is given to the following scheme where the chemical step is a dimerization process with a rate constant, k,, written here for a cathodic process.
+ ne-
electrode:
Ox
solution:
2Red
-
Red (E,)
products (C2i)
(1) (2)
This general scheme is of significance in a number of electrode reaction mechanismse6 The principle behind the use of feedback SECM for measuring coupled homogeneous chemical reactions has been discussed previouslys and is illustrated in Figure 1. For the ErC2iprocess, eqs 1 and 2, the tip ultramicroelectrode (UME) is held a t a potential at which Red is generated at a diffusion-controlled rate. 'Present address: Department of Chemistry, University of Warwick, Coventry CV4 7AL, U.K.
0022-3654/92/2096-4917$03.00/0
This establishes a competition between (i) the diffusion of Red to the conductive substrate, with the consequent regeneration and feedback diffusion of Ox, and (ii) the dimerization of Red to products (which are electroinactive at the potentials of interest), which diminishes the flux of Red at the substrate. At close tip-substrate separations, d (within about a UME diameter), the former process serves to increase the UME current, as compared to the steady-state current at the UME a t long distances from the substrate (greater than about 5 UME diameters). In contrast, the overall effect of the homogeneous reaction is to consume Red and so decrease the UME feedback current. The solution kinetics are determined by measuring the UME current as a function of the tipsubstrate distance (which governs the tipsubstrate diffusion time, of the order of &/D, where D is the diffusion coefficient of Red). In addition to the feedback mode, two SECM G/C modes are feasible, with the tip UME/substrate electrode pair operating in either the substrate generatingltip collecting (SG/TC) or tip generating/substrate collecting (TG/SC) modes (Figure 1). The latter G/C mode is similar to the feedback mode, except that now both the tip and substrate electrode currents are measured. For both G/C modes the generator electrode is held at a potential corresponding to the diffusion-controlled formation of the intermediate Red, with the potential of the collector electrode at a value where the oxidation of Red is diffusion-controlled. For the ErCzi process, eqs 1 and 2, in the TG/SC mode: tip:
Ox + ne-
-
gap:
2Red
products
- -
Red
(3)
(4)
substrate: Red - neOx (5) In the SG/TC mode, the reaction in eq 3 occurs at the substrate and that in eq 5 at the tip. Neither of the G/C modes have previously been employed for detailed quantitative kinetic studies of homogeneous or heterogeneous processes. However, the SG/TC mode described above 0 1992 American Chemical Society
