402
The Journal of Physlcal Chemistry, Vol. 83, No. 4, 1878
M. E. Shuman and W. Brennen
Experlmental Evldenee for a Langmulr-Rldeal Mechanlsm In Nitrogen Atom Recsmblnatlon on Glass M. E. Shurnan and W. Brennen* Department of Chemistry and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Phllsdelphla, Pennsylvanla 19 104 (Recelved April 3, 1978; Revlsed Manuscrlpt Recelved October 18, 1978) Publlcatlon costs aSSlSt8d by the Natlonal Sclence foundatloon
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Static decay experiments on active nitrogen in a Pyrex bulb have been analyzed using the Langmuir-Rideal mechanism for heterogeneous nitrogen atom recombination: N + E + F (kl, k-l), N + F N2 + E (kz),where E is an empty active catalytic site and F is one with a nitrogen atom adsorbed on it. This mechanism may be successfully used to model our experiments with the following average values of parameters: kl = 7.0 X cm3s-l, k-l = 2.4 X s-I, and kg = 4.2 X cm3s-l, The maximum active site concentration for the experiments analyzed was 1.6 X 1013cm-2.
Introduction The gas phase processes occurring in active nitrogen have been studied relentlessly since the work of Strutt (later Lord Rayleigh) early in the second decade of this century. Surface processes have tended to be either ignored or treated as a nuisance to be overcome to facilitate the study of the homogeneous processes. In spite of that, some early workers1-8did seriously examine various aspects of the general problem of heterogeneous nitrogen atom recombination. The surface of interest in most, but not all,5 of the early work was either that of a metal or a metal compound. In more recent work@leJ8the surface has most often been glass, Regrettably, the literature dealing with glass is greatly complicated by the widespread use of casually controlled and characterized surface coatings or treatments of many sorts, including inadvertent ones, It is rather difficult to find quantitative reported work, the principal objective of which was the investigation of heterogeneous recombination of nitrogen atoms on, in some sense, clean glass, Three methods have been used to study heterogeneous nitrogen atom recombination on bare or coated glass: (1) The static decay method, also called the Rayleigh method; (2) the flowing decay method; and (3) the Smith side tube or diffusion tube method. Historically, the bulk of the work has been done using the latter two of these methods. We have used the first and third methods, but this paper will be restricted to discussing data obtained by the Rayleigh method. The form of the rate law for nitrogen atom recombination on glass has never been firmly established, Sorne@l2 have favored a rate law first order in nitrogen atom concentration; others13 have found the surface process to be second order in atomic concentration; and still othersl4-l6have used or advocated a rate law consisting of a sum of first- and second-order terms. Long agoi7 and recentlyle it was found that data obtained by the Rayleigh method could not be successfully analyzed even through both first- and second-order terms were used in the rate law. Brennen and Shane18 attributed the difficulty to impurity effects of somewhat uncertain provenance. Although evidence suggests that the rate law for surface recombination of nitrogen atoms is not simply first order, it has been the custom to compare results by comparing values of y, the surface activity, which is defined as the probability per gas kinetic collision with the surface that an atom is permanently removed from the system. In our 0022-3654/79/2083-0492$0 1.OO/O
view, the diversity of reported y values is not merely the result of experimental error or the failure of experimental control but i s symptomatic of fundamental kinetic difficulties and results from attempting to fit experimental data into a mold from which they were not cast. We have recently investigated the formal kinetics of the Langmuir-Rideal adsorption-abstraction mechanism of heterogeneous recombination,19J0and in this paper we use this mechanism to analyze some of our own static decay data.
Experimental Section The apparatus is shown schematically in Figure 1. Commercial prepurified nitrogen was passed through a pair of needle valves bracketing a mercury manometer, through a removable, liquid nitrogen cooled spiral glass trap and through a third needle valve into the discharge region. A section of fused silica tubing passed through a Type 5 cavityz1where a 2.45-GHz discharge was sustained by a Kiva, 100-W power supply. The discharged gas flowed through a valve into a 5-2 Pyrex bulb, bulb A, through another valve, through a removable liquid nitrogen cooled U-trap to the pump. The U-trap and the upstream spiral trap were routinely removed after a day's experiments and cleaned with red, fuming nitric acid to remove back-diffused mechanical pump oil. In this way the system was thought to be kept free of contaminants which would have a significant effect on the catalytic activity of the glass. Pumping was provided by a Welch Duoseal Model 1402 mechanical pump and a three-stage water-cooled mercury diffusion pump. Bulb A was connected through a valve and a liquid nitrogen cooled spiral trap to a tilting McLeod gauge. Bulb A was also connected by a valve to bulb B, a 5-L Pyrex bulb situated within an oven which was itself contained within a light-tight wooden box. The oven, which was capable of maintaining temperatures in excess of 500 "C,was made of a Transite box within an aluminum box, with the 1.5411. space between them filled with Pyrex wool. The nichrome heating wire was strung on supports inside the Transite box. A chromel-alumel thermocouple was used to monitor the temperature at a single location on the surface of bulb B after it had been determined by using several thermocouples that the temperature along the surface of bulb B was reasonably uniform (&lo O C at 500 "C).Bulb B was connected to a 100-cm3bulb, bulb B', outside the box via a valve. All valves in the system with the exception of the needle valves before the discharge 0 1979 Amerlcan Chemical Society
7 +govENA ; The Journal of Physical Chemistry, Vol. 83,No. 4, 1979 493
Langmuir-Rideal Mechanism for Nitrogen Atom Recombination TRAP AND McLEOD GAUGE
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2450 MHz NzCYLINDER,+ TRAP AND NEEDLE VALVES
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Figure 1. Schematic diagram of the experimental apparatus
were Teflon high vacuum valves from Kontes Glass Co. (Models K-826500 and K826510). Bulb B was observed by an uncooled EM1 9558QA multiplier phototube operated at 860 V provided by a Northeast regulated high-voltage power supply. The photocurrent, was amplified by a Keithley 610B electrometer, and the signal was displayed on either a Leeds and Northrup Speedomax G recorder or a Tektronix Model 541 oscilloscope, depending on the speed of the decay. Observation access for the photomultiplier was provided by cutting holes through the oven and its wooden enclosure. A Pyrex beaker was used to plug the hole in the oven, and the photomultiplier, which was mounted on the outside of the wooden enclosure, observed bulb B through the bottom of the beaker. The phototube mounting was fitted with a filter set providing a transmission window from 5700 to 6000 A to admit the Av = 4 sequence of yellow first positive nitrogen afterglow bands. The light detection system was calibrated by adding a known amount of NO from bulb B' into a slowly decaying sample of active nitrogen in bulb B, measuring the steplike drop in afterglow intensity, and calculating the absolute atomic concentration corresponding to a particular value of the photocurrent. Fourteen of these titrations were performed to determine the constant K in the relation I = K[NI2[M](k [MI + l)-I1' where I is the relative intensity of the yellow akerglow measured with the photomultiplier, [MI is total gas pressure, and h, is a known quenching constant. A decay experiment was typically performed by achieving a stable flow of active nitrogen through bulb A and then rapidly opening and closing the valve between bulb A and the evacuated bulb B, allowing a sample of active nitrogen to be trapped in bulb B. After having followed the afterglow decay in bulb B, bulb A was evacuated and isolated, and the gas in bulb B was expanded into the combined volumes of bulbs A and B. A measurement of the pressure combined with a knowledge of the volumes yielded the pressure in bulb B during the decay. A typical in vacuo bake of observation bulb B involved raising the temperature quickly to 450 "C, holding it there for 1h, allowing the t,emperature to fall to 300 "C, holding that for 0.5 h, and cooling to room temperature. During this procedure the bulb was continually exhausted with the diffusion pump. Results and Discussion Initially we tried to analyze our experimental time histories of afterglow emission by the method of Brennen and Shane,18 which we may briefly summarize as follows: It was assumed that the rate law governing the disappearance of nitrogen atoms in the decay bulb could be written
-d[N]/dt = k,[NI2[M] + (h,[N]2+ .-l[N])
(1)
-43
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I
I
30
0
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120
90
Figure 2. An example of an apparently linear In ( A z l A t )vs. tgraph of experimental data. -I 5
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EXPERIMENT B FIT
-COMPUTED
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I 50
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100 t(sac1
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150
-I
200
Figure 3. An example of a noticeably curved In ( A t l A t )vs. tgraph of experimental data. This is experiment 6,and its computed fit is also shown.
where h, is the termolecular homogeneous recombination rate constant, k, is the sum of a (very small) homogeneous radiative recombination rate constant and a hypothetical second-order heterogeneous recombination rate constant, and 7-l is the traditional first-order heterogeneous recombination rate constant from which a surface recombination coefficient, y, could be calculated for a spherical where vessel of radius 01 from the formula, y = 4017-~/3c?, E is the mean atomic speed. Ignoring radiative recombination,22the terms in eq 1in curly brackets are supposed to represent the rate of surface recombination. The solution to eq l, when combined with the knowledge that the afterglow emission intensity at a particular pressure is proportional to [NI2,may be written z
E
( ~ o / ~ )=~ [Nlo/[N] /* = (1
+ A) exp ( t / ~-)A
(2)
where loand [N], are the values of light intensity and atom concentration at the arbitrarily chosen zero of time, and A = F[N],(k,[M] + ha). It follows from eq 2 that a graph of In (dzldt) vs. t should be a straight line with slope T-' and intercept In [T-'(1 + A)]. We approximated dz/dt using finite differences (Az/A t ) and prepared In ( A z / A t ) vs. t graphs. Some of these graphs appeared linear, as in Figgre 2; many were noticeably curved, as in Figure 3; and
M. E. Shuman and W. Brennen
494 The Journal of Physical Chemistry, Vol. 83, No. 4, 1979
I
I
1
I
-30k
1
I
I
where E is an empty active surface site and F is an active site on which a nitrogen atom has been adsorbed. The abstraction of an adsorbed atom by an impinging gaseous one in eq 4 is assumed to result in the instant departure of an N2 molecule from the surface, leaving an empty and still active site behind. The rate equations which govern the kinetics of this mechanism are -(V/A)(d[Nl/dt) = ki[Nl[El - [FIG-, - M N I ) (5)
1
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d[F]/dt = h,[NI[El - [F](k-, -COMPUTED
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tlsec)
Figure 4. An example of a In (AzlAt)vs. t graph of experimental data that shows an obvious, sharp minimum at short times. This is experiment A, and its computed fit is also shown.
some had confusingly bizarre shapes, as in Figure 4. In view of the special care we had taken to exclude carbonaceous impurities, we eventually ascribed our seeming inability to analyze the experimental decays to a deficiency of the assumed rate law, eq 1. Recently19,z0we have examined the formal kinetics of the Langmuir-Rideal mechanism for heterogeneous recombination of atoms, which we write as follows: N(g)
N(g) f F
k
2 F k-1
(3)
-5N&g) + E
(4)
f
E
(6)
where [N] is the gas phase nitrogen atom concentration in units ~ m -and ~ , [F] and [E] are surface contentrations in units cm-2. The kinetics of atom disappearance by the mechanism in eq 3 and 4 is determined by specifying six numbers, namely, the three rate constants, the concentration of active surface sites, [SI, the initial atom co_ncentration, [N],, and the initial fraction of sites filled, Po. Since we used experimental [N], values, we had five adjustable parameters. In our computational treatment of this mechanism we used dimensionless variables and parameters as follows: N = [N]/[N],, F = [F]/[S], 8 = hI[Nlot, p = k 2 / h l ,K = (kl/k-l)[N]o, and R = [S]A/[N],V. The bulb volume, V, was 4775 f 40 cm3 in our experiments. The area of the bulb interior, A, was approximated by the spherical-equivalent area with unity roughness factor and calculated from the formula A = 4 ~ ( 3 V / 4 7 r ) ~ Each /~. numerical integration of the rate equations (eq 5 and 6) gave the functions N(8) and F(8). We found that if such computed decays were treated as though they were experimental data by the method of Brennen and ShanelO and displayed on In (Az/A8) vs. 0 graphs, a variety of shapes was obtained. Representative
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Figure 5. Examples of In (Az/AO) vs. 0 graphs prepared from synthetic decays computed for four parameter sets ( R , p , was taken to be zero in these computations.
k). The value of
Po
Langmiiir-Rideal Mechanism for Nitrogen Atom Recombination
10
The Journal of Physical Chemistry, Vol. 83, No. 4, 1979 495 TABLE I: Model Parameters
I-----
06
0
EXPERIMENT A
0
EXPERIMENT B
-COMPUTED
i
FIT
quantity
1
1
I 100
I
I 150
I
I 200
expt €3
R
0.5
0.4
P
0.06 10 0.4 0.24 3.53 X BO" 6.8 X 4.1 x 1 0 4 5 2.4 x 6.2 X IOL2
0.06 32.6 0.8 Q.83 1.15 X l O I 3 7.2 X 4.3 x 1 0 4 5 2.5 x
ft
Ptime o scale factor [NI,, k,, cm3 s-l k,, cm3 s-'
50
expt A
k - ' , E" [SI,
1.6 x 1013
t(sac)
Figure 6. [ N ] I [ N ] , vs. t graphs of data from experiments A and B, together with fits computed using the Langmuir-Rideal mechanism.
results are shown in Figure 5. Such graphs provoked us to try to fit experimental decays with the Langmuir-Rideal mechanism, We chose to avoid additional computational complications by selecting experiments which had been carried out a t low pressure and low initial atom concentration. In this way we could ensure that the rate of heterogeneous recombination was much greater than the rate of homogeneous recornbination and also that the decay took place in the kinetic regime23 where the chemical impedance dominates the diffusional impedance. Two experiments with results of noticeably different character but both satisfying the selection criteria were chosen for fitting. Experiment A at 0.04 torr with [N], = 3.53 x 10l2cm had been one in a long series of experiments carried out at various pressures. Experiment B at 0.10 torr with [N], = 1.15 X 10l3cm-3 had been performed immediately after an in vacuo bake of the decay bulb at 450 O C , a treatment normally associated in our experience with an increase in catalytic activity of the glass. The reduced data from these experiments are shown in Figures 3 (expt B) and 4 (expt A). Also, graphs of [N]/[N], for these experiments are shown in Figure 6, from which it is clear that the atomic decay in experiment B is faster after the first 5 s, indicating the expected, generally greater wall activity. In retrospect we estimate for experiment B, for example, that the initial ratio of the heterogeneous rate of atom consumption to that of homogeneous consumption was approximately 200. The flexibility of the Langmuir-Rideal mechanism made it difficult to devise an inevitable, systematic procedure to use in fitting the experimental data. We adopted the philosophy that input data for the fits of experjments A and B should only differ in the values of [SI, Po, and of course the experimental [N],. The values of kl, kl,and h2 were assumed to be transferable from one experiment to another. The matter of Po is important to our result: and deserves comment. We considered the value of F,, the initial fraction of filled sites, to be variable because of the way in which the experiments were performed. During the act of introducing and isolating a sample of active nitrogen in the decay bulb, the atoms have already begun to interact with the putatively virgin surface. By the time the sampling is finished and the afterglow intensity reaches a maximum and begins to decline, which is around the time we arbitrarily choose to call t = 0, the concentration of filled sites is very likely different from zero. Indeed, our results imply that the initial net rates of atom adsorption, stacting with empty sites, are such that in 1 s the values of F in experiments A and B could reach 0.25 and 0.77, respectively, if the surface in each of those experiments were instantaneously exposed to the corresponding initial atom concentration, assumed to remain constant for- that 1 s. This is entirely consistent with the values of Fo we
found it necessary to use to fit the results. The fitting procedure was as follows: Using the experimental IN],, we searched for values of R, p, K , F,, and kl[N],, the scale factor connecting 0 to real time, to fit experiment A. Then, turning to experiment-I3 and its experimental [N],, we could construct a new K and time scale factor, p was the same, and search for values of R and Fo that would result in a fit. If a reasonable fit to experiment B could not be found, a different combin. t'ion of input parameters was tried for experiment A and the process was repeated. Eventually, this tedious and wasteful procedure resulted in a consistent, simultaneous, and fairly good fit of both experiments. The computed fits are shown as solid curves in Figures 3 , 4 , and 6. Our experience with the computation of a wide variety of time histories using the Langmuir -Rideal mechanism convinces us that a comparable fit could not be achieved with a radically different set of parameters. Table I shows the values of all the quantities used in and resulting from the fitting procedure. The degree to which the desired consistency has been achieved may be judged by comparing the values of hl, kl, and k 2 for the two experiments. It is obvious that the increased surface activity in experiment B, which is reflected in the increased rate of atom concentration decay in Figure 6, is due to the considerably larger concent,ration of active sites in that experiment. As a test of our derived rate constants we selected two additional experiments (experiments C and D) for fitting. Using average values of the three rate constants in Table I, along with experimental values of [N], as usual, we calculated values of p, K , and time scale factor for each of experiments C and D. We then used thest together with our computer program and found values of Po and [S] that gave a satisfactory fit in each case. Experiment C at 0.05 torr with [N], = 1.83 X 10l2cm-3 was fit with F, = 0.7 and [SI = 6.3 X 10l2cm-'. Experimen; D at 0.13 torr with [N], = 3.07 X 10'' cm-3 was fit with Fo = 0.7 and [SI = 4.3 x cm-'. The fits of the In ( A z / A t ) vs. t graphs for these experiments are shown in Figure 7. Having noticed that experiments A and C have essentially equal values of [SI, we checked and found that experiment C had been performed four days after experiment A; however, in the interval between A and C the apparatus had lain idle and evacuated. They were, therefore, consecutive experiments with no intervening disturbance of the surface. The effective surface recombination coefficient, y, may be written as follows for recombination governed by the Langmuir-Rideal mechanism:20 y ( t ) = y*(1 - P[1 - p
+ (Im-l])
(7)
where y* = 4kl[S]/c. Using the values of kl and [SI in Using eq Table I, we see that yB* = 2 . 6 y ~ *= 6.7 X 7 and Table I, we find that at t = 0 the values of *y for experiments A and B are, by happenstance, essentially the same (=1.5 X This initial equality of y values is
496
The Journal of Physical Chemistry, Vol. 83, No. 4,
r
1
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M. E. Shuman and W, Brennen
1979 I
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