Surface Science 157 (1985) L389-L394 L389 North-Holland, Amsterdam

SURFACE SCIENCE LETTERS

R E P L Y T O " A D S O R P T I O N - A S S I S T E D D E S O R P T I O N - R E A L I T Y

OR FICTION?" BY V.P. ZHDANOV

Taro YAMADA

Institute for Solid State Physics, The University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

Takaharu ONISHI

Institute of Resource Chemistry, Tokyo Institute of Technology, 4259 Nagatsuda, Midori-ku, Yokohama- shi, Kanagawa- ken 227, Japan

and

Kenzi TAMARU

Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162, Japan

Received 12 February 1985

This is a reply to Zhdanov's comment "The adsorption-assisted desorption - reality or fiction?" [1] on our previous paper "Adsorpt ion-desorpt ion kinetics of carbon monoxide on palladium polycrystalline surfaces" [2].

Zhdanov claims that the absolute rate of desorption ("net" rate of desorp- tion in ref. [2]) of CO could have been overestimated by our method of data treatment, and that the absolute rates of adsorption and desorption may be given by the following equations:

1 - 0 v+(@) = (2rrmkTo) 1/2NotSoP 1 -A@' (1)

v ( @ ) = v , e x p [ - ( E ° + Eg@2)/RT] @, (2)

where P is the gas-phase pressure in Pa, @ the coverage of CO on the surface, T the sample temperature in K, T O the gas-phase temperature in K, N O the maximum surface concentration of CO in molecules m -2, m the mass of a molecule in kg, S O = 0.9, A = 0.9, E°d = 39 kcal mo1-1, E ff = - 12 kcal mo1-1 and v 1=1016 s -1.

They seemingly reproduce the coverage and desorption rate at the adsorp- tion equilibrium. According to eq. (2), the absolute rate of desorption would be independent of the gas-phase pressure of CO, therefore the adsorption-assisted desorption may not really take place.

0039-6028/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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72 Yamada et al. / Adsorption-assisted desorption

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T. Yamada et al. / Adsorption-assisted desorption L391

According to our opinion, figs. 6 and 8 in ref. [2], which give the absolute rate of desorption under various temperatures and pressures, are valid and not due to a vital overestimation of the rates given by eq. (1) and (2). To corroborate our opinion we first give the experimental data of the coverages of 12C160 and 12caSo.

The detailed experimental procedures are described in ref. [2]. In brief, first a clean Pd surface at temperature T was exposed to 12C~80 at pressure P until

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Fig. 1 (continued). Series of results of coverage measurements for T = 380 K at different pressures P. Open circles (O) ate t - O plots. Others are t - 0* plots for corresponding q. (a) P = 1.3 × 10-6 Pa; (0) t 1 = 30 s, (g) 60 s, ( ~ ) 180 s. (b) P = 2.0×10 -6 Pa; (O) t 1 = 20 s, ( i ) 40 s, ( ~ ) 60 s, (v) 120 s. (c) P = 4.0 × 10 -6 Pa; (O) t I = 10 S, (1) 20 S, ( ~ ) 40 S (V) 60 S, (A) 120 s. (d) P = 8.1 × 10 -6 Pa; (O) t 1 = 5 s, (1) 10 s, ( ~ ) 20 s, (v) 60 s. (e) P = 1.3 × 10 -6 Pa; (O) q = 5 s, (1) 10 s, (41') 20 s, (v) 60 s. The plot (t(~91), O1) for 01 ~ 0.5 and 0.7 is by (+ ) . The chosen plots (q + t~, 0*(q + tl)) and (q + t 2, 0*(q + t22)) are marked in each figure by tying with a solid line.

L392 T. Yamada et al. / Adsorption-assisted desorption

time t = G, then the gas-phase was quickly switched from 12C180 to 12C160, and at time t = t 1 + t 2 the surface coverages of 12C160 and ~2C180, 0 and 0", were quickly measured by the flash desorption technique. Repeat ing those procedures for various t 1 and t 2, we obtained 0, O* and the total coverage @ = 0 + 0* as functions of time.

Figs. l a - l e show the raw data of @ = @(t) = O(G + t2) and O* = O*(t) = O*(G + t2) at various q, t 2 and P, f rom which the absolute rates of adsorpt ion and desorpt ion were calculated. Fig. 4 in ref. [2] is of the same kind as these figures. In most cases a rapid decrease of 0* was observed right after t~, at which the gas-phase was switched from 12C~80 to a2Ca60.

The exponential function (eq. (9) in ref. [2]) was adopted to make the best curve fitting for those plots. The results of this curve-fitting calculation are given in fig. 8 in ref. [2], which clearly demonstrates that the absolute rate of desorpt ion v is dependent on the gas-phase pressure P at every coverage of CO, O. That is the reason why we proposed eqs. (13) and (15) - (18) in ref. [2], and introduced the term "adsorpt ion-assis ted desorption".

A new type of calculation was further carried out to confirm the pressure dependence of the absolute rate of desorption at a coverage lower than the equilibrium coverage.

After time /1, both 12C160 and n C ~ 8 0 exist on the surface, while there is only 12C160 in the gas phase, therefore 8" is in differential form:

dO* /9" d r - Ov-(O) (t>tl). (3)

If an appropria te coverage O 1 is given, the time t(01), at which O reaches 01, is given on the t - O curve. Then v_(O1) is obtained by eq. (3) with values of dO*/dt and O* at t(01).

Since the t - O and t - 0* curves were given as discrete plots in our case, t(Ox), dO*/dt and 0* must be calculated by linear intra(extra)polation. First t (O 1) was calculated by intrapolat ion of the t - O curves. Then two succeeding t - O* plots which are on the series of the smallest t 1 and the nearest to t(01) were chosen. They are denoted as (tl + t 2, O*(G + t12)) and (G + t2, O*(G + t2)). Then the values of dO*/dt and 0* at t(O1), i.e. dO*(t(O1))/dt and 0*(t(O~)) are approximated by

dO* O*(G +t2) -O*(G +t~) (4)

d t ( t ( O 1 ) ) = (G+t22 ) ( t l + t ~ ) '

dO* O*(t(01))= --~i--(t(01)) [ t ( 01 ) - - ( t 1 +/~)] +O*(t 1 + t12). (5)

This procedure makes the absolute rate of desorpt ion free f rom overestima- tion due to the equilibrium. The estimated t(O1) and the chosen plots (q + t~, O*(G + t~2)) and (tx + t 2, O*(q + t2)) are shown in fig. 1, and the result of

T. Yamada et al. / Adsorption-assisted desorption L393

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Fig. 2. Absolute rate of desorption v_ at O = O I as a function of the gas-phase pressure P: (e) 01 = 0 .5 , (11) 0 1 = 0 .7 .

v_(01) is shown in fig. 2 as a function of P. The error bars were calculated with a relative error of 1% in each coverage value. Fig. 2 definitely proves the presence of adsorption-assisted desorption.

The experimental t-O* curves are hardly explained by Zhdanov's eqs. (1) and (2). If the absolute rates of adsorption and desorption v+(O) and v_(O) would be given by eqs. (1) and (2), then the total coverage O and the t2C180 coverage 0* under our experimental conditions are given by solving the following differential equations simultaneously:

dO = v + ( O ) - v ( 0 ) , (6) dt

dO* O* d ~ - O v_ (O) , (7)

0*(tl)= o(t,). (8) This set of equations was numerically solved with a computer. As for O ( t 1) we used the experimental values. An example of the results of the calculation is shown in fig. 3 along with the corresponding experimental plots and the exponential curves (eq. (9) in ref. [2]) fitted to those plots.

It is obviously seen that the desorption kinetics given by eqs. (1) and (2) is much less suitable than that given by eq. (9) in ref. [2]. The characteristic feature of the t-O* curves given by eqs. (1) and (2) is that they have an induction period from t I to the time when the coverage reaches the equilibrium

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T. Yamada et al. / Adsorption-assisted desorption

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Fig. 3. Result of curve-fitting calculations to the series of T= 380 K, P = 4.0× 10 -6 Pa (fig. lc). Open circles (O) are t - O plots; t-O* plots: (O) t I =10 s, (11) 20 s, (0 ) 40 s, (v) 60 s, (A) 120 s. The solid lines were given by Zhdanov's eqs. (1) and (2), and the dotted lines by eq. (8) in ref. [2] (exponential function).

value. D u r i n g this pe r iod the curve is a lmos t flat. This i n d u c t i o n pe r iod is due to the negl ig ib ly smal l ra te of d e s o r p t i o n at coverages smal le r t h a n the c o r r e s p o n d i n g e q u i l i b r i u m coverage. O u r e x p e r i m e n t showed a p re s su re -depen - d e n t decrease of 0* ra ther t h a n a n i n d u c t i o n per iod.

Th i s k i n d of p ressure d e p e n d e n c e of the abso lu t e ra te of d e s o r p t i o n was m o r e c lear ly obse rved o n Ni po lyc rys ta l l ine surfaces at low C O coverages, wh ich will be p u b l i s h e d shor t ly [21.

References

[1] V.P. Zhdanov, Surface Sci. 157 (1985) L384. [2] T. Yamada, T. Onishi and K. Tamaru, Surface Sci. 133 (1983) 533. [3] T. Yamada and K. Tamaru, to be published.