892
Langmuir 1989, 5, 892-899
Thermodynamic and Spectroscopic Characterization of Heterogeneity among Adsorption Sites: CO on Anatase at Ambient Temperature Edoardo Garrone," Vera Bolis, Bice Fubini, and Claudio Morterra Dipartimento di Chimica Inorganica, Chimica Fisica e Chimica dei Materiali, Universitd di Torino, Via P. Giuria 7, 10125 Torino, Italy Received October 25, 1988. I n Final Form: February 14, 1989 CO adsorbed on Ti02at room temperature may form up to two u-coordinated species, the most abundant of which shows clear deviations from ideal behavior in that (i) the stretching frequency linearly depends on adsorbed amount, (ii) the molar heat of adsorption decreases with coverage, and (iii) the adsorption isotherm follows a generalized version of the Temkin equation. All features observed are ascribed to the interplay between induced and structural heterogeneity, arising from the ability of the semiconductor Ti02 to transmit electronic effects, both among CO admolecules and among CO species and surface impurities (sulfates, hydroxyls, water), respectively. The availability of both adsorption and energetic data allows the Temkin model to be thoroughly checked and shown entirely valid. Introduction The surface chemistry of TiOz has been extensively investigated in our laboratories, mainly by means of infrared spectroscopy.' In order to characterize and measure the extent of the surface Lewis acidity, the adsorption of CO has been studied in particular detail by the combined use of infrared spectroscopy and adsorption microcalorimet r y . * ~In ~ agreement with earlier literature,H it has been found that, depending on crystalline modification, preparation route, and thermal pretreatment, titanium dioxide possesses one or two species of coordinatively unsaturated Ti4+ions capable of coordinating CO a t room temperature. On anatase, which is considered in the present paper, two CO species are usually seen. Surface sulfates, when present as impurities left during the preparation, suppress one CO species and alter somewhat the properties of the remaining ~ n e . ~ -Adsorption ~f of CO a t room temperature is fast and reversible. On the whole a simple process, the adsorption shows clear departures from ideality. In a recent paper,3 we have studied the adsorption of CO on various anatase samples by the joint use of IR spectroscopy and adsorption microcalorimetry, determining the spectroscopic features and the heats of adsorption on both types of sites in each case. These data have been noted to fit a correlation between the stretching frequency of adsorbed CO and the enthalpy of adsorption on non-d metal oxides, already p r o p o ~ e d .A ~ ~similar ~ correlation has been drawn between the molar extinction coefficient and the adsorption enthalpy. The molar entropy of adsorption a t vanishing coverage has been also calculated in each case and again a correlation has been noted between molar entropy and enthalpy of adsorption. A close examination of the adsorption isotherms, as well as of energetic and spectroscopic data, indicates that the CO/anatase system reveals features concerning heterogeneity among adparticles, both (1) Morterra, C. J. Chem. Soc., Faraday Trans. I 1988,84, 1617 and references therein. ( 2 ) Morterra, C.; Garrone, E.; Bolis, V.; Fubini, B. Spectrochim.Acta
1987,43A, 1577. (3) Bolis, V.; Fubini, B.; Garrone, E.; Morterra, C. J. Chem. Soc., Faraday Trans. I , in press. (4) Yaks, D. J. C. J. Phys. Chem. 1961, 65, 746. (5) Primet, M.; Bandiera, J.; Naccache, C.; Mathieu, M. V. J. Chim. Phys. 1970, 67, 535. (6) Busca, G.; Saussey, H.; Saur, 0.; Lavalley, J. C.; Lorenzelli, V. Appl. Catal. 1985, 14, 245. (7) Paukshtis, E. A.; Soltanov, R. I.; Yourchenko, S. N. React. Kinet. Catal. Lett. 1981, 16, 93.
0743-7463 18912405-0892$01.50/0
Table I. Spectral Features of the species una Aulina A 2186.5 13 13 A 2188.3 14 B 2203 13 TS673 A 2190.8 14 B 2206 13 TS823 A 2190.8 14 B 2207 15 TSS473 A 2196.9
IR Peaks
sample TS403 TS473
TSS673 TSS823
A A
2203.0 2199.5
15 14
cb
2.6 2.6 3.8 2.6 3.8 2.6 3.8 3.1 3.1 3.1
slope' -5.9 -5.9 -4.7 -4.7 -7.1 -7.1 -7.1
and Avl,2 in cm-'. * C in lo6 mol-' cm. CFor definition, see text; unit = lo6 cm-' mol" m2.
structural and induced. The simplicity of the system allows thermodynamic speculations of general interest. These are the themes of the present paper. Experimental Section Details of preparation and pretreatment of the samples are given We briefly recall here that the samples have been prepared through a sulfate process. The sulfate-free anatase is hereafter referred to as TS (specificsurface area 100-60 m2g-' depending on the pretreatment temperature). TSS is a sulfate-doped anatase (4-5% SO4 by weight), whose initial specific surface area is some 220 m2 g-', declining rapidly with pretreatment temperature. IR measurements have been carried out on a Bruker 113v Fourier transform spectrophotometer. The use of a FT apparatus allowed good quality spectra to be obtained, notwithstanding the very low transparency of the materials investigated. Heats of adsorption have been measured on a Tian-Calvet microcalorimeter connected to a volumetric apparatus, which enables the simultaneous determination of adsorbed amounts: and kept at 303 K, a temperature slightly higher than that of the ambient but close to the estimated temperature of the sample in the IR beam. Samples were prepared in the form of self-supporting pellets for IR measurements and as powders for the microcalorimetric ones. The temperature of the pretreatment is indicated after the symbol of the sample: e.g., TS673 stands for a sulfate-free sample outgassed at 673 K and briefly contacted with oxygen at the same temperature. The following samples have been studied: TS403, TS473, TS673, TS823, TSS473, TSS673, and TSS823. IR spectra have been computer simulated by using a Pascal program by Bruker. (8) Fubini, B. Thermochim. Acta 1988, 135, 19.
0 1989 American Chemical Societv
Langmuir, Vol. 5, No. 4 , 1989 893
Heterogeneity among Adsorption S i t e s 0. A
1.0
0.75
-
-
In
c m
c-
z
z
3
3
V W
W
‘ z I
z
m
m
v 0.5 U LT
a: 0 m
0 v,
a
U
m
m
0.25
0.0
0.0 2220
2210
2200 2190 2180 WRVENUMBERS CM-1
2170
0.1
2:
0
2220
2210
2200 2190 2180 WRVENUMBERS CM-1
0.2
L
D1
m
21i0
D2D3 W
D1 D2 E 3 - - I
2 0.06 I
z 3
;0 . 1 2 I
z
3
w
W
V
V
z a m
z a m (L
0 E
0
2 0.04
g 0.02 a
U
I
-0.04 2220
2210
2200 2190 2180 WRVENUMBERS CM-1
2170
2160
2220
2210
2200 2190 2180 WAVENUMBERS CM-1
2170
Figure 1. Infrared spectra of CO adsorbed on TS673 (absorbance vs wavenumbers). (a, Top) After background subtraction at decreasing CO pressures (in Torr): 1, 120; 2, 100; 3, 82; 4, 48; 5, 30; 6, 21; 7, 12; 8, 6; 9, 4; 10, 1; 11, 0.1. (b, Bottom) Difference spectra in a normalized absorbance scale: D1, 8 - 11;D 2 , 6 - 7; D3, 3 - 5.
Figure 2. Infrared spectra of CO adsorbed on TSS673 (absorbance vs wavenumbers). (a, Top) After background and gas-phase subtraction at decreasing pressures (in Torr): 1, 125; 2, 103; 3,
Results Infrared Data. The IR features of the adsorption of CO on the samples studied, described in detail in ref 3, are summarized in Table I. Examples of the spectra recorded are given in Figures l a and 2a for increasing coverages on TS673 and TSS673, respectively. As far as TS samples are concerned, one band is formed below 420 K (band A), whereas another resolved CO species is observed a t higher frequencies for higher temperatures of pretreatment (band B). As to TSS, only one band is seen for any pretreatment temperature, which we also label A, due to its strong similarities with species A on TS, notwithstanding an appreciable difference in frequency.
As evident in Figures l a and 2a, both bands A and B shift somewhat to lower frequencies with increasing coverage, species B showing a more limited shift. Table I reports vo, the frequency at zero coverage, for both species A and B: the former is evaluated with greater accuracy through a procedure described below. Both vo values depend on the sample pretreatment, that for species A more markedly. On TS, it is seen that vo for species A increases with increasing pretreatment temperature: the values for TS673 and TS823 are equal. The values for TSS samples first markedly increase for the thermal pretreatment a t 473 and 673 K and then decreases for the thermal pretreatment a t 823 K. Bandwidths of peaks A and B, also
84; 4, 64; 5, 48; 6, 33; 7, 23; 8, 13; 9, 7; 10, 4; 11, 1; 12, 0.1; 13,
background. (b,Bottom) Difference spectra in a normalized scale: D1, 11 - 13; D2, 8 - 10; D3, 5 - 7; D4, 1 - 4.
894 Langmuir, Vol. 5, No. 4, 1989
Garrone et al. 08 1 rd
1
I
‘‘E
I
0
20
60 83 100 120 p / torr Figure 4. Decomposition of the adsorption isotherm for TS673 into A (dashed) and B (dot-dashed) components.
0
1
I
02
04
CO/molecules
I
06
1
08
nm-2
Figure 3. Shifts of the CO stretching mode of species A as a function of the total amount of adsorbed CO per unit surface area: TS403, 0;TS473, O ;TS673, U; TS823, .; TSS473, 0;TSS673,
0;TSS823, 0 .
reported in Table I, remain fairly constant along the adsorption: the width of peak A on TSS appears to be larger than on TS. Both bands A and B are closely simulated by Gaussian functions. Dynamic coupling among the CO oscillators, which is known to take place in regular arrays of sites,g would, if present, increase the actual frequency of the CO stretch and lead to the underestimation of the extent of the red shift due to other causes. Measurement8 with ‘3CO/’2C0 mixtures have been performed, which clearly ruled out the occurrence of any dynamic coupling. It is noteworthy that dynamic coupling has been observed on the same system a t low temperature,*O where a much higher coverage is attained. Whatever the cause (structural or induced heterogeneity), the red shifts observed do not need any correction for dynamic coupling. Figures l b and 2b report some difference spectra on a normalized absorbance scale, again for TS and TSS, respectively. The behavior of band A is clearly seen in Figure 2b. Subtraction of spectra gives rise to positive bands of t h e same width,with a negative tail a t high frequencies. The shift of band A may thus be interpreted as being due to the formation of components a t lower frequency, accompanied by a small but significant disappearance of high-frequency components. This picture is confirmed by the difference spectra in Figure lb. The subtraction gives rise to positive peaks of the same half-width. The behavior of the difference spectra in the high-frequency region is not clear, and (9) Zecchina, A.; Scarano, D.; Garrone, E. Surf. Sci. 1986, 160, 492. (10) Tsiganenko, A. A.; Denisenko, L. A.; Zverev, S. M.; Filimonov, V. N.J. Catal. 1985, 94, 10.
40
probably negative contributions (decrement in intensity of peak A) are mingled with the changes due to species B. These are likely to shift, causing positive and negative contributions. It is evident that the larger the overall intensity of the spectrum, the larger the shift. Figure 3 illustrates this observation in quantitative terms for all the samples studied. The shifts observed in the various cases for band A are reported against the total adsorbed amounts, as evaluated from the adsorption isotherm^.^,^ It is noteworthy that a linear dependence is always seen, that all straight lines concerning TS and TSS have nearly the same slope, respectively, and that the slope for TSS samples is slightly larger than that for TS samples. Extrapolation of the plots in Figure 3 to zero coverage allows the precise determination of uo for species A. Adsorption Isotherms. As already reported in our previous paper^,^^^ it is possible to relate the intensity of spectra like those in Figures l a and 2a to the volumetric isotherms. On TSS, where only band A is present (Figure 2a), adsorption isotherms are directly comparable to the “optical” ones, obtained by plotting the integrated absorbances versus equilibrium pressures. The proportionality between the two plots allows the calculation of €A, the molar extinction coefficient of CO adsorbed on TSS. On TS, where two bands are present (Figure la), a somewhat more complex procedure has been adopted, which makes use of the fact that band B saturates rather quickly. At high pressures, variations in the adsorbed amounts may be ascribed only to increases in intensity of band A. This fact allows the determination of E A for TS samples. As the peaks due to both species A and B are fairly symmetric and well separated, it is possible to determine the integrated absorbance of A and B species, respectively, in any spectrum. By the use of EA, the amount of species A is determined; the difference between this amount and the overall amount is obviously the amount of species B, whose tg can therefore also be calculated. In our previous paper: it has been shown that the molar extinction coefficient of CO adsorbed on non-d metal cations depends upon the stretching frequency. This means that a change in t is expected during adsorption on TiOz: values calculated by the procedure just described are consequently average ones. Furthermore, different values of tA and t B are expected for different pretreatments. For simplicity, in Table I, average data are reported for species B and species A on both TS and TSS, respectively, due to the large differences in frequency observed in the two latter cases. By these procedures, the overall adsorption isotherms have been decomposed into the A and B components. An example of such decomposition, relative to TS673, is given in Figure 4. As anticipated, the curve for species B is seen
Langmuir, Vol. 5, No. 4,1989 895
Heterogeneity among Adsorption Sites
"'"I
I
01
d2
03
04 n,/pmol
05
m2
Figure 6. Integral heat of adsorption on TSS473 as a function of adsorbed amounts. Straight line: see text.
Opr 0
20
40
..
60
80
120 p / torr
100
140
I
160
Figure 5. Adsorption isotherms for species A. (a, Top): TS403, 0;TS473, a; TS673, a; TS823, For clarity, only one curve has been drawn for TS673 and TS823. (b, Bottom): TSS473, 0; TSS673, 8 ; TSS823, 0 .
Table 11. Adsorption Isotherm for Species A: Values of the Parameters in the Temkin Equation sample N,' Klb K2C TS403 TS473 TS673 TS823 TSS473 TSS673 TSS823
17 39 64 64 44 80 80
7.51 f 0.93 16.6 f 0.99 21.4 f 0.61 22.0 f 0.32 23.9 f 0.3 38.6 f 0.3 40.0 f 0.5
4.23 f 0.22 4.67 f 0.55 8.47 f 0.55 9.41 f 0.32 14.8 f 0.38 108.8 f 3.1 92.4 rt 16
Estimated as explained in the text; NM in b K , in lo-* molecule nm-2. in lo2 Torr-*.
molecule nm-2.
to saturate rapidly, whereas the other curve does not, even a t substantial CO pressures. In ref 3 it has been shown that the isotherm for species B is satisfactorily represented by a Langmuir expression:
e = Na/NM
= P / ( P + Plj2)
(1)
where N , is the adsorbed amourit, NM the monolayer value, and p l j 2 the pressure a t which 8 = l/z. No analytical representation was attempted for the isotherm concerning species A. We have now found that the equation
N , = Kl[ln (1 + K g ) ] (2) represents these isotherms within a 2% accuracy, Le., within the experimental uncertainty. Figure 5 shows the isotherms for species A on all seven samples. Note that, because of the nonlinear nature of eq 2, the parameters have been computed by a nonlinear least-squares procedure, also allowing the computation of the standard errors affecting K1 and Kz. The relevant parameters are reported in Table 11. Integral Heats of Adsorption. The nonideal nature of the adsorption of species A is rather evident, both from the occurrence of shifts of the CO stretching mode with coverage and the non-Langmuir nature of the relevant isotherms. The nonideality of the adsorption of species
A is also revealed by the calorimetric data. These have been measured for all the systems s t ~ d i e d . ~As B far as TS is concernted, TS403, where species A alone is present, shows a moderate adsorptive capacity, and consequently the energetic data are somewhat uncertain. TS pretreated at higher temperatures shows both species A and B, and thus it is not easy to arrive a t the energetic features of species A alone. Deviations from ideality are best studied on TSS samples, showing species A only: the most accurate are those concerning TSS473, which shows almost maximum specific adsorption of CO together with high surface area.3 The integral heat of adsorption for this system is reported as a function of adsorbed amounts in Figure 6. The straight line represents ideal behavior and has been calculated through a procedure described below. At the highest coverage attained, the repulsion energy is some 5% of the total energy. Discussion Overall Features of CO Adsorption. The presence of two distinct peaks (A and B) in the IR spectra of TS samples pretreated above 420 K indicates the existence of two nonequivalent Ti4+cation sites. Previous work' has shown that B sites carry hydroxyls before dehydration and the A sites molecular water. A structural difference between sites A and B is thus likely to occur; e.g., they probably involve five- and four-coordinate Ti4+cations, respectively. Such a picture is confirmed by the observation that surface sulfates are preferentially located on the surface a t sites B, as CO species B does not form on TSS samples. The present work is primarily concerned with species A. Species B has been dealt with in our previous paper.3 As quoted above, the related optical isotherms were found to be of the Langmuir type (eq l ) , and consequently, the behavior of species B was suggested to be close to ideality. Data in Table I show that the effect of pretreatment on the zero-coverage frequency is much the same for species A and B. In contrast, visual inspection of Figures l a and 2a indicates that the effect of coverage on the stretching frequency is much more limited for species B. A precise measure of the shifts of species B induced by coverage is not possible, due to the partial overlap of IR bands and the small amount of B species (some 15% at the most). A behavior of species B closer to ideality than species A is therefore suggested. Such a discrepancy among the two species may be due to structural differences3 Spectroscopic Features of Species A. Figure 3 shows that on all samples the CO stretching frequency decreases with coverage to an extent which reaches 8 cm-'. On the
896 Langmuir, Vol. 5, No. 4, 1989 other hand, the frequency at vanishing coverage uo is related to the sample history. Dehydration of TS samples causes the increase of uo. Above 623 K, when the surface is free of water' and a maximum coverage of CO adsorbed is attained, further treatment at higher temperature does not alter up Similarly, the elimination of molecular water from TSS samples at 623 K markedly increases uo: the decrease in vo observed when passing from TSS673 to TSS823 is related to some loss of surface sulfates, as monitored by the intensity of the relevant IR modes.' All these features can be rationalized if the stretching frequency of species A probes the electronic charge at the Ti4+sites. This is modified by the presence of either electron-withdrawing centers (sulfates) or electron-donating centers (water, CO), in that the presence at the surface of water decreases uo, as does CO, whereas surface sulfates increase yo. In this picture, it is vital to assume that anatase may easily transmit inductive electronic effects. For fully covalent or fully ionic solids, this ability is nominal, but it is significant for metals. In the case of semiconductors like TiOz or ZnO, such ability is expected to be substantial because of the presence of conduction electrons. Indeed, such phenomena have been observed on ZnO in our laboratory when studying the effect of CO on presorbed Hz." The Zn-H band initially at 1702 cm-' is observed to shift to a lower frequency with increasing CO coverage. The extent of the shift is proportional to the amount of adsorbed CO, in strict similarity with what is reported in Figure 3. Similar behavior was found by Griffin and Yates12 and Denisenko et al.I3 for the adsorption of CO alone on ZnO. As for TiOz, the ability to transmit electronic effects has been already documented in the case of water adsorption on TSS samples.' The sulfate mode initially at 1380 cm-' is observed to shift markedly. Because water is a strong donor, the plot of the shift against the amount adsorbed is linear only in the first stages of adsorption. During the adsorption of CO on TSS673, which Figure 2 refers to, the sulfate mode is also observed to shift to lower frequencies, and the extent is proportional to the adsorbed amount.' All A sites are probably equivalent from a structural point of view, as far as the immediate surrounding of Ti4+ ions is concerned. If the ability of anatase in transmitting electronic effects were perfect, all sites would have the same charge and thus be totally equivalent. It is instead probable that inductive effects due to the presence of a surface species fade away over a few lattice spacings. This fact has two implications. On one hand, it brings about the nonequivalency of the sites at zero coverage, i.e., an unavoidable second-order structural heterogeneity on a surface carrying surface species foreign to the one actually adsorbed, like hydroxyls, molecular water, sulfates. Perhaps, only in the case of clean surfaces like TS673 and TS823, where no sulfates are present as well as no water, there is no structural heterogeneity of the kind under discussion, although the presence of defects and the finiteness of the surface planes may bring about some. On the other hand, during CO adsorption, the mutual interaction of CO adparticles brings about the nonequivalency of sites, both occupied and empty, even in the absence of structural heterogeneity; i.e., it definitely causes an induced heterogeneity. Evidence for this is as follows. (11) Boccuzzi, F.;Garrone, E.; Zecchina, A.; Bassi, A,; Camia, M. J. Catal. 1978, 51, 160. (12)Griffin, G. L.; Yates, J. T., Jr. J . Chem. Phys. 1982, 77, 3751. (13) Denisenko, L. A.: Tsiganenko, A. A,: Filimonov, V. N. React. Kinet. Catal. Lett. 1984, 25, 23.
Garrone et al. The identity of the three slopes for T S on the one hand and for TSS samples on the other one in the plots of Figure 3 is indicative that the same phenomenon, Le., induced heterogeneity, is operative on both kinds of samples. The difference in slope between TS and TSS is again due to the presence, on the surface of the latter, of sulfate species, which are poor electron acceptors. The difference spectra, in particular those in Figure 2b, indicate that inductive interactions are taking place during the adsorption. The presence of small but definite negative bands at higher frequency shows the conversion of high energy sites into lower energy sites, because of inductive interaction. The extent of this conversion is apparently limited because, during the adsorption, it is accompanied by the filling of the adsorbate into new sites at higher energy. Spectroscopic evidence concerning the presence of heterogeneity at any step of adsorption, both structural and induced, comes from the shape of peaks A, which is invariably observed to be Gaussian. It is known'4 that in the absence of heterogeneity the shape of an IR peak is Lorentzian, at the most somewhat distorted by the finiteness of the spectral slits in the case of dispersive instruments or of their equivalent (resolution adopted) in the case of FTIR instruments. From a spectroscopic point of view, heterogeneity brings about the presence of several components at slightly different frequencies: the peak resulting from the overlap of close Lorentzians assumes a Gaussian shape.14 The heterogeneity involved in the present case appears limited, as the half-width of peak A is =13 cm-', close to the values usually found (10-12 cm-') for the stretching band of adsorbed CO. Thermodynamic Features of Species A. Equation 2 is a version of the Temkin isotherm. Because of the relevance of this isotherm to the present paper, details of its derivation are reported in the Appendix. Also reported is the proof that the Temkin isotherm can be derived under the assumption, more realistic than what usually done, that the site distribution function is constant over a relatively narrow range of adsorption energies, say between X,and XI. The extremely good fit of the experimental data to eq 2 is strong evidence in support of the applicability of the Temkin isotherm. Two other independent pieces of evidence are as follows. In the Appendix it is shown that, if the Temkin isotherm holds in the version of eq 2, the integral heat of adsorption must be Qint
= ( X , - R T ) N a- RTKIJx[l - exp(-x)]-'x dx 0
(3)
where x = N,/K, and the other symbols have their usual meaning. In the case of TSS473, K , is evaluated f r o m the adsorption isotherm (not reported for sake of brevity) to be 23.9 f 0.3 x lo-, molecule nm-', as reported in Table 11. The quantity y =
Qint + RTK,
JX[ l
- exp(-x)]-'x dx
has been evaluated as a function of N , and reported in Figure 6. This quantity, if the model is correct, is simply (X,- RT)Na. The proportionality of y to N , (solid straight line) is striking and allows X z to be calculated as 58 kJ mol-'. This is in good accord with the value (59 kJ mol-') (14) Morterra, C.: Ghiotti, G.; Garrone, E.; Boccuzzi, F.J . Chem. Sac. 1976, 72, 2722.
Langmuir, Vol. 5, No. 4 , 1989 897
Heterogeneity among Adsorption Sites
AFo = RT In K z
(5)
Our previous work3J5 has shown that a correlation exists between AS0 and AHo for u-coordinated CO, so that a correlation is also expected between A F ' O and AHo for the same type of adsorption. On the other hand, a correlation exists between AHoand the stretching frequency of adsorbed CO that is u-co~rdinated.~~~~' A correlation is thus expected between the Kz and uo set of values, as observed.
I ', 3 0 4 0 5 I
0
~ g vo-pco =
1
I
0 6 0 I cm-1
Figure 7. Correlation between In K2 and stretching frequency shifts (Au = v,, - UCO) for species A on various samples: TS403, 0;TS473,O; TS673,o; TS823, m; TSS473,O;TSS673,O;TSS823, 0.
obtained by the extrapolation at vanishing coverage of the differential heat curve.3 In the Appendix, it is shown that the standard entropy of adsorption is related to K2 and X 2 : ASo/R = 1 + In Kz - X 2 / R T We make use of the available calorimetric and adsorption data to calculate ASo, in the case of TSS473. It turns out to be ASo = -199 J mol-, K-l. This value is quite plausible and is very close to the standard entropy of adsorption calculated in the Henry region3 of -208 J mol-' K-'. Thus, the T e m k i n isotherm, in the generalized version given in the Appendix, accounts for the all thermodynamic features of the adsorption of species A , namely, energy, entropy, and isotherm. Further support for the validity of the Temkin isotherm comes from the analysis of the K , and K, set of values reported in Table 11. In the Appendix, it is shown that the K1 constant in eq 2 may be evaluated as K1 = NMRT/(Xz - X i ) (4) It is evident that if X2 and X 1were available, it would be possible to calculate NM, the monolayer capacity. X 2 is the adsorption heat at vanishing coverage, but X 1 is not known. By adopting an approximate value of NM, one can use eq 4 to estimate X 2 - X1. Conversely, as in deriving eq 2, the assumption is made (see the Appendix) that X2 - X1is larger than 3RT, so it should result that NM is larger than 3K1. A lower limit of NM in the various cases has been evaluated by assuming 1.3 times the coverage measured a t 90 Torr;3 from the relevant data, reported in Table 11, it is seen that such a lower estimate for NM is, however, 2-3 times larger than K1. The K2 values are observed to parallel the uo values reported in Table I: the correlation diagram is shown in Figure 7. The interpretation is as follows. As shown in the Appendix, the standard free enthalpy change of adsorption at vanishing coverage (from 1mol of gaseous CO at 1 Torr and 303 K to 1mol of CO adsorbed at vanishing coverage) is related to K,:
Conclusions The evidence gathered shows that the nonideal nature of the adsorption of species A arises from heterogeneity, both structural and induced. Both stem from the ability of the semiconductor TiO, to transmit inductive effects: the former is brought about by the presence of foreign surface species (hydroxyls, water, sulfates) and the latter by the interaction among CO admolecules. Structural heterogeneity is responsible for the varying frequency at zero coverage of species A and B on the various samples, for the parallel variations in the K2 parameter in the Temkin equation, and for the varying dependence of the frequency with coverage from sample to sample (different slopes of the diagrams in Figure 3). Both structural and induced heterogeneity are indicated by the following facts: (i) the linear dependence of the CO stretching frequency upon coverage (Figure 3), (ii) the decrease of the molar adsorption heat with coverage (Figure 6), and (iii) the non-Langmuirian behavior of the isotherms. These latter facts are reproduced extremely well by a two-parameter equation, which is a version of the Temkin isotherm. The applicability of the Temkin isotherm has been substantiated by several observations, especially the fact that the same Kz value accounts for the adsorption isotherm and the energetic data for TSS473. The classical derivation of the Temkin isotherm deals with structural heterogeneity only and assumes a constant distribution of sites in a range of energies extending down to zero. We have shown that the latter constraint is easily lifted, in that it is sufficient to assume a constant distribution in a narrow range of energies (some 3RT). On the other hand, we have shown that the Temkin isotherm is applicable also when heterogeneity among adparticles is partly induced. In the present case, the induced heterogeneity represents a relatively mild perturbation of the situation at zero coverage in that (i) the coverage attained is only 20% of the full capacity,'O (ii) the repulsion energy is a small fraction of the total energy as shown in the TSS473 case (5%; Figure 6), and (iii) the plots of the shift of the stretching mode with coverage, shown in Figure 3, are linear, in contrast with the case of electron-releasing agents stronger than CO.' Our feeling is thus that the validity of the Temkin isotherm could be related to the mildness of the induced heterogeneity, therefore representing a first-order perturbative approach to this old subject in adsorption studies. Appendix Generalization of the Temkin Isotherm. The Temkin isotherm, usually written as 8 = c1 + c, In p (AI) stems from the following model.16 Let us assume struc(15) Gamone, E.; Ghiotti, G.; Giamello, E.; Fubini, B. J. Chem. SOC., Faraday Trans. 1 1981, 77, 2613.
Garrone et al.
898 Langmuir, Vol. 5, No. 4, 1989 tural heterogeneity at a given surface, so that CW = n ( X ) d X is the number of sites whose adsorption energy ranges between X and X + dX. Let the sites be noninteracting, so that for any kind of site a "local" Langmuir isotherm holds:
w)= P / ( P + pljZ)
(A21
p l l z ,the pressure at which half of the sites of given energy X are filled, depends on X: pllz = a exp(-X/RT) (-43) a is the same for all kinds of sites and is related to the standard entropy change upon adsorption. Indeed" Ma= RT In pljz= AH" - TAS"
AH" = -X
+ RT
so that
AS" = R - R l n a
(A41
The total coverage 8 a t a given pressure is given by 8 = $[1
+ exp(-X/RT)
a/p]-'n(X) d X
(A5)
with $n(X) dX = 1
(A6)
The Temkin isotherm assumes that the function n ( X ) is a constant and that the energy of the sites ranges between a maximum value XMand zero: 647) from which c = 1/xM. Integration of eq A5 yields 8 = R T / X M In {[l + exp(XM/RT) p / a l / ( l + p/a)J (AS) It is usually assumed that p/a
> 1
(A10)
hence 8 = c1
+ cz In p
(All)
conditions concerning the site distribution. Let us suppose that the site distribution function n ( X ) is constant in a range Xz-X1 (Xz > X,). Then 0 = $x*[l XI
+ exp(-X/RT)
a/p]-'n(X) d X
(A13)
with .f%n(X) dX = 1, n(X) = c, and thus c = l/(X2- XI). 8 is easily calculated to be
which can also be written as e = RT/(X, . - 1 + exp(Xz/RT) P / a xl)In 1 + exp(X,/RT) exp[-(Xz - Xl)RT] p / a It is easily checked that for (X, - Xl)/RT of the order of 3, the denominator in the ratio reduces to unity for values of the pressure not enormous. Equation A14 then becomes N,/NM =
e=
R T In [ l (X, - Xl)
+ exp(Xz/RT) p / a ]
(A151 Equation A14 is correct for both p = 0 and p = m; in eq A15, the coverage diverges as the pressure tends to infinity. Equation A15 may be written as N, = K1 In (1 + K g ) (A161 This equation is formally equal to eq A12; the constants, however, have a slightly different meaning: NMR T K1= * KZ = exp(X,/RT)/a (A17) (XZ - Xl) ' For large p values, eq A17 reduces to N, = K1 In Kz K1 In p = C1 + Cz In p ( A B )
+
the usual form of the Temkin isotherm. It is thus concluded that the Temkin isotherm holds under much less restrictive conditions than is usually assumed. It is straightforward to check that the isosteric heat corresponding to eq A18 is (as expected) qst = x z - (X, - X1)0 (A191
with c1 = 1 - R T In a / X M and cz = RT/XM. This is the usual form of the Temkin isotherm. Note that eq A8 correctly yields 8 = 0 for vanishing p and 8 = 1 for infinite pressures: because of approximations A9 and A10, eq A1 does not, and it is applicable only in an intermediate range of pressures. If only approximation A9 is made, then 8 = N,/NM = cg In (1 + c4p) (AW
The integral heat of adsorption Qintis the quantity actually measured in our calorimeter. It is well-known that14
cg = RT/xM and c4 = exp(XM/RT)/a. Equation A12 has the form of eq 2 in the text. By definition, the isosteric heat of adsorption qst is
Le., the behavior with coverage is parabolic. Considering the case of eq A16, the computation of the isosteric yields
4st =
qdiff
-R
T
qdiff
= (SQht//SN,)
thus SQht/SN, = qst + RT. From eq A18 and A19, it turns out that Qht = (Xz - RT)N, - KlRT N,2
(-420)
- 4 d R = [6 In P / 6 (1/77le It is readily checked that eq A l l yields qst = XM(1 - 8 ) ; i.e., the isosteric heat linearly decreases with 8. The assumption of a constant distribution of sites between XMand zero is quite unrealistic and has taken merit out of the Temkin isotherm, which is often observed to hold, as in the present case. We show in the following that the same expression can be arrived at under less restrictive (16)Tomkins, F. C. Chemisorption of Gases on Metals; Academic Press: London, 1978; p 13.
The corresponding integral heat of adsorption is
Qint = (X, - RT)N, - RTKIJx[l 0
- exp(-x)]-'x dx
(A221 with x = N,/K,. The integral is deceivingly simple and is not explicitly computable: numerical integration is needed. The function to be integrated is that actually used to define Ber-
Langmuir 1989,5, 899-903 nouilli numbers:" it is close to 1 for small x and close to x for large values of x itself. Consequently, the integral is approximately x for small x and =x2/2 for large x .
As far as the standard changes of thermodynamic potentials upon adsorption are concerned, from eq A4 and A17 it results TASO = R T In K , - X,+ R T (A231 This equation can be given a simple interpretation. -X2 (17)Handbook of Mathematical Functions: Abramowitz,M., Stegun, I. A., Eds.; Dover Publications Inc.: New York, 1972;p 804.
899
+ R T is AHo at zero coverage; ASo is the standard entropy change a t any coverage, including 8 = 0. It results that R T In K , = -AFo
(A24
i.e., the standard free enthalpy change a t zero coverage is simply related to K,, which actually acts as the equilibrium constant for the adsorption a t vanishing coverage.
Acknowledgment. We thank the Italian Minister0 della Pubblica Istruzione, "Progetto Nazionale Struttura e Reattivita' della Superfici" for financial support. Registry No. CO, 630-08-0; TiO,, 13463-67-7.
Adsorption of Butadiene on Mo(100) below Room Temperature G. Bredael and W. T. Tysoe* Department of Chemistry and Laboratory for Surface Studies, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 5321 1
F. Zaera Department of Chemistry, University of California, Riverside, California 92521 Received October 8, 1988. I n Final Form: February 28, 1989 Ultraviolet photoelectron spectroscopy indicates that butadiene adsorbs molecularly onto Mo( 100) at 120-150 K. The occupied molecular orbitals are only minimally perturbed on adsorption, and work function measurements indicate that bonding to the surface is by electron donation from the metal to the adsorbed butadiene. Both near-edge X-ray absorption fine-structure measurements and angle-resolved photoelectron spectroscopy indicate that the molecular plane of butadiene is oriented at -40' to the metal surface. Warming a butadiene-covered surface to 200 K results in the thermal transformation of chemisorbed butadiene to a different surface species exhibiting a photoelectron spectrum that corresponds well to that of gas-phase trans-2-butene. This observation is in accord with theoretical predictions that suggest that the middle C-C bond of butadiene should be strengthened relative to the terminal C-C bonds on chemisorption. 1. Introduction The chemisorption of C4 hydrocarbons on well-characterized surfaces has received scant attention in the literature. The catalytic chemistry of olefins over molybdenum has, however, been examined in somewhat more detail, primarily because of its effectiveness as a catalyst for olefin metathe~is.'-~ In contrast to tungsten, single-crystal studies of the chemisorption of small hydrocarbons on molybdenum are rather rare. The majority of the work has focused on the decomposition of t h i ~ p h e n e ~and - ~ sulfur-containing molecules.1°-12 A recent study has reported the effect of coadsorbed sulfur or carbon on the reactivity of a range of C4 hydrocarbon^.'^ More recently, theoretical calcu(1)Goldwasser, J.;Engelhardt, J.; Hall, W. K. J. Catal. 1981,71,381. (2)Engelhardt, J.;Goldwasser, J.; Hall, W. K. J. Catal. 1981, 70,364. (3)Engelhardt, J.; Goldwasser,J.; Hall, W. K. J.Mol. Catal. 1982,15, 173. (4)Gellman, A. J.; Farias, M.; Somorjai, G . A. J.Catal. 1984,88,546. (5)Fulmer, J. P.;Zaera, F.; Tysoe, W. T.J. Phys. Chem. 1988,92, 4147. (6)Gellman, A. J.; Tysoe, W. T.;Zaera, F. Surf. Sci., in press. (7)Roberts, J. T.;Friend, C. M. Surf. Sci. 1987,186,201. (8)Gellman, A. J.;Farias, M. H.; Salmeron, M.; Somorjai, G. A. Surf. Sci. 1984,136,217. (9) Zaera, F.; Kollin, E. B.; Gland, J. L. Surf. Sci. 1987,184,75. (10)Roberts, J. T.;Friend, C. M. Surf. Sci. 1988,202,405. 1987,189,4423. (11)Roberts, J. T.;Friend, C. M. J. Am. Chem. SOC. (12)Roberts, J. T.;Friend, C. M. J. Am. Chem. SOC.1987,109,3872.
0743-7463/89/2405-0899$01.50/0
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lations by Baetzold have compared the chemistry of 1,3butadiene (subsequently referred to as just butadiene) with that of e t h ~ 1 e n e . l ~It is suggested in this work that the butadiene terminal carbon-carbon bonds are considerably weakened on chemisorption while the middle carboncarbon bond is at the same time considerably strengthened. The study also indicates that bonding to a metal surface, particularly when the metal is near the center of the periodic table, is by donation into the T antibonding orbitals, leaving the adsorbed molecule with a residual negative charge. These conjectures are borne out experimentally by the data presented below. Finally, Baetzold calculates an equilibrium geometry in which the molecules lie parallel to the (111) face of an fcc metal. The angle-resolved photoelectron spectroscopic and NEXAFS data presented below indicate that on Mo(100) the molecular plane of butadiene is, in fact, tilted with respect to the surface. 2. Experimental Section The angle-resolvedphotoelectron spectroscopy and near-edge X-ray absorption fine-structure (NEXAFS) experiments were carried out at the Brookhaven National Laboratory on the National Synchrotron Light Source on beam line U14A. The ap(13) Kelley, D. G.; Salmeron, M.; Somorjai, G . A. Surf. Sci. 1986,175, 465. (14)Baetzold, R. Langmuir 1987,3, 189.
0 1989 American Chemical Society
