3236
The Journal of Physical Chemistty, Vol. 83, No. 25, 1979
Halsey and Yeates
of the U.S. Department of Energy. This is Document No. NDRL-2006 from the Notre Dame Radiation Laboratory.
(10) R. A. Marcus, J. Chem. Phys., 24, 966 (1956); 20, 867, 872 (1957); Discuss. Faraday Soc., 29, 21 (1960); J. Phys. Chem., 07, 853 (1963); Annu. Rev. Phys. Chem., 15, 155 (1964). (11) (a) G. S.HarHey and J. W. Roe, Trans. Faraday Soc., 30, 101 (1940); (b) P. Murkeriee and K. Baneriee. J . Phvs. Chem.. 08. 3567 (1964). (12) M. S.Fernhdez and P. Fromherz, J. Phys. Chem., 81, 1755 i1977). (13) M. Almgren, F. Grieser, and J. K. Thomas, J. Am. Chem. Soc.,101, 219 (1979). (14) L. K. Patterson and J. Lilie, Int. J. Radiat. phys. Chem., 6, 129 (1974). (15) R. H. Schuler and G. K. Buzzard, Int. J . Radiat. Phys. Chem., 8, 563 (1976). (16) Farhatazis and A. B. Ross, Natl. Stand. Ref. Data Ser., Nafl. Bur. Stand., No. 59 (1977). (17) B. E. Huime, E. J. Land, and G. 0. Phillips, J . Chem. Soc., Faraday Trans. 1 , 68, 1992 (1972). (18) A study of fluorescence quenching on a NaLS micelle &ace indicates that an encounter between probe and quencher on the surface typicaliy occurs in 50 ns. M. Almgen and J. E. Lijfroth, to be p u b l i i . (19) M. Almgren, unpublished observations. (20) M. Gratzel, Nachr. Chem. Tech. Lab., 20, 515 (1976). (21) Y. I. Ibn, D. Meisel, and G. Czapski, Isr. J. Chem., 12, 891 (1974). (22) J. K. Thomas and M. Almgren in "Proceedings of the Section on Solution Chemistry of Surfactants", 52nd Surface and CdloM Science Symposium, Knoxville, TN, June 12-14, 1978, K. L. Mittal, Ed., in press.
References and Notes H. T. Witt in "Bioenergeties of Photosynthesis", Govindjee, Ed., Academic Press, New York, 1975. J. J. Grimaldi, S.Boiieau, and J.-M. Lehn, Nature (London),265, 229 (1977). W. E. Ford, J. W. &os, and M. Cabin, paper presented at 2nd DOE solar photochemistry research conference, Brookhaven National Laboratory, May 8-10, 1978. (a) A. Hengleinand M. Gratzel in "Sohr Power and Fuels", J. R. Bolton, Ed., Academic Press, New York, 1977. (b) M. Gratzel, J. J. Kozak, and J. K. Thomas, J. Chem. Phys., 02, 1632 (1975). (a) D. J. W. Barber, D. A. N. Morris, and J. K. Thomas, Chem. Phys. Lett., 37, 481 (1976); (b) D. J. W. Barber and J. K. Thomas, Radiat. Res., 74, 51 (1978); (c) W. Schnecke, M. Gratzel, and A. Henglein, Ber. Bunsenges. Phys. Chem., 81, 821 (1977). D. Meisel and G. Czapski, J . Phys. Chem., 79, 1503 (1975). D. Meisel and P. Neta, J . Am. Chem. Soc., 97, 5198 (1975). P. Neta, M. G. Simic, and M. Z. Hoffman, J. Phys. Chem., 80, 2018 (1976). (a) D. Meisel, Chem. F'hys. Lett., 34, 263 (1975); (b) D. Meisel and R. J. Fessenden, J. Am. Chem. Soc., 98, 2505 (1976).
Chemisorption of Hydrogen on Metals. The Inert Surface Model G. D. Halsey" and Alan T. Yeates Department of Chemistry, University of Washington, Seattle, Washington 98 195 (Received May 1 1, 1979) Publication costs assisted by the National Science Foundation
The thermodynamics of adsorption of hydrogen on Ni(lll), Ni(llO), Ni(100), Pd(lll), Pd(llO), and Pt(lll), as measured by Ertl and his collaborators, have been analyzed by means of the unperturbed or inert surface model for the Langmuir and mobile cases. We find the model inadequate, grossly so for the system Pt(ll1). An alternate explanation of the large surface entropy is found in the possibility of appreciable changes in binding between metal atoms in the surface of the sort that can lead to restructuring as a function of temperature or coverage.
Introduction The chemisorption of hydrogen on metal, surfaces has been one of the most widely studied of surface phenomena from Langmuir to the present day. The measurements of Ertl and his collaborator^^-^ provide interesting data for the adsorption of hydrogen on a variety of clean metal crystal faces. These measurements are made under similar conditions and cover roughly the same ranges of temperature and pressure. Although qualitatively similar, they show interesting differences. Shape of the Isotherms In Figure 1, we contrast the shape of the results on Ni(llO), Ni(lll), and Pt(ll1) with each other and with the = Langmuir equation in its dissociative form, (P/Po)1/2 8/(l - 8). The point of inflection as nearly as can be discerned is selected as 8 = 0.5 and the logarithmic pressure axis is shifted to make the isotherms coincide at this point. Note that the adsorption on Ni(ll0) is associative relative to the Langmuir equation. This has been interpreted as a tendency toward phase separati0n.l Ni(ll1) is adequately represented by the Langmuir equation, while the results on Pt(ll1) deviate in a manner characteristic of adatom repulsion. The remaining systems available for study, Ni(100), Pd(llO), and Pd(lll), are close to the Langmuir equation, and thus can be regarded as simple dissociative adsorption on independent sites. When, as in the case of Ni(llO), the isotherm becomes nearly vertical, and thus indicates a two-dimensional phase separation, there is no clear dis0022-3654/79/2083-3236$01 .OO/O
tinction from the standpoint of thermodynamics between atomic and molecular adsorption. However, entropies and enthalpies calculated below are in no way distinctive from the clear cases of atomic adsorption, and so we have analyzed all the cases from the atomic standpoint. Similarly, when the adsorption process is extended over more cycles of (logarithmic) pressure, this pheqomenon has an alternate explanation in terms of mobile adsorption. However, our isotherm is roughly symmetrical about 8 = 1 / 2 and this is not the case with mobile isotherm^.^ The deviations can be adequately represented by the crude Fowler-Guggenheim i ~ o t h e r mwhich , ~ includes an interaction energy w
(P/Po)1'2 = [e/(l
- @I
exp[(2w/(kT))@ - 1/21]
(1)
The value of w / ( k T ) required to fit the Ni(ll0) data is about -1.5 and that for Pt(ll1) is +2.3. The reported heats of adsorption are substantially constant over the range of interest, but small variations implied by these w values of a few R T could be lost in the inherent errors in the measurements, especially at the extremes of 0.
Values of AH' and A S o per Mole of Atoms The data are treated in the standard way; if Po is the pressure at half-coverage (in the middle of the temperature range studied) then we define AGO = (1/2)RT log (Po/760) (2) AH" = a(AG"/T)/a(l/T) 0 1979 American
Chemical Society
(= -qisosteric)
(3)
The Journal of Physical Chemistty, Vol. 83, No. 25, 1979 3237
Chemisorption of Hydrogen on Metals
E e d x e d o r e s u r e PIP0
Flgure 1. Selected data points estimated from published smooth curves compared with the Langmuir equation for dissociative adsorption.
ASo = (AHo - AG")/T = So(surf)- (1/2)s0H, (4) for the reaction (1/2)H2= Hads. Results for six cases are presented in Table I. The anomalous nature of the results on Pt(ll1) first pointed out to us by Professor Ertl are apparent. There should be no difficulty in explaining what amounts to only a small variation in the binding energy to the surface but the entropy value will be analyzed in greater detail.
The Inert Substrate Hypothesis In order to analyze these data further, we must assume a model for dissociative adsorption. Most simply, we assert that the underlying metal surface is unperturbed. The entropy of adsorption is determined by the motions of the hydrogen alone, which on the surface can be divided into configurational and vibrational parts. The configurational part can be eliminated if the analysis is based on Po, the pressure at 8 = 1/2. We will modify Hill's treatment of Langmuir adsorption6 to conform to the dissociative case. He writes P / ( k T ) = log [8/(1 - 8)ql (5) where q is the vibrational partition function for the adatom. When p is equated to 1 / 2 the chemical potential of gaseous H2 we find (in units per atom of H) 8 = XP'/Z/(l
+ xP1/2)
(6)
where log x = -log Po1/' = log + p 0 H 2 / ( 2 k T ) = log q + (H0~,/(2kT))- ( S O H ~ / ( ~ ~ ) =) -AG"/kT (7) Then a[-log Pol'2]/a(l/(kT)) = -AH0 = a 1% q/a(l/(kT)) From these two equations we find AS"/k = [log 4
f
H'H,/~ (8)
Ta log q/aT] - s o ~ , / ( 2 k ) (9)
This equation is equivalent to (in units per mole of H atoms)
= ( s O ~ ~ / 2 f)
Aso = Nk[lOg 4 + Ta log q / a q
= Sosurf(10) because the quantity in brackets is equivalent to S ~ b / kfor the three vibrations of the adsorbed H atom. Since the crude F-G isotherm has the same configurational entropy as the Langmuir case, the same equation for S,, will apply. Svib
Crude Validity of the Lattice-Gas Interpretation The accuracy of the column giving the entropy of hydrogen on the surface, aside from the model chosen, depends on two numbers. The first is the isosteric heats of adsorption per atom; these agree with one half the molar heats as given by Ertl within 0.1 kcal in each case. Errors listed are based on the scatter in the points read off the figures. Of more concern is the value of the pressure at one-half coverage, which because of the model must be identified with the point of inflection in the coverage vs. the logarithm of pressure plot. If this is off by a factor of 2, which seems rather extreme, there would be an error of about one in S / k . Since we are comparing a series of similar experiments with marked qualitative differences, these errors do not seem to be of serious consequence. Even thermal transpiration corrections would affect the results in a nearly constant fashion. Within the accuracy of the data, we have no basis for modifying the interpretation of the relation of A@ to coverage. As long as the function we interpret as coverage is symmetrical on the log P plot around what we interpret as half-coverage and lacks any incidents or bumps we are limited to a Langmuir-type interpretation. The relatively small values of w / ( k T ) , the lateral interaction term, show how close we are in form to the simple lattice statistics. Of course we have no direct clue as to the lattice site occupied by a single H, but that does not enter directly into the simple Langmuir theory. That is, in crystallographic terms, the maximum value of 8 can and often does assume values of 1 / 2 or perhaps 2, but for interpretation in terms of simple lattice theory these coverages must be normalized to unity, unless there are two kinds of sites with widely disparate binding energy, in which case the isotherms on the log pressure plot would show an intermediate plateau. We have nothing to offer in any reinterpretation of the change in contact potential vs. coverage, except to point to the relatively good fit of the data, as presented by Ertl et al., to a lattice equation. Evaluation of the Vibration Frequencies Wang and Weinberg7have made calculations of the first excited state for vibration perpendicular to the metal crystal faces, and these correspond to frequencies of vibration of about 3 X 1013for both Pd and Ni. The contribution of this degree of freedom would thus be of the order of S / k = 0.05 and is thus completely negligible for our purposes. We must therefore look for the entropy in the two modes parallel to the surface. The assumption of a common harmonic mode of vibration leads to an evaluation of the entropy given by eq 10 of the form - In (1 - e-hv/(kn)] S v i b = 2Nk[(hv/(kT))(ehV/@n (11)
TABLE I: Thermodynamic Quantities per Mole of H Atoms AH",kcal/mol Ni(100) Ni( 110) Ni( 111) Pd(ll0) Pd( 111) Pt( 111)
-11.3 i -11.5 i --11.2 It -11.4 I
0.2 0.2 0.2 0.3 -10.6I 0.2 -4.74 f 0.1
AS", cal/(mol K)
-9.5 i: -10.8 f -7.7 i -10.7 i -7.5 f +1.1i
0.6 0.5 0.5 0.9 0.7 0.2
BE, kcal/mol 63.5 i 63.7 i 63.4 ri: 63.6 i: 62.8 i 56.76 f
0.2 0.2 0.2 0.3 0.2 0.03
T,K
Po,torr
350 350 350 350 350 250
8.3 x 1 . 7 x 10-7 1.8 X 2.1 x 10-7 7.5 x 1.28 X
-___
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The Journal of Physical Chemistty, Vol. 83, No. 25, 1979
TABLE 11: Quantities Related to the Inert Surface Model S”I(Nk ) vexpt, s ’ Ni(100) 3.3 3.8 x 10l2 N i ( l l 0 ) 2.7 5.3 x 10l2 N i ( 1 l l ) 4.3 2.3 X 10” P d ( l l 0 ) 2.7 5.5 x 1 O I 2 P d ( l l 1 ) 4.4 2.2 x 10l2 P t ( l l 1 ) 8.1 2.5 X 10” a
Classical amplitude.
Avib =
x,a
area,& Avib,c 82 ‘42
a
1.01 0.71 1.66 0.70 1.66 12.9
6.20 8.76 5.37 10.7 6.55 6.65
3.18 1.58 8.69 1.52 8.66 525
Area per surface metal atom
7~3~’.
The values of S v i b calculated from eq 10 and the corresponding frequencies from eq 11 are given in Table 11. (Values of SoHzwere obtained from the JANAF tablesas) These frequencies are generally low when compared to bending modes in molecules where the reduced masses are roughly hydrogenic; for example, the lowest frequency for SiH48is 910 cm-l or 2.7 X 1013s-l. Some idea of the reasonableness of these values can be obtained by calculating the area swept out by the classical amplitude, x , of these supposed vibrations, from the formulas x = [ k T / ( 2 ~ ~ m ) ] ’ /or ~/v Avib
= nx2 = kT/(2xmv2)
(12)
Values of these areas are given in Table 11. Any value that exceeds the area per metal atom in the surface is clearly unreasonable, because such a wide excursion contradicts the model of localized adsorption.
Mobile Adsorption It is not generally considered that chemisorption can be represented by dissociative adsorption, with the adatom free to translate in two dimensions. However, Einstein and Schriefferghave made calculations for the binding energies of hydrogen on the 100 face of a transition metal, at top, bridge, and center locations in the cell. For certain values of the electron-filling parameter these energies cross each other and so assume the same value. Although not directly applicable to our systems, this calculation clearly shows the possibility of mobility coupled with strong vertical binding of the adatom. Again we modify the treatment of Hill for mobile adsorption on an inert surfaces6In the limit of low coverage the isotherm has the form d = xP1i2= (P/Po)li2
(13)
The reference state is the (extrapolated) pressure where 6’ = 1 (maximum coverage). If we use the Langmuir equation to crudely approximate nonideality, the pressure Po is approximated by the pressure at d = 1/2. With the same definition of‘ASO we again find that for mobile adsorption -
Strans = (S,,/2)
+ ASo = Nk[log q’+
Ta log q’/aTl = Psurf (14)
where if we neglect vibration normal to the surface q f = 2nmkTAo/(h20)
(15)
where A. is the area of the molecule when d = 1, at which value it is set for the calculation
St,,, = Nk(1og [2nmkTAo/(h2d)]+1) (at d = 1)
(16)
We note that this is a differential entropy and that SS dd from zero to unity gives the two-dimensional SackurTetrode entropy
Halsey and Yeates
S = Nk[log (2nmkTAo/h2) + 21
(17)
which differs by a factor of R. Note that for the classical limit the harmonic oscillator entropy given by eq 10 will equal the mobile entropy from eq 16 when log [ ( k T / ( h ~ ) )+~ ]1 = log (2nmkTAo/h2)
(18)
If we eliminate the frequency from eq 18 by the use of eq 12, we obtain the simple result that A. must equal the value of Avibin Table I1 multiplied by the base of natural logarithms. For mobile adsorption there is no requirement that the area per molecule of a complete surface film correspond to any unit area of the underlying surface, but rather that it be of the order of the supposed size of the adatom. The area so required on the Pt(ll1) surface is clearly an order of magnitude too large. Also, because of the pressure range of the isotherms on this surface, which extend to a much lower pressure at low coverage than the Langmuir equation predicts, the use of this equation to obtain the low-coverage Henry’s law constant is a rough approxima-tion, and the direction of the error is to underestimate Sbmsand thus Ao. We can thus assert that even the assumption of completely mobile adsorption over an inert substrate is also unreasonable for the case of Pt(ll1).
Mobile Vs. Immobile Adsorption We should remind the reader of the confusion over the meaning of “mobile” which dates back at least 40 years. In the English (Rideal-Roberts) literature “mobile” meant able to move from one site to the other by any means, and not be immobilized where the molecule landed. “Mobile” thus meant equilibrium adsorption. In the statistical mechanical literature (Fowler extended by Hill) it meant that (more strictly) a translational partition function was written for the two dimensions of freedom parallel to the surface at low coverage. Calculations such as those in ref 9 generally show that there is a periodic fluctuation of vertical binding energy over the surface, which renders matters difficult even at zero coverage, unless the periodic variation is strong enough to immobilize the adatom. We have noted that a similar but different area parameter is basic in both extremes: the area of a lattice site for binding, and the area per adatom in a close-packed mobile layer. The latter, by hypothesis, is independent of the underlying lattice, and is equivalent to the packing in a dense phase of H atoms. An exact evaluation of the latter depends on an extrapolation of the experiments to zero coverage, which is not possible with these data. All we can assert is that the areas are of the same magnitude, and must reasonably be of the order of molecular dimensions. An intermediate treatment with some mdbility and some lattice trapping would presumably be somewhere in between as with a temperature dependent interplay of the two parameters, and would not be expected to make any gross change in the analysis. Perturbation of the Metal Surface The failure of our calculations based on an inert metal surface to account for at least one of the cases considered prompts us to seek an alternate explanation. Evidence exists, in the form of two peaks in the flash desorption data, that there may be two binding states for hydrogen on Pt(ll1). There is certainly no evidence for any gross difference in binding in the heat of adsorption, which is constant, or the isotherm, which is smooth. Two slightly separated states might explain the apparent broadening we have tentatively accounted for by repulsion. A simple calculation with two areas and two Langmuir constants
Raman Spectra of Pentaborane(9)
shows, however, that the surface entropy is reduced by such a model; the greatest entropy is produced by random distribution between sites. We are thus led to consider the perturbation of the surface by a layer of adatoms. Dobrzynski and Mills’” have considered the model of a layer of adatoms half the mass of the underlying solid, and calculate effects of the order of the gas constant R per mole. This result is of qualitative interest to us only. The effect of a hydrogen atom on a platinum atom in the surface could possibly be more important than a small change in the reduced mass for the vibration of the platinum atom. Recently, an analysis by Barker and Estrupll has shown that restructuring of metal surfaces can be dependent on temperature, and that in fact the long-range structure appears at lower temperature rather abruptly, thus showing that it has a lower entropy than the underlying 1 X 1 structure. He has also cast doubt on the usual identification of integral coverages with thermal and LEED phenomena. These observations would suggest that the inert surface model of chemisorption is very inadequate, since if the position of atoms in the surface is so lightly fixed that a moderate temperature change will induce a quasi-phase change then the presence or absence of strongly bound adatoms might reasonbly be expected to cause binding changes in the metal layer. The accompanying entropy change would of course be reflected in the AS’ for adsorption. A recent study of the vibration amplitude of platinum atoms in the Pt(ll1) face12by Norton et al., by means of the temperature variation of surface relaxation times,
The Journal of Physical Chemistry, Vol. 83,No. 25, 1979 3239
corroborates that this surface is far from inert, and raises the question of whether surface adatom binding might also affect vibration amplitude and thus frequency. Similar studies might be possible in the presence of adsorbed hydrogen. It would be unwise to make any quantitative estimate of the change in vibration frequency in the metal atoms at the surface without an analysis that is beyond our ability at this time. Certainly the vibration would have to be in the classical range and the ratio of the frequency before and after adsorption would have to be of the order of two or more. Aside from the explanation of the thermodynamic data, such a change might have an important effect on such diverse processes as the catalysis of hydrogenation and the effect of chemically active gases on the sintering process.
References and Notes (1) K. Christmann, 0. Shober, G. Ertl, and M. Neumnn, J. Chem. Phys., 80, 4528 (1974). (2) K. Christmann, G. Ertl, and T. Pignet, Surf. Sci., 54, 365 (1976). (3) H. Conrad, G. Ertl, and E. E. Latta, Surf. Sci., 41, 435 (1974). (4) W. A. Steele, “The Interactian of Gases with Solid Surfaces”, Pergamon Press, Oxford, 1974. (5) R. Fowler and E. A. Ouggenheim, “Statistical Thermodynamics”, 2nd ed, Cambridge University Press, London, 1960, p 431. (6) T. L. Hill, “An Introduction to Statistical Thermodynamics”, Addlson-Wesley, Readlng, Mass., 1960, p 128. (7) S. W. Wang and W. H. Weinbarg, Surf. Scl., 77, 14 (1978). (8) JANAF Thermochemical Tables, 2nd ed., hbti. Stand. Ref. Data Ser., Natl. Bur. Sfand., No. 37 (1971). (9) T. L. Einstein and J. R. Schrieffer, Phys. Rev. E?, 7 , 3629 (1973). (10) L. Dobrzynskl and D. L. Mills, J. Phys. Chem. So/&, 30, 1043 (1969). (11) R. A. Barker and P. J. Estrup, Phys. Rev. Lett., 41, 1307 (1978). (12) J. A. Davies, D. P. Jackson, N. Matsunemi, P. R. Norton, and J. V. Anderson, Surf. Scl., 78, 274 (1978).
Raman Spectra and Vibrational Dephasing of Pentaborane(9)‘ V. F. Kalaslnsky Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762 (Received June 1 1, 1979) Publication costs assisted by Mississippi State Universi@
have been recorded for the gas and liquid phases. For the liquid state, the vibrational The Raman spectra of dephasing times associated with the totally symmetric skeletal vibrations have been found to be 3.0 and 2.2 ps at room temperature. The temperature dependence of the line widths are consistent with activation energies of less than 1 kcal/mol for dephasing. Additionally, moderately high resolution infrared spectra of the gas phase have been recorded and combined with the Raman data in order to assign natural isotopic data and verify previously proposed vibrational assignments.
Introduction The molecular symmetry of pentaborane(9) has been shown to be ClU by a number of techniques including microwave a b ~ o r p t i o nX-ray , ~ ~ ~diffraction: and electron As shown in Figure I., the boron atoms form diffra~tion.~ a square pyramid, and four of the hydrogen atoms are in bridging positions around the base. Vibrational spectra6-* indicate the existence of bridging and nonbridging hydrogen atoms and are fully consistent with the other data. In the recent microwave study2 of 15 isotopic modifications, a complete structure was determined, and there was an indication of a large amplitude vibration associated with the bridging hydrogen atoms. By virtue of its ClUsymmetry, pentaborane(9) is a symmetric top, and, as such, a study of the contours of its Raman lines for the liquid phase can, in principle, provide 0022-3654/79/2083-3239$01 .OO/O
information concerning vibrational dephasing and reorientational rela~ation.~ The latter relaxation process can be related to nuclear magnetic resonance experiments for quadrupolar nuclei like lIB, and Tl measurementslO carried out for pentaborane(9) indicate an activation energy of 1.6 kcal/mol for reorientation.ll The theoretical bases for both relaxation processes are fundamental to the understanding of interactions in the liquid state. At the outset it was our intention to measure the vibrational dephasing and reorientationd relaxation times for B,Hg. The natural distribution of logand IlB isotopes complicatesthe spectra considerably. Consequently,it has been necessary to reinvestigate the entire vibrational spectrum by using the higher resolution of current instrumentation. The results of this study are reported herein. 0 1979 American Chemical Society
