4
Langmuir 1987, 3, 4-12
it. Did he still believe in a single layer of adsorption, in spite of the fact that most isotherms did not obey it? His equation was one of the reasons for getting his Nobel Prize in 1932, and did he consider it untouchable? Certainly his strange silence implies resentment. It is very strange - that he did not declare himself pro or con. The BET paper was recommended for the Nobel Prize but did not receive it. [However, it is still, after almost 50 years, among the most frequently quoted papers in the
field. As for practical applications, suffice it to say that one place alone, the Institute of Catalysis of the USSR Academy of Sciences, makes some ten thousand BET surface area measurements per year.]’
Stephen Brunauer Clarkson Professor Emeritus (7) Added by the Editor.
The Langmuir Lectures Phase Transitions at Gas/Solid Interfaces G. Ertl Fritz-Haber-Institut der Max-Planck-Gesellschaft, 0-1000 Berlin 33, West Germany Received October 13, 1986 Langmuir’s concepts on gas/solid interactions are now accessible to direct experimental investigation by the use of well-defined single-crystal surfaces and the techniques of surface physics. The operation of interactions between adsorbed particles gives rise to a large variety of two-dimensionalphases and phase transitions. Chemisorption may even cause displacements of the surface atoms, and nonequilibrium transitions of this kind are coupled to kinetic oscillations in Langmuir’s “classical”catalytic reaction: CO oxidation on platinum.
Introduction: The Langmuir Adsorption Isotherm On April 21,1915, Langmuir wrote into his laboratory notebook:’ (1) The surface of a metal contains atoms spaced according to a surface lattice. (2) Adsorption films consist of atoms or molecules held to the atoms forming the surface lattice by chemical forces. The published version2 of these ideas reads as follows: “The surface of crystals resembles to some extent a checkerboard. When molecules of gas are adsorbed by such a surface these molecules take up definite positions with respect to the surface lattice and thus tend to form a new lattice above the old”. These (at that time revolutionary) conclusions were based on rather indirect evidence obtained from measurements of the equilibrium gas uptake of metal surfaces a t very low pressures and led to the famous Langmuir adsorption isotherm. Nowadays the preparation of surfaces of the kind Langmuir had in mind, namely, consisting of a single type of atoms which are (1) Langmuir, I. Laboratory Notebook No. 618,April 21,1915;p 30. Quoted from Gaines, G. L.; Wise, G. In Heterogeneous CatalysisSelected American Histories; Davis, B. H., Hettinger, W. P., Eds.;ACS Symposium Series 222;American Chemical Society: Washington, DC, 1983,p 13. (2)Langmuir, I. J. Am. Chem. SOC.1918,40, 1361.
equally spaced within a lattice with two-dimensional periodicity, i.e., clean single-crystal surfaces, is a matter of routine. Figure 1shows an experimental adsorption isotherm for CO on a Pd(ll1) surface,&together with various attempts to fit the data with a Langmuir isotherm: The agreement is poor with respect of the detailed shape of the isotherm, and there is an additional serious shortcoming if we consider the absolute coverage at saturation, :e, If we define 0 by the ratio of the number of adsorbed particles over the number of atoms forming the topmost layer of the solid, the actual value of e, is =0.7, rather than 1 as in the simple Langmuir picture. These deviations become also evident from a glance at the variation of the isosteric heat of adsorption Ed with coverage as derived from a family of adsorption isotherms taken at various temperatures3* (Figure 2). Instead of being constant up to 6’ = 1, Ead drops suddenly at 0 = and then starts to decrease markedly around 0 = 0.5, signaling the approach of saturation. Figure 3 shows the structures of the adlayers at various coverages as derived from LEED experiment^:^ Up to 8 (3)(a) Ertl, G.; Koch, J. 2. Naturforsch., A 1970,25A, 1906. (b)
Conrad, H.;Ertl, G.; Kiippers, J. Surf. Sci. 1978,76,323. (c) Bradshaw, A. M.; Hoffmann, F. M. Surf. Sci. 1978,72, 513.
0743-7463/87/2403-0004$01.50/00 1987 American Chemical Society
Langmuir, Vol. 3, No. I, 1987 5
The Langmuir Lectures
E
C O / Pd( 111 1 T2L53K
0
2
6
4
b = 0.9
8
12
10 b P Longmuir: 4 = 1 + bp
14 xl0”Torr
Figure 1. Experimental adsorption isotherm for CO/Pd(lll) at 453 K (dots) and several attempta to fit the experimental data with a Langmuir isotherm (dashed lines).
kx
Kcal mol , E a d
\
25
‘1
20
\
\--’
Figure 4. One-dimensional potential diagram for an adsorbed particle illustrating the superposition of the periodic potential from the substrate and the interaction potential with a second
particle.
0.4 Figure 2. Heat of CO adsorption on Pd(ll1) as a function of 0.2
0
coverage.
COlPd(111)
a
b
8 = 0.5
8 = 0.33
C
8 -063
d
8 - 066
Figure 3. Structures of CO overlayers on Pd(ll1) at various
coverages.
= 1/3 the CO molecules occupy identical adsorption sites with threefold coordination, leading to a periodic v’3X 1/3/R30O superstructure at 8 = 1/3 (Figure 3). Beyond this coverage the unit cell of the overlayer is continuously compressed (therefore the sudden drop of Ed at 8 = l/J until a ~ ( 4 x 2 )structure with twofold coordination is formed at B = 1 / 2 (Figure 3b). At even higher coverages, incommensurate structures (Figure 3c,d) appear in which the adsorbed particles approach a close packing with onlylittle correlation to the structure of the substrate. With adsorbed layers the formation of two-dimensional phases with long-range order is more the rule than the exception. This phenomenon is obviously caused by the operation of interactions between the adsorbed particles-an aspect which was missing in the simple Langmuir model. In the outlined example the repulsive interaction due to the “size” of the adsorbed molecules
determines the saturation coverage, rather than the density of surface atoms. However, he also recognized this problem: “The molecules of many gases will be so large that they cannot occupy adjacent elementary spaces on the crystal surface”.2 More generally, the periodic potential as “seen” by a single adsorbed particle due to the periodicity of the substrate lattice has to be superimposed by the mutual interaction potential if a second adsorbed particle is approaching. This situation is schematically illustrated by the one-dimensional diagram of Figure 4 The interplay between the substrate and the -interaction potential determines whether the second particle will still prefer a site given by the substrate geometry (leading to so-called lattice gas structures) or if ita location is governed by the mutual interaction (causing the formation of incommensurate structures). Frequently a compromise between both situations is met in that the lattice of an incommensurate structure (lattice constant b) matches with the substrate lattice (lattice constant a) after a certain number of lattice constants (e.g., 4b = 5a, “coincidence lattice”). The interactions between adsorbed particles may have different origin (van der Waals, dipole-dipole, “indirect”) and may be repulsive as well as attractive, giving rise to a large wealth of two-dimensional phases and phase transformation^.^ The “indirect” interactions are of particular relevance for chemisorption systems and are mediated by the valence electrons of the substrate through its lattice.6
Physisorption Systems and Multilayer Adsorption Physisorbed particles such as noble gases, N2, etc. are frequently characterized by the formation of incommensurate structures and more or less densely packed configurations characterize completion of the monolayer as (4) (e)Ordering in T w o Dimensions; Sinha, S . K., Ed.; Elsevier: New York, 1980. (b) Ber. Bunsenges. Phys. Chem. 1986, 90,184-316. (c) Fluwe Transitions in Surface Films; Dash,J. G., R u d d s , J., Eds.; Plenum: New York, 1980. (5) Einstein, T. L. CRC Crit. Rev. Solid State Mater. Sci. 1978,7,261.
6 Langmuir, Vol. 3, No. 1, 1987
The Langmuir Lectures
jz5.10-5
-6
"
L
655K
d 66LK
u 682K
T (Kelvin)
-
695K
/
P 1.10-6
[Torr)
Figure 7. Xe/Pd(100): Histogram of the layer population as a function of pressure and temperature. HlPd (1001
0 = 0.5
Figure 8. Structure of the ordered ~ 2 x 2phase formed by H
9599K
adsorbed on Pd(100).
rather than by the concentration of lattice points. As a consequence the ( n + 1)th layer is forming already before the nth layer is completed-leading to smooth isotherms without any discontinuities. Studies with uniform surfaces at low enough temperatures reveal that this is by no means the case.7 As an example, Figure 6 shows g series of isotherms for the adsorption of Xe on a stepped Pd(100) surface* which exhibit, at low enough temperatures, pror i nounced steps marking first-order phase transitions after o i 0 1 completion of the first, second, etc. monolayer. Only above 10-9 Ib-8 h - 7 7 0 - 6 io-5 ,b-~ 10-3 68 K the isotherms tend to become smooth, signaling the PRESSURE (Torr1 onset of n + 1 layer formation before the nth layer is Figure 6. Adsorption isotherms for Xe on a stepped Pd(100) completed. In the present case the use of ultraviolet surface. photoelectron spectroscopy (UPS) enabled direct determination of the equilibrium populations of the various in the preceding example of CO adsorption. This aspect layers as f ( p , T ) . The results presented in Figure 7 demwas again recognized by Langmuir about 70 years ago:2 onstrate indeed up to -68 K a layer-by-layer growth "The properties of adsorbed molecules may often determechanism, while above this temperature the third layer mine the amount adsorbed where the forces acting between becomes already partly occupied before the second layer adjacent adsorbed molecules are comparble with those is completed. This particular kind of phase transition is holding the molecules on the surface". called a "roughening transition", for which the theory was A large number of thermodynamic and structural indeveloped first in a quite different field, namely, crystal vestigations on such systems was first performed with growth, in a classical paper by Burton, Cabrera, and graphite and later extended also to metal single ~ r y s t a l s . ~ * ~Frank,g and was extended more recently by various inAs an example, Figure 5 shows two structures formed by vestigators.1° CO on graphite as reported by Fain.6C The natural extension of the Langmuir isotherm for the Chemisorbed Lattice Gas Systems description of multilayer formation in physisorbed systems We now return to chemisorbed systems for which is the well-known BET i ~ o t h e r m .The ~ model is inconsemultilayer formation plays no role, and if the temperature quent in so far as again "the forces acting between adjacent adsorbed molecules" are neglected, although the monolayer capacity is assumed to be determined by dense packing (7) Brunauer, S.; Emmett, P. H.; Teller, E. J.Am. Chem. SOC.1938, Y
, . , , . , , l , . , , , , , , , ,
~
-
- --
60. - - , RnQ..
( 6 ) (a) Thomy, A.; D u d , X.; Regnier, J. Surf. Sci. Rep. 1981,1,1. (b) Dash, J. G. Phys. Today 1985, 38, 26. (c) Fain, S. C. Ber. Bunsenges. Phys. Chem. 1986,90,211. (d) K e n , K.; David, R.; Palmer, R. L.; Comsa, G. Phys. Reu. Lett. 1985, 56, 620.
(8)Miranda, R.; Albano, E. V.; Daiser, S.; Wandelt, K.; Ertl, G.J. Chem. Phys. 1984,80, 2931. (9) Burton, K. W.; Cabrera. N.; Frank, F. C. Philos. Trans. R. SOC. London, A 1951, No. 243, 229.. (IO) Weeks, J. D.; Gilmer, G. Adv. Chem. Phys. 1979, 40, 157.
Langmuir, Vol. 3, No. 1, 1987 7
The Langmuir Lectures I
25
I1O~”AI
is
a
I I t
I
H /Fe (1101
I
I
T
300
b l
[ K ] 250
i
200
0
=$
Figure 10. Ordered structures (“2x1”and “3x1”) formed by H
adsorbed on Fe(ll0) at low temperature. 150 I I
100
I
_I-
,I---&--
,,‘
\,
,‘
\
-
‘8
‘,
2\-islands‘v.‘ d2x2)-kland;‘ 50 + diluted gas + dense gas ‘&x
I
! 0
-9 0.5
1,o
Figure 9. (a) H/Pd(100): Variation of the intensity of superlattice LEED spots with temperature at various coverages, reflecting the occurrence of continuous order-disorder transitions. (b) Phase diagram constructed from the data of Figure 9a (data pointa),together with the theoretical phase diagram (dashed lines) obtained by fitting the interaction energies between adsorbed particles.
is low enough the equilibrium pressure also becomes negligibly small-that means we may then concentrate on the equilibrium within the adsorbed layer without taking the gas phase into account. The simplest case of a lattice gas system is represented by a square net of adsorption sites with repulsive interactions between nearest-neighbor adsorbed particles. As a consequence, at low enough temperature and for 0 = 0.5 the adsorbed particles are expected to occupy only next-nearest-neighbor sites forming a checkerboard-like configuration on the surface. Such a situation is found with H atoms adsorbed on a Pd(100) surface at 0 = 0.5, for which the structure model is reproduced in Figure 8.11 Theoretically, this is equivalent to the two-dimensional Ising model,12for which an analytical solution was first presented in a famous paper by 0 n ~ a g e r . l ~This model predicts a continuous order(11)Behm, R. J.; Christmann, K.; Ertl, G. Surf.Sci. 1980,99,320. (12)Ising, E.2.Phys. 1925,31,253. (13)Onsager, L.Phys. Reu. 1944,65,117.
disorder transition (Le., a breakdown of the long-range order) upon increasing the temperature, whereby the transition temperature is determined by the interaction energy. In the present case the degree of long-range order can be monitored through the intensities of the LEED spots characterizing the c2X2 superlattice of the adsorbed layer. The intensity variation with temperature at various coverages is reproduced in Figure 9a, demonstrating clearly the continuous character of these phase transitions. If we identify the points of inflexion of these curves with the respective transition temperatures, we can construct the phase diagram shown in Figure 9b. The broken lines mark the best fit by theory,14whereby it turned out, however, that nearest-neighbor repulsions (0.4 kcal/mol) have to be suplemented by a weak attraction between next-nearest neighbors (-0.3 kcal/mol) and a nonpairwise “trio” interaction (-0.2 kcal/mol). A somewhat more complicated situation is found with the system H/Fe(llO) where two structures (corresponding to the “ideal” coverages l/z and 2/3) are formed (Figure 10).15 The phase diagram was determined in an analogous way as before and is reproduced in Figure lla.16 Again the phase diagram could be modeled theoretically (Figure l l b ) , in this case by adjusting a set of four interaction parameters.” One should realize that with both systems discussed the interaction energies are always
