- Email: [email protected]
Formic acid desorption from graphitized Ni(110)
Surface Science 54 (1976) 210-228 0 North-Holland Publishing Company
FORMIC ACID DESORPTION FROM GRAPMTIZED Ni( 110) J.G. MCCARTY * and R.J. MADIX ** Department of Chemical Engineering, Stanford, California 94305, U.S.A.
Stanford
University, Stanford, California 94305,
Received 10 July 1975; manuscript received in final form 30 September 1975
The adsorption/desorption behavior of formic acid from a monolayer of graphite carbon on Ni(ll0) was studied using AES, LEED and flash desorption spectrosmpy. Formic acid adsorbed at 165 K did not form multilayers of adsorbate. Instead, due to strong hydrogen-bonding interactions the formic acid formed a two-dimensional condensed phase on the surface and exhibited zero-order desorption kinetics initially for a 30-fold change in initial coverage. The zero-order desorption rate constant was kd = 10’s exp[-68.2 kJ mol-‘/RT] s-l, suggesting a desorption transition state with nearly full translational and rotational freedom on the surface. The desorption kinetics and the coverage limit were consistent with the formation of a surface polymer-monomer equilibrium.
1. Introduction The adsorption of vapor phase species with strong intermolecular forces may result in the formation of two-dimensional islands of adsorbate on the substrate. For example, Arthur and Cho [l] and Arthur [2] have reported the interesting observation that the rates of desorption of Cu and Ag adsorbed on graphite and Zn adsorbed on GaAs showed fraction order dependence on the adsorbate coverage. In all three systems the adsorption was interpreted in terms of condensation of the adsorbate into dense islands due to strong interaction between adsorbed atoms. Arthur concluded [2] that adsorption into islands is expected when the adsorbate-substrate interactions are relatively weak compared to adsorbate-adsorbate interactions. Similar behavior can arise following the adsorption of molecular species, provided the adsorbate-adsorbate interactions are sufficiently strong. In the case of carboxylic acids such as HCOOH, CH,COOH, etc., attractive forces due to hydrogen bonding may be sufficiently strong to produce island formation of adsorbed species over a
* In partial fulfillment of the requirements for the Ph.D. degree. Present address: Stanford Research Institute, 333 Ravenswood Ave., Menlo Park, California, U.S.A. ** To whom inquiries should be addressed.
J. C. McCarty, R J. MadixlFormic acid desorption from graphitized Ni(l IO)
211
wide range of surface coverage. The formation of hydrogen-bonded structures would be particularly likely on surfaces which do not rupture bonds within the molecule upon adsorption. In the course of our investigation of the formic acid decomposition on carburized and graphitized Ni(l10) [3], we discovered that the rate of formic acid decomposition on Ni(ll0) was reduced at least an order of magnitude by a monolayer of graphitic carbon, although the saturation coverage by formic acid was quite high. As discussed below, the flash desorption behavior observed indicated strong ad~rbate-adsorbate and weak adsorbate-substrate interactions. AES and LEED were used in this study to help characterize the structure and density of the graphite surface. The desorption rates were determined through use of the flash desorption technique as in previous studies of formic acid decomposition and Hz, CO,, Hz0 and CO adsorption on clean Ni(1 IO) [4,5].
2. Experimental The saturated Ni(ll0) graphite surface was prepared as discussed previously [3,6]. Graphite was deposited by exposing the clean surface to ethylene at 10e7 Torr (1.3 X 1Oh5 Pa) while the sample was held at temperatures between 750 and 825 K. AES was used to measure the relative carbon coverage and to verify the presence of the graphitic form of surface ,carbon [7,8] ; the adsorption behavior of this surface and its LEED characteristics indicated that one monolayer was deposited at saturation coverage. The LEED patterns of the saturated graphite surface indicated that a carbonaceous structure with the dimensions of crystalline graphite was deposited with the basal plane parallel to the (110) surface [9]. The single crystal sample (0.5 cm X 1.0 cm X 0.005 cm) was exposed to monodeuterated formic acid, DCOOH, through a hypoder~c syringe directed at the sample surface. The doser inlet pressure was held at 90 rt:5 pm Hg corresponding to the vapor pressure of DCOOH at the melting point of chlorobenzene (228 K). Doser exposures were calibrated by the adsorption of CO on clean nickel [3-51. Exposures were expressed as the product of the pressure behind the dosing syringe and the time of exposure. From the CO calibration, exposure to one P-S formic acid represented 1.75 X 101’ molecules/cm2. During formic acid exposure the sample was cooIed by thermal contact with a liquid nitrogen reservoir to temperatures approaching 165 K. The sample temperature was measured by a c~omel-alumel thermocouple welded to the edge of the Ni(ll0) sample. After adsorption the sample was rapidly heated by radiation from a tungsten filament located near the crystal face opposite the dosing syringe. Desorbing formic acid was detected by a quadrupole mass spectrometer in direct line-of-sight to the exposed surface using the 30 AMU, DCO+, fragment. The output current of the mass spectrometer was directly proportional to the desorption rate. Analysis of flash desorption data has been reviewed by several authors [lo- 13,261.
212
J. C. McCarty, R.J. MadixjFarmic
acid desorption from graphitized Ni(1 IO)
3. Results As shown in fig. 1 formic acid desorbed from the Ni(1 lO)-graphite surface in a manner that suggested two-dimensional phase separation had occurred. The initial desorption rate showed zero-order desorption kinetics over a 30-fold range of exposure, and the peak maximum shifted slightly to higher temperatures with increasing coverage, indicative of a transition from zero-order desorption to an order less than or equal to one [ 1,2]. These features are quite similar to the Cu, Ag-graphite and Zn-GaAs systems studied by Arthur [ 1,2]. It is important to note, however, that formic acid did not condense into multilayers of solid formic acid on the Ni(1 lO)graphite substrate. Saturation coverage by DCOOH was reached at a doser exposure equivalent to about 3 X 1015 molecules/cm2 for adsorption at 165 + 5 K. Only a small increase in coverage was observed as the doser exposure was doubled from 1.4 X 1Ol5 to 2.8 X 1015 molecules/cm2. The vapor pressure of solid formic acid at 160 and 170 K was estimated by extrapolation of data [ 141 using 13.9 kcal/gmole (58.3 kJ mol-l) as the heat of vaporization. The estimated vapor pressures were - 1OW7Torr (1 OF5 Pa) and - 10M6 Torr ( 10e4 Pa) at 160 K and 170 K, respectively. The effective pressure of the formic acid dose was - 4 X lo-* Torr (5 X 10V6 Pa) so that solid formic acid was not expected to form. Zero order desorption of formic acid was observed only from the graphitic surface. Minor amounts of formic acid desorbed from the (4X5)-C and clean Ni(l10) surfaces following adsorption at low temperature, but the flash peaks were broad and the symmetry of the peaks, i.e., the area under the high temperature side of the
[ doA
175 200 225 250 TEMPERATURE ( K)
175 200 225 25C TEMPERATURE ( K)
Fig. 1. Formic acid flash desorption from the saturated graphite surface. The doser exposures were (a) 4000 G-S, (b) 2400 p-s, (c) 1600 P-S, (d) 800 p-s, (e) 440 p-s, (0 240 P-S, (g) 120 P-S, where 1 MC-S = 1.75 X 10” molecules/cm’.
J.C. Mccmty, RJ. MadixlFormic acid desorptbn from graphitized Ni(Il0)
213
a ’ GRAPHITE
I
I
I
175 200
1
225
I
A
250 275 TEMPERATURE
I
I
300 ( K)
325
I
350
Fig. 2. Formic acid desorption from the saturated (4X9-C and saturated graphite surfaces. (a) (4X5)-C with 2400 p-s exposure, (b) graphite with 4800 M-Sexposure. The adsorption temperature was 175 K, and the heatingrate at 200 K was estimated to be 15 K/set; 1 p-s = 1.75 X 10” molecules/cm2.
flash curves compared to the area under the low temperature side, suggested first or higher order desorption. Most of the formic acid adsorbed on the (4X5) carbide surface subsequently decomposed upon flashing. Fig. 2 shows the formic acid flash peaks observed for desorption from the graphite and (4X5) carbide surfaces; the desorption rate from the carbide surface peaked at 213 f 5 K and the curve shape was similar to Hz0 desorption from the carbide surface [3]. The amount of formic acid desorbed as formic acid from the carbide surface was about lo-20% of the amount desorbed from the graphite surface when given the same exposure of 3 Langmuir (5 X 10d4 Pas) at 170 K. LEED observation of the graphite surface after saturation exposure to formic acid indicated an amorphous layer was formed. The LEED pattern of the formic acid on Ni(ll0) graphite initially showed a very bright background intensity obscuring the (1 X 1) spots. After a few seconds exposure to the LEED electron beam at 175 K the (1 X 1) spots reappeared and the pattern of the graphitic surface layer was restored. Repositioning the electron beam by moving the trimming magnets produced the bright background which again quickly faded. Evidently formic acid formed an amorphous layer on the graphitic surface and was easily desorbed by the electron beam.
4. Discussion The most striking characteristic of the saturated graphite surface was its ability to passivate the Ni(ll0) surface. The results presented elsewhere [3] showed that the graphitized surface was essentially inactive for the decomposition of formic acid und the adsorption of Hz, CO and H20. The amount of decomposition products and adsorbed HZ, CO or Hz0 was so small that it was impossible to distinguish be-
214
J. C. McGzrty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
tween adsorption on the Ni(ll0) graphitized surface and adsorption on other surfaces, e.g., the sample backside, the support wire, etc. From the observed chemical inactivity and the LEED results it was concluded that the graphitized surface was completely blanketed with at least a full layer of crystalline graphite. The magnitude of the carbon AES peak plus the fact that prolonged exposure to ethylene did not increase the carbon coverage above a saturation limit indicated that only a single layer of graphite was present. The graphite overlayer thus blocked chemisorption on the Ni(ll0) substrate. The graphite surface did, however, nondissociatively adsorb formic acid at temperatures below 200 K. Formic acid probably adsorbed on this surface in preference to CO, H2, Hz0 because of the strong hydrogen bonding between physisorbed formic acid molecules. The strength of a single hydrogen bond between two H20 molecules is - 2.0 kcal/mol(8.4 kJ mol-l) lower than the strength of a single hydrogen bond between two HCOOH molecules [15]. Although little H20 adsorbed on the graphite surface at 165 + 5 K, adsorption at temperatures below 150 K (which was beyond the capabilities of the cooling system used in this study) may well produce zero order Hz0 flash peaks. Assuming the zero-coverage sticking probability to be unity, the saturation coverage by formic acid was estimated to be near 1015 molecules/cm2. The amount of formic acid adsorbed on the saturated graphite surface could not be directly determined because formic acid was rapidly pumped by the chamber walls. However, the initial sticking probability and the saturation coverage could be related by the coverage versus exposure curve, provided either the saturation coverage or the initial sticking probability could be estimated. Fig. 3 shows the plot of the area under the flash peaks of fig. 1 versus the doser exposure. The actual saturation coverage equals the
EXPOSURE
Fig. 3. DCOOH
(IO”
MOLECULE/CM*)
coverage versus exposure for adsorption on the graphite surface.
J. C Mcclnty, R.J. MadklFormic acid desorption from graphitized
Ni(ll0)
215
product of the initial sticking probability (if known) and the exposure at the point where the solid line intersects the dashed line representing the area under the largest flash peak. Thus the combination of known exposure and the known or assumed initial sticking probability (so) can be used to calibrate the coverage axis. For SO= 1 the saturation coverage was found to be 7.8 + 1 X 1014 molecules/cm2. This appears to be a reasonable value for adsorption of a molecule the size of formic acid. The saturation coverage expected for a monolayer of formic acid was estimated from the dimensions of the molecule and will be discussed in more detail below. In the discussion that follows two points of view are presented which are consistent with the observed results. The fast phenomenologically relates the desorption kinetics to the formation of islands of adsorbate. The second places a more detailed interpretation on the structural nature of the condensed phase, relating the “zeroorder” desorption kinetics to the formation of hydrogen-bonded polymers on the surface. As the latter interpretation may suggest further experiments directed toward the structure of such hydrogen-bonded condensed phases, it is included in spite of its somewhat speculative nature. Both dissociation from the condensed phase and diffusion away from the boundaries of the condensed phase represent steps which can limit the rate of desorption. If these steps become rate-limiting the desorption rate will show coverage dependence. Arthur [2] reported that the flash evaporation of zinc films deposited on GaAs underwent a transition from zero order to half-order kinetics as desorption proceeded. In Arthur’s analysis the surface was conceived to contain weakly-bound mobile adatoms of concentration n surrounding dense islands containing a total coverage of N molecules with perimeters’ length proportional to N1j2. The net rate of change of n was taken to be dependent upon the rate of desorption of the mobile atoms, the rate of incorporation of mobile adatoms into the islands, and the rate of dissociation of atoms from the island edges. Accordingly, ii =
-kn-k,fl’12 t kdN1/2,
where k was the desorption rate constant, k, was the rate constant for incorporation of adatoms into the condensed phase, and kd was the rate constant for dissociation from the island edge into the rarefied phase. Using the steady state approximation for n, the rate of desorption (R) was found to be R = k kdN1i2/(k + kaN’j2) = -Ii’.
(2)
When k aNf12 % k 2then
R = W&,), and the desorption rate was independent of coverage; when kaN1j2 4 k, then and the desorption rate was proportional to the square root of the coverage. This analysis gave a good semiquantitative fit to Arthur’s data. Actually, any empirical expression for the desorption rate having a form similar to Arthur’s model will yield calculated flash curves like those of fig. 1 and Arthur’s
R = kdN1i2,
216
J. C. McGzrty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
Zn flash desorption curves. The essential features of the curves are: (i) the initial rate must be zero order, i.e., independent of initial coverage, and (ii) the rate must become greater than zero but less than first order as the flash proceeds so that the peak shifts to higher temperature with increas~g coverage. For example, the following rate expression, R = k k’N/(k + k”N),
(3)
would produce zero order kinetics when k”N S k and first order kinetics when k’N Q k. This rate expression can arise if desorption is rate-iimited by detachment from sites on the surface, such as kinks, ledges, etc., and if the species adsorbed at those sites is in equilibrium with the adsorbate on the surface. Diffusion away from the island perimeter rather than dissociation from the island edge can be responsible for the transition from zero to half order kinetics. When the desorption rate constant k is small, the condensed phase and rarefield phase are in equilibrium as suggested by Arthur, but as k becomes very large the desorption rate becomes limited by the rate of diffusion of molecules away from the island perimeter. The nature of the transition from equilibrium to diffusion-limited kinetics strongly depends on the geometry of the islands, i.e., the number of islands, the distribution of island radii, the separation between islands, etc. In order to see how diffu~on-l~ited desorption produces half order kinetics, consider the situation in which the rarefied phase has completely desorbed except within narrow regions near the island perimeters. The shape, radii, etc. of the island becomes unimportant and the concentration profile in the rarefied phase is given by the expression n(r) = n, exp(-r/X),
(4)
where r is the distance from the perimeter, ne is the rarefied phase concentration at the edges of the island, h = (~~k)1~2 is the mean distance the molecules travel into the rarefied phase before desorbing, and CDis the surface diffusion coefficient. The edge concentration, n,, increases with the rate of dissociation from the islands, k,, and decreases with the sum of the rate of incorporation into the island, kane, and the flux (in units of molecules~cm s) of adsorbed molecules diffusing away from the perimeter, so that kd-kan,
=-
Qdn(r)/dr ,
and therefore, from eq. (4), kd-k,n,
= -‘b ?+n,.
(5)
The term on the right-hand side of eq. (5) is the net flux of molecules away from the island per unit perimeter length and is equal to the net desorption rate per unit perimeter. Unless incorporation into an island involves a sizable energy barrier comparable to half the activation energy for desorption, then (k cb)lj2 4 k, and therefore n, = kJk,. Thus, since the total perimeter for the islands is proportional to the square root of their area, the desorption rate
J. C McCarty, R.J. Madix/Formic acid desorption porn graph&tied Ni(ll0)
R 0: (k&J
217
(kcD)1/2N1/2 ,
and the desorption kinetics are half order. Both the diffusion analysis and Arthur’s analysis have a common weakness for application to the results reported here; both do not account for the fact that the islands must grow together near saturation coverage and eclipse the rarefied phase. This island interference decreases the area available for desorption from the rarefied phase. Thus the desorption rate should decrease as the coverage approaches saturation unless the adsorbed molecules can desorb from both phases with equal rates. Since saturation coverage of HCOOH on the Ni(ll0) graphite surface ws reached, and as zero order desorption kinetics was observed initially for all coverages from low coverage up to saturation coverage, it appears that the surface area available for zero order desorption must have included both the area of the condensed and rarefied phases. An ideal two-dimensional lattice gas with attractive nearest neighbor pair potential cannot desorb directly from a condensed phase with the same rate as from a rarefied phase without simultaneous relaxation of the island. Direct desorption creates metastable vacancies within the condensed phase which require additional energy. Analysis of this point is given in Appendix A. The extra transition state barrier due to vacancy formation upon desorption from an island may be eliminated or avoided in two ways. If the adjacent adsorbate molecules can “relax” and fill the vacancy, before the desorbing molecules reach the transition state, the extra barrier could be reduced or eliminated altogether, This relaxation would require a liquid-like or mobile condensed phase. Alternatively, if the desorption can proceed via a physisorbed precursor state on top of the island, the desorption rates over the island and over the non-condensed phase can be equal. The concentration, 0 , of molecules in the second layer can be described by an equilibrium constant sim ipar to that of eq. (A.l). The overall desorption kinetics are then zero order regardless of the initial island coverage if the precursor and the rarefied phase have the same desorption transition state. If the two-dimensional “island” concept is to agree with the desorption rate data presented here, then it appears that the condensed phase of adsorbed formic acid must be either capable of rapid relaxation to fill vacancies or able to support a desorption precursor state. Though the “island” mechanism phenomenologically describes the desorption behavior observed, it is likely that the condensed phase of DCOOH adsorbed on the graphitic overlayer consisted of long chains, i.e., polymers, of hydrogen bonded, molecules. Solid formic acid [ 161 is composed of “infinitely” long chains of hydrogen bonded molecules, and the liquid 1171 was found to be polymeric rather than dimeric or monomeric. The hydrogen bond linking two formic acid molecules is quite strong. The heat of dissociation of the dimer is 14.1 kcal/mol(59.0 kJ mol-l) [ 181; the single hydrogen-bond strength is therefore about 7.0 kcal/mol(29.5 kJ mol-l). Assuming the energy required to separate the chains was comparable to the heat of fusion [ 191 of formic acid (12.6 kJ mol-l), the heat of dissociation of a single molecule from a formic acid polymer was probably between 7.0 and 10.0
218
J. C Mccorty R.J. Mad&/Formic acid desorption from graphitized Ni(l IO)
kcallmol(29.5 and 42.1 l~Jrnol_~). It seems likely that the condensed phase of formic acid adsorbed on the graphite surface consisted of clustered hydrogenbonded chains of formic acid molecules, while the rarefied phase consisted of physi~rbed monomers. The magnitude of the observed zero order activation energy for formic acid desorption from the graphite surface was consistent with the polymer bonding described above. The initial desorption rate of the flash curves in fig. 1 strictly followed zero order kinetics over a factor of 30 variation in initial coverage. Fig. 4 shows a plot of the natural logarithm of the average initial rate of desorption versus 1000 K/T for 13 different values of the initial coverage. The desorption rates of a flash peak were excluded from the average after the rate exceeded one-half the maximum or peak rate of that curve. The vertical error bars correspond to twice the standard deviation of the mean desorption rate at selected temperatures. Due to the mass spectrometer shot noise and the difficulty of precisely determining the baselines of the flash peaks, more uncertainty existed for low desorption rates, thereby limiting the observation of small systematic deviations from zero order kinetics. The slope of the best straight line through the average value of the initial rates in fig. 4 indicated the activation energy for zero order desorption was 16.3 kcal/mol (68.2 + 4.2 kJ mol-l), The frequency factor was 1018*1 Nsat SSC-~. From the discussion above the hydrogen-bond strength was estimated to be 7.0 kcallmol (29.5 kJ mol-I), and after attributing 3.0 kcal/mol (12.6 kJ mol-l) for the separation of clustered chains, the binding energy of the monomer was 10,Okcal/mol (42.1 kJ molB1) less than the binding energy of a molecule in a chain. Assuming 50-
;i
20-
I
‘P \
$o-
P \
d
-R x SLOPE = 16.3 KCAL P
25 \ P
0 2 I?
2-
B e
,_
\ P \
T
0.5 51
f\ 5.2 53 54 55 5.6 1000 K / TEMPERATURE
!
Fig. 4. Zero order desorption rate versusreciprocal temperature for DCOOHadsorbedon the saturated gxaphitesurface.
J. C. McCarty, R.J. MadixfFormic acid desorptbn from graphitized Ni(l10)
219
formic acid monomers had nearly the same heat of adsorption on graphite as CO2, the apparent activation energy for desorption from the chains would be 18.3 kcal/ mol(76.5 kJ mol-l), taking 8.3 kcal/mol(34.7 kJ mol-l) as the heat of physisorption of CO2 on graphite [22]. This value is only 2.2 kcal/mol higher than the experimentally observed value. The formation of condensed polymers of formic acid adsorbed on graphite appears quite consistent with the experimental data. The transition from zero order desorption kinetics to kinetics less than first order can be described qualitatively by an equilibrium between dissociated monomers and their parent clusters. The concentration of desorbing monomers is controlled through equilibrium with chains of various length. Assuming the rate of monomer desorption was much less than the rate of association and dissociation of polymers, the desorption and equilibrium steps could be expressed as follows: ko Ma --+M
3M-M a-
desorption
g
(7)
K3
equilibria
3a
%I
nM a+---+M
na
where Mna represents an adsorbed chain containing n monomers M. The total concentration, C,, of adsorbed formic acid is equal to the sum of monomers in all the chains, i.e., CT =
n$l nMna = ?/ n=l
nK,,x
,
(8)
where K, = 1. The rate of desorption
is
R = k,M,
(9)
and the change in total coverage is determined dC,/dt
= -k,M.
k,
(4&&T
+ 1)“2-l
where + W/RT).
kinetics. Following the analysis described
1’
(4&,CT + 1)1’2t 1
K. z exp(-So/R
rate. Thus (10)
eqs. (8) and (10) describe the desorption in Appendix C, the desorption rate _dCT =---dt Ku
by the desorption
(11)
220
J. C McCiuty, R.J. M&dix/Rwmicacid desorption from graphitized Ni (I 10)
The desorption rate expression (11) represents zero order desorption kinetics with a transition to first order as the coverage is exhausted. For 4KoCT iib 1,
dCT/dr = -koKo .
02)
For 4K0CT < 1, dC,,‘dt = -kOCT.
(13)
For small K,#ZT, eq, (11) becomes very similar to the zero/first order expression [eq. (3)] presented above, Rate “k&‘&l
+K&+).
04)
The flash desorption curves calculated from eq. (11) show good qucrlitative agreement with the data presented in fig. 1, as shown in fig. 5. The saturation coverage for DCOOH adsorption on the Ni(l tO)--graphite surface was estimated from the lattice parameters for crystalline formic acid. The bonding parameters for hydrogen-bonded/formic acid molecules as determined from the Xray diffraction patterns of solid formic acid [ 161 are listed in table 1. Fig. 6 shows the t~ee~d~~sion~ structure of solid formic acid with fl bonding based on the X-ray diffraction data of Holtzberg et al, [l&l. The nearest intramolecule approach of the carbon and oxygen atoms in solid formic acid are also listed in ta 0.9
08 0.7 06 0.5 O!l 0.3
00 175 It#)185 I90 TElWPEFMTLREfK1 Data from curve (a) of Fig. 5. Calculatedand expeiimentti formic acid desorption rates, fig* 1. (0) Caitculateddesorption rates from numeri& integration ofeq. (26); k&C@ = 3 X i033exp[-16.3 k~~rno~~~~: Ko = 1.3 x IO-” exp~6.Pk~l~mo~~~.
J. C iUcGuty, R.J. Madix/Formic acid deslorption from graphitized Ni(l IO)
221
Table 1 Bonding parameters of solid formic acid Bond length (A)
Bond angle (deg) 0
0
C-H= 1.05
‘C’ C
C-O = 1.26 C=O = 1.23 O-H...0
= 123 H
‘0’ C\o/
= 122 H = 114
= 2.58
Nearest intramolecular approaches (A) G.0 = 3.18 O..*O = 3.28 c***c = 3.15
table 1. For comparison,
fig. 7 represents the structure
of the formic acid molecule
1191. The density of molecules formed at the surface of solid formic acid with the bc plane of fig. 6 parallel to the surface was calculated to be 1 .O X 1015 molecules/cm2 with two molecules per bc cell. However, the molecules are oriented nearly edgewise to the bc plane with an oxygen atom directed away from the surface rather than along the surface plane. The coverage density of this bc plane is therefore expected to be higher than the coverage density for molecules lying parallel to the surface. A better estimate of the coverage density of adsorbed formic acid was given by the
Fig. 6. The crystal structure of solid formic acid.
222
J.C. McCWty, R.J. MzdixfFormic acid deswptbn fkomgraphitized NilI IO)
--x
Fig. 7. Geometry of the formic acid molecule.
0.
IA
Fig. 8. Folymerie models of formic acid adsorbed on the graphite surface: (a) 01~~~mation~ (b) p ~~~~at~n.
J. C McGzrty, R.J. Madiw/Formic acid desorption from graphitized Ni(l IO)
223
surface density along the ac plane, 7.3 X 1014 molecules/cm’ with 4 molecules per unit cell, although the chains do not lie parallel to this plane. Two possible bonding arrangements of polymeric formic acid adsorbed on the graphite surface are illustrated in fig. 8. The (Yand p forms were suggested [20] by the infrared spectra of formic acid crystals. The bond lengths and bond angles assigned to the (Yand /3 forms are listed in table 2. The spacing between the (Yand fl polymer-like rows in fig. 6 was adjusted so that the nearest C..-O intramolecular approach was 3.2 A. The O*-.O closest approach of the a form was less than 3.2 A because of the bond angles of an 01chain. The spacing between chains on the surface was determined by the distances of nearest approach in solid formic acid. The coverage densities of the two models in fig. 8 were 7.0 (o form) and 6.2 X 1014 molecules/cm2 (~3form). Thus the formic acid coverage density expected for formic acid adsorbed on the graphite surface was 6.6 + 1.0 X 1014 molecules/ cm2. Assuming the initial sticking probability was 1.0, the actual coverage estimated from fig. 2 was 7.8 f 2 X 1014 molecules/cm2. The consistency of these results lends support to the estimate of so = 1.
5. summary The graphitized Ni(ll0) surface was chemically inactive, adsorbing formic acid non-dissociatively at low temperature. The amount of Hz, H20 and CO adsorbed and the amount of formic acid decomposed by the saturated graphite layer was insignificant relative to the clean surface. Formic acid desorbed from the graphite surface in narrow flash peaks which initially followed zero order kinetics. The initial desorption rate was independent of coverage from 3 X 1013 molecules/cm2 to saturation coverage, 7 X 1014 molecules/ cm2. Formic acid adsorbed at 165 K on the graphite layer apparently formed chains of hydrogen-bonded molecules. This adsorbed state was consistent with the desorp-
Table 2 Bonding parameters of fii. 8 Bond length (A)
Bond angle (deg)
C=H c-o c=o O-H***0
o-c-o C-O-H C-O*** H C-O*.*H
= 1.05 = 1.25 = 1.245 = 2.58
Intramolecular closest approaches (A) OL form: C+O = 3.2,0***0 = 2.45 p form: C%O = 3.2,0...0 = 3.2
= = = =
1225 122.5 115 (p form) 122.5 ((uform)
224
J.C. McCarty, R.J. Madix/Formic acid desorption from graphitized Ni(ll0)
tion kinetics, the ~ximum coverage, and the LEED indication of disordered adsorption observed following adsorption at 165 K. The zero order kinetics were described by desorption of physisorbed monomers in equilibrium with clusters of the formic acid chains. The frequency-factor of the zero order rate constant, k,, = 1@3+1 exp(-68.2 f 4.2 kJ mol-i/~T)s-i, indicated that the transition state for desorption of the monomer had nearly full translational and rotational degrees of freedom.
Acknowledgements The authors gratefully acknowledge the National Science Foundation and the Center for Materials Research at Stanford for financial support of this research. Acknowledgement is also made to the Donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. We are also thankful for fellowship assistance from the National Science foundation for a portion of the duration of this work (J.G.M.).
Appendix A The following analysis shows that a lattice gas with an attractive nearest neighbor pair potential (w) cannot desorb directly from a condensed phase at the same rate as from the rarefied phase. Consider a lattice gas ex~bit~g two-dimen~on~ phase separation 1211 with m (2,3,4 or 6) nearest neighbors. If the system is far from the critical point, then the local fractional coverage within the condensed phase, Be, approaches unity, and then Or, the local fractional coverage in the rarefied phase, is given by or = Vrlf,)
exp(-(E,--E,)/RT),
(A-1)
where B, = n/M, E,-EC = (mJZ)w, M is the adsorption site density; fr, f,are the rarefied and condensed phase molecular partition functions, respectively, and Er and EC are the zero point energies of the molecules in the rarefied and condensed phases. The rate constant for desorption from the rarefied surface phase, k,, can be expressed as [22] kr = (kTlh)(f;f/f,)exp(-(~-E,)lRT),
(A.2)
and the desorption rate (per unit area) over the rarefied phase is given by the product of eqs. (A 1) and (A.2), R, = (kT/h)~If,)exp(-(E~-E,)IRT),
(A-3)
where fr* is the partition function and Ef is the zero point energy of the transition state for desorption from the rarefied phase. The rate of desorption directly from
J. C. McCarty, R.J. h&dix/Formic acid desorption from graphitized Ni(ll0.l
225
the condensed phase is given by R, = (k~~~)~~lf,)exp(-(~~-~~)/RT),
(A.4)
where ff and Ez represent the transition state for desorption from the condensed phase. The two rates are equal, regardless of initial coverage and temperature, only if
f: =fZ
and
E:=i?:,
i.e., if the desorption transition states are the same for both phases. However for the lattice gas system, E: f E,?, because the transition state for desorption from the condensed phase includes the creation of a metastable vacancy in the island. The average energy of an adsorbed island molecule due to interaction with its neighbors is (m/Z)w, but during desorption m interaction bonds are broken. The addition energy (m/2)w is the energy of formation of m unpaired bonds, i.e., the vacancy left behind. As a result, a lattice gas system as described above cannot show zero order desorption kinetics as the coverage approaches saturation.
Appendix B A high frequency factor is expected for the desorption of a formic acid molecule from a cluster of hydrogen-bonded chains. Consider as the initial bound state a molecule bonded within a chain as illustrated in fig. 8. The fact that desorption probably proceeds via a physisorbed monomer is of no concern here since the monomer is presumed to be in equilibrium with the condensed phase chains. The transition state is assumed to be a monomer with the properties of a two dimensional gas with rotational and vibrational modes unrestricted by the surface. The reaction coordinate is in the z direction with the x and y axes taken parallel to the surface. For the zero order rate from eqs. (A.3) and (A.4) & = (kWO(tc,/fJexp(-WW?, so that ko = RO =
(kTIh)Cf~yf~tif”)exp(-~lRT),
03.1)
where f:,, isthe two~ensio~l gas translation partition function, f& the rotational partition function of the transition state, AE is the zero point energy barrier, and fv is the vibrational partition function of the monomer in the chain, The internal vibration partition function of the molecule was assumed to be unchanged throughout desorption and the chains were assumed to be immobiie. Thus all internal vibrational modes were canceIled out by f$,except those modes involving the hydrogen bond in the condensed phase. The frequency factor for k,-, in eq. (B.l) can be expressed as
JL. M&arty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
226
y. = (kTlh)exp(~~/R),
where
03.2) For a two-~mensional gas at 200 K with molecular weight, MW, equal to 46 amu and site density, Ns = 8 X 1014 cm-2 [23], f;y
= 2nkT(MW)&h2,
yielding AS” = .502JK-1mol-1. XY *
(B-3)
For free rotation of formic acid,
f: = (T3/0,0203)1/2
)
yielding AS: = 65.7 J K-l mol-l ,
(B-4)
where 0,) 02, O3 are the characteristic temperatures [23] for rotation about the three principle axes of formic acid. The characteristic temperatures were calculated from the three rotational constants of formic acid, 76 800 MHz, 12 055 MHz, and 10 416 MHz, which were determined from microwave spectra [24]. The vibrational frequencies involving the hydrogen bond occur [25] at 90cm-’ due to C.ofH bending and 230 cm-l due to O-H.*+0 stretching; torsional modes requiring rotation perpendicular to the surface were neglected. Thus exp(-hvl/2kT)exp(-hv2/2kT) fv =
[l-exp(-hvl/kT)]
[l-exp(-hv2/k7’)]
’
and A$=
-19.7 JK-l mol-l .
tB.5)
Finally, after evaluating all the terms for the preexponential factor in eq. (B.l), vu = 4.2 X 1012 exp(96.2 J K-l mole1 /R)s-l , or v0 =: 1017.6 s-1 which is in good agreement with the observed frequency factor, 101** 1 s-l.
(B.6)
J.C. McCarty, R.J. MadixfFormic acid desorption fromgraphitized Ni(ll0)
221
Appendix C EZq.(8) can be simplified by the use of a convenient approximation for the equilibrium constants, K,. The equilibrium constants depend on the entropy and energy differences between the chains and the monomer, thus Cl)
K,, = expW,,lR-&,lRT), where as,
AH,, = En-nE+?T,
=s,-n&s,,
S, is the entropy of a chain of length n, En is the corresponding chain energy, Su is the monomer entropy, and E. is the monomer energy. AEn = (En-nEo) is approximately equal to -(n - 1) W where W is the hydrogen bond strength. This approximation rests on the following assumptions: (i) the interaction of each formic acid molecule with the substrate is unaffected by the formation of the chains, (ii) the hydrogen bond energy is not affected by the length of a chain, (iii) the total interaction energy sums linearly with the number of bonds in a chain, and (iv) hydrogen bonds formed by ring closure or dimer-type bonding represent an insignificant contribution to the total energy and entropy. The -RT term in AH,, is small (< 1.7 kJ mol-l) and shall be neglected below. Further, ASn is assumed to depend linearly upon the number of hydrogen bonds, and AS, z SO (n - 1) where SO represents the sum of the entropy lost due to the translational and rotational restrictions of a monomer in a chain and the entropy gained from the vibrational modes of the chain. This approximation for AS, also assumes that the translational and rotational components of S, equal SO. From eq. (C- 1) K, can be written as K, = exp(-S,-,(n-1)/R
+ W(n-l)/RT
or
Kn = Kim1 ,
(C.2)
where K. E exp(-SO/R Substituting
t W/RT).
K, into eq. (8) produces the sum,
C, = M +2KoM2 + 3K;M3
t . .. t nK;-lM”
t ..,
or C,=M(l
+2K,,M+3K;M2+
. . . +nK$-lMin-l
+ ...).
(C-3)
l?q. (C.3) can be reduced to C, = M(1-K,M)-2, enabling M to be readily calculated M= C, [(2K,,CT + l)-(4K&
(C-4) as a function
of CT. Thus,
+ 1)1/2]/2(KoCT)2.
(C.5)
228
J. C McGwty, R.J. Madix/Formic acid desorption from graphitized Ni (I IO)
References [l] [ 21 [3] [4] [S] [6] [7] [8] [9]
J.R. Arthur and A.Y. Cho, Surface Sci. 36 (1973) 641. J.R. Arthur, Surface Sci. 38 (1973) 394. J.G. McCarty and R.J. Madix, J. Catalysis 38 (1975) 402. J. McCarty, J. Falconer and R.J. Madix, J. Catalysis 20 (1975) 235. J.L Falconer and R.J. Madix, Surface Sci. 46 (1974) 473. J.G. McCarty, Ph.D. Dissertation, Stanford University, Stanford, California (1974). J.P. Coad and J.C. RiviQe, Surface Sci 25 (1971) 609. T.W. Haas, J.T. Grant and G.J. Dooley, J. Appl. Phys. 43 (1972) 1853. G. Ertl, in: Molecular Processes on Solid Surfaces, Eds. E. Draughs, R.D. Gretz and R.K. Jaffee (McGraw-Hill, New York, 1969) pp. 155-157. [lo] J. Falconer, Flash Decomposition Spectroscopy Study of Formic Acid Decomposition on Clean Ni(llO), Appendix A, Ph.D. Dissertation, Stanford University, Stanford, California (1974). (111 G. Ehrlich, Advan. Catalysis 14 (1963) 271. [12] P.A. Redhead, Vacuum 12 (1962) 203. [13] B. McCarroll, J. AppL Phys 40 (1969) 1. [14] D.R. Stull, Ind. Eng. Chem. 39 (1947) 517. 1151 G.C Pimentel and A.L. McClellan, The Hydrogen Bond (Freeman, San Francisco, 1960) p. 224. [ 161 F. Holtzberg, B. Post and I. Fankuchen, Acta Cryst. 6 (1953) 127. [17] D. Chapman, J. Chem. Sot. (1965) 225. [18] W. Waring, Chem. Rev. 51 (1952) 171. [19] A.I. Popov, Chem. NonAqueous Solv. 3 (1970) 339. [20] Y. Mikawa, R.J. Jakobson and J.W. Brusch, J. Chem. Phys. 45 (1966) 4750. [21] T.L Hill, An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, MA, 1960) ch. 14. [22] D.O. Hayward and B.M.W. Trapnell, Chemisorption (Butterworths, London, 1964) pp. 150-153. [23] T.L Hill, An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, MA, 1960) pp. 153-161. [ 241 RG. Lerner, B.P. Dailey and J.P. Friend, J. Chem. Phys. 26 (1957) 680. [25] R. Tubino and $ Zerbo, J. Chem. Phys. 53 (1970) 1428. [26] M. Smutek, S. Cerny and E. Buzek, Advan. Catalysis 24 (1975) 343.
FORMIC ACID DESORPTION FROM GRAPMTIZED Ni( 110) J.G. MCCARTY * and R.J. MADIX ** Department of Chemical Engineering, Stanford, California 94305, U.S.A.
Stanford
University, Stanford, California 94305,
Received 10 July 1975; manuscript received in final form 30 September 1975
The adsorption/desorption behavior of formic acid from a monolayer of graphite carbon on Ni(ll0) was studied using AES, LEED and flash desorption spectrosmpy. Formic acid adsorbed at 165 K did not form multilayers of adsorbate. Instead, due to strong hydrogen-bonding interactions the formic acid formed a two-dimensional condensed phase on the surface and exhibited zero-order desorption kinetics initially for a 30-fold change in initial coverage. The zero-order desorption rate constant was kd = 10’s exp[-68.2 kJ mol-‘/RT] s-l, suggesting a desorption transition state with nearly full translational and rotational freedom on the surface. The desorption kinetics and the coverage limit were consistent with the formation of a surface polymer-monomer equilibrium.
1. Introduction The adsorption of vapor phase species with strong intermolecular forces may result in the formation of two-dimensional islands of adsorbate on the substrate. For example, Arthur and Cho [l] and Arthur [2] have reported the interesting observation that the rates of desorption of Cu and Ag adsorbed on graphite and Zn adsorbed on GaAs showed fraction order dependence on the adsorbate coverage. In all three systems the adsorption was interpreted in terms of condensation of the adsorbate into dense islands due to strong interaction between adsorbed atoms. Arthur concluded [2] that adsorption into islands is expected when the adsorbate-substrate interactions are relatively weak compared to adsorbate-adsorbate interactions. Similar behavior can arise following the adsorption of molecular species, provided the adsorbate-adsorbate interactions are sufficiently strong. In the case of carboxylic acids such as HCOOH, CH,COOH, etc., attractive forces due to hydrogen bonding may be sufficiently strong to produce island formation of adsorbed species over a
* In partial fulfillment of the requirements for the Ph.D. degree. Present address: Stanford Research Institute, 333 Ravenswood Ave., Menlo Park, California, U.S.A. ** To whom inquiries should be addressed.
J. C. McCarty, R J. MadixlFormic acid desorption from graphitized Ni(l IO)
211
wide range of surface coverage. The formation of hydrogen-bonded structures would be particularly likely on surfaces which do not rupture bonds within the molecule upon adsorption. In the course of our investigation of the formic acid decomposition on carburized and graphitized Ni(l10) [3], we discovered that the rate of formic acid decomposition on Ni(ll0) was reduced at least an order of magnitude by a monolayer of graphitic carbon, although the saturation coverage by formic acid was quite high. As discussed below, the flash desorption behavior observed indicated strong ad~rbate-adsorbate and weak adsorbate-substrate interactions. AES and LEED were used in this study to help characterize the structure and density of the graphite surface. The desorption rates were determined through use of the flash desorption technique as in previous studies of formic acid decomposition and Hz, CO,, Hz0 and CO adsorption on clean Ni(1 IO) [4,5].
2. Experimental The saturated Ni(ll0) graphite surface was prepared as discussed previously [3,6]. Graphite was deposited by exposing the clean surface to ethylene at 10e7 Torr (1.3 X 1Oh5 Pa) while the sample was held at temperatures between 750 and 825 K. AES was used to measure the relative carbon coverage and to verify the presence of the graphitic form of surface ,carbon [7,8] ; the adsorption behavior of this surface and its LEED characteristics indicated that one monolayer was deposited at saturation coverage. The LEED patterns of the saturated graphite surface indicated that a carbonaceous structure with the dimensions of crystalline graphite was deposited with the basal plane parallel to the (110) surface [9]. The single crystal sample (0.5 cm X 1.0 cm X 0.005 cm) was exposed to monodeuterated formic acid, DCOOH, through a hypoder~c syringe directed at the sample surface. The doser inlet pressure was held at 90 rt:5 pm Hg corresponding to the vapor pressure of DCOOH at the melting point of chlorobenzene (228 K). Doser exposures were calibrated by the adsorption of CO on clean nickel [3-51. Exposures were expressed as the product of the pressure behind the dosing syringe and the time of exposure. From the CO calibration, exposure to one P-S formic acid represented 1.75 X 101’ molecules/cm2. During formic acid exposure the sample was cooIed by thermal contact with a liquid nitrogen reservoir to temperatures approaching 165 K. The sample temperature was measured by a c~omel-alumel thermocouple welded to the edge of the Ni(ll0) sample. After adsorption the sample was rapidly heated by radiation from a tungsten filament located near the crystal face opposite the dosing syringe. Desorbing formic acid was detected by a quadrupole mass spectrometer in direct line-of-sight to the exposed surface using the 30 AMU, DCO+, fragment. The output current of the mass spectrometer was directly proportional to the desorption rate. Analysis of flash desorption data has been reviewed by several authors [lo- 13,261.
212
J. C. McCarty, R.J. MadixjFarmic
acid desorption from graphitized Ni(1 IO)
3. Results As shown in fig. 1 formic acid desorbed from the Ni(1 lO)-graphite surface in a manner that suggested two-dimensional phase separation had occurred. The initial desorption rate showed zero-order desorption kinetics over a 30-fold range of exposure, and the peak maximum shifted slightly to higher temperatures with increasing coverage, indicative of a transition from zero-order desorption to an order less than or equal to one [ 1,2]. These features are quite similar to the Cu, Ag-graphite and Zn-GaAs systems studied by Arthur [ 1,2]. It is important to note, however, that formic acid did not condense into multilayers of solid formic acid on the Ni(1 lO)graphite substrate. Saturation coverage by DCOOH was reached at a doser exposure equivalent to about 3 X 1015 molecules/cm2 for adsorption at 165 + 5 K. Only a small increase in coverage was observed as the doser exposure was doubled from 1.4 X 1Ol5 to 2.8 X 1015 molecules/cm2. The vapor pressure of solid formic acid at 160 and 170 K was estimated by extrapolation of data [ 141 using 13.9 kcal/gmole (58.3 kJ mol-l) as the heat of vaporization. The estimated vapor pressures were - 1OW7Torr (1 OF5 Pa) and - 10M6 Torr ( 10e4 Pa) at 160 K and 170 K, respectively. The effective pressure of the formic acid dose was - 4 X lo-* Torr (5 X 10V6 Pa) so that solid formic acid was not expected to form. Zero order desorption of formic acid was observed only from the graphitic surface. Minor amounts of formic acid desorbed from the (4X5)-C and clean Ni(l10) surfaces following adsorption at low temperature, but the flash peaks were broad and the symmetry of the peaks, i.e., the area under the high temperature side of the
[ doA
175 200 225 250 TEMPERATURE ( K)
175 200 225 25C TEMPERATURE ( K)
Fig. 1. Formic acid flash desorption from the saturated graphite surface. The doser exposures were (a) 4000 G-S, (b) 2400 p-s, (c) 1600 P-S, (d) 800 p-s, (e) 440 p-s, (0 240 P-S, (g) 120 P-S, where 1 MC-S = 1.75 X 10” molecules/cm’.
J.C. Mccmty, RJ. MadixlFormic acid desorptbn from graphitized Ni(Il0)
213
a ’ GRAPHITE
I
I
I
175 200
1
225
I
A
250 275 TEMPERATURE
I
I
300 ( K)
325
I
350
Fig. 2. Formic acid desorption from the saturated (4X9-C and saturated graphite surfaces. (a) (4X5)-C with 2400 p-s exposure, (b) graphite with 4800 M-Sexposure. The adsorption temperature was 175 K, and the heatingrate at 200 K was estimated to be 15 K/set; 1 p-s = 1.75 X 10” molecules/cm2.
flash curves compared to the area under the low temperature side, suggested first or higher order desorption. Most of the formic acid adsorbed on the (4X5) carbide surface subsequently decomposed upon flashing. Fig. 2 shows the formic acid flash peaks observed for desorption from the graphite and (4X5) carbide surfaces; the desorption rate from the carbide surface peaked at 213 f 5 K and the curve shape was similar to Hz0 desorption from the carbide surface [3]. The amount of formic acid desorbed as formic acid from the carbide surface was about lo-20% of the amount desorbed from the graphite surface when given the same exposure of 3 Langmuir (5 X 10d4 Pas) at 170 K. LEED observation of the graphite surface after saturation exposure to formic acid indicated an amorphous layer was formed. The LEED pattern of the formic acid on Ni(ll0) graphite initially showed a very bright background intensity obscuring the (1 X 1) spots. After a few seconds exposure to the LEED electron beam at 175 K the (1 X 1) spots reappeared and the pattern of the graphitic surface layer was restored. Repositioning the electron beam by moving the trimming magnets produced the bright background which again quickly faded. Evidently formic acid formed an amorphous layer on the graphitic surface and was easily desorbed by the electron beam.
4. Discussion The most striking characteristic of the saturated graphite surface was its ability to passivate the Ni(ll0) surface. The results presented elsewhere [3] showed that the graphitized surface was essentially inactive for the decomposition of formic acid und the adsorption of Hz, CO and H20. The amount of decomposition products and adsorbed HZ, CO or Hz0 was so small that it was impossible to distinguish be-
214
J. C. McGzrty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
tween adsorption on the Ni(ll0) graphitized surface and adsorption on other surfaces, e.g., the sample backside, the support wire, etc. From the observed chemical inactivity and the LEED results it was concluded that the graphitized surface was completely blanketed with at least a full layer of crystalline graphite. The magnitude of the carbon AES peak plus the fact that prolonged exposure to ethylene did not increase the carbon coverage above a saturation limit indicated that only a single layer of graphite was present. The graphite overlayer thus blocked chemisorption on the Ni(ll0) substrate. The graphite surface did, however, nondissociatively adsorb formic acid at temperatures below 200 K. Formic acid probably adsorbed on this surface in preference to CO, H2, Hz0 because of the strong hydrogen bonding between physisorbed formic acid molecules. The strength of a single hydrogen bond between two H20 molecules is - 2.0 kcal/mol(8.4 kJ mol-l) lower than the strength of a single hydrogen bond between two HCOOH molecules [15]. Although little H20 adsorbed on the graphite surface at 165 + 5 K, adsorption at temperatures below 150 K (which was beyond the capabilities of the cooling system used in this study) may well produce zero order Hz0 flash peaks. Assuming the zero-coverage sticking probability to be unity, the saturation coverage by formic acid was estimated to be near 1015 molecules/cm2. The amount of formic acid adsorbed on the saturated graphite surface could not be directly determined because formic acid was rapidly pumped by the chamber walls. However, the initial sticking probability and the saturation coverage could be related by the coverage versus exposure curve, provided either the saturation coverage or the initial sticking probability could be estimated. Fig. 3 shows the plot of the area under the flash peaks of fig. 1 versus the doser exposure. The actual saturation coverage equals the
EXPOSURE
Fig. 3. DCOOH
(IO”
MOLECULE/CM*)
coverage versus exposure for adsorption on the graphite surface.
J. C Mcclnty, R.J. MadklFormic acid desorption from graphitized
Ni(ll0)
215
product of the initial sticking probability (if known) and the exposure at the point where the solid line intersects the dashed line representing the area under the largest flash peak. Thus the combination of known exposure and the known or assumed initial sticking probability (so) can be used to calibrate the coverage axis. For SO= 1 the saturation coverage was found to be 7.8 + 1 X 1014 molecules/cm2. This appears to be a reasonable value for adsorption of a molecule the size of formic acid. The saturation coverage expected for a monolayer of formic acid was estimated from the dimensions of the molecule and will be discussed in more detail below. In the discussion that follows two points of view are presented which are consistent with the observed results. The fast phenomenologically relates the desorption kinetics to the formation of islands of adsorbate. The second places a more detailed interpretation on the structural nature of the condensed phase, relating the “zeroorder” desorption kinetics to the formation of hydrogen-bonded polymers on the surface. As the latter interpretation may suggest further experiments directed toward the structure of such hydrogen-bonded condensed phases, it is included in spite of its somewhat speculative nature. Both dissociation from the condensed phase and diffusion away from the boundaries of the condensed phase represent steps which can limit the rate of desorption. If these steps become rate-limiting the desorption rate will show coverage dependence. Arthur [2] reported that the flash evaporation of zinc films deposited on GaAs underwent a transition from zero order to half-order kinetics as desorption proceeded. In Arthur’s analysis the surface was conceived to contain weakly-bound mobile adatoms of concentration n surrounding dense islands containing a total coverage of N molecules with perimeters’ length proportional to N1j2. The net rate of change of n was taken to be dependent upon the rate of desorption of the mobile atoms, the rate of incorporation of mobile adatoms into the islands, and the rate of dissociation of atoms from the island edges. Accordingly, ii =
-kn-k,fl’12 t kdN1/2,
where k was the desorption rate constant, k, was the rate constant for incorporation of adatoms into the condensed phase, and kd was the rate constant for dissociation from the island edge into the rarefied phase. Using the steady state approximation for n, the rate of desorption (R) was found to be R = k kdN1i2/(k + kaN’j2) = -Ii’.
(2)
When k aNf12 % k 2then
R = W&,), and the desorption rate was independent of coverage; when kaN1j2 4 k, then and the desorption rate was proportional to the square root of the coverage. This analysis gave a good semiquantitative fit to Arthur’s data. Actually, any empirical expression for the desorption rate having a form similar to Arthur’s model will yield calculated flash curves like those of fig. 1 and Arthur’s
R = kdN1i2,
216
J. C. McGzrty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
Zn flash desorption curves. The essential features of the curves are: (i) the initial rate must be zero order, i.e., independent of initial coverage, and (ii) the rate must become greater than zero but less than first order as the flash proceeds so that the peak shifts to higher temperature with increas~g coverage. For example, the following rate expression, R = k k’N/(k + k”N),
(3)
would produce zero order kinetics when k”N S k and first order kinetics when k’N Q k. This rate expression can arise if desorption is rate-iimited by detachment from sites on the surface, such as kinks, ledges, etc., and if the species adsorbed at those sites is in equilibrium with the adsorbate on the surface. Diffusion away from the island perimeter rather than dissociation from the island edge can be responsible for the transition from zero to half order kinetics. When the desorption rate constant k is small, the condensed phase and rarefield phase are in equilibrium as suggested by Arthur, but as k becomes very large the desorption rate becomes limited by the rate of diffusion of molecules away from the island perimeter. The nature of the transition from equilibrium to diffusion-limited kinetics strongly depends on the geometry of the islands, i.e., the number of islands, the distribution of island radii, the separation between islands, etc. In order to see how diffu~on-l~ited desorption produces half order kinetics, consider the situation in which the rarefied phase has completely desorbed except within narrow regions near the island perimeters. The shape, radii, etc. of the island becomes unimportant and the concentration profile in the rarefied phase is given by the expression n(r) = n, exp(-r/X),
(4)
where r is the distance from the perimeter, ne is the rarefied phase concentration at the edges of the island, h = (~~k)1~2 is the mean distance the molecules travel into the rarefied phase before desorbing, and CDis the surface diffusion coefficient. The edge concentration, n,, increases with the rate of dissociation from the islands, k,, and decreases with the sum of the rate of incorporation into the island, kane, and the flux (in units of molecules~cm s) of adsorbed molecules diffusing away from the perimeter, so that kd-kan,
=-
Qdn(r)/dr ,
and therefore, from eq. (4), kd-k,n,
= -‘b ?+n,.
(5)
The term on the right-hand side of eq. (5) is the net flux of molecules away from the island per unit perimeter length and is equal to the net desorption rate per unit perimeter. Unless incorporation into an island involves a sizable energy barrier comparable to half the activation energy for desorption, then (k cb)lj2 4 k, and therefore n, = kJk,. Thus, since the total perimeter for the islands is proportional to the square root of their area, the desorption rate
J. C McCarty, R.J. Madix/Formic acid desorption porn graph&tied Ni(ll0)
R 0: (k&J
217
(kcD)1/2N1/2 ,
and the desorption kinetics are half order. Both the diffusion analysis and Arthur’s analysis have a common weakness for application to the results reported here; both do not account for the fact that the islands must grow together near saturation coverage and eclipse the rarefied phase. This island interference decreases the area available for desorption from the rarefied phase. Thus the desorption rate should decrease as the coverage approaches saturation unless the adsorbed molecules can desorb from both phases with equal rates. Since saturation coverage of HCOOH on the Ni(ll0) graphite surface ws reached, and as zero order desorption kinetics was observed initially for all coverages from low coverage up to saturation coverage, it appears that the surface area available for zero order desorption must have included both the area of the condensed and rarefied phases. An ideal two-dimensional lattice gas with attractive nearest neighbor pair potential cannot desorb directly from a condensed phase with the same rate as from a rarefied phase without simultaneous relaxation of the island. Direct desorption creates metastable vacancies within the condensed phase which require additional energy. Analysis of this point is given in Appendix A. The extra transition state barrier due to vacancy formation upon desorption from an island may be eliminated or avoided in two ways. If the adjacent adsorbate molecules can “relax” and fill the vacancy, before the desorbing molecules reach the transition state, the extra barrier could be reduced or eliminated altogether, This relaxation would require a liquid-like or mobile condensed phase. Alternatively, if the desorption can proceed via a physisorbed precursor state on top of the island, the desorption rates over the island and over the non-condensed phase can be equal. The concentration, 0 , of molecules in the second layer can be described by an equilibrium constant sim ipar to that of eq. (A.l). The overall desorption kinetics are then zero order regardless of the initial island coverage if the precursor and the rarefied phase have the same desorption transition state. If the two-dimensional “island” concept is to agree with the desorption rate data presented here, then it appears that the condensed phase of adsorbed formic acid must be either capable of rapid relaxation to fill vacancies or able to support a desorption precursor state. Though the “island” mechanism phenomenologically describes the desorption behavior observed, it is likely that the condensed phase of DCOOH adsorbed on the graphitic overlayer consisted of long chains, i.e., polymers, of hydrogen bonded, molecules. Solid formic acid [ 161 is composed of “infinitely” long chains of hydrogen bonded molecules, and the liquid 1171 was found to be polymeric rather than dimeric or monomeric. The hydrogen bond linking two formic acid molecules is quite strong. The heat of dissociation of the dimer is 14.1 kcal/mol(59.0 kJ mol-l) [ 181; the single hydrogen-bond strength is therefore about 7.0 kcal/mol(29.5 kJ mol-l). Assuming the energy required to separate the chains was comparable to the heat of fusion [ 191 of formic acid (12.6 kJ mol-l), the heat of dissociation of a single molecule from a formic acid polymer was probably between 7.0 and 10.0
218
J. C Mccorty R.J. Mad&/Formic acid desorption from graphitized Ni(l IO)
kcallmol(29.5 and 42.1 l~Jrnol_~). It seems likely that the condensed phase of formic acid adsorbed on the graphite surface consisted of clustered hydrogenbonded chains of formic acid molecules, while the rarefied phase consisted of physi~rbed monomers. The magnitude of the observed zero order activation energy for formic acid desorption from the graphite surface was consistent with the polymer bonding described above. The initial desorption rate of the flash curves in fig. 1 strictly followed zero order kinetics over a factor of 30 variation in initial coverage. Fig. 4 shows a plot of the natural logarithm of the average initial rate of desorption versus 1000 K/T for 13 different values of the initial coverage. The desorption rates of a flash peak were excluded from the average after the rate exceeded one-half the maximum or peak rate of that curve. The vertical error bars correspond to twice the standard deviation of the mean desorption rate at selected temperatures. Due to the mass spectrometer shot noise and the difficulty of precisely determining the baselines of the flash peaks, more uncertainty existed for low desorption rates, thereby limiting the observation of small systematic deviations from zero order kinetics. The slope of the best straight line through the average value of the initial rates in fig. 4 indicated the activation energy for zero order desorption was 16.3 kcal/mol (68.2 + 4.2 kJ mol-l), The frequency factor was 1018*1 Nsat SSC-~. From the discussion above the hydrogen-bond strength was estimated to be 7.0 kcallmol (29.5 kJ mol-I), and after attributing 3.0 kcal/mol (12.6 kJ mol-l) for the separation of clustered chains, the binding energy of the monomer was 10,Okcal/mol (42.1 kJ molB1) less than the binding energy of a molecule in a chain. Assuming 50-
;i
20-
I
‘P \
$o-
P \
d
-R x SLOPE = 16.3 KCAL P
25 \ P
0 2 I?
2-
B e
,_
\ P \
T
0.5 51
f\ 5.2 53 54 55 5.6 1000 K / TEMPERATURE
!
Fig. 4. Zero order desorption rate versusreciprocal temperature for DCOOHadsorbedon the saturated gxaphitesurface.
J. C. McCarty, R.J. MadixfFormic acid desorptbn from graphitized Ni(l10)
219
formic acid monomers had nearly the same heat of adsorption on graphite as CO2, the apparent activation energy for desorption from the chains would be 18.3 kcal/ mol(76.5 kJ mol-l), taking 8.3 kcal/mol(34.7 kJ mol-l) as the heat of physisorption of CO2 on graphite [22]. This value is only 2.2 kcal/mol higher than the experimentally observed value. The formation of condensed polymers of formic acid adsorbed on graphite appears quite consistent with the experimental data. The transition from zero order desorption kinetics to kinetics less than first order can be described qualitatively by an equilibrium between dissociated monomers and their parent clusters. The concentration of desorbing monomers is controlled through equilibrium with chains of various length. Assuming the rate of monomer desorption was much less than the rate of association and dissociation of polymers, the desorption and equilibrium steps could be expressed as follows: ko Ma --+M
3M-M a-
desorption
g
(7)
K3
equilibria
3a
%I
nM a+---+M
na
where Mna represents an adsorbed chain containing n monomers M. The total concentration, C,, of adsorbed formic acid is equal to the sum of monomers in all the chains, i.e., CT =
n$l nMna = ?/ n=l
nK,,x
,
(8)
where K, = 1. The rate of desorption
is
R = k,M,
(9)
and the change in total coverage is determined dC,/dt
= -k,M.
k,
(4&&T
+ 1)“2-l
where + W/RT).
kinetics. Following the analysis described
1’
(4&,CT + 1)1’2t 1
K. z exp(-So/R
rate. Thus (10)
eqs. (8) and (10) describe the desorption in Appendix C, the desorption rate _dCT =---dt Ku
by the desorption
(11)
220
J. C McCiuty, R.J. M&dix/Rwmicacid desorption from graphitized Ni (I 10)
The desorption rate expression (11) represents zero order desorption kinetics with a transition to first order as the coverage is exhausted. For 4KoCT iib 1,
dCT/dr = -koKo .
02)
For 4K0CT < 1, dC,,‘dt = -kOCT.
(13)
For small K,#ZT, eq, (11) becomes very similar to the zero/first order expression [eq. (3)] presented above, Rate “k&‘&l
+K&+).
04)
The flash desorption curves calculated from eq. (11) show good qucrlitative agreement with the data presented in fig. 1, as shown in fig. 5. The saturation coverage for DCOOH adsorption on the Ni(l tO)--graphite surface was estimated from the lattice parameters for crystalline formic acid. The bonding parameters for hydrogen-bonded/formic acid molecules as determined from the Xray diffraction patterns of solid formic acid [ 161 are listed in table 1. Fig. 6 shows the t~ee~d~~sion~ structure of solid formic acid with fl bonding based on the X-ray diffraction data of Holtzberg et al, [l&l. The nearest intramolecule approach of the carbon and oxygen atoms in solid formic acid are also listed in ta 0.9
08 0.7 06 0.5 O!l 0.3
00 175 It#)185 I90 TElWPEFMTLREfK1 Data from curve (a) of Fig. 5. Calculatedand expeiimentti formic acid desorption rates, fig* 1. (0) Caitculateddesorption rates from numeri& integration ofeq. (26); k&C@ = 3 X i033exp[-16.3 k~~rno~~~~: Ko = 1.3 x IO-” exp~6.Pk~l~mo~~~.
J. C iUcGuty, R.J. Madix/Formic acid deslorption from graphitized Ni(l IO)
221
Table 1 Bonding parameters of solid formic acid Bond length (A)
Bond angle (deg) 0
0
C-H= 1.05
‘C’ C
C-O = 1.26 C=O = 1.23 O-H...0
= 123 H
‘0’ C\o/
= 122 H = 114
= 2.58
Nearest intramolecular approaches (A) G.0 = 3.18 O..*O = 3.28 c***c = 3.15
table 1. For comparison,
fig. 7 represents the structure
of the formic acid molecule
1191. The density of molecules formed at the surface of solid formic acid with the bc plane of fig. 6 parallel to the surface was calculated to be 1 .O X 1015 molecules/cm2 with two molecules per bc cell. However, the molecules are oriented nearly edgewise to the bc plane with an oxygen atom directed away from the surface rather than along the surface plane. The coverage density of this bc plane is therefore expected to be higher than the coverage density for molecules lying parallel to the surface. A better estimate of the coverage density of adsorbed formic acid was given by the
Fig. 6. The crystal structure of solid formic acid.
222
J.C. McCWty, R.J. MzdixfFormic acid deswptbn fkomgraphitized NilI IO)
--x
Fig. 7. Geometry of the formic acid molecule.
0.
IA
Fig. 8. Folymerie models of formic acid adsorbed on the graphite surface: (a) 01~~~mation~ (b) p ~~~~at~n.
J. C McGzrty, R.J. Madiw/Formic acid desorption from graphitized Ni(l IO)
223
surface density along the ac plane, 7.3 X 1014 molecules/cm’ with 4 molecules per unit cell, although the chains do not lie parallel to this plane. Two possible bonding arrangements of polymeric formic acid adsorbed on the graphite surface are illustrated in fig. 8. The (Yand p forms were suggested [20] by the infrared spectra of formic acid crystals. The bond lengths and bond angles assigned to the (Yand /3 forms are listed in table 2. The spacing between the (Yand fl polymer-like rows in fig. 6 was adjusted so that the nearest C..-O intramolecular approach was 3.2 A. The O*-.O closest approach of the a form was less than 3.2 A because of the bond angles of an 01chain. The spacing between chains on the surface was determined by the distances of nearest approach in solid formic acid. The coverage densities of the two models in fig. 8 were 7.0 (o form) and 6.2 X 1014 molecules/cm2 (~3form). Thus the formic acid coverage density expected for formic acid adsorbed on the graphite surface was 6.6 + 1.0 X 1014 molecules/ cm2. Assuming the initial sticking probability was 1.0, the actual coverage estimated from fig. 2 was 7.8 f 2 X 1014 molecules/cm2. The consistency of these results lends support to the estimate of so = 1.
5. summary The graphitized Ni(ll0) surface was chemically inactive, adsorbing formic acid non-dissociatively at low temperature. The amount of Hz, H20 and CO adsorbed and the amount of formic acid decomposed by the saturated graphite layer was insignificant relative to the clean surface. Formic acid desorbed from the graphite surface in narrow flash peaks which initially followed zero order kinetics. The initial desorption rate was independent of coverage from 3 X 1013 molecules/cm2 to saturation coverage, 7 X 1014 molecules/ cm2. Formic acid adsorbed at 165 K on the graphite layer apparently formed chains of hydrogen-bonded molecules. This adsorbed state was consistent with the desorp-
Table 2 Bonding parameters of fii. 8 Bond length (A)
Bond angle (deg)
C=H c-o c=o O-H***0
o-c-o C-O-H C-O*** H C-O*.*H
= 1.05 = 1.25 = 1.245 = 2.58
Intramolecular closest approaches (A) OL form: C+O = 3.2,0***0 = 2.45 p form: C%O = 3.2,0...0 = 3.2
= = = =
1225 122.5 115 (p form) 122.5 ((uform)
224
J.C. McCarty, R.J. Madix/Formic acid desorption from graphitized Ni(ll0)
tion kinetics, the ~ximum coverage, and the LEED indication of disordered adsorption observed following adsorption at 165 K. The zero order kinetics were described by desorption of physisorbed monomers in equilibrium with clusters of the formic acid chains. The frequency-factor of the zero order rate constant, k,, = 1@3+1 exp(-68.2 f 4.2 kJ mol-i/~T)s-i, indicated that the transition state for desorption of the monomer had nearly full translational and rotational degrees of freedom.
Acknowledgements The authors gratefully acknowledge the National Science Foundation and the Center for Materials Research at Stanford for financial support of this research. Acknowledgement is also made to the Donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. We are also thankful for fellowship assistance from the National Science foundation for a portion of the duration of this work (J.G.M.).
Appendix A The following analysis shows that a lattice gas with an attractive nearest neighbor pair potential (w) cannot desorb directly from a condensed phase at the same rate as from the rarefied phase. Consider a lattice gas ex~bit~g two-dimen~on~ phase separation 1211 with m (2,3,4 or 6) nearest neighbors. If the system is far from the critical point, then the local fractional coverage within the condensed phase, Be, approaches unity, and then Or, the local fractional coverage in the rarefied phase, is given by or = Vrlf,)
exp(-(E,--E,)/RT),
(A-1)
where B, = n/M, E,-EC = (mJZ)w, M is the adsorption site density; fr, f,are the rarefied and condensed phase molecular partition functions, respectively, and Er and EC are the zero point energies of the molecules in the rarefied and condensed phases. The rate constant for desorption from the rarefied surface phase, k,, can be expressed as [22] kr = (kTlh)(f;f/f,)exp(-(~-E,)lRT),
(A.2)
and the desorption rate (per unit area) over the rarefied phase is given by the product of eqs. (A 1) and (A.2), R, = (kT/h)~If,)exp(-(E~-E,)IRT),
(A-3)
where fr* is the partition function and Ef is the zero point energy of the transition state for desorption from the rarefied phase. The rate of desorption directly from
J. C. McCarty, R.J. h&dix/Formic acid desorption from graphitized Ni(ll0.l
225
the condensed phase is given by R, = (k~~~)~~lf,)exp(-(~~-~~)/RT),
(A.4)
where ff and Ez represent the transition state for desorption from the condensed phase. The two rates are equal, regardless of initial coverage and temperature, only if
f: =fZ
and
E:=i?:,
i.e., if the desorption transition states are the same for both phases. However for the lattice gas system, E: f E,?, because the transition state for desorption from the condensed phase includes the creation of a metastable vacancy in the island. The average energy of an adsorbed island molecule due to interaction with its neighbors is (m/Z)w, but during desorption m interaction bonds are broken. The addition energy (m/2)w is the energy of formation of m unpaired bonds, i.e., the vacancy left behind. As a result, a lattice gas system as described above cannot show zero order desorption kinetics as the coverage approaches saturation.
Appendix B A high frequency factor is expected for the desorption of a formic acid molecule from a cluster of hydrogen-bonded chains. Consider as the initial bound state a molecule bonded within a chain as illustrated in fig. 8. The fact that desorption probably proceeds via a physisorbed monomer is of no concern here since the monomer is presumed to be in equilibrium with the condensed phase chains. The transition state is assumed to be a monomer with the properties of a two dimensional gas with rotational and vibrational modes unrestricted by the surface. The reaction coordinate is in the z direction with the x and y axes taken parallel to the surface. For the zero order rate from eqs. (A.3) and (A.4) & = (kWO(tc,/fJexp(-WW?, so that ko = RO =
(kTIh)Cf~yf~tif”)exp(-~lRT),
03.1)
where f:,, isthe two~ensio~l gas translation partition function, f& the rotational partition function of the transition state, AE is the zero point energy barrier, and fv is the vibrational partition function of the monomer in the chain, The internal vibration partition function of the molecule was assumed to be unchanged throughout desorption and the chains were assumed to be immobiie. Thus all internal vibrational modes were canceIled out by f$,except those modes involving the hydrogen bond in the condensed phase. The frequency factor for k,-, in eq. (B.l) can be expressed as
JL. M&arty, R.J. Madix/Formic acid desorption from graphitized Ni(l IO)
226
y. = (kTlh)exp(~~/R),
where
03.2) For a two-~mensional gas at 200 K with molecular weight, MW, equal to 46 amu and site density, Ns = 8 X 1014 cm-2 [23], f;y
= 2nkT(MW)&h2,
yielding AS” = .502JK-1mol-1. XY *
(B-3)
For free rotation of formic acid,
f: = (T3/0,0203)1/2
)
yielding AS: = 65.7 J K-l mol-l ,
(B-4)
where 0,) 02, O3 are the characteristic temperatures [23] for rotation about the three principle axes of formic acid. The characteristic temperatures were calculated from the three rotational constants of formic acid, 76 800 MHz, 12 055 MHz, and 10 416 MHz, which were determined from microwave spectra [24]. The vibrational frequencies involving the hydrogen bond occur [25] at 90cm-’ due to C.ofH bending and 230 cm-l due to O-H.*+0 stretching; torsional modes requiring rotation perpendicular to the surface were neglected. Thus exp(-hvl/2kT)exp(-hv2/2kT) fv =
[l-exp(-hvl/kT)]
[l-exp(-hv2/k7’)]
’
and A$=
-19.7 JK-l mol-l .
tB.5)
Finally, after evaluating all the terms for the preexponential factor in eq. (B.l), vu = 4.2 X 1012 exp(96.2 J K-l mole1 /R)s-l , or v0 =: 1017.6 s-1 which is in good agreement with the observed frequency factor, 101** 1 s-l.
(B.6)
J.C. McCarty, R.J. MadixfFormic acid desorption fromgraphitized Ni(ll0)
221
Appendix C EZq.(8) can be simplified by the use of a convenient approximation for the equilibrium constants, K,. The equilibrium constants depend on the entropy and energy differences between the chains and the monomer, thus Cl)
K,, = expW,,lR-&,lRT), where as,
AH,, = En-nE+?T,
=s,-n&s,,
S, is the entropy of a chain of length n, En is the corresponding chain energy, Su is the monomer entropy, and E. is the monomer energy. AEn = (En-nEo) is approximately equal to -(n - 1) W where W is the hydrogen bond strength. This approximation rests on the following assumptions: (i) the interaction of each formic acid molecule with the substrate is unaffected by the formation of the chains, (ii) the hydrogen bond energy is not affected by the length of a chain, (iii) the total interaction energy sums linearly with the number of bonds in a chain, and (iv) hydrogen bonds formed by ring closure or dimer-type bonding represent an insignificant contribution to the total energy and entropy. The -RT term in AH,, is small (< 1.7 kJ mol-l) and shall be neglected below. Further, ASn is assumed to depend linearly upon the number of hydrogen bonds, and AS, z SO (n - 1) where SO represents the sum of the entropy lost due to the translational and rotational restrictions of a monomer in a chain and the entropy gained from the vibrational modes of the chain. This approximation for AS, also assumes that the translational and rotational components of S, equal SO. From eq. (C- 1) K, can be written as K, = exp(-S,-,(n-1)/R
+ W(n-l)/RT
or
Kn = Kim1 ,
(C.2)
where K. E exp(-SO/R Substituting
t W/RT).
K, into eq. (8) produces the sum,
C, = M +2KoM2 + 3K;M3
t . .. t nK;-lM”
t ..,
or C,=M(l
+2K,,M+3K;M2+
. . . +nK$-lMin-l
+ ...).
(C-3)
l?q. (C.3) can be reduced to C, = M(1-K,M)-2, enabling M to be readily calculated M= C, [(2K,,CT + l)-(4K&
(C-4) as a function
of CT. Thus,
+ 1)1/2]/2(KoCT)2.
(C.5)
228
J. C McGwty, R.J. Madix/Formic acid desorption from graphitized Ni (I IO)
References [l] [ 21 [3] [4] [S] [6] [7] [8] [9]
J.R. Arthur and A.Y. Cho, Surface Sci. 36 (1973) 641. J.R. Arthur, Surface Sci. 38 (1973) 394. J.G. McCarty and R.J. Madix, J. Catalysis 38 (1975) 402. J. McCarty, J. Falconer and R.J. Madix, J. Catalysis 20 (1975) 235. J.L Falconer and R.J. Madix, Surface Sci. 46 (1974) 473. J.G. McCarty, Ph.D. Dissertation, Stanford University, Stanford, California (1974). J.P. Coad and J.C. RiviQe, Surface Sci 25 (1971) 609. T.W. Haas, J.T. Grant and G.J. Dooley, J. Appl. Phys. 43 (1972) 1853. G. Ertl, in: Molecular Processes on Solid Surfaces, Eds. E. Draughs, R.D. Gretz and R.K. Jaffee (McGraw-Hill, New York, 1969) pp. 155-157. [lo] J. Falconer, Flash Decomposition Spectroscopy Study of Formic Acid Decomposition on Clean Ni(llO), Appendix A, Ph.D. Dissertation, Stanford University, Stanford, California (1974). (111 G. Ehrlich, Advan. Catalysis 14 (1963) 271. [12] P.A. Redhead, Vacuum 12 (1962) 203. [13] B. McCarroll, J. AppL Phys 40 (1969) 1. [14] D.R. Stull, Ind. Eng. Chem. 39 (1947) 517. 1151 G.C Pimentel and A.L. McClellan, The Hydrogen Bond (Freeman, San Francisco, 1960) p. 224. [ 161 F. Holtzberg, B. Post and I. Fankuchen, Acta Cryst. 6 (1953) 127. [17] D. Chapman, J. Chem. Sot. (1965) 225. [18] W. Waring, Chem. Rev. 51 (1952) 171. [19] A.I. Popov, Chem. NonAqueous Solv. 3 (1970) 339. [20] Y. Mikawa, R.J. Jakobson and J.W. Brusch, J. Chem. Phys. 45 (1966) 4750. [21] T.L Hill, An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, MA, 1960) ch. 14. [22] D.O. Hayward and B.M.W. Trapnell, Chemisorption (Butterworths, London, 1964) pp. 150-153. [23] T.L Hill, An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, MA, 1960) pp. 153-161. [ 241 RG. Lerner, B.P. Dailey and J.P. Friend, J. Chem. Phys. 26 (1957) 680. [25] R. Tubino and $ Zerbo, J. Chem. Phys. 53 (1970) 1428. [26] M. Smutek, S. Cerny and E. Buzek, Advan. Catalysis 24 (1975) 343.