J . Phys. Chem. 1990, 94, 6192-6791
6792
Surface Diffusion and Desorption of Pentane Isomers on Ru(001) M. V. Arena, A. A. Deckert,+ J . L. Brand,* and S. M. George* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: October 23, 1989; I n Final Form: March 16, 19901
The surface diffusion and desorption of n-pentane, isopentane, cyclopentane, and neopentane were examined on Ru(001). These investigations used the techniques of laser-induced thermal desorption and temperature-programmed desorption. The surface diffusion activation energies varied from &if = 3.0 f 0.3 kcal/mol for neopentane to &if = 4.4 i 0.2 kcal/mol for n-pentane. The desorption activation energies ranged from Edes = 10.7 f 0.2 kcal/mol for neopentane to Edes= 13.8 i 0.9 kcal/mol for n-pentane. The surface corrugation ratio, defined as 7 i Edif/Edes, was remarkably constant at Q = 0.30 for all the pentane isomers. In agreement with earlier results for n-alkanes on Ru(001), this constancy indicates a linear scaling between the diffusion activation energy and the desorption activation energy. These results suggest that the pentane isomers have similar binding configurations and move on the Ru(001) surface in a concerted process. The magnitudes of the surface diffusion and desorption activation energies were observed to scale inversely with the degree of branching of the pentane isomer. The Wiener index, W(G),was employed to characterize the degree of branching. In addition, a simple physisorption model using a Lennard-Jones (6-12) pair potential was utilized to predict surface binding energies and configurations. This model was also used to quantify the scaling between the activation energies and the degree of branching.
I. Introduction The diffusion of molecules on single-crystal surfaces is an important topic in surface chemistry and physics.] Surface diffusion uniquely probes the underlying adsorbate-surface and adsorbate-adsorbate Likewise, surface mobility may be the rate-limiting step in many surface kinetic processes. Unfortunately, few surface diffusion studies have been performed as a result of experimental difficulties. This scarcity is particularly noticeable on metal surfaces because surface mobility may influence the kinetics of heterogeneous catalysis. This paper examines the surface diffusion of pentane isomers on Ru(001) using laser-induced thermal desorption (LITD) techniques. Studies of hydrocarbons on transition-metal surfaces are important for an understanding of catalytic hydrogenation, dehydrogenation, and Fisher-Tropsch ~ y n t h e s i s . ~Ru(001) is a model group VI11 transition-metal surface that is effective in Fisher-Tropsch hydrocarbon ~ynthesis.~'In addition, the pentane isomers constitute an homologous series of hydrocarbons where the degree of branching can be varied systematically while keeping the molecular weight nearly constant. The kinetics of surface diffusion and desorption were measured for n-pentane, isopentane, cyclopentane, and neopentane on Ru(001). The investigations revealed a simple scaling between the surface diffusion activation energy, &if, and desorption activation energy, Ed,, These studies demonstrated that the surface corrugation ratio, defined as R = & i f / & $ , was constant at R = 0.30. This constancy indicates that the modulation of the surface potential parallel to the surface is similar for all the pentane isomers on Ru(001). This study of pentane isomers on Ru(001) extends previous LITD surface diffusion studies of h y d r ~ g e n , ~cy~loalkanes,'~ -'~ and carbon m o n ~ x i d e ' ~on . ' ~the Ru(001) surface. The majority of these earlier investigations explored the surface diffusion of model chemisorption systems composed of atomic and molecular species. The present study builds on the previous work and explores a series of physisorbed molecules. In agreement with recent results for n-alkanes on Ru(O01),17 these measurements suggest that a linear scaling exists between Edif and Edes for the pentane isomers on Ru(001). 11. Experimental Section
In the LITD surface diffusion an initial laser pulse is used to heat a well-defined area on the surface. The laser heating produces a rapid temperature jump that is large enough 'Present address: Department of Chemistry, College of the Holy Cross, Worcester, MA. 'Present address: 1BM Almaden Research Center. San Jose. CA.
0022-3654/90/2094-6792$02.50/0
to desorb the adsorbates within the heated area.19,20 After a time delay, a second identical probe laser pulse heats the same area and desorbs the adsorbates that have diffused into the initially evacuated region from the surrounding surface. The desorption flux at each delay time corresponds to the amount of diffusional refilling. The time-dependent refilling signals are then fit by using the appropriate solution to Fick's second law to determine the surface diffusion coefficient.s This prepare-and-probe LITD experimental procedure has been employed successfully in recent studies to measure surface diffusion on single-crystal metal surface^.^-'**^^-*^
(1) Ehrlich, G.; Stolt, K. J. Annu. Reo. Phys. Chem. 1980, 31, 603. (2) King, D. A. J . VUC.Sci. Techno/. 1980, 17, 241. (3) King, D. A. In Chemisiry ond Physics of Solid Surfuces; CRC Press:
Boca Raton, FL, 1979; Vol. 2. (4) Bileon, P.; Sachtler, W. H. M. Ado. Card. 1981, 30, 165. (5) Vannice, M. A. J . Card. 1975, 37, 449. (6) Vannice, M. A. J . C a u l . 1975, 37, 462. (7) Vannice, M. A. Carol. Reo. 1976, 14, 153. (8) Mak, C. H.; Brand, J. L.; Deckert, A. A,; George. S. M. J . Chem. Phys. 1986,85, 1676. (9) Mak, C. H.; Koehler, B. G.;Brand, J. L.; George, S. M. J . Chem. Phys. 1987, 87, 2340. ( I O ) Mak, C. H.; Koehler. B. G.; Brand, J. L.; George, S. M. Surf, Sei. 1987, 191, 108. ( 1 1 ) Mak, C. H.; Brand. J. L.; Koehler, B. G . ;George. S. M . Surf Sei. 1987, 188, 312. (12) Brand, J. L.; Deckert, A. A.; George, S . M. Surf.Sci. 1988, 194,457. (13) Mak, C. H.; Deckert, A. A.; George, S . M. J . Chem. Phys. 1988,89. 5242. (14) Mak. C. H.; Koehler, B. G.; George, S. M. J . VUC. Sei. Technol. 1988. A 6 , 856. (15) Deckert, A. A.; Brand, J. L.; Arena, M. V.; George, S. M. Surf Sei. 1989, 208, 441. (16) Deckert, A. A,; Brand, J . L.; Arena, M. V.; George, S. M . J . Vu?. Sei. Technol. 1988, A6, 194. (17) Brand, J . L.; Arena, M. V.; Deckert, A. A,; George, S. M. J . Chem. Phys. 1990, 92, 5136. (18) George, S. M.; De Santolo, A. M.; Hall, R. B. Surf. Sci. 1985, 159, L425. (19) Cowin, J. P.; Auerbach, D. J.; Becker, C.; Warton, L. Surf. Sei. 1978, 78, 545. (20) Wedler, G.; Ruhmann, H. SurJ Sci. 1982, 121, 464. (21) Viswanathan, R.; Burgess, Jr., D. R.; Stair, P. C.; Weitz, E. J . Vue. Sei. Techno/. 1982. 20. 605.
(24) Seebauer, E. G . ;Kong, A C. F.; Schmidt, L. D. J . Chem. Phys. 1988, 88. 6597
0 1990 American Chemical Society
Pentane Isomers on Ru(001)
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6193
The experimental setup for these LITD measurements of surface diffusion has been described previously.8 Briefly, the experiments were performed in an ion-pumped ultrahigh-vacuum Torr. (UHV) chamber with background pressures below 3 X Analysis of surface cleanliness and surface order was carried out with Auger electron spectroscopy (AES) using a single-pass cylindrical mirror analyzer (CMA) and low-energy electron diffraction (LEED) spectrometry. A TEM-00 Q-switched Nd:phosphate glass laser producing pulse lengths of 100-130 ns with Gaussian spatial profiles was employed.8 The reasons for using longer pulse lengths have been discussed previously.26 In the present study, the laser pulse energy before entering the UHV chamber was approximately 0.1 5 mJ/pulse. The pulses were focused by a 65-cm focal length lens to give a Gaussian spatial profile of 120 pm (fwhm) at the focus of the lens. The surface was positioned at the focus of the lens. The angle between the incoming laser pulses and the surface normal was 54O. Consequently, the desorption areas were elliptical with an aspect ratio of 1.7. The dimensions of the desorption spots obtained by using the spatial autocorrelation methodI8 were approximately 125 pm in diameter along the minor axis and 210 pm in diameter along the major axis. The pentane isomers were adsorbed onto the Ru(001) surface by using a glass capillary array doser. The doser was positioned -2 cm from the Ru(001) surface. The doser produced consistent coverages as determined by TPD analysis. The surface coverages were quantified by integrating the TPD peak and normalizing to the TPD area corresponding to a saturation monolayer coverage. The coverages of the various isomers were uniform to within *I 5% across the surface, using LITD spatial measurements. The surface-cleaning procedure involved exposing the Ru(001) Torr single-crystal surface to a background pressure of 2 X of O2 while cycling the temperature between 1100 and 1370 K several times. Repeated flashing to 1570 K then removed excess oxygen.8-" This cleaning procedure was conducted after each experiment. The surface cleanliness was monitored by using both AES and CO TPD peak temperatures as discussed previo~sly.'~-'~ Hydrocarbons have been observed to be unstable in the presence of electrons.27 Stray electrons from the ionizer of the mass spectrometer are one source of energetic electrons. Consequently, the Ru(001) crystal was biased to -80 V to repel any stray electrons for all the LITD and TPD experiments. For each surface diffusion experiment, the Ru(001) single crystal was scrupulously cleaned, dosed at a lower temperature, and subsequently heated to the desired experimental temperature. A matrix of 8-24 desorption spots was created by translating the laser beam across the Ru(001) single-crystal surface. This translation was accomplished by mirrors mounted on piezoelectric translators with optical encoders. The desorption spots were always separated by at least 850 pm. To ensure complete evacuation of the desorption area, each desorption spot was prepared with five consecutive laser pulses.26 Each of the desorption spots was probed with a second sequence of similar laser pulses at time delays ranging from 6 to 800 s. The piezoelectric translators returned the laser to each of the desorption spots with an accuracy of f0.5 pm. Control experiments indicated that adsorption from the background pressure in the UHV chamber was insignificant. Heats of desorption for the pentane isomers on Ru(001) were determined by using the variation of heating rates method attributed to Redhead.28 Heating rates between p = 0.04 and 30 K/s were produced by a temperature controller in conjunction with a voltage-programmed power supply. In all cases, the desorption of the pentane isomers from Ru(001) followed first-order desorption kinetics. Because there was no indication that pentane isomer adsorption on Ru(001) was activated, adsorption and (25) Seebauer, E. G.: Kong. A . C. F.; Schmidt, L. D. J . Vuc.Sci. Technol. 1987, AS, 464. (26) Brand. J. L.; George, S. M . Surf. Sci. 1986, 167, 341. (27) Firment, L. E.; Somorjai, G. A . J. Chem. Phys. 1977, 66, 2901. ( 2 8 ) Redhead, P. A . Vacuum 1962, I 2 , 203.
I
1
"
"
"
'
I
156 K 141 A 133
e
1
= 0.1 esa,
v)
Time (sec)
Figure 1. Diffusional refilling data for isopentane on Ru(001) at various Solid lines represent refilling curves corretemperatures at 0 = 0.10,. sponding to constant surface diffusion coefficients.
1.0 -
0.5 -
0
17' 0
50
100
AX
150
200
(microns)
Figure 2. Determination of the desorption hole size for isopentane at 140 K using the spatial autocorrelation method. These measurements yield a hole size of 1 15 wm along the minor axis.
desorption were assumed to be reversible. Surface diffusion and desorption measurements for various alkanes on Ru(001) have been performed on several Ru(001) crystals cut from the same boule. These measurements have been reproducible on different Ru(001) crystals and crystals subjected to few and thousands of laser shots. There was no evidence from LEED, adsorption, or desorption studies for any surface defects produced by the laser surface heating of Ru(001) under these experimental conditions. 111. Results I . Surface Diffusion Measurements. A . Temperature Dependence. The normalized refilling data for isopentane at e = 0.1Bat at a variety of temperatures are displayed in Figure 1. e,, is the coverage of the saturated isopentane monolayer on Ru(001). esatshould correspond to a coverage of Osat 2.9 X I O l 4 molecules/cm2 based on the area that the molecule occupies on the surface. The data points are not averages from several runs but are results from single prepare-and-probe sequences a t various delay times. Refilling curves, corresponding to constant diffusion coefficients, were fit to the experimental data and are shown as solid lines. To determine the value of the surface diffusion coefficient, the size of the desorption area must be known. Measurements of the LITD hole size for isopentane at 140 K using the spatial autocorrelation methodI8 are displayed in Figure 2. In the spatial autocorrelation method, the initial desorption signal is recorded. The laser beam is then translated a distance AX on the surface. Desorption from the region outside the area of the initial desorption region gives rise to the second desorption signal.I8 The normalized LITD signal is defined as the ratio between the second desorption signal and the initial desorption signal. The data shown in Figure 2 yield a hole size of 1 15 pm along the minor axis. Additional experiments measured a hole size of 195 gum along the major axis. Given this elliptical desorption area, surface diffusion coefficients can be assigned to the diffusional
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6794
Arena et al.
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
TABLE I: Summary of the Measured Surface Diffusion and Desorption Kinetic Parameters, Calculated Adsorption Energies, Wiener Indexes, and Corrugation Ratios for the Pentane Isomers on Ru(001) __ Edif, kcal/mol Do,cm2/s Edcr, kcal/mol "des* Ea,+,kcal/mol w(G) a -.n-pentane isopentane cyclopentane neopentane
4.4 f 0.2 4.1 f 0.3
3.0 x
3.3 f 0.3 3.0 f 0.3
6.0 X 104"o.1 4.0 X 10-2"o.1
10-1*0.9 10-2'0.'
5.5 x
13.8 f 13.5 f 11.9 f 10.7 f
0.9 0.4
0.5 0.2
1.8 x
14.6 12.6 11.1 10.5
1015'0.2
3.0 x 10'5*01 I .3 x 1014*0.1 4.0 x 1013*01
T (K) 160
-
150.
6
0.30 0.30 0.28 0.28
20 18 15 16 T (K)
5
1
180
1301
180
140
120
100
-6
Neopentane o n-Pentane
-
-7 -
A
0
% ',e
0
lsopentane Cyclopentane
-7
E,
-7 5 -
C
0 "
-
-8
n
-8
a
-m -8.5
66
62
70
74
-9 1000/T (l/K)
Figure 3. Arrhenius plot of the surface diffusion coefficients for isopentane on Ru(001) at 0 = 0.10,,. The measured surface diffusion kinetic parameters were Ed,[ = 4.1 f 0.3 kcal/mol and Do = 5 . 5 X
I O-L*o
cm2/s.
155
K
e
= 0.1 esa,
7
9
1
1000/T (1IK)
Figure 5. Arrhenius plot of the surface diffusion coefficients for all the pentane isomers on Ru(001) at 0 = 0.10,,. The measured surface diffusion kinetic parameters are given in Table I.
-
-6
T = 150 K
-6.E
al
0.8 w-
E, p
..
-7
c
:
-7.5
*
.
.
1
0
-8.5
0
200
400
600
800
0
Time (sed
Figure 4. Diffusional refilling data for n-pentane on Ru(001) at various temperatures at 0 = 0.10,,. Solid lines represent refilling curves corresponding to constant surface diffusion coefficients.
refilling data in Figure I . The Arrhenius plot of the temperature dependence of the surface diffusion coefficient for isopentane on Ru(001) at O = 0.16,', is displayed in Figure 3. The slope of the Arrhenius plot yields an activation energy for surface diffusion of Edir= 4.1 f 0.3 kcal/mol. Likewise, the y intercept yields a diffusion preexponential of Do = 5.5 X 10-2*o.l cm2/s. Uncertainties in the surface diffusion activation barrier and preexponential were based on the standard deviation of the slope and y intercept, using standard error propagation methods. Normalized diffusional refilling data were obtained versus temperature for the pentane isomers on Ru(001) at O = O.lOsat. Refilling curves similar to Figure 1 were obtained for all the pentane isomers on Ru(001). For example, temperature-dependent refilling curves for n-pentane at 0 = O.lO,, are displayed in Figure 4. Om, for n-pentane on Ru(001) should correspond to a coverage of O,, -- 2.6 X IOI4 molecules/cm2. Similar estimates for O,, can also be obtained by other method^.^^,^^ Figure 4 shows that all the refilling curves were fit well with constant surface diffusion coefficients. Desorption hole sizes for all the pentane isomers on Ru(001) were measured each day. These hole sizes allowed absolute surface diffusion coefficients to be assigned. All of the temperature(29) Gavezzotti, A.; Simonetta, M.; Van Hove, M. A,; Somorjai, G. A . Surj. Sci. 1985, 154, 109. (30) Firment. L. E.; Somorjai, G. A . J . Chem. Phys. 1978, 69, 3940.
0.2
0.4
0.6
0.8
lsopentane Coverage ( Q / O S a J
Figure 6. Coverage dependence of the surface diffusion coefficient for isopentane on Ru(001) at 150 K.
dependent surface diffusion coefficients for the pentane isomers on Ru(001) are summarized by the Arrhenius plots shown in Figure 5 . The surface diffusion coefficient measurements for cyclopentane on Ru(001) were obtained earlier.14 The Arrhenius parameters for the surface diffusion of the four pentane isomers on Ru(001) are summarized in Table I. B. Coverage Dependence. If adsorbate-adsorbate interactions are present, the surface diffusion coefficient may be coverage dependent.2s3*31These adsorbate-adsorbate interactions can be measured by LITD diffusional refilling experiments3]as has been recently demonstrated for CO on RU(OOI).I~*'~ The coverage dependence of the surface diffusion coefficients was measured for all the pentane isomers on Ru(001). Normalized refilling data for surface diffusion of the pentane isomers on Ru(001) were obtained at different initial surface coverages. Figure 6 displays the surface diffusion coefficient versus coverage for isopentane at 150 K. The surface diffusion coefficients for isopentane and n-pentane on Ru(001) were both coverage independent. Earlier measurements indicated that the surface diffusion coefficient of cyclopentane was weakly coverage dependent. The surface diffusion coefficient of neopentane on Ru(001) was strongly coverage dependent and has been discussed in detail elsewhere.32 The surface diffusion parameters given in Table
'
(31) Mak, C. H.; George, S. M. Sur/. Sci. 1%6, 172. 509.
Pentane Isomers on Ru(001)
The Journal of Physical Chemistry, Vol. 94, No. 17, I990 6795
210
-4,
-
(K)
Tp 190
150
1 A 0
-a -
C
-12
-
'. .' '.'.
A
5
t
l
m
Neopentane Cyclopentane lsopentane n-Pentane
\ k O
:@
170
i t , , E
,
,
,
,
j
2 11
12
13
14
0 0
Desorption Activation Energy (kcallmole)
Figure 8. Linear scaling between the surface diffusion activation energy and the desorption activation energy for the pentane isomers on Ru(001).
-15
10001T,
(1IK)
Figure 7. Redhead analysis of the TPD spectra for neopentane, cyclopentane, isopentane, and n-pentane on Ru(001) as a function of heating rate. The measured desorption kinetic parameters are given in Table I.
timated to be OC I0.02 monolayer.
IV. Discussion
I . Diffusion Mechanism and Linear Scaling. For the case of an adatom diffusing over a surface, the diffusion mechanism is assumed to involve an atom that resides in a specific minimumcyclopentane. At these low coverages, the effect of adsorbateenergy binding site. This binding site could be a 3-fold hollow adsorbate interactions should be minimal. site on a hexagonal lattice surface. The adatom then moves 2. Thermal Desorption Measurements. The desorption energies through a bridge site into the neighboring minimum-energy for the pentane isomers on Ru(001) were measured by the varbinding Consequently, the surface diffusion activation iation of heating rates method.28 TPD spectra with higher temenergy is approximately the potential energy difference between perature peaks, Tp, corresponding to faster heating rates, @, were the 3-fold hollow binding site and the bridge site. obtained for all the pentane isomers. The TPD spectra correThis picture for adatom diffusion serves as a model but cannot sponding to various heating rates between 0 = 0.04 and 30 K / s be easily applied to the diffusion of polyatomic molecules. For were analyzed by using the standard Redhead analysis.** The example, the pentane isomers adsorbed on Ru(001) reside over results of this analysis are shown in Figure 7. many Ru surface atoms. A distribution of binding configurations Desorption activation energies were obtained from the slopes could exist because there may be several minimum-eneigy states of these Arrhenius-like Redhead plots. Likewise, desorption with energies close to one another. Similarly, a unique transition preexponentials were determined from the y intercept and the state may not exist for pentane isomer surface diffusion on Ruslope. The Arrhenius parameters for the thermal desorption of (001) and the diffusion activation energy may be a thermal average pentane isomers from Ru(OO1) are given in Table I. Uncertainties over different transition states. Finally, the pentane isomers have in the desorption activation energies and preexponentials were additional rotational and vibrational degrees of freedom that a obtained by applying standard propagation of error techniques simple adatom does not possess. These additional degrees of to the standard deviation in the slope and y intercept. freedom could also influence surface diffusion. The desorption activation energies were observed to decrease Despite the lack of clearly defined binding and transition states, with the degree of pentane isomer branching. The desorption the diffusion and desorption data reveal general trends. For preexponentials also roughly decreased with the degree of pentane example, the activation energies for diffusion scale nearly linearly isomer branching. In addition, the desorption kinetics were with the activation energies for desorption as shown in Figure 8. coverage independent for all the pentane isomers except neoLinear relationships between diffusion and desorption activation pentane. Neopentane displayed a very weak coverage dependence energies have been observed earlier for n-alkanes on R u ( O O ~ ) ' ~ that has been discussed p r e v i o ~ s l y . ~ ~ and cycloalkanes on R ~ ( 0 0 1 ) . ' ~ 3. Additional Measurements. LEED measurements were Recent theoretical calculations also predict a nearly linear conducted to determine whether the pentane isomers formed scaling between diffusion and adsorption energies for n-alkanes, ordered overlayers on Ru(OO1). In accordance with measurements The cycloalkanes, and pentane isomers physisorbed on RU(OOI).~~ of c y ~ l o a l k a n e s ~and * ~ ~n-alkanesI7on Ru(OOl), no new diffraction calculations reveal that physisorption interactions alone are spots were observed. However, LEED measurements of hydrosufficient to explain measured desorption activation energies on carbons are difficult to perform and LEED patterns for n-alkanes Ru(001). The calculated physisorption energies, Ead,and the on single-crystal metal surfaces have only been observed for Ptmeasured desorption activation energies, Ed,, are given in Table and Ag( 1 1 Hydrocarbons are believed to be very (1 1 susceptible to electron-induced decomposition and d e s o r p t i ~ n . ~ ~ ~I .~ The ~ theoretical results were based on a simple summing of Lennard-Jones (6-1 2 ) pair potentials for carbon-ruthenium and Quantitative measurements of surface carbon determined hydrogen-ruthenium interaction^.^^ whether any of the pentane isomers decomposed on the Ru(001) 2. Surface Corrugation. The corrugation ratio, R Eda/Edif, surface. The amount of carbon on Ru(001) is difficult to measure is defined as the ratio of the diffusion activation energy, Edif,!o directly with AES. Consequently, oxygen uptake experiments were the desorption activation energy, Edes. The corrugation ratio performed to measure carbon on the Ru(001) s u r f a ~ e . ~Only .~~ provides a measure of the modulation of the surface potential negligible traces of carbon were detected by the oxygen uptake parallel to the surface. Figure 8 and Table 1 reveal that the experiments. The carbon coverage on Ru(001) after the desorption measured corrugation ratios are nearly constant at R = 0.30 for of a saturation exposure of any of the pentane isomers was esall the pentane isomers on Ru(OO1). The linear scaling between Edirand Ed= suggests that the (32) Westre: E : D.; Arena, M. V.; Deckert, A. A,; Brand, J. L.; George, pentane isomers share similar binding configurations and diffusion S. M.SurJ Sci., in press. mechanisms on Ru(OO1). The constancy of the corrugation ratio (33) Madey, T. E.; Yates, Jr., J. T. Surf. Sci. 1978, 76, 397. argues that the pentane isomers are locked in rigid orientations (34) Felter, T. E.; Hoffmann, F. M.; Thiel, P. A,; Weinberg, W. H. Surf.
I were measured at 0 = 0.1~9,~for neopentane and 8 = 0.20,, for
Sci. 1983, 130, 163. (35) Hoffmann, F. M.; Felter, T. E.; Thiel, P. A,; Weinberg, W. H. Suf. Sci. 1983, 130, 173. (36) Shi, S. K.; White. J. M. J . Chem. Phys. 1980, 73, 5889.
(37) Mak, C. H.; George, S. M. Chem. Phys. Lett. 1987, 135, 381. (38) Arena, M . V.;George, S. M., Manuscript in preparation.
Arena et al.
6796 The Journal of Physical Chemistry, Vol. 94, No. 17, 1990
lsopentane A
n-Pentane
'
Figure 9. Calculated minimum-energy surface binding configurations for n-pentane and isopentane on Ru(001). Top and side views are displayed.
to correlate the physical properties of molecule^.^^^^^ The Wiener index, W(G),is related to the sum of the number of carbon bond lengths separating each carbon atom from the other carbon atoms of the molecule. W(G) is the sum of all the unique C-C bond path distances in the carbon skeleton of the hydrocarbon. For the same number of carbon centers, a larger W(G) implies a less branched molecule. For molecules that have a similar branching pattern, a larger index implies a larger molecule. Hydrogen atoms are ignored by the Wiener index. The Wiener indexes for each pentane isomer are listed in Table I. Assuming that the surface diffusion and desorption activation energies should scale with the Wiener index, the predicted order for these activation energies is n-pentane
In contrast, the observed trend is n-pentane
Cyclopentane
Neopentane
Figure 10. Calculated minimum-energy surface binding configurations for cyclopentane and neopentane on Ru(OO1). Top and side views are displayed.
and move in a concerted manner on the Ru(001) surface. This constancy implies that conformational degrees of freedom and possible segmental or "reptilian" motion39do not influence the surface diffusion mechanism. Theoretical results for the binding configurations based on physisorption interactions were obtained by using the LennardJones (6-1 2) pair potentiak3* These calculations yielded the minimum-energy surface configurations for n-pentane and isopentane shown in Figure 9. Results for cyclopentane and neopentane on Ru(001) are displayed in Figure 10. The binding configurations shown in Figures 9 and 10 display the effect of isomer branching on the desorption and diffusion activation energies. As the branching increases, more carbon and hydrogen atoms are moved away from the Ru(001) surface. An increase in branching lowers both the calculated physisorption energies and the desorption activation energies as demonstrated by the Edesand Eadvalues given in Table I. The theoretical results also reveal similarities in the surface binding configurations of the pentane isomers. In general, the hydrogens that are closest to the Ru(001) surface are preferentially located over 3-fold hollow sites. The desorption and diffusion activation energies are roughly proportional to the number of hydrogens that are located over 3-fold sites. These hydrogens may be partially responsible for the linear scaling observed between Edif and Edes* 3. Wiener Index. Using a topological index, one can compare the trends observed for the surface diffusion and desorption activation energies with the degree of branching for each pentane isomer. A topological index is a number that reflects the relative degree of branching and size of the molecule. The Wiener index, W ( G ) ,is a topological index that is dependent on the graph, G , of the molecule and is inversely related to the degree of branching.40 The Wiener index has been used successfully in the past (39) de Gennes, P. G . Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (40) Wiener, H . J . Am. Chem. SOC.1947, 69, 17.
> isopentane > neopentane > cyclopentane > isopentane > cyclopentane > neopentane
The Wiener index displays the correct trend but switches the relative positions of neopentane and cyclopentane. This transposition could be related to the omission of hydrogen atoms from the Wiener index. However, the theoretical results for the adsorption energies of the pentane isomers on Ru(001) give the same ordering as the experimental desorption measurements. The diffusion and desorption activation energies are inversely dependent on molecular branching. The Wiener index is inversely dependent on molecular branching and qualitatively predicts the trends in the experimental measurements. After accounting for the uncertainties in the diffusion and desorption parameters, a quantitative comparison of the Wiener index and the measured activation barriers also reveals that the Wiener index scales approximately with the absolute experimental values. 4. Couerage-Dependent Diffusion. Measurements of surface diffusion and desorption provide direct information about the parallel and perpendicular surface potential^.'^ At low adsorbate coverages, the activation energies are dominated by the adsorbate-surface interaction. As the adsorbate coverage is increased, adsorbate-adsorbate interactions may become important and can influence surface d i f f ~ s i o n . ~ . ~The , ~ ' ,surface ~~ diffusion of CO on Ru(O0 1) was a clear example where repulsive nearest-neighbor interactions significantly influenced CO surface m ~ b i l i t y . ' ~ ~ ' ~ For isopentane on Ru(OOl), Figure 6 reveals that the surface diffusion coefficients were coverage independent. This behavior indicates that the parallel surface potential is dominated by adsorbate-surface interactions. The surface diffusion coefficient of n-pentane was also independent of coverage. Similarly, recent measurements of n-propane, n-butane, and n-hexane on Ru(001) have revealed surface diffusion coefficients that were coverage independent. The surface diffusion of cyclopentane on Ru(001) was mildly coverage dependent as has been described e1~ewhere.l~Briefly, the surface diffusion coefficient increased approximately a factor of 3 as the surface coverage increased from I9 = 0.1I9, to 8 = Om,. This coverage dependence is consistent with weak repulsive adsorbate-adsorbate interaction^.^*^*^' In contrast, the surface diffusion coefficient for neopentane displayed a strong dependence on surface coverage. This coverage dependence has been examined in detail in another paper.32 Briefly, the surface diffusion coefficient decreased approximately by a factor of 60 as the surface coverage increased from 8 = 0.058,,, to I9 = Os,,. This coverage dependence could be consistent with either attractive adsorba te-adsorba te interactions or a mu1tiple-site hopping model .32 5. Preexponentials. The surface diffusion and desorption preexponentials are listed in Table I. There is a general trend in the surface desorption preexponentials. As the molecule becomes more branched, the surface desorption preexponential (41) Rouvray, D.; Pandey, R. J . Chem. Phys. 1986,85, 2286. (42) Needham, D. E.; Wei, I.; Seybold, P. G . J . Am. Chem. SOC.1988, 110, 4186. (43) Bowker, M.; King, D. A. S w j . Sci. 1978, 71, 583.
J . Phys. Chem. 1990, 94, 6197-6804 decreases for most of the pentane isomers. A simple qualitative explanation using transition-state theory can explain this trend in the surface desorption preexponentials. In the minimum-energy binding configuration, the rotations of the molecule will be severely hindered. These rotations will become unhindered in the transition or gas-phase state. Consequently, the differences between the rotational partition functions in the transition states for the various pentane isomers will affect their relative desorption preexponentials. The rotational partition function, qr,is proportional to (IAIBIC)’/’ where I,, Ig, and ICare the principal moments of inertia of the molecule. As the molecular branching increases, the moment of inertia for the pentane isomers will decrease and the rotational frequency will increase. Likewise, the rotational partition function will decrease as the molecular branching increases. The rotational partition functions in the transition state, q:, will decrease with increased molecular branching. The ratio of the rotational partition functions q?/qr, where qr designates the hindered binding state, will also decrease as the molecular branching increases. Thus, smaller surface desorption preexponentials would be expected for the more branched pentane isomers. Assuming a rigid molecule, the principal rotational moments of inertia for the pentane isomers have been estimated by finding the eigenvectors for the moment of inertia tensor.44 These moments of inertia and appropriate symmetry numbersu predict the relative rotational partition functions of 19:ll: 1 1 :1 for isopentane:cyclopentane:n-pentanemeopentane. This explanation does not quantitatively predict the effect of branching on the desorption preexponential. Note that the estimated ratios for the desorption preexponentials span a range of X19, whereas the observed range is X75. The diffusion preexponentials for the pentane isomers on Ru(001) follow the same general trend as that observed for the surface desorption preexponentials. The diffusion preexponential tends to decrease as the pentane isomer becomes more branched. This trend can be explained by similar arguments based on (44) McQuarrie, D. A. Starisrical Mechanics; Harper & Row: New York, 1976.
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transition-state theory and rotational partition functions.
V. Conclusions The surface diffusion and desorption of n-pentane, isopentane, cyclopentane, and neopentane was examined on Ru(001), using laser-induced thermal desorption (LITD) and temperature-programmed desorption (TPD) methods. The surface diffusion activation energies varied from Edir= 3.0 f 0.3 kcal/mol for neopentane to &if = 4.4 f 0.2 kcal/mol for n-pentane. Similarly, the desorption activation energies ranged from Eds = 10.7 f 0.2 kcal/mol for neopentane to Ed- = 13.8 f 0.9 kcal/mol for npentane. The surface corrugation ratio, Q Edir/,!?+, was determined to be constant at Q Z= 0.30 for all the pentane isomers on Ru(001). In agreement with the earlier results for n-alkanes on Ru(001), this constancy indicates a linear scaling between the diffusion activation energy and the desorption activation energy. These results suggest that the pentane isomers have similar binding configurations and move on the Ru(001) surface in a concerted process. Conformational degrees of freedom do not appear to influence the surface diffusion mechanism. The surface diffusion and desorption activation energies scaled inversely with the degree of branching for the pentane isomers. was used to characterize the branching The Wiener index, W(G), and was found to correlate with the diffusion and desorption activation energies. Likewise, a simple physisorption model using a Lennard-Jones (6-12) pair potential was employed to determine the predicted surface binding energies and configurations. In agreement with the measurements, these physisorption calculations also displayed an inverse scaling between the adsorption energies and the degree of branching. Acknowledgment. This work was supported by the National Science Foundation under Grant CHE-8908087. Some of the equipment used in this work was provided by the NSF-MRL program through the Center for Materials Research at Stanford University. M.V.A. thanks the Eastman Kodak Co. for a graduate fellowship. S.M.G. acknowledges the National Science Foundation for a Presidential Young Investigator Award and the A.P. Sloan Foundation for a Sloan Research Fellowship.
Importance of Surface Reactions in the Photochemistry of ZnS Colloids Dave E. Dunstan,*qt Anders Hagfeldt,t*tMats Almgren,+ Hans 0. G. Siegbahn,*and Emad Mukhtart Departments of Physical Chemistry and Physics, Uppsala University, Uppsala, Sweden (Received: October 30, 1989; In Final Form: February 22, 1990)
The photochemistry of colloidal ZnS has been studied under a variety of experimental conditions. The time dependence of the photocorrosion has been examined by using time-resolved fluorescence, static fluorescence, and electron spectroscopy for chemical analysis (ESCA) techniques. A qualitative model for the semiconductor and its electrolyte interface is developed to explain the experimental observations where elemental Zn, S,and SO,” formed on the surface act as e-/h+ recombination centers. The photocorrosion products have been identified as SO4’-, SO,2-, and S. The importance of the surface chemistry in the photochemistry is shown via the correlation between the growth in the emission intensities and the formation of the photocorrosion products on the surface of the dried colloids.
Introduction Much has been written about semiconductor colloids and their photochemistry due to the recent explosion in interest in them as potential solar energy converters. A general review is that by
* Authdr to whom correspondence should be addressed. Present address: Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. ‘Department of Physical Chemistry. *Department of Physics. 0022-3654/90/2094-6797$02.50/0
Henglein’ while an extensive treatise on the photochemistry of ZnS is found in the book by Leverentz.’ However, because of the difficulty in understanding the complicated experimental results, no complete theory or physical explanation for their absorption and emission properties has been developed to date.3*4 ( I ) Henglein, A. Top. Curr. Chem. 1988, 143, 1 1 3 . (2) Leverenz, H. W. Luminescence of Solids; Wiley: New York, 1950. (3) Uchida, I. J . Pfiys. SOC.Jpn. 1964, 19, 670. (4) Samelson, H.;Lempicki, A. Pfiys. Reu. 1962, 125, 901.
0 1990 American Chemical Society
