The compensation effect and the manifestation of lateral
interactions in thermal desorption spectroscopy
Citation for published version (APA):
Niemantsverdriet, J. W., Markert, K., & Wandelt, K. (1988). The compensation effect and the manifestation of lateral interactions in thermal desorption spectroscopy. Applied Surface Science, 31(2), 211-219.
https://doi.org/10.1016/0169-4332(88)90062-1
DOI:
10.1016/0169-4332(88)90062-1
Document status and date: Published: 01/01/1988 Document Version:
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Applied Surface Science 31 (1988) 211-219 211 North-Holland, Amsterdam T H E C O M P E N S A T I O N E F F E C T A N D T H E M A N I F E S T A T I O N O F L A T E R A L I N T E R A C T I O N S I N T H E R M A L D E S O R P T I O N S P E C T R O S C O P Y J.W. N I E M A N T S V E R D R I E T
Laboratory of Inorganic Chemistry and Catalysis, Eindhoven University of Technology, Eindhoven, The Netherlands
K. M A R K E R T a n d K. W A N D E L T
Fritz-Haber-Institut der Max-Planck-Gesellschafi, Faradayweg 4-6, D-I O00 Berlin 33, Germany
Received 11 May 1987; accepted for publication 14 October 1987
If thermal desorption spectra are analysed in terms of the Polanyi-Wigner equation lateral interactions between the adsorbates may lead to coverage (0) dependent pre-exponential factors, ~, and activation energies of desorption, E. Evidence from the literature shows that E and ~ often satisfy the well-known compensation effect In v(0) = bE(O)+ c, with constants b and c. Here we insert this compensation effect into the rate equation of desorption and simulate spectra which illustrate the influence of the compensation effect in thermal desorption spectra of adsorbate systems where pairwise lateral interactions prevail.
1. Introduction
T h e r m a l d e s o r p t i o n spectroscopy (TDS) c o n s t i t u t e s a n i m p o r t a n t tool i n o r d e r to s t u d y i n t e r a c t i o n s b e t w e e n a d s o r b a t e s a n d s u b s t r a t e s as well as lateral i n t e r a c t i o n s b e t w e e n a d s o r b a t e s o n surfaces [1-5]. O n a n otherwise h o m o g e - n e o u s s u b s t r a t e the presence of lateral i n t e r a c t i o n s c a n b e i n f e r r e d f o r m the coverage d e p e n d e n c e of the a c t i v a t i o n energy of d e s o r p t i o n , E ( O ) . I n the case of pairwise i n t e r a c t i o n s o n e m a y a s s u m e
E ( O ) = E o - wO, (1)
with E 0 = E ( O = 0), w the i n t e r a c t i o n e n e r g y (negative for a t t r a c t i v e a n d positive for repulsive i n t e r a c t i o n s ) , a n d 0 the a d s o r b a t e coverage i n m o n o - layers (ML) [1-5]. C a l c u l a t e d d e s o r p t i o n traces b a s e d o n pairwise lateral i n t e r a c t i o n s b e t w e e n the a d s o r b e d particles b y G o l z e et al. [5] show t h a t in the case of first-order d e s o r p t i o n kinetics, attractive i n t e r a c t i o n s shift the d e s o r p - t i o n peaks to higher t e m p e r a t u r e s , whereas repulsive i n t e r a c t i o n s shift the peaks to lower t e m p e r a t u r e s . These c a l c u l a t i o n s , however, rest o n the a s s u m p -
0 1 6 9 - 4 3 3 2 / 8 8 / $ 0 3 . 5 0 © Elsevier Science P u b l i s h e r s B.V. ( N o r t h - H o l l a n d Physics P u b l i s h i n g D i v i s i o n )
212 J. lee Niemantsverdriet et al. / Compensation effect and lateral interactions in TDS 1.5
Compensution
/ Z
/
Effect
Ag/W(
d3
o 40 g/ x o~ Ag/Ru(001) ÷ 30f /
S "A 'w,110
I I 25 " i_ I "=- 200 300 400 500 600 E (k J/mot)Fig. 1. Plots of In p(0) against E(O) for thermal desorption of Ag and Au from W(ll0), W(100) [3] and Ru(001) [8,9] reveal the presence of the compensation effect.
tion that the pre-exponential factor of desorption, ~, see eq. (3), does n o t vary with coverage. This assumption, however, is not correct.
Several investigations on thermal desorption of Ag, Au, and Cu f r o m W ( l l 0 ) and W(100) by Bauer et al. [3], H 2 f r o m I r ( l l 0 ) by Wittrig et al. [6], CO from Ru(001) by PfniJr et al. [7], and of Ag and Au from Ru(001) b y our group [8,9], have shown that in general both E and u depend on coverage. Often they satisfy the well-known compensation effect:
In u ( 0 ) = b E ( O ) + c = E ( O ) / R T ~ + c, (2) E~ L-. C o m p e n s a t i o n e f f e c t in T D S o C ~/tc 1 / T
Fig. 2. When the compensation effect operates in thermal desorption, Arrherdus plots correspond- ing to different coverages intersect at a critical reciprocal temperature ] / T c (after Clark []0]).
J. W. Niemantsverdriet et al. / Compensation effect and lateral interactions in T D S 213
Table 1
Critical compensation effect temperatures for thermal desorption of metals from metals [3,8,9]
Adsorbate Substrate T~ (K) Ag W(ll0) 1145 Ag W(100) 1295 Au W(ll0) 1255 Au W(100) 1565 Cu W(ll0) 1635 Ag Ru(001) 1095 Ag Ag/Ru(001) a) 940 Au Ru(001) 1115
a) Second layer Ag on Ru(001).
in which b and c are constants, and T~ is defined as 1 / b R , with R the gas constant [10]. A few examples which comply with this compensation effect relate to the desorption of metal layers and have been compiled in fig. 1. F r o m these plots the values of b, c and T~ can be determined. The parameter T~ has a clear physical interpretation. It represents the temperature at which the Arrhenius plots for different adsorbate coverages intersect (see fig. 2). Values of T c calculated from E(O) and ~(0) data published for Ag and Au desorption from three different substrates reported by Bauer et al. [3] and ourselves [8,9] are given in table 1.
The purpose of this paper is to illustrate the influence of the compensation effect on the shape of simulated thermal desorption spectra, when lateral interactions between the atoms are present in the adsorbate layer.
2. Rate equation
The rate of thermal desorption of adsorbed particles from a single adsorp- tion state is generally described by the Polanyi-Wigner equation:
dO ~ ( 0 ) 0 n exp (3)
r dt R T '
in which r is the rate of desorption, 0 the coverage in monolayers (ML), t the time (s), u the pre-exponential factor, n the order of the desorption kinetics, E the activation energy of desorption (equals the adsorption energy when the adsorption is a non-activated process), R the gas constant and T the tempera- ture. Most generally, the coverage dependence of E can formally be expressed
as:
E ( O ) = Eo + A E ( O ) , (4)
where E 0 is the activation energy of desorption for a single adatom (0 ~ 0) and A E ( O ) represents the coverage dependent part of E. In agreement with
214 J . W . N i e m a n t s v e r d r i e t et al. / Compensation effect a n d lateral interactions in T D S
the experimental evidence cited above we assume that the coverage depen- dence of p is determined by the compensation effect:
In p(O) =
bE(O)
+ c = In u0 + A E ( O ) / R T ~ , in which % is the pre-exponential factor at influence of the lateral interactions and the obtained by combining eqs. (3)-(5):(5)
coverage zero. The c o m b i n e d compensation effect is then
dO oO expt
dt (6) g..2,
O . L . o TDS simulation n = l E0= 3 0 0 k J / m o lV 0 = 1013/S
attractive
interactions
W=-25kJ/mo[
*(I.67
l
r
e
p
u
l
s
i
v
e
~
interactions
W = .25kJ/mol
800
900
1000
1100 T(K) 1200
Fig. 3. Simulated thermal desorption spectra for first-order desorption with coverage-independent
pre-exponential factor. Top: coverage-independent activation energy of desorption. Middle and bottom: attractive and repulsive pairwise interactions, E ( O ) = E o - wO. The coverages for each
J. W. Niemantsverdriet et al. / Compensation effect and lateral interactions in T D S 215
I n order to illustrate the influence of the c o m p e n s a t i o n effect, we will present m o d e l calculations of thermal d e s o r p t i o n spectra for the special case of first-order d e s o r p t i o n kinetics a n d pairwise interactions (see eq. (1)), for which the following m o d i f i c a t i o n of eq. (6) holds:
dSdt
( Eo)~ [wO[X__RI
-f ~1)]
r = - ,0 0 exp - e x p [ - , (7)
with T = T o + / 3 t , where/3 is the linear heating rate. W e stress that eqs. (6) a n d (7) are n o t h i n g b u t empirical expressions, which, however, describe a n u m b e r of T D S observations successfully.
¢ Attractive Interactions/~.o67 Repulsive Interactions
"~ Eo=30OkJlmol
~1 ' Eo=300kJ/mol
o
= V o = l O 3 / s
~'11
Vo=lO'~/s
W = -25kJ/mol
/~//I
W = *25kJ/mol
Tc = ~ (3) 7 2 t
To= 1 0 0 0 ~
T c = 1 0 ~
F, 900 1000 1100 TIK) 900 1000 1 1 0 0 1200Fig. 4. S i m u l a t e d t h e r m a l d e s o r p t i o n s p e c t r a for f i r s t - o r d e r d e s o r p t i o n k i n e t i c s a n d a t t r a c t i v e (left) a n d r e p u l s i v e (right) l a t e r a l i n t e r a c t i o n s , a n d d i f f e r e n t v a l u e s of the c o m p e n s a t i o n effect t e m p e r a - t u r e T c. T h e d e s o r p t i o n e n e r g y varies w i t h c o v e r a g e as E ( O ) = E 0 - w 0 a n d t h e p r e - e x p o n e n t i a l f a c t o r varies a c c o r d i n g to the c o m p e n s a t i o n effect as In t, = - w S / R T c + In 1, 0. P a r a m e t e r v a l u e s : E o = 300 k J / m o l , w = + 25 k J / m o l , ~o = 1 0 1 3 s - 1 . T h e c o v e r a g e s for e a c h set of s p e c t r a v a r y
216 J. l'Id Niemantsverdriet et al. / Cornpensation effect and lateral interactions in T D S
3. Results
The spectra have been calculated by solving eq. (7) with a R u n g e - K u t t a method for the following parameters: E 0 = 300 k J / m o l , u0 = 1013 s-1, fl = 1 K s-5, w = _+ 25 k J / m o l , and different values of T~. Fig. 3 shows, for reasons of comparison, the influence of lateral interactions of the shape of first-order thermal desorption spectra when the pre-exponential factor is constant, that is when T c = oc. In the absence of lateral interactions (w = 0) the temperatures T m at peak maximum and the peak widths ( F W H M ) are independent of the initial coverages. When W < 0 (attractive interactions), T,n increases and F W H M decreases with 0, for repulsive interactions the opposite behavior is observed. N o t e that, although the interaction energy w is only small compared to E 0, the spectra deviate appreciably from those for w = 0. In practice such extreme shapes are rarely observed.
o t t r a c t i v e i n t e r o c t i o n s 1150 E I.-- 1100 1050 1000 0 0 5 1 T~ (K) e~ 5000 3000 2000 1400 lOOO 800 60O
40,0
1250 ~-~ 1200 1150 f 1100 1050 1000 0 r e p u t s i v e i n t e r a c t i o n s O5 1 T~(Ki 400 6OO 800 000 1&OO ! 0 0 0 iooo ;ooo o o I 150 125 ,~, 100 75 5O 25 0 600 8oo lOOO 14oo 2000 3000 5~o 1 e (ML) - - 150 125 100 75 50 25 0 0 e o ooo 0oo ooo 400 ooo 8oo 500 ~oo 0.5 1 E) [ML)Fig. 5. Variation of the peak m a x i m u m temperature T m and the full width at half m a x i m u m
F W H M of thermal desorption spectra with initial coverage for first-order desorption kinetics, for
attractive and repulsive lateral interactions, and for different values of the compensation effect
temperature T c. The desorption energy varies with coverage as E ( O ) = E o - w O and the pre-ex-
ponential factor varies according to the compensation effect as In p = - wO/RT~ + In %. Parame- ter values: E o = 300 k J / m o l , w = _+ 25 k J / m o l , ~'o - 1013 s - I.
J.W. Niemantsverdriet et al. / Compensation effect and lateral interactions in TDS 217
Fig. 4 shows calculated T D spectra for the case of attractive and repulsive pairwise interactions ( w = _+25 k J / m o l ) , when the pre-exponential factor changes according to the compensation effect eq. (2). The corresponding peak m a x i m u m temperatures and the widths of the spectra are shown in fig. 5. The top curves of fig. 4 correspond to those shown in fig. 3, for T c = oo. The next three sets of spectra show the influence of the compensation effect. As T~ decreases the compensation becomes stronger and the spectra look more and more like simple first-order desorption curves with coverage-independent desorption parameters. At a certain critical temperature T c around 1000 K, compensation is almost perfect. N o t e that, although b o t h E and u depend on coverage, T m and F W H M are virtually constant. At lower values of T~, the behavior of T m and F W H M reverses, and the spectra corresponding to attractive interactions look similar to those for weakly compensated repulsive interactions, and vice versa. Such a situation has been observed experimentally for thermal desorption of Au from W ( l l 0 ) and from Ru(001), in which E decreases but T m increases with increasing coverage [3,8,9].
4. Discussion
An important conclusion from the model calculations is that the tempera- ture of m a x i m u m desorption and the width of the spectrum are by no means reliable indicators for the b o n d strength between adsorbate and substrate. As a particularly interesting example we note that a set of T m and F W H M values which are virtually constant with initial coverage can in principle correspond to three cases: first-order desorption kinetics with (1) coverage-independent E and ~, (2) attractive and (3) repulsive interactions between the adsorbates, provided that u(0) and
E(O)
are related by a compensation effect of ap- propriate strength. It is important to realize that attractive interactions do not necessarily correspond todTm/dO>O
and repulsive interactions not to dT, n / d 0 < 0, as figs. 4 and 5 demonstate.This reinforces that T D spectra of systems where lateral interactions play a role should always be analyzed by those procedures which are based on a m i n i m u m n u m b e r of simplifying assumptions. Several procedures for the analysis of T D S data are presently used [2,3,11-14]; table 2 lists the assump- tions involved. A useful and rapid test proposed by Pervan et al. [14] indicates which of the assumptions are allowed for a given set of T D spectra.
The popular peak temperature method of Redhead [11] and the procedure of Chan, Aris and Weinberg [12], which is based on the T m and F W H M of the T D spectra, are inappropriate for adsorbates exhibiting lateral interactions; only the model-independent procedures proposed by King [2], Bauer et al. [3] and Habenschaden and Kiippers [13] should be used in those cases in which E and u may depend on coverage and in which the order of desorption is not a
2 1 8 J. V~ Niemantsuerdriet et a L / Compensation effect and lateral interactions in T D S T a b l e 2 A s s u m p t i o n s in v a r i o u s m e t h o d s o f T D S a n a l y s i s A s s u m p t i o n R e f e r e n c e s R e d h e a d C h a n K i n g a n d H a b e n s c h a d e n et al. B a u e r et al. a n d K i i p p e r s [11] [121 [2,3] [13] E a n d v d o n o t d e p e n d o n 0 + + n k n o w n + + v k n o w n + -
priori known. The essential feature of these procedures is that the factor 0 n in expression (3) is kept constant. F o r fixed values of 0, a plot of in r against
1 / T should then yield a straight line with slope - E ( O ) / R and intercept In v(O)+ n In 0. In this way E(O) can be determined without ambiguity. However, in order to seperate v(O) and n, further assumptions, usually on the value of n, are required.
The present simulations are justified by the experimental observation that in m a n y desorption systems E(O) and v(O) satisfy the compensation effect. Although in principle the formalisms including lateral interactions between adsorbates, as those proposed b y Cassuto and King [4], A d a m s [1] and Z h d a n o v [15] allow for non-constant pre-exponential factors, they do not seem to lead to a strict compensation effect as exhibited by the systems Ag and Au on Ru(001), W(100) and W ( l l 0 ) in fig. 1. The theory of Zhdanov, for example, predicts that v should vary even when E is constant [15], which would be a violation of the compensation effect.
A qualitative explanation of the compensation effect can easily be given when it is realized that E corresponds to the depth of an interatomic potential, an v to its curvature or steepness. As a deeper potential is automatically also a steeper potential, it is clear that v will increase when E increases . However, for Lennard-Jones or Morse potentials this principle is not equivalent with the mathematical expression of the compensation effect In v = bE + c. For other explanations of the compensation effect we refer to Clark [10].
In conclusion, several desorption systems including metallic and gaseous adsorbates, exhibit compensation effects between the pre-exponential factor and the activation energy of desorption. Simulated desorption spectra, based on an empirical rate equation for desorption which includes pairwise lateral interactions and a compensation effect, show that direct correlations between the shape of the spectra and the nature of the lateral interactions cannot be made. Thermal desorption spectra should therefore be analysed with proce- dures which rest on a m i n i m u m of further simplifying assumptions about the parameters of the P o l a n y i - W i g n e r equation.
J.W. Niernantsverdriet et al. / Compensation effect and lateral interactions in T D S 219 Acknowledgement J . W . N . a c k n o w l e d g e s f i n a n c i a l s u p p o r t f r o m a H u y g e n s - f e l l o w s h i p g r a n t e d b y t h e N e t h e r l a n d s O r g a n i z a t i o n f o r t h e A d v a n c e m e n t o f P u r e R e s e a r c h
(zwo).
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