Langmuir 2005, 21, 7311-7320
7311
Thermodesorption Studies of Energetic Properties of Ni/MgO-Al2O3 Catalysts. Determination of Adsorption Energy Distribution Functions Tomasz Panczyk,*,† Wojciech Gac,‡ Monika Panczyk,‡ Anna Dominko,‡ Tadeusz Borowiecki,‡ and Wladyslaw Rudzinski†,‡ Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30239 Krakow, Poland, and Faculty of Chemistry, Maria Curie-Sklodowska University, pl. M. Curie-Sklodowskiej 3, Lublin, 20031 Poland Received January 5, 2005. In Final Form: April 24, 2005 The thermodesorption spectra of hydrogen from coprecipitated catalysts (70-x)NiO-xMgO-30Al2O3 (x ) 0-50%wt) are reported. The catalysts were calcined at 400 °C and reduced with H2 at 20-800 °C and for 3 h at 800 °C. NiO reduction degree was between 49.3 and 92.1%. The active surface areas changed from 8.4 to 32.4 m2/g whereas mean size of nickel crystallites was between 3.7 and 9.7 nm. The TPD spectra were next analyzed in order to determine the adsorption energy distributions functions. To obtain these functions a theoretical model of adsorption/desorption kinetics based on the statistical rate theory (SRT) was applied. This approach allows for determination of the adsorption energy at nonequilibrium conditions as well as at quasiequilibrium conditions. The resulting distribution functions reveal the presence of two main bands of adsorption energy. Some correlation is found between the determined distributions of adsorption energy and the size of nickel crystallites determined using the XRD method. The presence of MgO favors creation of high energy adsorption sites on Ni crystallites.
1. Introduction Steam reforming of hydrocarbons is the most important way to prepare a synthesis gas. In this process, nickel catalysts play a crucial role. Therefore, many attempts were made to improve the activity of these catalysts and their resistance to deactivation during the reaction.1-4 These attempts were solely based on introduction of promoters or by changing the composition of the support. Any modification of a catalyst always results in changing its chemical properties, and these properties manifest themselves mainly in energetic properties of adsorbing surface. Thus, the knowledge about the energetic properties of catalysts surfaces is very important part in catalytic studies. Many attempts were made in the literature toward determination of these properties mainly by applying the temperature programmed desorption technique (TPD) of hydrogen from the investigated catalysts. These attempts were focused on determination of the activation energy for desorption, order of desorption process, and the preexponential factors.5 However, catalysts surfaces are often strongly energetically heterogeneous, and thus, a single activation energy of desorption parameter is not sufficient. Therefore, some attempts were made toward determination of a continuous distribution of the activation energy of desorption from the TPD spectra.6-9 However, * Corresponding author. E-mail:
[email protected]. † Polish Academy of Sciences. ‡ Maria Curie-Sklodowska University. (1) Twigg, M. V.; Ed. Catalyst Handbook; Wolfe: London, 1989. (2) Armor, J. N. Appl. Catal. A 1999, 176, 159. (3) Rostrup-Nielsen, J. R. In CatalysissScience and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Berlin, 1984; Vol. 5, p 1. (4) Tracz, E.; Schulz, R.; Borowiecki, T. Appl. Catal. 1990, 66, 133. (5) de Jong, A. M.; Niemantsverdriet, J. W. Surf. Sci. 1990, 233, 355. (6) Carter, G.; Bailey, P.; Armour, D. G. Vacuum 1982, 32, 233. (7) Ma, M. C.; Brown, T. C.; Haynes, B. S. Surf. Sci. 1993, 297, 312. (8) Seebauer, E. G. Surf. Sci. 1994, 316, 391. (9) Hunger, B.; Heuchel, M.; Matysik, S.; Beck, K.; Einicke, W. D. Thermochim. Acta 1995, 269/270, 599.
always the same microscopic model of adsorption/desorption kinetics was applied, i.e., the model based on the theory of activated adsorption/desorption.10 In the 1980, a new fundamental theory of the interfacial dynamics appeared. This was the statistical rate theory developed by Ward and co-workers.11 This new theoretical approach was next generalized for the case of energetically heterogeneous surfaces, and the method for determination of the adsorption energy distribution from the TPD spectra was proposed.12 In this work, we propose, however, a refinement version of this method based on a more correct way of generalization of the SRT kinetic equation for the case of energetically heterogeneous surface. Next, we use this method for the study of the energetic properties of a series of nickel catalysts prepared by coprecipitation of three oxides, i.e., NiO, MgO and Al2O3 with different ratios NiO:MgO. 2. Theory a. Fundamental Equation for Adsorption/Desorption Kinetics. The SRT links the rate of transport between phases with the difference in chemical potentials of the molecules in these phases. Originally, the SRT master equation was developed for an isolated system consisting of a constant number of molecules.11,13 It was, however, soon generalized for the case of open adsorption systems,14 including temperature programmed desorption,15 and for adsorption systems where the adsorbing (10) Clark, A. The Theory of Adsorption and Catalysis; Academic Press: New York, 1970. (11) Ward, C. A.; Findlay, R. D.; Rizk, M. J. Chem. Phys. 1982, 76, 5599. (12) Panczyk, T.; Rudzinski, W. J. Non-Equilib. Thermodyn. 2003, 28, 1. (13) Elliott, J. A. W.; Ward, C. A. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces; Rudzinski, W., Steele, W. A., Zgrablich, G., Eds.; Elsevier: Amsterdam, 1997; p 285. (14) Elliott, J. A. W.; Ward, C. A. J. Chem. Phys. 1997, 106, 5667. (15) Elliott, J. A. W.; Ward, C. A. J. Chem. Phys. 1997, 106, 5677.
10.1021/la0500326 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/25/2005
7312
Langmuir, Vol. 21, No. 16, 2005
Panczyk et al.
surface is not energetically uniform.12,16-18 Different ways of generalization of the SRT master equation has recently been reviewed by Panczyk and Rudzinski.19 This study showed that the most consistent way of generalization of the SRT equation is based on the assumption that the adsorption sites create one physical entity. The SRT kinetic equation for energetically heterogeneous surface takes then the following form:
dθt (µg-µs)/kT ) Kgsp(e)S(θ(e) - e(µs-µg)/kT] t )[e dt
(1)
where Kgs is essentially a constant parameter describing the frequency of collisions (per unit pressure) of the adsorbate species with the surface. Its temperature dependence may be neglected when compared to strong exponential dependence of the other factors. The function µs is the chemical potential of adsorbed species expressed as a function of the total coverage θt of energetically heterogeneous surface. The function S(θ(e) t ) describes the probability of finding an ensemble of free adsorption sites on the heterogeneous surface required for adsorption of one molecule. However, its value must be taken for the equilibrium coverage in a hypothetical isolated system (consisting of a constant number of molecules) created by “closing” of the real open system at a given instant of time and allowing it to reach the equilibrium state. Similarly, p(e) is the equilibrium pressure which will be established in the isolated system after reaching equilibrium state. In eq 1, µg is the chemical potential of gas-phase molecules, whereas k and T are Boltzmann’s constant and absolute temperature, respectively. The determination of the values of p(e) and θ(e) t can be done on the following basis.12,18,20 If we assume that the number of molecules in the gas phase is large compared to the number of molecules on the surface, then, after closing the system and equilibrating, the number of molecules in the gas phase will not change much. So, we can assume that p(e) ≈ p, and θ(e) t can be calculated from the equilibrium isotherm equation. We call this case volume dominated. We can also imagine that the number of molecules on the surface is large compared to this number in the gas phase. Then, at equilibrium, in the isolated system, the coverage will not change much, and ≈ θt. The equilibrium pressure in we can write θ(e) t the isolated system can then be calculated using an equilibrium adsorption isotherm. We call this case the solid dominated one. More detailed discussion concerning eq 1 and its constituents can be found elsewhere.11,13-15,20 In the case of thermodesorption experiments, the gas phase is always pumped off, so the number of molecules over the surface is kept low. Therefore, the suitable version of the SRT kinetic equation for TPD experiments is the solid dominated one. b. Chemical Potential of Molecules Adsorbed on the Energetically Heterogeneous Surface. Let us assume that the investigated surface is characterized by the continuous distribution of adsorption energies, χ. Next, let us assume that the local adsorption model is langmuirian since we consider the problem of chemisorption. (16) Rudzinski, W.; Borowiecki, T.; Dominko, A.; Panczyk, T. Langmuir 1999, 15, 6386. (17) Rudzinski, W.; Borowiecki, T.; Panczyk, T.; Dominko, A. Appl. Catal. A 2001, 224, 299. (18) Rudzinski, W.; Panczyk, T. J. Non-Equilib. Thermodyn. 2002, 27, 149. (19) Panczyk, T.; Rudzinski, W. Appl. Surf. Sci. 2005, in press. (20) Panczyk, T. Appl. Surf. Sci. 2004, 222, 307.
The chemical potential of the species adsorbed on the sites characterized by the adsorption energy is described by the following equation:21
µs θ ) ln kT (1 - θ)qinte/kT
(2)
where qint is the partition function of the internal degrees of freedom of the adsorbed molecule, θ is the local surface coverage, and is the adsorption energy. Equation 2 can be rewritten to the following FermiDirac-like form:
θ)
e(-c)/kT
(3)
1 + e(-c)/kT
where
c ) -µs - kT ln qint
(4)
is the adsorption energy at which ∂2θ/∂2 ) 0. Thus, the total coverage of the energetically heterogeneous surface θt can be calculated by averaging the local coverage of the sites characterized by energy with the probability of finding these type of sites on the surface, i.e. (-c)/kT
∫-∞∞ 1 +e e(- )/kTχ() d
θt(c,T) )
c
(5)
By utilizing the condensation approximation (CA),12,18,22 the integral (5) can be simplified. Thus, the kernel of the integral eq 5 is replaced by the unit step function located at ) c CA
θt(c,T) )
∫∞ 1‚χ() d ) H(∞) - H(c) c
(6)
In eq 6 the function H is the integral of χ. Thus, the chemical potential as a function of the total coverage θt can be found by inverting the function H. Let us note that if we differentiate eq 6 after c, we can recover the adsorption energy distribution function, i.e.
dθt dc
χc(c) ) -
(7)
The function χc is identical with χ only at the level of condensation approximation, i.e., for low temperatures or for strongly heterogeneous surfaces.12,18,22 However, when the CA approach is not fully correct the following relationship exists:
χc(c) ) -
dθt )dc
∫
(
)
dθ(,c) χ() d dc
(8)
where dθ/dc is the total derivative calculated from eq 3, i.e.
dθ(,c) ∂θ ∂θ dT ) + dc ∂c ∂T dc
(9)
(21) Hill, T. L. An Introduction to Statistical Thermodynamics; Dover Publications Inc.: New York, 1986. (22) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992.
Energetic Properties of Ni/MgO-Al2O3 Catalysts
Langmuir, Vol. 21, No. 16, 2005 7313
The explicit forms of the above partial derivatives read
e(-c)/kT ∂θ 1 )∂c kT [1 + e(-c)/kT]2
(10)
∂θ c - e(-c)/kT ) ∂T kT2 [1 + e(-c)/kT]2
(11)
whereas dT/dc can be found from relation between c and T for a particular system under investigation. Generally, the second term on the rhs of eq 9 is only a small correction and can often be neglected. It only introduces a small shift on the energy scale between the functions χc calculated from eqs 7 and 8. Let us consider, for illustration, the energetically heterogeneous surface characterized by the following quasi-Gaussian (QG) distribution of adsorption energy:
χ() )
e(-0)/c 1 c [1 + e(-0)/c]2
(12)
where 0 is the mean energy of this distribution, whereas the parameter c is proportional to its standard deviation, σQG ) cπ/x3. So, if we insert eq 12 into eq 6, integrate and solve the resulting equation with respect to c, we can obtain the explicit form of the chemical potential of the adsorbed molecules for the QG adsorption energy distribution. Because c ) -µs - kT ln qint, as defined in eq 4, this chemical potential reads
µs ) c ln
θt - 0 - kT ln qint 1 - θt
(13)
Thus, the coverage of the heterogeneous surface characterized by the QG distribution will be the following function of the chemical potential:
(
)
(
)
0 + µs + kT ln qint 0 - c exp c c ) θt ) 0 + µs + kT ln qint 0 - c 1 + exp 1 + exp c c (14) exp
(
)
(
)
The first part of eq 14 is the solution of eq 13 with respect to θt. The second part can be derived by substituting the term µs + kT ln qint by c, as defined in eq 4. Direct differentiation of eq 14 shows that the energy distribution function, calculated from eq 7, is identical with the original distribution (12). However, both functions are identical only at the level of condensation approximation. If we assume that the adsorbed molecules are in equilibrium with gas-phase molecules, and the chemical potential of these gas-phase molecules can be expressed using the equation for ideal gas, then the adsorption isotherm can be derived from eq 14 by substituting µs by µg, i.e.
θ(e) t )
(Kp(e)e0/kT)kT/c 1 + (Kp(e)e0/kT)kT/c
(15)
where 0
K ) qinteµg /kT
(16)
and µ0g is the standard chemical potential of ideal gas.
c. Prediction of the Thermodesorption Spectra from Energetically Heterogeneous Surface Characterized by the QG Distribution of Adsorption Energy. Let us consider the thermodesorption process from the surface characterized by the QG adsorption energy distribution. This process is described by the general equation (1); however, its explicit forms will depend on some factors as shown below. The probability of finding a suitable for adsorption ensemble of sites for nondissociative localized adsorption on heterogeneous surface may be defined in following way:
S ) 1 - θt
(17)
whereas for dissociative adsorption, when diatomic molecule decomposes into 2 atoms
S ) (1 - θt)2
(18)
So, the explicit forms of the term Kgsp(e)S(θ(e) t ) in eq 1 will depend on the version of the kinetic equation (volume or solid dominated) and whether the adsorption is dissociative or not. They are shown in Table 1. The function Kgs for nondissociative adsorption can be calculated from the expression describing the frequency of collisions per unit pressure of gas molecules with a flat surface, i.e.
Kgs )
SA
(19)
Mx2πmkT
where SA is the geometrical area of adsorbing surface (active surface area), m is the mass of a molecule, and M is the total number of adsorption sites on the surface. However, this equation is correct only for a flat surface and for a Maxwellian distribution of velocities of molecules. For dissociative adsorption, eq 19 is essentially the same; however, the flux of molecules is twice as that for nondissociative adsorption since one adsorbate molecule occupies two adsorption sites. So, the temperature evolution of the coverage for nondissociative localized adsorption on the surface characterized by the QG distribution function is described by the following equation for the volume dominated case:
[
( ) ( ) ]
Kgsp 1 - θt dθt 1 ) Kpe0/kT dT β 1 + (Kpe0/kT)kT/c θt
c/kT
-
1 -0/kT θt e Kp 1 - θt
c/kT
(20)
whereas for solid dominated
[
( ) ]
θt dθt 1 1 ) Kgs(1 - θt) p - 2 e-20/kT dT β 1 - θt Kp
2c/kT
(21)
These equations come from incorporation into eq 1 the expression for µs from eq 13 and the explicit forms of the term Kgsp(e)(1 - θ(e) t ) shown in Table 1. Also, the expression for the chemical potential of ideal gas (µg ) µ0g + kT ln p) is used in these equations. In both eqs 20 and 21 β ) dT/dt, i.e., the heating rate and the parameter K is the so-called Langmuir constant defined in eq 16. This parameter can often be treated as temperature independent since its variation with temperature is not strong. As mentioned the volume dominated version of the kinetic equation is not suitable for the thermo-
7314
Langmuir, Vol. 21, No. 16, 2005
Panczyk et al.
Table 1. Explicit Forms of the Term Kgsp(e)S(θ(e) t ) in Eq 1 and for Surface Characterized by the Quasi-Gaussian Adsorption Energy Distribution nondissociative dissociativea
volume dominated
solid dominated
Kgsp/[1 + (Kpe0/kT)] Kgsp/[1 + (Kpe20/kT)kT/2c]2
[Kgs/Ke0/kT][θt/(1 - θt)]c/kT (1 - θt) [Kgs/Ke20/kT][θt/(1 - θt)]2c/kT (1 - θt)2
*For dissociative adsorption K ) qint2eµg0/kT.
desorption process, so further considerations will be based essentially on the solid dominated version of the SRT kinetic equation. In the case of TPD carried out in an ultrahigh vacuum system, eq 21 directly describes the temperature evolution of the surface coverage for nondissociative adsorption/ nonassociative desorption. The TPD signal is directly proportional to -dθt/dT, whereas p may be considered as constant and equal to the background pressure. Further, in view of extremely low background pressures in UHV systems and very high pumping speed, eq 21 may be further simplified by neglecting the readsorption term, i.e., the first term in square bracket. However, in the experimental studies of catalysts using the TPD, more typical is the setup working in flow conditions. Then the readsorption of desorbed molecules sometimes cannot be neglected and the analysis of pressure changes in the experimental cell is required. So, let us assume that at a given period of time dt, dN molecules were desorbed due to temperature increase. In the same period of time, pF/kT dt molecules were removed from the cell due to pumping, where F is the flow rate of carrier gas and p is the pressure in the experimental chamber. So
MkT dθt F dp )p dT V dT Vβ
(22)
where V is the volume of the chamber and M is the number of adsorbate molecules on the surface corresponding to full saturation, i.e., 1 ML (it is assumed that thermodesorption process starts from fully saturated surface). Thus, the coverage and pressure evolution with temperature can be calculated by solving the set of two coupled differential equations, i.e., eqs 21 and 22. For high flow rates of carrier gas and a small volume of the chamber, i.e., when the removal of desorbed species is very efficient, or at low heating rates, one may assume that dp/dT ≈ 0. Then the set of two differential equations may be reduced to one differential equation by assuming that
p)-
MβkT dθt F dT
(23)
In most experimental situations, the condition dp/dT ) 0 is fulfilled, and dθt/dT may be derived from eqs 21 and 23 giving
( )
x
θt 1 - θt
2c/kT
that such surfaces remain unreconstructed under H2 exposure.23-28 The same model should exists also for nickel crystallites deposited on a support. So, the equation describing the kinetics of hydrogen adsorption should be that for the dissociative adsorption. Application of the SRT approach to the problem of dissociative adsorption implies a distinction of at least two steps during the dissociation and adsorption of a molecule.29,30 The first step is the creation of a transition state (TS), whereas the second step is decomposition of the transition state into fragments and their final adsorption on the surface. Depending on the assumed ratelimiting step the SRT kinetic equation takes different forms. If we assume that the creation of TS is fast compared to its decomposition, then the kinetic process is governed by the rate of transfer from TS to the adsorbed fragments. The chemical potential of TS can then be expressed as the chemical potential of gas-phase molecules since there is an effective equilibrium between molecules in the gas phase and the TS. Because the kinetic process concerns the transfer of atoms the difference in chemical potentials under the exponents in eq 1 will take the form: (1/2)µg µs. On the other hand, when the decomposition of TS is fast and its creation is the rate-limiting step, then the kinetic process concerns the transfer of molecules; thus, the difference in chemical potentials in eq 1 will be the following: µg - 2µs. In both cases µs is the chemical potential of the adsorbed fragments (atoms) on the energetically heterogeneous surface. Our recent analysis of hydrogen adsorption on nickel showed that in this case the rate-limiting step is the decomposition of TS and adsorption of hydrogen atoms on the surface.31 Thus, the solid dominated version of the SRT kinetic equation for the system H2/Ni will be as follows:
dθt Kgs (e) ) p (θt)(1 - θt)2[e(µg/2 - µs)kT - e(µs - µg/2)/kT] dT β (25) where p(e) describes the hypothetical equilibrium pressure in the isolated system created by closing of the real system at some instant of time. This pressure can be calculated from the equilibrium adsorption isotherm, i.e., from the following relation:
1 1 1 µs(θt) ) µg ) µ0g + kT ln p(e) 2 2 2
(26)
(24)
because µs is the chemical potential of atoms adsorbed on the surface, and the expression for the chemical potential of ideal gas was applied.
Thus, solving differential eq 24 one can obtain the temperature evolution of the coverage for the surface characterized by the QG adsorption energy distribution. d. Determination of Adsorption Energy Distribution from Hydrogen Thermodesorption from Nickel Catalysts. There is general agreement that hydrogen adsorbs dissociatively on all low-index Ni surfaces and
(23) Kresse, G.; Hafner, J. Surf. Sci. 2000, 459, 287. (24) Lapujoulade, J.; Neil, K. S. J. Chem. Phys. 1972, 57, 3535. (25) Lapujoulade, J.; Neil, K. S. Surf. Sci. 1973, 35, 288. (26) Christmann, K.; Schober, O.; Ertl, G.; Neumann, M. J. Chem. Phys. 1974, 60, 4528. (27) Winkler, A.; Rendulic, K. D. Surf. Sci. 1982, 118, 19. (28) Christmann, K.; Ertl, G.; Schober, O. Surf. Sci. 1973, 40, 61. (29) Findlay, R. D.; Ward, C. A. J. Chem. Phys. 1982, 76, 5624. (30) Panczyk, T.; Rudzinski, W. J. Phys. Chem. B 2004, 108, 2898. (31) Panczyk, T.; Rudzinski, W. Appl. Surf. Sci. 2004, 233, 141.
dθt )dT
F
Kgs(1 - θt)
xMkTβ2K2e2 /kT(F + MkTKgs(1 - θt)) 0
Energetic Properties of Ni/MgO-Al2O3 Catalysts
Langmuir, Vol. 21, No. 16, 2005 7315
Thus, eq 25 takes more particular form
[
dθt Kgs (2µs-µg0)/kT 0 ) e (1 - θt)2 xpe(µg /2 - µs)/kT dT β 1 (µs - µg0/2)/kT e (27) xp
]
where p comes from the incorporation of the expression for the chemical potential of ideal gas, but p is the real pressure in the experimental chamber. Let us note that if we add (kT ln qint) to µs in the exponents and, at the same time, subtract the same term from the other factors in the exponents we may rewrite eq 27 to the following form:
[
]
dθt Kgs -2c/kT 1 -c/kT ) e e (1 - θt)2 xKpec/kT dT βK xKp
(28)
where c is defined in eq 4, whereas 0
K ) qint2eµg /kT
(29)
Because dθt/dT is directly accessible from the experiment and p can be expressed as the function of the rate of desorption, we can determine the function c by solving eq 28. If the readsorption phenomenon can be neglected eq 28 may be further simplified, i.e.
Kgs(1 - θt)2 -3c/kT dθt )e dT βKxKp
(30)
dθt βKxKp 1 dT c ) - kT ln 3 Kgs(1 - θt)2
(31)
Thus
and the condensation approximation of the distribution of adsorption energy χc can be found by differentiation of the coverage θt (determined from integration of the TPD spectrum) after c, i.e., using eq 7. The real distribution of adsorption energy, χ(), can be determined from eq 5 by inserting to this equation the function θt(c,T) obtained from eq 28 (or eq 31) and solving the integral equation with respect to χ(). If we express the saturation coverage M as a number of atoms per gram of the sample used in the experiment, then
p)-
msMkTβ dθt 2F dT
(32)
where ms is the mass of the sample, F is the flow rate of the carrier gas (m3/s), and θt corresponds to the coverage of atoms. Next
Kgs )
2SA Mx2πmkT
(33)
where SA is the active surface area per gram of the sample. Of course expression (33) is not fully correct since the surface of the sample is always porous to some extent, and thus, it is not flat. The other parameter of eq 28, i.e., K is also unknown a priori. In the case when the readsorption can be neglected (application of eq 31) the most correct procedure would be
Table 2. Gas Phase Properties of Molecular Hydrogen and Assumed Oscillation Frequencies of the Adsorbed Hydrogen Atom on the Surface Tosc, K
Trot, K
σ
νx, s-1
νy, s-1
νz, s-1
6210
85.4
2
5 × 1012
5 × 1012
5 × 1013
to treat the quotient K3/2/Kgs as a one temperature independent parameter. Its determination would be possible by recording the TPD spectra for the same sample at different heating rates. The value of this parameter would be determined when the c(θt,T) functions for different heating rates overlap. However, if the full eq 28 have to be used then one can try to search a pair of values (Kgs and K) for which the functions c(θt,T), for different heating rates, overlap. However, the faster although probably more approximate method is to use eq 33 and to calculate the function K from molecular properties. To do it, we can take advantage of the definition of µ0g for the ideal diatomic gas21
[(
) ]
µ0g 2πmkT ) -ln kT h2
T kT - ln + σTrot
3/2
ln(1 - e-Tosc/T) -
D0 (34) kT
The values of all the components of eq 34 have been determined21 and are collected in Table 2. Let us note that the zero energy level in our considerations corresponds to the energy of hydrogen molecule in the gas phase. Therefore, the dissociation energy at 0 °K D0 has to be dropped from eq 34 since it is important only for the situation when the zero energy level corresponds to the separated atoms at rest. The calculation of qint is also possible since it concerns the partition function of the adsorbed hydrogen atom. In the harmonic oscillator approximation, this function can be expressed as follows:
qint )
∏
ehνi/2kT
hν /kT i){x,y,z}e i
-1
(35)
The frequencies νx and νy correspond to oscillations parallel to the surface, whereas νz is the frequency of oscillations perpendicular to the surface. Although these frequencies are not known exactly, we can take their rational values. It is generally known that νz is of order 1013 s-1, whereas the frequencies νx and νy are usually of order 1012 s-1.21 The uncertainty of the assumed values of these frequencies makes the determined energy scale not very accurate. However, the change of the frequency νz by 1 order of magnitude causes a shift in the energy scale not higher than 10 kJ/mol. 3. Experimental Section Catalysts (70-x)NiO-xMgO-30Al2O3 (x ) 0-50%wt) were prepared by coprecipitation method.32 After drying, the catalysts were calcined at 400 °C for 4 h. The total surface area of the catalysts after calcination and reduction performed at 800 °C for 3 h was determined by argon adsorption at the LN2 temperature in the static-volumeric apparatus. The active surface area of nickel after reduction was determined in the same apparatus by hydrogen chemisorption method at 20 °C under 100 mmHg (32) Borowiecki, T.; Denis, A.; Gac, W.; Ryczkowski, J. The influence of composition on the properties of Ni-MgO-Al2O3 catalysts, C. T. E. C. - Calorimetry and Thermal Effects in Catalysis, July 6-9, 2004, Lyon, France.
7316
Langmuir, Vol. 21, No. 16, 2005
Panczyk et al.
Table 3. Physicochemical Characteristics of the Investigated Catalysts monolayer capacity, M, µmol H/g
surface area, m2/g
mean size of nickel crystallites, nm
catalyst
from TPD
from static chemisorption
total, ST
active, SA
dH
dX
heating rate, β, deg/min
0MgO70NiO 10MgO60NiO 20MgO50NiO 30MgO40NiO 40MgO30NiO 50MgO20NiO
748 667 539 479 390 262
748 828 782 598 452 215
69.1 79.1 88.2 88.8 92.1 95.4
29.3 32.4 30.6 23.4 17.7 8.4
9.7 6.9 6.3 6.4 6.4 5.2
7.7 4.9 4.9 4.8 3.7 5.9
20.8 21.2 21.0 21.4 20.1 21.1
pressure assuming chemisorption stoichiometry H:Ni ) 1:1, and the surface area occupied by a single hydrogen atom 0.065 nm2. The size of nickel crystallites was determined using the relationship
dH ) 5 × 103/(γNiSH) (nm)
(36)
where γNi is the nickel density and SH is the surface area of 1 g of reduced nickel. The size of nickel crystallites (dX) was additionally calculated from the X-ray diffraction line width fitting the Warren-Scherrer equation. The measurements were carried out on a HZG-4 diffractometer using Cu KR radiation and monochromator. The TPD measurements were conducted by using the AMI-1 TPD apparatus (Altamira Instruments Inc.) coupled with the mass spectrometer HAL210RC (HIDEN Analytical). The experimental procedure was as follows: a sample of 0.05 g (particle size 0.3-0.6 mm) was heated to 800 °C in a stream of a mixture containing 6% vol of H2 in argon flowing at a rate of 30 cm3/min. The reduction process lasted for 180 min at 800 °C, and then the sample was cooled to room temperature in the same gas stream. After flushing with He at room temperature, the temperature was increased with 20 °C/min ramp rate. The values of the monolayer capacity M were determined from the integration of the TPD traces and from the static chemisorption. However, for further calculations, the values of monolayer capacity determined from the integration of TPD traces were used.
4. Results and Discussion The properties of the examined catalysts are collected in Table 3. The active surface areas changed from 8.4 to 32.4 m2/g, whereas mean size of nickel crystallites was between 3.7 and 9.7 nm. NiO reduction degree was between 49.3% (for the catalyst 50MgO) and 92.1% (for the catalyst 0MgO). The raw spectra for the series of the nickel catalysts are given in Figure 1. As can be seen, the TPD spectra from these catalysts differ significantly from the qualitative as well as from the quantitative point of view. The decrease of the intensity with increasing amount of MgO is due to parallel decrease of the amount of Ni in the catalyst. The first step in the analysis of the thermodesorption spectra is the determination of the function c(θt,T). This function can be calculated from eq 28 or from the simplified eq 31, where the readsorption can be neglected. Because in the applied experimental setup and conditions the readsorption cannot be excluded, we determined the function c(θt,T) by numerical solution of eq 28. The functions Kgs and K inherent in that equation are slightly varying functions of temperature and are defined in eqs 33 and 29, respectively. Values of the parameters required for the calculation of K are collected in Table 2, whereas values of the active surface areas and monolayer capacities necessary for calculation of Kgs are collected in Table 3. The problem of readsorption in the thermodesorption of hydrogen from supported nickel has recently been reviewed by Kanervo et al.33 They presented a detailed analysis of TPD-H2 from commercial nickel catalyst. Also, they proposed a model for quantitative analysis of
thermodesorption of hydrogen from supported nickel. The main assumption of their model is the existence of quasiequilibrium during the thermodesorption process, and this quasiequilibrium is kept thanks to fast readsorption occurring freely. Our preliminary studies based on application of the simplified eq 31 showed that neglecting the readsorption term in eq 28 produce unrealistically high adsorption energies. Therefore, we applied the full eq 28 and the resulting θt(c,T) functions are shown in Figure 2. Let us note that at quasiequilibrium conditions, i.e., when dθt/dT divided by the term before the square bracket in eq 28 is very small, eq 28 predicts the following relation to exist:
1 c(T) ) - kT ln Kp(T) 2
(37)
where the function p(T) is calculated from eq 32. Thus, a simple test can be made if the investigated thermodesorption process is really quasiequilibrium. In such a case, both eqs 28 and 37 should give very similar results. In the case of our TPD spectra shown in Figure 1, we stated that indeed the functions c(θt,T) calculated from eqs 28 and 37 are practically the same. Thus, in our experiments, the thermodesorption process was carried out at fully quasiequilibrium conditions. It implies that the model proposed by Kanervo et al.33 is valid for the analysis of H2 thermodesorption from supported nickel. However, our model is valid also for experiments where quasiequilibrium cannot be assumed a priori. In Figure 2 also, the condensation distribution functions χc, calculated by direct differentiation of the θt(c,T) functions (i.e., using eq 7), are shown. Although the functions θt vs c are very similar for different catalysts, the corresponding condensation distribution functions are significantly different and their shapes differ also from the shapes of corresponding TPD spectra. One important advantage of the χc functions (besides of ease of their determination) is the clear energy scale which is inaccessible in the analysis of the TPD spectra alone. However, as it was mentioned, the energy scale is not very accurate because the approximate expressions for Kgs and K functions have been applied. Nevertheless, the determined range of adsorption energy seems to be reasonable when compared to the results coming from the analysis of hydrogen adsorption on single low-index nickel surfaces.26 That means that the assumed values of the frequencies shown in Table 2 are reasonable. It should be noted that the energy, c, corresponds to the energy of adsorption of single hydrogen atom; thus, to obtain this energy per hydrogen molecule, the c should be multiplied by 2. The analysis of the χc functions does not provide clear information about the population of the sites characterized (33) Kanervo, J. M.; Reinikainen, K. M.; Krause, A. O. I. Appl. Catal. A 2004, 258, 135.
Energetic Properties of Ni/MgO-Al2O3 Catalysts
Langmuir, Vol. 21, No. 16, 2005 7317
Figure 1. TPD spectra for nickel-MgO catalysts recorded at the heating rate β ) 20 deg/min.
Figure 2. Functions θt vs c (]) determined from the TPD spectra (using eq 28) shown in Figure 1 and the functions χc(c) (b) determined from the differentiation of the functions θt(c), i.e., using eq 7. The parameters’ values assumed during calculations are shown in Tables 2 and 3. The solid lines show the χc(c) and θt(c) calculated from their definitions, i.e., eqs 8 and 5, and the determined real distributions of adsorption energy shown in Figure 3.
by a certain value of energy. This is because the χc function represents only a diffuse picture of the shape of the real distribution, i.e., χ. Therefore, a more suitable for analysis is the function χ which may be determined from the relation between χc and χ, i.e., eq 8. The functions χc shown in Figure 2 (represented by the symbols b) are obtained by numerical differentiation of polynomial fits of the corresponding θt(c) functions. They are not suitable as input functions while solving the integral eq 8 because
polynomial smoothing may produce “dummy” peaks in the resulting function χ. On the other hand, solution of the integral eq 8 requires very smooth input functions since even very small fluctuations in the input function cause very strong changes in the result of calculations. Therefore it is better to use the functions θt(c) (which are fairly smooth) and eq 5 which links the coverage of a heterogeneous surface and the real distribution function of adsorption energies. The solution of the integral eq 5
7318
Langmuir, Vol. 21, No. 16, 2005
Panczyk et al.
Figure 3. Adsorption energy distribution functions χ, obtained from the functions θt(c) shown in Figure 2 by solving the integral eq 5.
has been a matter of many works; hence, a lot of methods were proposed in the literature. It seems that the most stable solutions can be obtained using the regularization methods.9,34 Here we applied a similar method, i.e., the discretization of the integral (5) at nonequidistant nodes with subjecting the solution to a nonnegative constraint. It was stated that introduction of the regularization principle was not necessary during the minimization of the sum of the least squares. The results of these calculations are shown in Figure 3. To show the accuracy of the determined distributions, the θt(c) functions (solid lines) determined from eq 5 and functions χ are compared in Figure 2. Also condensation functions, χc, calculated from eq 8 are compared in Figure 2 (solid lines) with the result of direct differentiation of the functions θt(c), i.e., using eq 7. As can be seen, the agreement between condensation functions calculated in these two ways is very good up to the catalyst 30MgO. For the catalysts 40MgO and 50MgO, this agreement is significantly worse. However, the agreement between θt(c) functions is almost perfect for every catalyst. It is difficult to justify why the discrepancies between the χc functions, depicted as dots and as solid lines in Figure 2, appear for the catalysts 40MgO and 50MgO. It seems that the main reason is some inaccuracy in measuring the pure rate of hydrogen desorption for these two systems. The TPD spectra shown in Figure 1 do not tend to baseline at high temperatures. This suggests that at high temperatures an additional process (production of H2) may occur. This phenomenon is known in the literature35 and was justified by the reoxidation of nickel by water inherent in catalyst support. In the case of alumina supported nickel, it is reported, that the reoxidation starts at temperatures >600 K.33,35 Addition of MgO to the catalyst support may additionally gain this effect. For the catalysts 0-30MgO, the desorption signals are (34) von Szombathely, M.; Bra¨uer, P.; Jaroniec, M. J. Comput. Chem. 1992, 13, 17. (35) Zielinski, J. Polish J. Chem. 1995, 69, 1187.
strong and the contribution from the reoxidation effect is negligibly small. However, the TPD spectra for the catalysts 40MgO and 50MgO are more affected by this effect since the pure desorption signals are quite weak for these samples. That means that the condensation distribution functions calculated from eq 7 are distorted to some extent. On the other hand, the information obtained from the solution of the integral eq 5, that is χ functions, is more reliable since it comes from a combination of possible theoretical desorption signals and comparison of this combination to the experimental information. The lack of perfect agreement between “theoretical” and “experimental” condensation distribution functions (θt(c) as well) observed for the samples 40MgO and 50MgO is thus a positive effect. We expect that application of the integral equation for determination of χ functions extract the most important information from these distorted experimental results. A general conclusion which follows from the analysis of the results presented in Figure 3 is that every catalyst exhibits three main bands of adsorption energy (may be except the catalyst 20MgO which reveals also the existence of small fourth band at 40 kJ/mol). However, the addition of MgO has pronounced effect on the population of these bands of energy. Thus, the presence of MgO in the catalyst’s precursor modifies significantly the morphology of the nickel crystallites created during the reduction process. It is interesting that the resolved distribution functions are composed of quite narrow and sharp peaks. That means that the dispersion of adsorption energy around successive maxims is not high and the active centers on the surfaces are only of three kinds (or four for the catalyst 20MgO). This suggests that the distribution functions presented in Figure 3 can be well approximated using a simple linear combination of Dirac delta functions. Then the determination of the distribution functions (solution of the integral eq 5) would be very easy and fast. We attempted also this simplified method in order to check if the applied
Energetic Properties of Ni/MgO-Al2O3 Catalysts
Langmuir, Vol. 21, No. 16, 2005 7319
Table 4. Adsorption Energy for the Adsorbed Hydrogen Atoms Determined from Spin-Polarized DFT Calculations for 1 and 0.25 ML Coverage23 Ni(111)
hollow (fcc) hollow (hcp) bridge
Ni(100)
1 ML, kJ/mol H
0.25 ML, kJ/mol H
1 ML, kJ/mol H
0.25 ML, kJ/mol H
55 53 34
58 57 44
56
55
38
44
regularization procedure is not too sophisticated in this case. However, despite quite strong correlations between the values of optimized parameters of linear combination of Dirac delta functions, we also stated that the quality of resolving the θt(c,T) functions is significantly worse than this quality shown in Figure 2. Thus, it is necessary to allow for a certain dispersion of adsorption energy to get a good match between θt(c,T) taken directly from eq 28 and this function calculated from eq 5 using the distributions obtained from the applied regularization method. The model proposed by Kanervo et al.33 also assumes the linear combination of Dirac delta functions (although not explicitly stated) to represent the distribution of adsorption energy. They stated that only two Dirac delta functions (two values of adsorption energy on the surface) are sufficient to resolve the TPD spectra for the alumina supported nickel catalyst. The value of high energy state (58 kJ/mol), in the estimation carried out by Kanervo et al.,33 is in perfect agreement with our estimation for the catalyst 0MgO (only this one can be compared since it does not contain MgO in the support). The low-energy state in Kanervo’s estimation (36 kJ/mol) differs significantly from our result, i.e., 48 kJ/mol. However, this is not a serious discrepancy since the catalyst used in Kanervo’s experiments differs from ours by preparation technique (impregnation vs coprecipitation). Thus, both models, i.e., Kanervo’s and ours, give similar results for the similar catalyst (although not the same) and applied experimental conditions. This is a nice result since these models support each other. However, our model gives also the possibility of analyzing thermodesorption spectra determined at nonquasiequilibrium conditions. Moreover, it does not assume a priori what is the number of peaks in the distribution function as well as what is their shape. Comparison of the determined energy scale of the χ functions with the results coming from the experiments with single-crystal Ni surfaces and with the DFT calculations support our results. For all low-index planes of Ni, the heat of adsorption changes from 30 kJ/(mol H) (for high coverages) to 48-49 kJ/(mol H) at moderate and low coverages.26 The flash desorption spectra obtained by Christmann et al.26 show the existence of two states of adsorbed hydrogen atoms on Ni(100) and Ni(111) planes, i.e., β1 (desorbing at lower temperatures) and β2 (desorbing at higher temperatures). They are probably due to adsorption on bridge and hollow sites as follows from the DFT calculations.23 Kresse and Hafner have determined the adsorption energies for the possible states of hydrogen atoms on low index Ni planes.23 They are shown in Table 4. Comparison of the energies obtained by Kresse and our distribution functions rather does not allow for direct identification of the determined bands of adsorption energy. Only very careful conclusion can be stated that the nickel crystallites are composed mainly of low index Ni planes and the adsorption occurs on the hollow sites of these surfaces. On the other hand, the distribution
functions shown in Figure 3 reveal also the existence of small peaks at ∼75 kJ/mol (or ∼85 kJ/mol for the catalyst 50 MgO). Such a high energy cannot be attributed to adsorption on low index Ni planes. It may be due to adsorption on high index planes or on locally distorted parts of low index planes. However, it is more probable that these peaks are dummy results due to the reoxidation process occurring at high temperatures. Similarly, we do not attribute any physical significance to the peak at 40 kJ/mol for the catalyst 20MgO, although its significance cannot be fully excluded. Comparative analysis of the distribution functions shown in Figure 3 suggests that addition of MgO has a very important influence on the population and values of adsorption energy of the active centers on the catalysts surfaces. Addition of even a small amount of MgO (10%) to the catalyst support shifts the first two peaks on the distributions functions toward lower energies. At the same time, the population of lower energy centers (around 45 kJ/mol) decreases when the amount of MgO increases. On the other hand, the population of higher energy sites (around 55 kJ/mol) increases with an increasing amount of MgO in the catalyst support. However, high amounts of MgO, i.e., 50%, create again the band of active centers at 58-59 kJ/mol, observed previously for the catalyst 0MgO. However, the band at 45 kJ/mol is still present for the catalyst 50 MgO. Generally, the addition of MgO favors creation of high energy centers on the nickel crystallites created during the reduction process; simultaneously, the population of lower energy centers decreases. This effect may be due to increasing amounts of solid solutions NiO-MgO in the catalysts precursors when the amount of MgO increases. These solid solutions are difficult to reduce,36 and this resistance to reduction may favor creation of surface defects on Ni crystallites. Also, reduction of solid solutions may produce nickel crystallites exposing different planes than the crystallites coming from reduction of “pure” NiO. Looking at the values of mean size of nickel crystallites (dX), collected in Table 3, one can notice two rapid changes of this quantity when the amount of MgO increases. The first is strong decrease of dX after loading of 10% MgO to the support. For the catalysts 10-40MgO, dX is practically constant, whereas for the catalyst 50MgO, dX increases again. The behavior of dH, i.e., the mean size of Ni crystallites determined from hydrogen chemisortion, is very similar up to the catalyst 40 MgO. A qualitative discrepancy is visible between dX and dH when the amount of MgO changes from 40% to 50%. However, we believe that the values of mean size of Ni crystallites determined from the XRD method are more reliable. The distribution functions shown in Figure 3 also reveal two rapid changes when the amount of MgO changes from 0 to 10% and from 40 to 50%. For the catalysts 10-40MgO, the distribution functions change only quantitatively (when the small peak at 40 kJ/mol for the catalyst 20MgO is neglected). The catalysts 0MgO and 50MgO characterized by large size of nickel crystallites reveal the existence of one dominating peak on the distribution functions. That means that the active centers corresponding to those dominating peaks are probably located on large planes of nickel crystallites and the crystallites expose mainly single crystallographic planes. However, it seems that these planes are not of the same kind for the catalysts 0MgO and 50MgO since the adsorption energies corresponding to the dominating peaks on the energy distributions are different. (36) Hu, Y. H.; Ruckenstein, E. Catal. Rev.-Sci. Eng. 2002, 44, 423.
7320
Langmuir, Vol. 21, No. 16, 2005
The catalysts 10-40MgO reveal the existence of two bands of energy with comparable number of adsorption centers corresponding to these energies. These catalysts are also characterized by small (and comparable) sizes of Ni crystallites. It may suggest that these crystallites expose mainly two different crystallographic planes and the areas of these planes are of comparable size. Our preliminary studies concerning the activity of the investigated catalysts in steam reforming of methane have shown the existence of a fairly linear dependence between activity (per unit of active surface area) and the size of nickel crystallites, dX. The catalyst 0MgO is most active in this series; the catalyst 50MgO is significantly less active than the former. The catalysts 10-40MgO have still lower activity; however, it changes only slightly when the amount of MgO increases from 10% to 40%. Thus, some correlation is visible between the activity of these catalysts and the distributions of adsorption energy. The adsorption centers at ∼48 and ∼58 kJ/mol (observed for the catalyst 0MgO) are probably highly active. Incorporation of MgO to the support up to 40% follows to creation of adsorption centers characterized by lower values of energy, i.e., ∼45 and ∼55 kJ/mol. These centers are less active as follows from the activity measurements. Higher amount of MgO, i.e., 50% recovers again the active centers at ∼58 kJ/mol and hence this catalyst is more active. On the other hand, it is difficult to assess whether the pairs of centers at 45 and 48 kJ/mol or at 55 and 58 kJ/mol are really of different kinds. It is possible that these pairs correspond to the same local configurations of Ni atoms on the surface since smaller values of adsorption energies (by 3 kJ/mol) observed for the catalysts 10-40MgO may be due to some weakening of hydrogen-active center bonds on smaller nickel crystallites. This would mean that the role of MgO,
Panczyk et al.
in the properties of these type of catalysts, is essentially reduced to modification of the size of nickel crystallites. 5. Summary In this work, we presented the method of determination of adsorption energy distribution from the thermodesorption spectra of hydrogen. The method is based on application of the statistical rate theory for description of the rate of desorption from energetically heterogeneous surfaces. This approach allows for determination of the adsorption energy from the thermodesorption experiments carried out at quasiequilibrium conditions as well as at nonequilibrium conditions. The method was applied to study the energetic properties of nickel catalysts with different support composition. It was stated that addition of magnesium oxide to the support of the catalyst has important influence on the population and positions of the recovered adsorption energy bands. Generally, the addition of MgO favors creation of high-energy adsorption centers on the nickel crystallites. Also some correlations between the mean size of Ni crystallites and the adsorption energy distributions were found. Consequently, correlations between the activity of these catalysts in the steam reforming of methane and the distribution functions were recognized. However, it seems that the main role of MgO is only modification of the size of nickel crystallites. Thus, this is the direct factor affecting the energetic (and catalytic) properties of the investigated catalysts. Acknowledgment. This work was supported by the Polish State Committee for Scientific Research Grant No. 4 T09A 015 24 and PBZ/KBN/018/T09/99/5a. LA0500326
