he fundamentally interesting and practically imT portant problems confronting chemists and chemical engineers in the field of heterogeneous catalysis are intimately related to, and dependent upon, the physical and chemical behavior of the solid catalytic surface. The surface and molecules from the surrounding liquid or gas phases, represent an integral part of the reacting system. Problems of the choice of a catalyst for a given reaction, of the stability of catalyst performance and susceptibility to poisons, of catalyst promotion, doping, support, and selectivity can be rationally attacked and successfully pursued whenever the role played by the solid under reaction conditions is understood. Historically, adsorption and catalytic kinetics were initially developed with emphasis on the surrounding gas or liquid phases. The role of the solid was intuitively appreciated, but not taken directly into account for lack of a suitable theory of the solid state and meaningful measurements of solid state properties. The only exception to this situation was x-ray analysis of solid catalysts. This technique has been widely used to characterize the bulk of solid catalysts, but was not too helpful in bringing out the details of surface structure. This fact greatly limited the usefulness of the x-ray technique. With the development of the theories of metals and of the defect solid state of metallic salts in the ’40’s and ’ ~ O ’ S , a rational basis for the study and understanding of the role of the solid in catalysis was established. As a result, it was possible to initiate a quantitative attack, at the atomic level, on the problem of the chemical reactivity of solid surfaces. These investigations are currently in progress, and they benefit from a variety of sophisticated experimental techniques which permit, in many instances, the study of the nature, the concentration, and the lifetime of surface reaction intermediates, and correlation of this information with fundamental properties of the solid catalyst. While old, semiempirical and largely intuitive concepts on the role of the solid are at present put quantitatively to test, and simultaneously new ideas are advanced, it is instructive to summarize briefly the present status and indicate in a general fashion the broad avenues of attack likely to advance the present knowledge of the role of the solid catalyst in heterogeneous reactions and processes. General Considerations
A chemically interacting polyphase system, consisting of at least one solid and one liquid or gas phase, tends toward a state of chemical equilibrium, uniquely defined by the corresponding thermodynamic potentials. The equilibration reaction will produce changes in the composition of each phase, and, possibly, in the structure of the solid phase. If the solid-gas or solid-liquid combination represents a catalytic system, it is clear that the original composition of the solid catalyst will be modified as a result of the equilibration process. This applies to the interior as well as to the surface of the solid. It should be realized that the equilibration reaction takes place
SURFACE MODELS IN HETEROGENEOUS CATALYSIS G. PARRAVANO
Choosing a catalyst for a given reaction and measuring the stability and performance of existing catalysts are still difficult problems for the chemist and chemical engineer. In recent years the intuitive appreciation of the role of catalyst surfaces has given way to more orderly characterizations.
simultaneously with the net catalytic reaction. I t is therefore important to distinguish between two limiting possibilities according to the values of the relative rates of the equilibrium and the catalytic reactions. If the equilibration rate is slow in relation to that of the catalytic reaction, the solid-gas or solid-liquid equilibrium is not established and the chemical potential of the reactive surface is independent of the nature and thermodynamic activity of species from the surrounding phase (nonequilibrium or “frozen” surface). In this instance the catalytic activity of the surface is mainly determined by the preparative manipulations and, in principle, it is not influenced by events occurring during catalysis. In contrast to this, whenever the rate of equilibration is fast in relation to the catalytic reaction, rapid establishment of solid-gas or solid-liquid equilibria is achieved. In this second instance the activity of the surface is modified and determined by the nature and composition of the gas phase (equilibrium surface). These surface models represent limiting cases. However, they provide a convenient basis for the derivation of expressions for the kinetics and thermodynamics of surface reactions and permit a classification of and VOL. 5 8
NO. 9
SEPTEMBER 1966
45
correlations in the reactivity and catalytic activity of surfaces. I n many instances, however, it is evident that the situation will not be as clear cut as the models require and considerable overlapping between the two conditions will occur. For these cases, a more thorough knowledge of surface characteristics is required, the most important being the mechanism bb- which mass transfer at surfaces takes place. I n fact, surface behavior is strongly influenced by the exchange of matter among various parts of the surface. This exchange may take place by means of a distillation process via the gas phase and/or by diffusion through the bulk solid and/or along the surface. At catalytic temperatures the latter transport process is the predominant one and deserves brief consideration. To indicate the extent to which surface diffusion may occur at catalytic temperatures, let us consider three systems for which experimental results are available: Hz on W ( 4 ) ,Hz on Ni ( I O ) , O2 on \.V ( 3 ) . The surface diffusion coefficient, D ,is given by:
D
=
D o exp
Nonequilibrium Surfaces
{-&}
and the distance, x , traversed by a diffusing atom in a sime, t , is:
I n Equation 1, E is the activation energy and D O a constant. With the help of Equations 1 and 2 and the experimental values of D O and E , it is possible to calculate the average time for a surface diffusing atom to travel a distance of, say, 1 ,u at various temperatures. The results of these calculations are shown in Table I. The calculations show that, at catalytic temperatures, the time for transport by surface diffusion over macroscopic distances varies approximately between 0.1 to 10 sec. This time decreases to about 1 x l o F 3 sec. for distances at the atomic level. Since the average residence time of a molecule at 300’ C., and Q g 30 kcal./mole is: T
=
T~
exp{Q/RT)
x
1OI1
the diffusing particle may or may not return to the gas phase before traveling the full distance. Thus, many catalytic processes operate undcr borderline conditions with the possibility that surface migration plays a kinetically important role. T o assess this role, an insight into the fundamental parameters of surface diffusion must be obtained. Unfortunately, the values for surface diffusion coefficients and activation energies for most systems of catalytic interest are not completely known and even order-of-magnitude calculations are difficult. We may conclude that whenever surface diffusion and migration are sluggish or nonexistent, the “frozen” surface model provides a more logical basis for the discussion of the catalb-tic activity while the equilibrium model is more appropriate whenever conditions of fast surface diffusion and rapid mass exchange prevail. We shall now analyze the two approaches in some detail and compare the resulting reaction kinetics and thermodynamics with selected experimental results.
=
sec.
At relatively low temperatures and/or high activation energies for surface diffusion, the solid surface retains, practically unaltered, the original structural and compositional features. This includes mono- and multiatomic defects, crystal planes with different atomic densities, emergence of dislocatioiis and dislocation arrays, grain boundaries, and compositional inhoniogeneities of various kinds. This situation produces local variations in surface characteristics. For example, the binding of adsorbed atoms is mainly determined by the number of nearest neighbors occurring around thc surface positions available for adsorption (surface sites), If this number varies as one moves from site to site or within the same site as adsorption proceeds, the binding energy available at the surface site and the other surface parameters related to it will also be a function of the distance from a surface reference site and of the degree of filling of the site. This behavior is tantamount to rearrangement and disruption of the original surface as adsorption takes place. I t is claimed that this phenomenon of surface reconstruction through chemisorption may be actually
TABLEI. SURFACEDIFFUSIONTIMEOVERADISTANCEOFI ,uFORH,ANDO20NWANDNI
~~
46
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
observed in a number of cases (2). This behavior produces a variety of local configurations at each surface site. T o treat the problem realistically a statistical approach is needed. The use of statistical concepts to describe a solid surface is undoubtedly helpful, but it should be realized that the price to be paid in using statistical concepts is high, since the atomistic details are lost and definite conclusions about elementary steps cannot be reached. T h e statistical description of surface characteristics is obtained by means of a distribution function. Let the surface coverage 0 = VJV,, where V , and V , are the volumes of gas adsorbed at pressure p and at monolayer saturation, respectively, and suppose that by changing the surface coverage from 81 to 02, a surface property P varies from P I to P2. Then, the ratio (01 - 02)/(P1 P2) represents the variation in surface coverage per unit change in surface property. T h e limit
where p ( P ) is the distribution function of P among surface sites. This function is a surface characteristic which may be used to classify and describe the behavior of the surface itself. T h e property, P, may cover thermodynamic (adsorption equilibrium constant, adsorption enthalpy, and entropy) and kinetic variables (reaction rate constant, activation energy). T h e normalizing condition for p ( P ) is:
J1il
d0 =
Jpfina’
Figure 7 . Schematic representation of a surface site with two dimensional circular symmetry. Shaded circle represents surface site
p(P) dP = 1
Pinitial
T o apply these considerations it is necessary to develop explicit forms of the distribution function (Equation 3), based on the nature and configuration of the surface sites. A choice of the geometry of surface sites should be made. Several possibilities exist. One of the simplest representations of a surface site is that of a center with two dimensional circular symmetry (Figure 1). This model permits keeping the mathematical formulation to a minimum without sacrificing the structure of the reasoning. We shall consider only events occurring for rl 5 r _< r2 and ignore those taking place outside the limits r l and r2 of the center. Since the surface property, P , varies with r , it is reasonable to set
where g is a constant. For the model of our surface center, the relation between surface coverage, e, and the radius, r, is easily found. I n fact, if the number of adsorbed atoms is m, the differential change in surface coverage is
d0 = 2 nrmdr
(5 1
Equation 5 defines the distribution function of r, p ( r ) , as
de dr
p(r) = - = 2
nrm
Figure 2. Distribution function of P f o r g = 7 (g
>> 7 (- - -)
), and
AUTHOR G. Parravano is Professor of Chemical and Metal-
lurgical Engineering at the University of Michigan. This review was written while the author was on leave as Visiting Professor at Stanford Uniuersity He expresses his appreciation to Professor M . Boudart of Stanford for his hospitality and stimulating discussions. Fanancial support by the hrational Science Foundation for most of the experimental work referred to is gratefully acknowledged.
.
VOL. 5 8
NO. 9 S E P T E M B E R 1 9 6 6
47
.OC034
-. O K 3 2 Y
.OCEC1 10
30
20
40
50
E ACTIVATION ENERGY (kcaf./mole) Figure 3. Distribution function f o r p ( E ) the activation energy of the adsorption-exchange reaction of benzene vapor upon P t black ( 7 )
20
40
M)
80
100
120
K (Atmr&) Figure 4. Distribution function f o r the adsorption equilibrium constant p ( K ) of 0 2 on RuOz ( 9 )
From Equations 3, 4, and 6 one gets (7) :
where 2 irrl2rn A = gPlllu According to the value of the constant, g, several cases may be distinguished. Two are noteworthy: 1. g = 1 for the whole range of values of P. This condition defines a surface possessing a single valued distribution function independent of P [p(P) = constant, Figure 21. 2. g > 1. For large values ofg, Equation 7 becomes p(P) A / P , and a hyperbolic distribution function results (Figure 2). This function characterizes a truly heterogeneous surface formed by sites with a continuous spectrum of values of p(P). Depending upon 48
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
the extent of adsorption and the degree of coverage during reaction, surfaces with g >> 1 will'exhibit different values of the heat of adsorption, reaction rate constant, activation energy, and so on. For catalytic reactions which may yield various products, product composition becomes dependent upon the extent of surface coverage. This is a well known effect in heterogeneous catalysis. For example, in the hydrogenation and decomposition of CzHz on Ni catalysts, different products are obtained as the adsorption heat of CZHZthat is available during the reaction is modified by operating at different surface coverages. Thus, as the coverage decreases and the adsorption heat increases, the following products are obtained : desorption of CzHz without decomposition, ethylene, ethane, methane, carbon, and hydrogen (8). Similar results are known for the decomposition of isopropylalcohol on acid and base catalysts (8). Many cases of practical catalysis show this behavior. Catalyst selectivity and specificity are the most economically important catalyst properties whose understanding and control rest, to a large extent, upon the knowledge of surface distribution functions. The two cases discussed, g = 1 and g >> 1, do not exhaust all of the possibilities, rather they illustrate two typical surfaces. I t should be noted that for g = 0, Equation 4 shows that the property P is independent upon r , and no distribution function of P can be defined for this case (Langmuir surface). Let us now consider some examples. I n a recent study involving the adsorption and exchange of benzene vapor upon Pt black:
M'here C* is a radioactively tagged carbon atom, it was found that within a restricted range of values of the activation energy of the above reaction, the distribution function of the activation energy had a constant nonzero value ( I ) (Figure 3). Thus, between 10 and 35 kcal./mole, the distribution function of the activation energy was found independent of the value of the activation energy itself, while it dropped to negligible values outside that range. The result indicates that surface sites with an activation energy 35 kcal./mole did not play a significant role for the adsorption and exchange of benzene. Although the analysis does not permit, as observed previously, a unique definition of the nature of the surface centers for the adsorption of benzene, it does provide a meaningful identification and characterization of surface properties which are pertinent to a heterogeneous catalytic reaction. Thus in the example under discussion, it is of interest to inquire whether the influence of sulfur poisoning or chlorine promotion on Pt catalysts is related to modifications of the distribution function of the activation energy such as elimination of the low or the high tail end, respectively. Similarly, correlations between the type and shape of the distribution function and nature of support, degree of dispersion of the metal, extent of sintering may provide
useful insights into the influence of these variables on catalyst activity and allow a degree of control and prediction on the operation of the catalytic system. I n a study of the adsorption of 0 2 and RuOz (9), the equilibrium values of the amount of the RuOz surface covered with 0 2 were determined at different pressures and temperatures, and the adsorption equilibrium function, K = e/(l - f?)po,'/2,was calculated. I t was found that, at constant temperature, K was not constant, but dependent upon 0 or K = f(T',O). This fact suggested that the RuOz surface was composed by sites with values of K varying from site to site. From the experimental results, the distribution function of K , p ( K ) , was calculated at various temperatures; it could be simply expressed as (Figure 4) :
This result, corresponding to g >> 1 in Equation 7, shows that the RuOz surface may be considered to be made up preponderantly of sites with low values of K. Thus the statistical analysis affords a simple method for classifying the reactivity and catalytic activity of solid surfaces. From the analysis, correlations with practically important predictive values may emerge. For a more comprehensive application of the method, several problems must be solved. A more refined statistical analysis is needed, and a more realistic model for surface centers should be employed. The present model is too crude to be of value for the very important case of the derivation of the expression of the rates of adsorption and reaction. Also, effects resulting from the overlapping of growing surface centers, of ingestion of centers by other centers should be taken into consideration, since they become important at high surface coverages where most practical catalysts operate. Lastly, a theoretical derivation of numerical values of g must be attempted. The derivation may be based on known atomic force constants and on the physical and chemical structure of the solid surface. Equilibrium Surfaces
Whenever the rate of gas-surface interactions is fast in relation to the overall catalytic change, the chemical composition of the surface depends upon the composition of the gas phase, and significant variations in the former may take place. Let us, for instance, consider an oxidation reaction catalyzed by a metal oxide. If we provide the oxygen for oxidation in molecular form, it is generally necessary to dissociate the oxygen molecule into atoms, prior to the oxidation of the oxygen acceptor. This function is performed by the catalyst surface through dissociative adsorption of molecular oxygen. As a result of this adsorption, the metal/oxygen ratio of the oxide catalyst is modified. Since this ratio influences the physical and chemical characteristics of the oxide surface, we conclude that the composition of the reaction mixture affects the reactive properties of the solid surface. Particularly interesting is the effect upon the rate of
reaction. Here, gas phase composition has a twofold effect: I t determines the number of gas phase collisions occurring during the kinetically controlling step, and it influences the composition of the catalyst surface and, hence, its concentration of active sites. I t is obvious that for a correct interpretation of the catalytic kinetics of equilibrium surfaces, these two effects must be separately determined. Before discussing how this may be accomplished, it is instructive to review briefly the treatment of gas-solid equilibria of chemically reacting systems. Chemical Equilibrium with Bulk Solid Phases
Heterogeneous solid-gas equilibria are generally formulated in terms of the defect theory of solids. Let us consider some typical cases. For oxide compounds (FeO, NiO, COO) known to contain an amount of oxygen in excess of the 1 : l stoichiometric ratio and to accommodate the oxygen excess via the formation of vacant cation lattice positions, CV, and electron holes, e+, the following equilibrium reactions are typical :
'/z Oz(g) = CO&) = CV-2
+ 2 e+ + FeO + 2 e + + CO + FeO
(8)
(9)
Since ' / z [CV-2] = [ e + ] , the application of the mass action expression gives : l/2
[CV-Z]
= [e+] a
p,:'S
=
? g ) / 3
(10)
Equation 10 shows that variations in po2 will produce modifications in the concentration of cation vacancies (ionic defects) and electron holes (electron defects). For other oxide compounds a different situation may exist. I n magnetite, Fe304, the defect equilibrium reactions are :
+ 6 e+ + Fe304 4 COz(g) = 3 CV-2 + 6 e+ + 4 CO(g) + Fe304 2 Oz(g)
=
3 CV-2
(1 1) (12)
From measurements of the electrical conductivity of magnetite it is known that the former is not influenced by variations in the pressure of surrounding oxygen, or [ e + ] E constant. From Reactions (11) and (12) :
I n this instance the partial pressure of oxygen influences the concentration of ionic defects only. The equilibrium reactions for ZnO may be written as:
+ IC+ + e - = Z n O COz(g) + IC+ + e - = CO(g) + Z n O 1/2
Oz(g)
(13)
(14)
where IC+ is a Zn+ ion occupying a position in the interstitial space among normal lattice sites (interstitial ion). Since in ZnO, [IC] is large and may be considered constant, from Equations 13 and 14 one gets:
VOL. 5 8
NO. 9
SEPTEMBER 1966
49
Thus, in contrast to the case of Fe304, variations in Po2 induce modifications in the concentration of electronic defects only. I n general, the relation between PO, and the concentrations of ionic and electronic defects in metal oxides may be expressed as:
b In [ionic defect]
(15)
and
3 In [electron defect]
(
a InPo2
),
=
J'
Equilibrium with Solid Surfaces
I t is now necessary to expand the considerations of the previous section to cover the surface of a solid, typically a metal salt, and to investigate the conditions under which the extrapolation is valid and whether modifications are needed. Firstly, the conditions of the electrical field at the surface must be analyzed. I n fact, adsorption of gas phase species involves some type of localization of electrons or electron holes to produce surface bonds with a resulting gradient of electrical charges at the surface. If the thickness of this surface charge layer is large in respect to ionic radii, it is then clear that electrical equilibrium between surface and bulk is not readily established. Since the latter involves a rearrangement of electrical charges, ionic migration must be sufficiently fast, or the temperature sufficiently high for this condition to occur. If the thickness of the surface charge layer is of the same order of magnitude of ionic radii, the electrical surface-bulk equilibrium is readily established. I n general, the thickness, 6, of the electrical layer is evaluated by means of a formula originally derived by Debye, namely:
where e , k , n, e are the dielectric constants of the solid, the Boltzman constant, the electron (or electron hole) concentration, and the electron charge, respectively. I n solids with a relatively large concentration of charge carriers, n, (- 2lM), 6 becomes small enough and conditions of surface-bulk electrical equilibrium should prevail. Secondly, we shall assume that the following surface defect equation may be written: I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
e empty defect sites + filled defect sites
(18)
or, at constant temperature, [empty defect sites] x [filled defect sites] = K,, where K , is a constant. Thus, if 0 2 adsorption is considered to occur on surface excess cations, at any instant the product of excess cations (EC) and cation vacancies ( C V ) is constant, or [CV] a [ECI-I. The constant K , is typical for any given solid and may be modified by solid state doping. The situation is entirely similar to that occurring in electrolytes, like H 2 0 ,where the product
(16)
> J ' . From high temwhere J , J' are constants and J 2 perature equilibrium studies, the constants and the corresponding defect reactions are known for a majority of metal oxides and sulfides of interest in catalytic research (6). I n some important cases, however (Ti02 for instance), there is no unanimous agreement on the nature of the defects.
50
Total surface sites available
[ H 3 0 + ][OH-]
=
K,
and K,, the ionic product for water, is constant at constant temperature. We also extend the validity of Equation 18 to the equilibrium between electrons and electron holes so that at constant temperature: [e-] x [e+] = K , = constant. Let us consider now a few concrete possibilities of adsorption of a diatomic gas, X2, on the surface of a salt,
MX2: XZ ( 9 )
+
x
x
M X M X M X-+ M X M X 111 X
(A)
X2(P>
+
M M M X M X M X M X M X + M X iM X iM X
(B)
X&7)
+
Mi T M 0M X - t M X A4 X i M X
(C)
Case A represents the adsorption of Xz on a plane surface of M X , B on a surface with excess (adsorbed) cations of M (EC), and C on a surface with vacancies (0) in the lattice positions of M X generally occupied by X ( A V ) . Models A , B, and C do not complete all the possibilities. Other surface conditions may be envisaged with the participation of complex schemes and associations of ionic defects. Adsorption Thermodynamics and Kinetics
The application of the previous surface models to cover adsorption thermodynamics and kinetics is straightforward. T o this purpose it is necessary to write the expressions for the extent of surface coverage, 0, for cases A , B, and C. Since the adsorption of X for case A is equivalent to the formation of cation vacancies, CV, it is clear that 0 = [CV]. A similar reasoning gives 0 = [CV] a [EC]+for case B and 6 = [EA] CT [AVI-'. Let us now consider an example taken from the recent study on the adsorption of 0 2 on RuO2. At relatively high temperature, where the equilibrium conditions are likely to be fulfilled, the adsorption isotherm was ' ~ n = 4 at 385' C. found to be of the type 0 = ~ p l with and increasing sharply as the temperature decreased ( 9 ) .
If we assume that the preponderant solid state defects in RuO2 are cationic vacancies carrying four electrical charges [CV-4] and that 0 2 adsorption follows scheme A of the previous section, then for every 0 2 molecule adsorbed, one cationic vacancy is created, or 02(g) = CV-4 4 e+ crystal. Since according to scheme A, 0 = [CV--4] = K'j0:/6, which is in satisfactory agreement with the experimental result. If, however, 0 2 adsorption is considered to involve a different stoichiocrystal, metric relation, or 02(g) = 2 (CV--4) 8 e+ the adsorption isotherm becomes 0 = K'lpo:/l0, which is consistent with the experimental results at lower temperature (300' C., n = 9.06). T o derive an equation for the rate of adsorption, let us consider a generalized surface whose reactivity and catalytic activity are dependent upon the following adsorption sites : lattice surface atoms, electrons, surface excess atoms, and ions. Let us consider the individual adsorption reactions between a gas molecule X2 and each one of these surface centers:
+
+
+
ko
'/2
X2 -+ X(ads) l / 2 X2
+ e-
kl --t
+
(lattice surface atoms) X-(ads)
holes is practically independent of the p K 1 ~ / p H a ratio, which controls the concentration of cation vacancies only. This fact makes possible investigations on the role of ionic or atomic defects upon the adsorption of oxygen. I n general, for solid surfaces with a preponderant concentration of one type of defect, d, the rate Equation 19 becomes :
where [ d ] is the defect concentration and r is an integer 1. By means of Equations 15 or 16, the rate number Equation 20 becomes :
>
1 dPx2 - kpx~+rJ 2A d t Equation 21 is the theoretical rate expression for the adsorption of X2 upon the surface defect d acting as the adsorption center. Equation 21 is easily amenable to experimental verification. I n fact, the experimental results of the rate of adsorption may be generally expressed in the form :
(electrons)
+ EA + X(ads) (surface excess atoms) X Z + EA + e - + X(ads) (surface excess ions) ko'
'/z X2
kl'
l/2
The overall rate is given by the sum of the individual rates, namely (5): dpxz = f l x z { k o -I- k i [ e - ] 2 A dt
+ [EAIko' + ki'[e-]] (19)
where A is the catalyst surface area. This rate expression is similar to that for acid-base catalysis in liquid phase reactions, since as pointed out previously, the solid surface is here viewed as a solid electrolyte composed of undissociated neutral and ionic species of various kinds and in various concentrations, depending upon temperature and composition, including impurities and foreign additions to the solid. Equation 19 may be simplified by a careful choice of the solid catalyst. Using a solid with predominantly ionic or electronic defects, the corresponding concentration terms in Equation 19 are eliminated since the concentration of the respective defects may be considered constant during reaction. For example, Ag2S and Cu2S have a large concentration of cationic defects, while the concentration of anionic defects is constant. Thus, by modifying the ratio of @H2Q/@H2 in equilibrium with the solid phase, only the concentration of excess electrons (AgzS) or excess holes (Cu2S) is influenced. This situation provides the opportunity to test the role of excess electrons or holes in the adsorption of sulfur since the terms related to excess ions disappear from the rate Equation 19. A similar situation occurs in some spinel phases (CoCrzO4). O n the other hand, in Fes04 (as already pointed out) and CoFezO4, the concentration of excess electrons and
+
Whenever it is found that n E (1 Jr), Equation 21 is verified and the role of the surface defect, d , in the adsorption of X z is confirmed. From this discussion it is clear that the catalytic kinetics of equilibrium surfaces is dependent upon the type of surface defect acting as a reactive center, and that the fractional exponent of the empirical Equation 22, often found in catalytic rate formulations, may not be viewed as the result of surface effects which modify the ideal mass action relation in its macroscopic application, as it was found for nonequilibrium surfaces. Rather it is a consequence of the physicochemical equilibrium between surface and gas phase. Application to Catalytic Kinetics
To demonstrate the usefulness of the above considerations, let us consider a simple catalytic reaction and let us apply the previous analysis to derive mathematical expressions for the reaction rate. The majority of commercially important reactions involve catalytic activation of simple gas moleculesH2 in reduction, hydrogenation, hydrocracking, Fisher, and alcohol synthesis; 0 2 in oxidation and conversion; N2 in ammonia synthesis. Thus, a research program for the selection, development, and improvement of catalysts for these reactions is centered upon information on catalyst behavior for the activation of Hz, 0 2 , N2, and GO. We shall illustrate the application of the approach discussed to the activation of molecular H2 on a metal oxide catalyst, whose surface defect concentration may be controlled by equilibration with gas H2. A suitable reaction for phase mixtures of H2O this study is the ortho-para HZconversion:
+
o - H4 ~ p-H2 VOL. 5 8
NO. 9 S E P T E M B E R 1 9 6 6
(23) 51
By use of Equations 20 and 21, the rate of reaction for Case (u) may be written as: U, =
k@~,[oH-] = k‘pH,o”’PHz
(29)
and for Case ( b ) :
Me+2 OH- Me+‘ 0-2 Me+* OH- Me+*
-0-2
vo = k ’ ’ p ~ ~ [ e - = ] ~ kt‘3H:/pHz0 rwmn
Figure 5. Defect reaction of a metal oxide surface (Me+20-2) with H20 and HZ containing anionic vacancies (0)
(30)
Equations 29 and 30 show a different dependence between rate andpH20andPH,: vu is directly proportional to the ‘/2 power of p H 2 0 but v, is inhibited by pHso, v, is proportional topH,, and v b topH:. Experimental results upon the rate of Reaction 23 on the catalyst under investigation may be obtained by feeding to the reactor a mixture of HzO vapor and Hz containing a nonequilibriuni amount of the ortho form. By repeating the experiment at various bH20/bH2 ratios, the relation between the latter and the rate of reaction is obtained, and a direct test of the two possibilities may be obtained. Similar considerations may be discussed for the activation of oxygen and nitrogen. In these instances, isotopic tracer studies show great promise. Conclusions
Reaction 23 involves a rearrangement of the electron spins of the Hz molecule from a parallel position (ortho) to antiparallel (para). I n the absence of strong local magnetic fields (paramagnetic ions), the following steps may be envisaged for Reaction 23 :
t H - f H), +- 2( f W a d s .1 H - .1 HI, 2 ( .1 H ) a d s ( t H)ads + 2 ( 4 H)ads 2 (t H - 4 (
-
(
2
+
H)g
A study of the rate of Reaction 23 is essentially an investigation on the adsorption of molecular H2. Let us assume that the oxide catalyst to be tested for Hz activation has preponderantly anionic vacancy and electron excess defects, and that the surface defect reactions with H z O and Hz are as follows (Figure 5) :
HzO(g)
Hz(g)
+ AV(s) + O-’(S) = 2 OH-(s)
+ 2 O-’(s)
=
2 OH-($)
+ 2 e-
(24)
(25)
where A V(s) represents surface anionic vacancies. Application of mass action expression to reaction equilibria 24 and 25 with [0-2] constant gives:
[OH-] = Kz~(PH,o)”~ [OH-] = K~~+!IH;’~ [e-]-1
(26)
[ e - ] = K ’ p H ~ / ~-112 H20
(28)
(27)
Equations 26 and 28 suggest a method to find out which surface defects are responsible for Hz adsorption during Reaction 23. Two possibilities may be tested immediately: namely, surface centers identified as ( u ) OH- and ( b ) electrons. Case ( a ) corresponds to :
P-H2
+ OH-(s)
-
+ OH-(s)
+o-H~
while Case ( b ) corresponds to: p-H2 52
+ 2 e-
2 H-(s)
---r
o-Hz
+ 2 e-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
The analysis of the reactivity of solid surfaces and of the corresponding thermodynamics and kinetics may be approached from two directions. Whenever the equilibrium between surface and gas phase is not rapidly established, the structural and chemical features of the surface do not change and a statistical description of surface parameters and properties by means of a fixed distribution function is a logical approach. However, the resulting kinetic expressions are not too sensitive to the detailed model of the surface center. Additional independent information on surface structure is needed to improve the resolving power of the statistical analysis. The approach is advantageous since it permits a most comprehensive classification and correlation of surface reactivity. O n the other hand, the possibility of rapidly establishing gas-surface equilibrium brings surface reactivity problems into the framework of existing theories of the defect solid state. Both approaches are not novel, but are coming into prominence and usefulness since they may be directly based upon and correlated with ever increasing knowledge of the structure of solid surfaces. The methods promise to expand rapidly into interesting, fundamental tools of kinetic analysis of surface reactivity. REFER ENC ES J. A., Parravano, G., J . Calalysir 2,380 (1963). (2) Germer, L. H., McRae, A . V., Proc. ,$‘all. Acad. Sci. 4 8 , 997 (1962); Madden, H. H., Farnsworth, H. E., Bull. A m . Phys. Sac. 5,349 (1960). (3) Gorner, R., Huhn, J. U., Ibid., p. 1363. (4) Gomer, R., Wortman, R., Lundy, R., J. Chem. Phjs. 26, 1147 (1957). ( 5 ) Grabke, H. J., Ber. Btinrenges. Physik. Chem. 69, 48 (1965). (6) Kroger, F. A., “The Chemistry of Imperfect Crystals,” North Holland, Amsterd a m . 1964. -- - (7) Roginsky S. Z “Adsorption und Katalyse an Inhomvgenen Oberflaschen,” Akademie Gerlai,’Berlin, 1958. (8) Roginsky, S. Z., “Proceedings of the Second International Congress in Catalysis,” Editions Technic, Paris, 1960. (9) Sommcrfeld, J. T., Parravano, G., J. Phys. Chem. 69, 102 (1965). (10) Wortman, R., Gomer, R., Lundy, R., J. Chem. Phys. 27, 1099 (1957). (1) Brundege,
