J. Phys. Chem. 1983, 87, 1520-1524
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Gas Evolution Osclllators. 3. A Computational Model of the Morgan Reaction' Kenneth W. SmHh2 and Richard M. Noyes' Depertment of Chemistry, Universiiy of Oregon, Eugene, Oregon 97403 (Received August 20, 1982; In Final Form: December 6, 7982)
The oscillatory evolution of carbon monoxide from the dehydration of formic acid (Morgan reaction) has been modeled by computations which recognize that radii of bubbles may range by a factor of about lo5 and that in any solution bubbles larger than a critical size will tend to grow while those smaller than this size will tend to shrink. The model computations provide encouraging simulation of the experimental observations. Differential difference equations may provide an alternative approximate method to model such systems in terms of a single parameter. The model predicts that oscillatory gas evolution would be inhibited either in an orbiting satellite or in a centrifuge.
Introduction Morgan3first reported oscillatory release of gas during dehydration of formic acid in concentrated sulfuric acid. The phenomenon was confirmed by Okaya4but was then essentially ignored for over half a century until it was examined again by Showalter and N ~ y e swho , ~ could use a recorder to follow the dramatic evolution of gas in several sharp pulses per minute. Smith, Noyes, and Bowers1 (SNB) developed still better methods to follow the rate of gas evolution and also followed the consumption of formic acid as a smooth monotonic exponential decay. Total reaction can be described quantitatively by the stoichiometry of irreversible process T. HCOOH(so1n) CO(g) + H20(soln) (T) SNB showed that this stoichiometry could be separated cleanly into reversible chemical process C and almost irreversible physical process P. HCOOH(so1n) e CO(so1n) + H20(soln) (C) CO(so1n) CO(g) (P) When [HCOOH] 2 0.3 M, process C can be regarded as irreversible and first order except to the extent that product water may change the Hammett acidity function, H,,and thereby affect the rate.6 When [HCOOH] becomes as low as about 0.05 M, gas evolution may be slow enough that process C can approach "pseudoequilibrium" describable by the kinetics of a reversible first-order reaction. If process P exhibits oscillatory gas evolution, some bubbles are present in the solution at all times, but SNB demonstrated that in a large fraction of the solution volume the value of [CO(soln)]built up to about 80 times the equilibrium saturation value; spontaneous homogeneous nucleation of bubbles then occurred. Process P can be broken down further to steps P1 and P2. Although the rate of process P1 may be a complicated (P1) CO(so1n) CO(nuc1ei) CO(nuc1ei) CO(g) (Pa function of concentration, the rate from left to right will increase monotonicallywith [CO(soln)]. Regardless of the
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(1)Paper No. 53 in the series "Chemical Oscillations and Instabilities". Paper No. 52 is: Smith, K. W.; Noyes, R. M.; Bowers, P. G. J. Phys. Chem., preceding article in this issue. (2)Based on: Smith, Kenneth W. Ph.D. Dissertation, University of Oregon, Eugene, OR, 1981. Present address: Exxon Research and Engineering Co., P.O.Box 51, Linden, NJ 07036. (3) Morgan, J. S. J. Chem. SOC.,Trans. 1916,109, 274-83. (4)Okaya, T.h o c . Phys.-Math. SOC.Jpn. 1919,1, 43-51. (5)Showalter, K.; Noyes, R. M. J. Am. Chem. SOC.1978,100,1042-9. (6)Hammett, L. P. "Physical Organic Chemistry"; McGraw-Hill: New York, 1940; pp 277-8,283-4. 0022-3654/83/2087-1520!§01S O I O
detailed kinetics of process P1, a quantitative application of the "community matrix" methods of Tyson7will show that the sequence (C) + (Pl) + (P2) will not admit sustained oscillations. We have not yet included enough information to account for oscillatory gas evolution. The next possibility is to replace process P2 by steps P2a and P2b. Step P2a accomplishesthe desired objective of CO(nuc1ei) + CO(so1n) s BCO(bubb1es) (P2a)
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(P2b) CO(bubb1es) CO(g) putting a delayed feedback into the path by which process P occurs. The sequence 2(C) + (Pl) + (P2a) + 2(P2b) generates the stoichiometry 2(T). An appropriate choice of kinetic parameters could cause this model to generate an unstable steady state. Although this model could be considered the minimum complexity capable of producing oscillations, it is much too simplistic to deserve serious attention. We must recognize that the objects here separated into *nuclei'' and "bubbles" come in a wide range of sizes, each of which could be in equilibrium with a different value of [CO(soh)]. In the following sections, we shall summarize some well-known characteristics of bubble solubility and of nucleation kinetics and shall then attempt to develop a model that is detailed enough to provide a convincing approximation to reality yet simple enough to be tractable with modern methods of computer simulation. A list of symbols used is provided at the end of the text.
Factors Requiring Consideration Pressure Dependence of Bubble Solubility. A spherical bubble of radius r has volume u and surface area A. Let P, be the presssure in the bubble and let P, be the hydrostatic pressure (mostly determined by the pressure of gas above the solution). Finally, let u be the surface tension or surface free energy. Then the bubble will attain the size such that eq 1 is satisfied. (P, - PJdu = udA (1) Trivial manipulation generates the well-known eq 2. P, = P, + 2 a / r (2) If a solution attains equilibrium saturation with carbon monoxide at pressure P, we believe it will be a reasonable approximation to use Henry's law as eq 3. For the mod[CO(soln)] = KP (3) eling discussed below, we have chosen u = 60.5 dyn cm-' based on Lilerg and K = lo4 mol atm-' based on our ~
(7)Tyson, J. J. J . Chem. Phys. 1975,62, 101C-5.
0 1983 American
Chemical Society
The Journal of fhyslcal Chemistry, Vol. 87, No. 9, 1983
Computational Model of the Morgan Reaction
literature survey and our own experimental measurements.l If gravitational effects can be ignored, a single bubble in the solution would attain a stable equilibrium at a size such that eq 2 and 3 were satisfied simultaneously with P = P,. However, a population of identical bubbles in the same solution would represent an unstable steady state. If a fluctuation made a bubble a little smaller, the increased internal pressure would cause the gas to dissolve while the bubble shrank and ultimately disappeared. If a fluctuation made a bubble a little larger, dissolved gas would enter it and cause it to grow still more. The ultimate equilibrium state would have only a single extended gas phase in contact with the solution. Kinetics of Homogeneous Nucleation. A theory of bubble nucleation in liquids has been developed by Volmer.1° A fluctuation may create a microscopic bubble, but that species will collapse unless it is large enough that the internal pressure calculated by eq 2 is less than [CO( s o h ) ] / ~ Any . nucleus greater than this size will grow and become a macroscopic bubble. Let W be the expansion and surface work necessary to create a spherical cavity of radius r and internal pressure P,. W can be calculated from eq 4. W = aA - (P, - P,)u = -4nr2a - 16ag (4) 3 3(P,- P,)2 The experimental data by SNBl indicate that for the nucleation in this system it is a reasonable approximation to set P, - P, = 80 atm = 8.1 X lo7 dyn cm-2. Then W = 5.7 X erg and the radius of a critical nucleus in such a solution is 2u/(Pr - P,) = 1.49 X lo4 cm = 149 A. The rate of creation of nuclei will be proportional to eeWlkT.Because W/kT N 1.37 X lo4and because W varies approximately as [CO(~oln)]-~, a 0.02% change in the concentration of dissolved gas will change the rate of nucleation by a factor of over 200! In other words, as the concentration of dissolved gas increases, there is a critical concentration at which nucleation begins almost discontinu ou s1y. Kinetics of Bubble Growth. The number of moles of gas, n, in a bubble of radius r is given by eq 5.
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01
- .
-6
-'5
-4
-3
-2
-1
0
+'I
log ( t k,, /cm )
Figure 1. Logarithmic variation with time of a single nucleus in 1 mL of solution. Parameters: C o = 5.0 X mol ~ m - C~, , = 1.0 X lo-' mol ~ m - r~o ,= 3.16 X lo-' cm, f = 1.013 X lo6 dyn cm-2, u = 60.5 dyn cm-', T = 300 K.
5
4
3
-w0
E
\
c
0
s! 2
47rr3
+ 2a/r) (5) 3RT Let C be the concentration of gas in homogeneous solution and let C, be the concentration that would be in equilibrium with pressure P,. If at any time C differs from C, + 2 ~ a / r the , bubble will shrink or grow by transport of gas across the surface. Let K , be the rate constant for such transport in units of mol cm-2 (mol cm3-l s-l = cm s-l. Then if (which is implausible in a real system) there is no concentration gradient in the liquid phase, we obtain eq 6 and 7. n = -(P,
dn/dt = 4ar2K,(C - C, - 2 ~ a / r )
(6)
dr/dt = 3RTrk,,(C - C, - 2~a/r)/(3P,r + 4a) (7) We do not have an experimental measure of the rate constant for transport, K,, but Figure 1 shows a logarithmic plot of the growth of a single nucleus to a large bubble for (8) Units are not necessarily the same in all applications and are suggested here to clarify dimensionality. (9) Liler, M. 'Reaction Mechanisms in Sulfuric Acid";Academic Press: London, 1971; Chapter 1. (10) Volmer, M. 'Kinetik der Phasenbildung"; SteinkopE Leipzing, 1939.
1
0
Flgure 2. Variation with time of number of moles of gas in bubble of Figure 1.
plausible values of the other parameters. At short times when the bubble is very small, it grows slowly. Then follows a period when dr/dt is well approximated by RTK,(C - C.J/P, and the logarithmic plot has unit slope. When C is depleted almost to C,, growth will slow down again. Figure 2 uses the data from Figure 1 to plot n against t. During a significant period, the composition of the solution is almost unaffected by the growing bubble. Then most of the dissolved gas is transported into the bubble during a relatively short time. It is this slow initial growth which generates the delayed feedback that makes the system unstable and oscillatory.
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The Journal of Physical Chemistry, Voi. 87, No. 9, 1983
Smith and Noyes
The above discussion was restricted to a single bubble. Let there be N identical bubbles in solution volume V and let subscript zero refer to values at the initial time. If there is not chemical reaction, eq 8 relates concentration and bubble size at any future time,
C = Co - ( N / V ) ( n- no)
(8)
Development of a Model Description of Assumed Mechanism. The above discussion suggests a qualitative mechanism for the oscillatory release of gas. Five specific stages are involved: (1)Decomposition of formic acid generates a smooth nonoscillatory input of carbon monoxide to the homogeneous solution. (2) That solution becomes progressively more supersaturated but remains metastable until it attains a critical concentration at which spontaneous nucleation begins almost discontinuously. (3) The initial growth of small bubbles has little impact on the solution, and there is a period during which dissolved carbon monoxide is still being formed faster than it is being removed by the growing bubbles. During this period, a large reservoir of bubble nuclei is formed. (4) Once major bubble growth begins, the solution is depleted of dissolved gas more rapidly than it can be produced by chemical reaction. Nucleation is no longer possible, and the smaller existing bubbles redissolve. (5) When the bubble growth has almost stopped, the solution is cleared because existing bubbles rise and escape. The process then repeats itself. Assumptions Inherent in the Model. The system is obviously too complex for all possible features to be included. We have made the following specific assumptions in order to facilitate our computations: (a) Henry’s law (eq 3) is valid. The critical nucleation concentration is only about 0.05 M, and the dissolved gas is not ionic. (b) T h e ideal gas law is applicable in the bubbles. In the smallest nuclei with pressures up to 80 atm, there may be deviations of several percent, but they will become unimportant as the bubbles grow. No gas other than CO will be in a bubble. (c) Pressure in a bubble is uniform. (d) T h e surface relaxes rapidly enough that the equilibrium surface tension is always applicable. (e) T h e surface tension is independent of bubble size. Tolman’l has shown that this assumption is valid for spherical drops of liquid with radii greater than about 10* cm. (f) Rate of bubble growth is controlled by transport across the bubble surface and not by diffusion in the bulk solution. This may be the most questionable assumption. However, the solution is moderately stirred, and bubbles are constantly rising because of density differences in a gravitational field. That rise will prevent generation of gradients in the solution around a bubble. (g) Coalescence of bubbles is ignored. Coalescence would provide another way for small bubbles to become large. We could not model it with confidence and hope we are justified in assuming it is less important for very small bubbles than individual growth is. Once bubbles are large enough to see, coalescence should have rather little effect on subsequent behavior. (h) All bubble sizes escape the solution with equal probability. This assumption is also questionable, for large bubbles will rise faster than small ones. However, stirring (11) Tolman, R. C. J . Chem. Phys. 1949, 17, 333-7.
will bring all bubbles to the surface with almost equal probability. The model is designed so that it could be refined by abandoning this assumption. (i) Population distributions of bubbles sizes can be approximated by a “cell” model. Radii of bubbles and nuclei range from lo* to 0.1 cm, and we could not develop continuous equations that we could use to follow the constantly shifting population distributions. Instead, we chose a ”method of lines” such that all bubbles having radii in a particular range were assumed to behave identically. Basic Equations Generating the Model. Let the entire range of possible bubble sizes be approximated by M cells such that Nl is the number of the smallest bubbles (nuclei) and N M is the number of the largest bubbles considered to be of significance. In any specific solution, all bubbles larger than a certain size will tend to grow and all those smaller than that size w i l l tend to shrink. Then the change in number in cell j will be describable by one and only one of eq 9-11. In those equations, q, is a “bubble growth
m j + / d t = qj-lNj-1 - (qj + k e ~ ) N ~
m J - / d t = qj+1Nj+1- (qJ m j o / d t = -(qJ
kej)Nj
j
(9)
f
j f M (10)
+ keJ)NJ
(11)
coefficient” defined below and k, is a first-order rate constant for escape of a bubble from the solution. Equation 9 is applicable if bubbles in cell j - 1 tend to grow. Equation 10 is applicable if bubbles in cell j + 1tend to shrink. Equation 11 is applicable if bubbles in cell j 1 tend to shrink and bubbles in cell j + 1 tend to grow. Equation 11 must also be used for the special case j = M because the model requires a finite number of cells. Equation 1 2 applies to the special case when bubbles dN,+/dt = V J , - (41 + kel)N1
(12)
in cell 1tend to grow. Here J,,is the rate of formation of nuclei in units cm-3 s-l. Bubble Growth Coefficients. The quantity q, is the reciprocal of the time for a bubble to grow from rl - 6, to r, + 6, or to shrink from rl + 6, to rl - 6,. It is assumed that the 6’s can be chosen small enough that dr,/dt would be almost constant throughout this range if the concentration of dissolved gas did not change. Use of eq 7 then generates eq 13-15. A, = 6, + 6+] (13)
rJ = rl
+ 6+, + 6, +
1-1
‘1
=
1 dr,
1 3RTkt,rJ(C- C, - 2Ka/rJ)
%/GI= 41
(14)
A, 1=2
3P,rJ
+ 4u
1
(15)
Concentration of Dissolved Gas. Use of eq 6 leads to eq 16 for the rate of change of concentration C. dC l M _ - a - - 1Nj4nrj2kt,(Cv j=1 dt In this equation, Q, is the rate of process C and is a function of time given by eq 17, where [HCOOH],is concentration at time zero. @ ( t )= [HCOOH],k,e-kJ
(17)
The rate constant k, was measured as described in ref 1. For our model calculations, @ changed sufficiently slowly that we could treat it as a constant.
Nucleation Rate Term. We used two different methods to introduce the nucleation rate term, J,, in eq 12. The
The Journal of Physical Chemistry, Vol. 87, No. 9, 1983
Computational Model of the Morgan Reaction
r6
61
Figure 3. Model calculations of [CO(soln)] (solid curve) and of dCO(g)ldt (dashed curve). Parameters: @ = 2.5 X lo-' mol ~ m s-', - ~ [C~(soln)], = 4.5 X 1 0 - ~mol ~ m - r~, = , 2.0 x IO-^ cm, r, = 0.10 cm, M = 20, k , = 0.69 s-', k , = 0.1 cm s-', J , = 10000 s-' when [CO(soln)] 1 5.16 X lo-' M and = 0 otherwise. Values of P , , @, and Tare the same as in Figure 1.
method employed in most computations used a step function such that J , = 0 if C < C, + 2~u/r',and J , = constant for all larger values of C. The other method was to approximate the Volmer'O nucleation model and use eq 18. This method treated B J, = B exp[-S,/(C - C J Z ] (18) and S, as adjustable parameters. The two methods gave essentially identical results in the calculations. Discretization of r. As has been indicated, the radius r can range by a factor of lo5, and the most appropriate discretization seemed to be to make log r.+' - log r, a constant. The necessary parameters are defined by eq 19-22. These equations produce a discretization pattern rj = r1(rM/rl)G-1)/(M-') (19) Al = (r1r2)'/'(1 - r1r2)
(20)
Aj = (rj - rj-l)(r2/rL)'/'
(21)
dj = rj
+ 6,
= rj(r2/r1)'/'
(22)
that divides a logarithmic scale into cells of equal width with the r i s in the center of each cell. Results of Computations. The computations assigned the same k, to all kej consistent with assumption h. Then k,, J,, and k, were treated as disposable parameters while 9 and V were fitted to experimental data.l The coupled equations were integrated by the method of Gear12with use of PDP-10 and PDP-1091 computers at the University of Oregon Computing Center. Figure 3 is a typical plot showing behavior of rate of gas evolution and concentration of dissolved gas. The curves are encouragingly similar to the experimental observations as reported elsewhere.' A critical test for such computations is to change the number of cells within which bubble radii are partitioned. A trajectory of dC/dt against C was nearly the same while M changed from 20 to 80, but M = 10 generated a significantly different trajectory. I t appears that valid modeling can be accomplished with an acceptable number of cells. Variations of Parameters. The behavior of the model was dependent on the parameters 9 and k,. If the rate of formic acid dehydration, 9,was too large, oscillations did not occur'. Similarly, if 9 was small enough that the steady-state value of c fell below c, + 2KU/?'1, no oscilla(12) Hindmarah, A. C. "Gear.Ordinary Differential Equation Solver", UCID-30001Rev 3; Lawrence Livermore Laboratory: Livermore, CA, 1974.
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tions were possible. This behavior resembles our observations that for large initial concentrations of formic acid the oscillations occur at neither the beginning nor the end of a run. If the rate constant for escape, k,, was reduced from 0.693 to 0.0693 s-', the period increased by more than a factor of 10 but the amplitude increased only a little. If k , was increased to 6.93 s-', the period decreased by a factor of 10 and the amplitude decreased by a factor of 6. Further increase of k, reduced the oscillations to small ripples which then disappeared. These results may be relevant to our observations of effects of stirring rates. As required by assumption h, we used a single value of the escape parameter k,. We would expect that kej.would increase with increasing value of j . Such a modification should sharpen the pulses still more but is not necessary in order to get respectable consistency with experiment.
Additional Comments Possible Alternative Modeling. The model used here is a very simple application of standard theories about nucleation and growth of bubbles. Although a few parameters were introduced empirically, the consistency with experimental observations is sufficiently encouraging to leave little doubt that the general mechanism of the reaction is understood. However, the method developed here lacks mathematical "elegance". It is difficult to conceptualize the behavior of 20 simultaneous differential equations. It might be worth considering alternative approximate formulations which employ a smaller number of equations. Differential difference equations may permit such a formulation. The argument developed above and all previous treatments of specific chemical oscillators have employed the basic assumption of chemical kinetics that the instantaneous rate of a process is a unique function of the instantaneous state of the system. However, we are considering a system in which nuclei exist for a significant time before they suddenly grow rapidly and escape during a brief interval as shown in Figure 2. An approximate alternative way to describe the change of concentration of dissolved gas could resemble eq 23. (dC/dt)(t) = @ ( t -) LFJ,(t - 7) (23) In this equation, L is the number of moles of gas per bubble that escapes the solution, F is the fraction of nuclei that ultimately grow and escape, and 7 is the time between formation of a nucleus and escape of a bubble. An approximation like eq 23 could not be expected to simulate the system as well as the full model presented above, but it might be a useful approach for describing complex behavior in terms of a single variable like C. Nucleation of Condensed Phases. The above discussion has been concerned with nucleation of gas bubbles which then rise through the solution and escape. Liquid and solid phases can also nucleate from homogeneous solution either with or without the assistance of seed particles. Undoubtedly the best known example of periodicity in a heterogeneous system is the LiesegangI3 phenomenon, which involves a complex coupling of diffusion, nucleation, and growth of crystallites. Similarly periodicities are observed in a number of geologic formation^.'^ Sudden nucleation from homogeneous aqueous solution has been observed with sulfur sols,l5manganous sulfide,16 (13) Liesegang, R. E. Naturwiss. Wochenschr. 1896, 11, 353. (14) See, for example: McBirney, A. R.; Noyes, R. M. J . Petrol. 1979, 20,487-554. (15) LaMer, V. K.; Dinegar, R. H. J. A m . Chem. SOC.1950, 72, 4847-54.
J. Phys. Chem. lQ83, 87, 1524-1529
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and barium sulfate." Although these "one-shot" nucleations resemble a single pulse of the Morgan reaction, temporal oscillations do not occur because the small particles of condensed phase do not clear from the solution as rapidly as bubbles do. Implications for Gravitational Effects. If the phenomenon under consideration is indeed strongly influenced by the big difference in density between gas and liquid, it is amusing to speculate about a Morgan reaction system in an orbiting satellite. The analysis as developed here suggests that there should be no more than one pulse of pressure increase. Oscillations should also be inhibited in a centrifuge just as they are by vigorous stirring. On the other hand, a chemical system that generated a liquid or solid phase by initially homogeneous reaction might exhibit repetitive pulsed nucleations if it were centrifuged sufficiently strongly. Acknowledgment. This research was supported in part by a Grant from the National Science Foundation to the University of Oregon.
Symbols Useds A
c
surface area of a bubble, cm2 [ CO(soln)] = concentration of homogeneously (16) Causey, R. L.; Mazo, R. M.Anal. Chem. 1961,34, 163C-3. (17) Nielsen, A. E. Acta Chem. Scand. 1961, 15, 441-2.
KP,= equilibrium concentration at P, largest radius of bubble considered to be in cell j subscript from 1 to M defining the designation of a cell rate of nucleation, cm-3 s-' Boltzmann constant, erg K-' rate constant for consumption of formic acid, s-l rate constant for bubble escape to gas, s-' rate constant for transport between bubble and solution, cm s-' number of cells number of moles of gas in a bubble number of bubbles in cell j pressure inside a bubble of radius r , dyn cm-2 or atm hydrostatic pressure on solution bubble growth coefficient for cell j , s-' radius of bubble, cm gas constant, erg mol-' K-* time, s temperature, K volume of bubble, cm3 volume of solution, cm3 work necessary to create a bubble, erg 6+, + 6-, = width of cell j , cm Henry's law constant, mol cm-3 atm-' surface tension, dyn cm-' k,[HCOOH](soln)] = rate of consumption of formic acid, mol s-l Registry No. Formic acid, 64-18-6carbon monoxide,630-08-0.
Enhanced Catalytic Activity of Cobalt Tetraphenylporphyrin on Titanium Dioxide by Evacuatlon at Elevated Temperatures for Intensifying the Complex-Support Interaction Isao Mochlda, Katsuya Suetsugu, Hlroshl Fujltsu, and Kenjlro Takeshlta Research Institute of Industrial Science, Kyushu Unlversw 86, Kasuga 816, Japan (Receivd: June 14, 1982; I n Final Form: November 12, 1982)
Remarkable catalytic activity of cobalt tetraphenylporphyrin (CoTPP) supported on TiOz was found to be developed by the evacuation of the catalyst at 200 "C for the reduction and decomposition reactions of nitric oxide which were observed with a circulating reactor. The reduction reaction was detectable to as low as 50 "C, and the conversion of nitric oxide into nitrogen was completed at 100 "C within 4 and 1 h with hydrogen and carbon monoxide, respectively. The decomposition of nitric oxide into nitrous oxide without any reductant was also observable at 100 "C. Such an activity increase of roughly 20 times due to the evacuation was related to the increased capacity for the adsorption of hydrogen and the further activation of carbon monoxide and nitric oxide. These enhancements can be ascribed to the pronounced electron transfer from the support to the complex (to produce active Co2-' and anion radical which can be active sites for carbon monoxide and nitric oxide, and hydrogen, respectively) strengthened by the partial dehydration of the support which may produce on its surface the coordinatively unsaturated titanium ion surrounded by an appropriate number of TiOH groups. A spillover mechanism is proposed in the decomposition of nitric oxide where oxygen produced probably on the central metal ion of the complex can be transferred to the support. Introduction The roles of supports in the efficient performance of heterogeneous catalyses are multifold. The support disperses and stabilizes the catalytic species over its surface to provide a large effective surface area during the catalytic reaction. In addition to these rather physical consequences, a strong chemical or electronic interaction between the support and the catalytic species can modify the As intrinsic catalytic activity or selectivity of the (1) Boundart, M. Adu. Catal. 1969, 20, 153.
far as the metal oxide support is concerned, the modification of the catalytic species through contact with the support should be governed according to the boundarylayer4 and electronic6theories of semiconductors. Stong metal-support interactions have been reported in the methanation, adsorption of carbon monoxide and hydrogen (2) Cinneide, A. D. 0.; Clarke, J. K. A. Catal. Reu. 1972, 7, 213. (3) van Hardeveld, R.; Hartog, F. Adu. Catal. 1972, 22, 75. (4) Solymosi, F. CataE. Rev. 1967, I , 233. (5) Slinkin, A. A.; Fedorovskaya, E. A. Russ. Chem. Reu. (Engl. Transl.) 1971, 40, 860.
0022-3654/83/2087-1524$01.50/00 1983 American Chemical Society
