878
J. Phys. Chem. 1980, 8 4 , 678-679
(9) H. G. Hertz and W. Spalthoff, Z. Elsctrocbem.(Ber. Bunsenges Phys. Chem.), 63, 1096 (1959). (10) D. Waysbwt, M. Evenw,andG. Navon, I m g . Chem., 14,514(1975). (11) H. Pfeifer, Ann. Phys., 7 , 1 (1961). (12) K. Wuthrich and R. E. Connick, Inorg. Chem., 7 , 1377 (1968). (13) M. Karplus and G. Frankeal, J . Chem. Phys., 35, 1312 (1961).
(14) (a) H. M. McConnel and D. B. Chesnut, J . Chem. Phys., 28, 107 (1958); (b) H. E. Radford, Phys. Rev., 126, 1035 (1962); (c) G. P. Rabold, K. H. Bar-Eli, and K. Weiss, Chem. Commun.,3, 33 (1965). (15) R. J. Kurland and B. R. McGarvey, J . Magn. Reson., 2, 286 (1970). (16) D.Waysbort and G. Mvon, accepted for publication in Chem. Pbys. (17) U. Kaldor and I. Shavit, J . Chem. Phys., 45, 888 (1966).
COMMUNICATIONS TO THE EDITOR Role of Surface Diffusion in the Mechanism of Surface Reactions Publication costs asslsted by the State Unlversity of New York at Buffalo
Sir: The Langmuir-Hinshelwood mechanism, or more appropriately,' the Langmuir-Hinshelwood-HoughenWatson (LHHW) mechanism has found use in correlating and interpretating rate data for many reactions taking place on solid surfaces. Comprehensive reviews on the utility and interpretation of the mechanism, critical and otherwise, have been made quite For the high temperature reactions between carbon and gases, such as C02, H20, and 02,the LHHW mechanism was used not only to correlate the rate data,4but also to describe the reaction path from studies using radioactive tracer^.^ Many comprehensive reviews on the mechanisms of these reactions are a~ailable.~~' Among these reactions, the mechanism of the G O 2 reaction is relatively less understood in that the surface species are more complex and varied and are more difficult to characterize. Nevertheless, the reaction mechanism also falls in the general LHHW type. A common step involved in the oxidative reactions of carbon is O(ads) + C(s) e CO(ads) F! CO(g) The formation of the adsorbed CO is the rate-limiting step under most conditions encountered in industrial processes.8 However, only few sites on the carbon surface are energetic enough for the formation of such a species. For a graphite surface, these sites normally consist of carbon atoms adjacent to lattice imperfections and edges of the graphite structure. The fraction of the active sites on the surface of a Graphon carbon was determined by oxygen chemisorption to be a few percent? Following the above discussion, two fundamental questions may be raised (1)Does the adsorbed oxide migrate on the surface and finally land on an active site? (2) What is the contribution of the migrated oxide to the overall carbon gasification rate as compared to that caused by direct collision from the gas phase? For the mechanism of the C-O2 reaction under mild conditions, surface diffusion of the oxygen complex has been considered to be of importance in several studies.1°-12 Direct evidence of such a surface process has been obtained by Feates and Robinson by microscopic observation of the movement of etch-decorated rings on the basal plane of a natural graphite.13 Results on the solid-catalyzed oxidation of carbon, which takes place at some distance away from the catalyst, may serve as indirect evidence for the involvement of surface diffusion in the overall reaction.14J5 Difficulties in determining the role of surface diffusion in the overall mechanism lie mainly in the lack of tech-
niques for measuring the rate of surface diffusion of reactive species, the results of which would be necessary in answering the above questions. Several techniques are available for measuring the surface diffusion rate of nonreactive species.16 In this communication, preliminary results will be shown for the feasibility of a relatively simple experimental technique for measuring the rate of surface diffusion of a reactive species, and to provide direct evidence of the importance of surface diffusion in the C-O2 reaction mechanism. It has been well established that the reactivities of the edge carbon atoms on graphite are by several orders of magnitude higher than that of the atoms on the basal plane.17s1s Thus, the overall rate of reaction is predominantly due to the edge carbons, which may be considered as the active sites. Although the basal atoms are not energetic enough to effect a significant reaction rate, they can adsorb a substantial amount of oxygen and oxides. For example, based on their rate data, Darken and Turkdog a d 0 estimated that over 75% of the surface sites on carbon were occupied by a chemisorbed CO at 1100 "C at a CO partial pressure of 0.5 atm (50.6 kPa), with still more chemisorption at higher partial pressures. Consequent to the above discussion, it is reasonable to propose that the basal plane surface may serve as a collecting area for the active sites through a surface diffusion mechanism. This mechanism would cease to be operative under conditions where the replenishment directly from the gas phase to the active sites is much more rapid than that from the surface species. The following experiments were conducted to obtain information concerning the above questions and arguments. Rates of oxidation by O2 were measured of a disk of a "single crystal" carbon and of particles of the same material. The rate was measured gravimetrically by using a Cahn recording microbalance. The detailed experimental procedures have been described elsewhere.12 The rate was expressed as -(l/W)(dW/dt), where W is the weight and t is the time. The carbon sample was a high-purity-grade GTA graphite manufactured and supplied by Union Carbide Corp. The sample had a maximum mosaic spread, which is the degree of misallignment of the c axes, of 5". The two sides of the disk were the basal planes. Because of the 5" mosaic spread, there was a considerable number of imperfections and edge atoms on the basal plane. However, this sample was used to gather qualitative information. The samples were allowed to react at two temperatures with a mixture of oxygen and argon at a flow velocity of about 3 cm/s, which was high enough to eliminate the effect of gas-film resistance on the overall rate. The reaction commenced upon introduction of oxygen in the argon flow. Immediately after a steady rate was reached,
0022-3654/80/2084-0678$01.00100 1980 American Chemical Society
J. Phys. Chem. 1980, 84, 679-680 I
A
0 0
679
chemisorption and surface diffusion. The relative1 magnitudes of the two rate processes are dependent oinly on the nature of the surface for a given reaction system, e.g., C-O2 reaction. Consequently, the threshold partial pressure should depend only on the nature of the surface. To consider the problem quantitatively, one needs to solve the two-dimensional diffusion equation. Arkz0has shown an analytical solution for the steady-state case of surface diffusion/reaction with a linear rate of adsorption. This solution represents a special case for the Elovich-type rate of adsorption where the surface concentration is small. We are now measuring the rates of adsorption and desorption of the oxides on carbon, and solving both the steady and unsteady diffusion equations. Acknowledgment. Part of the work was performed at Brookhaven National Laboratory under the auspices of the Chemical Sciences Division, U.S. Department of Energy. Discussions with Dr. F. B. Growcock of Brookhaven and Drs. S. W. Weller and E. Ruckenstein of SUNY at Buffalo are appreciated.,
References and Notes OL-L..--l
0
1
0.5
1.5
1.0
TIME, M I N
Figure 1. Transient rates for carbon-oxygen reaction. (A) 1 % O2in Ar at 1 atm, the rates at unity are 6.2 X min-' for the 1.27-cm diameter disk (0)and 2.7 X min-' for the particles with sizes 841-1000 p m (A).(6)10% O2 in Ar in 1 atm, the rates at unity are 6.4X lo3 min'-' for the disk (0)and 2.8 X min-' for the particles (A). The dashed line indicates the threshold below which surface diffusion is important in the reaction.
oxygen was ohut off and an equal flow of argon was added to maintain a constant total flow. The most interesting results were the transient rates after the oxygen supply was shut off. The typical results are shown in Figure 1 as the normalized rates which are based on different scales on the ordinate such that the steady rates are shown on the same level. The time for the reactant gas to travel from the mass flow meters (where the oxygen was shut off) to the sample was estimated to be 15 s. From the transient rates, one may estimate the history of the partial pressure of oxygen near the sample by using a known rate expression. Nonetheless, the results showed that,,at 850 "C, the transient rates were identical for the disk and the particles, whereas at 700 " C the rates deviated substantially after a certain time. The deviation signified a region where the larger basal-plane surface contributed to the overall rate. Since it had been shown that the abstraction of carbon atoms from the basal plane was insignificant compared with edge carbon attack, the deviation was attributed to the contribution of surface diffusion to the overall rate. In this region, the basal plane served as a collecting area, and the surface oxygen complex migrated to the edge atoms which were promptly removed with the migrated oxygen. The resultx, showed that the surface diffusion mechanism is significant under relatively mild conditions, i.e., lower temperatures or partial pressures. The threshold partial pressure at 700 " C corresponds to the rate indicated by the dashed line in Figure 1. Below the threshold partial pressure, surface diffusion becomes increasingly important and, at still lower partial pressures, it is predominant in the overall reaction. Under the reaction conditions where surface diffusion is important, two rate processes operate on the basal plane: 0022-3654/80/2084-0679$0 1.OO/O
(1)J. J. Carberry, "Chemical and Catalytic Reaction Engineering", McGraw-Hill, New York, 1976,Chapter 8. (2) M. Boudart, AIChE J . , 18, 465 (1972). (3)S. W. Weller, Adv. Chem. Ser., No. 148, 26 (1975). (4)J. Gadsby, F. J. Long, P. Sleightholm, and K. W. Sykes, Proc. R . SOC.London, Ser. A , 193, 357 (1948). (5) F. Bonner and J. Turkevich, J. Am. Chem. Soc., 73, 561 11951). (6) P. L. Walker, Jr., F. J. Rusinko, and L. G. Austin, Adv. Catal., 11, 133 (1959). (7) S. Ergun and M. Mentser, Chem. Phys. Carbon, 1, 203 (1965). (8) C. Wagner, Adv. Catal., 21, 323 (1970). (9) N. R. Laine, F. J. Vastola, and P. L. Walker, Jr., J . Phys. Chem., 67, 2030 (1963). (10) P. L. Walker, Jr., F. J. Vastola, and P. J. Hart in "Fundamenitals of Gas-Solid Interactions", H. Saltsburg et ai., Ed., Academic Press, New York, 1967,p 307. (11) H. Marsh and A. D. Foord, Carbon, 11, 421 (1973). (12) R. T. Yang and M. Steinberg, J. Phys. Chem., 81, 1117 (1977). (13) F. S. Feates and P. S. Robinson, "Third Conference on Industrial Carbon and Graphite", Society of Chemlcal Industry, London, 1971, p 233. (14) J. T. Galiagher and H. Harker, Carbon, 2, 163 (1964). (15)D. W. McKee and D. Chatterji, Carbon, 16, 53 (1978). (16) R. T. Yang, J. 8. Fenn, and 0. L. Haller, AIChEJ., 20, 735 (1974). (17) G.R. Hennig, Proc. Carbon Conf., 5th, 1, 143 (1962). (18) E. J. Evans, R. J. M. Griffiiths, and J. M. Thomas, Science, 171, 174
(1971). (19) L. S. Darken and E. T. Turkdogan in "Heterogeneous Kinetics at Elevated Temperatures", G. R. Beiton and W. L. Warreli, Ed., Plenum Press, New York, 1970,p 25. (20) R. Aris, J. Catal., 19, 282 (1971). Depafiment of Chemical Englneering State University of New York at Buffalo Amherst, New York 14260
Ralph T. llang' Chor Wong
Received August 13, 1979; Revised Manuscript Received January 16, 1980
Effect of Deviations from the Lorentz Rule for the1 Additivity of Molecular Sizes on the Surface Tensions of Simple Liquid Mixtures Using a Monolayer Model
Sir: In a previous test' of a monolayer model for the surface tensions of simple liquid mixtures Dickinsonl and McLure obtained reasonably good agreement between prediction and experiment when for each mixture the constant 5 = c l z / ( c l l ~ z z ) l ~ z ,expressing the deviation of the energy cross-term parameter from the Berthelot or geometric-mean combining rule, was derived from fitting the experimental excess Gibbs free energy, using a treatment based on a van der Waals one-fluid model, and the constant p = 2 g l z / ( ~ l l+ azz)- 1, expressing the deviation of 0 1980 American Chemical Society
