SOTES
April, 1963
947
averaging of both techniques may cause a slight difference though our polymers were of good uniformity. Discussion Our results on polystyrene in toluene demonstrate that the thermal diffusion coefficient D',nearly independent of M and e, cannot be responsible for the thermofractionation effect on polymers, except perhaps for very low concentrations, So the regular diffusion coefficient 23, the pronounced molecular weight and concentration dependence of which is well known, seems to be the governing factor with this fractionation, proven to be effective, e.g., by Debye-Bueche,2b Langhammerj8and Kossler-Kresj asg (8) G. Langhammer, H. Pfenning, and K. Quitzsch, 2. Elektio ci,em., 62, 458 (1958). (9) 1. Kossler and J. Rresia, J . Polymer Sci., 67,509 (1962).
Fig. 1.-Concentration gradient of the migratirg boundary a t 60, 120, 180 min.: M = 9.5 x 105; c = 2 x 10-2 g./ml. 0,48
I
4 "
I
I
I
I
EFFECT OF AlLKALI Ah-D ALKSLINE EARTH PRONOTERS ON IRON OXIDE CATALYSTS FOR DEHYDROGENATIOh- OF ETHYLBENZENE IN THE PRESENCE OF STEAM BY EMERSON H. LEE AND LAWRENCE H. HOLMES, JR.
0,44
Hydrocarbons Dzvision, Monsanto Chemical Company, Texas Czty, Texas
042
Received October 6, 1969
0,40 0,38
0,36
0
6000
3000
12000
9000
15000
18000
Fig. 2.--Migration of the center of gravity of the boundary due t o a thermal gradient of 40°/cm. of polystyrene in toluene. 2.0 ',
\
'\ '\
D'.1o7
1 \
\ '
X
'.' \xx
1.5
\
\
\
330000 1000000 267000
\
1.0
0.5
0
1
0
3
2
c Fig. 3.-Thermal
4
102g/rnl
diffusion coefficients of polystyrene in toluene
us. concentration; the numbers are the molecular weights of the
samples : - - -, Hoffman and Zimm3; X X X , Herren and Ham6; -- , Nachtigall and Meyerhoff28,6 44,000-2,850,000; this work: 0 , 70,000; C), 950,000. ~
the cell are a few per cent smaller. This little difference can easily be explained by the different thermal difference, which were AT = 1-2"/cm. as compared with AT = 40-70°/cm. here. Also the different
The literature1 describes the use of alkali (group I) and alkaline earth (group 11) promoters on iron oxide catalysts for dehydrogenation of ethylbenzene to styrene, but this literature does not clarify the functions of these additives, except that they are known water gas and structural promoters. We have measured the intrinsic activities of promoted iron oxide catalysts for dehydrogenation of ethylbenzene, using a differential reactor. The group I and group I1 promoters increased the intrinsic activity of iron oxide in a regular trend for each group; an apparent relation between electronic and catalytic properties was observed and investigated. Experimental A. Catalyst Preparation and Activity Measurements.Catalysts were prepared from reagent grade materials. A paste of iron oxide powder and distilled water was mixed with the proper concentration of nitrates of the group I or I1 metals. The paste was oven dried and broken into granules, then calcined a t 800-900" in an electric furnace for two hours. 20 X 30 mesh granules of this material were used for activity measurements. For contact potential measurements, a finely ground paste was packed into each sample hole (described below), smoothed, dried, and calcined a t 800-900°. The specific surface areas of all of these catalysts were about 2 m.Z/g. as determined by nitrogen absorption isotherms and the B.E.T. equation, utilizing a flow system previously described.2 The catalyst activities were measured with a differential reactor, keeping conversions of ethylbenzene to styrene below 10%. The water used for the feed was distilled and de-ionized; the ethylbenzene was of 99.77" purity. Ethylbenzene and a 13/1 mole ratio of steam were metered and fed in the gas phase into a 20 mm. 0.d. horizontal Vycor reactor a t 1 atm.; 20 X 30 mesh (TJ.S. series) catalyst pellets were supported on a stainless steel screen in an open-ended quartz boat. Temperatures were measured by three thermocouples in a 8 mm. Vycor tube just above the catalyst bed. The temperature was 600 rt 2' alcove the 4 X 0.5 in. catalyst bed; temperature control was better than k0.5'. Tests were made for mass (1) K. K.Kearby, from P. H. Emmett, Ed., "Catalysis," Vol. 111, Reinhold Publ. Gorp., New York, N.Y.,1955,p. 453. (2) K. V. Wise and E. H. Lee, A n d . Chem., 34,301 (1962).
NOTES
948 Work firn?tion, c . v. 2 3
I
from total conversions t o give net catalytic conversion t o styrene. Thus the reported data are intiinsic catalyst activities, unmodified by mass transfer effects or gas phase reactions. The styrene concentration in the organic layer of the reactor effluent was determined by gas chromatography. B. Contact Potentials.-Contact potentials were measured by the vibrating condenser method introduced hy Zisman.4 The reactor mas a high temperatnure adaptation of the appartttus used by one of us to measure contact potentials in an evacuated system:, a vertical 2 . 2 5 X 25 in. Vycor reactoi tube was used with a conventional tube furnace for heating. The tube was flanged and sealed on the ends with metal flange plates and Teflon gaskets. The preheater coil in the top of the reactor and the reference surface, sample holder, and thermocouple well in the center of the reactor were of stainless steel. The sample holder was a circular disk supported by a threaded rod through the bottom flange. The disk contained four circular depressions in the top face for catalyst samples. The potential of each sample with respect t o the stainless steel reference was measured under steady state conditions of operation by aligning each eample in turn with the reference. Thus the differences of work function between catalysts were determined under reaction conditions and subsequently in an argon atmosphere. The feed, catalyst materials, andoperating conditions (1 atm., 600") were the same as those used in the differential reactor for activity measurements. Commercial grade argon was used for the inert gas feed,
4
1000
~
100
120 140 160 180 Ionization energy, koal./mole.
Vol. 07
200
Fig. 1.-Ln intrinsic activity of iron oxide catalysts vs. first ionization energy of the promoter atom on lower scale (solid lines) and us. electronic work function of the promoter metal on upper scale (broken lines).
Results and Discussion All promoter concentrations used mere in the range of 5 to 10% metal oxide by weight; the activities of the catalysts were insensitive t o promoter concentration in this range. The intrinsic activity of the iron oxide catalyst increased by a factor of ten and reached a plateau with about 1% KrO. The plateau was reached with a calculated 1-2 monolayers of potassium ions; it was also noted that the cesium-promoted catalyst was the most active. These facts suggested that the dehydrogenation reaction is promoted by bases a t the catalyst surface, and the solid that is the strongest electron donor is the most active catalyst. Figure 1 illustrates two possible correlations of the data, one with the first ionization potential of the promoter atom, the other with the electronic work function of the promoter metal. The latter correlation between ln rate os. work function occurred to us through analogy t o the equation for electron emission from a solid, where
and
In I / A T 2 = -W/kT
ABa ASr
ACa
Here
ANa
I = thermionic current A = constant T = temperature W = electronic work function
ABe
ANone
I
-0.8
(2)
I
I
1
-0.2 Contrtct potential, v.
-0.6
-0.4
I
0
I
+0.2
Fig. 2.-Ln intrinsic catalyst activity us. contact potential of iron oxide catalysts quenched in argon a t 600°, promoted with group I and group I1 metal oxides as indicated. The negative sign corresponds to a work function lower than that of the S.S. reference, and the contact potential differences correspond to effective differences in the work function of the catalysts. transfer limitations as previously described .s T h e styrene made from gas phase reactions in the empty reactor were subtracted
The increased reaction rate caused by the surface alkali ions is analogous to the well known increase in thermionic emission caused by the same. Thus the broken lines in Fig, 1 are a plot of equation 2 if In reaction rate is substituted for ln emission rate ( T is constant). To test this apparent correlation between work function and activity, contact potential differences between a stainless steel reference and various catalysts were measured in order to obtain effective differences of work function among the catalysts, as described in the Ex(3) E. H. Lee, Ind. Eng. Chem., 63,205 (1961). (4) W.A. Zisman, Rev. Sei. Inatr., 3, 367 (1932). ( 5 ) N. Haokerman and E. H. Lee, J. Phys. Chem., 69, 900 (1955).
$pril, 1963
949
SOTES
perimental section. The diff ereiices of work function under steady state conditions of reaction or subsequently in argon did not correlate with catalyst activity as shown by data in Fig. 2 on measurements in argon (contact potential measurements on rubidium and lit,hinm promoted catalyst,swere not madr). The values plotted are averages of t\vo or inorc sa’mplc preparations for each point; deviations from the average were normally no more than a few hundredths of a volt. Contact potentials under reaction conditions were randomly displaced from those shown in Fig. 2. No significance could be given to potential changes caused by different gases, because this changes the work function of both the catalyst and reference in an unknown way. The work function a t GOOo of the argon-quenched samples should be similar to those in vucuo, since no argon is adsorbed a t this temperature. The results with contact potential measurements indicat’ed that the group I or I1 promoters lowered the effective work function of the catalysts as expected. However, the lack of a monotonic trend in this direction indicates that different concentrations of promoter existed a t the surface in various cases. On the other hand, Fig. 1 indicates a correlation between atomic properties (ionization energies) of the promoters and catalyst activity. It is concluded that in this case, only a fraction of the catalyst surface was responsible for its catalytic activity, and thus the electronic work function, in this case integrated, over the whole surface, could not be related to catalytic properties. This illustrates the conclusion of Thompson and Wishlade6 that gross physical measurements on solids may not be related to catalyst propert,ies in some mses because only parts of the surface are catalytically active. On the other hand, Roginskii’ has demonstrated in some cases a direct relation between electronic work funct’ion and catalytic activity of solids. Acknowledgments.-We wish to thank H. C. Tucker for assistance on electronic gear, and Professors Herman Pines, W. H. Urry, and Norman Hackerman for helpful discussions.
When a linear porous body of length I, and containing dead-end pores is discharging matter by diffusion from the outflow end at steady state the initial conditions are
Definition of terms is given in the section labeled “Nomenclature.” If the outflow end is suddenly closed while the inflow end is maintained at constant concentratioii the boundaiy conditions are
bC - ( L ,t ) ax
= 0 and
C(0, t )
=
Cr,
(2)
The concentration at any point and time can be obtained1-3 by solving equations 3 and 4 subject to the conditions given by equations 1 and 2 . N ~ Z -C _ v ,_x 2 -- D -_
at
e2
bx’
vl at
(3)
The solution, by methods described p r e v i o ~ s l y , ~is- ~
where x
pn = (2n - 1) 2L
and 8, are all roots of
(6) S. J. Thompson and J. L. Wishlade, Trans. Faradag Soc., 58, 1170 (1962).
(7) 9. 2. Roginskii, Kinelika i Kataliz. I, 15 (1960) (English translation).
-
SURFACE COXCENTRATION BUILD-UP DURING DIFFUSION IT\’POROUS MEDIA WITH DEAD4EYD PORE VOLUME
That is
BY RICHARD C. GOODKNIGHT California Research Corporation, La Habra. California AND
IRVING FATT
Miller Institute for Basic Research in Science and Department of iMineral Xechnoloog, Univevszty of California, Rerkeleu, California
and
Received October 10, 1961
Recent t r e a t m e n t ~ l - ~ of non-steady state diffusion through porous media which contain dead-end pores did not include the case of surface concentration buildup when a linear system at steady state was sudd.enly closed off a t the exit end.4 This case is presented here. (1) R. C. Goodknight. W. 9. Klikoff, Jr., and I. F a t t , J . Phys. Chem., 64, 1162 (1960). (2) R. C. Goodknight and I. F a t t , ibid., 65, 1709 (1961). (3) 1. F a t t , ibid., 66, 760 (1962). (4) The equivalence of the equations describing non-steady state diffusion to those for flow of a slightly compressible fluid in [t porous medium has been
diaoussed in reference8 1 and 2.
Equation 5 was evaluated by use of a Fortran program on an IBM 704 computer for several laboratory systems of interest. Nomenclature Ao cross-sectional area of neck of dead-end pore C concn. in flow channels (variable) CL concn. a t downstream end Co concn. at upstream end Cz concn. in de&d+md pore
