58
ALBERT C. ZETTLEMOYER AND WILLIAM C. WALKER
REFERENCES (1) ANDERSON, R. B.: J . Am. Chem. SOC.68, 686 (1946). (2) BEEBE,R . A,, BISCOE,J., SMITH,W. R., A N D WENDELL, C. B.: J. Am. Chem. SOC.69,
95 (1947). S.: T h e Adsorption of Gases and Vapors, Vol. I, pp. 158-9. Princeton (3) BRUNAUER, University Press, Princeton (1943). (4) BRUNAUER, S., DEMING, L. S., DEMING, W. E . , A X D TELLER, E.: J. Am. Chem. SOC.60 309 (1938). (5) BRCNAUER, S., EMMETT, P. H., A N D TELLER, E.: J. Am. Chem. SOC.60,309 (1938). (6) CASSIE,A. B. D . : Trans. Faraday SOC.41, 450 (1945). (7) DE BOER,J. H . , A N D CUSTERS, J. F. H.: Z. physik. Chem. B26,225 (1934). P. H.:J. Am. Chem. SOC.68,1784 (1946). (8) EMMETT, (9)JOYNER, L. G., AND EMMETT, P. H.: 110th Meeting of the American Chemical Society, Division of Colloid Chemistry, Paper KO.45 (1946). (10) JOYNER, L. G., WEINBERGER, E . B., AND MONTGOMERY, C. W .: J. Am. Chem. SOC.67, 2182 (1945). (11) LANGMUIR, I.: J. Am. Cheni. SOC.40, 1361 (1918). (12) LENEL,F. V.: Z. physik. Chem. B23,379 (1933). (13) ORR,W. C. J.: Trans. Faraday SOC.36, 1’247 (1939). I. N.:Z.Elektrochem. 36, 25 (1930). (14) STRANSKI, (15) TAYLOR, H.S.: Proc. Roy. SOC.(London) A108,105 (1925);J. Chem. Phys. 1.68 (1933). A. C.,SCHWEITZER, E . D., AND WALKER, W . C.: J. Am. Leather Chem. (16) ZETTLEMOYER, Assoc. 41, 253 (1946). (17) ZETTLEMOYER,A. C., A N D WALKER, w. C.: Ind. Eng. Chem. 39, 69 (1947). A. C,, A N D WALKER, W. C.: J . Phys. Colloid Chem. 62,58 (1948). (18) ZETTLEMOYER,
ACTIVE MAGXESL4. APPLICaTION
OF
IT’
DUAL-SURFACE THEORY
ALBERT C. ZETTLEMOYER
AND
WILLIAM C. WBLKERS
W i l l i a m H . Chandler Laboratory of Chemistry, Lehigh Unicersity, Bethlehem, Pennsylvania Receiced August 26, 1947
In a previous paper (4)the unusual results of the adsorption of nitrogen on commercial active magnesias were presented. For these data the plots of the linear form of the multimolecular adsorption equation of Brunauer, Emmett, and Teller (2) showed a distinct curvature in the usually linear region. This curvature introduced an uncertainty in the position of the proper straight line for area determination by this method. It \vas suspected that the value oi v m obtained from the least-squares line might not be of significance, because the phenomenon that caused the curvature might erase the validity of a urn obtained Presented a t the Tn enty-first Sational Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the hmeriran Chemical Society at Palo Alto, California, June 18-20, 1947. * Post-Doctoral Fellow a t the Lehigh Institute of Research.
.-1PPI,IC'.QTIOW O F DUIL-bURFICE THEORT
59
from this plot. Accordingly the modifications of the B.E.T. theory in the IiterRture n-ere examined in an attempt to explain these data and more definitely establish z',~~. A4concept was required which would account for escessive adsorption at a relative pressure of about 0.35. Of the modifications in the literature only tlvo fiilfill this requirement. Both of these take into account net heats of adsorption beyond the first layer. Brunauer, Emmett, and Teller (2) have presented an equation to handle net heat in the second layer, and Anderson's modification (I) will handle excessive heat in the second and through about the ninth layer. These modifications did not give satisfactory fit to the data. netv approach was devised, however, which showed very satisfactory agreement. This modification is presented in the preceding paper (3), where it has been referred to as the dual-surface theory. Concepts involving pores have not been treated, since they predict less rather than more adsorption at pressures just beyond the usually linear region. In the follon-ing discussions n will be kept infinite for simplicity and only relative pressures below 0.35 will lie considered, so that the presence of pores can be fairly safely ignored. HEAT I 9 SECOSD LATER
Brunauer, Emmett, and Teller ( 2 ) have given the following equation, which does not include the usual assumption that the heat of adsorption in the second layer is equal to the normal heat of liquefaction: 2:
=
cmcx (1 - x ) 1
1 + ( b - 1)(2r - 2 ) + (c - l ) x + ( h - I)cz? _____.
where dl symbols have their usual significance and b = P ( ~ ~ - - & ~ ) ' ~ ' . For convenience in calculation this equation may be expressed in the following manner : l!
=
2'
cx
+ bcG
F = - r2
1--2
and
Cqiintion 2 can be put into two linear forms for testing its applicability to data hut in each case the value for one of the constants must be estimated before the plot in made, and the other tn o are evaluated from the resulting plot. The best estimate for the first constant is taken t o be the one which make,i the plot most nearly linear .
60
ALBERT C. ZETTLEMOTER .kKD WILLIAM C. W-kLKER
In the first linear form,
+
+
the value of b is estimated, and (.r b G ) 2' i i plotted against (x b F ) . When this equation was applied to data for the adqorption of nitrogen on commercial active magnesias, it was found that the plots uere concave to the (x b F ) axis iegardless of the value selected for b. Although the degree of curvature is almost independent of b , the values of vni and c vary greatly, as may be seen in table 1. Since the curvature of thi. plot n-as so insensitive to b, equation 2 n-as put into another linear form,
+
where the value of
6
1.0
1
. I I
i.WL
39.5
1
c
44
1
~
2.0
C
32.8
'C-sing this equation the qhape of the plot varied considerably ivith the choice of un,,but in no case was it linear over an appreciable pressure range. I n spite of the non-applicability of thi.: equation to the data, one of the best isotherms calculated from it was compared with the data for a typical run (run S o . 42, grade 2642) and the deviation is plotted in figure 1 for comparison with the other theories. HI3 I T IS sKCOSD 4 S D S'C'CCEEDISG I..\YER?
Anderson ( I ) has ( l e v i d a modification of the B.E.T. theory in which the heat of adsorption in the secontl and qncceetling layers is assumed to be different from the heat of liquefaction :
This equation is applied by finding by trial and error the value of k for n-hich the plot of .r u ( l - kx) LIS. s is a straight line. In a large number of cases -4nderson has been able to fit the equation t o the data up t o relative pressures of 0 . i to 0.9. In the case of nitrogen adsorption on active magnesia (run S o . 42, grade 2642) k \\-as found to equal 1.20. This value gave a plot that 11-asmost nearly linear over
t h e greatest range, 1)ut thii range \vas very short arid eltended up to a relative pressure of only about 0.35. -It higher prtqsures the points deviate drastically in the direction of too little adsorption. Thiii: the equation i s foiind to apply well at low pressures but iiot at tlie higher pressures for which it mas designed. I BET TPEORY
2 B E T THEOQY r"iITH '$ 3 ANDERSON'S MOZIFiCATICF
20
4 DUAL SJRFACE THEORY
DEV ATION
10
M L/G
00
0.0
0.I RELATIVE
0.2 PRESSURE
03
FIG.1. Deviation of nitrogen adsorption isotherm from isot h e ~ ~ lcalrulated is by various theories.
METHOD
U.E.T.. . . . . . . 13.E.T. (with second layer) Anderson, . . . . . Dual surfarc Graphical. . . .$lyebraira
S P E C I L COIiSTAIiT
h = 1 . 5 to 1.7 f = 1.20
38.6 26-34 34.8'7 45.1 (11.3 i33.S) 46.9
(12.3
+ 33.6)
I ~
I
i
60.3 70-90 09 I.:%~,I:w
I ~
1.21, I N
Khen k is greater than 1.0, the lieat of ad.orption in tlir secoiicl and ~uccreding layers is greater than the heat ot liqueiuction. The L alllei of tile conytants obtained from the linear portion o f t h e plot oi equation 7 for h = 1.20 are given in table 2 , and the agreement of tlie evperimental data with the isotherm calculatd from these values iy ehonn in hgure 1.
DTIL-STRF.ACL THEORY
While seeking for an explanation for the curvature of the R.E.T. plotsfor nitrogen adsorption on commercial active magnesias, the authors examined the effect of surface duality on the linearity of the usual B.E.T. plot (31. It was found that if one portion of the surface has a very low heat of adsorption, the B.E.T. plot is concave to the pressure axis. Since these theoretical plots are very similar to the experimental ones, the dual-surface equation:
11as applied
to these data The only direct method of evaluating the four constants of this equation is by the solution of four simultaneous equations obtained from four points on the isotherm. Since this method is very cumbersome and is based on only four of the measured points, it was very desirable to get an independent value for one of the constants. In contrast to the curvature obtained with the commercial active magnesias from sea mater, the adsorption of nitrogen on C.P. magnesia gave a perfectly linear B.E.T. plot. This observation indicated that the surface duality incommercial active magnesia is probably due to impurities which cover part of the surface. If this notion is correct, then one portion of the dual surface should be magnesium oxide, and the c for this portion should be obtainable by adsorption on the C.P. material. Several runs with C.P. magnesia showed the c to be 130 (f4). With this independent value for one of the c’b, it is possible to use either the solution of three simultaneous equations or a graphical method to evaluate the remaining constants. The use of simultaneous equations is much le3b satisfactory than a graphical solution, since a slight error in one oi the chosen points may introduce considerable error into the resultb. The graphical solution v a s carried out as previously described (3). Yalues for z’,,~~ for the clean part of the surface were estimated. For each estimate the isotherm for adsorption on the clean part of the surface was calculated, using the B.E.T. equation for I I = x . This isotherm was subtracted from the experimental data to give the isotherm for adsorption on the other portion of the surface. Tliis isothcrm ~ v a 5then plotted according to the linear form of the B.E.T. equation. The estimate for z’,>-& which made this plot most linear was considered to 1)ethc correct one, and :~ndr B Tverc obtained from the slope and intercept of this btraiglit line. Plots ior four ehtimates of unCAfor activc magnesia 2642 are s11own in figure 2 . It \\ill he noted that thc shape of the plot changes radically with u small change in z~,,~.~.The figure indicates that a v , , of ~~ 33.8 produces a very satisfactory straight line fyom 0.05 t o 0.35 relative presbure which gives value5 of z’T.B and cB of 11.3and 1.35, rwpectively. ’This combination of n normal and a very 10x1- c should produce the observed curved B.K.T. plot according to the dud-surfacc theory. The total isotherm calculated using thcse constants is in very do>e sgrwment with the experimental (lata. In figure 1the ti,,,&
63
APPLICSTION O F DUAL-SURFACE THEORY
deviation of the experimental data from the calculated isotherm of the dualsurface equation is compared with the deviations from the isotherms calculated from the other concepts discussed above. This graph clearly shows that surface duality affords a much more adequate explanation of nitrogen adsorption on active magnesia than any of the other modifications of the B.E.T. theory. It is of interest to note that this analysis of magnesia 2642 attributes to it a total u, of 45.1 ml. per gram, a value which is considerably in excess of that obtained by any other method. These result>sare compared in table 2. Where IO 9 x V(I-x)
8
.IO’
7 6 5 00
01 02 R E L A T I V E PRESSURE
0.3
FIG.2. Graphical application of dual-surface theory t o run KO.42 on magnesia 2642
TABLE 3 Application o j dual-surface equation to commercial actire inagnesias
SP . . . . . . . . . . . . . . . 2642 . . . . . . . . . . . . . . 2642.. . . . . . . . . . . . 2642’. . . . . . . . . . . ., ,
44 42 49
P
~
1
130; 1 . 0 3 130; 1 . 3 5 130; 2 . 3 8 130; 3.47
~
48.5 33.8 32.8 37.5
+ 17.0 = 65.5 + 11.3 = 4 5 . 1 + 8.7 = 41.5 + 9 . 5 = 47.0
54.9 38.6 34.0 44.0
* Degassed for 20 hr. a t 490°C. instead of 1 hr. at 250°C. dual-surface analysis applies, total vm will always be higher than that obtained from any form of the B.E.T. equation. It should be pointed out that while the dual-surface equation contains four constants, only three were varied to fit the equation to the data. Thus, in this application the dual-surface equation contains only three adjustable constants, as do the other modifications with which it has been compared here. In order to confirm the uniqueness of the evaluation of the dual-surface constants discussed above, four points on the isotherm were selected and used to set up four simultaneous equations which could be solved for the constants. Solution of these equations gave results in very close agreement with the graphical results as indicated in table 2. This calculation also demonstrated that this solution is the only real one.
The above divxb-ion i. centered aboiit run S o . 42 on actire magnesia 2642. The results of the applicatioii of the dual-surface rqu:ition t o several other measurements on different 1)ntchri. of magileiin 2612 a i wrll a- magnesia XP nrr shown in table 3. The data in talde 3 indicate that the total z olitainetl from the dual-surface equation are approsimntrly 20 per cent greater than thow from the B.E.T. cquation. These incrwseq in area place the nitrogen adsorption areas in much better agreement with the areaq obtained from x-ray diffraction measurements ( 5 ) . These data also q h o that ~ the surface usiially contains about 25 per crnt of surface with low heat nf atlqorption. SUAIX'IRE
'1'2ie non-conformity of the datu for nitrogen adsorption on commercial active magnesias to the N.E.T. eqiiation could not be explained by any modification of the B.E.T. theory already in the literature. The dual-surface equation \vnq found to be in very excellent agreement lvith the data, however. :lpplication of this equation to typical data showed 7 5 per cent of the surface to havc :I c of 130, Tr-hile the remainder had a c of 1.35. The total area was found t o lie greater than that found by other methods. Solution of simultaneou.; eqrintioni 4ioir-ed this r w d t to he unique.
