THE JOURNAL OF
PHYSICAL CHE (0Copyright,
(Registered in U. S. P a t e n t Office)
VOLUME64
ISTRY
19CO. by t h e American Chemical Society)
SEPTESIBER 23, 1960
SUMBER 9
THE FAILURE OF DISPERSION ENERGY CALCULATIOKS TO REPRODUCE HEATS OF ADSORPTIOS O S GRAPHITIC CARBOK BY D o s . 4 ~GRAHAM ~ Orgnnic Chemicals Department, Research Contribution No. 191,Jackson Laboratory, E. I . du Pont de iYemows and Company Inc., Wilmington, Delaware Received March 7, 1960
Isosteric heats of adsorption of nit,rogen on diamond, amorphous carbon, and thermally graphitized P-33 differ but little a t the coverage approaching completion of the first monolayer. The effect of the much greater density of diamond is thus balanced by :i correspondingly greater contribution (per atom) from the electrons of the graphitic carbons. Calculated dispersion energies fail to reproduce this result, indicating the possible importance of other forms of electronic interaction.
Introduction Heats of physical adsorption are calculated with some success as sums of dispersion energies of interaction between the units involved. The formal treatment of dispersion interaction between an adsorbed molecule and the adsorbent involves three factors. (1) The dispersion constant, a measure of the energy of interaction between an adsorbent atom and an adswhed molecule a t the equilibrium distance or the depth of the potential well. The currently favclred approximation for the dispersion constant is that of Kirkwood and Riuller,l in which c =
(-*)
Gmc2 -
x1 +
xz
m represen1,s the mass of the electron, c the speed of light and the a’s and X ’ S , respectively, the polariz-
abilities and diamagnetic susceptibilities of the interacting units. ( 2 ) A force law relating energy of interaction with distance of separation between any two interacting units. For dispersion energies, the LennardJones (6-12) potential is commonly employed, assuming a decay of attraction with the Gth power of the separation distance and decay of repulsion with the 12th power of the separation distance. (3) h summation of the interactions of the adsorbed molecule with all of the atoms of the solid. To a first aDproximation, this is proportional to the number of atoms per unit volume of the solid or to (1) A. Muller, P r o c . Roy. Sac. (London), A164, 624 (1936).
its density. (This summation does not include the lateral interaction between adsorbed molecules.) This treatment, particularly the approximation for the dispersion constant assumes an isotropic non-polar, non-conducting solid adsorbent and spherical adsorbate molecules having no permanent dipole moment. illthough graphite is an anisotropic semiconductor, such a treatment of the adsorption of argon on Graphon (a graphitized carbon black) gave results in good agreement with experiment.2 Fair success also was reported in the application of this theory to the adsorption of krypton on graphitized carbon black and, surprisingly, also on copper and iron.3 Investigators have realized for some time, homever, that although treatment of graphitized carbon as a non-conducting adsorbent may give reasonable calculated heat values, a correct approach must include recognition of its electronic properties. ;in early consideration of this question, in relation to the heats of adsorption of nitrogen and argon on graphite, gave somewhat low values when covalent bonding (diamond structure) was assumed and quite high values when the model was an isotropic met a1.* The results of a more recent study have indicated that heats of adsorption on carbon can be explained in large part as an interaction between an electric field outside the carbon surface (caused by protrud(2) E. L. Pace, J . Chem. Phys., 27, No. 6, 1311 (1957). (3) R. A. Pierotti and G. D. Ifalsey, Jr., THISJ O ~ H N A L 63, . 6SO (1959). (4) R. AI. Barrer, Proc. Roy. Sac. (London), 161A, 476 (1937).
1089
DONALD GRAHAM
1090 P 14T 776'Kl
0
'
--.LL-L-l
01
'
" '
I IO 100 PRESSURE IN MILLIMETERS Hg ( A T 9 0 4 ' K l
Fig. 1.-Adsorption
~
I60
of nitrogen on diamond a t 90.4 and 77.6"K.
T'ol. 64
chloric acid and distilled water. It then was dried, heated under vacuum a t 150' and purged repeatedly with nitrogen. The amorphous carbon was prepared by the reaction of hexachlorobenzene with sodium amalgam.8 The product, after extraction, steaming, and finally sweeping with nitrogen a t a temperature above 500", contained less than 0.57, chlorine. It showed no graphite lines in the X-ray powder pattern but was jet black in color, indicating a high degree of conjugation and, to this extent, may be considered graphitic. The sample of P-33 carbon black (heat treated a t 2700") was obtained from Rlr. W. D . Schaeffer, then of the Research and Development Department of Godfrey L . Cabot, Inc . The nitrogen was obtained from the Linde Air Products Co. as 99.9970 high-purity dry nitrogen. The oxy en used in the gas thermometer (for measurements a t 90.4$.) was Linde's spectroscopic grade. The equipment and methods used in obtaining the adsorption isotherms have been described in an earlier paper.7 Liquid nitrogen and liquid oxygen baths were employed to maintain adsorbent temperatures of 77.6 i.0.1"K. and 90.4 5 0.1 OK., respectively. Isosteric heats were calculated by conventional application of the Clausius-Clapeyron equation to the isotherms.
Results The adsorption isotherms are plotted in Figs. I , 2 and 3 with logarithmic pressure scales t o show the low coverage values more clearly. The isosteric heats of adsorption as functions of coverage are shown in Fig. 4. The adsorption data from the diamond sample failed to give a satisfactory BET plot but the coverage representing the first monolayer was quite clearly defined by the characteristic sharp drop in the heat curve. h second diamond sample of larger particle size was studied with similar results. A very high degree of heterogeneity may be re40 A v e r o g e V, 196 m i l 9 sponsible for this behavior. e 01 The adsorption data from the amorphous carbon 10 IO IO 100 PRESSURE IN MILLIMETERS H Q ( A T 9 0 4 ' K I sample, like that from diamond, showed a very high Fig. 2.--Adsorption of nitrogen on amorphous carbon a t 90.4 degree of heterogeneity and gave curved BET lines. and 77.6"K. Xgain it was necessary to determine the content of iiig coilduction electrons) with a dipole induced by the first monolayer from the heat curve. This point is less well defined than in the case of diamond, that field in an adsorbate mo1ecule.j Disregard of the structural anisotropy of gra- possibly due to condensation ill small capillaries. The P-33 data are an extension of those prephit,ic carbon adsorbents finds some support in the repeatedly observed high degree of energetic surface T4ously r e p ~ r t e d . ~ Discussion iiniforniity of certain graphitized carbon blacks.".' However any success in ascribing heats of adsorpAIeasuremeiit of the effects of differences in crystion on graphitic carbon to dispersion energies tal structure upon the net energy nith which caralone may have involved the possible wide latitude bon holds an adsorbed nitrogen molecule requires in selection of values for the variables which make comparison of the isosteric heats a t a coverage up the dispersion constant or the parameters of the favorable to separation of that part of the heat of force law. It is therefore useful to compare meas- adsorption due t o lateral adsorbate interaction. ured heats of adsorption of a non-polar gas on car- The extensive heterogeneity of the diamond and bon adsorbents of different crystal structure with amorphous carbon samples precludes comparison t,hose predict,ed from dispersion energy calculat'ions at low coverage because the minority strong site.. using the most self-consistent values available. are occupied first. The coverage selected is thereThis has been done using, as adsorbents, diamond, fore that just preceding the sharp drop in heat due an aniorphous carbon, and a thermally graphitized t o approaching completioii of the first monola~*er c:arbon black (P-33). niid onset of appreciable second layer deposition (6 0.85). Since the isosteric heat is a differenExperimental tial quantity and since the minorit)+ strolig sites Materials. -Diamond dust was obtained from Kay and Warren Co. (33 Box Street, Brooklyn 22, N. Y.) as gem have been occupied below this coverage, there is grade, S o . 1 size (largest diniension 8), approximately the same for the thrw systems. Its N
-
( 6 ) 11.H. I'oII~J-,Tv. D. Fcliaeffer and W . 57, 4li9 (1953). ( 7 ) 11. Graham, ibid., 61, 1310 (1957).
R. Smith, Tiria JOURNAL. ( 8 ) J C,ibwn, \ I (1948)
Hololinn And I1 I
R ~ l e\ , .I
('hem
,sur
iiL
DISPERSION ENERGY CALCULATIONS
Sept., 1960
value is obtained from the heat-coverage plot for nitrogen on P-33 as the difference between the heat zLt coverage near zero and that a t the maximum (e 0.85). The very few strong sites in the surface of this particular adsorbent influence only a minute first portion of the curve and the resulting rise near zero coverage (Fig. 7, ref. 7) is not shown here. The coiitribution of lateral interaction at 8 0.85 is thus approximately 400 cal./mole. Its subtraction from the isosteric heat's a t e 0.85 leaves t,he net heat of interaction between the carbon and the adsorbed nitrogen as shown in Table I.
-
-
- 3--501
P (AT 77 6'Kl IO ,
I'
,
19
,
-
,'"
TABLE I I
HEATS O F riDY3RPTIOS (IN CAL./MOLE)
O F NITROGEN O N
Adsorbent
Amor-
phous carbon
Diamond
Isosteric heat of adsorption Heat of lateral interaction S e t heat of atlsorbentadsorbate interaction Ratio of net heat to that on diamond
Graphitized
-2960
-2920
-2820
-
400
- 400
- 400
- 2560
- 2520
- 2420
1.oo
0.98
0.95
TION O F NITROGE?; WITH C.4RBON A4DSORBENTS
Nitrogen Diamond Amorphous carbon Graphitized
Diamagnetic susceptibility (emu./rnolecule or atom) Value Ref.
- 2 . 0 x 10-29 - 0.90 x 10-29
9
io
- 1.00 x 1 0 F g 11 - lT.5
Averope V,
,
I
I PRESSURE
Fig. 3.-Adsorption
IN
2 80 m l l g
I
10 MILLIMETERS Hg
loo0
100 ( A T 90 4 P K l
of nitrogen on P-33 a t 90.4 and T7.6'h.
I
TABLE I1 DISPERSION CONSTAKTS REPRESENTING INTERAC-
Substance
,/.-a-'
01
P-33
These net heats are, like the isosteric heats, closely similar although the adsorbents vary widely in density ('Table 111). The greater density of diamond is balanced by correspondingly greater contSributionsfrom each atom of the lighter graphitic carbons which means that the energy with which an atom in an adsorbent attracts an adsorbed molccule varies markedly with the nature of its bonds to other atoms within the solid. The next step is to determine the extent to which these compensations are reflected in the results of dispersion energy calculations. The physical constants employed in calculation of the dispersion const'aiits me listed (with source references) in Tnble 11. DATA FOR
"*,.
,
3
OF DIFFERENT CRYSTAL STRUCTURE>
1'43
1091
x
11
Polarizability, em.' Value Ref.
1.76 x 10-24 0.93 x 10-24
12 13
1.07 X
14
1.07 X
14
The dianiugiietic susceptibility aiid polarieabilit,y va1uc:s for nit,rogen and for diamond differ (9) E. C . Storier. "h1;agnetisin." Methuen and Co.. L t L , London, 1948, p. 30. (10) A. Sigamony. Pmc. lrtdian &ad. Sci., l S A , 310 (1944). (11) H. T. Pirnick, P h y s . Rev., 94, 319 (1954). (12) J. 0 . H1isclifelder, C . F. Curtis and R. B. Bird, "l\Iolecular Tlirory of Gases a n d Liquids," John Wiley and Sons, Inc., New York, S . Y., 1954, p. 950. (13) J. A. Ke ;elaar, "Chcmical Constitution," Elsevier Pub. Co., X e w York, N. r., 1953, p. 90. ' 1 )-I I,andolt-l3ornstein, "Zahleni~erte und Funktionen," Springer, 1%-,1. { I . ? u f l . EIcI I .; 1). > 1 : 3
LL
3000
0
w
c
0 v?
2030; 0
~
-~_ ~ ____ _
___-
FRACTIONAL COVERAGE
I
L
IO
~
-
12
(e)
Fig. 4.-Isosteric heats of adsorption for nitrogen on diamond, amorphous carbon and P-33.
but little from those employed by earlier inl-estigators. Since the effects of anisotropy upon the diamagnetic susceptibility of graphite are reduced with crystallite size, l 1 , l 6 the value for amorphous carbon differs but little from that of diamond. The value selected for the polarizability of amorphous carbon and of graphite is that given by Landolt-Bornstein for aromatic carbon. It is only about 15% greater than that of diamond. The greatest variation from earlier usage is in the diamagnetic susceptibility of graphitized P-33. Fortunately, there are considerable data indicating the approximate level and one measurement on a similarly graphitized sample of P-33. For interpreting these results, the diamondnitrogen system is the selected standard of reference because its physical constants are best known and because, being isotropic, covalently bonded and non-conducting, it most nearly fulfills the requirements for pure dispersion interaction. Since we are interested only in the ratios of the adsorption energies of the other systems to this standard, and since the assumption of dispersion energies implies a common force law, we may assume that the dispersion energies are, to a first approximation, proportional to the product of the adsorbeiit density times the dispersion constant. These values arp (1.5) S . Gangnli, Phzl.
M ~ Q21, , 355 (1936).
DONALD GRAHAM
1092
given in Table I11 in comparison with the corresponding measured net heat ratios. TABLE I11 A COMPARISON OF CALCULATED DISPERSION ENERGIES WITH MEASURED NET HEATSOF INTERACTION Diamond
Density (D) Dispersion constant (C)
x
lob9
CD Product ( X IO6@) Ratio
CD CD
Adsorbent Amorphous Graphitized carbon P-33
3.5
1.9
2.2
-4.22 -14.7
-4.74 -9.0
-9.62 -21.1
1.00
0.61
1.44
1.00
0.98
0.95
(Diamond)
(Net heat of intern.) Ratio (Net heat of iiitern.)Diamond
The ratios compared in Table I11 indicate failure of the dispersion energy calculation to reproduce measured net heats of adsorption. It may be significant, in relation to the results of earlier calculations, that an average of the calculated values from amorphous carbon and from graphitized P-33 would be an acceptable result. It is possible that this failure lies in one or more of the values selected for the variables making up the dispersion constants. It seems more probable, however, that interaction energies, other than those of dispersion, may arise from the peculiar electronic properties of graphitic carbon. For example, nuclear magnetic resonance measurements have demonstrated an interaction of unpaired electrons in the surfaces of graphitic carbon with adsorbed molecules.16 In the three systems considered here, the effects of variation in adsorbent density (up to a factor of almost 2) are compeiisated by some combination of electronic effects to the extent that the over-all variation in adsorption energy is small. This conclusion makes it easier to accept the observed (and repeatedly confirmed) high energetic uniformity of the adsorbent surfaces of certain graphitic carbon blacks which may involve an analogous electronic compensation for the effects of structural anisotropy. Finally, the results of this study emphasize the importance of differences in electronic properties of solid adsorbents in general and the necessity for their consideration in any realistic theoretical treatment.
DISCUSSION It. A. PASTERNAK (Stanford Research Institute).-To
what extent could the carbon surfaces have been covered by contamination such as chlorine or oxygen? DOXALDGRAHAM.-The surfaces of all of the carbon samples studied were essentially clean. The least pure (16) D. Graham and W. D. Phillips, Proc. Second Internall. Congr SurJnce Acliaily, 2 , 22 (1957).
Vol. 64
was the amorphous carbon, which contained less than 0.5% chlorine. Since the value of Va (content of the first monolayer) for nitrogen on this sample was 198 ml./g., only a very small fraction of the total surface could have been covered by chlorine, even if all of it was on the surface. PHILIPL. WALKER,JR.(Pennsylvania State University). -Why i s the diamond surface so heterogeneous? Is it possible that the carbon arrangement a t the surface is not that of diamond? DONALD GRAHanl.-~lectron micrographs show the diamond particles to be rough and irregular with little evidence of clean fracture along normal cleavage planes. Also, since diamonds are valence crystals, bonds are broken a t cleavage leaving free valences which are probably quickly satisfied by random interaction with each other. The bonds between the surface atoms are therefore no longer tetrahedral and possibly not even symmetrically distributed. Care was taken t u avoid temperatures, in conditioning the sample, which might permit surface graphitization. Although it seems improbable that the distortion of bonds between the diamond surface atoms Lvould materially alter the energy of interaction between the particle and an adsorbed molecule, the observed surface ruughriess may, a t least in part., explain the observed heterogmeity.
GEORGER. LESTER(Universal Oil Products).-What is the nature oi the BLT plot for rijtrogeii on the amorphous carbon? Did the form of the eqiiatioii for low values of n yield a better plot? D O ~ A L~ D R . % H A ~ I .normal - ' ~ ~ ~BET plot was not linear but a better line was obtained by use of lower coverage data as suggested by h1acIwr and Emmett ( J . Phus. Chem., 60, 824 (19W)). This gave a V,, ~ i 217 ' ml./g. compared with t,he 198 nil./g. indicated ~ J the Y heat curve. GEORGEIt. LESTER.-IS it proper t,o consider the dispersion coiistant-density product as reimsentiiiy interaction energy for such high area mat,erials as t'he amorphous carbon, especially in view of the suggested cage-like structure proposed by Gibson, et al. I realize the product is only relative, but question the comparison of these products for materials so different in area as amorphous carbon and diamond dust or P-33. DONALDGRaHhu.--'l'he dispersion constant-density product is, of course, oiily proportional as a first approximation to interaction energy and does indeed suffer from the extreme porosity of amorphous carbon. The effects of wall thinness and pore condensation oppose each other with the resulting over-all error probably tending t>omake the calculated value high. The obscrved discrepancy, however, is quite large and in the oplmite direction, so any improvement in the approximation would be expect,ed to show the dispersion energy calculation to be still less satisfactory.
D. J. C. YATES(Columbia University).-Would you care to comment on the rather surprising similarit of the heat curves for diamond and amorphous carbon? might seem that t,he heat curves are rather insensitive t'o changes in the cryst,allographic nature of carbon. DONALDGRAHAx-The similarity of the heat curvcs for the adsorption of nitrogen on diamond dust and on amorphous carbon is particularly significant because of the roughly two-fold difference between their densities. The effect of difference in crystal structim, or more, explicitly, electronic character, is thus opposite and approximately equal to the effect of the difference in density. The heterogeneity of the amorphous carbon surface was expected. That of the diamond dust was consistent v i t h the surface roughness indicated by electron microscopy.
?)
