NOTES
1596
adsorbed diamine molecule may be too low to react with an wid site. In the case of the oxidized chromia-alumina, the butylamine titer exceeds that of the reduced catalyst by 0.09 meq./g. while the ethylenediamine titer is 0.13 meq./g. higher. This result would indicate that for 64% of chromia acid sites an ethylenediamine molecule is able to neutralize two chromia acid sites (or one alumina site plus one chromia acid site). This might indicate that the distance between two chromia acid sites or between a chromia and an alumina acid site is less than the distance between two alumina sites. The nature of the acid sites on oxidized chromia catalysts is not completely clear. It seems reasonable thak the increased Hammett acidity in the oxidized state is associated to a large extent with higher valent chromium ions (C+) on the surface. The high, electrical conductivity of oxidized chromia is thought to be associated with the presence of both C r f 3 and on the surface. It thus appears that the acid sites are related to the defects which are also responsible for the semiconductivity properties. The l-Iamm,ett acidity exhibited by reduced chromia (unsupported) is a property inherent with the reduced state of the surface. In contrast, it is not possible at this point to completely distinguish between chromia acid sites and alumina acid sites on reduced chromia-alumina. It does seem reasonable, however, that the large portion of the acidity is due to reduced chromia sites. The exact nature of the acid sites on reduced chromia and chromiaalumina catalysts is more obscure than that of the acid site:: on the oxidized catalysts.
THE ISTERACTION OF ARGON WITH HEXAGONAL BOROS NITRIDE B y i
R A. PIEROTTI' A N D J. C. PETRICCIANI
Department of Clremzstry, Universzty of Nevada, Reno, Nevada Received M a g 1 1 , 1960
The interaction of the rare gases with graphite has been extensively investigated experimentally and theoretically by numerous authors. Barrer12 Crowell and Young3 and Pace4 have calculated the heat of adsorption of an isolated argon atom over various positions on the basal plane of graphite. The results of Crowell and Young and of Pace indicated that the graphite surface was energeticdly homogeneous with respect to the adsorption of argon and that the adsorbed argon film was mobile or non-localized. Their conclusions have been verified experimentally.4J Barrer's results were inconsistent with the others. X-Ray diffraction studies indicate that the hexagonal modification of boron nitride has a crystal structure which is remarkably similar (1) School of Chemistry, Georgia Institute of Technology, Atlanta
13, Georgia. ( 2 ) R. M. Barrer, Proc. Roy. SOC.(London), 8161, 476 (1937). (3) A. D. Crowell and D. AI. Young, Trans. Faraday SOC.,49, 1080 (1953). (4) E. L. Pace, J. Chem. Phys.. 87, 1341 (1957). (5) Sydnty Ross rrnd W. R. Pulto, J. Colloid Sci., 13, 397 (1968).
Yol. 64
to that of graphite.6 The 2earest neighhor distance in boson nitride is 1.44 A.,7 in graphite it is 1.42 $he interlaminar spacing in boim in graphite it is 3.35 A.a nitride is 3.33 The aims of the present investigation were i o calculate the heat of adsorption for the argonboron nitride system, to compare these calculations with similar calculations for the argongraphite system, and to compare the calculated results to the experimental data for the two systems. Results The interaction of an isolated argon atom with a covalent, non-polar solid can be calculated by assuming a Lennard-Jones (6-12) potential and summing over all pairwise interactions of the argon atom with the atoms of the solid. Thc total interaction energy $C of the atom with the solid then is given by
where r i is the distance of the argon atom from the ith atom of the solid, C is the dispersion force constant and is obtained from the KirkwoodMuller f~rmula,g.~O ro is a repulsive constant which can be evaluated semi-empirically. Barrer and Pace used the equilibrium distance of an argon atom above a graphite surface as the value of r0. Crowell and Young justly criticized this choice of ro and instead evaluated it by calculating potential energy versus distance curves for several values of r0 until a value mas found which gave a minimum in the potential energy at the equilibrium distance (assumed to be the mean of the interlaminar distance in graphite and the internuclear separation of a pair of argon atoms in crystalline argon). In the present work, the rots for an argon atom interacting with either a boron atom or a nitrogen atom are assumed to be equal. The value of rO then was selected so that it yielded a minimum in the potential energy a t the equilibrium distance, The equilibrium distance over a boron atom was chosen to be the mean of the interlaminar distance in boron nitride and the internuclear separation of two argon atoms in crystalline argon. It should be mentioned that Crowell and Young state that ro is the equilibrium distance between an argon atom and an isolated atom of the solid. This is not correct, since repulsive forces are not pairwise additive as are dispersion forces. The summations were carried out over four different sites of the basal plane of boron nitride: (a) over the center of the hexagon, (b) over a boron atom, (c) over a nitrogen atom and (d) over a position midway between a boron and nitrogen atom. The nearest 300 atoms were included in both the attractive and repulsive summations. The additional attractive interactions were ob(6) W. Hackel, "Structural Chemistry of Inorganic Compounds," Elsevier Publishing Co., Amsterdam, 1951,Vol. 11, p . 598.. (7) A. A. Giardini, U. S. Bur. Mines Info. Circular 7664, 1953. (8) H. Lipson and A. R. Stokes, Proc. Roy. Soc. (London), A l S l , 101 (1942). (9) A. Muller, ibid., Al64, 624 (1936). (10) R. A. Pierotti and G. D. Halsey, THISJ O U R N A L 63, 680 (1959).
NOTES
Oct., 1960
1597
tained by integration and amounted to 6Yq of the total; the additional repulsive interactions were shown to be negligible. The physical constants used in the calculations are shown in Table I. The results of the calculations for the argon-boron nitride system are listed in Table 11. Included there are: 4, the interaction energy; re, the equilibrium distance over each site; eo, the zero-point energy (calculated from the curvature of the potential energy curve in the region of the minimum) ; and AHo, the heat of adsorption a t 0°K. Table I11 contains the same quantities calculated by Crowell and Young for the argon-graphite system.
These calculations can be compared to the experimental data obtained by Ross and P ~ l t z . ~ They measured isotherms of argon adsorbed 011 boron nitride a t 78 and a t 90°K. and determined the isosteric heat of adsorption and the entropy of the adsorbed film. The experimental heat of adsorption a t low coverages is 2200 cal./mole a t 84°K. The calculated heat a t 0°K. plus the contribution due to the heat capacity of the film (about 100 cal./mole a t 85°1
