P. Y. HSIEH
1068
Surface Energy Distributions of a Homogeneous Surface and a Heterogeneous Surface from Argon Adsorption Isotherms
by P. Y. Hsieh The National Cash Register Company, Dayton 9, Ohio
(Received October E6, 1963)
The adsorption isotherms of argon on carbon black, MT-3100, and a silica-alumina cracking catalyst a t 77.8OK. are given. The site-energy distributions of these surfaces were obtained from the isotherms using the method proposed by Adamson and Ling. The results show that the cracking catalyst is heterogeneous while the carbon black is a homogeneous surface. The site-energy distribution on the carbon black is gaussian-like, as assumed by Ross and Olivier, which implies that the method suggested by Adamson and Ling is rather insensible to the local isotherm selected.
Introduction The equation relating adsorption of a gas onto a solid surface to the experimental quantities P , T can be written in general as
where @(P,T) is the observed adsorption function and is usually obtained as an adsorption isotherm 0 ( P ); f(Q) is the site-energy distribution function; e(P,T,Q) is the adsorption function representing adsorption for regions obeying local isotherm e; and Q is the adsorbent-adsorbate interaction energy. The distribution function may be expressed as f(&) = dF/dQ, where F(Q) is the integral site-energy distribution, i.e., F is the fraction of sites with energy
2 Q. The problem of obtaining site-energy distributions of a solid surface from adsorption isotherms is that of finding the solution of eq. 1. The solution to this problem, that is the inversion of this Stieltjes integral to give f(Q), would not be difficult, if B(P,T,Q) and 0(P,T) were known in simple analytical form. For the analytical integration of eq. 1, the Langmuir equation has been used for e and certain simple functions such as the Freudlich and Temkin isotherm equations for 0 by many workers.' The approach is convenient mathematically; however, it is practical only for certain types of assumed functions 6 and 0. The Langmuir model postulates no lateral The Journal of Physical Chmistrg
interaction, homogenity of substrate, and a localized adsorbed film. Another approach was taken to solve eq. 1 by Ross and Olivier.2 They took a two-dimensional van der Waals equation of state for 0 and assumed a gaussian distribution of adsorptive energies for f(Q). A number of model adsorption isotherms have been computed, using various assumed values of the parameters involved. The site-energy distribution was finally obtained by comparing the computed isotherms with the experimental isotherms. The use of a two-dimensional van der Waals equation was based on the experimental findings of Ross and his co-workersa that an adsorbed gas film is a mobile, two-dimensional nonideal type, and that the more uniform the surface the more closely can the adsorption isotherm be described by the van der Waals equation. Unfortunately, their method does not provide any possibility for an independent check of the proposed distribution. It is generally believed that experimental adsorption isotherms can be fitted by a number of semiempirical equations, and agreement with some partic(1) R. Sips, J . Chem. Phys.. 16, 490 (1948); J. M.Honig, ibid., 24, 510 (1956); J. M.Honig and L. H. Reyerson, ibid., 23,2179 (1955); J. M.Honig and E. Hill, ibid., 22, 851 (1954). (2) S. Ross and J. P. Olivier, J . Phys. Chem., 6 5 , 608 (1961). (3) S. Ross and W. Winkler, J . Am. Chem. Soc., 7 6 , 2637 (1964): J . Colloid Sci., 10,319,330 (1955):S. Ross and W. W. Pultz, ibid., 13, 397 (1958).
1069
SURFACE ENERGY DISTRIBUTIONS OF A HOMOGENEOUS SURFACE
ular one provides no assurance that its basic assumptions are correct. Recently, Adamson and Ling4 have demonstrated a convenient way of obtaining the site-energy distributions from the experimental isotherm itself and from any arbitrarily chosen local isotherm function 8. The adsorption isotherms of butane and oxygen on TiOa and of nitrogen on both Graphon and TiOz have been used in the illustration of the m e t h ~ d . The ~ method was applied to find these distributions functions for silica-alumina cracking catalysts from ammonia adsorption isotherms. The result appeared to agree with the calorimetric heat measurements.5 I n the present study this method was tested on two extreme substrates: a homogeneous and a heterogeneous surface. The adsorbents chosen were a highly graphitized carbon black, MT-3100, and a silica-alumina cracking catalyst previously used in the ammonia adsorption. Argon was used as the adsorbate. The site-energy distribution obtained from the argon adsorption isotherm on MT-3100 may be used to crosscheck the result reported by Ross and Olivier.2 Although an independent check cannot be made for the distribution obtained from the adsorption isotherm on the silica-alumina catalyst, it should show the heterogeneous nature of the surface and it should give some comparison with that obtained from the ammonia adsorption isotherm.
Experimental The adsorbents used in the present study were a carbon black, Sterling MR-3100, and a silica-alumina cracking catalyst. The carbon black was graphitized a t 3000 h 300" in the absence of air and was supplied by the courtesy of Dr. W. R. Smith of Godfrey L. Cabot Corp. The surface area of 6.3 m.2/g., was reported by Beebe, et aZ.6 The catalyst was 25% alumina on silica and was kindly supplied by the courtesy of Dr. M. @. Throckmorton of the Texaco Research Center. The surface area of the catalyst from1 nitrogen B.E.T. measurements was found to be 525 m2/g. Argon was obtained from Air Reduction Sales Co. as spectroscopically pure and was used directly from the glass container. Measurements of the adsorptions were carried out with the vacuum apparatus described earlier5 a t liquid nitrogen temperature, 7724°K. The outgassing condjtions were a minimum of 12 hr. a t 150' for the carboin black and a minimum of 40 hr. a t 260' for the cracking catalyst.
Results and Discussion The experimental data of argon adsorption on MT3100 at 773°K obtained previously7 are shown in Fig.
4 and also shown as 8 (= u/v,) us. l / p in Fig. 1. This graphical form of e and the Langmuir equation for e were used for making successive graphical approximations of the integral site-energy distribution F(&), following the procedure described by Adamson and Ling. Multilayer corrections, which were small in this case, were made by the equation
e
=
( v / v ~ > (-~ P / P )
(2)
and are indicated by the solid circles. The vapor pressure of solid argon which is 212 mm. was used for Po. The dashed line indicates the final F us. b distribution for the isotherm, where b is the constant in the Langmuir equation. In order to calculate 8, the monolayer capacity, V,, of 2 cc.(STP)/g. was obtained from the isotherm "B" point. The value of 2.3 cc. was reported by Ross and Olivier2 from their approach. If based on the surface area of 6.3 m.2/g. and 14.6 for the cross
1.0
0.8
6
0.1
Ill
,..
'4
0.4
0.2
0 0.2
1
10
l/P
= b , mm.-1
Figure 1. Adsorption isotherm of argon a t 77.8"K. on , 8 US. I / p ; - - - -, final approximation MT-3100: t o F US. b; 0, V/Vm; 0 , (V/Vm)( 1 - X). ~
_ _ _ _ ~
~
_
_
(4) A. W. Adamson and I. Ling, Advances in Chemistry Series, No. 33, American Chemical Society, Washington, D. C., 1961, p. 51, (5) P. Y. Hsieli, J. Catalysis, 2 , 211 (1963). (6) W. B. Spencer, C. H. Amberg, and R. A. Beebe, J. Phgs. Chem., 62,
719 (1958).
(7) P. Y. Hsieh, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N. Y., 1959.
Volume 68, Number 6 Mag, 196.4
P. Y. HSIEH
1070
section of argon, the value of Vm would have been about 1.6 cc. Since it was assumed that the active sites consist of patches, the local isotherms of which obey the Langmuir isotherm, the interaction energy Q was obtained from the relation b
=
bOeQ/RT
=
The values of 14.6 and sec. (see ref. 8) were used here for uo and TO, respectively. The collection of constants bo was 9.2 X a t 77.8OK. and pressure was in mm. The differential site-energy distribution was then obtained by finding the slope of F us. Q and is shown in Fig. 2. The site-energy distribution obtained this way appears to be gaussian-like as assumed by Ross and Olivier.2 The agreement was striking despite the difference in the local adsorption function assumed, that is, the Langmuir isotherm in this work and van der Waals equation of state in Ross and Olivier's paper. Strictly, Langmuir's adsorption isotherm may not be applied to a mobile adsorption film such as argon on carbon black. However, there is no way to confirm that the active site patches really do not obey the Langmuir isotherm. It appears more likely that Adamson and Ling's method is rather insensitive to the isotherm
6
10
12
14
Q, kcal./mole.
Figure 3. Differential site-energy distribution for ammonia on silica-alumina catalyst.
0
ai:
2 120
0.1
Pressure, mm. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.1
I " ~ " " " " l .
. ti
h
PI
h
" $
% -8
9
H
2.0 r+
100
0
80
1.6
60
1.2 -E
40
0.8
20
0.4
$ 8
0
0
0
4
8
12
16
20 24 28 Pressure, mm.
32
36 40
B
2
9
44
Figure 4. Adsorption isotherm of argon a t 7723°K. on silica-alumina cracking catalyst (upper curve) and MT-3100 (lower curve).
tc
8
$ 6
% 4
2
0
8
I /I 2.6
2.7
2.8 Q,koal./mole.
2.9
Figure 2. Differential site-energy distribution for argon on MT-3100.
The Journal of Physical Chemistry
I
3.0
selected, and that any local isotherm function e may be arbitrarily chosen without giving an entirely different distribut
