The Effect of Lateral Interaction on Monolayer Adsorption J. G. ASTON, E. S. J . TOMEZSKO, and HAKZE CHON Cryogenic Laboratory, College of Chemistry and Physics, The Pennsylvania State University, State College, Pa.
On a smooth surface rare gas molecules interact laterally according to a two-dimensional van der Waals equation. This equation can be used to cal culate the lateral interaction energy on the smooth Downloaded by UNIV OF ARIZONA on March 9, 2017 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch034
part
of
a
heterogeneous surface.
When
the
lateral interaction energy is thus taken into ac count, a reasonable model of a heterogeneous surface can be used to calculate an adsorption iso therm in good agreement with experiment.
Par
tial molal enthalpies (differential heats) of adsorp tion can be calculated on the same basis.
For the
first time reasonable agreement with experiment is obtained.
(jome time ago it was demonstrated conclusively that high heats of adsorption were due to many-sided sites on the surface of the absorbant (5). Previously attempts to predict differential heats of adsorption and the detailed nature of the isotherm up to a monolayer had had only indifferent success (2). It was, however, suggested that the real difficulty lay in the inability to treat lateral interaction on a heterogeneous surface (2). Recently a surprisingly simple method for doing this has become available. As a result, the situation with regard to predicting differential heats of adsorption and isotherms up to a monolayer on the basis of a simple model is now more en couraging. This paper demonstrates to a first approximation what the nature of the lateral interaction energy is, and how to allow for this with a reasonable degree of accuracy. Lateral Interaction on a Smooth Surface It can be demonstrated that the molal integral lateral interaction energy on a completely smooth surface is given by the equation (1)
where a and b are the van der Waals constants, θ is the coverage, and E is the molal interaction energy ( 1 ). Figure 1 shows graphs of the differential heats of A
325
Copeland et al.; SOLID SURFACES Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
326
ADVANCES IN CHEMISTRY SERIES
Downloaded by UNIV OF ARIZONA on March 9, 2017 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch034
adsorption of neon, argon, and krypton which have been analyzed previously (I) on graphitized carbon plotted against the coverage. Figure 2 is a graph of the heats of adsorption of argon on a single crystal of zinc (3) plotted against coverage.
COVERAGE
Figure 1. Heats of adsorption of neon, argon, and krypton on graphitized. carbon black The graphs for the three rare gases on graphitized carbon clearly show the effect of a small amount of heterogeneity at low coverages in increasing the dif ferential heats of adsorption. The graph for argon on zinc shows less of this effect, probably since the work was done on a single crystal. An inspection of the graph on zinc indicates that the tangent drawn at the point of inflection has a slope which corresponds to the formula Ε = 1100 θ (2) for the differential heat of lateral interaction. The value of a/b for argon is 1020 cal. mole cm~ . The deviation of this graph from a straight line at low coverages is due either to a failure of the formula at low surface concentrations or to some surface effects of the single crystal. Rhodin estimates that about 10% of the surface is rough. In view of this it seems natural to draw similar tangents on graphs of the differential heats of adsorption vs. coverage for the rare gases on graphite at the point where the curves have the maximum slope. These tangents are drawn in Figure 1. When this is done, the slopes are very closely equal to - 1
2
Copeland et al.; SOLID SURFACES Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
ASTON ET AL.
Lateral Interaction in Monolayer Adsorption
327
300ϋι
CL CC Ο CO α
"* 2000 ~
< Lu I Ο
CE
ω
1000
CO
ο
Downloaded by UNIV OF ARIZONA on March 9, 2017 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch034
CO
0 0
1.0
2.0
COVERAGE
Figure 2. Heats of adsorption of argon on single crystals of zinc the value of the ratio a/b for all three rare gases, as can be seen from Table I. In all four graphs the differential heats of adsorption fall sharply at the monolayer. Part of this sharp fall is due to a compressive effect of the molecules in the second layer which tend to reduce the lateral interaction. The evidence just given that the energy of lateral interaction on a smooth surface is given by Equation 1 is sufficiently strong to justify the application of this formula to the smooth parts of a heterogeneous surface. The effect of the sites other than on the flat surface is obviously to isolate the molecules and prevent lateral interaction. Thus it is hard to imagine a molecule on a three-sided site having much opportunity to interact with other absorbed molecules. Thus allowance for the effect of lateral inter action was made in the fraction of molecules located on the one- and two-sided sites. This device has been used in what follows. There is no physical significance whatever to such a procedure and it might be better to neglect entirely the lateral interaction for all molecules not on the flat surface. Table I.
Measured and Theoretical Energy of Lateral Interaction
Helium Neon Argon Krypton a
Ει/θ, Max., Cal. IMole
a/b, Cal. I Mole
105» 360 1160 1400
35 300 1005 1410
From data of ( 7).
Heterogeneous Surfaces In Figure 3 is presented a graph of the differential heat of adsorption of helium vs. coverage on a titanium dioxide surface which has been covered with various amounts of argon (5). It is evident that at 6/10 of a monolayer of argon the differential heat of adsorption of helium on the surface is essentially constant over the surface. This is because the lateral interaction energy of helium is small, as can be seen from the value of a/b. There is very little doubt on the basis of the
Copeland et al.; SOLID SURFACES Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
328
ADVANCES IN CHEMISTRY SERIES
Downloaded by UNIV OF ARIZONA on March 9, 2017 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch034
data in this figure that the high heats of adsorption at low coverages are due to many-sided sites. The heat of adsorption of helium on titanium dioxide where no argon has been added is also shown in Figure 3. This graph is a clear indication of the heterogeneity of the bare surface. An attempt has been made to calculate the adsorption isotherm and the curve for differential heat of adsorption against cover age for neon on the surface of the same sample of titanium dioxide (rutile). The model adopted was essentially that used previously for adsorption on a heterogeneous surface ( 2 ) , modified by the addition to the energy of the oneand two-sided sites of a term dependent on the coverage of the site which would allow for the lateral interaction energy.
O
BARE
3
Ti0
•
T i 0 + 0 . 6 0 LAYER OF ARGON
C
Ti0 +
2
Ti0
2
+ 0 . 3 6 L A Y E R OF ARGON
2
2
1 . 0 5 L A Y E R OF ARGON
COVERAGE
Figure 3. Helium heats of ad sorption on titanium dioxide covered with various amounts of argon The equations used for calculating the isotherms and the differential heats of adsorption were those used previously ( 2 ) . Only four types of sites were used with energies ei, e , e , and e , respectively, because of interaction with the ad sorbent alone such that 2
3
4
e = 4ei, € = 3ei, e> = 2ei, ei = 300 cal. per mole 4
3
(3)
These sites correspond roughly to the flat surface and two-, three-, and four-sided sites, respectively. Molecules adsorbed on the flat surfaces and two-sided sites are assumed to have energy due to mutual lateral interaction, in addition to e i and €> respectively, given on a molal basis by Equation 1 . The value of θ used is the 2
Copeland et al.; SOLID SURFACES Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
ASTON FT AL.
Lateral Interaction in Monolayer Adsorption
329
fraction of the surface covered by the flat surface and the two-sided sites together. On the three- and four-sided sites lateral interaction was neglected. Thus, on a molal basis the energies of adsorption per molecule for one- and two-sided sites, are, respectively, — ( ci + aQjlb ) and — ( e + aOjZb ) while for three- and foursided sites they were simply — c and — e , respectively. This choice assumes that the two-sided sites surround flat areas, making a single area in which all molecules interact equivalently. The equations of Aston, Tykodi, and Steele thus become 2
3
=
=
FiOi
Σ
F
I
'
4
X
+ P~V(T)
exp -
(€.· +
(4)
eia/2b)/RT
gi
= 1
i
Downloaded by UNIV OF ARIZONA on March 9, 2017 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch034
i = 4 Q
=
Σ
i
Z
