Oct., 1954
CHARACTERIZATION OF PHYSICAL ADSORPTION SYSTEMS
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THE CHARACTERIZATION OF PHYSICAL ADSORPTION SYSTEMS. 11. THE EFFECTS OF ATTRACTIVE INTERACTION BETWEEN ADSORBED MOLECULES BY DONALD GRAHAM Contribution No. 155 f r o m Jackson Laboratory, E. I . du Pont de Nemours and Co., Wilmington, Delaware Received March 6,1964
Factora determining the role of attractive interaction in adsorption are outlined. A method for calculating its contribution to the differentialfree energy of adsorption on uniform surfaces is described and illustrated by application to adsorption data from typical systems.
Introduction Interaction between adsorbed molecules has been one of the most misunderstood aspects of the adsorption process. This factor has been treated in many different ways by different investigators; sometimes by addition of a parameter to an adsorption isotherm, sometimes by use of an attraction constant in a two-dimensional equation of state. These methods fail in general application to the first monolayer through neglect of the effects of localieation or of the entropy change in coalescence. It is, therefore, useful to define some of the factors which determine the character of adsorbate interaction and to measure the contribution of this interaction to the adsorption bond in real systems.
Discussion Interaction between two or more molecules adsorbed on adjacent sites may cause these molecules to either repel or attract one another. Repulsion may occur when molecules are adsorbed on sites so closely spaced that some interpenetration of atomic radii is required. Also, in the adsorption of similarly charged ions, electrostatic repulsion may overcome the van der Waals attraction, leaving the over-all effect one of repulsicjn. However, in most cases observed experimentally, the dominant interaction is one of attraction resulting from van der Waals forces, dipole-dipole interaction, or hydrogen-bonding. This paper is, therefore, primarily concerned with the effects of attractive interaction between adsorbed molecules. Adsorbed molecules which attract one another are bound to the adsorbent surface more strongly than if alone. The energy required t o remove one of them must be sufficient to overcome both its bond to the adsorbent and its attraction for its neighbors. Polar substitution of the adsorbate molecules can either weaken or strengthen this interaction. If the polar groups form relatively strong bonds (for example, hydrogen bonds) with specific atoms or groups in the adsorbent surface, the resulting localization may prevent any appreciable interaction between the adsorbed molecules. On the other hand, if the adsorption bond involves only van der Waals energy, localization is less important and any polar substituents of the adsorbate are free to interact with each other. I n the absence of hydrogen-bonds to the adsorbent, orientation, or polarization, the inherent tendency for adsorbed molecules t o attract one another is related to their latent heat of vaporization. Opposing the tendency for adsorbed molecsIes to
interact, is their tendency to assume the most random distribution or to increase the entropy of the system. Coalescence of adsorbed molecules is accompanied by a reduction in entropy, other factors remaining constant. If the adsorbed, partially filled monolayer could be considered an ideal twodimensional gas (both before and after coalescence), the reduction in entropy with coalescence would be -Ah' = R In l/O, a quantity very large a t low coverage and approaching zero logarithmically a t completion of the monolayer. At low coverage, there will be a strong tendency for the adsorbed molecules to keep as far apart as possible. As the average distance between them is reduced, with increasing coverage, the tendency for interaction will increase. The coverage at which interaction becomes important may be expected t o vary inversely with the inherent strength of the interaction as measured by the latent heat of the adsorbate. Application of these relations to real adsorption processes requires a measurement, from adsorption data, of the contribution of interaction between the adsorbed molecules to the strength of the adsorption bond. A qualitative approach to the problem is found in a previous paper.' A simple equilibrium function2 is developed which, for ideal monolayer adsorption, yields the equilibrium constant. Ideal conditions are approached in adsorption on uniform surfaces a t values of 8 below that at which the effects of attractive interaction between adsorbed molecules become appreciable. The resulting constant value of the equilibrium function, from data a t low coverage, E.F.,,, thus represents the system in its ideal (non-interacting) state. In systems which permit the adsorbed molecules to interact, the effects of this interaction appear a t a value of 0 below 0.5 as an increase in E.F. with increasing 8. This increase may be considered due only to this interaction up to the point a t which multilayer adsorption becomes important, usually above 0 = 0.7 but varying with the strength of adsorption of the first monolayer. The above concept is now given more quantitative character by the calculation of free energy changes. The strength of adsorption may be measured as the differential free energy of edsorption ( - A F ) , defined as the change in free energy accompanying the transfer of one mole of adsorbate from the saturated gas to the adsorbed film a t any (1) D. Graham, TEISJOURNAL, 67, 665 (1953). (2) E.F.= 6/(l O)(P/Pu),where e = fraction of surface covered, Pa = vapor pressure of liquid adsorbate, P = equilibrium pressure.
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DONALD GRAHAM
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specified coverage (e) and absolute temperature (5"). This quantity is calculated from adsorption data in the usual way - A F = RT In Po/P
The corresponding free energy change for an ideal system (without interaction) is obtained from the low coverage equilibrium function
The values of (-AF) and (-AFideal) are the same in the ideal region, but ( - A F ) becomes the larger as the contribution of lateral interaction becomes important. From this point, up to that at which the effects of other factors (such as multilayer adsorption) appear, the difference between these two values represents the contribution of lateral interaction between the adsorbed molecules ( -AFintersction) = (
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not provide specific atoms or groups capable of direct interaction (either electrostatic or dipoledipole), the adsorption bond i s limited to van der Waals energies. Localization, in this case, is less important than in hydrogen-bonded adsorption, and the adsorbed molecules tend to interact in a manner and to a degree determined by the character of the system as illustrated below. 1. The Effect of Adsorption Strength.-The effect of adsorption strength upon lateral interaction is illustrated in Fig. 2 by data from the adsorption of nitrogen (A), on the 110 face of crystalline copper a t 78.1°K.4aand (B), on Graphon a t 78.4°K.4b
- AF) - ( - AFidea.1)
Application to Adsorption Data A. Hydrogen-bonded, Non-interacting Adsorption.-Prevention of lateral interaction by strong localization in hydrogen-bonded adsorption is illustrated by the adsorption of water on asbestos as represented in Fig. l.3.
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5 120 h
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100
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li 0 0.2 0.4 0.6 0.8 1.0 Fraction of monolayer covered e. Fig. 2.-Effects of absorption strength: A, nitrogen on 110 face of copper a t 78.1"K. (from data of Rhodin); B, nitrogen on Graphon at 78.4"K. (from data of Joyner and Emmett).
The decreasing value of E.F. with increasing coverage shows some degree of surface non-uniformity (asbestos is both silicate and aluminate), but the extent is not sufficient to obscure any appreciable effect of interaction between the adsorbed molecules. I n localized adsorption, some of the molecules must occupy adjacent sites a t any value of 0 above 0.5. The first upward inflection of E.F. occurs a t 8 = 0.7, a coverage a t which second layer deposition becomes appreciable. B. Attractive Interaction in van der Waals Adsorption.-If the chemical natures of the adsorbent surface and the adsorbate molecules do
I n the case of nitrogen on copper, with adsorption of only moderate strength (E.F.0 = 61.5), the . lateral interaction contribution appears a t e = 0.35, rising almost linearly to a value exceeding 100 cal./mole at 0 = 0.65. In the very much stronger adsorption on Graphon (E.F.o = 2600), this contribution appears a t only slightly higher coverage (0 = 0.40). Also, the slope of the curve immediately above this point is approximately the same. A wide variation in adsorption strength thus produces very little effect on either the coverage a t which appreciable 'interaction appears or the strength of the interaction. This is consistent with the thought that these factors are determined by the inherent strength of the interaction and by an entropy which varies with e but not by adsorption strength. An important difference between these two sys-
(3) From work reported in part by A. C. Zettlemoyer, G . J. Young, J. J. Chessick and F. H. Healey, THISJOURNAL, 67, 649 (1953). The data summarized in Fig. 1 were received in a private communication from Professor Zettlemoyer.
(4) (a) T.N. Rhodin, J . Am. Chem. Soc., 72, 5691 (1950); (b) L. G . Joyner and P. H. Emmett, ibid., 70, 2353 (1948). Original data, runs 3 and 5 smoothed, Document 2530, American Documentation Institute, 1719 N S t . N.W., Washington, D. C.
0.2 0.4 0.6 0.8 1.0 Fraction of monolayer covered e. Fig. 1.-Localized adsorption of water on asbestos a t 23' (from data of Zettlemoyer, et d.), 0
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CHARACTERIZATION OF PHYSICAL
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terns is indicated by the fall off in the nitrogenGraphon curve above 0 = 0.6. This suggests a delayed equilibration involving the necessity for some shifting of adsorbed molecules to permit occupancy of the last portion of the adsorbent surface. This "crowding" may be a resuIt of strong adsorption which tends to magnify the localizing effects of slight variations in energy of adsorption which occur over even the most uniform surfaces. 2. The Effect of Latent Heat of Vaporization of the Adsorbate.-Three different adsorbates representing a wide range of latent heats of vaporization, all adsorbed on Graphon, illustrate the effects of differences in latent heat. The first is nitrogen (the data cited in the preceding paragraph) ; the second, ethyl ~ h l o r i d e and , ~ the third, methanoI.6 Pertinent data are summarized in Table I and Fig. 3. ADSORPTIONON Adsorbate Temp. of
"K.
TABLE I GRAPHON OF SUBSTANCES O F DIFFERENT LATENTHEATS Nitrogen
Ethyl chloride
Methanol
273
273
0000
9100
adsorption, 78.4
Latent heat of adsorbate 1300 (cal./mole) Ideal equilibrium function E.F.0 2600 Obsd. differential free energy of adsorption ( - A F ) at 0 = 0 . 5 (cal./mole) $1257 Ideal differential free energy of adsorption ( - A F i d e a l ) at 0 = 0 . 5 (cal. /mole) 4-1232 Contribution of lateral interaction to ( - A P ) (cal./mole) 25 Coverage (4 a t which strong interaction ap0.4 pears
0.28
10.8
1-1820
+696
+I300
-084
0.07
0
0.2 0.4 0.6 0.8 1.0 Fraction of monolayer covered 0. Fig. 3.-Effects of latent he'at of adsorbate: A, nitrogen on Graphon a t 78.4"K. (from data of Joyner and Emmett); B, ethyl chloride on Graphon at 0" rom data of Mooi, Pierce and Smith): C, methanol on raphon a t 0' (from data of Pierce and Smith).
8
panded phase during further addition to the monolayer. Adsorption, therefore, proceeds from the beginning of condensation to essential completion of the monolayer without change in the equilibrium pressure. This means that throughout the condensation the value of (- AF) is no longer a function of 6 but is a constant. Two-dimensional condensation of a monolayer on an adsorbent surface is thus analogous to the more familiar three-dimensional condensation of a vapor pumped into a vessel of fixed volume. I
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For these particular adsorbates, an increase in the latent heat is accompanied not only by a rise in the contribution of adsorbate interaction to the strength of adsorption but also by a marked drop in the strength of non-interacting adsorption. No explanation is offered a t this time for the latter effect but the extremely weak adsorption of methanol a t low coverage is consistent with the recognized hydrophobic character of pure carbon surfaces. 3. Two Dimensional Condensation.-Absorptjon a t temperatures below the two-dimensional critical point,'.* if not strongly IocaIized, may involve two-dimensional condensation. When this occurs, the onset of appreciable interaction is accompanied by formation of a condensed phase which tends to maintain equilibrium with the ex( 5 ) J. Mooi, C. Pierce and R. N . Smith, T H I SJ O U R N A L 5'7, , 1157 (1953). (6) C.Pierce a n d R. N. Smith, ibid., 54, 354 (1950). (7)J. H.d e Boer, "The Dynarnical Clmracter of i\dsorl~tion." The
Oxford University Press, London, 1958.
. ( 8 ) H. Clark and 9. Rose, J . A m . Chem. Soc., '75, GO81
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ADSORPTION SYSTEMS
(10.53).
0.02 0.06 0.10 0.14 Relative pressure (P/P,). Fig. 4.-The two-dimensional condensation of ethane on cube NaCl a t 90"II. (from data of Ross and.Winkler).
.A clean cut example of two-dimensional condensation is found in the adsorption of ethane on cube NaCl a t 90°K.9 The isotherm is shown in Fig. 4 employing the following parameters (9) S. Ross a n d W. Winkler, ibid., 76, 2637 (1954).
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DISCUSSION
-8
800
a;
-> + J
A
3
600
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.-8 Y
f?400 8
a d
’CI
9 ha 84 200
tx
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Fraction of monolayer covered 6. Fig. 5~--Two-dimensional condensation of ethane on cube NaCl at 90°K. (from data of Ross and Winkler). V , = 353 cc. mm./g. = 0.465 cc. S.T.P./g. (detd. from a l / P vs. l / V plot of the lower portion of the iso. therm) Po = 0.007 mm.10 0
Since (-AF) is not a function of e during the condensation process, a plot of (- AFinteraction) VS. e would have little meaning. Figure 5 shows the change in (- AF) for the three partsof the process. Up to a coverage of 0 = 0.42, the ideal curve (E.F.0 = 19.5) is followed quite closely. At this point, condensation’ begills and continues a t (- AF) = 587 cal,/mole until essential completion of the monolayer. Theoretically, with perfect equilibration, the adsorption should follow the isobar to the point of intersection with the Curve for E.F.a(second layer), at a e ‘*05. The experimelltal points, not showing a sharp transition at completion of the monolayer, do join and follow the theoretical curve (E.F.,, = 1.55) for the second layer UP to 8 = 1.3 where multilayer adsorption becomes important. Achowledgment’-The author wishes to thank Professor Sydney Ross and Professor A. Zettlemoyer for access to unpublished data, and Dr. A. Di Giacomo and Dr. R, Pariser for helpful discussion of the entropy change in coalescence.
c.
(10) A. W. Tioknerand F. P. Lossing, THIS JOURNAL, 55,733 (le51).
W. B. INNES -This approach appears to be a simple and quantitative one for studying interaction on uniform surfaces. Do you think a similar procedure would be useful in studying non-uniformity of surfaces? Do you consider your equilibrium function “EFJ’as the practical equivalent of the BET “C” value and the actual equivalent for the case where adsorption is limited to a single layer? DONALD GRAHAM.-The quantitative method outlined here is limited to systems in which the adsorbent is uniform with respect t o the adsorbate. Qualitative treatment of interaction on heterogeneous adsorbents was covered in reference ( 1 ). Heats of adsorption derived from the BET “C” value are rough a proximations at best. The relation of the EF to the stancfard free energy of adsorption is presented in reference (1). M. L. CORRIN -Two pertinent points may be mentioned here in connection with this paper. (1) It is possible to adopt one of two extreme points of view in considering the thermodynamics of the adsorption process. (a) One may assume that the effect of the adsorbent is exclusive1 one of perturbing the adsorbate. Perturbation of the azorbent by the adsorbate is considered negligible. This point of view seems intuitively to be in error a t low surface coverages. It is not true in systems containing liquid surfaces. With solids one might expect that the lattice spacings and potential functions in the surface regions would be altered when adsorption occurs. The free energy function described by the author is derived on the basis of this view (a) and any terms involving surface effects other than in the perturbation of the gas is neglected. (b) The surface region may be considered as an entity and only over-all effects in this region considered. This approach is the one successfully employed with liquid systems. The thermodynamics of this system are similar to those employed, for example, when gravitational effects are significant. With surfaces, surface energy terms are employed. Thus if the chemical potential of the adsorbate in the surface region is defined as equal to that in the gas, the free energy expression will contain not only a term relating the chemical potential of the gas to its standard state but a term relating to the change in free surface energy occurring on adsorption. h (2) We have observed the following with respect to the two dimensional phase changes discussed by the author. For the adsorption of krypton on a calcium halophosphate a t liquid nitrogen temperature, an apparent first order phase transition is observed if thirty-minute points are taken; the sample was contained in the usual cylindrical adsor tion hulb. A similar effect was observed if the solid was &aced in a tray s stem. If, however, the first increment of gas was a ~ ~ o w remain e ~ ~ in o contact with the soliduntil equilibrium was attained (a matter of several days), no such transition was obRerved and the smooth isotherm obtained was found to join the previous discontinuous isotherms just above the region of apparent transition. We do not know a t this time whether the effect noted above is a general one. DONALD GRAHAM.-Perturbation of the lattice of a solid adsorbent, unquestionably contributes to thp free energy of the system. However, if this factor is not appreciably altered by interaction between the adsorbed molecules, it essentially disappears when the effect of interaction is evaluated as the difference between the differential free energies of the real and ideal systems.
