DIFFERENTIAL HEATSOF ADSORPTIONAS
A
FUNCTION OF PARTICLE SIZE
where invasion through the smallest pore is thermodynamically preferred. Without more intimate knowledge of the pore structure, the relative importance of this latter mechanism cannot be assessed ; however, a bulk diffusion mechanism would require excessively large diffusion coeficients. An alternate process of surface diffusion into the interior of the grains and into dead-ended pores would be attractive since the bulk rates would not need to be as large. The pores could be left highly populated by hexane as long as the surface is covered by two to three molecular layers of water. This emphasizes that the calorimetric nieasurements here performed are not necessarily sensitive to the equi-
Heats of Immersion.
317
librium microscopic liquid structure of the pore but only the adsorptive state of the pore surfaces. In conclusion, the heats of displacement indicate that the exchange process is rapid and quantitative but in the case of gels with internal pore structure it is impossible to tell if there is complete exchange of bulk pore liquid. Acknowledgment. The authors wish to thank the American Petroleum Institute and the Robert A. Welch Foundation for continued support of these studies. Appreciation is expressed to RIr. James E. Gardner for performing the microcalorinietric measurements.
VIII. Differential Heats of Adsorption as a Function
of Particle Size for the Alumina-Water System
by Raymond I,. Venable, William H. Wade, and Norman Hackerman Department of Chemistry, The University of Tezas, Austin, Tezas 7871.9 (Received August 27, 1964)
Differential heats of adsorption have been determined from measurement of ths heats of immersion of alumina powders pre-equilibrated with various amounts of water vapor. The data are interpreted to show that there is a wide distribution of adsorption energies and that both localized and niobile adsorption occur during formation of the first monolayer. The energy of adsorption in the second layer is not zero and differs significantly for the three samples. Entropy calculations show the inert adsorbent model to be invalid.
Introduction It has been shown in previous communications from this that there is a significant decrease in the heat of imniersion/cni.2 (mi)with increased specific surface area of silica and alumina samples on immersion in water. The present work investigates this phenomenon in more detail. The objective was to locate the regions of the differential heat-coverage curves wherein the specific differences among the saniples give rise to the differences in the integral heats of immersion.
Experimental The alumina samples used have been described previouslya and only essential information is given in Table I. The samples were outgassed at n m . for 48 hr. a t 160 =J= 3" before admitting water vapor to them A. C. Makrides and N. Hackerman, J. Phys. Chem., 6 3 , 594 (1959). (2) W. H.Wade, R. L. Every, and N. Hackerman, ibid., 64, 355 (1960). (3) W: H. Wade and N. Hackerman, ibid.. 64, 1196 (1960). (1)
Volume 69,Number 1 January 1966
R. L. VENABLE, W. H. WADE,AND N. HACKERMAN
3 18
Table I
T
Sample
Area, m.P/g.
Crystal
A
2.72 104" 221
a-AlzOi r-AlzOs Amorphous
B C
Sample B was previously reported to have a specific surface area of 109 m.2/g.
The pressure of the water vapor in equilibrium with the adsorbent was measured with a manometer containing Apiezon C oil. The samples were allowed to equilibrate with water vapor until no measurable pressure change could be observed over a period of 1 hr. Water vapor was added in repeated small doses allowing only minor pressure fluctuations. This was done to minimize any effects due to adsorption irreversibility. For all samples the heat of immersion curves were determined with pressure increasing. Samples B and C were also saturated with water vapor and the heat of immersion curves were determined for samples equilibrated on the desorption branch of the isotherm. The calorimeter is of the twin adiabatic type with thermistor temperature-sensing elements and has been described previously. 1 All measurements were made a t 25 i 0.1". For samples B and C, thin-walled spherical Pyrex bulbs which shattered completely upon breaking were used. The measured heats for these samples were corrected for the heat of bulb breaking. For sample A, thick walled cylinders with breakable tips were used. The heat of tip breakage for such bulbs has been found to be negligible.2 For samples A and B, the adsorption isotherms previously determined4 were used. For sample C, the adsorption and the desorption isothernis were determined in this work using a volumetric apparatus already de~cribed.~ The integral entropies of adsorption were calculated from the equation6
I n this equation, X, is the entropy per mole of the adsorbate, X,is the entropy per niole of bulk liquid adsorbate, L' is the heat of inimersion of the solid with ns moles of water preadsorbed, Uo is the heat of immersion of the clean solid, and T is the free energy of adsorption calculated from the Gibbs equation. Equation I assumes that the adsorbent is inert. The Gibbs equation was used in the form The Journal of Physical Chemistry
=
RT
s,"r d l n P
In this work, r was replaced by n, which is expressed as moles of adsorbate/g. of adsorbent, and A was calculated in units of kcal./g. of adsorbent using plots of n,/P us. P / P oand integrating graphically.
Results and Discussion Figure 1 shows the isotherms used for this work. Those for A and B were reported4 to be reversible at all relative pressures. In ref. 4, the desorption process was riot carried to very low relative pressures so that these data are not available. The isotherm for sample C as obtained in this study has an open loop which did not disappear upon measurement. The heat of inimersion curves are presented in Figure 2 as plots of A H , in kcal./g. us. n,/g. Calorimeter samples were outgassed, film equilibrated, and immersed in duplicate. Each heat of immersion curve
Figure 1. Adsorption isotherms for water on alumina powders with ns in moles adsorbed/g. of adsorbent X IO3 ( X IO4 for sample A): A, - - -; B, -; adsorption - - - -; C, desorption - - - -.
c,
(4) R. L. Every, W. H. Wade, and N. Hackerman, J . Phys. Chem.. 65, 937 (1961). (5) N. Hackerman and A . C. Hall, ibid., 62, 1212 (1958). (6) G. Jura and T. L. Hill, J . Am. Chem. SOC.,74, 1598 (1952).
D~FFERENTIAL HEATSOF ADSORPTIONAS
A
FUNCTION OF PARTICLE SIZE
consists of 50 to 75 duplicate points over the entire relative pressure spectrum. For the sake of clarity, experimental points are not shown. The majority of points were for low relative pressures where AH, varies rapidly. The curves for A and B are typical for immersion in water of nonporous metal oxide powders having nonhomogeneous surfaces. Sample C is a gel and the heat curve is typical of samples possessing internal pore s t r ~ c t u r e . ~When plotted as A H , us. P/P in the inset of Figure 2, it can be seen that the heat curve obtained for B after adsorbing to saturation pressure and then desorbing progressively reproduces the curve obtained corresponding to the adsorption branch from saturation pressure back to a relative pressure of approximately 0.1. From a relative pressure of 0.1 back to samples evacuated a t 25" for 96 hr., the heats of immersion of the desorption samples are lower than those obtained from the adsorption branch a t equal relative pressures. This indicates that part of the water adsorbed after outgassing B at 160" is very strongly bonded. The heat
24
I
12
319
5.00
4.00
% (Kcal/molal
3.00
2.00
I .oo
0
0.3
0.7
1.1
1.5
e
Figure 3. Differential heat of adsorption,
QdJ
1.9
vs. coverage, 0 :
A and B for e less than 0.7, -; A for e greater than 0.7, - - - -; B for e greater than 0.7; C, adsorption, - - - -; C, desorption - -. In the inset: A and B, --; C, adsorption, - - -.
- 0.
i
4
n,
6
0
Figure 2. Heat of immersion, A H , , in kcal./g. X I O 3 us. n, in moles adsorbed/g. X lo3: A, - - - ( A H , and n, multiplied by 5 X l o 4 ) ; B, -; C, adsorption, _ _ _ -; C, desorption, - - -. Inset shows A H , in kcal./g. X 103 vs. P!Pa: B, adsorption, , B, desorption, for P/Po less than -0.15 and -for P / P q greater , than -0.15; C, adsorption, - - -; C, desorption, - - -.
-
of imniersion curve obtained upon desorption for C is lower a t all relative pressures than the heat curve obtained when following the adsorption branch of the isotherm. This reflects the irreversible adsorption which prevented closing of the hysteresis loop of the adsorption isotherm. The differential heats obtained by graphical diff erentiation of the heat of immersion curves of Figure 2 are shown in Figure 3 and are relative to the liquid state. Points below a coverage of 0.3 monolayer are shown in the inset. From the inset it can be seen that, at coverages below 0.2 monolayer, the diff ereritial heat curves are approximately linear and decrease extremely rapidly with increasing coverage. There are two possible causes for this drastic decrease i n differential heat with coverage: extreme heterogeneity of the surface and repulsive interactions between adsorbat e niolecules. At these low coverages when the adsorbate niolecules are far apart the latter possibility can be ruled out
I -
-
(7) J J Chessick and A. C Zettlemoyer, Adtan Cntalyszs, 11, 263 (1959).
Volume 65. .Vumber 1 JanitarU 1.963
3 20
R. L. VESABLE,W. H. WADE,AND 9. HACKERMAN
almost completely. The most plausible explanation is that the decrease in differential heats a t these low coverages is caused by adsorption onto a rather wide distribution of energy sites all having relatively high adsorption energies. It would appear that the distribution of these high energy sites is approximately the same for all samples. Adsorption in this region probably results in very strong localized bonding of the adsorbate. I n the rcgion of 0 . 2 4 . 3 monolayer there is a change in slope and another linear portion of the differential heat curve appears where the differential heats still decrease, but niuch less rapidly than before. Since this linear portion begins a t the rather low coverage of 0.3 monolayer, it seems unlikely that the change in slope was caused by interactions between adsorbate molecules. The explanation offered here is that these portions of the curves represent more or less mobile adsorption in the first layer. There must once again be a rather wide distribution of adsorption energies for this mobile adsorption. There is a second transition region in the vicinity of 0.7-0.8 nionolayer which probably represents the onset of adsorbate interactions. For samples A and B this is followed by a third approximately linear portion of the differential heat curve extending almost to the complchtion of the second layer. After completion of the second layer, the differential heat relative to the liquid stale is practically zero for A and B. This clearly shows that the energy of adsorption for the second layer is quite different from that for subsequent layers, which probably resembles the unperturbed liquid stat(.. Sample C has a iiiininiuni and a maximum in this region and there is another such niinimuin and maximum a t higher relative pressures which are not shown here. Those mininia and maxima are thought to be related to capillary condensation in pores8-l0 and will be discusscbd in a subsequent publication. It has been shown" that the surface areas of powders pre-equilibrated with vapors decrease with the amount of vapor adsorbed. In the case of sample C, this change of surface area was shownI3 to be as great as 40y0 a t less than .nonolayer coverage. This certainly invalidates any quantitative concept of surface coverage for C. However, for comparison with saniples of other
not significant because the differential heats for this coverage range were obtained from the very steeply sloping portions of the heat of immersion curves of Figure 2 and the adsorption isotherms of Figure 1. Therefore, small errors in the graphical differentiation process lead to rather large errors in the differential heats obtained. It should be pointed out, though, that when the differential heats are plotted i n kilocalories per mole of water adsorbed us. moles of water adsorbed, the areas under the respective curves give the experimental heats of adsorption, exclusive of the heat of liquefaction of water, within ~ 5 % . This means that the differential heats shown are probably very nearly correct. Since the differential heats in the low coverage region are considered to be due to localized adsorption, this similarity of differential heats probably indicates that the energy distribution of these adsorption sites is quite similar for the three samples. The differential heats in the coverage range from 0.3 to 0.75, which are thought to represent mobile adsorption during formation of the first layer, are very nearly the same for A and B. However, the differential heats during formation of the second layer are niuch higher for A than for B. This indicates that the longrange forces responsible for the energy of interaction of the second layer are stronger in -4than in H. Therein probably lies the reason for the heat of immersion in ergs/cni.2 for the clean solid being higher for A than for B.3 The energy of mobile adsorption during formation of the first layer is lower for C than for ,4or B. This is probably the reason that the heat of immersion of the clean solid is even lower for C than for B. Figure 4 shows plots of the integral entropy of adsorption, A&, us. coverage. It is interesting to note that during formation of the first layer, the entropy change per mole of adsorbate is very close for all three samples a t equal coverages. During formation of the second layer, the entropy change per mole of adsorbate on A is greater than for B or C. This would result from a greater ordering of the adsorbate molecules in the second layer on A and can be correlated with the greater energy of interaction as seen from the differential heat curves. The magnitude of the entropy change for adsorption cannot be overlooked. The entropy per mole of liquid
samples Seem t o be approximately equal at, equal coverages. h y apparent differences probably Stre
(12) Pierce, ibid.. 62, 655 (1958). (13) N. Hackerman and W. H. Wade. ibid., 68, 1592 (1964).
The .Journal of Physical Chemistry
c.
DIFFERENTIAL HEATSOF ADSORPTION AS
A
FUNCTION OF PARTICLE SIZE
32 1
impossible to separate the contribution of the adsorbent from that of the adsorbate.
Summary and Conclusions
0
-4
AS (e.u.1
-0
-12
-I 6
-20
0.3
0.7
1.1
e
1.5
I .9
Figure 4. Entropy of adsorption A S in cal. deg.-l mole-' us. coverage, e: A, - - -, B and C, -.
water a t 2 j a is 16.72 cal./deg. Since ASa is negative and greater than 16.72 cal./deg. a t low coverages, this indicates perturbation of the solid adsorbent. I n fact, adsorption theory based on an inert adsorbent requires a minimum in the integral entropy curve in the neighborhood of the monolayer.6 There is normally an increase in the entropy of the adsorbate a t low coverages relative to the entropy of the liquid state followed by a decrease a t high coverages. No minima are observed in the entropy curves presented here. It should be remembered that the A S calculated by eq. 1 contains the entropy change of the adsorbent as well as that of the adsorbate. If the entropy change of the solid is large and negative, it can override the increase in entropy of the adsorbate a t low coverages. This change in the entropy of the adsorbent invalidates the concept of calculating the thermodynamics function of the adsorbate species in such systems because it is
Heats of immersion have been measured as a function of coverage with preadsorbed water for the alumina samples with widely differing specific surface areas. From these heat of immersion curves, the differential heats of adsorption relative to the liquid state were obtained by graphic differentiation. The differential heats showed that the adsorption energies for formation of the first layer on the substrates apparently can be divided into two broad classifications: one representing localized adsorption and the other mobile adsorption. Differences in the adsorption energies for mobile adsorption in the first layer are probably the reason that the heat of immersion of the clean solid in ergs/ cm.2 for sample C is lower than for h or B.3 The differences in the heats of immersion for samples A and B appear to arise because the adsorption energies for formation of the second layer are higher for A than for B. The energies of adsorption during formation of the second layer are clearly shown to be considerably greater than for subsequent layers. The differential heat curves for both the adsorption and desorption branches of the isotherm for saniple C have maxima and minima which are related to capillary condensation. These data appear to support the previous hypothesis that the major differences between different A1203 surfaces lies in differences in surface order or crystallinity. The electrostatic field strength and hence field-dipole interaction energies are greater a t large distances for ordered (low-area) samples. The apparent high second layer heats of the high-area gel sample arise from extraneous factors such as capillary condensation and extreme surface area diminution.
Acknowledgments. The authors wish to thank the American Petroleum Institute and the Robert A. Welch Foundation for their support of these studies. Also, appreciation is expressed to 11r. ,James E. Gardner for making the calorimetric measurements and to A h . Jerry ;\[atlock for deterniining one of the adsorption isotherms.
Volume 69, Number I
January 1966
