J. J. FRIPIAT AND J. UYTTERHOEVEN
800
Vol. 66
HYDROXYL CONTENT I N SILICA GEL “AEROSIL” BY J. J. FRIPIAT AND J. UYTTERHOEVEN Laboratoire des colloides (I.N.E.A.C.) et de Chimie Mindrale, Agronomic Institute of the University, Heverlee, Louvain, Belgium Received August $4, 1961
Changes in the hydroxylic surface of silica gel as a function of temperature are studied by different techniques. From the comparison between infrared data and thermogravimetric determination, a distinction can be clearly made between constitution and adsorbed water. New chemical methods for the determination of surface hydroxyls also are described, using the reaction either with CHaMgI or CHaLi and volumetric measurement of the CHaevolved. The discussion and interpretation of the results collected from physical and chemical methods permit the distinction between adsorbed water, inner hydroxyls, and surface hydroxyls.
I. Introduction The relative distribution of the two classes of hydroxyls in silica gels, one corresponding to physically adsorbed water and the other to constitution hydroxyls, never has been completely resolved. Thermogravimetric or differential thermal analysis does not permit the distinction since, upon heating silica gels, a continuous loss of water occurs over a large temperature range. Infrared spectroscopy gives considerably more information: the H20 deformation band around 6 p and the -OH stretching vibration in the 3 p region do not overlap but water hydroxyls contribute t o the intensity of the last one and the separation between inner and surface hydroxyls is not easy. The diborane technique allows, according to Shapiro and Weiss,l and Iiaccache and Imelik,2 the distinction between hydroxyls and adsorbed water by studying the hydrogen/diborane ratio as a function of the outgassing temperature. Their assumption is based on the fact that, following the increase in the distance between hydroxyls, this ratio will change from two t o one. However, whether hydroxyls in close proximity mill behave as water molecules or not is still open to question. These authors found that a portion of the hydroxyls are located inside the gel particles. The objective of this paper was to combine infrared and chemical determinations in order to distinguish adsorbed water from constitution hydroxyls and, by a new method, to separate inner and surface hydroxyls. The basis of the chemical technique was to use OH- specific organometallic reagents. Zugaeff and Zere~vitinoff~were the first t o make use of methylmagnesium iodide (CH3MgI), while Gilman, Benkeser, and Dunn4 proposed methyllithium (CH3Li),in which the stronger ionic character of the carbon-metal bond increases the reactivity. In both cases, reaction with water or hydroxyls occurs as HzO
+ MCHs
CHd
+ MOH
or (1) J. Shapiro and II. G. Weiss, J . Phya. Chem., 67, 219 (1953); H. G. Weiss, J. A. Knight, and I . Shapiro, J . Am. Chem. Soc., 81, 1823 (1959). (2) C1. Naccaohe, J. Frangois-Rosetti, and B. Imelik, BulE. sor. china. France, 404 (1959); C1. Naccache and B. Imelik, {bid., 553 (1961). (3) V. Grignard, G . Dupont, and R. Locquin, “Trait6 de Chimie Organ.,” Tome V, Masson et Cie., Paris, 1937. (4) H. Gilman, R. A. Benkeser. and G. E. Dunn, J . Am. Chem. Soc., l a , 1689 (1950).
=Si-OH
+ MCHs +S S i O M + CH,
& represents !I either MgI or Li. Deue16was the first to propose the application of methylmagnesium iodide to the quantitative determination of surface hydroxyls in clays by volumetric measurement of methane. Fripiat, Gastuche, and Uytterhoeven6 published a comparison of data obtained for kaolinite from isotopic exchange and by an organometallic reaction. 11. Experimental (1) Sample.-Aerosil “Degussa” was used for this research. It is a high purity silica gel, prepared by flamehydrolysis of SiC14. The B.E.T. surface area amounts to 180 m 2g.-1. Granulonietric distribution, as given by the maker, shows a sharp maximum for a diameter of 20 p . The surface distribution as a function of the average pore radius is given in Fig. 1, according to the Pierce? method. Even the narrower pores allow an easy accessibility of the whole surface to both kinds of organometallic molecules. Films suitable for infrared study were made by spreading 20 t o 40 mg. of the gel between two polished steel blocks. Pressing under about 2000 p.s.i. for 5 min. produces a film, weighing 10 to 20 mg./cm.2, coherent enough to permit careful handling. (2) Chemical Device.-The control of the sample hydration level is absolutely necessary: for this reason a device was built in order to allow preparation of sample and reagent under vacuum. It is represented in Fig. 2. Samples were dehydrated in furnace 1 under vacuum a t a given temperature. This operation requires about 15 hr., down to a residual pressure of 1 0 - b mm. The stopcock between I and I1 is closed and reagent is introduced into vessel I1 and outgassed for half an hour. The sample is introduced in vessel I1 by withdrawing the magnetic rod supporting the sample holders in furnace I. A good mixing is obtained with a magnetic stirrer. The methane is purified by distillation a t low temperature in 3a and 3b, trapped in 3c, according to a technique proposed by Coppens,8 and introduced in volumetric vessel 5 by means of a Topler pump 4. Mass spectrometric analysis has confirmed the purity of methane collected. Averaged results for several analyses were the following: 99.30% of CHI; 0.44% Nz; 0.15% 02; 0.11% CZhydrocarbons. (3) Reagents.-CHaMgI was easily produced by mixing CHI1 and n’Ig in anisol; its concentration is about 0.2 mole 1
1.
-1
-
CHsLi is obtained in diisoamylic ether by mixing Li and CHJ, added progressively with good stirring and under nitrogen atmosphere. A concentration of about 0.2 mole l.-lwas obtained. (4) Infrared Spectroscopy.-The thin film is carefully inserted in a copper block having a rectangular hole 2 X 1 cm. The film was held in place by, a thin platinum screen. The block, containing a heating wire and a thermocouple, can be introduced in a vacuum cell, the design of which (5) H. Deuel and G. Huber, Helu Chim. Acta, 34, 1697 (1951). (6) J. J. Fripiat, M. C. Gastuche. and J. Uytterhoeven, Pbdologie, 7, 39 (1057). ‘(7) C. Pierce, J . Phys. Chem., 57, I49 (1953). (8) L. Coppens, Bull. SOC. chim. Belg., 43, 335 (1934).
HYDROXYL ComEivr
May, 19G2
IN
SILICA GSL
801
ha- been given elsewhere.19 The spectra can be recorded either under vacuum or a t atmospheric pressure. Infrared spectra were obtained using B Beckmrtn IR4 double beam, fitted with CaFl optics. Two spectral regions were covered: the first around 2.8 p for the OH stretching band and the second one around 6.1 p for the &O deformation hand. In this region, a harmonic 01 a S i 0 vibration could be exnected. accordine to Little and Mathieu.Q Tatlock and Iiocho+ hsve shown that ahsorption a t 6.1-6.2 p &p ears in molecules where B silicon atom carries two hydroxyi hut the same hand-even more i n t e n s c i s ahserved for the corresponding disodium salts. Moreover, Irom theoretical considcrstions of the expected
e::
frequency 01 the Si
deformation, it may he concluded that
gcminxl hydroxyl pairs carried by silicon cannot produce m ahsorption hand in the lrequency range where the water deformation hand is found.
III. Theoretical Basis 1. Infrared Determinations.--Let
I be the
integrated intensity of either considered band
0
20
60
40 i,
(A,).
80
100
Fig. 1.-Pore distribution: relative specific surface area developed by pores with radii wider than i, (in A,).
where A , is the absorbance at the frequency Y. We will prove that the Beer-Lambert law is obeyed, but radiation loss by scattering must be taken in account. If X represents the individual OH belonging to the gel and Y the water molecules physically absorbed, the total hydroxyl content N is given by N = X + 2 Y
Therefore
(2)
Ir = krlN
- A2
(3%)
I , = k$Y
- As
(3h)
and Where k3 and k6 arc the absorption Coefficients, 1 the optical path through the sample, AS the scattering loss in t,hc 3 p region, and A s the scattering loss in the G p rrgion plus the absorbance due to an eventual Si0 harmonic. I 3 and Is are obtained by graphical integration of the curve of absorbance us. wave number. They are measured at different temperatures, in other words, at different OH and €LO contents, and can be comparcd with gravimct,ric detcrminat,ions. From @)and (3), we may write
-+
(4)
Wherela* = la A,. A~iscalculatedfromextrapolation to N 0 of the linear plot 1 3 us. N , N bring known from gravimrtric determinations (Vig. 3). Let us write formally thr differential of ( 2 ) and (3) with resprct to N . The optical path 1 is equal to (l/k,)(dIa*/dN) and
If wc consider a theoretical rehydralion process, X will reach slowly a constant valuc whrn N in-
creases, since tho surface becomrs saturated in hydroxyls. Therefore, by measuring the derivatives d16/dN and d13*/dN at the beginning of the dehydration process of a saturated gcl, the ratio (9) L. H. Little and M.
V. Matbieu. dcue, I 1 Intern. Conv. ColdyPoria. 1, 771 (1861). (lo) W. S. Tatlock and E. 0.Rocboa. J . 010. Chcm.. 17, 1555 (ie5a).
sia.
Fig. 2.-Appar&us
v
for surface O H dsterminntion (ace tcxt).
of absorption coefficients lc3/k6 is given by assuming dX/dN = 0. It follows that, in relationship (i written as
(3,
the first member contains known values only. If plotted against temperature, it will decrease until reaching the A& constant level. This ratio is graphically determined. Introduced in (6), Y is calculated in the range of temperature where physically adsorbed water exists upon the surfacc. When it disappears, N is equal to X according to relationship 2. In this way, hydration water and hydroxyls can be distinguished and estimated. The main implicit approximation involvrs assuming k~ constant whatever the kind of hydroxyls includcd in the band. (2) Chemical Determinations.-lteactions hrtween organometallic molecules and hydroxyls proceed fundamentally in two ;qtcps. The first one is characterized by a very rapid methane evolution which becomes much slower during the srcond step. In this case, the amount of gas collrcted increases linearly with time. We believe that the
J, J, FRIPIAT AND J. UYTTERHOEVFN
882
Vol. 66
This graphical procedure thus was used for the silica gel study. The apparatus does not allow the kinetic study of the first step: it is impossible to measure volumetrically the CH4 produced within the first 10 min., and beyond this limit the first step is
2.8 -
2.4 -
over.
-8
8
- 6 q
-5
-4 -3
400 500 600 700 800 900 Temp., C". Fig, 3.-In abscissa : sample outgassing temperature under vacuum. Curve 1, OH (gravimetric) content (including HzO); curve 2, evolved CH4 for the reaction with CH3Li ( 0 )and CH3MgI ( 0 ) ; curve 2a, correction for physically adsorbed water (see text); curve 2b, true OH surface content; curve 3, H20 content (in OH) as determined by infrared.
100
200
300
As far as reagent autolysis is concerned, opinions differ widely according t o experimeiitersll-ls but they agree in concluding that decomposition compounds contain mainly CZ hydrocarbons. This seems in contradiction with our mass spectrometer measurements. L. A. Woodl4 observed some methane evolution from methyl derivatives of Li and Mg. He considers a possible uptake of hydrogen from ether molecules, used as solvent. With triphenylmethane and anisol, methyllithium reacts either with hydrogen located in the ortho positioii of the aromatic ring or directly with the methane hydrogen. In our experiments, the spontaneous CH, evolution during the second step amounted t o 0.3 mole
3 210
2oo
I
t
TABLE I REXCTIOK O F ORGANOMETALLICS
Run
vI VI1
0
20
40 60 80 Time, min. Fig. 4.-fi-moles CH, evolved with respect to the time (in min.): 1, autolvsis of CHzMgI; 11 and 111, a u t o b i s of CH3Li; IV, V, VI, and VII, reaction with increasing amounts of @-naphthol(see Table I).
Introduced amt.
(&moles)
118 124 154 192
WITH P-XAPHTHOL CH4 evolved (pmoles) Reagent
121 133 153 201
CHsLi CH3Li CHsLi CHsMgI
min.-' at 20' in the usual concentration range, about 0.2 mole l.-I. As compared with the first step, errors due to autolysis accounted for a few per cent. only. IV. Experimental Results (1) Chemical Determinations.-Experimental results are gathered in Fig. 3. It may be observed that both organometallic derivatives give the same results. This suggests the absence of steric hindrance since the radii of CHJ!lgI and CH3Li molecules are very different. Ip close packing, the l\lgI radical covers about 17 A. The solvation also must be considered, CH&Tg;I forming a very stable "dietherate" complex. However, results obtained with this reagent using anisol or isoamyl ether as
May, 1962
HYDROXYL CONTENT IN SXLICA GEL
The low frequency OH, corresponding t o strongly h ydr logen bonded hydroxyls disappears before the high frequency OH, from the weaker hydrogen bridges. Young,15 Sidorovle, Zhdanov, l7 and Kiselev and LyginlS already have observed this fact. In favorable conditions three components a t least may be distinguished: isolated OH are responsible for the 3750 cm.-l band, hydrogen bonded hydroxyls for the 3660 em.-' component, and adsorbed water for the low frequency one, a t 3456 cm.-l. In the OH range, the distinction is not very clear but it appears clearly in the OD region according to Fripiat, Gastuche, and Bricha,rd.Ig From the study of the OD stretching, they were able to calculate the relative OD contents corresponding with the three main absorption peaks observed in this spectral range. In Table 111, these figures are comlpared with the ones obtained by the method under discussion. The two independent sets of measurements can be considered in accord despite the poor distinction of the three main stretching characteristics. The intensity of the HzO deformation band at 6 p decreases regularly with increasing temperature. Figure 5 gives, for different film weights, the variation in the ratio 13*(T0)/13*(20') against the N ( T o ) / N (20') ratio. The linearity of the experimental results verifies relationship 3a. The k3/JC6 ratio was calculated for six experiments, run with six different films. The mean value amounts to 14.8 f 0.9. Table I1 contains the OH ( X ) and HzO ( Y ) contents, calculated according to the theory given above (relationship 6), taking into account the experimental gravjmetric content of Fig. 3. At temperatures higher than 300°, adsorbed water has completely disappeared. As soon as the HzO ( Y ) content is known, experimental curves of Fig. 3 may be corrected since, when reacting with organometallics, a water molecule accounts for one hydroxyl only (see Fig. 3).
803
preciably.
1.0
e
0.4
0.2
0.4 0.6 0.8 1.o I,*/&* msx. Fig. 5.--Ia*( T0)/13*(200) plotted against N ( To)/N(2O0) for different film weights: 0,22.2 mg.; 0 , 21.2 mg.; V, 27.5mg.; A,24.5mg.; 0,28.6mg.; 0,27.8mg.percm.2. 0
0.2
TABLEI11 COYPARISOX BETWEEN Y AND X OBTAINED FROM RELATIONSHIP 6 AND THE CORRESPOKDING VALUESCALCULATED OK THE BASISOF THE OD ABSORPTION BAND'@ ( Y OR X I N 10-3 MOLEG.-1 AT ATMOSPHERIC PRESSURE)
+
OC.
Y
DzO
X
Isolated OD deuterium bonded deuteroxyls
25 60 90 140 200
1.56 0.94 .44 .24 .10
1.27 0.83 .54 .34 .18
2.78 2.92 3.10 2.97 2.95
3.37 3.13 2.97 2.76 2.67
Temp.,
The averaged hydroxyl contents measured under vacuum or a t atmospheric pressure agree very well and may be considered as constant below 300". Beyond this limit, X becomes confounded with N TABLE I1 (gravimetric), since Y = 0. WATER( Y ) AND HYDROXYL COXTEXT (X) FROM INFRARED DETERMINATIONS (IN MOLEG.-l) Since corrected results for organometallics and ----Under vacuumY A t atm. pressure-. gravimetric curves do not coincide, it may be conTemp. Temp. cluded that only a portion of the hydroxyls is ("C.) Y X (OC.) Y X located on the surface. 20 0.42 2 76 25 1.56 2.78 60 .30 2.90 60 0.942 2.92 The ratio of surface hydroxyl to total hydroxy 100 .23 2.75 100 .44 3.10 content can be estimated from the ratio [(CH,) 140 .I7 2 96 140 .24 2.97 Y ] / X , where (CH4) represents evolved methane. Calculated values are expressed with respect to 200 .06 3.03 200 .10 2.95 240 03 2 94 temperature in Fig. 5. Av. hydroxyls content: Av. hydroxyls content: The ratio is constant and approximately equal t o 2.89 (below 300") 2.94 (below 300") 42y0 below 240'. Above this limit, it decreases and reaches a minimum at about 500', afterwards (15) G.I. Young, S. Colloid Sei., 13, 67 (1958). it increases sharply up to 100%. O'Reilly,20from (16) A. N. Sidorov, Optics and Gpectroscopy, 8, 424 (1960). n.m.r. determinations, has shown that above 500' (17) S. P. Zhdanov, ZhUt. Fiz. Khim.. 32, 669 (1968). residual protons in silica gel belong to isolated and (18) A. V. Kiselev and V. I. Lygin, Colloid J., 21, 561 (1959); Proc. See. Intern. Congt. Surface Activity, London, 11, 1957; A. V. randomly distributed silanols. Kiselev, 10th Colston isymposium, Butterworths, London, 1958, p. 210. (19) J. J. Fripiat, NL C.Gastuohe, and R. Briohard, J. Phys. Chom., 66,805 (1962).
(20) E. D. O'Reilly, Am. Chem. SOC. National Meeting, Boston, Bpril, 1959, Abstracts, p. 157.
J. J, FRIPIAT AXD J. UYTTERHOEVEN
804
-
0
200
600
400
800
Temp., "C. Fig. 6.-Relative surface hydroxyl content as a, function of outgassing temperature.
V. Discussion de Boer, et al., have shown from adsorption isotherms that physical adsorption of water vapor on silicas ceases a t temperature above 120'. The results of Table I1 demonstrate that individual water molecules still exist beyond this limit . The main argument which supports this viewpoint is that either under vacuum or at atmospheric pressure, numbers of water molecules represented by the Y values of Table I1 reach zero simultaneously a t approximately 300'. On the other hand it seems that the intimate structure of silica gels affects the temperature of removal of adsorbed water. The same argument holds for the distribution of constitution hydroxyls. Young,14by infrared, and Shapiro and Weissl and Naccache and Imelik,2 from the diborane technique, arrived a t the conclusion that a part of the hydroxyl content must be located inside the primary particles. From their results, it follows that the nature of the gel has a deep influence. I n Table IV, we compare our results with those found by others. and indicate also the critical temperature range beyond which the removal of individual water molecules is completed. The data obtained from infrared spectra agree satisfactorily with the observations of Naccache and Imelik.2 TABLE IV RELATIVE SURFACE HYDROXYL CONTENT AS A FUNCTION OF TEMPERATURE Gel
Ref.
Xerogel Xerogel Aerogel Aerosil
1 2 2
This work
-Temperature156O 400°
73%
..
68% 95% 48% 93% 42% 30%
-.
750'
100%
Critical temp. range, OC.
...
.. .
300-400
90%
300 300
...
Vol, 66
In order t o compare our results concerning hydroxyl distribution with those of others, the physically adsorbed water must be taken into consideration. In our calculations, it haa been discarded as indicated. This was not done for the data of the other authors cited in Table IV. Since only temperatures higher than 159" are used, errors should not be very considerable. It follows that Aerogel and Aerosil have a low relative surface hydroxyl content as compared with Xerogel. At the right side of Fig. 3, a OH surface density scale has been drawn, taking into account the B.E.T. surface area. It may be observed that the hydroxyl packing below 300' amounts to 4.2 units per 100 A.2. de Boer and Vleeskens121when dehydrating and rehydrating siIica gels several times, have shown the maximum OH density never exceeds 4.6 units per 100 A.z. Aerosil, by the preparation used here, presents a close analogy with the gels studied by de Boer and Vleeskens. StoberlZ2 from structural considerations, proposes 4.4 OH per 100 A.2 as a theoretical value for the surface hydroxyl density; experimentally he found 3.75 for aerosil. Our result agrees very well with predicted surface density and confirms indirectly the hypothesis previously exposed. IlerZaestimated, from a structural analogy between silica gel and cristobalite, the OH surface density to be equal to 7.85 OH groups per 100 while Dzisko et proposed 6.70 OH per 100 daZ.It is probable that surface density for xerogels tends toward this value while aerogels, or aerosil, are characterized by a lower surface density, closer to the value proposed by Stober, i e . , 4.4 OH/100 A.2. I n the first case, a high percentage of surface silicon is bonded to two hydroxyls, in the second one the average ratio (OH/Si) would be closer to one. Kaccache and Imelik,2 Bastick,26 and Youngt5 observe that the sintering temperature of an aerogel is lower than for a xerogel (500' against 700'). It generally is accepted that sintering results from condensation of OH groups belonging to different primary particles followed by siloxane-bridge formation. The change of the relative hydroxyl content of the surface with respect to temperature (Fig. 6) suggests, however, another interpretation. Between 300 and 500' dehydroxylation takes place by condensation of surface hydroxyls, as indicated by the decrease of the relative OH surface density. At higher temperature, diffusion of inner hydroxyls toward the surface becomes very important. At the same time, sintering occurs and it may be that it is the diffusion of inner constitution water rather than the condensation of OH belonging to different particles which is a t the origin of the phenomenon. The diffusion of internal water may greatly modify the gel structure. This hypothesis needs further investigation. (21) J. H. de Boer and J. H. Vleeskens, Koninkl. Ned. Aload. Wetenechap. PTOC., BG1, 3 (1958). (22) W . Stober, Kolloid-Z., 145, 17 (1956). (23) R. K. Iler, "The Colloid Chemistry of Silica and Silicates," Cornel1 Univ. Press, Ithaca, N. Y., 1855. (24) V. A. Dzisko, A. Vishneskaja, and V. S. Chesalova, Zhur. Ftz. Khim., 24, 1416 (1950). (25) J. Bastick, Bull. E O C . chkm. France, 20, 437 (1953); Chsm. & 2nd. (Paris), '78, 2' (1957).
SURFACE HETEROGENEITY IN SILICAGEL
May, 1962
The experimental results presented here also may contribute to the knowledge of water absorption sites on silica gel surfaces. Sidorovlfl and Zhdanov” published experimental evidence that hydroxyl pairs (as opposed to isolated OH) may be the main. adsorption sites, but they define “sites of second kind” as oxygen from siloxane bridges. Young does not distinguish between hydroxyls and considers the silanol radical as the mater adsorption site. Kiselev and Lyginl* emphasize the importance of hydroxyl pairs resulting in the formation of the “ring” st,ructure. H
-Si.- I
H
I
0--Si-
I
I
Between 20’ a,nd 250-300’, the amount of surface hydroxyls (Fig. 3, curve 2a) remains constant and equal to 1.2 X mole g.-l. If each water molecule is held by two hydroxyls, the surface provides a maximum of 0.6 X mole g.-I adsorption sites. On the other hand, a primary adsorbed molecule can act as a center for further condensation.
805
Table I1 gives the amounts of adsorbed water either under vacuum or a t atmospheric pressure. By assuming that under vacuum, “primary” molecules only subsist, it may be concluded that the amount of physically adsorbed water does not exceed the possibilities offered by hydroxyl pairs but remains far below the theoretical value given for isolated hydroxyls. This is not presented as a direct argument for Kiselev and Lygin’s model but as an indication favorable to it. Fripiat, Gastuche, and Brichard,l$ by isotopic exchange, have given more direct evidence which agrees with this viewpoint. Young15 has shown that after silica gel has been activated a t a temperature higher than 650’, rehydration produces a OH stretching absorption band where the shoulder a t 3456 cm.-l, attributed to water hydroxyls, decreases in intensity and finally disappears under vacuum. The thermal activation beyond 650’ causes the surface available for water to decrease simultaneously. Results given in Table I11 show that the intensity of adsorption a t 3460 em.-’ follows approximately the evolution of the water content ( Y ) and disappears completely only above 300’. Young’s results may be explained on the basis that the activation procedure eliminates the more powerful adsorption sites.
SURFACE HETEROGENEITY I N SILICA GEL FROM KINETICS OF ISOTOPIC EXCHANGE OH-OD BY J. J. FRIPIAT, M. C. GASTUCHE, AND R. BRICHARD Laboratoire des collo?des (I.N.E.A.C.),Institut Agronomique, UniuersitS de Louuain, H&erlS-Louvain, Belgium Received November 8, 1961
The heterogeneity of the hydroxylic surface of a silica gel is demonstrated by following the isotopic exchange OH-OD by infrared spectroscopy using the three main components of the stretching vibration band. The first-order law is obe ed but the rate constants-which can be measured separately-differ according to the OH species. These are introducedl in the Marcus relationships assuming limitative models in order to decrease to three the number of transport coefficients. The nature of the hydroxylic surface and the values of the first-order constants permit the use of the most likely diffusion model as -+ isolated hydroxyls vapor phase 6 bridged hydroxyls+adsorbed water The privileged location in this sequence of the bridged hydroxyls probably comes from the fact that they constitute the main adsorption sites.
I. Introduction Several studies dealing with surface heterogeneity have been published during recent years. Isotopic exchange has been widely used in order t o investigate the number of different adsorption sites present a t the solid-gas interface.1 Generally, the change of isotope atomic fraction x in the gas phase is followed in function of the time t. For homogeneous surfaces, a first-order law in the distance from equilibrium is observed. For heterogeneous ones, this must be replaced by a sum of exponentials such as I---= zm
i=n-I
e’=l
~
i
e
-
~
1
~
(1)
where xm represents the equilibrium value in the (1) G. 2. Ropinsky, J . ehim. phys. U.R.S.S., 4, 737 (1968).
gas phase; i, the index number of the different site classes; (n - 1) site classes being present in the solid phase, and finally A i and ai are kinetic constants. When observing the gas phase only, the development of the experimental function (1 - x/xm) into (n - 1) exponentials is only theoretical, because, in the most favorable case, the resolution does not (n/2)(n - l ) ]unallow the calculation of [n known coefficients since 2(n - 1) parameters only are given.2 Hence, it becomes necessary to make a limitative choice among the possible exchange processes in order to decrease the number of unknowns. Sheppard and Householdera have studied the
+
(2) W.K. Hall, private communication. (3) C. W. Sheppard and A. S. Householder, J . A p p l . Phya., 22, 510 (1961).
