A MULTILAYER MODELFOR
THE
SURFACE TRANSPORT OF ADSORBED GASES
= 0.6 mol fraction. The maximum pressure of KMg2C15would be about 3 mm, compared with a value of 21 mm for KMgCL. The absence of corresponding species such as CsPb2C16 and KPb2C15 from both transpiration and mass spectrometrics evidence is possibly related to the inability of PbC12 to dimerize, in contrast to niIgClz and extent in the latter CdC1z Only to a case17J8). ZMgCla
2365
Acknowledgment. This work was supported by a grant from the Australian Research Grants Committee. J. W. H. was the recipient of a Titan Products Research Fellowship. The specially selected cadmium rods used for preparing cadmium chloride were donated by the Electrolytic Zinc Co. of Australasia, Ltd. (18) F. J. Keneshea and D. D. Cubiciotti, J . Chem. Phys., 40, 1778 (1964).
A Multilayer Model for the Surface Transport of Adsorbed Gases by Weldon K. Bell and Lee F. Brown Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80506
(Received October 60, 1967)
A model for the multilayer flow of adsorbed gases is developed and its application to surface migration in microporous media is investigated. Transport within a n individual layer is viewed as resulting from a twodimensional spreading-pressure gradient, and momentum exchange between adjacent layers is represented by a simplified law. Equations for the concentration of each layer are developed within the framework of B E T adsorption theory. Employing a circular-pore geometry, a two-parameter relation results which describes the adsorbed flux. The model is applied to published experimental data. The values obtained for the two parameters exhibited concentration dependence, temperature dependence, and relationship with each other in agreement with physical expectations. The quantitative values of the parameters are dependent upon the assumed number of adsorbed layers, however, and this represents a weakness of the model.
Introduction Previous investigators of the surface transport of adsorbed gases have described it by a single-phase flow utilizing a spreading pressure or with models based on random molecular movement between adsorbed sites. These models do not consider the possible multilayer nature of adsorption nor do they allow for the diluteliquid behavior of these adsorbed layers. This article presents a multilayer model for the flow of adsorbed gases and investigates its application to surface transport in microporous media. For many years the transport of adsorbed gases has been generally accepted and has come to be known as “surface migration” or ‘(surface diffusion.” A recent review of the surface diffusion of adsorbed molecules is that by Dacey.’ Hayward and Trapnel12 provide a fairly complete discussion of the surface mobility of chemisorbed species. I n Dacey’s review, four regions for surface flow in porous solids are considered. The first region occurs at very low pressures where surface coverages are very small. At somewhat higher surface concentrations, a region of less-than-monolayer coverage occurs. Multilayer coverage is significant in the third region, while capillary condensation exists in the fourth.
To explain the surface flow in these regions, several models have been p r o p o ~ e d . ~ -While ~ none correlates the data in all regions, the models proposed by Smith and I v l e t ~ n e rand ~ ~ by ~ Gilliland, et a1.,4t5have had fair success. Smith and Metzner’s equation for surface flow was derived from a basis of random molecular motion between adsorbed sites and fits data well at low coverage. Gilliland, et al., proposed a single-phase flow resulting from a spreading pressure and obtained the best results at low- and intermediate-adsorbed concentrations. Both assumed only a single surface layer. Since multilayer coverage begins to assume significant (1) J. R. Dacey, Ind. Eng. Chem., 57, 27 (1965). (2) D.0.Hayward and B. M. W. Trapnell, “Chemisorption,” 2nd ed, Butterworths and Co. Ltd., Washington, D. C., 1964. (3) 5. Kruyer, Koninkl. Ned. Akad. Wentenschap. Proc., 56B, 274 (1952). (4) J. 8. Russell, 8c.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1963. (6) E. R. Gilliland, R. F. Baddour, and J. S. Russell, A.I.Ch.E. (Amer. Inst. Chem. Eng.) J., 4 (1958). (6) R. K.Smith, M.Ch.E. Thesis, University of Delaware, Newark, Del., 1963. (7) R. K.Smith and A. B. Metsner, J. Phgs. Chem., 68,2741 (1964). (8) J. A. Weaver and A. B. Metsner, A.I.Ch.E. (Amer. Inst. Chem. Eng.) J . , 12, 656 (1966). Volume 78, Number 7
July 1968
WELDONK. BELLAND LEE F. BROWN
2366 proportions at concentrations far below that corresponding to a BET monolayer, it was decided to study theoretically the possible behavior of surface flow in multimolecular layers.
Derivation of the Model A . Basic Assumptions. This section presents a simplified model for the multilayer flow of adsorbed molecules utilizing a two-dimensional “spreading pressure” within the different layers. The model is based on the following assumptions. (1) The net transport within an individual layer is caused by a gradient in the spreading pressure. ( 2 ) The two-dimensional pressure in a layer is a function only of the concentration within that layer. (3) The momentum possessed by a given layer is proportional to the product of the concentration and velocity of that layer. The momentum exchanged between two layers is proportional to the difference in the momenta of the two layers. (4) The concentration within a layer is equal to that predicted by the BET adsorption theory. ( 5 ) The two-dimensional pressure is characterized by a two-dimensional equation of state. (6) The thickness of each adsorbed layer equals the diameter of the adsorbed molecule as calculated from the critical volume. In order to determine the concentrations of each layer, the multilayer adsorption theory developed by Brunauer, Emmett, and Teller (BET)s is used. I n the BET derivation st is defined as the area of surface which is covered by only i layers of molecules ( i e . , so is the free area and s1 is the area covered by only one layer but not the total area of the first layer). It is also shown that si = zsi-1
= z-s1
(1)
This relationship according to the BET theory holds for any number of layers. B . Concentration within an Individual Layer. If the BET theory of multilayer adsorption is accepted, the concentration of any layer can be found as a function of the total adsorbed concentration and the relative pressure. The concentration within a layer, x j , is proportional to the sum of the BET areas covered by j or more lavers. Thus The total adsorbed concentration, y, is then the sum of the individual-layer concentrations, so that in general
Figure 1. Momentum balance for the circular pore.
the concentration of that layer and its average net velocity. The total adsorbed flow is the sum of the flows in each layer. It is possible to describe surface flow in a catalyst pellet by a circular-pore geometry. The momentumbalance diagram for multilayer flow in a circular pore is shown in Figure 1. Since the momentum exchange between two layers is assumed proportional to the difference in the momenta of the layers, a momentum balance on layer i yields the following rates of momentum exchange: at r+ in
+k22nr+xt-lul-lAL
out
-k22nr+xiutAL
in
+k2*2 nr-xi+Iut+4L
out
-k2*2~r-x:Iu:IAL
in
+k32nrtx iui
out
-kk32nrt(xiut
at r-
at L at L
+ AL
+ Axtui)
The forces in the direction of flow are: at L, 2 ~ r t 4 ~ ; and at L AL, 2 ~ r t ( 4 ~ A4J. The term Axiuuiin eq is equal to eerO because it is assumed that there is no net transfer of material from one layer to the next. Hence from continuity considerations xtui is constant. It is also assumed that the rate of momentum exchange between any two layers has the same proportionality constant, so that ICz = k2*. Summing the terms and taking the limit as AL approaches zero
+
+
in which the ratios r+/r and r-/r are evaluated for each layer. If n layers are allowed to fill the catalyst pore, these ratios become (n
(3) :I
’Ores* The adsorbed flow *‘ within in an individual layer is proportional to the product of
The Journal of Physical Chemistry
(4)
+ 1 - i) =
(n -
‘/2
- i)
Ct
(6)
(9) S. Brunauer, P. H. Emmett, and E. Teller, J . Amer. Chem. Soc., 60,309 (193s).
A
n/IULTILAYER
);(
MODEL FOR
= I
THE
SURFACE TRANSPORT OF ADSORBED GASES
(n - i) = el (n - ’/z - i)
(7)
2367 N/Acs = ( P / ~ ) I * U
(15)
Solving eq 11
For the first layer, the momentum balance is Combining eq 13, 15, and 16 The constant describing momentum exchange between the first adsorbed layer and the solid (kl) is assumed to be different from that between adjacent layers (kz). de Boer’o shows the spreading pressure can be expressed in terms of concentration by the use of twodimensional equations of state analogous to those for three-dimensional gases. An equation of state analogous to the Volmer equation was chosen for study. This enabled some compensation for nonidealty. The van der Waals equation of state was not used because of uncertainty in the attractive force constant under adsorbed conditions. For the Volmer equation of state 4i(A
- iitb) = EiRT
(9)
and, noting that Bi/A = xt/S
Separating variables and integrating
Equation 18, relating the catalyst properties, the momentum-transfer constants, pressure, pressure drop, and adsorbed concentration to the adsorbed flux, is the basic equation for the multilayer surface-transport theory proposed in this paper. The two-dimensional constants for the Volmer equation of state can be evaluated from its three-dimensional counterpart as presented by de Boer’O b = -3b3 4d
By using the set defined by eq 5 and 8, a system of n simultaneous equations determining the velocities of each of the n layers in terms of their concentrations and spreading-pressure gradients can be obtained. This set of equations in matrix form is
where d = d(3ba/2N,,)1’a. In order to obtain a measure of the thickness of an adsorbed layer, an effective diameter based on volumetric measurements is used. This relation, presented by Moore,” is
0.74~~
For the circular-pore geometry, the maximum number of layers filling the pore is given by
n = D/2t (21) Once n is determined, the matrix and vector elements of the integrand in eq 18 may be evaluated.
L and
H = (RT/S)[g*dxddLI
(13)
I n the above, f = kz/kl. The expression for the total adsorbed flux in terms of the concentrations and surface velocities of each layer is 1
( 14)
Because the adsorbed molecules follow a tortuous path through the microporous plug, the surface velocity and distance along the surface can be related to their average components by the tortuosity factor. So L = rLp and ai = (l/r)ut. Writing eq 14 in vector notation
Investigation and Discussion of the Multilayer Model In order to investigate the multilayer model and to compare it with previous models, data in the form of observed fluxes and the pressure drops at several mean adsorbed concentrations were required. The adsorbedflow measurements selected, which were believed to be the most complete currently available, were those presented by R u ~ s e l l . ~I n addition to surface-flow measurements for ethylene, propylene, and isobutane on Vycor a t three temperatures, the required adsorp(IO) J. H. de Boer, “The Dynamioal Character of Adsorption,” Oxford University Press, London, 1953. (11) W. J. Moore, “Physical Chemistry,” Prentice-Hall Ino., Englewood Cliffs, N. J., 1962. Volume 7.8, Number 7 Julu 1068
WELDONK. BELLAND LEE F. BROWN
2368
9
ADSORBED
CONCENTRATION I N
~rng-rnoleslgrnc,.,)
Figure 2. Flux ratios for propylene a t 298°K. : 0,multilayer; n, Russell; A, Smith.
tion isotherms and the physical description of the adsorbent were included. The parameters for all models were evaluated at the minimum of the sum of the squares of the differences between the predicted and observed values of the surface flux. For the models requiring a single parameter, a linear least-squares method was used. For the multilayer model a search technique was employed to find the values of kl and k2 corresponding to the minimum of the sum of the error squared. No prior assumptions were made concerning the values of or relationships between k1 and kz. The technique is fully described by one of the authors.lZ Comparison with Other Models. Typical results obtained for the multilayer model and the models of Smiths and Russell4 are shown in Figure 2. If the entire concentration range is considered, Smith’s model gave by far the poorest results. Because this model was derived for a unimolecular layer, it might be expected to correlate the data only a t low coverage. At low adsorbed concentrations, the slope of the flux-ratio curve approached zero, indicating that Smith’s model gave its best results in this range. Russell’s model was found to fit the data most satisfactorily a t the higher coverage ranges but showed negative deviations at low concentrations. The multilayer model fits the data in the higher concentration regions as well as the prior models but a t low surface coverages predicts fluxes considerably higher than those observed. The breakdown of the present multilayer surface-cliffusion model within this range is not unreasonable. Ih this model, the momentum exchange between the first adsorbed layer and the surface is characterized by kl. This parameter is probably reladed to the attraction of the adsorbed molecule to the surface. Young and C r o ~ e l lindicate ‘~ that heats of adsorption, also related to the attraction of the adsorbed molecule to the surface, can vary considerably with coverage at low concentrations. While no precise correlation between the heat of adsorption and ICl is suggested, it is probable that on the surface a distribution of the attraction between the surface and the adsorbed molecule exists; at low coverage the value l’he Journal of Physical Chemistry
of kl would be concentration dependent. At lower concentrations the higher energy sites would be selectively filled, and kl would be expected to decrease with increasing coverage. Because kl was found by considering all the data from a given run, the value used to predict the fluxes at low concentrations would be smaller than it should have been, and fluxes that were too large resulted. At higher coverage the possible leveling of the distribution of the attracting sites would eliminate this effect. Behavior of Parameters kl and kz. Comparison of kl and ICz for each data set in Table I indicates that kz is smaller in every case. This would be expeoted, since the molecules in the first layer would be attracted strongly to the solid surface and a momentum exchange with the solid more rapid than that between adjacent layers would result. Table I : Momentum-Transfer Coefficients for the Multilayer-Model Volmer Equation of State Temp,
lo-lokl,
OK
880-1
10-’0kz, 8ec-1
273 298 313
Ethylene 5.818 6.935 5.940
0.1060 0.0469 0.0459
273 298 313
Propylene 3.783 3.107 3.749
0.2417 0.1740 0.0826
273 298 313
Isobutane 5.897 1.879 1.875
0.5390 0,4721 0.3016
The value of kz decreases steadily with temperature in all three of the cases studied. The momentum transfer between adsorbed layers is indicated to decrease with increasing temperature much as the momentum transfer within liquids decreases, as evidenced by the change. of viscosity with temperature. (In gases, on the other hand, viscosity increases with temperature.) The liquidlike behavior between adjacent layers is not unreasonable. Within an adsorbed layer, molecules may be relatively far apart resulting in gas behavior. However, the distances between the centers of molecules in adjacent layers in the direction normal to the surface is of the order of the molecular diameter-the same separation as in liquids. Inspection of the parameter kl indicates no apparent trend with temperature. It is believed that the opti(12) W. K. Bell, M.S. Thesis, University of Colorado, Boulder, Colo., 1967. (13) D. M. Young and A . D. Crowell, “Physical Adsorption of Gases,” Butterworths and Co. Ltd., London, 1962.
A MULTILAYER MODELFOR
THE
SURFACE TRANSPORT OF ADSORBED GASES
mization techniques used to find these parameters would disguise all but strong trends in the data, and thus a hidden temperature dependence for kl may exist. E$ect of the Number of Layers. Because fewer than the maximum number of adsorbed layers could exist during surface migration, a more satisfactory relation for the circular-pore model was considered possible if fewer than this number was assumed. To investigate the effect of the number of layers, two sets of data (isobutane at 40" and ethylene a t 25") were examined. The number of adsorbed layers was varied from one to the maximum in each case. The results are presented in Figure 3 and Table 11.
Table 11: Effect of the Number of Layers in Multilayer Model 7---------No.
1
Ethylene 298°K Isobutane 313°K
-2
of layers------107E-------3
4
5
0.398
2.32
0.382
0.393
0.397
0.81
0.49
0.51
0.54
When the effect of the number of layers from two to the maximum is considered, the differences in mean errors are small and the greatest deviations occur at the low-concentration range, where the model has been shown to err. Since optimum values of the momentumexchange parameters were chosen, the effect of increasing the number of layers was just offset by increases in kl and kz. Because the data are correlated with approximately the same accuracy for any number of adsorbed layers between 2 and 5 , absolute values for kl and kz must be considered unreliable. This insensitivity to the number of layers must be regarded as a weakness of the model in its present form. When a single adsorbed layer is considered, the multilayer model contains only one adjustable parameter. Although with one layer the present model is similar to Russell's single-phase model, this model differs from Russell's single-parameter model in two fundamental respects. ( 1 ) The momentum transfer between the adsorbed gas and the solid for the Russell model is proportional to only the velocity of the phase, while in the present study it is proportional to the product of the concentration and the velocity. (2) For the present model the gradient in spreading pressure is related to the gas pressure via the adsorption isotherm and a two-dimensional equation of state. I n the Russell case, the Gibbs adsorption isotherm relates gas-phase pressure to spreading pressure. For the isobutane the deviation of the single-layer
2369
limit is smaller than for the Russell model, but the opposite is true for the ethylene data (see Table 11). These comparisons show that if the present theory were limited to one layer, thus possessing the advantage of only one parameter, it is possible that this model would predict results as satisfactorily as those of Russell. Extension to a Flat Plate. If the number of adsorbed layers is large, a flat-plate geometry may better describe the surface. Assuming a flat plate the area correction elements, ct and et, of matrix 2 become unity. Also, if the number of adsorbed layers is allowed to become very large, the terms in eq 3 may be approximated by their infinite sums resulting in further simplification. The flux on a flat surface resulting from migration in n adsorbed layers can now be considered. Because of the symmetry of 8 ,a general relation for the inverse can be found. The total adsorbed flux can then be obtained as a function of adsorbent properties, spreading-pressure gradients in each layer, momentum-exchange parameters, and the number of adsorbed layers by using eq 16. This procedure has been carried out by one of the authors.12 The resulting flux relation is
where K = l / f . If the spreading-pressure gradient in the first layer is nonzero, the total flux increases without limit as n becomes large, if only the first term in the series is considered. Since all additional terms are positive, these remaining terms only aggravate the situation. Finite values of the flux are thus unattainable if kl is finite and n increases without limit. The flat-plate model using an infinite number of adsorbed layers, therefore, cannot be considered a reasonable approximation of an existing physical situation describing surface flow. Comparison of Equations of State. I n order to estimate the effects of the Volmer correction for nonideality, the results of using a two-dimensional ideal equation of state were compared with the results of using the Volmer equation. The results using a two-dimensional van der Waals equation of state were also obtained to estimate the value of further corrections for nonideality. A typical comparison of the predicted :observed flux ratio as a function of adsorbed concentration for the three equations of state is shown in Figure 4. All three equations present similar curves, although the Volmer equation does give somewhat better results than the other two. Poorest behavior is shown by the van der Waals equation, presumably caused by the difficulty of determining a realistic value for the two-dimensional attractive-force constant. The superiority of the Volume 78, Number 7 July 1968
WELDONK, BELLAND LEE F. BROWN
2370
PROPYLENE 298O K
0.I
0.2
0.3
0.4
ABSORBED CONCENTRATION IN ( rng-moles/gmcAT)
Figure 4. Comparison of equations of state for the multilayer model: - - -, ideal ( 0 ) ; -, Volmer (0); -.-. , van der Waals (A).
I
I 0.1
I 0.2
I 0.3
ADSORBED CONCENTRATION ( mg-rnoles/gmCAJ
Figure 3. Effect of the number of layers on the multilayer model: 0, 1 layer; 0,2 layers; 0 , 3 layers; A, 4 layers; 0, 2, 3, and 4 layers.
Volmer equation, though slight, existed in seven of the nine cases studied. It should be pointed out that there are some internal inconsistencies in the model presented here. The BET adsorption theory assumes localized adsorption in all layers, yet this model assumes completely mobile molecules in the adsorbed layers, with concentrations derived from BET theory. A second inconsistency lies in the use of an equation of state to determine the spreading pressure. Once the concentration within a two-dimensional adsorbed phase is known, the spreading pressure in theory can be obtained from the Gibbs adsorption equation. When this is applied to the present system, the resulting equations are quite complicated, and the simpler picture was adopted to obtain a mathematically tractable system. It is still believed, in spite of these inconsistencies, that this model presents a useful approach to the problem of surface transport.
Conclusions I n the development of the multilayer model, transport within individual adsorbed layers is viewed as a result of a gradient in a two-dimensional spreading pressure. This spreading pressure is found through the use of simple two-dimensional equations of state. A simplified representation of momentum transfer between adjacent layers is devised, and equations are developed to describe the concentrations of the individual layers using the BET adsorption theory. Relations describing the adsorbed flux are then derived. Two geometries describing the adsorbent surface are considered-a flat plate and a circular pore. The Journal of Physical Chemistry
Within a circular pore, the number of layers is limited, and the model predicts finite fluxes. The equations describing the flux are applied to data for surface flow. Comparison with previous models indicates that the multilayer model correlates the data as accurately as the best of the previous models in regions of intermediate and high surface coverage. At low adsorbed concentrations the multilayer model predicts fluxes higher than those observed. This deviation a t low coverage is attributed to surface nonuniformity. No prior assumptions are made regarding the quantitative values or properties of the coefficients describing momentum transfer. Values of these coefficients are obtained by comparing the theory with experimental data. Behavior of the two parameters with relation to each other and to surface coverage and temperature is in agreement with physical reality. The model’s principal weakness is that the calculated values of the momentum-transfer parameters depend strongly upon the number of adsorbed layers.
Acknowledgment. The authors thank the National Science Foundation for its support of this project. Mr. Bell received fellowships from Dow Chemical Co. and Continental Oil Co. during this study.
Notations
si
Cross-sectional area of the plug, cmz Two-dimensional van der Waals repulsion term, ergs cmZ/mol Three-dimensional van der Waals repulsion term, erg8 cms/mol Two-dimensional Volmer correction, cma/mol Three-dimensional Volmer correction, cm*/mol Coefficient of resistance, g/sec om2 Ratio of the outer radius to the mean radius in layer i Diameter of the pore, cm Molecular diameter, cm Square root of the average error in the flux squared, mg-mol Ratio of the inner radius to the mean radius in layer i Momentum-exchange ratio, k z / k ~ Nonideality spreading pressure gradient correction
K
1If
A 08 a aa
b bs
CR ci
D d
E ei
f
ADSORBED HYDRO~E CYANIDE N ON POROUS GLASS
LP
N
N , V
n iii
P
Po R
s
si
T
Momentum-exchange rate constants, sec-l or (g/gmol)( goat/cm2)sec-1 Length in the direction of flow on the surface, cm Length in the direction of flow through the plug, cm Molar flow rate, mg-mol/sec Avogadro's number of molecules, molecules/mol Number of layers Number of moles, mol Gas-phase pressure, mm Vapor pressure, mm gas constant, mg cmZ/sec2 mg-mol deg Specific surface area, cma/g,.t BET areas, cm2 Temperature, OK
2371 t u1
ui vc
xi Y z
Thickness of adsorbed layer, cm Velocity of layer 1 on the surface, cm/seo Velocity of layer i in the direction of the plug axis, cm/sec Critical volume, cma Concentration of layer i, mg-mol/gc.t Total adsorbed concentration, mg-mol/g,,t Relative pressure, p / p o
Greek Letters Apparent catalyst density, gCat/cma 7 Tortuosity factor Spreading pressure in layer i, dyn/cm ?i Spreading-pressure gradient in layer i, dyn/cmR di P
Infrared Spectrum, Surface Reaction, and Polymerization of Adsorbed Hydrogen Cyanide on Porous Glass by M. J. D. Low, N. Ramasubramanian, P. Ramamurthy, and A. V. Deo Department of Chemistry, New York University, New York, A7ew York 10468
(Received October 26, 1067)
Infrared spectra of H C N sorbed on highly dehydroxylated porous glass as well as on pure and boria- and alumina-impregnated silica were recorded. Some H C N dissociates, boria on the porous glass acting as the adsorption and dissociation center, and new B-OH and Si-OH groups are formed. Physical adsorption of H C N occurs by hydrogen bonding to both types of surface OH groups and to oxygen atoms through the H C N hydrogen atom. H C N is also bound through the nitrogen atom to aluminum ions present as an impurity on the porous glass surface. Polymerization occurs, the aluminum acting as reaction center.
I n their report of the study of the infrared spectrum and surface polymerization of HCN adsorbed on porous glass, Kozirovski and Folman' noted that the band due to surface OH groups may appear as a closely spaced doublet if the glass was degassed at 900". The reason for the appearance of the doublet was not clear to them, but they suggested that one of the bands may have been due to OH groups attached to boron atoms present in small amounts in the glass (the other being due to surface silanols). Later work showed the validity of their suggestion. A sharp band at 3748 cm-I due to free surface silanol groups and a second, sharp baad a t 3703 cm-l due to surface B-OH groups were reported. 2 , s Kozirovski and Folman noted the adsorption of HCN occurring on two different sites at small surface coverage as well as the hydrogen bonding of adsorbed HCN to two types of OH groups at higher coverage, but they did not give any further consideration to surface B-OH groups. It has been found, however, that the presence of boron affects the silica skeleton of the glass. Surface boron acts as an ad-
sorption and reaction center in the hydration of porous g l a s ~ , and ~ , ~ provides Lewis-acid-type sites for the adsorption and reactiona of NHs. We have consequently studied the sorption of HCN. The present work was carried out with highly degassed porous-glass specimens in order to be able to observe clearly the changes occurring in the B-OH band, whereas a part of Kozirovski and Folman's work was done with specimens degassed a t 450". The B-OH band is not developeda unless an appreciable amount of water is removed by degassing above 600", but high-temperature treatments lead to a diffusion of (1) Y . Kozirovski and M. Folman, Trans. Faraday SOC.,60, 1532 (1964). (2) M. J. D.Low and N. Ramasubramanian, Chem. Commun., 499 (1965). (3) M. J. D. Low and N. Ramasubramanian, J . Phya. Chem., 70, 2740 (1966). (4) M. J. D. Low and N. Ramasubramanian, ibid., 7 1 , 730 (1967). (6) M. J. D.Low and N. Ramasubramanian, ibid., 71, 3077 (1967). (6) M. J. D.Low, N. Ramasubramanian, and V. V. S. Rao, ibid., 7 1 , 1726 (1967). Volume 72*Number 7
July 1968
