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Surface flow of adsorbable gases through magnesium chromite: Carbon dioxide surface flow
Surface Flow of Adsorbable Gases through Magnesium Chromite: Carbon Dioxide Surface Flow DANIELLE CIOSMAK-GALLAND FacultE des Sciences Mirande, Laboratoire de Recherches sur la REactivitE des Solides associE au C.N.R.S., 21000 Dijon, France
AND DENISE DELAFOSSE UniversitE Paris VI, Laboratoire sur la CinEtique des REactions Superficielles E R 133, T 55, place Jussien, 75005 Paris, France
Received December 29, 1975; accepted April 30, 1976 We first established that helium, which is not adsorbable through magnesium chromite, may be regarded as a "calibrating gas" in flow rate measurements. Then, we studied carbon dioxide flow through the same plug, in a range of temperatures such that the CO2 adsorption on the solid is a chemisorpfion: A surface flow of the COs chemisorbed molecules is determined and its value leads us to consider them as mobile at the surface. INTRODUCTION
I n the physical adsorption range, helium usually corresponds to these criteria. I t proved necessary to check whether it was the same under our experimental conditions. The results relating to helium and carbon dioxide are reported in this paper.
Numerous researchers (1-11) have found evidence of the surface flow of adsorbable gases through a porous medium. Their studies were carried out in the physical adsorption range, usually at low or room temperature. Thus, it seemed interesting to know whether this phenomenon also occurred in the chernisorption range. Flow studies on ammonia, carbon dioxide, sulfur, and oxygen dioxide at 100°C through a powdered magnesium chromite plug had already revealed the existence of a surface flow for these gases comparative to those of helium, neon, argon, and k r y p t o n (12). I n order to clarify the chemisorption range, we investigated the ammonia, oxygen, and carbon dioxide flows through magnesium chromite versus temperature. To prove a surface flow, it is necessary that comparisons be made in the same temperature and pressure ranges and, for the same sample, the flow of a nonadsorbable gas.
FLOW EQUATIONS When an adsorbable gas flows through a porous medium, the total flow J results from the sum of two parallel flows:
Jg and Ys are the gas phase and surface flow through a unit cross section of the porous m e d i u m normal to the direction of flow. If those flow studies are performed at low pressure, in a range where the mean free path ), of the gaseous molecules is much larger than the diameter of the pores, Jg follows the Knudsen law (13), i.e., it remains proportional to the pressure gradient from 84
Journal of Colloid and Interface Science. Vol. 59, No. 1, March 15. 1977 ISSN
0021-9797
Copyright ~ 1977by AcademicPress. Inc. All rights of rel~roductionin any formreserved.
SURFACE FLOW OF-ADSORBABLE-GASES
Thus, a can be determined by measuring the helium permeability coefficient Quo for the given plug :
which it arises:
8+K Jg
S dt
dP
3kl A krrMRT/ dx'
[2]
Quo =
where : S = the cross-sectional area of the porous plug. the number of molecules flowing W through the plug during time t. = (2 - - f ) / f , f representing the proportion of molecules striking the surface, which are randomly reflected. e = the porosity. A = specific surface area (in cm2/cma). k, = shape factor correcting the noncylindrical capillaries. M = gas molecular weight. T = plug temperature. = structure factor of the plug. In the steady state, dP/dx = AP/1. ~ P = -P2 -- P1 is the pressure drop between the upstream and downstream plug volume and l is its length. 8~K,2(
2
'~AP
Jg = ----\--]A IrMRT 3ki
-T"
[3]
This equation allows the gas phase permeability coefficient Q~, to be determined as follows.
&
dP =
--
C4]
Q+--,
dx
85
-
-
(M~,,T)~
[7]
and for the same temperature:
/MHo\½ kM/ Let Q stand for the total permeability coefficient defined by
dP Y = -Q--. dx
[9]
The surface flow efficiency in the total flow can be calculated at a given temperature: Q - Q~ T
-
Q
[m]
Assuming that the total flow obeys a diffusion law and applying Fick's law to the surface flow:
dC+
J~ = - - D + - - , dx
[11]
where D+ is the surface flow coefficient and C~ is the adsorbed phase concentration in moles per unit volume of the porous medium. EXPERIMENTAL TECHNIQUES
Og - - 3#1 A \ ~ - - M - ~ ]
"
[5]
Thus, like most authors (1-7), if we consider that helium is not adsorbed on the investigated medium, it can be used as a calibrating gas to determine the amount of gas phase flow in the total flow of an adsorbable gas. In fact, for a given plug, 8, K, e, kl, and A are independent of gas and temperature:
Og
(MT)(
[6]
1. Perraeability The permeameter used in our flow studies was described in a previous paper (12). Flow rates are measured in steady state, which is obtained by keeping constant the respective pressures P2 and t)1, upstream and downstream of the cell (P2 > t)1). A pressure range, 50-200 Torr, and a pressure drop AP (2-25 Torr) were chosen. At a given temperature T, a pressure P2, and a pressure drop AP, the number of molecules which has left the upstream compartment by flowing
Journal of Colloid and interface Science, Vol. 59, No. i, March 15, 1977
86
CIOSMAK-GALLAND AND DELAFOSSE TABLE I Physical Characteristics of Magnesium Chromite Samples
Sample I Sample II
A (m2.g-l)
p (g.cm-3)
d = 6/(pA) (A.)
dzeE (£)
35 50
4.45 4.62
386 260
400 270
acteristics of each plug are given in Table II, where m stands for its mass. During flow experiments, each plug was degassed at 430°C and the system evacuated to a pressure of 10-4 Tort for 3 days. For a given gas, between flow runs, the plug was degassed under the same conditions.
2. Adsorption through the plug, can be measured. Flow J through the plug can be deduced, expressed in mole cln-~ sec-1. Our flow Studies were carried out on three plugs, A, B, C, with different characteristics. Each plug was made of powdered magnesium chromite compacted within a cell described in (12). Two magnesium chromite samples were prepared according to a process similar to that of Adkins-Connor's synthesis (14) for copper chromite. The X-ray powder diffractograms correspond to that of MgCr204 and chemical analysis yields Cr/Mg = 2. Nitrogen adsorption and desorption isotherms at liquid nitrogen temperature are coinciding curves with the sigmoidal form observed on solids where the diameters of rnacropores are larger than 250 A (15). The specific surface areas were measured by the BET method and the densities with Gerard's pycnolneter (16). These various results are shown in Table I. It can be noted that the mean diameters of the solid particles calculated from d = 6/pA (for spherical, nonmicroporous particles) are in good agreement with those assessed through electron microscopy. Thus, in both samples, chromite does not seem to have pores whose diameters are between 25 and 250 h and the porosity of the plugs is, therefore, intergranular. The geometrical charTABLE II Geometrical Characteristics of Plugs A, B, and C Plug
m (g)
l (cm)
S (cmS)
A B C
12.8637 9.1876 9.5256
5.77 4.40 4.10
1.54 1.54 1.54
p e (g.cm 3) (cm3/cm~) 4.45 4.45 4.62
0.675 0.695 0.673
COs adsorption on magnesium chromite was studied by Gillot, Moreau, and Delafosse (17). About 2 g of magnesium chromite from sample I was used. Degassing was effected under a pressure of 5 )< 10-q Torr. The adsorption isotherms were determined between 164 and 324°C. EXPERIMENTAL
RESULTS
1. Helium Helium flow rates were measured in the following temperature ranges. plug A: 82-299°C, plug B : 30-329°C, plug C : 24-261°C. At a given temperature, J was measured in terms of various, selected values of P2 and AP. These results are listed in Tables IIIa, b, and c. For each plug, at a given temperature, whatever the values of P~ and AP, the plotting TABLE I I K Helium Flow R e s u l t s t h r o u g h P l u g A T
J / A P )< 10-9
82 99 121 131 145 169 174 182 205 245 249 299
2.80 3.30 3.50 3.75 3.80 4.15 3.95
(°C)
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
(mole/cm~ .sec.mmHg)
4.15
4.60 5.40 5.15
6.00
Q(MT)½X 10-9 Measurements (cgs units) order 0.458 0.552 0.603 0.654 0.675 0.758 0.684 0.769 0.873 1.066 1.020 1.245
1 6 5 4 10 11 2 8 3 12 7 9
SURFACE FLOW OF ADSORBABLE GASES
87
TABLE IIIb
TABLE IV
Helium Flow Results through Plug B
Pores Mean Diameters, Compared with X,~
T (°C)
j / A p X 10-9 (mole/cm~ -sec .mmHg)
Q(MT) ½ X 10~ (cgs units)
30 88 147 200 264 329
11.60 10.50 9.70 9.15 8.40 8.20
1.35 1.33 1.33 1.33 1.33 1.33
Plug
A B C
of J versus AP is always a straight line. This may, therefore, mean that the helium flow through each plug, in steady state, occurs according to a diffusion process that can be a Knudsen flow. I t requires a condition for the mean free path of the gaseous molecules. X is given (18) by X=
1 1 2'
[-12.]
zr2~nd
T
Xm
2r
(°K)
(i)
(i)
355 303 297
10340 8826 8651
173 179 119
In each case X,,~>> 2r, thus validating the assumption of a Knudsen law. Moreover, in a Knudsen flow, for a given plug, Q(MT)~ remains constant whatever the gas and temperature. Figure 1 shows Q(MT)~ variations versus T, for the three plugs. B and C, indeed, give a constant value. For A, however, Q(MT)~ increases linearly versus T from 0.458 X 10.9 at 82°C to 1.245 X 10-9 at 299°C and fits equation Q(MT)½ = 0.348 X 10-11 T + 0.17 X 10-9. In this case, the observed flow is not consistent with a Knudsen flow type.
2. Carbon dioxide where d is the molecule mean diameter (for helium d---2.00 A); n is the number of molecules per unit volume (in the present case n was calculated from V0 at 0°C; under a pressure of 1 atm from (17), V0 = 22396 cm3). By choosing a system of parallel, cylindrical capillaries as a pore model, the mean radius of the pores, for each plug, can be calculated (19). r =
2e/A.
[13-]
Adsorption. At temperatures between 164 and 324°C, and pressures ranging from 0 to 200 Torr, the Freundlich type isotherms are observed (cf. Fig. 2) following in particular Halsey's equation : V
RT
--
=
0 =
[-14]
aoP
v,~
qm (1 - r r )
and showing a heterogeneous distribution of
Table IV lists the minimum values X,~ of X in our experimental conditions and the mean diameters of the pores of the three samples. 0 2
TABLE IIIc Helium Flow Results through Plug C T (°C)
J / A P X 10-9 (mole/cm2 -sec-mmHg)
Q ( M T ) t X 10-~ (cgs units)
24 59 83 158 261
1.75 1.65 1.60 1.45 1.30
0.185 0.185 0.186 0.185 0.185
1
~ I00
J
200
300
TC
FIG. 1. Helium flow through magnesium chromite: Y plug A; • plug B ; [] plug C. Journal of Colloid and Interface Science, VoL 59, No. 1, March 15, 1977
88
CIOSMAK-GALLAND AND DELAFOSSE ] J
2
TABLE VIB
Io 9
Carbon Dioxide Flow Results through Plug B >o
>o
1.5
Y
T
(°C) 150 190 215 322 381
0.5
0
324 P
0
5
10
I~5 P tort
FIG. 2. CO~ adsorption isotherms on magnesium chromite.
adsorption sites. The COs molecule is chemisorbed without dissociation, which is confirmed by conductivity measurements. The isosteric adsorption heat, measured in the reversible chemisorption region is AH = 21 4 - 2 kcal/mole, when 0 tends toward zero. The activation energy of adsorption, E = 16.5 Kcal/mole, was calculated from adsorption kinetics. After calculation of the entropy change due to adsorption and its comparison with 1° translation loss, it m a y be concluded that the molecule is perfectly mobile on the adsorbant surface.
TABLE VIC
T
CO2 flow measurements were carried out on plugs B and C in the same temperature
21 49 81 97 114 133 164 180 200 228 244 256
TABLE V CO2 Mean Free Path Values
21 256 381
1625 2923 3614
1.640 1.669 1.664 1.648 1.632
Carbon Dioxide Flow Results through Plug C (°C)
X (A)
3.60 3.50 3.40 3.05 2.88
Q(MT)½ X 10-9
range. In each set of measurements, at a given temperature and whatever Ps and Ap, the plotting J versus &P is a straight line. This leads one to think that the flow rate does not contain any streamline component. Table V gives the mean free path values X of carbon dioxide molecules calculated for the maximum value P2 = 200 Torr and the temperature limits chosen for our experiments. The pores mean diameters of plugs B and C, respectively, 179 and 119 A, are in both cases much smaller than X, a condition required for a Knudsen flow through the pores. Tables VI(B) and (C) show the permeability results. Figures 3 and 4 show the variations of Q(MTfi versus T for COs and He, for plugs B and C. The straight lines representing the behavior of helium are, in both cases, below the COs curve, showing a maximum around 180°C.
FLOW
T (°c)
J / A P X 10-9
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
J / A P X 10-9
0.550 0.525
0.500 0.490 0.475 0.465 0.445 0.445 0.435 0.420 0.412 0.405
Q(MT)½X 10-~
0.1925 0.1920 0.1920 0.1920 0.1910 0.1915 0.1901 0.1935 0.1933 0.1921 0.1914 0.1905
SURFACE FLOW OF ADSORBABLE GASES
89
c~ 'o
DISCUSSION
1. Helium as a Nonadsorbable Calibrating Gas Analysis of the experimental results requires two remarks : (1) The helium flow, for plugs A, B, C, follows the law, J = KAP, k representing a constant related to temperature. (2) Moreover, for plugs 13 and C, the law observed in terms of the temperature is in agreement with a Knudsen law. Helium, thus, seems to behave as a nonadsorbable gas on MgCr2Q. However, for plug A the results can be interpreted neither by a streamline flow (Eq. [15]) nor by a "slip flow" (Eq. [163).
i)I+ P~
PAP J=k2
with
t5___,
RT /SAP :
/
2
~}
=
RT
[15]
2
[16]
MrMRT/
where k2, ka, k4 are constants reIated to the plug geometry. In both flows, J depends not only upon AP but also upon/5 and, moreover, Q(MT)½ varies with 1/T}, whilst they are T-dependent in our experiments. Can the assumption of a surface diffusion of adsorbed helium, in addition to a Knudsen law in gaseous phase, be put foward? Hwang (11) has formulated such an assumption stipulating a helium surface diffusion through vycor glass at 77.36°K as well as 586.8°K. Barrer (20) has carried out a systematic investigation of helium flow through carbons between - 2 0 0 and 300°C. He assigns some of the deviations from the Knudsen law to a mercury condensation from the manometers onto the porous medium, which leads to a permeability decrease at 100°C. Besides, Barrer suggests that the plug aging (6) should be taken into account. However, by taking great care in the plug degassing, he observed only a very small deviation from the Knudsen law. He concluded that helium can be used as a nonadsorbable calibrating gas.
1.5
He 1.3
c - i
=
2o0
3;0
4;o ~°c
Fro. 3. COs flow through MgCr204 in plug B. Concerning the results reported here, the
Q(MT)~ measurements were not made in an increasing order of temperature (Table IIIa). Furthermore, they were obtained over a period of 7 months during which some degassings were effected between the runs. The recorded deviation with respect to the Knudsen law is systematic and it seems difficult to attribute it to aging, as identical values of Q(MT)~ are found for the same temperature after several months. ~ The apparatus used (12) consisted of mercury manometers. At the lowest temperatures, mercury condensing in some pores can cause the gas phase flow to decrease. But there is no reason why condensation should occur in a reproducible way in the same pores. Successive degassings should yield values somewhat different from those obtained for Q(MT)~ at the same temperature. On the contrary a good reproducibility of Q(~T)~ = f ( t ) is observed over time. Does that mean that we must envisage, as Hwang did, a helium surface diffusion? o
'o 0
1.9 He~
•
J 1.8
z
lO0
200
J
I ~'C
Fro. 4. CO2 flow through MgCr~O4in plug C.
Journal of Colloid and Inlerface Science, V o l . 5 9 , N o . 1, M a r c h
15, 1 9 7 7
90
CIOSMAK-GALLAND AND DELAFOSSE
!I
served, thus, seems to be well linked to the plug and not to the helium-magnesium chromite system, and, therefore it seems justified to consider helium as a calibrating gas relative to surface flow measurements of chemisorbable gases. 2. Case of an Adsorbable Gas: Carbon Dioxide
0.5
1 Va ml. g~l
Fzo. 5. Variations of D, versus 0 and T for plug B. Even in a Knudsen flow of a "nonadsorbable gas," an adsorption is involved: The molecule strikes the wall and is then retained at the surface until it is reemitted according to the diffuse reflexion law with a velocity equal to the mean thermal speed of the gas at the temperature of the experiment. In fact, a number of studies (20) have shown that a sticking time of helium on copper surfaces could exist at room temperature. The measurements have been made in transient state: The measurement of the "time lag" specific to the setting up of the steady state allows surface diffusion to 'be calculated. But, in most cases, helium surface diffusion, in steady state, is undetectable. Our measurements were made in steady state. Moreover, this phenomenon, related to the properties of the gas adsorption on the solid, should also have occurred with plugs B and C. Above 100°C, the sticking time of the helium molecule on magnesium chromite will no doubt be extremely short. To assign the phenomenon observed to a surface diffusion of helium, therefore, does not seem to be justified. The results relating to this plug seem to be much more linked to wall effects inherent to the plug constitution, depending on how the magnesium chromite grains located themselves relative to one another. We shall, indeed, see that during ammonia flow through this plug, the Q ( M T f i curve obtained remains parallel and very close to that obtained for helium, in the range where the amount of ammonia adsorbed is very low. The phenomenon ob-
We assign the difference between both flows to the existence of a surface flow of the COs molecules adsorbed on magnesium chromite. J and Jg (deduced from the helium flow measurements) are independent of P2 and proportional to AP. According to Eq. [1-1 it is, thus, the same for Js which follows a diffusion law (Eq. [11]). In a similar study, Thornton (10) observes that the adsorbed phase is in equilibrium with the gas phase and he verifies that the pressure gradient through the plug is constant. He writes Ds = -- (J~/AP)L/(dC~/dP).
[17-]
dC~/dP, then, is the slope of the adsorption isotherm. Our D~ values were calculated according to this method for different temperatures and pressures in the range where carbon dioxide chemisorption on magnesium chromite is reversible, namely, between 182 and 324°C. Figures 5 and 6 give the variations of D~, being a function of both temperature and adsorbed quantity, for each plug. Ds increases with the adsorbed quantity, T being constant and increases with the temperature, 0 being constant. Barrer (22) has shown, on numerous
257°C] 218°C 182°C
016
019
1[.2VamLg-I
FIc. 6. Variations of D, versus 0 and T for plug C.
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
SURFACE FLOW OF ADSORBABLE GASES examples, that the surface diffusion due to the physical adsorption of a gas, is an activated phenomenon to which the Arrhenius law is applicable: Ediff
D~ = Do e x p - - .
F18~
"T ®
91
. . . . . . . . . . . . . . . . . .
............
o
E o u
2c~\ \
RT
\ \
Eai~f, the activation energy for surface diffusion is deduced from the variations of D~ with the temperature. In our case, the good alignment of the plots in logarithmic coordinates, confirms the assumption of an activated process for the surface diffusion due to CO2 chemisorption. Figure 7 shows the variations of Edi, and AH versus 0. Curves (B) and (C), for both plugs, are very close to each other and possess the same limit. - ~ d l f f = 3.5 kcal/mole when 0 tends toward zero. Barrer (22) has studied the ratios •diff/Ag in the case of physical adsorptions. For an activated adsorption, the ratio Ediff/ Ea,s of the activation energy for surface diffusion to energy of desorption, expresses the ability of the gaseous molecule to migrate on the surface before acquiring the energy necessary for a complete desorption. By an experimental method using a field emission microscope, Gomer et al., and other authors, have studied the mobilities of several gases, among which, hydrogen (23), oxygen (24), and carbon monoxide (25) chemisorbed on tungsten. The ratio Ediff/Edos varies from 0.09 to 0.45, from hydrogen to carbon monoxide, and tends to increase with the size of the chemisorbed molecule. For carbon dioxide, we obtained Eaiff/Edos = 0.1, a value located in the same range. Although it is difficult to compare the chemisorption of gases on metals with the chemisorption of gases on metal oxides, the low value of this ratio, nevertheless, suggests that the carbon dioxide chemisorbed on magnesium chromite is very mobile on its surface. However, if the value of Ediff is compared to the thermal energy of the molecules, the latter is noticed to be much smaller and, thus, carbon dioxide must not be considered as a two-dimensional, mobile gas. Its
IC
o'.~
o'.2
0'.3
,~
FIO. 7. Variations of AH and Ediff for plug B and C versus 0: • AH; • Ediff plug B; [] Ediff plug C. mobility is linked to the jump from site to site thanks to a migration energy which is low relative to the desorption energy. I t belongs to the "activated mobilities" as defined by Haul (26).
ACTIVATED SURFACE DIFFUSION H w a n g and Kammermeyer (11) have put forth an activated surface diffusion model for the flow of gases through porous media, in the physical adsorption range, and established the following flow equation. A Q(MT)~ = A + B T exPT ,
[-19]
where A stands for the Knudsen flow; B is a surface flow coefficient which is constant for a gas-adsorbant system as well as fx which is defined by E*
--
= - - ;
E
E20]
K ~* is the minimum potential energy for an adsorbed molecule, ~ is the activation energy of surface diffusion for an adsorbed molecule. Figure 8 gives the variations of L o g ( ( Q ( M T ) ~ - - A ) / T ) versus 1/T for this study and in the range of reversible chemi-
Journal of Colloid and Interface Science, Vol. 59, No. i, M a r c h 15, 1977
92
CIOSMAK-GALLAND AND DELAFOSSE 1.6
1.8
2
2.2
o Ca.9
i~.4
obtained diffusion we can sorption the solid
for the activation energy for surface with those for desorption energy, consider the carbon dioxide chemias an activated mobile adsorption on surface. REFERENCES
~.2
~
13.7
r 2.1
~ T
0-3
FIG. 8. Hwang equation test: • plug B; • plug C. sorption. We have calculated quantity A with respect to helium. Our results are in good agreement with Hwang's equation, and give the following values. --plugB:
A=0.8X
103 °K, e * - - e = 1.6 kcal/mole,
-- plug C: A = 1:31 X 10~ °K,
1. CARMAN',P. C. AND MALHERBE~P. LE R., Proc. Roy. Soc., Set. A 203, 165 (1950). 2. CARMAN,P. C. AND RAAL, R. A., Proc. Roy. Soc., Ser. A 209, 38 (1951). 3. BARRER, R. M. AND BARRIE, J. A., Proc. Roy. ~ Soc., Set. A 213, 250 (1952). 4. BARRER, R. M. AND STRAe~AN, E., Proe. Roy. ~,~ Soc., Ser. A 231, 52 (1955). 5. BARRER, R. M. AND GABOR,T., Proc. Roy. Soc., Ser. A 2S1, 353 (1959). 6. As~, R., BARRER, R. M., AND POPE, G. G., Proe. Roy. Soc., Ser. A 271, 1 (1963). 7. AYLMORE, L. A. G. AND BARRER, R. M., Proc. Roy. Soc., Ser. A 290, 477 (1966). 8. VON HAUL, R. AND MOESTA, H., Z. Electrochem. Ber. Bunsenges. F. Phys. Chem. 66, 754 (1962). 9. DACEY, J. R., Advances in Chemistry Series,
e*-- e = 2.6 kcal/mole. Both values lead to e * = 4.5 kcal/mole for 8 = 0.6 (the permeability experiments were performed with high coverages), which is consistent with the value AH = 4 kcal/mole found for the considered 0 range. Nevertheless, the theoretical expressions call for statistical thermodynamics rigorously applicable to physisorbed molecules. The numerical values calculated from these expressions, in the case of a chemisorption, are not necessarily comparable to those deduced from experimental measurements. CONCLUSION The study of helium flow through magnesium chromite plugs has shown that, over the high-temperature range helium could be considered as a nonadsorbable calibrating gas on magnesium chromite. Moreover, for carbon dioxide, over the temperature range where it is chemisorbed on magnesium chromite, an activated surface diffusion contributing to the overall flow can be p u t in evidence. This diffusion is related to the amount adsorbed and to temperature. B y comparing the values
10. 11. 12. 13. 14. 15. 16.
No. 33, pp. 172-181, American Chemical Society, Washingtoi/, D.C., 1961. T~IORI~TON,A. W., Thesis, Ohio State University, 1968. HWAN% S. T., Thesis, State University Iowa, 1965. GALLAND,D. COINTOT, A., AND BARRET, P., J. Chim. Phys. 68, 588 (1971). KNIYDSEN,M., Ann. Phys. 28, 75 (1909). ADKINS, H. AND COI~NOR, R., J. Amer. Chem. Soc. 53, 1901 (1930). MOREAU,M., Th~se, Dijon, 1969. GERARD, N., Th~se de Doctorat d'Etat, Dijon, 1967.
17. GILLOT, B., MOREAU, M., AND DELAFOSSE, D., Bull. Soc. Chim. Fr. 4, 1330 (1970). 18. MOORE,W..1., "Chimie Physique," Dunod, Paris, 1961. 19. CARMAn,P. C., "Flow of Gases through Porous Media," Academic Press, New York, 1956. 20. ASH, R., BARIZER,R. M., AND LOWSON, R. T., Surf. Sci. 21, 265 (1970). 21. ARM:AND,G., LEJAY,Y., J. Mdeanique 1, 5 (1968). 22. BARRER, R. M., "The Solid Gas Interface," pp. 557-609, Dekker, New York, 1967. 23. GOMER, R., WORTMAN, R., AND LUND¥, R., J. Chem. Phys. 26, 1147 (1957). 24. GOM~R,R. AND HULM, J. K., J. Chem. Phys. 27, 1363 (1957). 25. KLEIN,R., J. Chem. Phys. 31, 1306 (1959). 26. voN HAUL, R. AND Ht3BNER, K., Z. Electrochem. Bet. Bunsenges. Phys. Chem. 79, 9 (1975), 777.
Journal of Colloid and Interface Science, Vol. 59, No. I, March 15, 1977
AND DENISE DELAFOSSE UniversitE Paris VI, Laboratoire sur la CinEtique des REactions Superficielles E R 133, T 55, place Jussien, 75005 Paris, France
Received December 29, 1975; accepted April 30, 1976 We first established that helium, which is not adsorbable through magnesium chromite, may be regarded as a "calibrating gas" in flow rate measurements. Then, we studied carbon dioxide flow through the same plug, in a range of temperatures such that the CO2 adsorption on the solid is a chemisorpfion: A surface flow of the COs chemisorbed molecules is determined and its value leads us to consider them as mobile at the surface. INTRODUCTION
I n the physical adsorption range, helium usually corresponds to these criteria. I t proved necessary to check whether it was the same under our experimental conditions. The results relating to helium and carbon dioxide are reported in this paper.
Numerous researchers (1-11) have found evidence of the surface flow of adsorbable gases through a porous medium. Their studies were carried out in the physical adsorption range, usually at low or room temperature. Thus, it seemed interesting to know whether this phenomenon also occurred in the chernisorption range. Flow studies on ammonia, carbon dioxide, sulfur, and oxygen dioxide at 100°C through a powdered magnesium chromite plug had already revealed the existence of a surface flow for these gases comparative to those of helium, neon, argon, and k r y p t o n (12). I n order to clarify the chemisorption range, we investigated the ammonia, oxygen, and carbon dioxide flows through magnesium chromite versus temperature. To prove a surface flow, it is necessary that comparisons be made in the same temperature and pressure ranges and, for the same sample, the flow of a nonadsorbable gas.
FLOW EQUATIONS When an adsorbable gas flows through a porous medium, the total flow J results from the sum of two parallel flows:
Jg and Ys are the gas phase and surface flow through a unit cross section of the porous m e d i u m normal to the direction of flow. If those flow studies are performed at low pressure, in a range where the mean free path ), of the gaseous molecules is much larger than the diameter of the pores, Jg follows the Knudsen law (13), i.e., it remains proportional to the pressure gradient from 84
Journal of Colloid and Interface Science. Vol. 59, No. 1, March 15. 1977 ISSN
0021-9797
Copyright ~ 1977by AcademicPress. Inc. All rights of rel~roductionin any formreserved.
SURFACE FLOW OF-ADSORBABLE-GASES
Thus, a can be determined by measuring the helium permeability coefficient Quo for the given plug :
which it arises:
8+K Jg
S dt
dP
3kl A krrMRT/ dx'
[2]
Quo =
where : S = the cross-sectional area of the porous plug. the number of molecules flowing W through the plug during time t. = (2 - - f ) / f , f representing the proportion of molecules striking the surface, which are randomly reflected. e = the porosity. A = specific surface area (in cm2/cma). k, = shape factor correcting the noncylindrical capillaries. M = gas molecular weight. T = plug temperature. = structure factor of the plug. In the steady state, dP/dx = AP/1. ~ P = -P2 -- P1 is the pressure drop between the upstream and downstream plug volume and l is its length. 8~K,2(
2
'~AP
Jg = ----\--]A IrMRT 3ki
-T"
[3]
This equation allows the gas phase permeability coefficient Q~, to be determined as follows.
&
dP =
--
C4]
Q+--,
dx
85
-
-
(M~,,T)~
[7]
and for the same temperature:
/MHo\½ kM/ Let Q stand for the total permeability coefficient defined by
dP Y = -Q--. dx
[9]
The surface flow efficiency in the total flow can be calculated at a given temperature: Q - Q~ T
-
Q
[m]
Assuming that the total flow obeys a diffusion law and applying Fick's law to the surface flow:
dC+
J~ = - - D + - - , dx
[11]
where D+ is the surface flow coefficient and C~ is the adsorbed phase concentration in moles per unit volume of the porous medium. EXPERIMENTAL TECHNIQUES
Og - - 3#1 A \ ~ - - M - ~ ]
"
[5]
Thus, like most authors (1-7), if we consider that helium is not adsorbed on the investigated medium, it can be used as a calibrating gas to determine the amount of gas phase flow in the total flow of an adsorbable gas. In fact, for a given plug, 8, K, e, kl, and A are independent of gas and temperature:
Og
(MT)(
[6]
1. Perraeability The permeameter used in our flow studies was described in a previous paper (12). Flow rates are measured in steady state, which is obtained by keeping constant the respective pressures P2 and t)1, upstream and downstream of the cell (P2 > t)1). A pressure range, 50-200 Torr, and a pressure drop AP (2-25 Torr) were chosen. At a given temperature T, a pressure P2, and a pressure drop AP, the number of molecules which has left the upstream compartment by flowing
Journal of Colloid and interface Science, Vol. 59, No. i, March 15, 1977
86
CIOSMAK-GALLAND AND DELAFOSSE TABLE I Physical Characteristics of Magnesium Chromite Samples
Sample I Sample II
A (m2.g-l)
p (g.cm-3)
d = 6/(pA) (A.)
dzeE (£)
35 50
4.45 4.62
386 260
400 270
acteristics of each plug are given in Table II, where m stands for its mass. During flow experiments, each plug was degassed at 430°C and the system evacuated to a pressure of 10-4 Tort for 3 days. For a given gas, between flow runs, the plug was degassed under the same conditions.
2. Adsorption through the plug, can be measured. Flow J through the plug can be deduced, expressed in mole cln-~ sec-1. Our flow Studies were carried out on three plugs, A, B, C, with different characteristics. Each plug was made of powdered magnesium chromite compacted within a cell described in (12). Two magnesium chromite samples were prepared according to a process similar to that of Adkins-Connor's synthesis (14) for copper chromite. The X-ray powder diffractograms correspond to that of MgCr204 and chemical analysis yields Cr/Mg = 2. Nitrogen adsorption and desorption isotherms at liquid nitrogen temperature are coinciding curves with the sigmoidal form observed on solids where the diameters of rnacropores are larger than 250 A (15). The specific surface areas were measured by the BET method and the densities with Gerard's pycnolneter (16). These various results are shown in Table I. It can be noted that the mean diameters of the solid particles calculated from d = 6/pA (for spherical, nonmicroporous particles) are in good agreement with those assessed through electron microscopy. Thus, in both samples, chromite does not seem to have pores whose diameters are between 25 and 250 h and the porosity of the plugs is, therefore, intergranular. The geometrical charTABLE II Geometrical Characteristics of Plugs A, B, and C Plug
m (g)
l (cm)
S (cmS)
A B C
12.8637 9.1876 9.5256
5.77 4.40 4.10
1.54 1.54 1.54
p e (g.cm 3) (cm3/cm~) 4.45 4.45 4.62
0.675 0.695 0.673
COs adsorption on magnesium chromite was studied by Gillot, Moreau, and Delafosse (17). About 2 g of magnesium chromite from sample I was used. Degassing was effected under a pressure of 5 )< 10-q Torr. The adsorption isotherms were determined between 164 and 324°C. EXPERIMENTAL
RESULTS
1. Helium Helium flow rates were measured in the following temperature ranges. plug A: 82-299°C, plug B : 30-329°C, plug C : 24-261°C. At a given temperature, J was measured in terms of various, selected values of P2 and AP. These results are listed in Tables IIIa, b, and c. For each plug, at a given temperature, whatever the values of P~ and AP, the plotting TABLE I I K Helium Flow R e s u l t s t h r o u g h P l u g A T
J / A P )< 10-9
82 99 121 131 145 169 174 182 205 245 249 299
2.80 3.30 3.50 3.75 3.80 4.15 3.95
(°C)
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
(mole/cm~ .sec.mmHg)
4.15
4.60 5.40 5.15
6.00
Q(MT)½X 10-9 Measurements (cgs units) order 0.458 0.552 0.603 0.654 0.675 0.758 0.684 0.769 0.873 1.066 1.020 1.245
1 6 5 4 10 11 2 8 3 12 7 9
SURFACE FLOW OF ADSORBABLE GASES
87
TABLE IIIb
TABLE IV
Helium Flow Results through Plug B
Pores Mean Diameters, Compared with X,~
T (°C)
j / A p X 10-9 (mole/cm~ -sec .mmHg)
Q(MT) ½ X 10~ (cgs units)
30 88 147 200 264 329
11.60 10.50 9.70 9.15 8.40 8.20
1.35 1.33 1.33 1.33 1.33 1.33
Plug
A B C
of J versus AP is always a straight line. This may, therefore, mean that the helium flow through each plug, in steady state, occurs according to a diffusion process that can be a Knudsen flow. I t requires a condition for the mean free path of the gaseous molecules. X is given (18) by X=
1 1 2'
[-12.]
zr2~nd
T
Xm
2r
(°K)
(i)
(i)
355 303 297
10340 8826 8651
173 179 119
In each case X,,~>> 2r, thus validating the assumption of a Knudsen law. Moreover, in a Knudsen flow, for a given plug, Q(MT)~ remains constant whatever the gas and temperature. Figure 1 shows Q(MT)~ variations versus T, for the three plugs. B and C, indeed, give a constant value. For A, however, Q(MT)~ increases linearly versus T from 0.458 X 10.9 at 82°C to 1.245 X 10-9 at 299°C and fits equation Q(MT)½ = 0.348 X 10-11 T + 0.17 X 10-9. In this case, the observed flow is not consistent with a Knudsen flow type.
2. Carbon dioxide where d is the molecule mean diameter (for helium d---2.00 A); n is the number of molecules per unit volume (in the present case n was calculated from V0 at 0°C; under a pressure of 1 atm from (17), V0 = 22396 cm3). By choosing a system of parallel, cylindrical capillaries as a pore model, the mean radius of the pores, for each plug, can be calculated (19). r =
2e/A.
[13-]
Adsorption. At temperatures between 164 and 324°C, and pressures ranging from 0 to 200 Torr, the Freundlich type isotherms are observed (cf. Fig. 2) following in particular Halsey's equation : V
RT
--
=
0 =
[-14]
aoP
v,~
qm (1 - r r )
and showing a heterogeneous distribution of
Table IV lists the minimum values X,~ of X in our experimental conditions and the mean diameters of the pores of the three samples. 0 2
TABLE IIIc Helium Flow Results through Plug C T (°C)
J / A P X 10-9 (mole/cm2 -sec-mmHg)
Q ( M T ) t X 10-~ (cgs units)
24 59 83 158 261
1.75 1.65 1.60 1.45 1.30
0.185 0.185 0.186 0.185 0.185
1
~ I00
J
200
300
TC
FIG. 1. Helium flow through magnesium chromite: Y plug A; • plug B ; [] plug C. Journal of Colloid and Interface Science, VoL 59, No. 1, March 15, 1977
88
CIOSMAK-GALLAND AND DELAFOSSE ] J
2
TABLE VIB
Io 9
Carbon Dioxide Flow Results through Plug B >o
>o
1.5
Y
T
(°C) 150 190 215 322 381
0.5
0
324 P
0
5
10
I~5 P tort
FIG. 2. CO~ adsorption isotherms on magnesium chromite.
adsorption sites. The COs molecule is chemisorbed without dissociation, which is confirmed by conductivity measurements. The isosteric adsorption heat, measured in the reversible chemisorption region is AH = 21 4 - 2 kcal/mole, when 0 tends toward zero. The activation energy of adsorption, E = 16.5 Kcal/mole, was calculated from adsorption kinetics. After calculation of the entropy change due to adsorption and its comparison with 1° translation loss, it m a y be concluded that the molecule is perfectly mobile on the adsorbant surface.
TABLE VIC
T
CO2 flow measurements were carried out on plugs B and C in the same temperature
21 49 81 97 114 133 164 180 200 228 244 256
TABLE V CO2 Mean Free Path Values
21 256 381
1625 2923 3614
1.640 1.669 1.664 1.648 1.632
Carbon Dioxide Flow Results through Plug C (°C)
X (A)
3.60 3.50 3.40 3.05 2.88
Q(MT)½ X 10-9
range. In each set of measurements, at a given temperature and whatever Ps and Ap, the plotting J versus &P is a straight line. This leads one to think that the flow rate does not contain any streamline component. Table V gives the mean free path values X of carbon dioxide molecules calculated for the maximum value P2 = 200 Torr and the temperature limits chosen for our experiments. The pores mean diameters of plugs B and C, respectively, 179 and 119 A, are in both cases much smaller than X, a condition required for a Knudsen flow through the pores. Tables VI(B) and (C) show the permeability results. Figures 3 and 4 show the variations of Q(MTfi versus T for COs and He, for plugs B and C. The straight lines representing the behavior of helium are, in both cases, below the COs curve, showing a maximum around 180°C.
FLOW
T (°c)
J / A P X 10-9
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
J / A P X 10-9
0.550 0.525
0.500 0.490 0.475 0.465 0.445 0.445 0.435 0.420 0.412 0.405
Q(MT)½X 10-~
0.1925 0.1920 0.1920 0.1920 0.1910 0.1915 0.1901 0.1935 0.1933 0.1921 0.1914 0.1905
SURFACE FLOW OF ADSORBABLE GASES
89
c~ 'o
DISCUSSION
1. Helium as a Nonadsorbable Calibrating Gas Analysis of the experimental results requires two remarks : (1) The helium flow, for plugs A, B, C, follows the law, J = KAP, k representing a constant related to temperature. (2) Moreover, for plugs 13 and C, the law observed in terms of the temperature is in agreement with a Knudsen law. Helium, thus, seems to behave as a nonadsorbable gas on MgCr2Q. However, for plug A the results can be interpreted neither by a streamline flow (Eq. [15]) nor by a "slip flow" (Eq. [163).
i)I+ P~
PAP J=k2
with
t5___,
RT /SAP :
/
2
~}
=
RT
[15]
2
[16]
MrMRT/
where k2, ka, k4 are constants reIated to the plug geometry. In both flows, J depends not only upon AP but also upon/5 and, moreover, Q(MT)½ varies with 1/T}, whilst they are T-dependent in our experiments. Can the assumption of a surface diffusion of adsorbed helium, in addition to a Knudsen law in gaseous phase, be put foward? Hwang (11) has formulated such an assumption stipulating a helium surface diffusion through vycor glass at 77.36°K as well as 586.8°K. Barrer (20) has carried out a systematic investigation of helium flow through carbons between - 2 0 0 and 300°C. He assigns some of the deviations from the Knudsen law to a mercury condensation from the manometers onto the porous medium, which leads to a permeability decrease at 100°C. Besides, Barrer suggests that the plug aging (6) should be taken into account. However, by taking great care in the plug degassing, he observed only a very small deviation from the Knudsen law. He concluded that helium can be used as a nonadsorbable calibrating gas.
1.5
He 1.3
c - i
=
2o0
3;0
4;o ~°c
Fro. 3. COs flow through MgCr204 in plug B. Concerning the results reported here, the
Q(MT)~ measurements were not made in an increasing order of temperature (Table IIIa). Furthermore, they were obtained over a period of 7 months during which some degassings were effected between the runs. The recorded deviation with respect to the Knudsen law is systematic and it seems difficult to attribute it to aging, as identical values of Q(MT)~ are found for the same temperature after several months. ~ The apparatus used (12) consisted of mercury manometers. At the lowest temperatures, mercury condensing in some pores can cause the gas phase flow to decrease. But there is no reason why condensation should occur in a reproducible way in the same pores. Successive degassings should yield values somewhat different from those obtained for Q(MT)~ at the same temperature. On the contrary a good reproducibility of Q(~T)~ = f ( t ) is observed over time. Does that mean that we must envisage, as Hwang did, a helium surface diffusion? o
'o 0
1.9 He~
•
J 1.8
z
lO0
200
J
I ~'C
Fro. 4. CO2 flow through MgCr~O4in plug C.
Journal of Colloid and Inlerface Science, V o l . 5 9 , N o . 1, M a r c h
15, 1 9 7 7
90
CIOSMAK-GALLAND AND DELAFOSSE
!I
served, thus, seems to be well linked to the plug and not to the helium-magnesium chromite system, and, therefore it seems justified to consider helium as a calibrating gas relative to surface flow measurements of chemisorbable gases. 2. Case of an Adsorbable Gas: Carbon Dioxide
0.5
1 Va ml. g~l
Fzo. 5. Variations of D, versus 0 and T for plug B. Even in a Knudsen flow of a "nonadsorbable gas," an adsorption is involved: The molecule strikes the wall and is then retained at the surface until it is reemitted according to the diffuse reflexion law with a velocity equal to the mean thermal speed of the gas at the temperature of the experiment. In fact, a number of studies (20) have shown that a sticking time of helium on copper surfaces could exist at room temperature. The measurements have been made in transient state: The measurement of the "time lag" specific to the setting up of the steady state allows surface diffusion to 'be calculated. But, in most cases, helium surface diffusion, in steady state, is undetectable. Our measurements were made in steady state. Moreover, this phenomenon, related to the properties of the gas adsorption on the solid, should also have occurred with plugs B and C. Above 100°C, the sticking time of the helium molecule on magnesium chromite will no doubt be extremely short. To assign the phenomenon observed to a surface diffusion of helium, therefore, does not seem to be justified. The results relating to this plug seem to be much more linked to wall effects inherent to the plug constitution, depending on how the magnesium chromite grains located themselves relative to one another. We shall, indeed, see that during ammonia flow through this plug, the Q ( M T f i curve obtained remains parallel and very close to that obtained for helium, in the range where the amount of ammonia adsorbed is very low. The phenomenon ob-
We assign the difference between both flows to the existence of a surface flow of the COs molecules adsorbed on magnesium chromite. J and Jg (deduced from the helium flow measurements) are independent of P2 and proportional to AP. According to Eq. [1-1 it is, thus, the same for Js which follows a diffusion law (Eq. [11]). In a similar study, Thornton (10) observes that the adsorbed phase is in equilibrium with the gas phase and he verifies that the pressure gradient through the plug is constant. He writes Ds = -- (J~/AP)L/(dC~/dP).
[17-]
dC~/dP, then, is the slope of the adsorption isotherm. Our D~ values were calculated according to this method for different temperatures and pressures in the range where carbon dioxide chemisorption on magnesium chromite is reversible, namely, between 182 and 324°C. Figures 5 and 6 give the variations of D~, being a function of both temperature and adsorbed quantity, for each plug. Ds increases with the adsorbed quantity, T being constant and increases with the temperature, 0 being constant. Barrer (22) has shown, on numerous
257°C] 218°C 182°C
016
019
1[.2VamLg-I
FIc. 6. Variations of D, versus 0 and T for plug C.
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
SURFACE FLOW OF ADSORBABLE GASES examples, that the surface diffusion due to the physical adsorption of a gas, is an activated phenomenon to which the Arrhenius law is applicable: Ediff
D~ = Do e x p - - .
F18~
"T ®
91
. . . . . . . . . . . . . . . . . .
............
o
E o u
2c~\ \
RT
\ \
Eai~f, the activation energy for surface diffusion is deduced from the variations of D~ with the temperature. In our case, the good alignment of the plots in logarithmic coordinates, confirms the assumption of an activated process for the surface diffusion due to CO2 chemisorption. Figure 7 shows the variations of Edi, and AH versus 0. Curves (B) and (C), for both plugs, are very close to each other and possess the same limit. - ~ d l f f = 3.5 kcal/mole when 0 tends toward zero. Barrer (22) has studied the ratios •diff/Ag in the case of physical adsorptions. For an activated adsorption, the ratio Ediff/ Ea,s of the activation energy for surface diffusion to energy of desorption, expresses the ability of the gaseous molecule to migrate on the surface before acquiring the energy necessary for a complete desorption. By an experimental method using a field emission microscope, Gomer et al., and other authors, have studied the mobilities of several gases, among which, hydrogen (23), oxygen (24), and carbon monoxide (25) chemisorbed on tungsten. The ratio Ediff/Edos varies from 0.09 to 0.45, from hydrogen to carbon monoxide, and tends to increase with the size of the chemisorbed molecule. For carbon dioxide, we obtained Eaiff/Edos = 0.1, a value located in the same range. Although it is difficult to compare the chemisorption of gases on metals with the chemisorption of gases on metal oxides, the low value of this ratio, nevertheless, suggests that the carbon dioxide chemisorbed on magnesium chromite is very mobile on its surface. However, if the value of Ediff is compared to the thermal energy of the molecules, the latter is noticed to be much smaller and, thus, carbon dioxide must not be considered as a two-dimensional, mobile gas. Its
IC
o'.~
o'.2
0'.3
,~
FIO. 7. Variations of AH and Ediff for plug B and C versus 0: • AH; • Ediff plug B; [] Ediff plug C. mobility is linked to the jump from site to site thanks to a migration energy which is low relative to the desorption energy. I t belongs to the "activated mobilities" as defined by Haul (26).
ACTIVATED SURFACE DIFFUSION H w a n g and Kammermeyer (11) have put forth an activated surface diffusion model for the flow of gases through porous media, in the physical adsorption range, and established the following flow equation. A Q(MT)~ = A + B T exPT ,
[-19]
where A stands for the Knudsen flow; B is a surface flow coefficient which is constant for a gas-adsorbant system as well as fx which is defined by E*
--
= - - ;
E
E20]
K ~* is the minimum potential energy for an adsorbed molecule, ~ is the activation energy of surface diffusion for an adsorbed molecule. Figure 8 gives the variations of L o g ( ( Q ( M T ) ~ - - A ) / T ) versus 1/T for this study and in the range of reversible chemi-
Journal of Colloid and Interface Science, Vol. 59, No. i, M a r c h 15, 1977
92
CIOSMAK-GALLAND AND DELAFOSSE 1.6
1.8
2
2.2
o Ca.9
i~.4
obtained diffusion we can sorption the solid
for the activation energy for surface with those for desorption energy, consider the carbon dioxide chemias an activated mobile adsorption on surface. REFERENCES
~.2
~
13.7
r 2.1
~ T
0-3
FIG. 8. Hwang equation test: • plug B; • plug C. sorption. We have calculated quantity A with respect to helium. Our results are in good agreement with Hwang's equation, and give the following values. --plugB:
A=0.8X
103 °K, e * - - e = 1.6 kcal/mole,
-- plug C: A = 1:31 X 10~ °K,
1. CARMAN',P. C. AND MALHERBE~P. LE R., Proc. Roy. Soc., Set. A 203, 165 (1950). 2. CARMAN,P. C. AND RAAL, R. A., Proc. Roy. Soc., Ser. A 209, 38 (1951). 3. BARRER, R. M. AND BARRIE, J. A., Proc. Roy. ~ Soc., Set. A 213, 250 (1952). 4. BARRER, R. M. AND STRAe~AN, E., Proe. Roy. ~,~ Soc., Ser. A 231, 52 (1955). 5. BARRER, R. M. AND GABOR,T., Proc. Roy. Soc., Ser. A 2S1, 353 (1959). 6. As~, R., BARRER, R. M., AND POPE, G. G., Proe. Roy. Soc., Ser. A 271, 1 (1963). 7. AYLMORE, L. A. G. AND BARRER, R. M., Proc. Roy. Soc., Ser. A 290, 477 (1966). 8. VON HAUL, R. AND MOESTA, H., Z. Electrochem. Ber. Bunsenges. F. Phys. Chem. 66, 754 (1962). 9. DACEY, J. R., Advances in Chemistry Series,
e*-- e = 2.6 kcal/mole. Both values lead to e * = 4.5 kcal/mole for 8 = 0.6 (the permeability experiments were performed with high coverages), which is consistent with the value AH = 4 kcal/mole found for the considered 0 range. Nevertheless, the theoretical expressions call for statistical thermodynamics rigorously applicable to physisorbed molecules. The numerical values calculated from these expressions, in the case of a chemisorption, are not necessarily comparable to those deduced from experimental measurements. CONCLUSION The study of helium flow through magnesium chromite plugs has shown that, over the high-temperature range helium could be considered as a nonadsorbable calibrating gas on magnesium chromite. Moreover, for carbon dioxide, over the temperature range where it is chemisorbed on magnesium chromite, an activated surface diffusion contributing to the overall flow can be p u t in evidence. This diffusion is related to the amount adsorbed and to temperature. B y comparing the values
10. 11. 12. 13. 14. 15. 16.
No. 33, pp. 172-181, American Chemical Society, Washingtoi/, D.C., 1961. T~IORI~TON,A. W., Thesis, Ohio State University, 1968. HWAN% S. T., Thesis, State University Iowa, 1965. GALLAND,D. COINTOT, A., AND BARRET, P., J. Chim. Phys. 68, 588 (1971). KNIYDSEN,M., Ann. Phys. 28, 75 (1909). ADKINS, H. AND COI~NOR, R., J. Amer. Chem. Soc. 53, 1901 (1930). MOREAU,M., Th~se, Dijon, 1969. GERARD, N., Th~se de Doctorat d'Etat, Dijon, 1967.
17. GILLOT, B., MOREAU, M., AND DELAFOSSE, D., Bull. Soc. Chim. Fr. 4, 1330 (1970). 18. MOORE,W..1., "Chimie Physique," Dunod, Paris, 1961. 19. CARMAn,P. C., "Flow of Gases through Porous Media," Academic Press, New York, 1956. 20. ASH, R., BARIZER,R. M., AND LOWSON, R. T., Surf. Sci. 21, 265 (1970). 21. ARM:AND,G., LEJAY,Y., J. Mdeanique 1, 5 (1968). 22. BARRER, R. M., "The Solid Gas Interface," pp. 557-609, Dekker, New York, 1967. 23. GOMER, R., WORTMAN, R., AND LUND¥, R., J. Chem. Phys. 26, 1147 (1957). 24. GOM~R,R. AND HULM, J. K., J. Chem. Phys. 27, 1363 (1957). 25. KLEIN,R., J. Chem. Phys. 31, 1306 (1959). 26. voN HAUL, R. AND Ht3BNER, K., Z. Electrochem. Bet. Bunsenges. Phys. Chem. 79, 9 (1975), 777.
Journal of Colloid and Interface Science, Vol. 59, No. I, March 15, 1977