SURFACE
SCIENCE 23 (1970) 299310 8 NorthHolland
ADSORPTION
ISOTHERMS
B. KINDL*,
E. NEGRI
OF NOBLE
Publishing Co.
GASES ON GLASSES
and G. F. CEROFOLINI**
SAES Getters Research Laboratories, Via Gallarate 215, 20151 Milano, Italy Received 20 April 1970 The adsorption of argon and krypton on glasses which had previously undergone various thermal treatments, has been studied. In the case of krypton it has been found that at 77.3”K the DubininRadushkevich (DR) isotherm is satisfied. The number of adsorption sites and the average binding energy have been evaluated. For argon a significant deviation from the DR equation has been observed. On the (s2, In 9) plane the isotherm has a typical broken line structure. Three models have been proposed to describe the system and the relative validity of the models is compared by careful analysis of the experimental results.
1. Introduction: The DR isotherm Dubinin
and Radushkevichl)
proposed the following adsorption isotherm
lnN=lnN,BE’,
(1)
where : E = RTln (p/pJ is the Polanyi potential N =number of molecules adsorbed per unit area of the surface N, = a constant, characteristic of the adsorbent/adsorbate pair B =constant related to the average binding energy R = universal gas constant T = absolute temperature p = pressure p0 = vapour pressure of adsorbate. Kaganers) has shown that for some systems, for which the BrunauerEmmettTeller (BET)3) isotherm and the DR isotherm are simultaneously valid, the constant, N,, coincides for all practical purposes with the number * Now at: Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada. ** Now with: Gruppo di Fisica dei Solidi, Istituto di Fisica dell’ Universita, Via Celoria 16,201OO Milano, Italy. 299
300
B. KINDL,
E. NEGRI
AND
G. F. CEROFOLINI
of sites per unit surface area as determined by the BET method. quentIy N, is called the DR area of the surface. With these considerations eq. (1) is written in the form ln$=
 B.z2.
Conse
(2)
In this form eq. (2) has shown itself to be valid for a large number of adsorbentadsorbate systems*+) at temperatures below the condensation temperature of the gas and also for coverages between low6 and 10r when taking p. as the vapour pressure of the liquidd) or the solids). Let us now consider a surface formed of two noninteracting zones, the first characterized by an isotherm 9,(p) and the second by an isotherm Q2(p). The isotherm for the whole surface is therefore $(p)=a9,(P)+fla)9,(p),
(3)
where r~is that fraction of the surface characterized by the isotherm 9, (p). If, in particular, the isotherms are DR, then iV2(E) = N,, exp ( B,E') .
K (8) = N,, exp(  &a’), Eq. (3) then gives
N(E) = N,, exp(  B,E’) + N,,exp( 
B,E~),
(4)
and if B, > B, ,
Ns,
9
h’s,,
(9
then the following relationships hold ~,+003N(~)~N,~exp(B,~‘), E+0
=s
N(E)= N,,exp(
B,e').
From the latter two relationships it is observed that, if the system is under the conditions for which eq. (4) holds true and the local DR isotherms satisfy conditions (5), then on the plane {E’, In N) the extremes are rectilinear with different slopes. 2. Experimental For the experimental determination of the adsorption isotherms the apparatus used was similar to that already adopted in analogous experiments4Q) (see fig. 1). The oil pumping system, of a conventional type (rotary, diffusion), had a Biondi alumina traplo) above the diffusion pump. The layout for the determination of the isotherms was that of Hansen*) with two BayardAlpert ionization gauges one at either end of a tubulation of known conductance (FA= 1.66 cm3/s, FKr= 1.17 cm3/s). Cooling of the adsorption cell
ADSORI’TlON
ISOTHERMS
OF NOBLE
GASES
ON GLASSES
301
to pumps
Fig. 1. Diagram of experimentalsystem. was by liquid nitrogen. It was assumed that 90 min was sufficient time for thermal equilibrium to be established between the glass and the liquid nitrogen, at which point the pressure reaches 3 x lo‘* Torr. Suitable regulation of the pressurep, indicated by the gauge IGI controls the flux across the tubulation so that an equilibrium pressure pg, indicated by IG2, is established in the adsorption cell. The equilibrium pressures in the cell are obtained by adding to p a correction for the thermomol~ular flux”). Noble gas pumping by the gauges was kept to a low level as an ionization current of only 100 PA was used. Because of the low pumping speed of the surface, an accurate relative calibration of the gauges was performed. Spectroscopically pure gases were used. 3. Experimental results The adsorption of krypton and argon was examined on the following glass samples : (a) a sphere of Corning 7740 Pyrex blown by machine; (b) an extruded tube of Hysil from Joblin ; (c) a sphere obtained from (b) by hand glass blowing; (d) a sphere as (c) but annealed (flame heated) until no further strains were visible in polarized light. The behaviour of the glasses depended upon the test gas being used and so discussion of the experimental results will thus be considered in two parts.
302
B. KINDL,
E. NEGRI AND G. F. CBROFOLINI
3.1. KRYPTON
In the case of krypton, all glasses followed the DR isotherm, showing the usual “tail” at low E. The vapour pressure of the adsorbate is assumed to be equal to that of the solids) at 77.3”K: pz7.31 = 1.742 Torr. The results obtained for krypton have been summarized in table 1 which gives* IV,,Bf and c=
i$IcFln
(
>
+,
that is the standard deviation of the results with respect to the DR straight line calculated by the method of least squares. A typical isotherm, referred to sample (a) is shown in fig. 2.
(for the determination Sample
TABLE 1 Gas krypton of Ns and Bt the low energy values have been eliminated)
Bt (kcal/mole)
Ns (sites/cm2)
(4
9.59 2.83 7.36 2.51
(b) (c) (d)
x 10’3 x 1014 x 1013 x 1013
10'8 _
10”
1.263 1.317 1.221
0.0362 0.0346 0.0326
1.301
0.0609
SAMPLE:
a.
GAS:
K
_
10’2
I 0
5
2.5 E2 Fig.
2.
(
7.5 KCAL*MOLE*
10
)
Typical isotherm using krypton on glass sample (a).
* When the condensation approximation energy 4 by 12) 4 = $T*B+.
holds Bt is related to the average binding
303
ADSORPTION ISOTHERMSOF NOBLE GASES ON GLAS.WS
3.2. ARGON When argon was used, the glasses showed a behaviour very different from that reported in the literature5*ss9). Whilst (b) showed a straight line (fig. 4),
10’2 0
4
25
frJ
Fig. 3, Isotherm using argon on sample (a).
SAMPLE
: b
CRS:
A
. 2.5
7.5 f2(:
CA12MOtE2)
Fig. 4. Isotherm using argon on sample (b).
10
_A
304
B. KINDL,
E. NEORI AND ~3. F. CEROFOLINI
is it seen that for glasses (a), (c) and (d) on the {E’, In N} plane, the isotherms show a typical broken line structure (fig. 3, 5 and 6). The vapour pressure of adsorbate is assumed to be that of solid argon 7) PY3 = 202.625 Torr.
SAMPLE:
c
GAS:
0
5
2.5 E2(K
Fig. 5.
CAL?MOLE’
A
7.5
70
)
Isotherm using argon on sample (c).
SAMPLE:
lo’*
GAS:
d A
10" 10’6
/G: Y 10’5 is !3 P 10’4 z 10’3
10’2 0
5
2.5 E2
Fig. 6.
7.5
(K CAL2UOLE2)
Isotherm using argon on sample (d).
10
ADSORPTIONISOTHERMSOPNOBLE
305
GASESONGLASSES
The isotherms (a), (c) and (d) have been studied in the light of 3 models: (i) considering the experimental points as being in accordance with DR; (ii) considering the experimental points on the {E’, In N) plane as forming a broken line; (iii) considering the experimental points as being in accordance with an isotherm of expression (4) under conditions (5). The values of IV,, B* and 0 for case (i) and IV,,, By",Ns2, B;* and o for cases (ii) and (iii) are shown in tables 2, 3 and 4 (for the way in which these parameters are evaluated see Appendix). From the tables it is clear that description (i) does not agree with the experimental data; on the other hand the third interpretation is upheld by physical consideration related to the surface heterogeneity (see next footnote). TABLE 2 Gas
argon  plot for one straight line Bt
Sample
N, (sites/cm2)
(kcal/mole)
(4
4.96 x 1015
(b)
1.17 x 1015
u
u’
0.979
0.1845
0.2109
1.150
0.0776
0.0849
6.19 x 1015
0.963
0.1301
0.1582
3.28 x 1015
0.980
0.1064
0.1375
TABLE 3 Gas
Sample
(d)
Nsl (sites/cm2)
argon  plot for a broken line B1t
NS2
(kcal/mole)
(sites/cm2)
B2’
(kcal/mole)
(T
2.16 x 1014
1.151
1.39 x 10’6
0.914
0.0752
1.98 x 10’5 1.17 x 1015
1.015 1.032
2.21 x 1016 7.34 x 1015
0.880 0.920
0.1414 0.1234
TABLE 4 Gas
Sample
(d)
argon  plot for a sum
B1t
B2’
NSl (sites/cm2)
(kcal/mole)
Ns2 (sites/cm2)
(kcal/mole)
1.08 x 1Ol3 1.71 x 1015 8.82 x 1014
1.375 1.021 1.044
1.60 x 10ls 7.49 x 1016 1.52 x 10’6
0.902 0.780 0.830
(I
0.0555 0.0524 0.0484
306
B. KINDL,
E. NEGRI
AND
G. F. CEROFOLINI
4. Discussion of the results
For krypton the experimental results are in substantial agreement with those in the literature. Ricca, Medana, and Bellardos) give B*= 1.379 kcal/mole, N,= 6.93 x 1Ol3 atoms/cm’. Endow and Pasternake) give B*= 1.340 kcal/mole, N, = 4.7 x 1014 atoms/cm’. Both results are comparable with those obtained from the present experiments (see table 1). For argon, however, this agreement was not found. On the contrary, a superactivity of the glass was observed [already seen by Ross and Roberts’s) using the BET technique] corresponding to an increase by a factor between 10 to 100 in the total number of sites when compared to glass before treatment. Assuming interpretation (iii) to be correct* it is deduced that as a result of the heat treatments [from (b) to (c) or from (b) to (d)] the glass undergoes a profound structural change. The following interpretation is proposed: On heating, a part of the alkali metal oxides leaves the glass and is later redeposited on the surface giving rise to a new surface overlaying that of an oxide starved surface. The isotherm
10’8

1.
l
14 hours 4OO’C
2.
0
28 hours  4OO’C
3.
l
42 hours
4OO’C
lO”_
lo=_ c t: 3
10’5
_
z 2 E/
,o14
R
10’3
_
10’2 0
2.5
5 t2
Fig. 7.
7.5
10
( KCAL2tiOLE2)
Isotherms using argon on sample (e) after indicated thermal treatments.
* If the condensation approximation 1s) holds then the energy distribution function can be written v, (8) =  &9(s)/&, so that if Q(E) has an angular point [as in the case of interpretation ii)] then the distribution function has a discontinuity whose existence is difficult to explain.
307
ADSORPTiON ISOTHERMSOF NOBLE GASESON GLASSES
corresponding to the oxide is that (of higher energy) which prevails at high E, whilst the less energetic isotherm corresponds to the underlaying oxide depleted glass. We can presume that this state is thermodynamically unstable as the concentration of oxide at the surface of the glass is much greater than that of the first few internal layers. As diffusion is an activated process it is to be expected that the glass can be made relatively more stable by simply heating it for a sufficient time at a temperature less than that required for oxide evaporation. A sample (e) was chosen which had been treated as sample (c) and repeated baking under vacuum at 400°C caused the adsorption isotherm to go from case 1 to cases 2 and 3 of fig. 7 passing from a sum to a single line. This is confirmed by the TABLE 5 Gas
Sample
W (e2) (e3)
argon  plot for one straight line
Bt (kcal/mole) 0.987 0.974 0.927
NS (sites/cm2) I.68 x 10’5 1.75 x 1015 5.79 x 10’5
r?
0.1572 0.1187 O&416
data given in table 5 which show better linearity for the isotherms obtained for surfaces which have been heated for a long time. As krypton and argon interact with the glass through Van der Waals forces only, the difference of behaviour between the two gases must be explained. In essence, two models can be postulated to explain this fact. The first consists in supposing that the surface obtained after annealing has a molecular sieve structure with diameters of the micropores between those of argon and krypton. The second consists in supposing that a large part of the surface is not exposed to the gas and because of the greater mass of krypton it moves with greater difficulty along the surface to the less exposed zones. Thus the pressure measurements would refer to an unstable state with a relaxation time greater than the duration of an entire adsorption experiment (about 103s). If rA is the relaxation time for argon and DA is its diffusion coefficient along the glass surface, it can be assumed that, for krypton
308
B.KINDL,
E. NEGRI
AND G. F. CEROFOLINI
where the preexponential factors t for krypton and argon are assumed to be approximately equal and AE* indicates the activation energy for surface diffusion. The reported values of the preexponential factors show large differences depending on the nature of the gas and the state of the surface. We have adopted an “average” interpretation for which the preexponential factor is proportional to the elastic constant of the bond. A detailed discussion is given elsewhere 153is). As argon equilibrium is reached in a short time (less than the response time of the instruments, pessimistically of the order of 5 s) whilst rKrg lo3 s, it would be necessary that AE& AE,* has a value greater than can be realistically considered. It is estimated from known datai4) that: A&
 AE: < 100 Cal/mole.
Naturally it cannot be excluded, and it is even probable, that there is the simultaneous presence of a molecular sieve structure and a low exposed zone structure. 5. Conclusions A superactivity has been observed for argon on Pyrex following thermal treatment (annealing). A mechanism has been postulated which is capable of explaining this fact and also the different behaviour of krypton and argon. The proposed model was suggested as a result of using the DR isotherm experimental method which is more flexible in the submonolayer range than the BET method and which is capable of giving information concerning surface energy heterogeneity. Acknowledgements
The authors would like to thank Dr. P. della Porta for permission to publish this work and Dr. T. A. Giorgi for his continuous encouragement. The authors are also grateful to Mr. M. Borghi who performed the numerous calculations. Appendix
This appendix describes the methods used for determining meters N,, B* and 6. t The ratio of the preexponential mass ratios.
factors is approximately
the para
given by the square root of the
ADSORPTION ISOTHERMS OF NOBLE GASES ON GLASSES
309
For krypton the points on the tail of the isotherm at low s2 have been excluded from the calculation. For argon the results corresponding to very high s2 have also been rejected as they are subject to large experimental errors. For model (i) the best straight line fitting the experimental results was obtained using the method of least squares. For model (ii) two “confidence zones” (one at low and the other at high s2 values) were defined in which the behaviour is approximately rectilinear. In these zones the method of least squares was used to determine the straight lines which were then extrapolated to evaluate the intercepts with In N axes. The root mean square deviation was calculated for all points with respect to the previously determined broken curve. For model (iii) it is seen from relationships (5), (7) and (8) that the line determined by method (ii) in the second confidence zone is a good approximation (by excess) in the same zone at eq. (4), and similarly for the line in the first confidence zone. Subtracting, in the first confidence zone, from the isotherm the line extrapolated from the second confidence zone (and similarly for the line in the second confidence zone) one obtains by the method of least squares two new lines which are seen to be approximations by defect. An iterative procedure leads to a succession of lines which eventually converge. The procedure is continued until the distance (evaluated according to the Lagrange definition) between the lines approximated by excess and by defect is less than l/lOOth of the root mean square deviation determined for the broken line. The line chosen is the bisector of the last two approximations obtained by excess and by defect. The calculations required 5 min using the IBM 7040 of the Computing Centre at the Milan Polytechnic. The results are given in tables 1, 2, 3 and 4 from which it appears evident the interpretation (iii) has the closest agreement with the experimental results. It is useful to note that d for model (i) sometimes has values lower than those for model (ii) as the best fit for model (i) uses all the experimental points whilst model (ii) uses only those points in the confidence zones. If model (i) is treated in the same way as model (ii), the values 6’ are obtained which are larger (as they should be) than the Q values of model (ii). References 1) M. M. Dubinin M. M. Dubinin, 2) M. G. Kaganer, 3) S. Brunauer, P.
and L. V. Radushkevich, Dokl. Akad. Nauk SSSR 55 (1947) 331; J. Am. Chem. Sot. 81 (1959) 235. Dokl. Akad. Nauk. SSSR 116 (1957) 251. H. Emmett and E. Teller, J. Am. Chem. Sot. 60 (1938) 309.
310 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
B. KINDL,
E. NEGRI
AND G. F. CEROFOLINI
N. Hansen, Vakuum Technik 11 (1962) 70. J. P. Hobson and R. A. Armstrong, J. Phys. Chem. 67 (1963) 2000. N. Endow and R. A. Pastemak, J. Vacuum. Sci. Technol. 3 (1966) 196. P. Haul and B. A. Gottwald, Surface Sci. 4 (1966) 321. F. Ricca, R. Medana and A. Bellardo, Z. Physik. Chemie NF 52 (1967) 291. A. Schram, Suppl. Nuovo Cimento 5 (1967) 309. M. A. Biondi, Rev. Sci. Instr. 30 (1959) 9. M. J. Bennett and F. C. Tompkins, Trans. Faraday Sot. 53 (1957) 185. G. F. Cerofolini, Submitted to Surface Sci. J. R. H. Ross and M. W. Roberts, J. Catalysis 4 (1965) 620. F. Ricca, Suppl. Nuovo Cimento 5 (1967) 339; G. Erlich, Brit. J. Appl. Phys. 15 (1964) 349. 15) J. F. Antonini, Suppl. Nuovo Cimento 5 (1967) 354. 16) L. A. Petermann, Suppl. Nuovo Cimento 5 (1967) 364.