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Film area hysteresis in porous Vycor
$OUI~NAL OF COLLOID AND INTERFACE SCIENCE 24, 366--371
(1967)
Film Area Hysteresis in Porous Vycor C L A R E N C E B. F E R G U S O N A~
The area of porous Vyeor has been measured at various degrees of saturation with water. A plot of pore area versus location on both the adsorption and desorption branches of the isotherm was constructed. From such a plot it is clear that the pores cannot have cylindrical geometry and that two or more pore geometries contribute to the pore structure. INTRODUCTION In a previous publication from this laboratory (1), the area of pores interlacing packed spheres was obtained from N2 adsorption measurements and subsequent B.E.T. analysis of the data. Particular attention was focused on such pores which had been preequilibrated with water vapor, this latter being frozen in situ prior to each area determination. The substrate's pore structures were generated by compression of an unconsolidated powder into pellets. Pores are generated randomly with such a procedure, and any local order is certainly not perpetuated over many sphere diameters. As a result the N2 B.E.T. areas obtained from the desorption branches of the water isotherms and the desorption branches of the water isotherms themselves show that there is a considerable spread in pore aperture sizes as is normally found in most real systems. The only material now known which hopefully could approach any simple irreversible pore filling/emptying model is porous Vycor. This material has been the subject of numerous studies dealing with adsorption hysteresis (2-5). The usual observation is that pore filling (adsorption) is not discontinuous, whereas the onset of pore emptying (desorption) occurs precipitously. This latter is synonymous with considerable uniformity of pore necks. Such behavior is to be expected for "ink bottle" shaped pores with uniform necks, although many other pore configurations can give rise to similar
characteristics. The application of the Kelvin equation to the desorption branches of isotherms on porous Vycor as a consequence gives a very narrow distribution of radii of curvature of the meniscus. Despite the m a n y reported studies on this material, little is known about its detailed pore structure other than the remarkable uniformity of pore neck sizes. It was thus decided that a simultaneous evaluation of pore area and pore volume hysteresis distributions might be of some assistance in elucidation of the pore structure of porous Vycor. In particular, one would like to know the relation between the development of open pore area and volume on the desorption branch. Such relationships can help distinguish the more exotic pore shapes the area to volume ratios of which differ markedly from capillary shaped pores or pores arising as the interstices between packed spheres. EXPERIMENTAL The sample of porous Vycor, designated 7930 by the manufacturer, was obtained from Coming Glass Works and is believed to be similar or identical to samples used in previously reported studies (2-5). The sample (~/~ in. in diameter and approximately 1/~ in. long) was heated in oxygen at 350°C. to oxidize any adsorbed organic impurities, soaked in boiling distilled water, and finally heated and evacuated at 200°C. and 10-6 torr to remove the imbibed and physically adsorbed water. A water isotherm was then 366
FILM AREA HYSTERESIS IN POROUS VYCO~ obtained at 2 5 ° C . using a volumetric adsorption apparatus (6). Two complete scans of the hysteresis loop were taken. This identical sample was then transferred to a second volumetric adsorption apparatus where after once again outgassing at 200°C. and 10-8 tort, the sample was then preequilibrated with water at various relative pre.~sures corresponding to both the adsorption and desorption branches of the isotherm. Following equilibration the sample was slowly cooled (7) to approximately 77°K. and N2 isotherms were obtained. The molecular area of N2 was chosen to be 16.2 A< A total of 35 such N2 isotherms, each consisting of 5-8 experimental points in the region of 0.02 < p/po < 0.22, were taken. The complete water isotherm itself consists of approximately 200 points.
and 20 torr, the initial isotherm did not completely close at lower pressures. However, on the second complete scan, a completely closed loop was obtained by virtue of some enhanced adsorption on the ascending branch at lower pressures. Apparently some slow rehydration of siloxane groups had occuffed on the first scan. Also shown in Fig. 1 are the B.E.T. areas calculated from N2 isotherms. T h e y are plotted as a function of the H20 pre-equilibration pressures. The N2 isotherms themselves are not shown; however, randomly selected B.E.T. plots are shown in Fig. 2. All such plots have demonstrated quite acceptable Hnearity over the relative pressure region shown. T h e y are for the sample's actual weight of 0.1493 g. The B.E.T. c constants decrease from ~-~200 for the outgassed surface to ~ 1 0 0 for surfaces with > 2 statistical layers of H20 preadsorbed. Also displayed in Fig. 2 is the B.E.T. plot for the water isotherm. On the basis of a surface area ~--~x2 = 125.5 m?/g. for the outgassed surface, the calculated H20 molecular area
RESULTS The water isotherm is displayed in Fig. 1. It is very similar to that obtained by Amberg and McIntosh (5). In addition to the large hysteresis loop existing between 16
120
367
o Adsorption • Desorption
I00
]200
80-
160
O
E Pq
60 r
q
>
40-
20 b-
0"~ o
~--,-,z*-~.~--'~
,
I 4
t 8
-- 1
,
I 12
,
I ~,-,16
--,-{
-4 4 o
AIo
20
P (Torr)
Fie. 1. Water adsorption isotherm (right ordinate) and N2 film areas (left ordinate) as a function of tt20 pressure. Open circles refer to the adsorption branch and closed circles to the desorption branch.
368
FERGUSON AND WADE
E = 56.7
= 25.7 V = 0.204
0.14
V = 0.140
0.12
Z = 51.2
V = 0.099
%
0.10
"1-
E = 72,0 V = 0.074 ~'o >~ v
0.08
:=Sk-7 . ' ~
i
nO9
o
Z=96.5 V = 0.042
0.06
E = 125.5
LLI
rd
V = 0.00 0.04
o
o, •
from N 2 from
odsorpion bronch H20
desorpfion
branch
e H20
o~ o
I
I
0.04
I
I
I
0.08
I
0.12
I
I
0.16
I
I
0.20
l
P/P0
Fie. 2. B.E.T. plots for N2 on frozen H20 films and for the H~O isotherm itself. Open circles are from the adsorption branch, closed circles from the desorption branch, and bisected open circles for the I-I~O isotherm. For the N~ plots, the calculated Z(m.~/g.) and V (cclq/g.) are given. = 12.2 .~2. All B.E.T. calculations were terminated at p/po < 0.2 to minimize contributions from capillary condensation to the experimental isotherms. DISCUSSION If the proposed pore model consists of open-ended capillaries as assumed by Amberg and McIntosh (5), then the apparent pore radius can be calculated from the desorption branch of the isotherm by the suitable application of the Kelvin equation: In p/pO =
,,/17 (\ ~1 + ~1 ) ,
[1]
where V is the molar volume of water, Ra is the gas constant, 1' is the water liquid/vapor interfacial tension, T is the absolute temperature, and pl and p~ are the principal radii of curvature of the meniscus. If the contact angle 0 of the liquid in the pore is assumed to be zero, then Eq. [1], for a hemispherical meniscus, reduces to
lnP/P° = _ "y~" ._2 RaT r~ '
[2]
where r, is the apparent pore radius. To obtain the true pore radius r~ an increment t (the thickness of the residual adsorbate fol-
FILM AREA HYSTERESIS IN POROUS VYCOR lowing pore opening) must be added to ra. And Eq. [1] finally reduces to In p / p O = - "yV RaT
isotherm, and indeed a plot of dZ/dr~ for the film area taken on the desorption branch is very similar to d V / & ~ with the maximum occurring once again at 30 A. On closer intercomparison of V and Z interesting details appear. This is brought out by Fig. 3, where film area is plotted versus adsorbate coverage taken from both branches of the isotherm. Two points are of particular note regarding this graph. First, there is a break in the plot at the lower closure point of the loop. Second, there is a hysteresis loop in this plot. Both observations clearly show that the pores are not simply open-ended capillaries. Although from the present data it is obviously incorrect in detail, we shall assume the pores to be true open-ended capillaries. Then from geometrical considerations o
[3]
2 (r~ -- t)"
With no prior knowledge of the neck geometry, rt should be regarded as an equivalent pore radius. Since for porous Vycor the majority of the irreversible desorption branch is located in a narrow pressure band (16.3-16.8), it is particularly feasible to assume t is constant over this range at ~ 1 - 2 layers or ~ 5 A (4). The slope d V / & h of the desorption branch gives an apparent pore volume distribution. Such a distribution for the present data is very similar to that of Amberg and McIntosh (5) but with the maximum shifted from 28 A to 30 A for r~. This shows there is a slight difference in the samples used in the two studies. At first glance the film areas (~) plot versus P appears to be a mirror image of the
1201-\ ~
~
369
r
= ~(r,~ -
It,-
t]~)/
[4]
and = 2 ~ - ( r , - t)l,
[5]
r =50
I00
80
~60
ption
v
Adsorption
40
20
O
I
1
40
I
/ 801
!
I
120 V (cclq/g x IO3)
1
I
160
~
I \\
200
I
FIG. 3. Plot of ~(m3/g.) versus V (eclq/g. X 10~) is from the data of Figure 1. Plots based on a cylindrical capillary model for radii of 30, 35, and 40 A are also given.
370
'
FERGUSON AND WADE
where l is the length of any particular pore. Given a distribution of r, and l, the total volume of adsorbate and film area could be plotted as a function of t if the regions of pore intersection are of minor importance. Particularly suited to the present study, however, rt can be apoproximated as a constant of 30 -k 5 = 35 A. Once again in detail the hysteresis loop indicates a minor percentage of smaller pore neck sizes which must be overlooked. From the saturation value of 0.200 cclq/g,, then a graph of V versus E can be plotted. This predicted behavior is also shown in Fig. 3. For co:mparison, rt = 30 and 40 A are also plotted. It would be better to use a saturation value of 0.210 cclq/g, since the value of Z remains negligible over this range indicating a small percentage of pore volurae with negligible area. This would not significantly change the shape of the model plots of Fig. 3. There is a complete discordance between the experimental data and the expected behavior of simple open-ended cylinders. In particular, there is a more rapid drop in Z at small V and a less rapid drop in Z at large V than would be expected. The initial rapid decrease of ~ with V within experimental limitations could be explained by cylindrical geometry in that with sufficiently small pores this rapid decrease could be obtained. It is noted that the simple open-ended model shows an increasing initial drop in going from 40 A to 30 A pores. Cylindrical pores 15-20 A in radius would fit the ~ (V) behavior in the low-V region. However, the pores would need to be closed-ended since such pores reversibly disappear and reappear below ~-~0.070 cclq/g. At larger volumes adsorbed pores have an area/volume ratio less than that for cylindrical geometry with a radius of 35 A. The behavior in this region could well be approximated by capillaries of 50-55 A in radius, which would need to be open-ended to be consistent with the observed hysteresis loop. Of course this would be discordant with the position of the isotherms hysteresis loop in terms of the Kelvin equation. In addition, the existence of the hysteresis loop in Fig. 3 is discordant with an open-ended cylindrical capillary model for, with this model, no hysteresis loop o
should occur. Such a loop clearly dictates that within the hysteresis loop region the open pores have a different area/volume ratio on each of the two branches. If once again open-ended cylindrical capillaries were assumed, then with the use of a true pore radius of 35 A from Eq. [3], a reasonable guess of 5 A for t, and a total pore volume of 0.220 cclq/g., the true pore area would be _ 2V _ 126 m.2/g.;
[6]
rt
this agrees, fortuitously well, with the measured B.E.T. value of 125.5. Agreement such as this usually is used as an argument for cylindrical geometry. Such a conclusion is not warranted in light of the present data. In fact, it has been previously shown that the pores formed between randomly packed spheres can have a similar area/volume ratio (1). In general it must be concluded that pores of many different geometric shapes may show an apparent likeness to capillaries as Everett (8) has so correctly noted. Unfortunately, this then sets a limitation on the usefulness of a graph such as Fig. 3. It can be used to rule out any particular but mathematically describable pore geometry, but cannot be of complete definity. Qualitatively, such behavior as evidenced in Fig. 3 would permit the pores to be interstices between packed spheres, nonuniform diameter capillaries with approximately constant neck aperture sizes, or a mixture of reversibly filled open-end and irreversibly filled closed-end capillaries, where the end areas are significant ink bottles with uniform necks but divergent area/volume ratios; however, the one geometry definitely excluded by the present data is the simple cylindrical capillary (singular or bimodal). This, of course presents the added complication of invalidating all pore volume distributions which have been based on such a geometry. Hopefully this data can be used in the future by investigators seeking to test the validity of proposed pore models for porous Vycor. And it might be advantageous for workers proposing a pore model for other
FILM
AREA
HYSTERESIS
m a t e r i a l s to p e r f o r m the same t y p e of measu r e m e n t s as a definitive test of their model. ACKNOWLEDGMENTS The authors wish to thank The Robert A. Welch Foundation of Houston, Texas, for their continued interest and support, and Mr. Arnold C. Falk, who performed many of the area measurements. REFERENCES 1. VENABLE,R., ANDWADE,W. H., or. Phys. Chem. 69, 1395 (1965).
IN POROUS
VYCOR
371
2. KINGTON, G. L., AND SMITH, P. S., Trans. Faraday Soc. 60, 705 (1964). 3. BARRER, R. M., AND BARRIE, J. A., Proc. Roy. Soc. (London) 213A, 250 (1952). 4. DE BOER, J. H., Proc. Colston Res. Soc. 10, 68 (1958). 5. AMBERG, C. H., AND MCINToSH, R., Can. Y. Chem. 30, 1012 (1952). 6. MEYER, D. E., AND HACKERMAN,N., J. Phys. Chem. 70, 2077 (1966). 7. WADE, W. H., J. Phys. Chem. 68, 1029 (1964). 8. EVERETT, D. H., Proc. Colston Res. Soc. 10, 95 (1958).
(1967)
Film Area Hysteresis in Porous Vycor C L A R E N C E B. F E R G U S O N A~
The area of porous Vyeor has been measured at various degrees of saturation with water. A plot of pore area versus location on both the adsorption and desorption branches of the isotherm was constructed. From such a plot it is clear that the pores cannot have cylindrical geometry and that two or more pore geometries contribute to the pore structure. INTRODUCTION In a previous publication from this laboratory (1), the area of pores interlacing packed spheres was obtained from N2 adsorption measurements and subsequent B.E.T. analysis of the data. Particular attention was focused on such pores which had been preequilibrated with water vapor, this latter being frozen in situ prior to each area determination. The substrate's pore structures were generated by compression of an unconsolidated powder into pellets. Pores are generated randomly with such a procedure, and any local order is certainly not perpetuated over many sphere diameters. As a result the N2 B.E.T. areas obtained from the desorption branches of the water isotherms and the desorption branches of the water isotherms themselves show that there is a considerable spread in pore aperture sizes as is normally found in most real systems. The only material now known which hopefully could approach any simple irreversible pore filling/emptying model is porous Vycor. This material has been the subject of numerous studies dealing with adsorption hysteresis (2-5). The usual observation is that pore filling (adsorption) is not discontinuous, whereas the onset of pore emptying (desorption) occurs precipitously. This latter is synonymous with considerable uniformity of pore necks. Such behavior is to be expected for "ink bottle" shaped pores with uniform necks, although many other pore configurations can give rise to similar
characteristics. The application of the Kelvin equation to the desorption branches of isotherms on porous Vycor as a consequence gives a very narrow distribution of radii of curvature of the meniscus. Despite the m a n y reported studies on this material, little is known about its detailed pore structure other than the remarkable uniformity of pore neck sizes. It was thus decided that a simultaneous evaluation of pore area and pore volume hysteresis distributions might be of some assistance in elucidation of the pore structure of porous Vycor. In particular, one would like to know the relation between the development of open pore area and volume on the desorption branch. Such relationships can help distinguish the more exotic pore shapes the area to volume ratios of which differ markedly from capillary shaped pores or pores arising as the interstices between packed spheres. EXPERIMENTAL The sample of porous Vycor, designated 7930 by the manufacturer, was obtained from Coming Glass Works and is believed to be similar or identical to samples used in previously reported studies (2-5). The sample (~/~ in. in diameter and approximately 1/~ in. long) was heated in oxygen at 350°C. to oxidize any adsorbed organic impurities, soaked in boiling distilled water, and finally heated and evacuated at 200°C. and 10-6 torr to remove the imbibed and physically adsorbed water. A water isotherm was then 366
FILM AREA HYSTERESIS IN POROUS VYCO~ obtained at 2 5 ° C . using a volumetric adsorption apparatus (6). Two complete scans of the hysteresis loop were taken. This identical sample was then transferred to a second volumetric adsorption apparatus where after once again outgassing at 200°C. and 10-8 tort, the sample was then preequilibrated with water at various relative pre.~sures corresponding to both the adsorption and desorption branches of the isotherm. Following equilibration the sample was slowly cooled (7) to approximately 77°K. and N2 isotherms were obtained. The molecular area of N2 was chosen to be 16.2 A< A total of 35 such N2 isotherms, each consisting of 5-8 experimental points in the region of 0.02 < p/po < 0.22, were taken. The complete water isotherm itself consists of approximately 200 points.
and 20 torr, the initial isotherm did not completely close at lower pressures. However, on the second complete scan, a completely closed loop was obtained by virtue of some enhanced adsorption on the ascending branch at lower pressures. Apparently some slow rehydration of siloxane groups had occuffed on the first scan. Also shown in Fig. 1 are the B.E.T. areas calculated from N2 isotherms. T h e y are plotted as a function of the H20 pre-equilibration pressures. The N2 isotherms themselves are not shown; however, randomly selected B.E.T. plots are shown in Fig. 2. All such plots have demonstrated quite acceptable Hnearity over the relative pressure region shown. T h e y are for the sample's actual weight of 0.1493 g. The B.E.T. c constants decrease from ~-~200 for the outgassed surface to ~ 1 0 0 for surfaces with > 2 statistical layers of H20 preadsorbed. Also displayed in Fig. 2 is the B.E.T. plot for the water isotherm. On the basis of a surface area ~--~x2 = 125.5 m?/g. for the outgassed surface, the calculated H20 molecular area
RESULTS The water isotherm is displayed in Fig. 1. It is very similar to that obtained by Amberg and McIntosh (5). In addition to the large hysteresis loop existing between 16
120
367
o Adsorption • Desorption
I00
]200
80-
160
O
E Pq
60 r
q
>
40-
20 b-
0"~ o
~--,-,z*-~.~--'~
,
I 4
t 8
-- 1
,
I 12
,
I ~,-,16
--,-{
-4 4 o
AIo
20
P (Torr)
Fie. 1. Water adsorption isotherm (right ordinate) and N2 film areas (left ordinate) as a function of tt20 pressure. Open circles refer to the adsorption branch and closed circles to the desorption branch.
368
FERGUSON AND WADE
E = 56.7
= 25.7 V = 0.204
0.14
V = 0.140
0.12
Z = 51.2
V = 0.099
%
0.10
"1-
E = 72,0 V = 0.074 ~'o >~ v
0.08
:=Sk-7 . ' ~
i
nO9
o
Z=96.5 V = 0.042
0.06
E = 125.5
LLI
rd
V = 0.00 0.04
o
o, •
from N 2 from
odsorpion bronch H20
desorpfion
branch
e H20
o~ o
I
I
0.04
I
I
I
0.08
I
0.12
I
I
0.16
I
I
0.20
l
P/P0
Fie. 2. B.E.T. plots for N2 on frozen H20 films and for the H~O isotherm itself. Open circles are from the adsorption branch, closed circles from the desorption branch, and bisected open circles for the I-I~O isotherm. For the N~ plots, the calculated Z(m.~/g.) and V (cclq/g.) are given. = 12.2 .~2. All B.E.T. calculations were terminated at p/po < 0.2 to minimize contributions from capillary condensation to the experimental isotherms. DISCUSSION If the proposed pore model consists of open-ended capillaries as assumed by Amberg and McIntosh (5), then the apparent pore radius can be calculated from the desorption branch of the isotherm by the suitable application of the Kelvin equation: In p/pO =
,,/17 (\ ~1 + ~1 ) ,
[1]
where V is the molar volume of water, Ra is the gas constant, 1' is the water liquid/vapor interfacial tension, T is the absolute temperature, and pl and p~ are the principal radii of curvature of the meniscus. If the contact angle 0 of the liquid in the pore is assumed to be zero, then Eq. [1], for a hemispherical meniscus, reduces to
lnP/P° = _ "y~" ._2 RaT r~ '
[2]
where r, is the apparent pore radius. To obtain the true pore radius r~ an increment t (the thickness of the residual adsorbate fol-
FILM AREA HYSTERESIS IN POROUS VYCOR lowing pore opening) must be added to ra. And Eq. [1] finally reduces to In p / p O = - "yV RaT
isotherm, and indeed a plot of dZ/dr~ for the film area taken on the desorption branch is very similar to d V / & ~ with the maximum occurring once again at 30 A. On closer intercomparison of V and Z interesting details appear. This is brought out by Fig. 3, where film area is plotted versus adsorbate coverage taken from both branches of the isotherm. Two points are of particular note regarding this graph. First, there is a break in the plot at the lower closure point of the loop. Second, there is a hysteresis loop in this plot. Both observations clearly show that the pores are not simply open-ended capillaries. Although from the present data it is obviously incorrect in detail, we shall assume the pores to be true open-ended capillaries. Then from geometrical considerations o
[3]
2 (r~ -- t)"
With no prior knowledge of the neck geometry, rt should be regarded as an equivalent pore radius. Since for porous Vycor the majority of the irreversible desorption branch is located in a narrow pressure band (16.3-16.8), it is particularly feasible to assume t is constant over this range at ~ 1 - 2 layers or ~ 5 A (4). The slope d V / & h of the desorption branch gives an apparent pore volume distribution. Such a distribution for the present data is very similar to that of Amberg and McIntosh (5) but with the maximum shifted from 28 A to 30 A for r~. This shows there is a slight difference in the samples used in the two studies. At first glance the film areas (~) plot versus P appears to be a mirror image of the
1201-\ ~
~
369
r
= ~(r,~ -
It,-
t]~)/
[4]
and = 2 ~ - ( r , - t)l,
[5]
r =50
I00
80
~60
ption
v
Adsorption
40
20
O
I
1
40
I
/ 801
!
I
120 V (cclq/g x IO3)
1
I
160
~
I \\
200
I
FIG. 3. Plot of ~(m3/g.) versus V (eclq/g. X 10~) is from the data of Figure 1. Plots based on a cylindrical capillary model for radii of 30, 35, and 40 A are also given.
370
'
FERGUSON AND WADE
where l is the length of any particular pore. Given a distribution of r, and l, the total volume of adsorbate and film area could be plotted as a function of t if the regions of pore intersection are of minor importance. Particularly suited to the present study, however, rt can be apoproximated as a constant of 30 -k 5 = 35 A. Once again in detail the hysteresis loop indicates a minor percentage of smaller pore neck sizes which must be overlooked. From the saturation value of 0.200 cclq/g,, then a graph of V versus E can be plotted. This predicted behavior is also shown in Fig. 3. For co:mparison, rt = 30 and 40 A are also plotted. It would be better to use a saturation value of 0.210 cclq/g, since the value of Z remains negligible over this range indicating a small percentage of pore volurae with negligible area. This would not significantly change the shape of the model plots of Fig. 3. There is a complete discordance between the experimental data and the expected behavior of simple open-ended cylinders. In particular, there is a more rapid drop in Z at small V and a less rapid drop in Z at large V than would be expected. The initial rapid decrease of ~ with V within experimental limitations could be explained by cylindrical geometry in that with sufficiently small pores this rapid decrease could be obtained. It is noted that the simple open-ended model shows an increasing initial drop in going from 40 A to 30 A pores. Cylindrical pores 15-20 A in radius would fit the ~ (V) behavior in the low-V region. However, the pores would need to be closed-ended since such pores reversibly disappear and reappear below ~-~0.070 cclq/g. At larger volumes adsorbed pores have an area/volume ratio less than that for cylindrical geometry with a radius of 35 A. The behavior in this region could well be approximated by capillaries of 50-55 A in radius, which would need to be open-ended to be consistent with the observed hysteresis loop. Of course this would be discordant with the position of the isotherms hysteresis loop in terms of the Kelvin equation. In addition, the existence of the hysteresis loop in Fig. 3 is discordant with an open-ended cylindrical capillary model for, with this model, no hysteresis loop o
should occur. Such a loop clearly dictates that within the hysteresis loop region the open pores have a different area/volume ratio on each of the two branches. If once again open-ended cylindrical capillaries were assumed, then with the use of a true pore radius of 35 A from Eq. [3], a reasonable guess of 5 A for t, and a total pore volume of 0.220 cclq/g., the true pore area would be _ 2V _ 126 m.2/g.;
[6]
rt
this agrees, fortuitously well, with the measured B.E.T. value of 125.5. Agreement such as this usually is used as an argument for cylindrical geometry. Such a conclusion is not warranted in light of the present data. In fact, it has been previously shown that the pores formed between randomly packed spheres can have a similar area/volume ratio (1). In general it must be concluded that pores of many different geometric shapes may show an apparent likeness to capillaries as Everett (8) has so correctly noted. Unfortunately, this then sets a limitation on the usefulness of a graph such as Fig. 3. It can be used to rule out any particular but mathematically describable pore geometry, but cannot be of complete definity. Qualitatively, such behavior as evidenced in Fig. 3 would permit the pores to be interstices between packed spheres, nonuniform diameter capillaries with approximately constant neck aperture sizes, or a mixture of reversibly filled open-end and irreversibly filled closed-end capillaries, where the end areas are significant ink bottles with uniform necks but divergent area/volume ratios; however, the one geometry definitely excluded by the present data is the simple cylindrical capillary (singular or bimodal). This, of course presents the added complication of invalidating all pore volume distributions which have been based on such a geometry. Hopefully this data can be used in the future by investigators seeking to test the validity of proposed pore models for porous Vycor. And it might be advantageous for workers proposing a pore model for other
FILM
AREA
HYSTERESIS
m a t e r i a l s to p e r f o r m the same t y p e of measu r e m e n t s as a definitive test of their model. ACKNOWLEDGMENTS The authors wish to thank The Robert A. Welch Foundation of Houston, Texas, for their continued interest and support, and Mr. Arnold C. Falk, who performed many of the area measurements. REFERENCES 1. VENABLE,R., ANDWADE,W. H., or. Phys. Chem. 69, 1395 (1965).
IN POROUS
VYCOR
371
2. KINGTON, G. L., AND SMITH, P. S., Trans. Faraday Soc. 60, 705 (1964). 3. BARRER, R. M., AND BARRIE, J. A., Proc. Roy. Soc. (London) 213A, 250 (1952). 4. DE BOER, J. H., Proc. Colston Res. Soc. 10, 68 (1958). 5. AMBERG, C. H., AND MCINToSH, R., Can. Y. Chem. 30, 1012 (1952). 6. MEYER, D. E., AND HACKERMAN,N., J. Phys. Chem. 70, 2077 (1966). 7. WADE, W. H., J. Phys. Chem. 68, 1029 (1964). 8. EVERETT, D. H., Proc. Colston Res. Soc. 10, 95 (1958).