JOURNAL
OF
CATALYSIS
4, 319-323 (1965)
Studies
on Pore Systems
in Catalysts
V. The t Method
B. C. LIPPENS*
From the Department
of Chemical
AND
J. H.
Technology, Technological
Received
March
DE
BOER
University
of Delft, The Netherlands
3, 1964
Valuable information
about the specific surface area, the size, and the shapes of pores,
the setting in of reversible capillary condensation and of complete filling of pores may be
obtained by plotting the experimental
volumes of adsorbed nitrogen, Vo, aa a function
of the statistical thickness, 1,of the adsorbed layer, as given in Paper I of this series. The
Va-t plot, together with the experimental
adsorption and desorption isotherm gives a
very good picture of the whole pore system.
1.
va-t
PLOTS
In Part I of this series (1) we showed that
for several well-selected samples of aluminum
hydroxides and oxides in which the multimolecular layer of adsorbed nitrogen could
be formed freely on all parts of the surface,
its statistical thickness t = 15.47 V,/SBET is
practically independent of the nature of the
sample.
The experimental values of V, (the volume
of nitrogen adsorbed in cm3 STP/g of adsorbent) which are obtained as a function
of the relative pressure, X, may, with the aid
of Table 1 of Part I of this series (1) be
transformed to functions of t. By plotting
then V, for an unknown sample as a function
of the experimental t, we obtain a straight
line as long as the multilayer is formed unhindered. This straight line goes through the
origin and its slope is a measure of surface
area
St = 15.47v,/t
This quantity St will not always be exactly
equal to SBET, as instead of the various C
values in the BET equation (depending on
the sample) an average value is used by
introducing the t curve.
* Present
address:
Laboratory
for Inorganic
Chemistry and Catalysis, Technological
University
Eindhoven, The Netherlands.
319
Figures 1, 2, and 3 show the V,-t plots for
a number of our samples. These samples are
described in Part II of this series (z?). In
almost all cases the first part of the curves is
a straight line through the origin, from which
St can be calculated; it is in good agreement
with X~ET (Table 1).
At higher relative pressures (higher t
values) deviations from a straight line occur.
We may distinguish three cases:
(a) The surface is freely accessible up to
high relative pressures; the multilayer can
form unhindered on all parts of the surface;
the adsorption branch of the isotherm has
entirely the shape of the t curve; the V,-t
plot is one straight line.
(b) At a certain pressure capillary condensation will occur in pores of certain
shapes and dimensions; the material takes
up more adsorbate than corresponds to the
volume of the multilayer;
the adsorption
branch lies above the t curve; the slope of the
V,-t plot increases.
(c) In some types of pores capillary condensation is not possible unless at very high
relative pressures [slit-shaped pores or large
holes (S)]. As long as the multilayer adsorption is unhindered, the V,-t plot is a straight
line. If the pressure increases the free space
in the pores becomes smaller owing to the
growth of the adsorbed layer. Large holes
will only be filled by capillary condensation
320
LIPPENS
AND
DE
BOER
30
20
10
i
:.
.
-t
A
FIG.
1. V,t
0.1
215
FIQ.
plot of A and BOW preparations.
0.2
0.3
l,llll.llll,lllllll,l,II
5.0
2. Vbt
0.L
0.5
06
I
0.7
I I
7:5
plot of BOG preparations.
I
I
I
lo:o
0.8
I
I
I
125
PORE
SYSTEMS
FIG. 3. V,-t
IN
CATALYSTS
plot of By preparations.
TABLE
COMPARISON
OF SURFACE
AREA
321
V.
CALCULATED
1
WITH
BET
THE
EQUATION
AND
FROM V,&
PLOT
p/p0 at the beginning of
Sample
A
A
A
A
120
200
450
750
ssm
609
580
414
280
St
586
56s
409
275
Cap. cond.
Hysteresis
-
0.26
0.26
0.34
0.63
0.40
0.40
0.51
0.63
-
0.70
0.70
0.76
0.40
s,
BOW 120
BOW 450
64.0
92.1
65.6
93.5
68.0
BOG 450
BOG 580
BOG 750
17.1
65.7
19.1
17.2
65.0
19.1
5.1
17.2
-
>0.86
>0.86
>0.86
0.46
0.44
0.48
26.5
489
462
414
245
134
26.6
483
440
386
243
127
8.7
20.1
20.6
21.5
-
0.70
>0.86
>0.86
>0.86
0.24
0.24
0.47
0.46
0.47
0.48
0.42
0.46
By
By
By
By
By
By
200
250
270
450
580
750
at relative pressures near unity. In a slitshaped pore, however, again no capillary
condensation can occur, but at a certain
moment the pore may be completely filled
-
by the adsorbed layers on both parallel
walls. The surface area in such pores is no
longer accessible above a certain relative
pressure; the Va-t plot will now get a smaller
322
LIPPENS AND DE BOER
slope, corresponding to the surface area still
accessible.
2. CONCLUSIONS, DRAWN FROM V,-t PLOTS
Some conclusions which can be drawn
from the I’,-t plots of our samples are in
agreement with the conclusions we drew in
Parts II (2) and III (4).
Samples obtained from gelatinous boehmite (A 120, etc., Fig. 1 and Table 1) generally show capillary condensation at a
relative pressure lower than that corresponding to the beginning of the hysteresis loop
(Table 1). de Boer (2) has already pointed
out that this reversible capillary condensation can take place in the cones and wedges
formed, e.g. by the planes of crystals touching each other. For Sample A 750 the beginning of the capillary condensation almost
coincides with that of the hysteresis loop; at
a temperature of 750°C a noticeable sintering has already occurred; the sharp edges
are apparently rounded by this sintering.
The same conclusion has already been drawn
from the changes of the shape of the desorption isotherms [Part II (2)J.
Sample BOW 120, consisting of small flat,
six-sided, crystals of boehmite shows a
straight line up to a relative pressure of
about 0.70, somewhat below the beginning
of the hysteresis loop. Sample BOW 450,
obtained by heating BOW 120 above the
decomposition
temperature
of boehmite,
shows a v,-t curve with two breaks, one at
a relative pressure of about 0.26, the other
at 0.70. The first break must apparently be
explained by pores being closed by the
adsorbed layer. Assuming that this will occur
when the thickness of the adsorbed layer is
equal to half the width of the narrow pores,
we $ind for this width a value of 2.4.75 =
9.5A. From the slope of the second part of
the V,-t curve we can calculate that the
remaining surface area of the wide pores
amounts to 68.0 m”/g Al203 (indicated as
S, in Table l), approximately
the same
as the SBET or St value of BOW 120. The
extra surface area of about 25 m”/g, which
BOW 450 shows, is apparently present in
narrow slit-shaped pores formed during the
heating at 45O’C. Capillary condensation
in BOW 450 occurs only at a relative pressure
of 0.7, just as with BOW 120, showing that
apparently nothing has changed in the outer
shape of these particles. The hysteresis loop
of BOW 450, however, closes at a relative
pressure of 0.4. Comparing the hysteresis
shapes in Fig. 2 of Part II (2) shows that
BOW 450 shows a small extra B-type hysteresis curve superimposed on the curve
shown already by BOW 120. The heating at
450°C has, apparently, also produced some
wider slit-shaped pores of about 25A width
and a surface area of about 5 m2/g, as can
be calculated from the distribution curve of
Fig. 2 of Article III (4).
During the heating of the well-crystallized
hydroxides (BOG and By) also narrow slitshaped pores are formed, as follows from the
V,-t curves. These narrow pores disappear
again on heating at still higher temperatures
(Figs. 2 and 3, Table 1). For samples having
a hysteresis loop of type B, capillary condensation starts again at a relative pressure
much higher than that at which the hysteresis loop is closed. The cumulative surface
area calculated from the desorption branch
of the isotherm, down to z = 0.3 [Part
III (4)] is, in all these cases, greater than the
surface area S, of the wide pores calculated
from the second part of the V,-t curve. This
may indicate that in these cases we are
dealing with relatively
wide pcres with
narrower openings [of about 25A, as described in Part IV of this series (5)]. If this
conclusion is right, the complete absence of
capillary condensation at relative pressures
up to 0.86 on the adsorption branch indicates
that either the volume of these “openings”
of the wide pores is negligibly small, or that
the openings themselves are formed by slitshaped pores. In view of the crystallographic
properties (6, 7) of these materials the last
supposition is the most probable one.
Samples By 580 and By 750 apparently
have a completely different pore structure.
The wide pores are still present but other
pores have a shape in which capillary condensation on adsorption is possible. Consequently severe sintering must have occurred.
This could also be shown by electron microscope observations, as we have published
elsewhere (7’). Whereas at low temperature
the 7 alumina shows a strict pseudomorphosis
323
PORE SYSTEMS IN CATALYSTS V.
to the original bayerite particles, recrystallization occurs at higher temperatures giving
small rod-shaped crystals, which still show
some preferred orientation, but no strict
pseudomorphism. As already observed in
Part II (9) the hysteresis loops of By 580
and By 750 are combinations of the B-type
loop of By 200 (and other By preparations
up to By 450) and an E-type loop. This
latter loop and the Va-t curves of these
preparations show that the narrow slitshaped pores have disappeared; they seem
to have been replaced by pores with rectangular cross sections with varying diameters.
In this connection the work of de Boer,
Steggerda, and Zwietering (8) should be
mentioned. From measurements of the
optical birefringence
of heated gibbsite
crystals they arrived at the conclusion that
at lower temperature slit-shaped pores are
formed, which are separated by platelike
particles parallel to each other and perpendicular to the c axis of the original gibbsite. At higher temperatures,
however,
rodlike particles are formed which are
perpendicular to the c axis of the original
gibbsite and parallel to each other. They also
observed a marked change in the shape of
the adsorption isotherm of their samples.
These optical observations give a picture
analogous to that we developed for the
dehydration products of bayerite.
REFERENCES
1. LIPPENS, B. C., LINSEN, B. G., AND DE BOER,
J. H., J. Catalysis 3, 32 (1964).
2. DE BOER, J. H., AND LIPPENS, B. C., J. Catalysis
3, 38 (19644).
3. DE BOER, J. H., “The Shape of Capillaries,”
in
Evereth, D. H., and Stone, F. S., “The Structure and Properties
of Porous Materials.”
Butterworth,
London, 1958.
..$. LIPPENS, B. C., ASD DE BOER, J. H., J. Catalysis
3, 44 (1964).
5. DE BOER, J. H., VAN DEN HEUVEL, A., AND LINSEN, B. G., J. Cutalysis 3, 268 (1964).
6. LIPPENS, B. C., Thesis, Delft, The Netherlands,
1961.
7. LIPPENS, B. C., AND DE BOER, J. H., Acta Cryst.
17, 1312 (1964).
8. DE BOER, J. H., STECGERDA,J. J., AND ZWIETERINC,
P., Proc. Koninkl.
Ned. Akad. Wetenschap.
B59, 435 (1956).