Pore connectivity of alumina and aluminium borate from nitrogen isotherms

Article abstract of DOI:10.1039/a706581g

The effects of calcination temperature on the connectivity of pore networks of alumina and aluminium borate samples, prepared by coprecipitation methods and low-water sol-gel processes, have been investigated based on the percolation analysis of their nitrogen adsorption isotherms. The mean coordination number (Z) was determined with the aid of the recently proposed Seaton theory. Values of Z obtained with this method cover the range 2-3, implying a low connection of pores in all the examined porous samples. Thermal effects may increase or decrease Z values depending on the samples. On the other hand, Z values of aluminium borate samples obtained from the coprecipitation method were slightly larger than those from the sol-gel process. It was also found that for sol-gel processed samples, Z values of alumina were slightly larger than that of aluminium borate.

Full text of DOI:10.1039/a706581g

View Article Online / Journal Homepage / Table of Contents for this issue
Pore connectivity of alumina and aluminium borate from nitrogen
isotherms
Chung-Kung Leea* and Cherng-Shyan Tsayb
a Department of Environmental Engineering, V an-Nung Institute of T echnology, Chung-L i, 32054,
T aiwan, Republic of China
b Department of Chemical Engineering, National Central University, Chung-L i, 32054, T aiwan,
Republic of China
The e†ects of calcination temperature on the connectivity of pore networks of alumina and aluminium borate samples, prepared
by coprecipitation methods and low-water solÈgel processes, have been investigated based on the percolation analysis of their
nitrogen adsorption isotherms. The mean coordination number (Z) was determined with the aid of the recently proposed Seaton
theory. Values of Z obtained with this method cover the range 2È3, implying a low connection of pores in all the examined
porous samples. Thermal e†ects may increase or decrease Z values depending on the samples. On the other hand, Z values of
aluminium borate samples obtained from the coprecipitation method were slightly larger than those from the solÈgel process. It
was also found that for solÈgel processed samples, Z values of alumina were slightly larger than that of aluminium borate.
with a cylindrical pore model. Then, the bond occupation
1
Introduction
probability f is obtained as a function of percolation probabil-
ity F from the adsorption and desorption isotherms, using the
PSD obtained above as an input. Finally, the best Z and L
values are obtained by Ðtting the experimental scaling data (F,
f ) obtained above to a generalized scaling relation between F
and f. For a detailed description one may refer to the work of
Seaton.3 In our analysis, the generalized scaling relation
It is well known that the macroscopic properties of solid
materials are closely connected to their porous microstructure,
which is usually characterized by quantities such as density,
surface area, porosity, pore size, pore size distribution (PSD),
pore geometry and topology. These common terms used to
describe the microstructure of a porous material are in fact
parameters related to certain macroscopic measurements.
Many techniques have been applied to characterize porous
solids. They range from simple pycnometry, gas adsorption,
Ñuid penetration and calorimetric measurements, to the more
recent radiation scattering, xenon NMR, size exclusion chro-
matography or ultrasonic methods.1 Among these techniques,
gas adsorption is the most popular for the characterization of
porous solids. From the standard nitrogen isotherms, values
such as total pore volume, BET surface area and PSD can be
obtained. However, more information can still be extracted if
new theories are adopted. Among them is percolation
analysis, which pays special attention to the connectivity of
the pore system and its relation to the adsorptionÈdesorption
hysteresis loop.2
Percolation means spreading or penetration from one side
of the system to another. It is appropriate to describe how the
connectivity of a system a†ects its macroscopic properties.
Since the observed hysteresis in nitrogen isotherms may be
related to the topology of the pore network, the natural lan-
guage to describe this phenomenon is percolation theory. The
mapping between adsorption hysteresis and the percolation
process has been employed previously by several authors to
extract structural information from adsorption data.2 Taking
the desorption isotherm as a bond percolation phenomenon
and the assumption that pore network e†ects dominate, i.e.,
the thermodynamic contribution to the observed hysteresis is
neglected, Seaton and co-workers3h7 have proposed a method
to determine the mean coordination number of the pore
network, Z, and the characteristic size of the particles, L ,
expressed as the number of pore lengths.
Lb@lZF \ G[(Zf [ 3/2)L1@l]
where the critical exponents b and l have values of 0.41 and
0.88, respectively, was constructed using the simulation data
of Kirkpatrick.9
For this analysis, some further comments are in order. (1) It
gives information only about the network of micro- and meso-
pores. No structural information about macropores can be
obtained since no nitrogen condenses in macropores during
the adsorption process. (2) It is suitable for the IUPAC type
H1 and H2 loops and is difficult to use for analysis of H3 and
H4 loops. (3) Only the data points where F is signiÐcantly
di†erent from zero and from f can be used in the Ðtting pro-
cedure. The other points are far away from the percolation
threshold and are therefore outside the range of validity of the
generalized scaling relationship. (4) Although a mean coordi-
nation number is obtained, no information about the distribu-
tion of coordination number within the pore network is
available.
Alumina gel is technically an important porous material.
Apart from conventional applications as adsorbent and cata-
lyst support, many potential new usages of this oxide have
been proposed in electronics, optics and other advanced
Ðelds.10h14 For these practical applications, it was found that
the microstructure of such porous oxides may play a key role
in determination of their macroscopic characteristics. One
example is when used as adsorbents and catalyst supports,
both the geometry (the shape and distribution of size) and
connectivity of the pore space are critical for the transport or
reaction behavior in such porous materials. However, the
structure and physical properties of these porous oxides
depend strongly on the synthetic conditions and processes as
The procedures for the determination of Z and L from the
experimental adsorption data can be summarized as follows:3
Ðrst, the PSD is obtained using the method of Barrett et al.8
J. Chem. Soc., Faraday T rans., 1998, 94(4), 573È577
573

View Article Online
well as treatment temperature. For the former, two examples
are the incorporation of boron into the alumina structure
which may increase the surface area15 and solÈgel processing
which can produce very porous ([90%) alumina xerogels
with small and narrowly distributed pores.16 For the latter,
the examination of timeÈtemperature evolution of some
alumina and aluminium borate samples by nitrogen adsorp-
tion, transmission electron microscopy, thermal analysis, IR
absorption and X-ray techniques17h21 indicated that thermal
e†ects can strongly a†ect the microstructure of such materials.
In this study, e†ects of calcination temperature and synthesis
processes (coprecipitation method and solÈgel process) on the
pore connectivity of alumina and aluminium borate will be
examined through the percolation analysis of some carefully
measured nitrogen isotherms.
3
Results and Discussion
In our analysis of the nitrogen isotherms, we strive to identify
a key parameter which can provide an adequate character-
ization of the pore network of alumina and aluminium borate
gels for a wide variety of calcination temperatures. The porous
microstructure of solid materials is usually characterized from
the nitrogen isotherm by parameters such as BET surface
area, pore size and PSD. However, there is yet more informa-
tion one can extract from the isotherms, for instance perco-
lation analysis can give a measure of the connectivity of the
pores. Below we Ðrst give basic structural information of
alumina and aluminium borate gels obtained from nitrogen
isotherms.
3.1 Surface area, pore size and PSD
Fig.1 shows the nitrogen adsorptionÈdesorption isotherms we
have measured on the alumina and aluminium borate gels cal-
cined at di†erent temperatures. Some key features are seen
directly from Fig. 1. The monolayer capacity, and thus the
BET surface area, decreases with increasing calcination tem-
perature. Also evident is that the BET surface areas of samples
from solÈgel processing are slightly larger than those obtained
from coprecipitation at low calcination temperatures. The
incorporation of boron into the alumina structure using the
solÈgel process leads to a slight increase in the surface area.
All adsorption isotherms except for samples calcined at
1250 ¡C exhibited obvious capillary condensation at an inter-
mediate relative pressure. The isotherms for the 1250 ¡C
samples showed virtually no uptake until close to saturation
pressure, where capillary condensation in the few large voids
between a-alumina crystalline grains started. Owing to the
increase of condensation pressure with increasing calcination
temperature, thermal e†ects may increase the mean pore size.
The PSDs calculated from the capillary condensation model
are shown in Fig. 2. As demonstrated in Fig. 2(b) and (d), the
2
Experimental
The aluminium borate mixed oxide derived by the coprecipi-
tation process was synthesized according to the procedure
outlined by Peil et al.21 Aluminium nitrate [Al(NO ) É 9H O,
3 3
2
98.5%, Merck] and boric acid (H BO , [99.8%, Merck)
3
3
were mixed with B/Al \ 1/9 and the pH was controlled to
close to by deionized water. An ammonia solution
2
(pH \ 11.5) was used as precipitant for the aluminiumÈborate
solution in the coprecipitation process. The two solutions
were slowly added into a third container with deionized water
to maintain a constant pH of 9. The resulting precipitate was
Ðltered, washed with deionized water (three times), oven-dried
at 100 ¡C for 24 h, and then calcined at di†erent temperatures
for 4 h. The alumina was synthesized with a similar process
except for the absence of boric acid.
The solÈgel process derived aluminium borate xerogel was
prepared from a low-water non-aqueous sol synthesized from
aluminum tri-sec-butylate MAl[OCH(CH )C H ] (ATSB),
3
2 3
2 5 3
97%, MerckN, tributyl borate MB[CH (CH ) O] (TB), 99%,
3
3
AldrichN, absolute ethanol (C H OH, [99.8%, Merck),
2
5
deionized water and nitric acid (HNO , 65%, Merck). The
3
molar ratio of ATSB, TB, H O, EtOH and HNO used is
2
3
0.1 : 0.0111 : 0.025 : 10 : 0.0065, where the water to alkoxide
ratio is only half that suggested by Yoldas.22
Initially, 0.0111 mol TB was mixed with 10 mol absolute
ethanol in a round bottomed Ñask, then heated to 80 ¡C on a
heating mantle, and stirred vigorously with an electric stirrer.
Preheated water (0.0125 mol) and HNO (0.003 mol) were
3
added and the Ñask contents were continually reÑuxed for 1 h.
ATSB (0.1 mol) was then added with vigorous stirring. After
the addition of a preheated mixture of additional water
(0.0125 mol) and HNO (0.0035 mol), the contents in the Ñask
3
were stirred under the same conditions for 4 h. When the
obtained sol was cooled to room temperature, it formed a gel
in ca. 70 h in a 70% Ðlled and tightly sealed 100 ml beaker.
The glassy gel was dried at 110 ¡C for 10 h, and calcined to
the desired temperature with a heating rate of 60 ¡C h~1 and a
Ðnal holding time of 4 h. At ca. 500 ¡C the xerogel turned dark
brownish due to carbonization of organic residues. This color
disappeared at ca. 700 ¡C as the carbon was burned o†. The
alumina xerogel was synthesized by a similar process except
for the absence of TB.23
We denote the coprecipitation method derived alumina and
aluminium borate as C10A and C9A1B while the solÈgel
derived counterparts are denoted S10A and S9A1B, respec-
tively.
XRD patterns of the calcined samples were measured on a
Siemens D-500 instrument with Cu-Ka radiation (30 mA and
40 kV). Nitrogen adsorption isotherm and desorption hyster-
esis loops were measured at 77 K with a Micromeritics ASAP-
2000 instrument. All samples were outgassed at 350 ¡C for 24
h before adsorption measurements.
Fig. 1 Nitrogen adsorption isotherms of (a) S10A, (b) S9A1B, (c)
C10A and (d) C9A1B calcined at di†erent temperatures; (L) 500, (K)
700, (|) 900, (¾) 1100 for (a) but 1000 for (b)È(d), and ()) 1250 ¡C
574
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
lead to the absence of any bimodal distribution, indicating
that the presence of borate alters the chemical environment of
alumina and changes the structure of alumina as indicated by
the solid state NMR results of Peil et al.21 For S10A, a two-
step isotherm was observed for calcination at 1100 ¡C, leading
to a bidisperse pore structure shown in Fig. 2(a). The appear-
ance of di†erent pore sizes can be understood from the XRD
patterns shown in Fig. 3(a). The gel was completely amorp-
hous after calcination at 700 ¡C, but transformed to c-alumina
at 900 ¡C. a-Alumina appeared at 1100 ¡C and the transform-
ation was complete at 1250 ¡C. The bidisperse pore structure
observed for the 1100 ¡C sample thus corresponds to the
coexistence of two di†erent solid phases. This phenomenon
was also observed for C10A at 500È700 ¡C. As displayed in
Fig. 1(c), a slight two-step adsorption or desorption isotherm
corresponds to a bidisperse pore structure shown in Fig. 2(c)
and a mixture of a-Al(OH) , g-Al O and c-AlOOH, etc.
3
2 3
phases [Fig. 3(c)].
Finally, the alkoxide derived alumina xerogels (S10A)
display a di†erent crystallization route compared to those
obtained from the coprecipitation method, as displayed in Fig.
3. Gibbsite and bayerite phases as well as the h-Al O phase
2
3
are all absent in the transformation to a-alumina. Another
Fig. 2 Pore size distribution of (a) S10A, (b) S9A1B, (c) C10A and (d)
C9A1B calcined at di†erent temperatures
PSD of alumina borates showed a lack of any bimodal pore
distribution, as would be expected for materials consisting of
simply a mixture of two oxides, thereby indicating that these
materials are not just physical mixtures of alumina and
diboron trioxide. On the other hand, it was found that for
samples calcined at lower temperatures, the PSDs were rather
narrow. It can also be seen that the PSDs of samples synthe-
sized by the solÈgel process were narrower than those from
the coprecipitation method, especially in alumina samples.
Finally, according to the saturation adsorption capacity Fig. 1
also suggested a decrease of the total pore volume for calcina-
tion at higher temperatures (except for S9A1B at 900 ¡C and
C10A at 700 ¡C). Obviously, the densiÐcation under heating
leads simultaneously to widening of the pores and shrinkage
of the bulk. There were fewer but generally larger pores after
calcination. The porous structure characteristics, including
BET surface area, pore size and pore volume, obtained from
the conventional analysis of nitrogen isotherms are collected
in Table 1. The pore volume of samples obtained from copre-
cipitation was rather stable upon calcination, until the appear-
ance of the a-alumina crystalline phase. For C10A, thermal
densiÐcation of coarsened microstructure was accomplished at
1250 ¡C with the pore size becoming smaller.
It is noteworthy that for C10A, a bimodal PSD was found
at 500È700 ¡C, while at higher calcination temperatures broad
PSDs were observed. A low addition of borate (C9A1B) can
Fig. 3 XRD patterns of (a) S10A, (b) S9A1B, (c) C10A and (d)
C9A1B calcined at di†erent temperatures. Also shown are the pat-
terns of pure a-Al O and aluminium borate.
2
3
Table 1 Pore structure characteristics of alumina and aluminium borate obtained from conventional analysis of nitrogen isotherms
S10A
S9A1B
C10A
C9A1B
calcination
temperature
/¡C
pore
pore
pore
pore
pore
pore
pore
pore
BET/ diameter/ volume/
BET/ diameter/ volume/
BET/ diameter/ volume/
BET/ diameter/ volume/
m2 g~1
Ó
cm3 g~1 m2 g~1
Ó
cm3 g~1 m2 g~1
Ó
cm3 g~1 m2 g~1
Ó
cm3 g~1
500
700
900
1000
1100
1250
430.8
311.9
128.7
È
53.5
8.7
62.7
70.7
80.9
È
È
505.8
0.79
0.61
0.35
È
0.32
0.09
452.5
343.8
207.3
49.2
È
76.9
79.5
104.0
137.1
È
0.70
0.40
0.71
0.24
È
396.8
310.4
113.7
46.2
È
36.0
42.3
119.8
255.7
È
0.37
0.38
0.36
0.36
È
358.1
286.1
166.1
75.0
È
35.9
45.7
74.8
123.3
È
0.34
0.35
0.37
0.31
È
9.3
502.6
0.07
4.67
147.8
0.01
20.9
321.8
0.15
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
575

View Article Online
interesting feature in Fig. 3 is the continued amorphous
nature of coprecipitation derived aluminium borate (C9A1B)
at calcination between 500 and 700 ¡C, whereas upon calcina-
tion of C10A in the same temperature range a mixture of
alumina hydrates was observed. For solÈgel derived counter-
parts alumina hydrates existed in S9A1B.
3.2 Pore connectivity: percolation analysis
As shown in Fig. 1, the hysteresis loops formed between the
adsorption and desorption branches of the isotherms for the
calcined S10A, S9A1B and C9A1B samples belong to IUPAC
type H2 loops (except that for the 1250 ¡C samples, which is a
typical H3 loop). Isotherms of C10A are H3 type (900È
1250 ¡C) or of slight two-step nature (500È700 ¡C), which are
difficult to analyze using Seaton theory. On the other hand, it
was found that the knee of the hysteresis loops moves to the
right and the desorption branch Ñattens slightly as the calcin-
ation temperature increases. According to Seaton theory, if
the major contributor to the observed H2 type hysteresis loop
is the connectivity of the pore network, this connectivity-
related phenomenon may be appropriately described by the
percolation process.
Fig. 6 Fitting of the ( f, F) data calculated from the measured iso-
therms on C9A1B to that calculated from the generalized relationship
(solid line)
S10A were excluded either because of the absence of micro-
and meso-pores or bimodal pore size distribution.
All the values of Z obtained are in the range 2È3, with a
slight increasing (S10A and S9A1B) or decreasing (C9A1B)
trend vs. calcination temperature. These are surprisingly low
values compared to the values of 5È7 obtained by Seaton3 for
a range of silica and alumina gels. The increase of Z with
increasing temperature is readily understood. According to
percolation theory, the “kneeÏ of the desorption isotherm indi-
cated in Fig. 1 corresponds to the percolation threshold. In a
highly connected network, it is easier to form a spanning
cluster of vapor-Ðlled pores. Once a few pores contain vapor,
other pores will be easy to access by the vapor phase. Hence,
the location of the desorption “kneeÏ is more to the right.
Accordingly, the isotherms in Fig. 1 suggest a slight increase
of pore connectivity with increasing calcination temperature if
the hysteresis loop is purely determined by the e†ect of the
pore network. On the other hand, the decrease of Z with
increasing temperature is difficult to interpret by this analysis.
Since both thermodynamic factors (single-pore mechanism)
and pore networks can contribute to the adsorption hyster-
esis, one explanation is that the hysteresis loop is not uniquely
determined by the pore connectivity and the thermodynamic
contribution to the adsorption hysteresis is not negligible.
Examination of the Z values of S10A and S9A1B showed
that the incorporation of boron into the alumina structure
slightly decreases the connectivity of pore network. On the
other hand, Z values of C9A1B are larger than those of
S9A1B. Since the C9A1B sample obtained from the coprecipi-
tation method consists mainly of aggregates of small primary
particles whereas S9A1B synthesized from a low-water non-
aqueous solution of alkoxide is a spanned cluster of poly-
cationic polymers of aluminium borate, the above analysis
implies that the polymeric aluminium borate gel has a smaller
pore connectivity than its colloidal counterpart.
Fitting results from the isotherms for the calcined S10A,
S9A1B and C9A1B samples are given in Table 2 and Fig. 4È6.
The isotherms for 1250 ¡C samples and the 1100 ¡C sample of
Fig. 4 Fitting of the ( f, F) data calculated from the measured iso-
therms on S10A to that calculated from the generalized relationship
(solid line)
Along with the calculation of Z, values of L are obtained
from the Ðtting. However, it is difficult to link L values to any
well deÐned dimension in the systems. Furthermore, it has
been found in our study that the Ðtting was sensitive to both
L and Z values. Hence, the values of L must be taken with
some caution.
Fig. 5 Fitting of the ( f, F) data calculated from the measured iso-
therms on S9A1B to that calculated from the generalized relationship
(solid line)
4
Conclusions
Table 2 Results of percolation analysis of nitrogen isotherms on
The present study provided well measured nitrogen isotherm
data for solÈgel and coprecipitation derived alumina and alu-
minium borate gels at a variety of calcination temperatures.
Percolation analysis was then performed on those nitrogen
isotherms to evaluate the value of pore connectivity, Z. Both
the alumina and aluminium borate gels showed low pore con-
nectivity with Z values in the range 2È3. The pore connectivity
does not change signiÐcantly during thermal treatment,
despite a large increase in pore size. It was also found that
the incorporation of boron into the alumina structure by the
S10A, S9A1B and C9A1B
calcination
temperature
/¡C
S10A
S9A1B
C9A1B
Z
L
Z
L
Z
L
500
700
900
2.1
2.8
3.0
È
18.5
5.2
2.2
È
1.9
2.1
1.8
2.3
7.3
3.5
10.3
5.0
3.2
2.6
2.6
2.3
4.2
6.1
6.6
2.7
1000
576
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
7
8
H. Liu and N. A. Seaton, Chem. Eng. Sci., 1994, 49, 1869.
solÈgel process may decrease the pore connectivity. On the
other hand, Z values of solÈgel derived samples di†er from
those of samples obtained by coprecipitation, indicating that
the pore connectivity of materials obtained from polymeric
and colloidal mechanisms is di†erent.
E. P. Barrett, L. G. Joyner and P. H. Halenda, J. Am. Chem. Soc.,
1951, 73, 373.
9
S. Kirkpatrick, in III-Condensed Matter, ed. R. Balian, R.
Mayward and G. Toulouse, North-Holland, Amsterdam, 1979, p.
324.
These results conÐrm that it is helpful to use percolation
analysis for comparative studies of changes of the initial pore
structure of porous materials, caused by a particular treat-
ment or modiÐcation. Since this method needs no extra data
except the nitrogen isotherms or mercury penetration curves,
such analysis can be viewed as an additional standard tech-
nique.
10 J. Livage, Solid State Ionics, 1996, 86-88, 935.
11 S. Suda, K. Yamashita and T. Umegaki, Solid State Ionics, 1996,
89, 75.
12 C. A. Browne, D. H. Tarrant, M. S. Olteanu, J. W. Mullens and
E. L. Chronister, Anal. Chem., 1996, 68, 2289.
13 K. Kuraoka, H. Tanaka and T. Yazawa, J. Mater. Sci. L ett.,
1996, 15, 1.
14 T. Skapin and E. Kemnitz, Catal. L ett., 1996, 40, 241.
15 M. C. Tsai and Y. W. Chen, Catal. L ett., 1990, 6, 225.
16 B. E. Yoldas, Am. Ceram. Soc. Bull., 1975, 54, 286.
17 S. J. Wilson and M. H. Stacey, J. Colloid Interface Sci., 1981, 82,
507.
The work was supported by grant NSC86-2214-E238-001 of
the National Science Council (Taiwan, ROC).
18 V. Saraswati, G. V. N. Rao and G. V. R. Rao, J. Mater. Sci.,
References
1987, 22, 2529.
19 A. Ayral and J. Phalippou, Adv. Ceram. Mater., 1988, 3, 575.
20 G. V. R. Rao, S. Venkadesan and V. Sarawati, J. Non-Cryst.
Solids, 1989, 111, 103.
21 K. P. Peil, L. G. Galya and G. Marcelin, J. Catal., 1989, 115, 441.
22 B. E. Yoldas, in Ultrastructure Processing Advanced Ceramic, ed.
J. D. Mackenzie and D. R. Ulrich, Wiley & Sons, New York,
1988, p. 333.
1
J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. H.
Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing and K. K.
Unger, Pure Appl. Chem., 1994, 66, 739.
C. K. Lee, A. S. T. Chiang and C. S. Tsay, in Key Engineering
Materials, ed. D.-M. Liu, Trans Tech Publications, Switzerland,
1996, vol. 115, p. 21.
2
3
4
N. A. Seaton, Chem. Eng. Sci., 1991, 46, 1895.
H. Liu, L. Zhang and N. A. Seaton, Chem. Eng. Sci., 1992, 47,
4393.
23 C. S. Tsay, C. K. Lee and A. S. T. Chiang, Chem. Phys. L ett.,
1997, 278, 83.
5
6
H. Liu, L. Zhang and N. A. Seaton, J. Colloid Interface Sci., 1993,
156, 285.
H. Liu, L. Zhang and N. A. Seaton, L angmuir, 1993, 9, 2576.
Paper 7/06581G; Received 9th September, 1997
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
577