Monitoring the thermal stability of the porous structure of hybrid SiO2-TiO2 materials by means of mass transport coefficient calculations
*H. S. Silva§, G. F. Larsen#, R. B. Venturini§, J. E. González§
§Facultad de Ingeniería - Universidad Nacional de San Juan - Av. Libertador San Martín
1109 (Oeste) - (5400) San Juan - Argentina
e-mail: hsilva@unsj.edu.ar
#Department of Chemical Engineering- University of Nebraska-Lincoln
228 Avery Laboratory, Lincoln, NE 68588-0126, USA
e-mail: glarsen@unlserve.unl.edu
* Author to whom the correspondence should be
addressed
Abstract The physical characterization of solids, mainly the
surface area measurement and the pore size distribution
determination by means of nitrogen adsorption and
mercury porosimetry, respectively, might be a matter of
controversy in the case of materials that can suffer
important structural changes between 77K and their
operation temperatures (room or higher), or whose pore
structure may be damaged due to the mercury intrusion.
The goal of this work is to identify changes in the
physical structure of solids when they are exposed to
temperatures similar to those used in conventional thermal
pretreatments, when they are used as catalysts, by means
of mass transfer coefficient measurements. Our working
hypothesis is that, if structural changes occur, these should
be easily detected via noticeable changes in the mass
transfer coefficient for a selected adsorbate.
The calculation of relaxation constants, which
characterize the transport of cyclohexane through the
hybrid materials is carried out by modeling the
experimental data corresponding to the transient state of
the adsorption tests.
Keywords Hybrid materials; Structural changes; Mass transfer coefficients; Oscillating Microbalance.
1. Introduction
Among the novel materials with desired properties
(thermal and electrical conductivity, effective
diffusivity, mechanical strength, transparency, etc.),
required for many fields related to science and
technology, the inorganic/organic gels, obtained by
hydrolysis and condensation of organic and inorganic
precursors, can combine some of the properties that
define organic polymers (e.g. flexibility), with the
mechanical strength that is typical of inorganic
materials. The physical properties of the final product,
depend on the way in which molecules or particles are
linked to form the hybrid structure (Ballard et al., 1999).
Adsorption experiments is the most frequent techniqueused to describe the porous structure of solids.Nitrogen,
helium and recently neopentane (Larsen et al., 2000a),
are the most popular adsorbates to carry out
physisorption tests. An adequate characterization of the
porous structure is a central issue in order to predict the
behavior of the material with regard to the mass and
energy transport. When a solid structure is characterized
by means of an adsorption test, an important point must
be taken into account. Some solids have a porous
structure that changes substantially with temperature.
For these solids, the information gathered from an
experimental adsorption test at 77K is virtually useless.
In these cases, adsorption tests at higher temperatures
should yield useful information about the actual
physical structure of the solid at temperatures similar to
those of its practical applications (Larsen et al., 2000b).
In this work, the evaluation of the thermal stability of
hybrid SiO2-TiO2, is carried out. These materials which
are proposed as catalysts for C5-C8 olefine epoxidations
(Larsen et al., 1999; Muller et al., 2000a,b), are
thermally pretreated before their use. From adsorption
tests of cyclohexane over the hybrid materials obtained
from different organic precursors, the calculation of the
coefficients that characterize mass transport, is carried
out. These experiments are performed in a oscillating
microbalance.
2. Experimental
2.1 Sample preparation
The hybrid SiO2-TiO2 gels were prepared by the hydrolysis and condensation of silicon precursors according to the protocol recently described (Larsen et al., 1998). Basically, two-thirds of the total amount of moles of silicon was added in the form of tetraethylortosilicate (inorganic silicon precursor) and one-third in the form of the organic precursor (hexamethilcyclotrisiloxane, for the hybrid labeled as SiO3-Ti and decamethylcyclopentasiloxane for the hybrid labeled as SiO5-Ti). The mixture was prehydrolyzed for 5 hours at 338 K, before the addition of the precursor of titanium. The samples were placed in open containers, in an oven at 338 K, with no forced air circulation, for slow gel and evaporation. Although the samples gelled in less than 24 hours, all the samples were removed from the oven after 60 hours.
2.2 Adsorption studies
The adsorption experiments were carried out with the aid of an oscillating balance reactor (Fig. 1), which was initially developed for quantification of particulate in air (Patashnik et al.,1992). Recently this device was adapted for in situ catalysis research (De Chen et al., 1996; Liu et al., 1997) or for adsorption studies (Hershkowitz and Madiara, 1993) It consists of a detector unit which behaves as a physical pendulum, a control unit which fixes the experimental parameters (basically the temperature program) and a PC as the input/output data unit. The oscillating element is a quartz tube and the solid is placed as a packed bed at its end (Fig. 2). The basic idea is that the solid packed bed is made to oscillate at its natural frequency by means of an electronic device and instantaneous mass changes are detected and processed by a computer.
A commercial unit from Ruppert & Patashnik
Company was used. The main feature of this form of
microbalance is that it has the ability to detect minute
weight changes with excellent mass-time resolution,
and the flow profile is much better defined compared
with those which take place in conventional microbalances, given its packed-bed geometry.
The experimental arrangement includes a bubbler/
saturator assembly, where a constant flow of a carrier
(helium), measured with a 5850 Brooks mass flow
controller, is saturated with cyclohexane at 280 K. The
hybrid solids were dried in situ in the microbalance at
383 K, for 1 hour under a constant flow of nitrogen. The
temperature was then stabilized at 313 K, under a
helium flow. The helium flow was then switched to
helium saturated with cyclohexane. This flow passes
through the oscillating element of the microbalance and
the adsorption of cyclohexane takes place. The same
protocol is used for the adsorption of cyclohexane on
hybrid materials pretreated at 423 K, 463 K, 503 K and
543 K.
3. Results and Discussion
Figures 3 and 4 show the cyclohexane dynamic adsorption results over the two hybrid materials.When the transport of a fluid in spheroidal heterogeneous catalyst pellets (radius Rc), is considered, Fickian diffusion is assumed. Then, the porous structure is considered a rigid one, and the expected concentration profile for a fluid whithin the particle, shown in Fig. 5, basically depends on the mass transport coefficient value (i.e., the effective diffusivity, Deff).
In this case the time dependant uptake M(t) of the
adsorption test, relative to the total uptake M¥ (t®¥),
that is, the relative uptake, can be calculated from
![]() |
(1) |
For relative uptakes < 0.3, an approximate form of Eqn. (1) is generally adopted (Crank, 1976)
![]() |
(2) |
In polymer research it is usual to deal with swellable materials instead of rigid porous matter. Mass transport phenomena in those solids have been loosely defined as"anomalous" or non-Fickian diffusion, which is characterized by the following features: a) As the fluid penetrates into the porous structure, a sharp advancing boundary separates the inner non swollen core from the swollen shell. b) The boundary between the swollen porous structure and the non swollen core advances to the center of the spherical particle with constant velocity. c) The swollen gel behind the advancing boundary is at uniform state of swelling. According to this, the concentration profile for a penetrant within the particle is the one shown in Fig. 6.
In the region R(t)³r³0, there is basically no
penetrant. C0 is the penetrant equilibrium concentration in the already swollen shell (i.e., the equilibrium
concentration of penetrant at R(t)<r<Rc).
If k0, the relaxation constant (mol m-2 s-1), is defined as
the parameter that characterizes the non Fickian mass
transport and is assumed to be constant, the kinetic
equation that describes the mass transport through the
outer surface on N(R) spherical particles of radius R is
![]() |
(3) |
The amount of penetrant M(t) absorbed in an array of uniform spheres in a time t (i.e., the uptake measured in a typical test carried out in the oscillating microbalance) will be:
![]() |
(4) |
From this conceptual model, Enscore et al. (1977), derived the following formula for diffusion of penetrants in glassy and swellable materials:
![]() |
(5) |
where a0 is k0/C0
The power n adopts the value 1 for films, 2 for
cylinders and 3 for spheres. Equations 2 and 5 provide a
quick test to determine whether mass transport is either
non-Fickian or Fickian, since only the latter produces
M(t)/M¥ vs. t1/2 linear plots. Figures 7 and 8 show these plots for the hybrid materials, which have in fact been
wetted (organic polymer style) by cyclohexane. No
linearity is observed over the whole range of time.
To better understand the transport data, we point to the deviations of the adsorption curves from linearity. The sigmoid shape of the curves can either be due to pure non-Fickian transport or a combination of Fickian and non-Fickian behavior. In the last case, the total uptake could be calculated from the fractional contribution due to the Fickian transport (FF) and that from the non- Fickian transport (FNF). This yields:
![]() |
(6) |
Two competing factors have to be considered to analize
the cyclohexane diffusion in these hybrid materials.
Removal of unreacted (pendant) alkoxi groups tends to
open up the structure only if their elimination does not
produce cross-linking of the polymer chains. The
saturation uptakes for the SiO3-Ti samples pretreated at
different temperatures are practically identical (0.242 at 383 K, 0.243 at 423 K, 0.245 at 463 K, 0.239 at 503K
and 0.240 g/g at 543 K), which indicates that the pore
volume stays essentially unchanged. A similar behavior
is observed for the SiO5-Ti hybrid until 503K, but the
final uptake for the hybrid pretreated at 543K decreases
markedly, which indicates that the pore volume has
changed substantially.
The stiffening of the porous structure is monitored
by the transient adsorption data. The analysis indicates
that the porous structure of the SiO3-Ti hybrid relaxes
more rapidly as the preheating temperature increases but
the opposite holds true for the SiO5-Ti material.
To determine whether the mass transport is controlled
by either a single mechanism or a combination of both
(Eqn. 6), some information about the texture of the
material is necessary. An average particle size of 31 nm
has been determined by scanning electron microscopy
(SEM) for the oven dried materials. They are composed
of largely irregular particles with aspect ratios
comparable to those of a sphere.
The C0 value is determined from the vapor pressure
of cyclohexane corresponding to the bubbler /saturator
temperature using the ideal gas law.
An empirical first order non-Fickian term for long
adsorption times, was proposed as a preliminary test.
According to this, Eqn. (6) can be written:
![]() |
(7) |
If ln[1-M(t)/M¥] is plotted against time, the intercept
value will allow for the determination of the controlling
mechanism in the event it would exist. If the Fickian
transport controls (FF~ 1), ln[(6/p2)FF] must be bound
between [-¥, -0.5].
In case the non-Fickian transport is the controlling
mechanism (FF~0), the intercept must lie between [-¥, 0]. Figures 9 and 10 show, by back-extrapolation to
t=0, that a non-Fickian controlling transport can be
predicted.
The intercept obtained by linear regression of the
t>0.7 regions for all adsorption tests, converge to zero
or to a value slightly above 0. Values slightly above
zero are accepted. Within scattering of data, we take this
as an indication that these hybrid solids have FNF »1,
and it should therefore be modeled by Eqn. (3).
The results of such modeling are summarized in Table 1. The relaxation constant values indicate that
thermally induced transport changes in these two solids
do not follow the same trend.
Despite the fact that 29Si MAS-NMR, conventional nitrogen adsorption, temperature programmed decomposition techniques and DRIFTS had been unable to detect important differences between these two solids, it is clear that the ring size of the organic Si precursor determines, in a subtle way, the residual reactivity (cross-linking) and permeability of these porous matrices.
4. Conclusions
The two hybrid materials studied here show different
behavior when they are thermally pretreated in the same
temperature range. While that made from the cyclic
trimer (SiO3-Ti) improves the mass transfer coefficientas the pretreatment temperature increases, the opposite
holds true for the SiO5-Ti hybrid. It seems that the key
factor is the ability of the structure to eliminate
unreacted alkoxide groups without concerted crosslinking.
This is one of the central features that have tobe considered when these materials are proposed in
some industrial uses (e.g., catalysts).
In conclusion, flow-through vibrational microbalances
can be used to monitor subtle changes in the
transport properties, due to mild thermal treatments, of
hybrid porous glasses. With the right design of gas
supply manifold, the technique is useful and reliable to
measure diffusion processes in the order of seconds.
This is a key information in order to predict the
behavior of these materials respect of the mass transfer
of a defined fluid, under operating conditions similar to
those used in their industrial applications.
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Received: August 11, 2001.
Accepted for publication: December 28, 2001.
Recommended by Subject Editor R. Piacentini.