Dynamics of formation of self-organized mesoporous AlO(OH)·αH2O structure in Al-metal surface hydrolysis in humid air

Article abstract of DOI:10.1111/j.1151-2916.2003.tb03605.x

In humid air, a nascent Al-metal surface (S) with a surface Hg²⁺ catalyst hydrolyzes in divided reaction centers (micelles) with a vigorous exothermic reaction, {Al + 2OH^-} + αH₂O → AlO(OH)·αH₂O + 3e^- + H⁺. It yields amorphous AlO(OH)·αH₂O with a huge ～90% porosity with α = 0.25. The primary driving forces of the reaction are the chemical potential μ_e between the reaction species, the mechanical stress σ induced in expansion of S, and the flow of the reaction species. They drive it in a common direction perpendicular to S. The heat released in it flows primarily along S. It disrupts and stops the directional hydrolysis if the local temperature in the micelle reaches a critical value T_c (hot spot). The hot spot cools to the operating value T₀, and the reaction restarts and runs over to T_c in a periodic manner, at a time scale of Δt_i ～ 5 s, per the dynamics of hot spots, forming a self-organized mesoporous structure of 15-50-nm diameter ellipsoidal shaped particles (halo) separated through 3-5-nm pores. A pore, in continuous formation of the sample, forms in disrupted reaction during the hot spot as it cools from T_c to T₀. The result is modeled in terms of the microstructure and dynamics of the hot spots.

Full text of DOI:10.1111/j.1151-2916.2003.tb03605.x

J. Am. Ceram. Soc., 86 [12] 2037–43 (2003)
journal
Dynamics of Formation of Self-Organized Mesoporous AlO(OH)⅐␣H O
2
Structure in Al-Metal Surface Hydrolysis in Humid Air
S. Ram
Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India
In humid air, a nascent Al-metal surface (S) with a surface
pure Al metal exposed in air or water results in an instantaneous
2
؉
Hg catalyst hydrolyzes in divided reaction centers (micelles)
formation of a thin oxide molecular surface layer, which prevents
؊
10–12
with a vigorous exothermic reaction, {Al ؉ 2OH } ؉ ␣H O 3
further reaction.
The thickness of the native layer formed
2
؊
؉
11
AlO(OH)⅐␣H O
؉
3e
؉
H . It yields amorphous
spontaneously lies within 3–5 nm. It can be increased by anodic
oxidation in corrosion- and abrasive-resistant films of typically
100 ␮m. The reaction involves S hydrolysis in boehmite,
2
AlO(OH)⅐␣H O with a huge ϳ90% porosity with ␣ ؍ 0.25.
2
1
1
The primary driving forces of the reaction are the chemical
potential ␮e between the reaction species, the mechanical
stress ␴ induced in expansion of S, and the flow of the reaction
species. They drive it in a common direction perpendicular to
S. The heat released in it flows primarily along S. It disrupts
and stops the directional hydrolysis if the local temperature in
AlO(OH)⅐␣H O, which later decomposes into a stable dense
2
1
3,14
Al O in an integral part of the reoxidized metal surface.
2
3
In this series, we explored an activated self-induced S hydro-
2
ϩ
lysis of a nascent Al-metal surface (with a surface Hg catalyst)
1
3,14
in humid air at room temperature (RT).
It does not involve
the micelle reaches a critical value T (hot spot). The hot spot
c
other electrolytes and gives a pure hydrolyzed product of Al metal
cools to the operating value T , and the reaction restarts and
0
in AlO(OH)⅐␣H O (porous), a precursor of alumina or sapphire. At
2
runs over to T in a periodic manner, at a time scale of ⌬t ϳ
c
i
300°C or above, it transforms into a porous Al O according to the
2
3
5
s, per the dynamics of hot spots, forming a self-organized
final temperature. It presents a novel chemical method, if com-
1
4,15
16
mesoporous structure of 15–50-nm diameter ellipsoidal shaped
particles (halo) separated through 3–5-nm pores. A pore, in
continuous formation of the sample, forms in disrupted reac-
pared with common sol–gel chemistry
or alkoxide methods,
for synthesizing a monolithic Al O or derivatives. The dynamics
2
3
of the Al-metal surface hydrolysis in porous AlO(OH)⅐␣H O is
2
tion during the hot spot as it cools from T to T . The result is
c
0
analyzed and modeled with microstructure in this paper.
modeled in terms of the microstructure and dynamics of the
hot spots.
II. Experimental Procedure
I. Introduction
A high-purity (99.99%) polycrystalline Al-metal foil (of a FCC
crystal structure of lattice axis a ϭ 0.405 nm and average
MONOLITHIC solid with fine pores of 2–50-nm size forms a
1
7
1
–7
crystallites of size 50 nm ) was used for the S hydrolysis in
humid air at 80%–90% humidity. It was degreased, washed in
distilled water, and treated with 0.1M HCl for 10 min followed by
washing in water. Electropolishing in a 4:4:2 mixture of H PO ,
A
new class of high-technology mesoporous materials.
It
displays many unique properties and has received a great deal of
attention for fundamental interest and technological applications.
1
–4
Its potential applications include high-performance catalysts,
3
4
2
,4
2,3
H SO , and H O caused its smooth surfaces with a roughness at
components of sensors, separation membranes, microelec-
2 4 2
3
,5,7
4
7
20–30 nm at a lateral scale of 10 ␮m. As such, a thin surface oxide
passivation is still present and it does not permit their S hydrolysis
in humid air at elevated temperature. Activated S hydrolysis occurs
tronic circuits,
phosphors, and hot gas filters. Porous ceram-
ics present considerably improved mechanical, chemical, and
thermal resistance over the bulk values, promising a superior
structural as well as electronic material. Size, morphology, and
distribution of particles through the pores largely influence their
electronic structure and related properties. Moreover, a variety of
pure metals, metal oxides, and other materials of confined size of
the pore can be incorporated in the pores for designing a meso-
porous composite material of desirably modified properties of its
2
ϩ
after treating the surface with Hg cations; i.e., the specimen is
2
ϩ
dipped in an aqueous 0.1M Hg solution for ϳ30 s and then
2
ϩ
rinsed with deionized water to remove the excess Hg and other
byproduct impurities caused during the processing.
When the specimen is placed face up in humid air, a self-
induced spontaneous exothermic reaction occurs at the nascent Al
surface with air by forming a hydrolyzed product of Al atoms in
2
–7
components.
A porous Al O forms on an Al-metal surface (S) upon its
AlO(OH)⅐␣H O molecules at S. They grow in fibers (as long as
2
2
3
1
3
2
0–50 mm in ϳ30-␮m diameter ) in a self-organized manner in
a direction perpendicular to S. As will be discussed later, the Hg
hydrolysis under an anodic bias in an electrochemical cell with a
2ϩ
8
,9
6
liquid electrolyte. Recently, Jessensky et al. explored this idea
in developing mesoporous Al membranes by S hydrolysis of an
electropolished Al-metal foil in a dilute acid. The membranes have
a self-ordered pattern of hexagonal pores, with a fairly well
controlled, 25–40-nm, size distribution, which offer many appli-
cations. Furthermore, it is also reported that, being an active metal,
cations eventually help in thinning down the spontaneous surface
oxide (SSO) layer to a specific thickness ⌬l below the critical
value ⌬l in a stable barrier layer to inhibit the S hydrolysis at
c
elevated temperature. The S hydrolysis thus presumably occurs at
⌬
l Ͻ ⌬l under favorable conditions of temperature and other
c
parameters.
The microstructure was studied with a transmission electron
microscope (TEM) or a scanning electron microscope (SEM) in
conjunction with an energy dispersive X-ray spectrum analyzer for
in situ elemental analysis. X-ray diffraction was studied with a
diffractometer using filtered CoK␣ radiation of wavelength ␭ ϭ
S.-I. Hirano—contributing editor
0
.179 05 nm. A Perkin–Elmer thermal analyzer was used to study
Manuscript No. 188383. Received July 20, 2000; approved November 25, 2002.
This work has been financially supported by a research grant from the Aeronautical
Research and Development Board, Government of India.
thermal transformation of the sample by DTG (differential ther-
mogravimetric) analysis. The porosity was determined from its
2
037

2
038
Journal of the American Ceramic Society—Ram
Vol. 86, No. 12
NH2
bulk density, which was measured using the Archimedes principle
in N gas with a Penta Pyknometer (of Quanta Chrome).
}
2
ϩ
Ϫ
3
ϩ
2Hg ϩ NO ϩ 4NH ϩ H O 3 HgO⅐Hg
ϩ3NH4
2
3
2
{
NO3
(2)
III. Results and Discussion
2
ϩ
2
؉
confirming the Hg cations to be present in the solution in the
amalgam.
(1) Dynamics of Reaction of Hg Cations on
Al-Metal Surface
The surface treatment of the Al-metal surface by a surface
2
ϩ
(2) Process and Dynamics of the Al-Metal
Surface Hydrolysis
As demonstrated in diagrams (a) and (b) in Fig. 1, as soon as it
is put in humid air at RT, the nascent Al S with an atomically thin
catalyst of Hg
self-induced S hydrolysis of it in humid air or water. According to
cations plays a crucial role in activating a
2
ϩ
the surface treatment, the Hg cations react with the specimen
and thin down the SSO layer, ⌬l Ͻ ⌬l , so that the reaction species
c
Al–Hg surface film sets up a weak activation barrier E between
of H O molecules from the air pass through the SSO layer to react
a
2
Ϫ
the reaction species of Al atoms (A) at the surface and the OH or
with the nascent Al-metal surface underneath it. A value of ⌬l , in
c
2
Ϫ
1
1
O
anions (B) from the air over it. The chemical potential ␮e
this specific example, is pretty large at 3–5 nm, i.e., roughly,
0–20 Al O molecular layers. Whatever the mechanism of the
between A and B initiates their reaction against the E energy
1
a
2
3
barrier in a specific AB direction perpendicular to S (Fig. 1(b)).
reaction, there is no doubt that, at an early stage of the reaction, the
Ϫ
2
2
ϩ
ϩ
The reaction is more efficient with OH anions, which involve a
Hg
cations move through the SSO layer and form a thin
relatively small E value. It persists over a long time scale of
Hg –Al interface at S. Al atoms at the interface co-reduce the
a
2
ϩ
minutes and permits its measurement with a continuous S hydro-
lysis on nascent S. This is not feasible with O anions , under
these conditions, which form a highly stable nonporous Al O
surface layer on the nascent reaction surface that instantaneously
stops the reaction.
Hg cations into Hg metal that ultimately forms a thin amalgam
film with Al atoms in the interface. Otherwise, the Hg metal does
not adhere so intimately to the Al metal surface and peels off in
2
Ϫ
2
3
2
ϩ
independent Hg metal. The Hg 3 Hg co-reduction reaction
3
ϩ
Ϫ
2
3
Al ª 2Al ϩ 6e
Other forces, which support the unidirectional reaction, are the
mechanical stress ␬ induced in expansion of S during the reaction
and the flow of the reaction species. Both of them occur in a
common AB direction and assist the directional S hydrolysis along
2
ϩ
Ϫ
Hg ϩ 6e ª 3Hg
3
ϩ
it. A noninterrupted migration of Al
cations (from the Al
2
ϩ
3ϩ
2
Al ϩ 3Hg ª 2Al ϩ 3Hg
(1)
surface) through the AB interface performs a noninterrupted
growth of hydrolyzed Al metal in AlO(OH)⅐␣H O, with ⌬H ϭ
Ϫ1971.6 kJ/mol being the standard enthalpy of formation. This
Њ
f
2
involves a large value of the resultant chemical potential ⌬␾ ϭ
␾ Ϫ 2f␾ ϵ 5.877 V. That drives the reaction so fast that it lasts
20
3
1
occurs in divided reaction centers (micelles) on S nucleated in
2
ϩ
Ϫ
only over a few seconds. The reaction Hg ϩ 2e ª Hg has a
positive ␾ ϭ 0.851 V value while that of Al ϩ 3e ª Al has
a negative ␾ ϭ Ϫ1.662 V value.
2ϩ
divided reactions of Hg cations on it according to its granular
3
ϩ
Ϫ
1
structure (grain size ϳ 50 nm), which determines the structure of
1
8
2
micelles or the reaction through channels at S. As described
The thin Al–Hg amalgam film very intimately adheres to the
13
2ϩ
earlier, on a nascent Al S, Hg cations form directional Al–Hg
reaction thorough channels perpendicular to S. They collimate a
directional S hydrolysis of the specimen of the nascent Al S in
humid air. ␬ affects the kinetics of the S hydrolysis through the
creation of additional active sites for the S hydrolysis during the
reaction.
nascent S and induces the initial SSO layer, if any, thereon to
3
ϩ
segregate and float over the surface together with traces of Al
cations formed in reaction (1). All these surface impurities are easy
to wash away along with the excess amalgam, if any, in water. A
specimen so obtained has primarily a nascent S protected with a
thin residual amalgamated surface, which is as thin as possible at
The heat released in the highly exothermic S hydrolysis reaction
in micelles flows primarily along the Al-metal S (good thermal
conductor). It disrupts directional S hydrolysis in the perpendicular
direction if instantaneous temperature in the micelle increases to a
critical value T , well above its average value, T , during the
1
3,14
an atomic scale and inseparably adheres to the metal surface.
The Hg atoms, being prone to amalgamating the Al atoms, hardly
leaves behind a residual SSO between the two regions. Neverthe-
less, one cannot ignore the SSO present in the pitting centers
caused during sampling in an acidic solution. Those peel off in the
course of S hydrolysis in surrounding active centers and impart a
c
av
13
reaction. Per the average reaction rate, a model temperature
profile of ABH is predicted in Fig. 2(a). It governs the drift
homogeneous reaction. H gas, which evolves in the hydrolysis,
2
velocity v of the reaction species along AB, as schematically
z
promotes the process. The SSO peels off in the distinct character-
istic color (grayish) of the specimen, inducing the hydrolysis in a
product of fibers.
The validity of reaction (1) is confirmed in a separate experi-
2
ϩ
ment by co-reducing a Hg salt (solid) into a pure Hg metal
liquid) by milling it with Al chips or granules in a closed reactor.
(
2
ϩ
An efficient Hg 3 Hg co-reduction reaction also occurs if Al
chips are ground in an aqueous Hg solution. The pure Hg metal
is easily recovered since it is automatically segregated by its large
2
ϩ
3
density ␳ ϭ 13.6 g/cm . It does not adhere to the byproducts or the
remaining Al metal after the reaction. This is analyzed with the
1
9
characteristic chemical tests as follows.
i) A freshly prepared specimen with a thin Al–Hg amalgam
(
film at an Al plate, as described above, is immersed in HCl (12N).
3
The Al metal dissolved, Al ϩ 3HCl 3 AlCl ϩ H , in part of the
3
2
2
specimen, leaving behind a silver white Hg metal. No such Hg
metal is recovered from residual Al chips after the bulk reaction
with a Hg salt in the other case.
(ii) In another experiment, the specimen was immersed in
HNO . The HNO dissolved both the components of the amalgam
and A1 metal in a clear solution. On adding an ammonia solution,
a white precipitate appears in mercury(II) amidonitrate,
3
3
Fig. 1. Schematic diagram of Al-metal surface hydrolysis in humid air:
(a) the pure metal surface before the reaction and (b) expansion of it in the
formation of its hydrolyzed product.

December 2003
Formation of Self-Organized Mesoporous AlO(OH)⅐␣H O
2039
2
in humid air in Fig. 3. The thermogram consists of a thermal
desorption peak in desorption of ␣H O (or of any interstitial gas)
2
at ϳ340 K, which follows a similar peak at ϳ405 K in molecular
dissociation of the specimen into Al O with a total of 21% loss in
2
3
its mass per its molecular structure with ␣ ϭ 0.25. In contrast to
6
other reports, the result unambiguously confirms that Al hydro-
lysis in an aqueous electrolyte or in humid air does not give a
hydrolyzed Al-metal product of Al O directly. IR analysis con-
2
3
1
4
firms the as-received product to be a metastable AlO(OH)⅐␣H O.
2
We performed several experiments of S hydrolysis of Al metal in
humid air at different temperatures from 273 to 380 K and found
that an effective reaction occurs only at Tav Յ 320 K. It stops if Tav
increases above 350 K due to the heat produced in the exothermic
Ϫ
S hydrolysis reaction of OH anions on Al atoms.
Our results are consistent with the studies of electrochemical
1
2
behavior of Al metal with a thin SSO layer. According to
these studies, the rate of H evolution in the hydrolysis behaves
2
as a nonlinear function of temperature in this region. The SSO
thermal stability, microstructure, and surface chemistry govern
the process. AlO(OH), which transforms to Al O in this
2
3
region, modifies the reaction dynamics according to other
parameters. This is one of the regions in which protection
efficiency of SSO against the hydrolysis varies in different
1
0–12
environments.
A newly formed SSO layer thus can be
described as the best in a product of pseudoboehmite.
In the proposed model, the H spots move with the flow of heat
3
ϩ
(
phonons) along S and cease the drift of Al cations in directional
3ϩ
S hydrolysis in its perpendicular direction along AB. These Al
cations are lost to the Al surface and are prerequisite for the
discontinuous (porous) growth of hydrolyzed Al metal into
Fig. 2. (a) Model temperature (T) profile in the local heating and cooling
in a micelle in the Al-metal surface (S) hydrolysis in humid air. The
3
ϩ
AlO(OH)⅐␣H O. Only the Al cations, which cross the interface
2
through the barrier E in a single noninterrupted step, contribute a
hydrolysis stops at the mobile hot spots at H and HЈ at T Ն T . (b) Drift
a
c
3
ϩ
velocity v of the reaction species of Al cations perpendicular to S. The
noninterrupted S hydrolysis in the AB direction. After a certain
z
straight line (dashed) indicates the flow of the hot spots.
time interval ⌬t , with ⌬t ϭ 0 at T ϭ T , the H spot cools down
i
i
c
to the operating value T0 and S hydrolysis occurs again. As
schematically shown in Fig. 2(b), this occurs in successive steps in
shown in Fig. 2(b). A value of Tav as large as 350 K has been
a periodic interval ⌬t . From the TEM micrograph of the sample,
i
observed in this experiment. At T Ն T , the micelles involved in
in Fig. 4(a), it appears that a single, separated AlO(OH)⅐␣H O
c
2
the exothermic S hydrolysis reaction become hot spots H and
particle by a pore (which forms in a subsequent disrupted reaction
step) forms in a single noninterrupted reaction. The particles, in an
ellipsoidal shape of diameter D ϭ 15–50 nm, are self-organized
through pores in a specific fashion according to directional S
hydrolysis. An average diameter in pores between particles is 3–5
nm. The electron diffractogram corresponding to TEM, in Fig.
4(a), has a broad halo in Fig. 4(b) of radius d ϭ 0.235 nm, an
3
ϩ
disrupt the reaction by arresting the uniaxial drift of the Al
cations from S along AB. Actually, at T Ն T , 2AlO(OH)⅐␣H O 3
c
2
Al O ϩ (1 ϩ 2␣)H O thermal decomposition occurs and deposits
2
3
2
in a hard Al O -surface film (amorphous) over hot S and that
2
3
inhibits further S hydrolysis.
This is clearly demonstrated by the DTG thermogram of
2
1,22
recovered AlO(OH)⅐␣H O from S hydrolysis of a nascent Al metal
intrinsic characteristic of an amorphous structure.
2
Fig. 3. (a) DTG thermogram of a porous AlO(OH)⅐␣H O, ␣ ϭ 0.25, measured by heating it at 0.33 K/s. The dashed curves are the guidelines for two
2
components in the two-step thermal desorption transformation of AlO(OH)⅐␣H O in Al O .
2
2 3

2
040
Journal of the American Ceramic Society—Ram
Vol. 86, No. 12
Fig. 4. (a) TEM and (b) corresponding electron diffraction in a mesoporous AlO(OH)⅐␣H O powder from hydrolysis of Al metal in humid air, and the
2
2
ϩ
Al-metal surfaces in SEM (c) before and (d) after treating with Hg
cations to form a thin amalgam surface layer.
Particles in Fig. 4(a) have a shell structure as can be seen in
close observation of their surfaces, which suffer throughout from
a lack of uniform contrast. A few white images are present in
region A in the peeling-off part of thin surface walls in some
particles. An average 3–5-nm thickness (␦) is estimated by images
of the cross section in broken surface walls. A shell particle of an
average 30-nm diameter thus encloses ϳ40% shell volume at ␦ ϳ
The encapsulated shell inside the particle is formed by trapping
H gas during its formation by S hydrolysis of the Al metal. H O
molecules (from the air) dissociate at the nascent Al-metal surface
2
2
and produce H gas, part of which gets trapped inside the growing
2
particles in micelles perpendicular to S. The H gas encapsulated
2
in the particles (which behave as H -gas-filled balloons) assists
2
their directional growth perpendicular to S in the open air
according to its low pressure. The pores between the particles
mediate a rather free growth of sample in separated particles
driven by the above driving forces. An elongated ellipsoidal shape
of particles is indicative of their directional growth along their
4
nm in approximation of its spherical shape. It covers a major part
of observed porosity ⌽ ϳ 90% in the sample (Table I). SEM
micrographs (c) and (d), in Fig. 4, give an idea of the Al-metal
surfaces used in the S hydrolysis. A microstructure (Fig. 4(d)) of
micelles, 30–100-nm diameter, is developed on treating the
major axes in the direction of ␮ (AB). Dynamics of pores along
e
2
ϩ
surface (Fig. 4(c)), after the electroplating, in a Hg solution.
Porous anodic SSO films in a reaction of Al metal with H PO had
S during the H spots are cooling from Tc to T0 and that
3
4
1
1
similar micelles. The sample in Fig. 4(d) has been boiled in
water to inhibit the hydrolysis, with an enriched SSO layer, which
allowed the measurement. Otherwise, this sample hydrolyzes very
rapidly, making examination of the structure difficult.
Table I. Structure, Bulk Density, and Porosity in the
Samples Obtained by Al-Metal Surface Hydrolysis in Humid
Air at Room Temperature Followed by
Annealing at Selected Temperatures
†
Density
Porosity
(%)
3
Sample
Annealing
Structure
(g/cm )
AlO(OH)⅐␣H O As received Amorphous 0.23 (2.25)
90
51
47
2
Al O
2 h at 600 K Amorphous 1.80 (3.67)
2 h at 900 K Crystalline 1.95 (3.67)
2
3
␥
-Al O
2
3
†
Fig. 5. Model surface hydrolysis of (a) a refreshed Al-metal S into (b) a
The theoretical values of the density, given in the parentheses, are taken from
hydroxyl product in a reaction with H O molecules through a thin SSO
Refs. 14 and 17. For a lack of data, the theoretical value for the amorphous phase is
taken to be the same as that for the crystalline phase.
2
layer. The product behaves as a weak acid.

December 2003
Formation of Self-Organized Mesoporous AlO(OH)⅐␣H O
2041
2
Fig. 6. Model of activated hydrolysis of a nascent Al-metal surface (with a thin amalgam layer) in AlO(OH)⅐␣H O in humid air.
2
perpendicular to S in the subsequent S-hydrolysis step attenuate
this particular particle structure as follows.
As mentioned above, the H gas being produced in the inter-
mediate reactions in Eq. (3) gets easily locally trapped within the
2
Al-atomic density in Al metal is decreased roughly by a
nascent AlO(OH)⅐␣H O molecules in the divided reaction centers.
2
factor f ϳ 5 upon its hydrolysis in AlO(OH)⅐␣H O. This
The volume in the gas enclosed inside a group of molecules grows
2
involves a volume expansion of it by an order of magnitude per
as a shell by accumulation of more and more H molecules (from
2
3
the diminished bulk density ␳ ϭ 0.23 g/cm in AlO(OH)⅐␣H O
the reaction) as a function of their growth into a particle in a
continuous reaction. Obviously, the gas drives directional molec-
ular growth perpendicular to the reaction surface per its initial
internal pressure and other driving forces.
2
3
from ␳ ϭ 2.70 g/cm in the Al metal (Table I). As mentioned
above, the hydrolysis induces a mechanical stress ␶ in the
specimen during its S hydrolysis as a possible origin of forces
between the neighboring pores (discontinued hydrolysis) and/or
the particles (continuous hydrolysis). As the S hydrolysis takes
place at the entire pore bottom simultaneously, the material can
only expand in the vertical direction so that the existing pore
walls are pushed symmetrically upward in the same direction as
the particles growing in a noninterrupted S hydrolysis. The
dynamics of the pores, therefore, attenuates the dynamics of an
(4) Modeling of the Discontinuous Al Surface Hydrolysis
Mathematically, the temperature profile of micelles in Fig. 2(a)
can be represented by a presumed empirical function,
n
nЈ
T ϭ ␣͓T ϩ ␤t ͔ Ϫ ͑1 Ϫ ␣͒͑T Ϫ ⌬T͒ exp͕Ϫ͑t/␶͒ ͖
(4)
i
c
ordered pattern of self-organized AlO(OH)⅐␣H O particles
where T is the initial temperature and ␣ ϭ N /N and (1 Ϫ ␣) ϭ
i 1 0
2
through the pores. Three driving forces of the directional
N /N are the fractions of the micelles N shared in the internal
2 0 0
reaction are (i) ␮ , (ii) the longitudinal component of the
heating (N ) and cooling (N ) processes in the regions of ABH and
1 2
e
mechanical stress ␬ , and (iii) the flow of the reaction species.
All of them drive the observed pattern of the reaction in a
common direction perpendicular to S.
BHЈ, respectively. Other parameters in this relation are the
correlation constant ␤, the exponents n and nЈ, and the relaxation
time ␶. The exponential function in the second term represents a
well-known thermal or structural relaxation of a physical property
zz
2
1,22
P in general.
temperature ⌬T ϭ T Ϫ T, overshooting the operating value T by
Here, it describes simply the release of the excess
(
3) Dynamics of Formation of AlO(OH)⅐␣H O Molecules
2
c
0
internal heating in the first term, as a function of time t by T
approaching T0.
Equation (4) is rewritten for the average heating process in a
In general, all metal oxides react with H O in the sur-
2
2
3,24
face.
The degree of the reaction (hydrolysis) varies from
case to case according to their chemistry. As demonstrated in
sample of N heating micelles as
Fig. 5, a metal surface thus reacts with H O via a thin oxide
1
2
layer of its own and extends its hydrolysis in a metastable
2
3
N1
n
hydroxyl product, which behaves as a weak acid. An activated
reaction occurs in absence of the surface barrier layer. In humid
air, a nascent Al-metal surface (with a thin surface amalgam)
T ϭ N0 ͓T ϩ ␤t ͔
(5)
(6)
i
which reduces to
dissociates H O molecules (from the air) at the surface into
2
Ϫ
ϩ
Ϫ
n
OH and H ions. The OH anions react on Al atoms at S in
T ϭ T ϩ ␤t
i
successive steps and cause its S hydrolysis in AlO(OH)⅐␣H O
2
in a self-controlled manner. This is shown schematically in Fig.
for a single micelle or for a system of a single micelle, N and its
1
ϩ
6
. The intermediate [Al(OH)2] reaction species in Eq. (3b)
equivalent; ␣N ϭ 1. It represents a parabolic T profile, as shown
0
n
1
2
transforms into a stable AlO(OH) molecule just by releasing a
in Fig. 2(a), with an arbitrary value of ␤ ϭ (30 K)/s with n ϭ ⁄
ϩ
proton H only. Since it involves a minor redistribution of its
and the initial experimental temperature T ϭ 295 K. It gives a rise
i
local properties of internal energy and electronic charges, it
occurs fast before another OH group recombines to it and
in T over T by 67 K with a final value of T ϭ 362 K within t ϭ
i
Ϫ
5 s of the reaction begun at t ϭ 0. That can be treated as the T ϭ
c
forms a stable Al(OH) molecule. Further, an AlO(OH) mole-
362 K value, which is a consistently larger value if compared with
the average Tav ϭ 320 K value measured at S during the S
hydrolysis.
3
cule so deduced takes up a controlled amount of water of
hydration from the medium in a subsequent step of the reaction
with H O and ultimately converts into AlO(OH)⅐␣H O. This
This kinetic analysis reveals that the time interval ⌬t of
2
2
i
grows very fast in AlO(OH)⅐␣H O molecular fibers. It does not
overshooting of T in a micelle in the S hydrolysis lies at a scale of
2
dissociate, giving a weak acid behavior.
s. The overshooting of the internal T in a micelle to T stops the S
c

2
042
Journal of the American Ceramic Society—Ram
Vol. 86, No. 12
Fig. 7. X-ray powder diffractograms of (a) as-received AlO(OH)⅐␣H O and that annealed 2 h at (b) 600 and (c) 900 K in air. The diffraction peaks of
2
recrystallized ␥-Al O in (c) are marked by their (hkl) values.
2
3
hydrolysis at it. This cools back to T by releasing the ⌬T per the
(5) Microscopic Structure of AlO(OH)⅐␣H O Particles
0
2
second term in Eq. (4), which in a more realistic form is rewritten
as
The AlO(OH)⅐␣H O particles, D ϭ 15–50 nm (Fig. 4(a)), have
2
a prominent X-ray diffraction halo (Fig. 7a) at wavevector q ϭ
1
Ϫ1
nЈ
6.8 nm {defined by q ϭ (4␲ sin ␪)/␭}and two weak halos at
i
Ϫ1 Ϫ1 Ϫ1
⌬
T ϭ ⌬T exp͕Ϫ͑t/␶͒ ͖
(7)
c
q2 ϭ 26.9 nm and q ϭ 44.5 nm . The q ϭ 26.9 nm halo
3
2
compares well in the position with the electron diffraction halo in
Fig. 4(b). A large peak-width D(2␪1/2) ϳ 10° or larger in these
halos signifies an amorphous structure of the sample. For a time
being, if we assume a crystalline structure of it, then a Debye–
Scherrer analysis of D(2␪1/2) values predicts a crystallite size
r Յ 0.8 nm (diameter), which is smaller than the critical r* Ն 3.8
with ⌬T being the optimal value of ⌬T. As schematically shown
c
in Fig. 2(a), curve HBЈ represents a monotonically decreasing
signal of the release of excess ⌬T in Eq. (7), i.e., relaxation of
phonons excited in high-energy levels, with t. The curve of HBЈ is
reproduced with nЈ ϭ 0.6 and ␶ ϭ 25 s in Eq. (7). Similar values
for nЈ and ␶ appear in a structural relaxation of excitons or phonons
2
6
2
2
value for a stable AlO(OH)⅐␣H O crystallite calculated with the
or in a local structure in amorphous or crystalline solids.
A
2
2
0
relation
comparison of the results with the phonon-assisted tunneling of
small polarons, which successfully describes the motion of muons
2
5
1
2␴
or protons, implies a hopping rate
r* ϭ
(11)
2
⌬Gv
Ϫ
␶
͑T͒ ϭ ␷ exp͕Ϫ⌬E/kT͖
(8)
0
2
with ␴ ϭ 0.70 J/m (its surface-energy density) and ⌬G ϭ 0.74 ϫ
1
v
9
3
with
0 J/m (the change in the Gibbs free energy on its formation). In
Ϫ1/ 2
the absence of the absolute values, the values of ␴ and ⌬G used are
␷0
ϭ AiT
(9)
20
the same as those for a pure Al O . The average r value deduced
2
3
2
2
Ϫ1/ 2
from D(2␪1/2) comes to be even smaller than the average size, d ϭ
A ϭ J ͑4␩ ⌬E/k͒
(10)
i
1/3
V
Х 0.75 nm, of its single crystal unit cell of volume V. The
where J is the tunneling matrix and ⌬E is the difference between
the adjacent energy levels.
In this formalism, the dynamics of the two processes, which
occur one after another in a periodic interval ⌬t ϳ 5 s, are
crystal unit cell, of a monoclinic structure, consists of eight
molecules, lattice parameters a ϭ 0.886 nm, b ϭ 0.506 nm, c ϭ
1
4
0.983 nm, and ␤ ϭ 94°34Ј. In fact, a single crystal unit cell is
never stable. A stable crystallite of size r* consists of several
crystal unit cells.
i
interdependent. As a result, T , in Fig. 2(b) (dashed line), regularly
c
decreases with t in the periodic S hydrolysis in micelles by a
According to the Bragg’s relation, the halo q1 lies at d ϭ
␭/(2 sin ␪) ϳ 1.0 nm. This is a larger value than is possible for an
interplanar distance dhkl in this series. All the results ultimately
have a single implication that the sample is not in a crystalline
state. It has an amorphous structure of small configurations or
periodic variation in v of the reaction species. The straight line
z
represents a linear decrease in T with t and the S hydrolysis
c
automatically stops as its final value reaches T . The ⌬T ϭ T Ϫ
0
c
c
T0 dictates the driving path or potential for S hydrolysis. That
vanishes at ⌬T ϳ 0 and stops the S hydrolysis.
microscopic domains of AlO(OH)⅐␣H O molecules of r ϭ d ϳ 1
2

December 2003
Formation of Self-Organized Mesoporous AlO(OH)⅐␣H O
2043
2
2
7
nm in size. Most likely, a strong surface reflection of the X-ray
AlO(OH)⅐␣H O phase forms. A bulk reaction with a sufficiently
2
3
ϩ
-
beam occurs from their confined surfaces and results in the
prominent diffraction halo q Х 6.5 nm . The other two halos,
which are characteristically week in intensity, are common
and refer to average atomic reflections with two prominent pair
distribution functions of atoms in an amorphous AlO(OH)⅐␣H O
large Al –OH interface in other methods results in the equilib-
Ϫ1
13,16
rium Al(OH) ⅐␣H O phase.
In general, the results are useful
1
3
2
2
1,22
for understanding and modeling (i) formation of self-ordered
structure and (ii) underlying mechanisms of physical processes in
porous materials and for designing (iii) their electronic devices and
components.
2
structure.
All three diffraction halos marginally shift at lower q ϭ 6.3
1
Ϫ1
Ϫ1
Ϫ1
nm , q ϭ 23.7 nm , and q ϭ 42.5 nm values on thermal
2
3
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2
1
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7
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0
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c
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1
2
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13
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2
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4
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15
2
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1
Ϫ1
Ϫ1
16
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2
3
5
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17
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1
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2
18
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19
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/3
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4
20
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2
1
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21
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Ϫ
3ϩ
22
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25
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2
Њ
26
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Њ
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27
f
3
2
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ϩ
-
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19 Microcrystals in Borate Glasses,” Phys. Rev. B, 51, 6280–86
self-controlled reaction at which only the intermediate
Ⅺ