Elasticity through nanoscale distortions in periodic surfactant-templated porous silica under high pressure

Article abstract of DOI:10.1021/jp013497n

High-pressure infrared absorption spectroscopy is used to examine changes in local bonding upon hydrostatic compression in both ordered surfactant-templated mesoporous silica and sintered sol-gel silica with a goal of connecting atomic scale structural changes with variations in nanoscale periodicity. High-pressure IR absorption spectra are analyzed on the basis of a noncentral force model. It is found that the intertetrahedral bond angle and its distribution width in both the dense and the mesoporous silica decrease at elevated pressure up to 4 GPa. With increasing pressure above this value, decreases in the average bond angle and distribution width cease in the mesoporous silica, while they continue in the bulk material. The results suggest that in the mesoporous silica the nanometer length scale of the silica framework makes it energetically unfavorable to form high-density atomic scale structures at higher pressures (>4 GPa). Instead, further compression of the mesoporous silica takes place by distortion of the periodic pore structures on the nanometer scale (deformation of pores). Surprisingly, upon the release of pressure, structural changes on both the nanometer and atomic length scales are reversible. The results suggest that reversible nanometer scale distortions in periodic porous materials can replace the irreversible atomic scale distortions Observed in bulk amorphous silica.

Full text of DOI:10.1021/jp013497n

J. Phys. Chem. B 2002, 106, 5613-5621
5613
Elasticity through Nanoscale Distortions in Periodic Surfactant-Templated Porous Silica
under High Pressure
Junjun Wu,† Liang Zhao,‡ Eric L. Chronister,‡ and Sarah H. Tolbert*,†
Department of Chemistry and Biochemistry, UniVersity of California at Los Angeles,
Los Angeles, California 90095-1569, and Department of Chemistry,
UniVersity of California at RiVerside, RiVerside, California 92521-0403
ReceiVed: September 12, 2001; In Final Form: January 24, 2002
High-pressure infrared absorption spectroscopy is used to examine changes in local bonding upon hydrostatic
compression in both ordered surfactant-templated mesoporous silica and sintered sol-gel silica with a goal
of connecting atomic scale structural changes with variations in nanoscale periodicity. High-pressure IR
absorption spectra are analyzed on the basis of a noncentral force model. It is found that the intertetrahedral
bond angle and its distribution width in both the dense and the mesoporous silica decrease at elevated pressure
up to 4 GPa. With increasing pressure above this value, decreases in the average bond angle and distribution
width cease in the mesoporous silica, while they continue in the bulk material. The results suggest that in the
mesoporous silica the nanometer length scale of the silica framework makes it energetically unfavorable to
form high-density atomic scale structures at higher pressures (>4 GPa). Instead, further compression of the
mesoporous silica takes place by distortion of the periodic pore structures on the nanometer scale (deformation
of pores). Surprisingly, upon the release of pressure, structural changes on both the nanometer and atomic
length scales are reversible. The results suggest that reversible nanometer scale distortions in periodic porous
materials can replace the irreversible atomic scale distortions observed in bulk amorphous silica.
1. Introduction
than values measured for bulk vitreous silica7 were obtained if
both the nanometer-scale order and local atomic-scale bonding
By optimizing the secondary structure of composite materials,
mechanical properties superior to the starting single-component
material can be obtained. Honeycomb-structured composite
materials are one such example. They have been widely used
to make light but stiff materials, both in our daily life and by
nature, on a variety of length scales.1,2 Recently we have found
that surfactant-templated porous silicas with hexagonal periodic-
ity exhibit excellent mechanical propertiessstiffness and stabil-
ity under hydrostatic compression (up to 12 GPa) and revers-
ibility of changes to the nanoscale order upon the release of
pressure.2 Such materials, labeled MCM-41, are formed by the
cooperative self-organization of surfactant molecules with
soluble silicate species.3 The pore structure in the material has
p6mm symmetry (a honeycomb) with pore diameters around
30 Å and wall thicknesses of the amorphous silica framework
around 10 Å. In recent years, the pore size of the material has
been expanded to 300 Å with varying wall thickness, and many
new periodicities are also available by controlling synthetic
conditions.3-6
In our previous experiments, we used high-pressure, low-
angle X-ray diffraction to examine the compressibility of
periodic hexagonal, surfactant-templated silicas under hydro-
static compression.2 The results indicate that mesoscopic order
in these materials can be retained up to 12 GPa and that pressure-
induced distortions are reversible. We also found that postsyn-
thetic treatment can greatly enhance the mechanical properties
of the porous material. Bulk moduli equal to and even higher
were optimized.2 It should be noted, however, that when
compressed under non-hydrostatic conditions in air (for example,
in a steel die),8-10 ordered mesoporous silica structures are
essentially destroyed between 0.2 and 0.6 GPa, a process which
occurs mechanochemically through the hydrolysis of Si-O-
Si bonds.9,11,12
We also studied the molecular environment of the organic
component of periodic silica/surfactant composites under ele-
vated pressure using a rigidochromic Re complex as a molecular
probe.13 The amphiphilic organometallic complex was incor-
porated into the organic component of the silica/surfactant
composite during synthesis. Shifts in the luminescence peak
position of the Re complex indicated changes in the rigidity or
viscosity of the surrounding matrix. Again, the results confirmed
conclusions from earlier experiments on the mechanical proper-
ties of silica/surfactant composites under high pressure.2 While
an increase in viscosity was observed with increasing pressure,
the molecular environment did not become fully rigid until
pressures as high as 10 GPa had been reached. This pressure is
significantly higher than the solidification point of most pure
organic phases and suggests that the mechanical strength of the
silica framework provides a protected molecular scale environ-
ment for organic molecules situated within the silica nanopores.
At the highest pressures, luminescence did indicate a rigid
environment, suggestive of pore collapse on compression. Upon
release of pressure, however, this collapse appeared reversible.
To understand the unique mechanical properties of the
mesoporous silica under hydrostatic compression, we need to
first understand what happens at the atomic scale upon applica-
tion of pressure in bulk materials. We thus begin by reviewing
* Corresponding author. E-mail: tolbert@chem.ucla.edu.
† University of California at Los Angeles, Los Angeles.
‡ University of California at Riverside.
10.1021/jp013497n CCC: $22.00 © 2002 American Chemical Society
Published on Web 05/10/2002

5614 J. Phys. Chem. B, Vol. 106, No. 22, 2002
Wu et al.
the behavior of both crystalline and vitreous bulk silica under
high pressure. A summary of experimental conclusions on the
behavior of bulk silica under high pressure is presented briefly
below.
It is of great interest to theoretically relate the above
experimental IR absorption peaks to microstructural properties
in silica, such as the intertetrahedral bond angle. Galeener has
applied the Sen and Thorpe central force model for the dynamics
of AX2 networks.24-26 The model predicts that the high-
frequency vibrational mode is due to an asymmetric Si-O
stretching (AS) vibration within a fully polymerized tetrahedral
silicate network. The existence of a uniform effective electric
Under high pressure, vitreous silica undergoes a variety of
rearrangements. The structures of these materials, including
short-range and intermediate-range order and the dependence
of these quantities on pressure, are of fundamental concern. The
structure of vitreous silica is usually described by a continuous
random network (CRN) of tetrahedral silicon oxide (SiO4) units
interconnected by bridging oxygen atoms. The intertetrahedral
bond angle that connects two tetrahedral units is one of the most
important structural parameters for the CRN-type amorphous
oxides as it determines, among other things, the overall density
and stiffness of the solids. Experimental results from X-ray
diffraction have shown that for both crystalline (quartz) and
vitreous silica, the change in Si-O bond length is negligibly
small under compression below 8 GPa.14-16 In this pressure
range the deformation in silicon oxide tetrahedral units is slight
and the changes are reversible. Compression occurs through
bending of the Si-O-Si intertetrahedral angles. For quartz it
decreases from around 144° at ambient pressure to 130° at 8
GPa.14,15,17 It is suggested that the compaction of vitreous silica
follows a similar mechanism16,18svolume compression occurs
through bending of the Si-O-Si intertetrahedral angles (i.e.,
decreasing Si-Si separations), with little change in the indi-
vidual SiO4 tetrahedral unit.
field in the glass splits this mode into transverse (∼1070 cm-1
)
and longitudinal (∼1200 cm-1) optical modes (TO and LO
modes).27,28 The main reason for the existence of the effective
electric field in amorphous silica is the considerable effective
charge caused by the ionicity of the Si-O bond.28,29 The
vibrational band at intermediate frequency (800 cm-1) is mainly
associated with motions of silicon atom against its tetrahedral
oxygen cage, with little associated oxygen displacement30-32
and it will be labeled as the symmetric stretching (SS) band.
The lowest frequency mode observed in IR is ascribed to mainly
oxygen displacement in the plane bisecting Si-O-Si24 and
labeled as the rocking mode.
In our experiments, IR absorption spectra of MCM-41 type
materials under pressure show behavior that is different from
that generally observed for vitreous silica glass from the
literature and from a sintered sol-gel silica sample that we have
used for comparison in our experiments. Analysis of the IR
spectra based on calculations using the noncentral force model
in ref 33 provide us with information on changes in intertetra-
hedral bond angle distribution under high pressure, thus enabling
us to relate modifications in atomic structures to the evolution
in mesoscale order. In addition, 29Si magical angle spinning
(MAS) nuclear magnetic resonance (NMR) spectroscopy is used
to obtain intertetrahedral bond angle distributions in samples
under ambient condition.34-36 The data are then used as input
parameters for the IR analysis to examine change in bond angle
distribution under high pressure.
Above 8 GPa, the SiO2 glass can be irreversibly densified
by up to 20% after decompression.19,20 By using a uniaxial
pressure-transmitting device, however, densification in SiO2
glass at room temperature begins when subjected to pressure
greater than about 2 GPa,21 i.e., shear stresses accelerate the
irreversible densification process. This irreversible densification
can be explained by a decrease in the average Si-O-Si bond
angle through the formation of smaller ring structures that are
meta-stable upon release of pressure.22 Upon further compres-
sion to above 20 GPa, the SiO4 tetrahedra in vitreous silica
become destabilized, and there is a gradual increase in Si
coordination from 4 to 6.16,18 Quartz undergoes a similar increase
in coordination number under high pressure and high temper-
ature,23 although amorphization15 is usually observed at room
temperature.
The lack of irreversible densification2 of the silica framework
up to 12 GPa and the excellent mechanical properties in the
mesoporous silica under high pressure pose interesting ques-
tions: how does the silica atomic structure (e.g., the intertet-
rahedral bond angle distribution) in the porous silica behave
under high pressure? And how are the structural rearrangements
in the material on the two different length scales (the atomic
scale and the nanometer scale) related to each other? We hope
that the answer to the first question concerning the changes in
microstructure under high pressure will lead us to the key to
the second questionsthe relation between microstructure and
observed mechanical properties of this material.
2. Experimental Section
The details of the silica/surfactant composite synthesis and
the subsequent surfactant removal are described in ref 2. Briefly,
hexadecyl-trimethylammonium bromide was used to synthesize
the surfactant/silica composite using tetraethyl orthosilicate
(TEOS) as the silica source under basic conditions. The product
was hydrothermally treated to optimize the mesoscale order and
polymerization in the silica framework. The surfactant template
was subsequently removed by calcination in oxygen at 500 °C.
The resulting sample had a porosity of about 70 volume %.
The sintered sol-gel sample, in contrast, was prepared under
acidic conditions. Tetramethyl orthosilicate (TMOS), water and
methanol were mixed together and homogenized in a mole ratio
of 1:4:2; the pH was kept at 1.5. The sol was then sealed, aged
at room temperature until a gel formed, and then further treated
at 60 °C and 90 °C in air for 1 day each. The sintering process
was carried out by heating the sample in air at 1000 °C for
more than 30 h, followed by slow cooling to room temperature.
For the high-pressure experiments, finely ground powder
samples were loaded into a Merrill-Bassett type diamond anvil
cell (DAC). Argon was used as the pressure medium, which is
known for its excellent hydrostatic properties.37 For these
experiments, changes in X-ray contrast indicate that the liquid
Ar fills the channels of the mesoporous sample during cryogenic
loading. After compression the pores remain filled with soft
solid Ar, which serves as a compressible phase, much like the
surfactant in uncalcined silica/surfactant composites. In some
experimental runs, N2 was also employed as a pressure medium
To answer these questions we use vibrational spectroscopy
tools, specifically in-situ high-pressure micro-FTIR absorption
spectroscopy. IR and Raman spectroscopy have been used
widely to elucidate atomic structural properties of AX2 type
amorphous oxide at ambient and elevated pressures. The general
features in the IR absorption bands below 2000 cm-1 at ambient
pressure will be briefly summarized below. There are three main
features: a high-frequency band between 1000 and 1300 cm-1
,
an intermediate-frequency band centered around 800 cm-1, and
a low-frequency band at ∼ 460 cm-1
.

Elasticity in Porous Silica under High Pressure
J. Phys. Chem. B, Vol. 106, No. 22, 2002 5615
Figure 1. X-ray diffraction patterns of mesoporous silica at ambient
pressure before compression and after decompression from 7.7 GPa.
Good recovery of the nanoscale order is observed.
with very similar results. This indicates that the conclusions
presented below are general to the mesoporous silica samples
and not dependent on the details of the high-pressure experi-
mental configuration. The pressure in the high-pressure cell was
determined using the conventional ruby fluorescence tech-
nique.38 X-ray diffraction spectra from the samples under high
pressure were either taken at the Stanford Synchrotron Radiation
Laboratory or using a Rigaku rotating anode X-ray generator;
both were recorded with a Roper Scientific X-ray CCD camera.
A Bruker Equinox 55 with an IR Scope I was used to collect
the infrared spectra of the samples in a high-pressure cell
equipped with type II diamonds with 500 µm culets. The
resolution of the spectra was set at 4 cm-1. The 29Si MAS NMR
data were obtained using a Bruker Avance300 solid-state NMR
spectrometer at a spinning rate of 4000 Hz. The length of the
π/2 pulse was 6 µs, and the recycle delay was 240 s.
Peak widths and positions were determined by fitting both
low angle XRD and IR absorption with a series of Gaussian
functions with appropriate baselines. The statistical error in all
cases can be assumed to be smaller than the size of the actual
data point. Systematic errors in the fits, however, are somewhat
larger and can be approximated by the overall variations in the
data across pressures.
Figure 2. In-situ high-pressure X-ray diffraction patterns of mesopo-
rous silica and changes in the q10 peak position with pressure. (a) X-ray
diffraction patterns from mesoporous silica under pressure. (b) Variation
in q10 peak position from the diffraction patterns in part (a) as a function
of pressure. Here, b indicates data taken upon compression, while 0
indicates data collected during decompression. Linear compressibility
is observed up to about 4 GPa.
sample that is lost during the cryogenic loading of the Ar
pressure medium. The relationship between silica framework
bonding, sample hydration, and the reversibility of nanometer
scale distortions is discussed in detail in ref 2.
3. Results
Despite good recovery of low angle X-ray diffraction peak
intensity and position upon release of pressure, significant
changes in both peak intensity and position are observed as
pressure is applied. The change in d10-spacing under pressure
is presented in Figure 2. This sample is prepared in a manner
similar to the sample used for the experiment in Figure 1 but
has a slightly smaller d10-spacing. Both samples have similar
properties under high pressures. As shown in Figure 2 (top), at
1 GPa the X-ray diffraction pattern still exhibits a clear higher
order peak. Under a pressure of 8.2 GPa, the diffraction intensity
is very low, which indicates a significant decrease in the
periodicity of the sample. Since the pores in the sample are
already filled with solid Ar during the cryogenic Ar loading
step,37 the loss of diffraction intensity at 8.2 GPa must be due
to the distortion of the pore structure and a loss of coherence
on the nanometer length scale, not to a decrease in electron
density contrast caused by infilling the pores with Ar.
3.1. Ambient and High-Pressure X-ray Diffraction Pat-
terns. The mesoporous silica samples show intense X-ray
diffractions at ambient pressure. A typical X-ray diffraction
pattern of the ordered mesoporous sample at ambient pressure
in a diamond anvil cell (without pressure medium and before
compression) is shown in Figure 1 (solid curve). The intense
(10) diffraction peak and the existence of the two higher order
peaks, (11) and (20) indicate the p6mm periodicity of the pore
structure. For this sample the d spacing of the (10) lattice plane
is about 52 Å. Also shown in Figure 1 is the X-ray diffraction
pattern of the same sample after being compressed up to 7.7
GPa under hydrostatic conditions and released to ambient
pressure (short dashed curve). The recovery of the (10) peak
intensity after decompression is at least 72%. The peak position
and peak width also retrace the ambient pressure pattern very
well. This means the pore structure in the sample has been well
preserved after compression, without irreversible collapse under
elevated pressure. We note that a recovered intensity lower than
100% may be due to some irreversible inelastic deformation of
the sample. It could, however, also result artifactually from
As shown in Figure 2 (bottom), the change of the d10-spacing
upon compression of the sample continues fairly linearly up to
about 4 GPa; beyond this point, little additional change is
observed. At the highest pressures, the d10-spacing seems to

5616 J. Phys. Chem. B, Vol. 106, No. 22, 2002
Wu et al.
increase slightly. As discussed in ref 2, we ascribe this behavior
to a loss of periodicity on the nanometer scale. The diminished
and broadened diffraction peak at high pressures (6 GPa and
up) may be assigned to a combination of diffuse small angle
scattering from the pore structure of the material, and coherent
Bragg scattering like that observed at ambient pressure. As the
pressure is released, there is some hysteresis in the change of
the d10-spacing, and after complete decompression the d10-
spacing is slightly smaller than that in the original starting
material. It should be pointed out that the peak shape and the
intensity of the diffraction peaks show good recovery, i.e., the
decompressed sample still shows excellent p6mm periodicity
and retains the ordered pore structure. The reversibility in the
d spacing suggests that little or no permanent densification in
the amorphous silica framework takes place in the mesoporous
silica samples under elevated pressures. Similar effects have
been observed to pressures as high as 12 GPa.2
On the basis of the changes in the X-ray diffraction presented
above we generate the following schematic pictures of what
could be happening in these ordered porous silicas at elevated
pressure. As a first step in the compression process at pressures
below 4 GPa, the compression occurs through the compaction
of the amorphous silica walls. The reduction in diffraction
intensity at moderate pressures indicates some distortion of the
nanometer scale pore structure at the same time. The combined
effect of compaction of the silica framework and distortion leads
to smaller d spacings and weaker diffraction intensity. At higher
pressures, distortion in pore structure causes accelerated loss
in diffraction intensity and much broader diffraction peaks. It
is known that further atomic scale compaction in bulk vitreous
silica starts to introduce irreversible densification. However, the
absence of irreversible densification up to 12 GPa in our
experiments suggests that compaction of the ordered porous
silica framework on the atomic scale does not follow the same
route to densification as bulk silica at high pressures. Our
experimental results in the next few sections will demonstrate
the plausibility of the proposed mechanism and its microstruc-
tural origins.
Figure 3. IR absorption spectra of silica samples under pressure. Top,
Sintered sol-gel silica; bottom, mesoporous silica. For both samples
a low-pressure spectrum, a high-pressure spectrum (∼8 GPa), and a
recovered ambient pressure spectrum are shown. Exact pressures are
indicated on the figure.
3.2. Ambient and High-Pressure FTIR Absorption Spec-
tra. Infrared absorption spectra between 700 and 1400 cm-1
for both sintered sol-gel silica and MCM-41 silica under
different pressures are presented in Figure 3. The usually strong
IR band near 460 cm-1 is not detectable due to limitations in
the mid-IR detector used for the experiment. The hydrogen-
bonded water band at around 3400 cm-1 (not shown) in the
mesoporous silica is also distinctive, while in the sintered sol-
gel silica it is almost nonexistent.12
The ambient pressure infrared spectrum of the sintered sol-
gel silica in Figure 3 (top) is composed mainly of two bands
around 800 and 1100 cm-1. As described in the Introduction,
the band at 800 cm-1 is labeled as the symmetric stretch (SS)
band, while the one at 1100 cm-1 is labeled as the asymmetric
stretch (AS) band. Under pressure there is a continuous linear
shift to higher frequency in the SS band from 803 to 834 cm-1
(diamonds, Figure 4) with a pressure derivative of 4.6 cm-1
GPa-1. The peak width increases with pressure as well. The
AS band broadens significantly under pressure but does not shift
as much as the SS band (Figure 5a). As a result, the SS and AS
bands approach each other as pressure increases. According to
the central force model proposed by Galeener,25 this indicates
that the inter-tetrahedral Si-O-Si bond angle is moving toward
smaller values.
Figure 4. Peak position of the symmetric stretching (SS) IR absorption
band for both mesoporous silica and dense sintered sol-gel silica
samples under pressure. Here ] ) sintered sol-gel silica under
compression, O ) mesoporous silica under compression, and b )
mesoporous silica upon decompression. Similar shifts are observed for
both materials.
component peak at lower frequency is usually ascribed to the
TO mode. It can be seen that the peak position of the TO mode
changes very little with pressure. Both theoretical39 and
experimental22,40 results of Raman spectra for vitreous SiO2
under pressure indicate that the Raman peaks in this frequency
range shift to slightly lower frequency under pressure. Infrared
absorption experiments on SiO2 glass under pressure also show
that the position of this band is almost invariant to pressures
near 10 GPa,17 as observed in our experiment. On the other
The pressure dependence of the component peaks of the AS
band of the sintered silica is relatively flat (Figure 5a). The

Elasticity in Porous Silica under High Pressure
J. Phys. Chem. B, Vol. 106, No. 22, 2002 5617
structure becomes more defective after the application of a
compressive force. As a result the structural changes in the
sintered silica under even relatively modest pressure are
irreversible.
Compared to the sintered sol-gel silica the changes in the
infrared absorption spectra of the ordered mesoporous silica are
more monotonic. As pressure increases, all infrared absorption
bands in our observation range shift smoothly to higher
frequency up to 8.0 GPa (Figure 3, bottom). The SS band
behaves similarly to that observed in sintered sol-gel silica,
increasing from 802 to 840 cm-1 with the same pressure
derivative as the bulk material (circles, Figure 4).
The mesoporous silica has a much more pronounced shoulder
than the sintered silica. This shoulder, which is located near
1200 cm-1 (LO mode) on the high frequency side of the AS
band, is due to the extremely high surface area of the sample.42
Because electromagnetic waves are transverse, IR radiation
normal to a surface can be absorbed by the TO phonons but
not by the LO phonons in an infinite (thick) solid. By contrast,
the p polarized component of radiation obliquely incident on a
surface will have electric field components both parallel and
perpendicular to the surface, thus interacting with both TO and
LO modes, respectively. As a result, the existence of large
amounts of randomly oriented internal pore surface in meso-
porous silica makes it possible to have a significant amount of
IR radiation incident at an oblique angle to the surface, thus
allowing for strong LO mode absorption. For example, it has
been found that the ratio of the LO mode to TO mode absorption
in hybrid silica-titania sol-gel films clearly decreases as the
porosity in the film decreases with heat treatment.43
At the same time the high surface area in mesoporous silica
leads to a relatively large amount of nonbridging oxygen atoms
in the form of unsaturated Si-OH groups on the surface.
According to 29Si MAS NMR most of the silicon oxide species
in the sample exist in the form of fully polymerized tetrahedral
clusters (Q4 species) or with one unsubstituted Si-O bond (Q3
species). The Q3 species consists of both surface silanol groups
and NBOs within the silica framework. The unsaturated Si-O
bonds in the Q3 species show up as a small IR absorption peak
at 940-950 cm-1 in bulk samples. In the diamond anvil cell
this peak is overlapped by the strong AS band and not resolved,
although a corresponding peak around this frequency is requisite
in the fitting of the AS band under pressure.
Figure 5. Shift in the component peak positions for the asymmetric
stretching (AS) IR absorption band of both mesoporous silica and dense
sintered sol-gel silica samples under pressure. (a) Sintered sol-gel
silica; (b) mesoporous silica. Empty symbols indicate compression while
filled symbols indicate data collected upon decompression. Unlike the
symmetric stretch, different behavior is observed for the dense and
mesoporous samples.
hand, Velde and Couty41 have utilized infrared absorption on
pure silica glass pressurized up to 2.9 GPa, and reported positive
shifts in the positions of the 460, 800, 1000 cm-1 bands with
pressure. The other major component peak of the AS band at
around 1200 cm-1 is associated with the LO mode. Under
pressure the peak position of the LO mode increases slightly
from the ambient position and eventually reaches a stable value
at moderate pressures.
Unlike much of the bulk vitreous silica studied in the
literature,22,41 changes in IR absorption of sintered silica under
pressure are not completely reversible after decompression even
in the pressure range below 8 GPa (Figure 3). For the sintered
sol-gel silica sample, upon release of pressure from 7.4 GPa,
the maximum of the SS peak seems to shift to slightly lower
frequency and becomes weaker compared to the original
spectrum at ambient pressure. The higher frequency edge
(∼1250 cm-1) of the AS band, by contrast, moves back to near
its ambient position. It also appears that there is some new
intensity around 940 cm-1, compared to that observed in the
sample before compression. IR absorption peaks in amorphous
silica in this frequency range are assigned to Si-O bond
stretches involving nonbridging oxygen (NBO). These experi-
mental observations suggest that the sintered sol-gel silica is
meta-stable under high pressure, possibly due to the existence
of ionic contaminants or NBOs and indicate that the atomic
To fit the AS band for the mesoporous silica well, three
component peaks have to be used (Figure 5b). At ambient
pressure, as in sintered silica, the lower frequency peak around
1070 cm-1 is ascribed to the TO mode. The LO mode consists
of the two higher frequency components. The peak around 1200
cm-1 is the LO mode as observed in the sintered silica sample.
The highest frequency peak around 1242 cm-1 is completely
absent in the sintered silica and may be due to an AS LO type
mode with significant surface (Q3) character. The pressure
derivative for the TO mode is 3.3 cm-1 GPa-1. For the LO
mode at 1200 cm-1 it is 1.6 cm-1 GPa-1, and 3.2 cm-1 GPa-1
for the mode at 1242 cm-1. These shifts in the AS band under
pressure contrast with the relatively invariant peak positions in
sintered sol-gel silica (Figure 5a). The broadening in the overall
AS band under pressure is also much smaller than that observed
in the sintered sol-gel silica. This suggests that in mesoporous
silica there are smaller changes in the 4-fold silicon environ-
ments (e.g., distorted tetrahedral) at high pressure than in the
sintered sol-gel silica. Upon decompression, all of the observed
peaks (SS and AS) return to the original peak positions observed
before compression. This correlates directly with the excellent

5618 J. Phys. Chem. B, Vol. 106, No. 22, 2002
Wu et al.
reversibility of p6mm periodicity on the nanometer scale
observed in the X-ray diffraction measurements.
with a single R/â ratio using eq 1.52 This demonstrates the
validity of the noncentral force model calculations in eq 1. Also
the fact that a single constant R/â ratio describes SiO2 with many
different bridging angles under ambient condition suggests it
should be reasonable to assume that this ratio is fairly invariant
under pressure (<8 GPa) as well. This is supported by the fact
that the major modification of the silica structure under low
pressure is the reduction in the bridging angle with little
accompanying change in bond lengths. We note that the absolute
values of the force constants will increase at elevated pressures
as a result of increased atomic interactions.
To calculate the mean bridging Si-O-Si bond angle in silica,
an additional relation between IR absorption frequency and
atomic parameters is required. The frequency of the TO mode
of the SS band, ωSTSO (∼800 cm-1), is given by an approximate
relation (eq 2) from ref 33.
3.3. 29Si MAS NMR and Inter-tetrahedral Bond Angle
Distribution under Ambient Conditions. Following the ex-
perimental technique and theoretical analysis detailed in ref 36,
we obtain the inter-tetrahedral bond angle distribution for the
four coordinated SiO2 species in both sintered sol-gel silica
and mesoporous silica. It is found that in the sintered silica the
most probable bond angle is 142° with a distribution width at
half-maximum around 24°. In the mesoporous material, the
angle distribution is deconvoluted from the component of the
NMR signal due to the unsaturated Q3 species. The angle
distribution of the Q4 species peaks at 141° with a distribution
width close to 20°. It should be pointed out that the NMR
analysis only applies to the fully polymerized Q4 SiO2 speciess
meaningful information about the large fraction of surface silica
species with one or more unsaturated Si-O bonds is not
obtainable by the above analysis. Because Q3 species must be
excluded, the calculations described above probably underes-
timate the real width of the distribution of Si-O-Si bond angles
in mesoporous silica. The bond angle and its distribution will
be used as the input parameters and comparison for the IR
analysis in the next section.
1/2
4
3MSi
SS
TO
ω
≈
(R + 2â)
(2)
[
]
Here, MSi is the mass of a silicon atom, and R and â are de-
fined as in eq 1. The atomic motion of this mode involves
mostly motion of silicon atoms,30,31 and so the lack of a specific
Si-O-Si bond angle dependence may be reasonable. We can
use eq 2 and the peak positions from the SS band (Figure 4) to
calculate the force constants assuming a fixed force constant
ratio as a function of pressure. The validity of the approximate
relation in eq 2 and the assumption of a fixed ratio of force
constants will be discussed in more detail later.
4. Discussion
4.1. Changes in Si-O-Si Bond Angle Distribution for
Silicas under Pressure. There is a considerable amount of
theoretical research aimed at relating the experimentally ob-
served vibrational spectra to the microscopic properties of
vitreous silica.44-46 Analytical expressions for the vibrational
spectra of silica have been proposed on the basis of a variety
of force field models and other calculation methods.24,25,33,47
Generally these expressions relate the vibrational frequency to
various force constants and the inter-tetrahedral bond angle in
bulk silica. The calculations by Lehmann et al.33 are particularly
interesting. In their calculations, the Born potential48 is used to
model the short-range interactions in SiO2. Both a central force
constant for Si-O stretching (R) and a noncentral force constant
for perpendicular displacement of the O atom in the Si-O-Si
bridge (â) are used. In addition to the short-range potential, they
also introduce an effective electric field acting on the ions in
By using the most probable Si-O-Si bridging angle obtained
from NMR data, the frequency of the TO mode of the AS band
from ambient pressure IR absorption spectra, and eqs 1 and 2,
the force constant ratio can be calculated. A value of 4.98 is
found for both mesoporous silica and the sintered sol-gel silica.
Using this value (4.98), combined again with eq 2, the central
force constant, R, is found to increase from 572 N m-1 at
ambient pressure to 617 N m-1 at 7.4 GPa in sintered silica.
For mesoporous silica the force constant changes from 570 N
m-1 at ambient pressure to 626 N m-1 at 8.0 GPa.
Once the force constants under different pressures are known,
eq 1 and the frequency of the AS TO mode can be used to
calculate the inter-tetrahedral Si-O-Si bond angle. The results
for both sintered and mesoporous silicas are shown in Figure
6a, circles and squares, respectively. In the sintered sol-gel
silica (empty circles) under pressure there is a continuous
decrease in the bridging angle from 142° at ambient pressure
to around 114° at 7.4 GPa, a reduction of 28°. In crystalline
silica polymorph such as quartz the reduction in bond angle at
8 GPa is about 13° from an ambient pressure value of
143°.14,15,17 Compared to the experimental results in the quartz,
the decrease in the Si-O-Si bond angle in the sintered silica
is quite high, which may be due to different sample conditions,
but more likely, is due to the approximations made in our
calculations.
There have also been many experiments utilizing a wide
range of experimental techniques to probe the change in the
Si-O-Si bridging angle in densified amorphous silica. The
reduction in the average Si-O-Si angle after a densification
between 16% and 25% is found to be around 5°.53-55 However,
these measurements on the densified silica were taken after the
pressure was released, a situation unlike our current experiment.
Theoretical studies of in-situ densification show larger changes
with a decrease from 147.4° for normal density to 133.7° for a
20% densified sample under pressure.39 Thus, both theoretical
and experimental data suggest that the model we use predicts
silica in order to calculate the LO-TO splittings. The analytical
AS
relation for the TO mode ω (∼ 1100 cm-1) of the asym-
TO
metric stretching (AS) band as a function of atomic parameters
is listed below in eq 1:
1/2
2
MO
θ
2
θ
2
AS
TO
ω
)
R sin2 + â cos2
(1)
(
)
[
]
Here, R and â are the central and noncentral force constants, θ
is the Si-O-Si bridging bond angle between adjacent SiO4
tetrahedra, and MO is the mass of the oxygen atoms. The use of
both central and noncentral force models in the literature is
abundant and fruitful.49-51
Usually in the analysis of experimental infrared absorption
spectra, force constants R and â are chosen to reproduce the
measured TO frequencies. For example values of R ) 600 N
m-1 and â ) 100 N m-1 have been used to describe the entire
IR spectrum of relaxed amorphous SiO2.33 In these analyses
the ratio between the force constants R and â is often considered
to be constant. It is found that the relation between measured
IR asymmetric stretching TO mode frequency and the bridging
bond angle, which ranges from ∼120° to ∼180° in various
crystalline and amorphous silica polymorphs, can be described

Elasticity in Porous Silica under High Pressure
J. Phys. Chem. B, Vol. 106, No. 22, 2002 5619
in magnitude to what happens in bulk amorphous silica in a
comparable pressure range, and so this might be described as
the normal elastic range. As pressure is increased above 4 GPa,
the change in d spacing slows and even turns slightly to higher
values, as discussed in Section 3.1. At the same time the
reduction in the bridging bond angle stops, suggesting that
deformation of the hexagonally periodic pore structure begins
to take the central role. This also explains the significant
degradation in the diffraction patterns at higher pressures. The
invariance of the inter-tetrahedral bond angle in mesoporous
silica above 4 GPa appears also to be related to the atomic scale
memory effect, which leads to surprisingly good reversibility
upon decompression. This will be discussed further later.
It should be noted that there are two significant approxima-
tions in the above analysis: constant R/â ratio and the use of
the approximate relation in eq 2. An alternative set of ap-
proximations can be made if the behavior of the low-frequency
IR rocking mode at high pressure is known and eq 3 is applied.
1/2
2
MO
OR
TO
ω
)
â
(3)
(
)
Here MO is the mass of an oxygen atom. TO and OR refer to
the TO mode of the rocking mode that involves solely the
motion of oxygen atoms.31 It is known from the literature that
the frequency of the rocking mode (ωOTOR) is relatively constant
at elevated pressures.17 Since â can be calculated directly from
OR
TO
ω
using eq 3, this result suggests that a reasonable alterna-
tive approximation is to assume that the force constant â is
invariant as a function of pressure. By keeping â constant and
combining eqs 1 and 2, the variation in bridging angles at high
pressure can again be calculated. The results are shown in Figure
6b. Although different in absolute values from the data
calculated using a fixed R/â ratio, the qualitative trend in
bridging bond angle variation is exactly the same as in Figure
6a with a decrease in slope near 4 GPa. This suggests that
despite quantitative difference, the qualitative results presented
here are robust across calculations.
We note that for both models, the bond angle decrease is
smaller for the mesoporous silica than for the sintered sol-gel
silica, even below 4 GPa. This may correlate with the higher
bulk modulus measure for the nanoscale material in this low-
pressure regime (47 ( 6 GPa) compared to the bulk value of
∼32 GPa obtained over the same pressure range.2,7,56 This higher
compressive modulus may be the direct result of reduced atomic
scale distortions.
Figure 6. Inter-tetrahedral Si-O-Si bond angle calculated for both
mesoporous silica and dense sintered silica samples under pressure
calculated from the data shown in Figures 4 and 5. (a) Bond angle
changes calculated assuming an invariant force constant ratio; (b) Bond
angle changes calculated assuming an invariant rocking mode frequency
as a function of pressure. See text for details. Qualitatively similar
results are obtained with either assumption. For both graphs, O )
sintered sol-gel silica under compression, 0 ) mesoporous silica under
compression, and 9 ) mesoporous silica released from 8.0 GPa. In
both cases, marked differences are observed between the dense and
mesoporous silica samples.
an exaggerated angle change and that therefore we should look
for qualitative rather than quantitative trends.
Besides the average bridging bond angle, the width of the
distribution of the bond angles is a good indication of the
intermediate range order in silica. The bond angle distribution
width is directly related to the TO mode of the AS band by
differentiation of eq 1.
In the mesoporous silica, the change in the inter-tetrahedral
bond angle (Figure 6a, squares) follows a different trend from
that seen in the sintered sol-gel glass. The reduction in the
bond angle occurs at a slower rate up to 4 GPa, decreasing from
141° to about 126°. After that, the change in the bridging angle
flattens, instead of decreasing continuously as in sintered silica.
Near 8 GPa, the Si-O-Si bond angle is only about 123°. This
turning point at 4 GPa agrees well with the turning point for
the change in periodic repeat distance (q10) in the mesoporous
silica (Figure 2b), as determined by X-ray diffraction.
2ωATOSMO
AS
TO
∆θ )
∆ω
(4)
(R - â) sin θ
AS
TO
Here, ∆ω
is the peak width at half-maximum of the
On the basis of the calculated change in Si-O-Si bond
angles, it appears that the main feature of the micro-structural
evolution below 4 GPa is the gradual reduction in the inter-
tetrahedral bond angles and rearrangement of tetrahedral units
to produce a denser silica framework. At the same time these
atomic scale rearrangements lead to a gradual decrease in the
quality of the nanoscale periodicity, i.e., distortion in the pore
structure. The rearrangements in the silica framework are similar
measured IR absorption band. From an analysis of IR absorption
spectra for the silicas under ambient conditions using KBr
pellets, the width of the bond angle distribution in sintered sol-
gel silica is 50° while that in mesoporous silica is 32°. These
calculated distribution widths are wider than those obtained by
29Si MAS NMR. This may be due to the approximations made
in the above calculations. Because there is some broadening of
the IR absorption spectra obtained on samples contained in the

5620 J. Phys. Chem. B, Vol. 106, No. 22, 2002
Wu et al.
mesoporous silica under hydrostatic compression. The compac-
tion of vitreous silica in the elastic region happens by the
cooperative rotation of the SiO4 tetrahedra.18 At high pressure
the corner-linked SiO4 tetrahedra are forced to rotate toward
each other, resulting in smaller bridging angles. In bulk vitreous
silica, this leads to high-density/high-energy structures, such as
three- and four-membered rings of tetrahedral SiO4 in samples
above 8 GPa.22,31,57,58 As pointed out in recent molecular
dynamics simulations,59,60 there are localized mechanical in-
stabilities in silica glass. As pressure increases, the barriers
between the localized energy minima disappear and the silica
structure transforms to a higher density phase. Upon release of
pressure, these transformations are not reversible, and so dense
meta-stable silica is recovered.59-61
However, in the silica framework of mesoporous silica the
formation of dense silica may be limited, perhaps by the finite
wall thickness (<10 Å). For example, structures with higher
density could be unable to form within the silica framework
without disrupting the continuous random network of SiO4
tetrahedra in the silica framework, which would be a very
energy-costly route. As a result, at higher pressures (>4 GPa),
nanometer scale distortion or buckling of the hexagonal periodic
pore structures in mesoporous silica further accommodates the
compression applied on the material. Even if formation of high-
density silica is not a higher energy process in mesoporous silica,
nanometer scale distortions might still become energetically
more favorable, compared to atomic scale changes, at pressures
above 4 GPa. The data presented in Figure 6 is strong evidence
for this type of mechanismsif densification of the silica
framework continued at pressures above 4 GPa, a continued
decrease in Si-O-Si bond angles would be observed.
When the pressure is released, the rotated SiO4 tetrahedra in
the silica framework can decompress and restore the ambient
inter-tetrahedral bond angle distribution. This can occur because
even at high pressure, atomically, the silica never samples meta-
stable dense configurations59-61 and mesoscopically, the pore
structure is mostly intact. This is shown in Figures 6 and 7 (filled
square) by the complete restoration, within experimental error,
of the bond angle and bond angle distribution back to ambient
pressure values. It is likely that this atomic recovery process is
coupled to the recovery of the diminished nanometer-scale order.
As the lowest energy atomic scale configurations are regained,
the pore structure is restored as well, resulting in excellent
mechanical stability and reversibility. Data on surfactant
containing composites show that this effect continues up to 12
GPa,2 well beyond the point where irreversible changes are
observed in bulk silica.19,20
Figure 7. Relative distribution width for the inter-tetrahedral
Si-O-Si bond angle for both mesoporous silica and dense sintered
silica samples under pressure calculated using the data presented in
Figures 4 and 5. Top, relative peak width at half-maximum of the TO
mode for the AS band of both dense and mesoporous silicas under
high pressure; bottom, calculated relative distribution width for the inter-
tetrahedral bond angle for both samples under pressure. For both graphs,
O ) sintered sol-gel silica under compression, 0 ) mesoporous silica
under compression, and 9 ) mesoporous silica released from 8.0 GPa.
Again, a marked difference is observed between the dense and
mesoporous silica samples.
diamond anvil cell (even those at ambient pressure), the
measured distribution widths appear even greater for these
samples. To compare changes in the bond angle distribution
width under high pressure, it is thus more reasonable to look at
the relative change with respect to the distribution at ambient
pressure in the DAC.
The change in Si-O-Si bond angle distribution is shown in
Figure 7 (bottom). Also shown in Figure 7 (top) is the relative
peak width of the TO mode versus pressure. Again we see a
similar trend as in Figure 6. The reduction in the bond angle
distribution in sintered sol-gel silica is almost continuous, while
the distribution width turns to a stable value around 4 GPa in
the mesoporous silica. The decrease in the bond angle distribu-
tion in vitreous silica at high pressure has been proposed on
the basis of the narrowing of Raman bands with increasing
pressure.22 This again demonstrates that the major changes in
the microstructure of mesoporous silica below 4 GPa are similar
to those in bulk amorphous silicasa decrease in the bridging
bond angle and narrowing in its distribution. At higher pressures,
however, atomic scale changes in the silica framework become
more energetically costly and are replaced by distortion of the
nanoscale pore structure.
Beyond any nanoscale confinement effect in the silica
framework of these mesoporous materials, the hexagonal pore
structure must also be of vital importance for withstanding
compression under pressure. Sol-gel silica with porosity, pore
diameter, and silica wall thicknesses similar to our mesoporous
silica can be readily made, but this family of porous material is
characterized by weak mechanical strength under pressure and
low bulk moduli.62,63 As discussed above, for mesoporous silica
at pressures greater than 4 GPa, the densification of the silica
framework through atomic scale structural rearrangements stops
as nanoscale deformations become energetically favorable.
Compression above 4 GPa thus appears to be mediated by
distortion of the ordered pore structure. In sol-gel silica lacking
an ordered pore structure, distortion on the nanoscale is likely
to be favorable, compared to atomic scale distortions, at all
pressures and so a compressive force results in collapse of the
porous silica framework.
4.2. Nanoscale Confinement and Structural Transforma-
tions in Mesoporous Silica. The different behavior of the
microstructures in mesoporous silica and bulk amorphous silica
may shed light on the extraordinary mechanical properties of

Elasticity in Porous Silica under High Pressure
J. Phys. Chem. B, Vol. 106, No. 22, 2002 5621
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Porous silica with nanometer-scale p6mm periodicity has been
shown to have excellent mechanical stability and reversibility
under hydrostatic pressure (up to 8 GPa). High-pressure infrared
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Acknowledgment. This manuscript includes data collected
at the Stanford Synchrotron Radiation Laboratory (SSRL), which
is operated by the Department of Energy, Office of Basic Energy
Sciences. This work also made use of equipment supported by
the National Science Foundation under Grant DMR-9975975
and equipment acquired under an Air Force Office of Scientific
Research Grant (F49620-98-1-0475). This research was sup-
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