Characterization of Mesoporous Thin Films by
Specular Reflectance Porosimetry
Nuria Hidalgo,# M. Carmen López-López, # Gabriel Lozano, Mauricio E. Calvo, Hernán
Míguez*
Instituto de Ciencia de Materiales de Sevilla, Consejo Superior de Investigaciones CientíficasUniversidad de Sevilla, Avda. Américo Vespucio 49, 41092 Sevilla, Spain.
KEYWORDS: porous films, pore size distribution, specular reflectance, porosimetry
ABSTRACT
The pore size distribution of mesoporous thin films is herein investigated through a reliable and
versatile technique coined specular reflectance porosimetry. This method is based on the analysis
of the gradual shift of the optical response of a porous slab measured in quasi-normal reflection
mode that occurs as the vapor pressure of a volatile liquid varies in a close chamber. Fitting of
the spectra collected at each vapor pressure are employed to calculate the volume of solvent
contained in the interstitial sites, and thus to obtain adsorption-desorption isotherms from which
pore size distribution and internal and external specific surface areas are extracted. This
technique requires only of a microscope operating in the visible range attached to a
1
spectrophotometre. Its suitability to analyze films deposited onto arbitrary substrates, one of the
main limitations of currently employed ellipsometric porosimetry and quartz balance techniques,
is
demonstrated.
Two
standard
mesoporous
materials,
supramolecularly
templated
mesostructured films and packed nanoparticle layers, are employed to prove the concept herein
proposed.
INTRODUCTION
Nowadays there is an intense research activity in the field of mesoporous thin films made of a
wide range of materials, such as silicon,1 metal oxides,2-5 clays,6 polymers,7,8 etc., presenting
different structures, like nanowires,9 nanotubes,10 nanoparticles,11 or aerogels.12 These materials
have attracted a great deal of interest because they present an open porous network, i.e.
accessible from outside, that can be used to incorporate into the structure different guest
compounds. This feature makes them appealing for applications in fields such as sensing, 13
photovoltaics,14 or membranes.15 The typical thickness of these films is comprised between a few
nanometers and a few microns. Most commonly employed techniques used to obtain the pore
size distribution of a mesoporous thin film are quartz balance 16 and ellipsometry.17 The first one
allows extracting information about the pore network of a slab from the analysis of the changes
of the vibrational frequency of a quartz crystal slide, onto which the film is deposited, as the
weight of such film increases while being exposed to a condensable gas. On the other hand,
ellipsometry works by measuring the change of the polarization state of a linearly polarized
collimated light beam after being reflected by the film. By analyzing this reflected beam,
information about the refractive index and the thickness of the material can be obtained. By
2
following the evolution of these parameters while the film is exposed at a rising partial pressure
of a gas, a complete characterization of the porous network is achieved. Both techniques have
strict limitations regarding the substrate that can be used to support the porous film. In a quartz
balance, the film must be grown on a small area gold coated quartz substrate, whereas in
ellipsometry the substrate cannot produce an interference with the incoming light beam, which
made one-side polished silicon wafers the preferred substrates for this sort of optical analysis. In
the case of ellipsometric data, analysis presents a complexity that makes difficult its application
to multilayered systems. Also, gravimetric techniques require a high mechanical stability and are
very lengthy. Alternatively, small angle X-ray scattering (SAXS) can also be applied to measure
the pore size distribution of a film,18 being the high costs the main limitation of this approach.
For a full description of the main features of these and others useful porosimetry techniques, we
refer the reader to the comprehensive review by Maex and coworkers.19
Recently, we have shown that a relatively simple analysis of the specular reflectance of porous
multilayers, collected at a gradually varying vapor pressure of a solvent, allows us to obtain
precise adsorption-desorption isotherms and, from them, information on the rich interplay
between the sorption properties of stacked layers
20-24
Also, other authors have employed a
similar technique to characterize the sorption properties of either porous silicon or of porous
layers not compatible with the abovementioned techniques, such as anodically oxidized porous
alumina films.25 In all those cases, samples were either self-standing or deposited on different
types of transparent glasses, which would have prevented or complicated a similar analysis by
gravimetric or ellipsometric techniques.
Herein we show that the information extracted from the analysis of specular reflectance spectra
at varying solvent vapor pressures can be used to realize a complete characterization of the pore
3
size distribution (PSD) and specific surface areas of standard mesoporous thin films. Our
approach, hereby coined specular reflectance porosimetry (SRP), was developed in order to
obtain a full characterization of the pore network of films deposited on the actual substrates of
either research or technological interest, hence overcoming one of the main limitations found in
the techniques previously used in the field. SRP requires, as in the case of ellipsometric
porosimetry, plane parallel and optically homogeneous films in order to avoid off-axis
reflections caused by variations of the surface curvature or diffuse scattering, respectively. As a
proof of concept, two standard mesoporous materials, i.e., TiO2 supramolecularly templated
mesostructured films and SiO2 packed nanoparticle layers are employed.
EXPERIMENTAL SECTION
Samples preparation
Two types of porous films were used for this study. Surfactant templated TiO2 films with
highly ordered mesostructure were prepared using standard synthetic procedures based on the
formation of a self-assembled network of block copolymer. This micellar structure serves as
scaffold for TiO2 that is a product of the controlled hydrolysis and condensation of TiCl4. After
the elimination of the organic phase, an open porous well ordered structure is obtained. In this
case, films of such material were obtained by dip-coating flat borosilicate glass slides in the
formerly described solution. Also, porous SiO2 nanoparticle layers were prepared by spincoating of a suspension of commercially available silica colloids onto borosilicate glass. In this
case, disordered packings presenting a random network of interconnected pores are attained. Full
4
details on the synthetic methods and deposition protocols, as well as electron microscopy
characterization results, are provided in the Supporting Information.
Experimental set-up
The experimental SRP setup is schematized in Figure 1. The technique is based on the analysis
of the variations of the specular optical reflectance of a film supported onto a substrate when it is
exposed to different vapor concentrations in a closed chamber. The chamber possesses a flat
quartz window through which the reflectance spectra at quasi-normal incidence were measured.
A white light source and a Fourier transform visible–near infrared spectrophotometer (Bruker
IFS-66), equipped with a Si photodiode detector, attached to a microscope operating in reflection
mode was employed to carry out all the optical characterization herein presented. A 4x objective
with 0.1 numerical aperture (light cone angle ±5.7o) was used to shine the films and collect the
light reflected by them. In order to control the vapor pressure in the sample chamber, a bulb
containing isopropyl alcohol is connected to it through a needle valve. The internal pressure of
the chamber was measured with a dual capacitance manometer (MKS model PDR 2000). A
second needle valve connects a vacuum pump to the sample chamber. Samples are annealed at
120°C overnight to remove any moisture from the voids of the porous structures before carrying
out the gas adsorption-desorption process. Then, samples are introduced in the chamber and keep
under dynamic vacuum (10-2 torr) during half an hour. After that, the system is closed and
pressure into the chamber monitored to confirm that there were no leaks. The first reflectance
spectrum is obtained at the lowest pressure value achievable (P0) in the chamber. Then, the
pressure in the chamber is gradually increased by opening the needle valve that connects it with
the bulb containing the solvent until the desired pressure is reached. Once equilibrium is reached,
reflectance spectra were measured at each fixed pressure, P. Although the time to reach
5
equilibrium in the chamber depended on the sample analyzed, it did not exceed five minutes in
any case. This process was repeated sequentially at different solvent vapor pressures until
saturation pressure (PS) was reached. Desorption experiments are made following the same
protocol, a gradual decrease of the pressure being obtained by opening the valve connected to the
vacuum pump. Again, spectra are taken at slowly decreasing pressures until the initial value is
attained.
The evolution of the specular reflectance spectra, measured at normal incident when relative
pressures of isopropanol are varied from 0 to 1, are shown in Figure 2. In this case the sample is
a mesoporous film of 450 nm thickness made of 30 nm size SiO2 nanoparticles. The spectral
variations of intensity observed are characteristic of thin film interference phenomena. The
spectral separation between lobes depend on the optical thickness of the film, which is calculated
by multiplying its effective refractive index by its actual geometrical thickness. As the pressure
of solvent vapor in the chamber increases, gas molecule adsorption onto the pore walls occurs.
Eventually, capillary condensation within the pores takes place. Both phenomena lead to an
increment of the effective refractive index of the film, shifting the oscillation to higher
wavelengths, as it can be readily seen in Figure 2. All measurements were taken at room
temperature.
We used isopropanol as adsorbate to characterize the mesostructure of the samples. This low
molecular weight alcohol has been previously proven to yield excellent results for the analysis of
the vapor sorption properties of mesostructured and nanoparticle based multilayers.20,21 In
addition, accurate adsorption-desorption isotherms in porous alumina has already been observed
and discussed by Sailor and coworkers using also isopropanol as probe.25,26 In our case, when
water or toluene were used as adsorbates, some instabilities in the pressure readout were
6
detected, principally during the desorption process. In the case of water, this behavior can be
explained in terms of the irreversibility of the dissociative adsorption process on the pore walls,
whereas, in the case of toluene, hydrophobic/hydrophilic interactions may be preventing the
wettability of the internal surface of the layers.20,21 However, it should be noticed that, in the
pioneering works of Baklanov and coworkers,17 poro-ellipsometric measurements were realized
with satisfactory results using non-polar solvents by introducing them in the chamber at slower
speeds than those employed by either us or Sailor and coworkers.
RESULTS AND DISCUSSIONS
Fitting of Optical Reflectance Data
In order to calculate the effective refractive index of the film from the spectrum attained at each
pressure step, a code written in MatLab based on the transfer matrix formalism 27 was employed
to fit the experimental data and extract information on the optical constants. In this script, the
reflection and transmission of electromagnetic radiation by a thin dielectric layer located
between two semi-infinite media is considered, as shown in Figure 3a. Assuming that all the
media can be described using a homogeneous and isotropic refractive index; the layered structure
can be depicted by
𝑛(𝑥) = {𝑛2 ,
𝑛1 , 𝑥 < 0
0< 𝑥<𝑑
𝑛3 , 𝑑 < 𝑥
(1)
Since in the experiments the direction of incidence of light is quasi perpendicular to the film
surface, which is homogeneous in the yz-plane at the visible wavelength length scale, hence no
polarization effects are expected and the electric field vector E(x) can be written as:
7
𝐴𝑒 −𝑖𝑘1 𝑥 + 𝐵𝑒 𝑖𝑘1 𝑥 , 𝑥 < 0
𝐸(𝑥) = {𝐶𝑒
+ 𝐷𝑒 𝑖𝑘2 𝑥 ,
0< 𝑥<𝑑
𝐹𝑒 −𝑖𝑘3 𝑥 ,
𝑑< 𝑥
−𝑖𝑘2 𝑥
(2)
The complex amplitudes A, B, C, D and F are constants and k1, k2 and k3 are the wave vectors
ki =
2π
λ
ni
(3)
where 𝜆 is the wavelength in vacuum. The constant A is the amplitude of the incident wave and
therefore B/A and F/A represent the reflection (r) and transmission coefficient (t), respectively.
In order to obtain these amplitudes we solve the set of equations established by imposing the
continuity of the electric, E, and the magnetic field, H, across the interfaces x = 0 and x = d
using a transfer matrix formalism. In particular, r and t are retrieved from the following
expression
m11
t
1
[ ] = M [ ] = [m
0
r
21
m21
t
m22 ] ∙ [0]
(4)
where the so-called transfer matrix, M, is given by
1
{[
𝑖𝑘1𝑥
−1
1
1
]} [
−𝑖𝑘1𝑥
𝑖𝑘2𝑥
1
𝑒 𝑖𝑘2𝑥 𝑑
] {[
−𝑖𝑘2𝑥 𝑖𝑘2𝑥 𝑒 𝑖𝑘2𝑥 𝑑
𝑒 𝑖𝑘2𝑥 𝑑
]}
−𝑖𝑘2𝑥 𝑒 −𝑖𝑘2𝑥 𝑑
−1
(5)
We consider the thickness d and effective refractive index of the thin layer, n, as fitting
parameters and a linear least squares method to fit the experimental reflectance using the one
calculated as
𝑚
2
𝑅 = |𝑟|2 = |𝑚21 |
11
(6)
8
Figure 3b displays the experimental curve obtained at a specific isopropanol vapor partial
pressure (P/Ps=0.65) from a packing of nanoparticles and the corresponding fitting performed by
the method herein described.
Evolution of free volume fraction: optical adsorption-desorption isotherms
The fittings of the reflectance spectra allow us to calculate the variation of the refractive index
as the vapor pressure in the chamber increases and, therefore, the evolution of the free pore
volume fraction, as explained in what follows. When the spatial inhomogeneity of the dielectric
constant in the film is small compared to the wavelength of light, the concept of effective
refractive index is meaningful as far as far field transmission and reflection coefficients are
concerned. Thus, the effective refractive index of an inhomogeneous medium can be determined
given the properties of its constituents under certain assumptions. There exist a vast collection of
choices in the scientific literature to find the effective dielectric function. In our case, we apply
the Bruggeman equation for a three-component dielectric medium,28 which is based on an
effective medium theory.29 We consider our inhomogeneous medium as composed by inclusions
of two different constituents, namely, the material of which the pore walls are made of, with
refractive index nwall, and the adsorbed solvent present in the pores when the pressure starts
increasing, nsolvent, embedded in an otherwise homogeneous matrix of nmedium=1. The effective
refractive index of the composite material, n, can then be obtained from:
𝑓𝑤𝑎𝑙𝑙
2
𝑛𝑤𝑎𝑙𝑙
−𝑛2
2
𝑛𝑤𝑎𝑙𝑙
+2𝑛2
+ 𝑓𝑠𝑜𝑙𝑣𝑒𝑛𝑡
2
𝑛𝑠𝑜𝑙𝑣𝑒𝑛𝑡
−𝑛2
2
𝑛𝑠𝑜𝑙𝑣𝑒𝑛𝑡
+2𝑛2
+ 𝑓𝑚𝑒𝑑𝑖𝑢𝑚
2
𝑛𝑚𝑒𝑑𝑖𝑢𝑚
−𝑛2
2
𝑛𝑚𝑒𝑑𝑖𝑢𝑚
+2𝑛2
=0
(7)
9
Here fwall, fsolvent and fmediumare the volume fractions of the material composing the pore walls,
the solvent and the surrounding medium, respectively. Knowing nwall (taken as nSiO2 = 1.45 and
nTiO2 = 2.45) and nsolvent (nisopropanol = 1.37) and extracting the effective refractive index of the
film, n, from the fittings of the specular reflectance measured under vacuum (fsolvent=0) and by
means of equation (7), we can estimate fwall and thus the total pore volume (fmedium=fpore=1-fwall) of
the starting material. Then, from the effective refractive index of the film obtained at different
pressures, we can estimate the volume fraction occupied by the adsorbed, and eventually
condensed, species, fsolvent, since we can write fmedium=1-fwall-fsolvent, leaving fsolvent as the only
unknown parameter. The ratio fsolvent/fpore is the ratio between the volume occupied by the
adsorbed species, Vads, and the originally free pore volume, Vpore. The refractive index of the
interstitial sites, npore, and the quotient Vads/Vpore are plotted versus the solvent partial pressure,
P/PS, in Figure 4, for increasing (adsorption) and decreasing (desorption) pressure in the
chamber for both types of mesoporous films herein analyzed as a proof of concept. It should be
remarked that several adsorption/desorption cycles are performed in order to stabilize the
supramolecularly templated films, since modifications of the structure of those mesoporous films
caused by vapor condensation has been described before and attributed to changes in the pore
geometry and small fluctuation of the layer thickness, in particular for the case of
supramolecularly template oxides.30 For that reason, the data presented in Figure 4a were
collected after subjecting our films to at least one adsorption-desorption process. An example of
the results attained for different consecutive cycles is shown in the supporting information
section.
The values taken from the vapor adsorption cycle are drawn as black dots, while those extracted
from desorption measurements are plotted as grey ones. For both types of samples, a clear
10
hysteresis between adsorption and desorption processes can be readily identified. Adsorption
isotherms shape is characteristic of type IV isotherms31 according to IUPAC classification
whereas hysteresis profile resembles H1 shape. Such shapes are expected when the samples
present pores accessible through different channels and interconnected, as it is the case herein.32
In general, when adsorption is taking place, capillary condensation occurs from metastable vapor
states, whereas, during desorption, capillary evaporation of the liquid from the mesopores occurs
at the equilibrium transition, giving rise to hysteresis, as was demonstrated for cylindrical open
pores.33
Pore size distribution
The suitability of the proposed technique is proven by performing an analysis of the PSD, which
is based on the assumption that a layer of adsorbed molecules of the alcohol is formed at low
partial pressures and its condensation is governed by Kelvin law,31 which has the form:
ln P Ps   
2VL 1
RT rK
(8)
Where P/Ps is the ratio between the condensation pressure in a pore of rK radius and the
saturation pressure at a defined temperature T, VL and γ are the molar volume and the surface
tension of the adsorbed liquid, respectively, and R is the gas constant. This equation is
considered valid for analyzing pore radios between 1 and 20 nm. This upper value limits the
validity of Kelvin Law to P/PS< 0.95. Corrections to this model to include the effect of pore
shape and liquid-solid phase interactions have been thoroughly discussed.30 For the purpose of
this paper, we will restrict ourselves to the standard model, although modifications based on
11
more precise assumptions could be implemented later on without compromising the validity of
the technique herein discussed.
The PSD of a specific film can be obtained from the analysis of the adsorption-desorption
curves presented in Figure 4. After equation (8), at each P/PS value, the fraction of pores with the
corresponding Kelvin radius, rK, is filled by solvent condensation, So, large variations of the
volume occupied by adsorbed species at a given P/PS indicate the presence of a large fraction of
pores of the corresponding rK, So, there is a direct correlation between the fraction of pores of a
given Kelvin radius present in the film and the slope of the Vads/Vpore versus P/PS curve plotted in
Figure 4. The actual pore radius, rpore, is the result of adding rK to t, the thickness of a layer of
solvent molecules that is adsorbed on the walls of the porous network at low pressures
(P/PS<0.3). The expression chosen to calculate this parameter is based on the BET (Brunauer,
Emmet and Teller) equation:17,31
𝑃
𝑡=
𝑑0 𝐾𝐶(𝑃 )
𝑠
𝑃
𝑃
[1−𝐾𝐶(𝑃 )][1+𝐾(𝐶−1)(𝑃 )]
𝑠
𝑠
(9)
In this expression, K is a fitting parameter that varies between 0.7 and 0.76 depending on the
solvent used and its estimation is based on the assumption that the number of molecular layers at
Ps in an open porous material is finite (5 or 6 monolayers);31 C is the BET constant; and d0 is the
thickness of a monolayer of solvent molecules. In this analysis we consider that d0 is equal to the
diameter of a single molecule of the vapor used as test probe, which is estimated from the molar
volume.34
The C constant depends on the interaction between the solvent and the wall of the film and it is
extracted from the BET plot,35 which can be expressed as:
12
P
Vads (P−Ps )
=
1
Vm
+
C−1 P
Vm C PS
(10)
where Vm is the ratio between the volume of a monolayer adsorbed on the pore walls and the
total porous volume of the sample. This linear relation is valid for the ratio pressures (P/Ps) in the
range of 0.05-0.3, where no capillary condensation occurs. The BET plot of the samples under
study is also provided in the supporting information section.
The PSDs of the different films are presented in figure 5 as the fraction of pores versus
rpore=rK+t. In the case of ordered mesostructured TiO2 films (Figure 5a), the porous network is
known to be composed by a series of interconnected ellipsoidal cavities arranged in a FCC
structure, as extracted from field emission scanning electron microscopy (FESEM) and X-ray
diffractograms (see Supporting Information). The size of the voids is estimated from the
absorption branch while the interconnecting neck size is estimated from the desorption branch.36
Therefore, the average pore and neck diameter sizes for F127 templated TiO2 (Figure 5a) are 9.6
nm and 8.2 nm respectively, which is in good agreement with the data measured from the
FESEM images (see supporting information) and concords with ellipsometric measurements
reported in previous works that use F127 templated TiO2 films.30Error! Bookmark not
defined.,37,38 On the other hand, the porous geometry of the nanoparticle SiO2 layer is not
regular, thus the PSD is much broader than in the case of the supramolecularly templated TiO2
film, as it can be seen in Figure 5b. In the silica film case, isopropanol adsorption is expected to
start at the narrow meniscus formed between touching spheres while condensation takes place
within the irregularly shaped pores delimited by concave spherical surfaces. Vapor desorption is
limited by the smallest aperture, which the vapor must go through to exit the structure. The
estimated cavity and window sizes in the SiO2 nanoparticle film are 5.8 nm and 7.3 nm,
13
respectively. It should be noticed that the method herein presented allows discriminating total
from open or accessible porosity. As mentioned above, the value of total porosity is extracted
from the fitting of the optical reflectance of the emptied sample, reached after thermal and
vacuum treatments. The total open accessible porosity can be estimated from the response of the
sample when it is immersed in liquid isopropanol. Finally, the total condensable porosity is
obtained from the reflectance spectrum attained under vapor saturation conditions in the
chamber. These data are provided in Table 1. As we can see, the accessible porosity of SiO2
nanoparticle layer is higher than the analyzed porosity. This feature is caused by the presence of
larger pores in the structure where condensation is not occurring.
Specific surface area
Critical information to be extracted when porous films are analyzed is the specific surface area.
To that end, the so called t-plots from the two types of films herein characterized are displayed in
Figure 6. In these curves we represent the change of volume of solvent in the sample versus the
statistical thickness, t, as given by equation (9), calculated from the adsorption branch in the
isotherm cycle. Following a standard procedure, the total specific surface area, Stot, is estimated
from the analysis of the t-plot at low values of t, whereas the external specific surface area, Sext,
is calculated from high t regions of the curves. In this way, the actual specific surface area of the
mesoporous network is obtained as the difference between Stot and Sext. The data collected from
the different samples are given in Table 1. In the case of the supramolecularly templated TiO2
sample, the value of specific surface area is of the order of magnitude of previous determinations
by environmental ellipsometry.30Error! Bookmark not defined. On the other hand data for the
surface area of thin films made with SiO2 particles are scarce. Estimations based on SiO2 particle
14
size and porosity yields a surface area per volume unit of 120 m2/cm3. This value must be
understood as a top limit as the expected flattening of touching SiO2 particles is not considered.
CONCLUSIONS
We have shown that specular reflectance porosimetry (SRP) is a reliable and versatile technique
to obtain information on the pore size distribution of mesoporous thin films. Fitting of the quasinormal incidence reflectance spectra, collected at different gradually varying pressures of a
solvent in a chamber where the film is placed, are employed to calculate the volume of solvent
contained in the interstitial sites, and thus to obtain adsorption-desorption isotherms from which
pore size distribution and internal and external specific surface areas are extracted. The
suitability of these technique to analyze different sorts of films deposited onto arbitrary
substrates, one of the main limitations of currently employed poroellipsometry and quartz
balance techniques, is demonstrated by analyzing two standard mesoporous materials:
supramolecularly templated mesostructured films and packed nanoparticle layers deposited on
glass slides. This technique could be easily implemented by adapting a chamber like the one we
have devised for this proof of concept experiments to already existing combinations of visible
spectrophotometers attached to an optical microscope.
AUTHOR INFORMATION
Correspondence and request of materials should be addressed to hernan@icmse.csic.es
# These two students equally contributed to this work.
ACKNOWLEDGEMENTS
15
H.M. thanks the Ministry of Science and Innovation for funding under Grants MAT2011-23593
and CONSOLIDER CSD2007-00007, as well as Junta de Andalucía for Grants FQM3579 and
FQM5247.
16
Figure 1. Schematics of the Specular Reflectance Porosimetry set-up.
17
Figure 2. Reflectance spectra of a mesoporous SiO2 nanoparticle film exposed at different
pressures of isopropanol vapor in the chamber. The direction of the spectrum shift caused by the
pressure increase is indicated by an arrow.
18
Figure 3 a) Reflection of electromagnetic radiation in a thin dielectric layer. b) Simulated (red
dashed line) and experimental (black solid line) normal specular reflectance spectra of a SiO2
nanoparticle monolayer at partial pressure P/Ps = 0.65.
19
Figure 4. Adsorption (black dots) and desorption (grey dots) isotherms showing the variation
of the refractive index (upper graphs) and of volume fill fraction of solvent (lower graphs) in the
porous network for films made of a) block copolymer templated TiO2 and b) packed SiO2
nanoparticles.
20
Figure 5. Pore size distribution of the layers built with a) TiO2 templated with F127and b) 30 nm
SiO2 nanoparticles.
21
Figure 6. t-plot obtained from the analysis of the isotherm corresponding of a mesoporous
monolayer of a) F127 templated TiO2 and b) SiO2 nanoparticles. In black is represented the line
fitted used to obtain the specific area of the samples.
22
Table 1. Data obtained from SRP analysis.
Sample
name
neffective
(P0)
Porosity
(%)
Open
accessible
porosity
(%)
F127-TiO2
1.85
37.5
98
30-SiO2
1.25
44
86
Total
condensable
porosity (%)
Stot
(m /cm3)
Sext
(m /cm3)
95
100
21
61
60
28
2
2
23
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