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 Científicas-

Universidad 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 spin-coating

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 formalism27 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 )={ n1 , x<0n2 , 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

E ( x )={ A e−i k1 x+B e i k1 x , x<0C e−i k2 x+D e i k2 x ,0<x<d

F e−i k3 x , d<x (2)

The complex amplitudes A, B, C, D and F are constants and k1, k2 and k3 are the wave vectors

k i=2 πλ

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

[1r ]=M [ t0]=[m11 m21

m21 m22]∙ [ t0 ] (4)

where the so-called transfer matrix, M, is given by

{[ 1 1i k1 x −i k1 x ]}

−1

[ 1 1i k2 x −i k2 x ]{[ e i k2 x d e i k2x d

i k2 x ei k2 x d −ik 2 x e−i k2 x 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

R=|r|2=|m21

m11|2

(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:

f wallnwall

2 −n❑2

nwall2 +2 n❑

2 + f solventnsolvent

2 −n❑2

nsolvent2 +2 n❑

2 + f mediumnmedium

2 −n❑2

nmedium2 +2n❑

2 =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

hysteresis between adsorption and desorption processes can be readily identified. Adsorption

10

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 /P s )=−2 γV L

RT1

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

more precise assumptions could be implemented later on without compromising the validity of

the technique herein discussed.

11

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

t=d0 KC ( P

P s )[1−KC ( P

P s )][1+K (C−1 )( PP 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

PV ads ( P−P s )

= 1V m

+ C−1V m C

PPS

(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/P s) 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.30,37,38 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

13

the SiO2 nanoparticle film are 5.8 nm and 7.3 nm, 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.30 On the other hand data for the surface area of thin films made

with SiO2 particles are scarce. Estimations based on SiO2 particle size and porosity yields a

14

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 quasi-

normal 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

(%)

Total condensable porosity (%)

Stot

(m2/cm3)Sext

(m2/cm3)

F127-TiO2 1.85 37.5 98 95 100 21

30-SiO2 1.25 44 86 61 60 28

23

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