Characterization of Mesoporous Thin Films by ... - ACS Publications

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Characterization of Mesoporous Thin Films by Specular Reflectance Porosimetry Nuria Hidalgo,† Carmen López-López,† Gabriel Lozano, Mauricio E. Calvo, and Hernán Míguez* Instituto de Ciencia de Materiales de Sevilla, Consejo Superior de Investigaciones Científicas, Universidad de Sevilla, Avda. Américo Vespucio 49, 41092 Sevilla, Spain S Supporting Information *

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 closed chamber. The fitting of the spectra collected at each vapor pressure is employed to calculate the volume of solvent contained in the interstitial sites and thus to obtain adsorption−desorption isotherms from which the pore size distribution and internal and external specific surface areas are extracted. This technique requires only a microscope operating in the visible range attached to a 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 proposed herein.

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INTRODUCTION Nowadays, there is intense research activity in the field of mesoporous thin films made of a wide range of materials, such as silicon,1 metal oxides,2 clays,3 and polymers,4 presenting different structures, such as nanowires,5 nanotubes,6 nanoparticles,7 and aerogels.8 These materials have attracted a great deal of interest because they present an open porous network (i.e., one that is accessible from outside) that can be used to incorporate different guest compounds into the structure. The typical thickness of these films is a few nanometers to a few micrometers. The most commonly employed techniques used to obtain the pore size distribution of a mesoporous thin film are quartz balance9 and ellipsometry.10 The first one allows the extraction of information about the pore network of a slab from the analysis of the changes in the vibrational frequency of a quartz crystal slide, onto which the film is deposited, as the weight of such a film increases while being exposed to a condensable gas. Ellipsometry works by measuring the change in the polarization state of a linearly polarized collimated light beam after being reflected by the film. By analyzing this reflected beam, we can obtain information about the refractive index and the thickness of the material. By 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 © 2012 American Chemical Society

an interference with the incoming light beam, which made oneside polished silicon wafers the preferred substrates for this sort of optical analysis. In the case of ellipsometric data, the analysis presents a complexity that makes its application to multilayered systems difficult. Also, gravimetric techniques require a high mechanical stability and are very lengthy. Alternatively, grazing incidence small-angle X-ray scattering (GISAXS) can also be applied to measure the pore size distribution of a film,11,12 with the high cost being 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 co-workers.13 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.14,15 Also, other authors had employed a similar technique to characterize the sorption properties of either porous silicon or porous layers not compatible with the above-mentioned techniques, such as anodically oxidized porous alumina films.16,17 In all of those cases, samples were either self-standing or deposited on different types of transparent glasses, which would have Received: June 26, 2012 Revised: September 13, 2012 Published: September 17, 2012 13777

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used to illuminate the films and collect the light reflected by them. 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 in the porous structures before carrying out the gas adsorption−desorption process. Then, samples are introduced into the chamber and keep under dynamic vacuum (10−2 Torr) for half an hour. After that, the system is closed and pressure in the chamber monitored to confirm that there are 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 to the bulb containing the isopropanol until the desired pressure is reached. Once equilibrium is reached, reflectance spectra are measured at each fixed pressure, P. Although the time required to reach equilibrium in the chamber depended on the sample analyzed, it did not exceed 5 min in any case. This process was repeated sequentially at different solvent vapor pressures until saturation pressure (Ps) was reached. Desorption experiments are conducted following the same protocol, with a gradual decrease in 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 incidence when relative pressures of isopropanol are varied from 0 to 1, is shown in Figure 2. In this case, the sample is a

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 the complete characterization of the pore size distribution (PSD) and specific surface areas of standard mesoporous thin films. Our approach, hereby coined specular reflectance porosimetry (SRP), was developed 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 offaxis reflections caused by variations in 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.

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EXPERIMENTAL SECTION

Samples Preparation. Two types of porous films were used for this study. Surfactant-templated TiO2 films with highly ordered mesostructures were prepared using standard synthesis procedures based on the formation of a self-assembled network of a block copolymer. This micellar structure serves as a 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 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 details of the synthesis methods and deposition protocols, as well as electron microscopy characterization results, are provided in the Supporting Information. Experimental Setup. The experimental SRP setup is schematized in Figure 1. The technique is based on the analysis of the variations of

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. mesoporous film of 450 nm thickness made of 30 nm SiO2 nanoparticles. The observed spectral variations of intensity are characteristic of thin film interference phenomena. The spectral separation between lobes depends on the optical thickness of the film, which is calculated by multiplying its effective refractive index by its actual geometrical thickness. As the vapor pressure 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 in the effective refractive index of the film, shifting the intensity oscillation to higher wavelengths, as can be readily seen in Figure 2. All measurements were made at room temperature. We used isopropanol as an 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.14,15 In addition, accurate adsorption−desorption isotherms in porous alumina have already been observed and discussed by Sailor and co-workers also using isopropanol as a probe.16,18 In our

Figure 1. Scheme of the specular reflectance porosimetry setup. the specular optical reflectance of a film supported on 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 recorded. A whitelight 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 were employed to carry out all of the optical characterization herein presented. A 4× objective with a 0.1 numerical aperture (light cone angle ±5.7°) was 13778

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case, when water or toluene was used as adsorbates, some instabilities in the pressure readout were 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.14,15 However, it should be noticed that, in the pioneering work of Baklanov and co-workers,10 poro-ellipsometric measurements were realized with satisfactory results using nonpolar solvents by introducing them into the chamber at slower speeds than those employed by either us or Sailor and coworkers.

represent the reflection (r) and transmission coefficients (t), respectively. To obtain these amplitudes, we solve the set of equations established by imposing the continuity of the electric field, E, and the magnetic field, H, across interfaces x = 0 and x = d using a transfer matrix formalism. In particular, r and t are retrieved from the following expression ⎡ t ⎤ ⎡ m11 m21 ⎤ ⎡ t ⎤ ⎡1⎤ = M⎢ ⎥ = ⎢ · ⎣⎢ r ⎦⎥ ⎣ 0 ⎦ ⎣ m21 m22 ⎥⎦ ⎢⎣ 0 ⎥⎦

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

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−1 ⎫−1 ⎡ e ik 2d ⎧⎡ 1 ⎪ 1 ⎤⎫ ⎡ 1 1 ⎤⎧ e ik 2d ⎤⎪ ⎢ ⎥ ⎨⎢ ⎬ ⎥⎬ ⎢ ⎥⎨ −ik d ⎪ ik d ⎪⎢ ⎩⎣ ik1 −ik1⎦⎭ ⎣ ik 2 −ik 2 ⎦⎩ ⎣ ik 2e 2 −ik 2e 2 ⎥⎦⎭ ⎡ e ik3d 0 ⎤ ⎢ ⎥ ⎢⎣ ik 3e ik3d 0 ⎥⎦ (5)

RESULTS AND DISCUSSION Fitting of the Optical Reflectance Data. 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 19 was employed to fit the experimental data and extract information from the optical constants. In this script, the reflection and transmission of electromagnetic radiation by a thin dielectric layer located between two semi-infinite media are considered, as shown in Figure 3a. Assuming that all of the media can be described using a homogeneous, isotropic refractive index, we can depict the layered structure by ⎧ n1 , x < 0 ⎪ n(x) = ⎨ n2 , 0 < x < d ⎪ ⎩ n3 , d < x

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 from R = |r |2 =

m21 m11

2

(6)

Figure 3b displays the experimental curve obtained at a specific isopropanol vapor pressure (P/Ps = 0.65) from the packing of nanoparticles and the corresponding fitting performed by the method described herein. Evolution of the 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 the 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,20 which is based on an effective medium theory.21 We consider our inhomogeneous medium to be composed of inclusions of two different constituents, namely, the material of which the pore walls are made, 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

(1)

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.

Because in the experiments the direction of incident light is quasi-perpendicular to the film surface, which is homogeneous in the yz plane on the visible wavelength length scale, no polarization effects are expected and the electric field vector E(x) can be written as ⎧ A e−ik1x + Be ik1x , x < 0 ⎪ ⎪ E(x) = ⎨C e−ik 2x + De ik 2x , 0 < x < d ⎪ ⎪ F e−ik3x , d < x ⎩

(4)

fwall

(2)

Complex amplitudes A, B, C, D, and F are constants and k1, k2, and k3 are the wave vectors 2π ki = ni (3) λ

n wall 2 − n2 2

n wall + 2n

2

+ fsolvent

nsolvent 2 − n2 nsolvent 2 + 2n2

+ fmedium

nmedium 2 − n2 nmedium 2 + 2n2 =0

where λ is the wavelength in vacuum. The constant A is the amplitude of the incident wave; therefore, B/A and F/A

(7)

Here f wall, fsolvent, and f medium are the volume fractions of the material composing the pore walls, the solvent, and the 13779

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molecules of the alcohol is formed at low partial pressures and its condensation is governed by Kelvin's law,23 which has the form

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 eq 7, we can estimate f wall and thus the total pore volume (f medium= f pore = 1 − f wall) 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, because we can write f medium = 1 − f wall − fsolvent, leaving fsolvent as the only unknown parameter. The ratio fsolvent/ f pore is the ratio of the volume occupied by the adsorbed species, Vads, to 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

⎛P⎞ 2γVL 1 ln⎜ ⎟ = − RT rK ⎝ Ps ⎠

(8)

where P/Ps is the ratio between the condensation pressure in a pore of radius rK 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 to be valid for analyzing pore ratios of between 1 and 20 nm. This upper value limits the validity of Kelvin's 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.22 For instance, as briefly mentioned above, in the particular case of mesostructured films obtained by supramolecular templating, changes in film thickness may also occur during capillary condensation as a result of the contraction of both pores and walls. Such evolution, as well as the associated deformation of the pores, could also be analyzed by the technique proposed herein by assuming that the fitting parameter d (film thickness) in eq 5 is also a function of the vapor pressure, like the average refractive index n although with a much weaker dependence. A modified version of Kelvin equation should also be considered in that case. For the purpose of this letter, we will restrict ourselves to the standard model, although modifications based on more precise assumptions could be implemented later without compromising the validity of the technique discussed herein. The PSD of a specific film can be obtained from the analysis of the adsorption−desorption curves presented in Figure 4. After eq 8, at each P/Ps value, the fraction of pores with the corresponding Kelvin radius, rK, is filled by solvent condensation, so large variations in the volume occupied by adsorbed species at a given P/Ps indicate the presence of a large fraction of pores of the corresponding rK. Therefore, 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:10,23

Figure 4. Adsorption (black dots) and desorption (gray dots) isotherms showing the variation of the refractive index (upper graphs) and the 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.

(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 to stabilize the supramolecularly templated films because 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 in the layer thickness.22 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, and those extracted from desorption measurements are plotted as gray ones. For both types of samples, a clear hysteresis between adsorption and desorption processes can be readily identified. The adsorption isotherm shape is characteristic of type IV isotherms23 according to IUPAC classification whereas hysteresis profile resemble the H1 shape. Such shapes are expected when the samples present pores that are accessible through different channels and interconnected, as the case herein.24 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.25 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

()

d0KC t=

⎡ 1 − KC ⎣⎢

P Ps

( )⎤⎦⎥⎡⎣⎢1 + K(C − 1)( )⎤⎦⎥ P Ps

P Ps

(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 (five or six monolayers),23 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 a test probe, which is estimated from the molar volume.26 The C constant depends on the interaction between the solvent and the wall of the film, and it is extracted from the BET plot,27 which can be expressed as 13780

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Langmuir P 1 C−1P P = + Vads(P − Ps) Vm VmC Ps Vads(P − Ps) 1 C−1P = + Vm VmC Ps

Letter

nanoparticle layer is greater 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 that regarding specific surface area. To that end, the so-called t plots from the two types of films characterized herein are displayed in Figure 6. In these

(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

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. The fitted line used to obtain the specific area of the samples is shown in black.

curves, we represent the change in volume of the solvent in the sample versus the statistical thickness, t, as given by eq 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 S1. In the case of the supramolecularly templated TiO2 sample, the value of the specific surface area is on the order of magnitude of previous determinations by environmental ellipsometry.22 However, data for the surface area of thin films made with SiO2 particles are scarce. Estimations based on the SiO2 particle size and porosity yield a surface area per volume unit of 120 m2/cm3. This value must be understood as a top limit because the expected flattening of touching SiO2 particles is not considered.

Figure 5. Pore size distributions of the layers built with (a) TiO2 templated with F127 and (b) 30 nm SiO2 nanoparticles, as extracted from the adsorption (black dots) and desorption (gray dots) isotherms.

mesostructured TiO2 films (Figure 5a), the porous network is known to be composed of a series of interconnected ellipsoidal cavities arranged in an FCC structure, as extracted from field emission scanning electron microscopy (FESEM) and X-ray diffractograms (Supporting Information). The size of the voids is estimated from the absorption branch, and the interconnecting neck size is estimated from the desorption branch.28 Therefore, the average pore and neck diameter sizes for F127templated TiO2 (Figure 5a) are 9.6 and 8.2 nm, respectively, which is in good agreement with the data measured from the FESEM images (Supporting Information) and agrees with ellipsometric measurements reported in previous work that use F127-templated TiO2 films.22,29,30 However, 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 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 and condensation takes place within the irregularly shaped pores delimited by concave spherical surfaces. Vapor desorption is limited by the smallest aperture that the vapor must go through to exit the structure. The estimated cavity and window sizes in the SiO2 nanoparticle film are 5.8 and 7.3 nm, respectively. It should be noticed that the method presented herein allows the discrimination of total from open or accessible porosity. As mentioned above, the value of the total porosity is extracted from the fitting of the optical reflectance of the emptied sample, reached after thermal and vacuum treatments. The open accessible porosity can be estimated from the response of the sample when it is immersed in liquid isopropanol. Finally, the condensable porosity is obtained from the reflectance spectrum attained under vapor saturation conditions in the chamber. These data are provided in Table S1 in the Supporting Information. As we can see, the accessible porosity of the SiO2

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CONCLUSIONS We have shown that specular reflectance porosimetry (SRP) is a reliable and versatile technique for obtaining information on the pore size distribution of mesoporous thin films. Fitting of the quasi-normal incidence reflectance spectra, collected at different gradually varying vapor pressures in a chamber where the film is placed, is employed to calculate the volume of solvent contained in the interstitial sites and thus to obtain adsorption−desorption isotherms from which the pore size distribution and internal and external specific surface areas are extracted. The suitability of these technique for analyzing different sorts of films deposited onto arbitrary substrates, which is 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 such as the one we have devised for these proof of concept experiments to existing combinations of visible spectrophotometers attached to an optical microscope. 13781

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porosity and water adsorption in TiO2 thin films prepared by glancing angle deposition. Nanotechnology 2012, 23, 205701. (13) Maex, K.; Baklanov, M. R.; Shamiryan, D.; Iacopi, F.; Brongersma, S. H.; Yanovitskay, Z. S. Low dielectric constant materials for microelectronics. J. Appl. Phys. 2003, 93, 8793−8841. (14) Colodrero, S.; Ocaña, M.; González-Elipe, A. R.; Míguez, H. Response of nanoparticle-based one-dimensional photonic crystals to ambient vapor pressure. Langmuir 2008, 24, 9135. (15) Fuertes, M. C.; Colodrero, S.; Lozano, G.; González-Elipe, A. R.; Grosso, D.; Boissiere, C.; Sanchez, C.; Soler-Illia, G. J. A. A.; Miguez, H. Sorption properties of mesoporous multilayer thin films. J. Phys. Chem. C 2008, 112, 3157−3163. (16) Casanova, F.; Chiang, C. E.; Li, C. P.; Schuller, I. K. Direct Observation of cooperative effects in capillary condensation: the hysteretic origin. App. Phys. Lett. 2007, 91, 243103. (17) Casanova, F.; Chiang, C. E.; Li, C. P.; Roshchin, I. V.; Ruminski, A. M.; Sailor, M. J.; Schuller, I. K. Gas adsorption and capillary condensation in nanoporous alumina films. Nanotechnology 2008, 19, 315709. (18) Casanova, F.; Chiang, C. E.; Li, C. P.; Roshchin, I. V.; Ruminski, A. M.; Sailor, M. J.; Schuller, I. K. Effect of surface interactions on the hysteresis of capillary condensation in nanopores. Europhys. Lett. 2008, 81, 26003. (19) Lozano, G.; Colodrero, S.; Caulier, O.; Calvo, M. E.; Míguez, H. Theoretical analysis of the performance of one-dimensional photonic crystal-based dye-sensitized solar cells. J. Phys. Chem. C 2010, 114, 3681−3687. (20) van de Hulst, H. C. Light Scattering by Small Particles; Dover Publications: New York, 1981. (21) Nagy, N.; Deak, A.; Horvolgyi, Z.; Fried, M.; Agod, A.; Barsony, I. Ellipsometry of silica nanoparticulate Langmuir−Blodgett films for the verification of the validity of effective medium approximations. Langmuir 2006, 22, 8416−8423. (22) Boissiere, C.; Grosso, D.; Lepoutre, S.; Nicole, L.; Brunet Bruneau, A.; Sanchez, C. Porosity and mechanical properties of mesoporous thin films assessed by environmental ellipsometric porosimetry. Langmuir 2005, 21, 12362−12371. (23) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Harcourt Brace and Co.: Orlando, FL, 1997. (24) Condon, J. Surface Area and Porosity Determinations by Physisorption: Measurements and Theory; Elsevier: Amsterdam, 2006. (25) Cohan, L. H. Sorption hysteresis and the vapor pressure of concave surfaces. J. Am. Chem. Soc. 1938, 60, 433−435. (26) CRC Handbook of Chemistry and Physics, 88th ed. Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2008. (27) Brunauer, S.; Deming, L. S.; Deming, W. S.; Teller, E. On a theory of the van der Waals adsorption of gases. J. Am. Chem. Soc. 1940, 62, 1723. (28) Mason, G. The effect of pore space connectivity on the hysteresis of capillary condensation in adsorptiondesorption isotherms. J. Colloid lnterface Sci. 1982, 88, 36−46. (29) Bellino, M.; Tropper, I.; Duran, H.; Regazzoni, A.; Soler-Illia1, G. J. A. A. Polymerase-functionalized hierarchical mesoporous titania thin films: towards a nanoreactor platform for DNA amplification. Small 2010, 6, 1221−1225. (30) Sanchez, C.; Boissière, C.; Grosso, D.; Laberty, C.; Nicole, L. Design, synthesis, and properties of inorganic and hybrid thin films having periodically organized nanoporosity. Chem. Mater. 2008, 20, 682−737.

ASSOCIATED CONTENT

S Supporting Information *

Experimental section. SEM image of a cross section and a top view of a templated TiO2 layer and a SiO2 nanoparticle film. Evolution of the ratio between the adsorbed or condensed volume of solvent inside the sample and the total pore volume as a function of the partial pressure for three subsequent isotherm cycles. X-ray diffractogram of a TiO2 mesostructured film that has been supramolecularly templated with Pluronic F127. Data obtained from SRP analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions †

These two students contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS H.M. thanks the Ministry of Science and Innovation for funding under grants MAT2011-23593 and CONSOLIDER CSD200700007 as well as Junta de Andaluciá for grants FQM3579 and FQM5247.

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REFERENCES

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dx.doi.org/10.1021/la3025793 | Langmuir 2012, 28, 13777−13782