Bimodal mesoporous titanium dioxide anatase films templated by a block polymer and an ionic liquid: influence of the porosity on the permeability.

In the present paper, we report the synthesis of bimodal mesoporous anatase TiO2 films by the EISA (Evaporation-Induced Self-Assembly) method using sol-gel chemistry combining two porogen agents, a low molecular weight ionic template and a neutral block copolymer. The surfactant template (C16mimCl) generates non-oriented worm-like pores (8 to 10 nm) which connect the regularly packed ellipsoidal mesopores (15 to 20 nm diameter) formed by an amphiphilic block copolymer of the type poly(isobutylene)-b-poly(ethylene oxide) (PIB-PEO). The surfactant template can also significantly influence the size and packing of the ellipsoidal mesopores. The mesostructural organization and mesoporosity of the films are studied by Environmental Ellipsometry-Porosimetry (EEP), Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) and electron microscopy techniques. Electrochemical characterization is performed to study the permeability of the films to liquid solutions, using two types of probe moieties (K3Fe(III)(CN)6 and Ru(bpy)3(2+)) by the wall-jet technique. An optimum ratio of C16mimCl/PIB-PEO provides anatase films with a continuous bimodal mesopore structure, possessing a permeability up to two times higher than that of the mesoporous films templated by PIB-PEO only (with partially isolated mesopores). When C16mimCl is used in large quantities, up to 20% weight vs. PIB-PEO, large overall porous volume and surface area are obtained, but the mesostructure is increasingly disrupted, leading to a severe loss of permeability of the bimodal films. A dye-sensitized solar cell set-up is used with anatase films as the photoelectrode. The photosensitizer loading and the total energy conversion efficiency of the solar cells using the mesoporous films templated by an optimal ratio of the two porogen agents C16mimCl and PIB-PEO can be substantially increased in comparison with the solar cells using mesoporous films templated by PIB-PEO only.


Introduction
Titanium dioxide (TiO 2 ) is a cheap and abundant material presenting unique electronic and optical properties 1 for applications in photocatalysis, 2 photovoltaics, 3 energy storage, 4 and sensing. 5Nanoporous TiO 2 has been under intensive development for the last decade, 1,2,3b-d,f,4a,b,d the objective being to increase the surface area of the material, because interfacial electron transfer is usually the key phenomenon for the aforementioned applications.2][3][4] Crystallized mesoporous metal oxides possess a higher chemical stability than amorphous ones. 8Non-commercial block copolymers enable the generation of mesoporous and fully crystalline anatase lms by a simple and fast process aer annealing at 600 C. 2a,7a,b,9a Fully crystalline and homogeneous TiO 2 mesoporous lms can be obtained with the conventional PluronicsÒ block polymer, but a more complex process is required than that for block copolymers of the "KLE" type.3b,c,4b The standard heat treatment based on PluronicsÒ is stopped at 500 C, 3c but these lms are not fully crystallized.2a,9a These dip-coated mesoporous lms are of potential interest as photoelectrodes for Dye-Sensitized-Solar-Cells (DSSCs, Grätzel Cells).3c However, such lms usually lack the required thickness, so that the integral properties are not sufficiently pronounced for most of the possible applications.The production of well ordered and fully crystallized mesoporous lms with a thickness over 0.5 mm is still a challenge, 3c,f,9 requiring either multilayer coatings or a dip-coating process at very low speed, 10 while the photoelectrodes composed of sintered anatase particles are usually $12 mm thick. 11An interesting trend has emerged recently in the synthesis of these materials which is based on the replacement of sol-gel molecular precursors by preformed nanoparticles (NPs). 12he fabrication of thin lms from NPs offers several advantages: the NPs are not chemically reactive, thus the process of lm formation is easier to control than when using molecular precursors.Also, the NPs can be synthesized in a highly crystalline form under soened sintering conditions, achieving less shrinkage.Yet it appears that such lms are not necessarily superior and can be even less effective as photoelectrodes than the corresponding mesoporous TiO 2 lms issued from the classical sol-gel route.Hartmann et al. 12d found that even annealing at 550 C did not develop sufficient interparticular sintering in the case of NP-based lms.Consequently, the materials possess a high concentration of grain boundaries which impede charge transport.Szeifert et al. 12c presented a promising approach named "Brick and Mortar", which is based on mixing molecular precursors (TiCl 4 ) and preformed TiO 2 NPs, templated by a block polymer.Unfortunately, the mobility of the photo-excited electrons is still moderate with respect to their use as photoelectrodes.12e A promising general option to improve the properties of mesoporous TiO 2 lms for electrochemical applications is to increase the total surface area and the accessibility of pores by the multi-hierarchy strategy. 13Various methods have been developed in the past few years to produce multi-hierarchical porous SiO 2 lms, for instance by combining the KLE block copolymer 13f-h,j,14 with a surfactant-like ionic liquid (IL), e.g.1-hexadecyl-3-methylimidazolium chloride (C 16 mimCl).13f-h,j, 15 The nal materials exhibit a hierarchical mesopore structure (14 nm from the KLE template and 2-3 nm mesopores from the IL template), which cannot be achieved by using PluronicsÒ as the block copolymer template.13f Such multimodal nanoporous silica with a well-dened mesoporous structure can be obtained as a powder or lm.13f-j The presence of worm-like mesopores (originating from C 16 mimCl) increases the porous volume and surface area of silica.Furthermore, the worm-like pores act as nanochannels connecting the mesopores generated by the KLE template.In the present study, this methodology is applied to the generation of corresponding TiO 2 lms with bimodal mesoporosity.
The pore size, surface area and pore volume of such lms are generally considered to be the most relevant porosity parameters of thin lms, which can be measured by physisorption 13i, 16 and Ellipsometry-Porosimetry. 2,3d,17 The topology of the pores and their connection inuences mass transport of free molecules in liquid media through the pores.13i,17a,18 The regular packing of pores is assumed to facilitate propagation of free molecules through the porous network in mesoporous templated lms, in contrast to mesoporous lms with irregular shape and irregular pore packing. 19It was recently demonstrated that a bicontinuous, through-connected mesoporous structure facilitates mass transport. 20By contrast, 2D-hexagonal mesoporous lms having pores parallel with the substrate can completely block the accessibility of the sublayer to free molecules in solution. 21Control and optimization of mass transport in nanoporous lms are crucial in sensing applications, 22 and also in the case of DSSCs regarding the photosensitizer loading of the TiO 2 -photoelectrodes ion transport in the working cell.
The study of mass transport can be carried out with classical electrochemical techniques and appropriate models: conductive substrates (usually ITO or FTO) are covered by porous lms and used as the working electrode in a classical 3-electrodes electrochemical cell.A redox probe must propagate from the bulk solution through the lm in order to reach the conductive substrate and to initiate electron transfer (electrochemical current).Recently, the "walljet" technique was introduced by Massari et al. 23 to measure the molecular transport in liquid systems through metallopolymeric and porphyrin thin lms.Walcarius et al. adapted this technique for characterization of mesoporous metal-oxide lms formed by EISA 17a,24 and Electro-Assisted-Self-Assembly (EASA) 13i,25 methods.In a recent study on silica lms with bimodal porosity formed by EASA, 13i it was shown that liquid molecular transport through bimodal macroporous-mesoporous lms was higher in comparison with the corresponding monomodal mesoporous or macroporous lms.
Based on these reports and the relevance of porous TiO 2 for various electrochemical applications, the present study was dedicated to investigate the liquid molecular transport through TiO 2 lms possessing a bimodal mesoporous architecture.The synthesis of such bimodal mesoporous TiO 2 lms uses a new non-commercial block copolymer template poly(isobutylene)-bpoly(ethylene oxide), labeled (PIB-PEO) recently applied by Mascotto et al. 13j PIB-PEO polymers present, similar to KLE, 14 a strong (complete) segregation between the hydrophilic and the hydrophobic blocks (Fig. S1 †).The well dened micelles, the large molecular weight of the polymers used and their good thermal stability allow formation, by a simple method, of fully crystallized and mesoporous homogeneous TiO 2 -anatase lms 4a,13j and even mesoporous powders, 26 which cannot be achieved with the standard PluronicsÒ.Films templated by PIB-PEO polymers 13j present, similar to the lms templated by KLE, 2a,4b,7c,8a,b,12a,13g a cubic packing of the ellipsoidal mesopores, emerging from originally spherical micelles.However, such cubic packing of PIB-PEO and KLE-based micelles potentially results in low connectivity of the corresponding mesopores.In order to increase the pore connectivity Mascotto et al. synthesized bimodal mesoporous silica powder using the combination of C 16 mimCl and PIB-PEO.The pore structure obtained was found to be similar to silica templated by C 16 mimCl-KLE with regard to the pore shape and arrangement.However, the authors proved by in situ Small Angle X-ray Scattering (SAXS) and Small Angle Neutron Scatterings (SANS) combined with gas physisorption 13h,j that the accessibility of the pores is greatly improved in the case of the C 16 mimCl/PIB-PEO combination in comparison with that in the C 16 mimCl/KLE combination.In this work, we present the synthesis of bimodal mesoporous anatase lms adapted from the recipe developed by Mascotto, i.e. starting from a molecular precursor for TiO 2 .13j The present study did not utilize preformed nanoparticles, since the size of the nanoparticles is incompatible with the small size of the small micelles formed by the C 16 mimCl template, which is of the order of several nanometers only.Furthermore, the electrochemical properties of lms prepared from preformed nanoparticles are still a matter of more fundamental research.12d The anatase lms templated by PIB-PEO only are used as the reference for low permeability materials and the lms templated by C 16 mimCl/PIB-PEO to investigate the inuence of the geometric pore connectivity on the permeability of the lms.Note that highly crystalline anatase lms synthesized with the standard PluronicsÒ as the porogen agent do not appear to be a good reference material because they possess a high amount of micropores (high connectivity between the ellipsoidal mesopores) and high permeability. 24The amount of IL was varied whilst using a constant amount of the block copolymer "PIB-PEO-3000", and the inuence of the C 16 mimCl/PIB-PEO-3000 weight ratio (m IL /m PIB-PEO ) on the nal mesoporous anatase lms was investigated by extensive characterization.Wide-Angle X-ray Scattering (WAXS), Grazing Incidence Small Angle X-ray Scattering (GISAXS), Environmental Ellipsometric Porosimetry (EEP), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) were applied to characterize the mesostructure and crystallinity.
Based on such thorough structural characterization of the materials, the goal of this study was to investigate the inuence of such modied porous networks on the permeability of the lms.Access to the electrode surface was systematically estimated by wall-jet experiments for lms templated with different m IL /m PIB-PEO ratios and for different lm thicknesses, using Ru(bpy) 3 2+ and Fe(CN) 6 3À .Thereby, the present study addresses a fundamental question in the eld of nanoporous materials, namely the inuence of mesopore connectivity on transport phenomena, exemplied for suitable probe ions.
In order to assess if such bimodal mesoporosity is indeed benecial, we studied the loading of Ru-dye (N719), used for DSSCs, as a function of the porosity, addressing a possible improvement of dye graing on the pore surface.

Wide Angle X-ray Scattering (WAXS)
The WAXS patterns (Fig. 1a) of calcined mesoporous TiO 2 lms on silicon wafer indicate formation of only anatase as the crystal phase.This nding is conrmed by electrochemical investigations of lms deposited on FTO-coated glass, since cyclic voltammetry data are typical of pure anatase TiO 2 (Fig. S2 †).2b,4b,d Increasing the amount of IL decreases the average diameter of the nanocrystallites (Fig. 1b) from $28 nm (only PIB-PEO template) down to $10 nm (m IL /m PIB-PEO $ 50 to 100%).
The inuence of the template quantity on the crystal size of anatase has already been previously studied, by varying the amount of PIB-PEO template to form mesoporous TiO 2 lms.13j Two possible effects were then postulated: (i) the higher the ratio of template to TiO 2 , the thinner the pore walls (thus anatase crystals) are (Fig. 1b).(ii) Surface active molecules and carbonaceous species obtained therefrom aggravate nucleation and possibly crystallization due to coverage of the surface.
All lms were annealed simultaneously in the same oven and the lms dip-coated on a similar surface area of Si wafers at the same withdrawal rate, so that the lms contain quite similar amounts of metal oxide.Aer the lm formation by the EISA method, fast annealing up to 600 C is considered to be sufficient to obtain fully crystalline anatase mesoporous lms. 7 Fattakhova-Rohlng et al. investigated the crystallinity of the monomodal mesoporous anatase lm formed by a similar recipe and process as the ones we used.4b Even if the exact crystallinity of the matrix depends on the nature of the template used, annealing at 610 C for thin mesoporous TiO 2 lms provides a matrix crystallinity of up to 90% according to this study.
2.2.Mesostructure 2.2.1.Electron microscopy.TEM (Fig. 2) and top-view SEM (Fig. 3) lm images conrm the mesoporosity of the matrix.Moreover, SEM images conrm the EEP measurements (Fig. 4) and the GISAXS data (Fig. S4 †), suggesting that the mesostructure strongly depends on the m IL /m PIB-PEO ratio used.Under the present conditions, the IL initiates worm-like pores up to a diameter close to 8-10 nm (Fig. 4d).In addition, the presence of IL in the mother solution has an obvious inuence on the pore size and the pore packing of the mesopores generated by the PIB-PEO template (Fig. 3, 4 and 6).
2.2.2.Pore morphologies and porosity.The templating of pure C 16 mimCl is conrmed by the formation of worm-like mesopores in the anatase lms (Fig. 3 and 4).When only C 16 mimCl is used as the porogen agent, the pore size distribution (PSD) of the mesoporous lm, calculated from EEP, is centered around 9 nm diameter (Fig. 4d).The high slope value of the water adsorption-desorption isotherm for p/p 0 < 0.6 conrms the important contribution of the small mesopores in   the porous volume of the lms templated with C 16 mimCl only (Fig. 4b).
When the two porogen agents, PIB-PEO and C 16 mimCl, are used together, even for the smaller m IL /m PIB-PEO ratio, the mesoporous crystallized anatase-TiO 2 lms present a much narrower hysteresis than the lm templated with PIB-PEO only (Fig. 4a and b).It certies an increase of large mesopores connectivity.The evolution of the porous volume and the evolution of the pore size versus m IL /m PIB-PEO (Fig. 4c) show two different regimes: -At low amounts of IL, 2.5% # m IL /m PIB-PEO < 20%, the average pore size is ca.20 nm and the porosity (dened as the porous volume with respect to the total volume of a lm) is ca.24.5%, while these values are respectively 17 nm and 20% when only PIB-PEO was used as the template.Sel et al. 13f described a similar effect for a combination of C 16 mimCl/KLE, and the growth of the micelles of the amphiphilic block copolymers was attributed to the tendency of C 16 mimCl to enter the polyethylene-oxide (PEO) hydrophilic shell of the block copolymer, the templated mesopore thereby being increased and only several small wormlike pores are formed between the ellipsoidal pores (Fig. 3b and 5).
-For ratios m IL /m PIB-PEO $ 20%, the average pore size decreases continuously while the overall porous volume continuously increases, simply because of the larger amount of the template present.Above a certain threshold concentration of IL, phase-separation from the block copolymer occurs, which results in the appearance of additional worm-like mesopores (Fig. 3c and 5).The pore size distribution becomes sharper and its maximum decreases to lower values when the ratio m IL /m PIB-PEO increases (Fig. S3 †).It corresponds to a continuous increase of the contribution of the small mesopores to the mesoporous volume, as already seen in the slope of the water adsorption-desorption isotherm for m IL /m PIB-PEO ratios from 20% to 100%.Interestingly, the PIB-PEO templated mesopores themselves decrease in size with increasing amount of IL template.Films templated by m IL /m PIB-PEO ¼ 100%, compared to lms templated with PIB-PEO only, clearly present a smaller pore size than the ellipsoidal pores generated by PIB-PEO as seen in SEM images (Fig. 3b and c) and in the PSD calculated from EEP (Fig. S3 †).
It has to be noticed that the EEP method was not able, in the present work, to make any evidence of the bimodal porosity when IL and PIB-PEO templates were both used, and it is in contradiction to direct observation with the SEM images (Fig. 3).We attribute this apparent contradiction to the difference in morphology between the worm-like and ellipsoidal mesopores and the small difference in their respective diameters (see ESI † for more detailed discussion).
2.2.3.GISAXS.The GISAXS setup allowed the acquisition of 2D images (Fig. S4 †).Intensity proles of measurements given in Fig. 6 were taken from a cut along the y-axis, integrated between Q y ¼ 0.38 and 0.43 nm À1 .Scans probing the lateral mesoscopic order (y-direction) showed distinct Bragg maxima for the PIB-PEO templated lms, corresponding to the dened in-plane order of the large mesopores (Fig. 4).The difference in porosity suggested by SEM and EEP was also observed by GISAXS.
The lms produced with m IL /m PIB-PEO < 20% present GISAXS patterns similar to those of the anatase lms templated with  PIB-PEO only.The GISAXS patterns indicate a well-dened arrangement of mesopores, since even a second maximum is observed at Q ¼ 0.52 A À1 .These maxima can be interpreted either as a second order maximum or the oscillation of a form factor of uniform mesopores.Both interpretations are in compliance with a well-dened, regular mesostructure.A dspacing of ca. 25 nm can be extracted from the rst maximum, corresponding to the pore-to-pore distance of a cubic packing (Fig. 1b).13j, 27 For larger ratios m IL /m PIB-PEO > 20%, the cubic pore packing of the block polymer micelles is increasingly disturbed, since the rst GISAXS reection is signicantly wider.Also, the average pore-to-pore distance calculated from the position of the rst Bragg interference (Fig. 6b) decreases from 23.5 nm to 19.5 nm and to 18.5 nm for m IL /m PIB-PEO ¼ 20, 50 and 100%, respectively (Fig. 1b).

Film permeability
The measurements were conducted in a 50 mM aqueous hydrogen phthalate electrolytic solution (pH $ 4.2).Under such conditions crystallized metal oxide lms can be considered as stable. 8Two different electrochemical probes displaying opposite charges were used, FeCN 6 3À (anionic) and Ru(bpy) 3 2+ (cationic), in order to take the possible electrostatic interactions with the surface of the metal oxide into account.17a The cyclic voltammetry (CV) method (Fig. 7 and S5 †) was rst applied to obtain qualitative information about the inuence of the bimodal structure on the lm permeability.The mass transport quantication of the different lms was continued with the wall-jet electrochemical technique.A bare FTO electrode was used as the reference.2.3.1.Cyclic voltammetry.For the thin lms (thickness $ 110 nm) CVs measured in the presence of the two different probes show similar results: (1) The lms templated by PIB-PEO only (Fig. 7a and b) exhibited restricted response to both redox probes (lower peak current) and also hindrance to electron transfer with FeCN 6 3À (higher peak potential separation).
(2) All the lms templated by a mixture of IL and PIB-PEO exhibit quite similar response features, and the intensity of the peaks was quite close to that of bare FTO, indicating almost unhindered access to the back contact for the electron transfer.13g Electrochemical detection of the molecular probes at the modied FTO is probably restricted in the case of the thin lms templated by PIB-PEO only, because of poor interconnection between the ellipsoidal mesopores, originating from pristine ideally spherical micelles.13g,j In the case of lms using a mixture of the PIB-PEO and the IL as templates, the well connected mesoporous network (Fig. 3 and 5) facilitates the access to the FTO substrate for electrochemical detection.13g For thicker lms (thickness $ 240 nm) restrictions to electronic transfer from the redox probes to the FTO are not observed for the monomodal lms (Fig. S5 †).This could be explained by the presence of some nanometer-sized cracks previously described for such lms.13j Note that the other characterization methods (SAXS, WAXS, EEP.) cannot distinguish between thick lms ($240 nm) and thin lms ($110 nm) with respect to the crystallite size and porosity.Possible structural differences between thick lms ($240 nm) and thin lms ($110 nm) are probably induced during the dip-coating process and annealing.
2.3.2.Wall-jet electrochemical experiments.Wall-jet electrochemistry allows quantication of the molecular transport in liquid media through thin lms deposited on at electrodes.13i,17a,24,25 The differences between the electrochemical signals collected from the bare FTO and the covered FTOs are considered to depend only on the mass transport processes in the upper mesoporous anatase lms, while the electron kinetic transfer is assumed to be optimized by the operating conditions used. 28The chronoamperograms (Fig. 8a) collected under controlled ux show a clear difference between the various mesoporous anatase lms of this study.The model by Massari et al. 23 can be used to estimate the permeability of the lms from these data.The relationship between the diffusion-limited current, I lim , and the current due to mass transport through solution, I MT , and the permeation through the lm, I perm , is given by eqn (1) 1 A wall-jet electrode is dened as a planar electrode of known area (wall) and an imprinting ow of solution (jet) that provides well-dened hydrodynamics normal to the electrode.I lim of a wall-jet electrode covered by a thin lm can be expressed by eqn (2) In this equation v is the kinematic viscosity of the solution, a is the diameter of the solution jet, n is the electron stoichiometry for the electrochemical reaction of the redox probe, F is the Faraday constant, C is the concentration of the redox probe, D s is the diffusion coefficient through the solution phase, V is the ow jet, r is the radius of the wall electrode, d is the lm thickness, A is the electrode area, P is the partition coefficient, and D f is the diffusion coefficient through the thin lm.Film permeability is dened as the molecular transport of the free species dissolved in the liquid phase through the porous network of the lm.The lm permeability is expressed as PD f , i.e. the product of D f and P.
Increasing the ow allows us to disregard the rst term of the equation related to mass transport in solution (1/I MT ).The second term of the equation is then easily determined by plotting 1/I lim vs. 1/V 3/4 (Fig. 8b), the rst term of the equation being null at the intersection with the y axis.Note that two scenarios have been proposed in the literature to describe mass transport processes in thin lms, through pinholes or through homogeneous membranes. 29Here it was assumed that only the latter model applied to the mass transport through the anatase lms, as no visible defects and pinholes could be observed in the lms with the available methods of characterization.The PD f values have been estimated on thin ($110 nm, Fig. 9a) and thick lms ($240 nm, Fig. 9b).The rather homogeneous behaviour for different thicknesses validates the choice of the membrane model to describe the mass transport processes.Moreover, only small differences are observed between the variations in the permeability of the two electrochemical probes displaying opposite charges.As shown previously, FeCN 6 3À anions display very low permeability through mesoporous silica thin lms.13i,17a,25a By contrast, anatase lms here restrict the permeability to negatively charged probes to a much lesser extent.It could be ascribed to the surface complexation of the anatase by phthalate species, modifying the surface charge of the titania.The dependence of PD f on m IL /m PIB-PEO (Fig. 9) shows that an optimum m IL /m PIB-PEO ratio exists whereby the most permeable mesoporous anatase lm can be achieved for each of the two probes.Even for the lowest amount of IL (m IL /m PIB-PEO ¼ 2.5%) the thinner lms ($110 nm) show an increase in their permeability of about one order of magnitude in comparison with the lms templated by the PIB-PEO polymer only (Fig. 9a).
We attribute this nding to the concomitant increase in large mesopore connectivity (see part 2.2.2.) and the conservation of good meso-ordering (see part 2.2.3.)ensuring an efficient percolation of the porous network through the lm.However a possible inuence of signicant uncovered parts of the FTO surface cannot be ruled out.13g A slight increase in the IL concentration (5% < m IL /m PIB-PEO < 20%) enhances the pore connectivity and the accessibility of FTO correspondingly.When the amount of IL is increased further (m IL /m PIB-PEO > 5% with FeCN 6 3À and >20% with Ru(bpy) 3 2+ as redox probes) the lm permeability is reduced.In the latter case, the packing of the mesopores is signicantly disturbed (see part 2.2.3.) to compensate for the increase in porous volume and the percolation quality of the mesopores decreases signicantly.Interestingly, the permeability of the monomodal lms templated only by the IL is quite close to that of the most permeable bimodal lms, suggesting that pores formed in this way are highly connected or can be long enough to span the entire lm thickness.We note that the synthesis of crack-free anatase lms templated with IL only is limited to thin lms, thickness ( 200 nm (Fig. S6 †).
The enhancement of permeability of the thicker lms ($240 nm) templated by IL and PIB-PEO is relatively small in relation to the thicker lms templated by PIB-PEO only (Fig. 9b).As previously discussed (see part 2.3.1.),we assume that the anatase lms templated with PIB-PEO contain a signicant amount of nano-cracks.The addition of worm-like IL mesopores to favor the ellipsoidal mesopore percolation thus has a lower impact in this case than on the thinner lms (featuring no micro-cracks).An optimum m IL /m PIB-PEO ratio allows the lm permeability to be increased twice and 3.5 times for FeCN 6 3À (ratio 5%) and Ru(bpy) 3 2+ (ratio 20%), respectively (Fig. 9b).For m IL /m PIB-PEO > 20%, the permeability of the thick lms drops because of the drastic disturbance of the packing of the large ellipsoidal mesopores.Large amounts of IL reduce the permeability of the lms generated by IL and PIB-PEO templates even below the value of lms generated by PIB-PEO only as the template (Fig. 9b).Because of the presence of macrocracks (Fig. S6 †) the thicker lms ($240 nm) using only C 16 mimCl as templates cannot be considered as homogeneous membranes, and thus the model by Massari et al. is consequently not applicable.Such macro-cracks have not been observed for the other lms templated by PEO-PIB (only or mixed with IL).

Photovoltaic properties
A rather high U OC (around 760 mV) is observed for N719 sensitized anatase lms templated by PIB-PEO only and anatase lms templated by m IL /m PIB-PEO ¼ 10% and 20% (Fig. 10), which is in good agreement with the values reported in the literature for TiO 2 lms (both nanoparticulate and dipcoated lms) sensitized with various ruthenium dyes, ranging from 600 to 860 mV. 30A slightly lower average U OC value is found for the cells composed of the lms templated by m IL /m PIB-PEO ¼ 20% (Table 1).The short-circuit current density reaches its highest value of 1.055 mA cm À2 in the cells composed of the electrode templated by m IL /m PIB-PEO ¼ 10%.
Compared to the solar cells using an anatase electrode lm templated by PIB-PEO only, the increase in photocurrent for lms templated by using m IL /m PIB-PEO ¼ 10% is explained by the higher dye loading (Table 1).It is caused by the higher lm permeability and porous volume of the anatase lms templated by m IL /m PIB-PEO ¼ 10% (see part 2.2.1.).Compared to DSSCs with nanoparticulate TiO 2 lms, which generate j SC ¼ 16 to 22 mA cm À2 with ruthenium sensitizers, 31 the j SC value achieved with the bimodal anatase (m IL /m PIB-PEO ¼ 10%) electrode appears rather small at rst sight.It should be emphasized that our DSSC study was not intended to develop cells with high efficiency, but to utilize DSSCs as a suitable tool to   address the inuence of porosity on photoelectrochemical properties and dye loading.If a comparison is made nevertheless, it has to be considered that our lms have a thickness of about 110 nm, which is less than 1% of the typical thickness of the nanoparticulate lms (ca.12 mm) 11 and which obviously cannot result in competitive performance parameters.Zukalová et al. reported a short-circuit current density of 2.7 mA cm À2 for mesoporous N945 sensitized TiO 2 lms from a similar dip-coating process to the one used in our study.3f The higher value of their lms is explained by a greater thickness of approximately 270 nm 3f as well as the red-shied absorption maximum and higher extinction coefficient of the N945 dye compared to N719, which leads to $40% higher photocurrents in very thin lms. 30Considering this fact, the lms of Zukalová et al. would deliver approximately 1.9 mA cm À2 with N719 as the sensitizer.In comparison, our mesoporous anatase lms templated by m IL /m PIB-PEO ¼ 10% generate up to 66% of the corresponding photocurrent for an active lm twice as thin.Since both lms are very thin, an approximately uniform distribution of the light absorption throughout the lm thickness can be assumed.This comparison proves that the anatase lms with m IL /m PIB-PEO ¼ 10% is a promising photoelectrode due to complete crystallization 3d and high dye content.Note that the anatase lm templated by PIB-PEO only generates about 50% of the photocurrent compared to the lm of Zukalová et al. 3f This nding is in good agreement with the difference in the lm thickness and indicates a similar porosity and surface area if no IL template is used.
Surprisingly, the solar cells using the anatase lms templated by m IL /m PIB-PEO ¼ 20% exhibit the smallest photocurrents despite their further increased dye load.In principle, this may be explained by a lower electron collection efficiency or by a lower accessibility of the dye molecules to the electrolyte.In order to determine the electron collection efficiency h coll , we carried out Intensity Modulated Photocurrent Spectroscopy (IMPS) and Intensity Modulated photoVoltage Spectroscopy (IMVS) measurements (Fig. 11).With the frequencies found at the minima of each semicircle f min the electron transport times s d (in the case of IMPS) and electron life times s n (in the case of IMVS) were calculated with eqn (3). 32 These values were used to calculate the electron collection efficiencies (Table 2) with the help of eqn (4). 33 The results clearly show that h coll is rather high and nearly constant for all three kinds of lms, which rules out differences in h coll as a reason for the inferior performance of the anatase lms templated by m IL /m PIB-PEO ¼ 20%.
The electrochemical accessibility of the porous network in the different lms was investigated by impedance spectroscopy.As an example, Fig. 12 shows a selection of typical impedance spectra of an anatase lm templated by PIB-PEO only.The spectra exhibit a small semicircle at high frequency (i.e. at low resistance values), followed by a large semicircle at lower frequency, which starts to atten at its low frequency end due to ion diffusion.Bisquert et al. 34 attributed the high frequency semicircle in the impedance spectra of dye-sensitized solar cells to the counter electrode.The following small section of linear increase is due to electron diffusion in the porous TiO 2 lm and the second semicircle represents the electron transfer from the TiO 2 lm to the electrolyte.The resistance of the latter was found to increase towards more positive potentials (i.e.smaller voltages) due to the decreasing electron concentration in the TiO 2 lm, which is also the case in our results.However, tting with the model by Bisquert et al. did not give satisfactory results.Much better tting results were obtained with the simple model (Fig. 13) to represent the two observed semicircles.
The resistances R and capacities C obtained in the ts for the two semicircles are plotted against the cell voltage for all lms (Fig. 14).It is obvious that R and C show no signicant potential dependence in the case of the high frequency semicircle.This is generally the case for the impedance of the counter electrode.On the other hand, the observed R values are much too high to be explained by the resistance of the counter electrode, usually  in the range of a few Ohms.For such a high resistance, the signal of the counter electrode seems to be hidden in a larger potential-independent impedance (appearing also at relatively high frequency).Such a phenomenon can be attributed to an electron back reaction from the conducting back contact or the contact impedance between the conducting back contact and the anatase lm.It is clear, however, that this semicircle is not directly attributed to the anatase lm.The R-U curves show that the resistances of the monomodal lms and the bimodal lms templated by m IL /m PIB-PEO ¼ 10% are nearly equal, but the resistance for the anatase bimodal lms templated by m IL /m PIB-PEO ¼ 20% is signicantly higher.This strongly indicates that a substantial part of the inner surface is not electrochemically accessible in the latter.In addition, it is most likely that the dye is conned in such a high quantity on the surface of the small pores that the redox electrolyte can hardly access it (pore blocking or aggregation).

Preparation of initial solutions
The synthesis of a mesoporous TiO 2 for m IL /m PIB-PEO ¼ 5% is as follows.Preparation of the TiCl 4 alcoholic solution was slightly modied from a previous recipe.13j A mixture of PIB-PEO-3000 (78 mg, Fig. S1 †) and IL (3.9 mg) is dissolved in absolute EtOH (2.05 g) under sonication at 50 C. Aer complete dissolution, the solution labeled solution "1" is le under magnetic stirring at ambient temperature for 5 minutes.In parallel, TiCl 4 (0.52 g, 0.3 ml) is dissolved in absolute EtOH (2.05 g) under magnetic stirring under ambient conditions, and labeled solution "2".Aer 5 minutes solution "1" is added slowly to solution "2" with magnetic stirring under ambient conditions.Aer 5 minutes deionized water (0.66 ml) is slowly added with stirring under ambient conditions, and the solution is stirred for 2 hours and then ltered (pore diameter is 0.2 mm) before use.
The quantity of PIB-PEO-3000 is always constant in different recipes.The lm templated only with the IL used an identical amount of IL to that of PIB-PEO-3000 alone, i.e. 78 mg.

Film preparation
Silicon wafers were previously heated at 550 C for 5 hours (room atmosphere) and then washed with ethanol prior to use.Films were deposited on Si wafers or on FTO-covered glass at room temperature (20-22 C) by dip-coating on substrates at constant withdrawal rates (1.5 and 5 mm s À1 to obtain thin and thick lms respectively).The relative humidity inside the dipcoating chamber was controlled between 20 and 22%.The lms were then put into a muffle oven at 80 C for at least 20 min and annealed at 200 C for 1 hour (ramp of 2 C min À1 ), and then the lms were calcined at 300 C for 12 hours (ramp of 2 C min À1 ).Aer calcination, the lms were annealed up to 610 C (ramp of 2 C min À1 up to 500 C, 7 C min À1 up to 610 C) and were then removed immediately from the oven.The entire procedure is done in the same muffle oven in an ambient atmosphere.Crack-free dense lms, references for EEP measurements, were prepared using a similar solution without any template.The dip-coating was conducted at a withdrawal rate <0.5 mm s À1 .

Permeability investigations
All measurements were performed with a PGSTAT Autolab potentiostat/galvanostat (Eco Chemie) in a conventional 3electrode cell.The TiO 2 -anatase mesoporous lms deposited on FTO-covered glass were used as the working electrode.The surface of the electrode was delimited by an O-ring (1 mm thick and 9 mm inner diameter) on which a Teon reservoir containing the electrolyte solution was placed.The uncovered surface electrode corresponded to the central part of each lm, and the corresponding thickness was then either 240 AE 20 nm or 110 AE 10 nm when the lms were formed for dip-coating withdrawal at 5 and 1.5 mm s À1 respectively (checked by pro-lometry).A Pt wire served as the counter electrode and an Ag/ AgCl electrode (Metrohm) was used as the reference electrode.The experiment for quantitative analysis of permeability in the mesoporous thin lms was carried out using a self-built wall-jet electrochemical setup.13i,17a,24,25 The probe solutions were operated for concentrations of 5 mM (K 3 Fe(CN) 6 and Ru(bpy) 3 Cl 2 $6H 2 O) in a buffer solution of aqueous KHP (50 mM, pH $ 4.2).

Dye adsorption
The anatase lms were dried at 120 C for one hour.Aerwards the lms were sensitized in a solution of 0.5 mM N719 dye in acetonitrile-tert-butanol (50 : 50) for 24 hours and dried at 80 C for one hour.

Cell preparation
Teon tape ($100 mm) with a circular cut-out of 5 mm in diameter, to dene the active surface of the electrode, was used as the spacer between the dye-sensitized TiO 2 electrode (deposed on FTO) and the transparent Pt-coated counter electrode (Dyesol, Pt-coated test cell TEC15 FTO glass).The circular cut-out was located on the upper part of the lm dip-coated at a withdrawal rate of 1.5 mm s À1 , the corresponding lm thickness was 110 AE 10 nm.A sufficient amount of the redox electrolyte (Dyesol, EL-HSE, containing I À /I 3 À as the redox couple, 3-methoxypropionitrile as the solvent and an imidazole compound, inorganic and organic iodide salts as additives) was added between the electrodes.

Photoelectrochemical measurements
The prepared DSSCs were illuminated through the dye-sensitized lm with the white light of an Xe arc lamp ltered with an Oriel AM 1.5D lter (100 mW cm 2 ).All measurements were performed with a Zahner IM6e electrochemical workstation.A green LED (530 nm, 10 mW cm -2 modulated with +/-0.6 mW cm -2 ) served as light source for IMPS and IMVS.j-V curves were measured at four cells of each anatase electrode templated by PIB only, m IL /m PIB-PEO ¼ 10% and 20%, respectively.

Determination of the dye load
The N719 dye was desorbed from the sensitized TiO 2 lms in a solution of 0.1 M NaOH in ethanol-water (50 : 50) for 30 minutes.The UV-Vis absorption spectra of the obtained dye solutions were measured with a Varian Cary 4000.The desorbed lms were colorless.

Characterization
Grazing Incidence Small Angle X-ray Scatterings (GI-SAXS) were recorded on a Nanoviewer from Rigaku (CuK a radiation).The angle of incidence of the X-ray beam with respect to the lm surface was set at 0.22 .Wide Angle X-ray Scattering (WAXS) measurements were performed using a PANanalytical (CuK a radiation).The EEP measurements were performed on an M2000 UV-visible (from 450 to 1000 nm) Variable Angle Spectroscopic Ellipsometer (VASE) from Woollam with an incidence angle of 70 .Data analysis was performed with the WVase32 soware.Ellipsometric analysis of the crystallized mesostructured anatase lms was performed immediately aer the crystallization step at ambient temperature (25 C) under dry air ux of relative humidity <2%.An assumption is that the optical properties of the matrix of porous and of dense materials are the same.The goal is to use the dense lms as reference to determine the contribution of the anatase matrix to the refractive index of the porous lms during the water adsorption-desorption steps.The EEP measurements consist of plotting the water adsorption-desorption isotherms from the variation of the lm refractive index induced by the change of particle pressure of gas water above the lm.The use of a pulsed air ow with controlled relative pressure of water allows a fast relative pressure equilibration for each point of the isotherm.Optical properties of porous lms and dense lms were obtained using a Cauchy model in the visible wavelength range for transparent lms and a Lorentz model for light absorbing lms.absorbed water) with the Bruggeman effective medium approximation (BEMA, eqn (5)).
f A and f B are the volumetric fraction of A (air) and B (inorganic) media of known dielectric constants 3A and 3B within a volume unit of measured dielectric constant 3 (porous lm).
V water absorbed /V lm is then assumed to be expressed by eqn (6) The pore size determination was based on a modied Kelvin, eqn (7) RT ln P P 0 ¼ gV L cos q dS dV where g is the liquid-air surface tension of water, dS is the adsorbate liquid-air interface surface area variation, when the volume V of adsorbate evolves by dV, q is the wetting angle measured by water contact angle analysis at 5 , and V L is the molar volume of the adsorbate aer capillary condensation.Considering that metal oxide surfaces have a high preference for the adsorption of water over air molecules (N 2 , O 2 , and CO 2 ), we assumed that the relative humidity is equal to P/P 0 .The value of dS/dV has been calculated to be 1.43 following the procedure described in ref.
17b by considering the pore geometry of the and taking separately the contraction of a pure TiO 2 lm aer a similar thermal treatment published in ref. 35 and the contraction of a mesoporous lm made of TiO 2 and KLE block copolymer.7c This value of pore anisotropy was considered constant for all samples.
EEP experiments were performed three times with completely new sets of lms each time.Both isotherms and pore size distributions are reproducible in each case.
The electron microscopy was performed using an HSEM 982 Gemini from LEO (SEM), and for the TEM pictures a CM30 STEM from Philips (presently FEI) was used.

Conclusions
The present study aimed at addressing a fundamental issue regarding mesoporous metal oxides, namely, the inuence of pore connectivity on permeability.As the model material mesoporous TiO 2 lms were synthesized with distorted spherical mesopores of ca. 15 to 20 nm diameter, templated by a block copolymer of the PIB-PEO type, the connection of which can be varied by the addition of a second template, the long-chain ionic liquid (IL) C 16 mimCl, generating smaller mesopores in between the larger ones and inuencing signicantly the size of larger mesopores.The permeability was studied using redox probe molecules and suitable electrochemical measurements (wall-jet technique).Our study revealed that the variation of the relative amounts of the mesoporogen agents tends to greatly inuence the mesopore networks of mesoporous anatase lms.An optimal ratio between the surfactant ionic liquid and the amphiphilic block copolymer, 5% < m IL /m PIB-PEO < 50%, allows formation of anatase lms with bimodal mesoporosity and a permeability at least double that of the reference mesoporous lms templated with the amphiphilic block copolymer only.These permeability data were in full agreement with those obtained through characterization of the mesopore structure (GISAXS, EEP, electron microscopy), proving that the lm exhibiting the highest permeability possessed an ordered arrangement of the larger mesopores, connected by a high concentration of mesopores of 8-10 nm size generated by the IL.
When mesoporous anatase lms templated by the combination of the surfactant ionic liquid and the amphiphilic block copolymer are used as the photoelectrode in a DSSC set-up, the solar energy conversion can be improved by 20% in comparison with the reference lm templated with the amphiphilic block copolymer only.This nding is attributed to the 10% increase in dye loading.However, the lms exhibiting the highest permeability and porosity (measured by EEP) do not present the best performance.This apparent paradox can be explained by the preferential localization of the dye in the small worm-like pores (ca.8 to 10 nm in size) leading to reduced accessibility for the redox electrolyte.
We thus believe that these fundamental insights of the study are of general importance, as they not only demonstrate the possibility to improve lm permeability and material loading by tuning the mesoporosity, but also scrutinize the limitations of hierarchical pore structures.These ndings are therefore of relevance in applications where surface modication is a key factor, for instance in the case of DSSCs.Thus, our study helped to establish a general methodology to separate the impact of structural features of mesoporous lms, namely pore volume, pore size, pore connectivity and surface area on transportrelated properties such as permeability.

Fig. 4
Fig. 4 (A and B) Water adsorption-desorption isotherms (derived from EEP measurements) of mesoporous anatase films for different templating conditions.(C) Porous volume and average pore diameter evolution versus m IL /m PIB-PEO .(D) Pore size distribution (PSD) for a mesoporous anatase film templated by IL only, calculated from the water-adsorption branch of the corresponding isotherm.

Fig. 5
Fig. 5 Schematic representation of the final anatase mesoporous films.

Fig. 7
Fig. 7 Cyclic voltammograms measured in the presence of 5 mM FeCN 6 3À (A) or Ru(bpy) 3 2+ (B) on the bare FTO electrode and FTO electrodes modified by thin mesoporous anatase films (thickness $ 110 nm).Legend for (A) and (B) is the same.

Fig. 9
Fig. 9 Evolution of the film permeability (PD f ) versus m IL /m PIB-PEO for mesoporous anatase thin films possessing a thickness of $110 nm (A) and $240 nm (B).The pore volume evolution (squares) is issued from Fig. 4c.Redox probes are Fe III CN 6 3À (diamonds) and Ru(bpy) 3 2+ (grey dots).Triangles in (A) correspond to the permeability values of mesoporous films templated by IL only (the same color code for the redox probe used).Lines are used as a guide for the eyes.EEP and electrochemical measurements were all carried out on the same central position of the films corresponding to similar thicknesses contributing to the respective signals in the case of the thick films.

Fig. 10
Fig. 10 Comparison of j-U curves of N719 sensitized anatase films prepared by different template combinations.

Fig. 12
Fig. 12 Typical impedance spectra of a mesoporous anatase film templated by PIB-PEO only measured at À800 mV, À600 mV and À400 mV.

Fig. 13
Fig.13Fitting model for the obtained impedance spectra, series connection of a series resistance (R s ) and two impedances consisting of a resistance (R1,R2) and a constant phase element (CPE1,CPE2) in parallel connection, respectively.Fig. 14 Dependencies of resistance (A) and capacity (B) for the first (R1 and C1) and the second semicircle (R2 and C2) of mesoporous anatase films PIB only, m IL / m PIB-PEO ¼ 10% and m IL /m PIB-PEO ¼ 20% on the potential.

Fig. 14
Fig.13Fitting model for the obtained impedance spectra, series connection of a series resistance (R s ) and two impedances consisting of a resistance (R1,R2) and a constant phase element (CPE1,CPE2) in parallel connection, respectively.Fig. 14 Dependencies of resistance (A) and capacity (B) for the first (R1 and C1) and the second semicircle (R2 and C2) of mesoporous anatase films PIB only, m IL / m PIB-PEO ¼ 10% and m IL /m PIB-PEO ¼ 20% on the potential.

Table 2
Frequencies f min from minima in IMPS and IMVS spectra, the resulting electron transport time s d , electron life time s n and electron collection efficiency h coll 12324 | Nanoscale, 2013, 5, 12316-12329 This journal is ª The Royal Society of Chemistry 2013 2,3d,17The porous volume, V p , is determined by EEP by tting the volumetric fraction of air and of the titania matrix within the dry mesoporous lm using the dense lm as the reference.
17bV water absorbed /V lm is determined by tting the volumetric fraction of the dry stabilized mesoporous lm (dry conditions, pores are empty) and the water saturated mesoporous lm (relative humidity ¼ 98%, pores are lled by 12326 | Nanoscale, 2013, 5, 12316-12329 This journal is ª The Royal Society of Chemistry 2013