J. Phys. Chem. C 2007, 111, 7605-7611
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Pores in Nanostructured TiO2 Films. Size Distribution and Pore Permeability Dulce Vargas-Florencia, Tomas Edvinsson, Anders Hagfeldt, and Istva´ n Furo´ * DiVision of Physical Chemistry, Department of Chemistry, Royal Institute of Technology, SE-10044 Stockholm, Sweden ReceiVed: January 15, 2007; In Final Form: March 14, 2007
Nanoporous films of crystalline anatase with intended application in dye-sensitized photovoltaic cells were investigated by NMR cryoporometry, NMR diffusiometry, electron microscopy, and X-ray diffraction. The nanoparticles from which the films were subsequently sintered were prepared in two ways, one with an acidic and one with a basic aqueous process environment and along different temperature regimes. The average morphology was similar in all films as indicated by the roughly identical 〈2κV/S〉 values where κ is the mean curvature of the pore surface and S/V denotes the surface-to-volume ratio. Self-diffusion of water in the pores is strongly reduced with respect to that of bulk and is influenced both by micrometer-scale obstructions to molecular displacement and by pore-size effect in pore interconnectivity. The investigated samples exhibit different transport regimes as concerning those phenomena. In this initial study performed on a limited set of samples, we found no linear correlation between particle and pore sizes. Instead, total porosity is controlled by particle-particle jamming which, together with particle size polydispersity, may also dominate the effects that lead to the observed pore size distributions for the different samples. The rich variation of structural effects and transport properties among the few prepared films call for further studies in order to find an optimal film structure.
Introduction Nanostructured films consisting of titanium dioxide nanoparticles are interesting in a wide range of applications including chemical sensing,1,2 photocatalysis,3 and solar energy conversion.4,5 Dye sensitized nanostructured solar cells are a promising technology for clean energy production at a low price. Their top efficiency has exceeded 10% in lab cells,6,7 and full-scale outdoor performance tests have shown advantages over commercial silicon cells, in terms of increased performance at high temperature and efficiency at low solar angles.8 In these systems, there are numerous studies of the sizedependent optical and electrical properties of the separate particles and the nanostructured film.9 Although the electron transport through the nanostructured semiconductor network has been thoroughly investigated, the dependence of ion transport on the morphology of the pores in the nanoporous network is less examined. The pore network, interstitial to the constituting particles, has implications for the functional devices and limits both the performance of the device as well as the available components used in these devices. In particular, to exchange the almost exclusively used (I-/I3-) redox system to a less corrosive and volatile one, a lot of interest is directed toward ionic liquids and solid-state hole conductors where the mass transport is slower than in a liquid redox system. In this context, the size and interconnectivity of the pores will strongly influence the mass transport. Here we investigate in detail the pore size distribution and the permeability of the porous network in nanostructured TiO2, intended for nanostructured semiconductor electrodes in monolayer dye solar cells. In particular, the pore size distribution affects the dye adsorption process and limits the mass transport in the redox system that regenerates the dye * Corresponding author. Tel: +46 87908592. Fax: +46 87908207. E-mail:
[email protected].
cation after the photoinduced electron transfer to the TiO2. We examine materials prepared by two different sol-gel synthesis routes of TiO2: the acidic and the basic routes of which the latter one is known to produce larger particles.10 One of the principal problems in characterization of nanoporous TiO2 is to access information about the pore size distribution in a straightforward way. The methods that are at our disposal differ both with regard to the measurement principle and the range over which they measure the pore size.11-14 In the past, transmission electron microscopy (TEM), mercury porosimetry, nitrogen adsorption, and X-ray diffraction (XRD) have been used to characterize porous nanostructured films; however, all of those methods present some disadvantages. TEM gives an average diameter and a statistical particle size distribution but the analysis may be biased by overlap which makes it difficult to determine the proportion and size of the smaller constituting particles. Moreover, TEM micrographs are representative only for a small portion of the full sample. Broadening of XRD peaks is, in contrast, most informative about the average size of the crystalline domains and, hence, provides a lower limit to the average particle size. More importantly, both of these methods report about the particles and not directly about the voids among them. The nitrogen adsorption technique (and, in its simplest and most popular form, the Brunauer-EmmettTeller or BET analysis of predominantly low-pressure data11) is very sensitive to small particles with large surface-to-volume ratio S/V and may therefore be subject to large errors for populations having broad pore size distributions and considerable agglomeration. Moreover, this experiment typically demands a large amount of sample which is often not available for thin film materials. Mercury porosimetry relies on pressuredriven imbibition of mercury, a nonwetting liquid, into the pores. The high pressure required during the measurements in small pores can deform the porous network leading to artifacts. Ideally,
10.1021/jp070321y CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007
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TABLE 1: Comparison of Mean Particle Diameters Obtained from XRD and TEM for the Two Investigated Series of TiO2 and the Width of the Particle Size Distribution as Obtained by TEM and Measured as Smallest and Largest Observed Linear Sizes of Particles sample/route/ temperature of treatment (°C)
mean crystal diameter from XRD (nm)
mean particle diameter from TEM (nm)
width of particle size distribution from TEM (nm)
A1/acidic/200 A2/acidic/230 B1/basic/200 B2/basic/220
13 16 16 16
11 15 16 20a
9-15 10-24 11-39 11-44
a
18-20 nm depending on the micrograph analyzed.
a combination of several techniques would give more detailed and reliable information about the porous network. During the past decade, NMR cryoporometry has emerged as a new and promising technique for accessing information such as pore size distribution in a wide range of porous materials including biodegradable polymers,15 polymers,16 mineral pigments used in the paper coating industry,17 silica glasses and gels,18-21 bone,22 and, incidentally, filter membranes made of TiO2.23 Akin to DSC-detected thermoporometry,24-26 NMR cryoporometry19,27,28 detects the depression of the solid-liquid phase transition point of a suitable liquid that has been imbibed into the porous material and is confined to the pores. Described by the Gibbs-Thomson equation, this depression is inversely proportional to the pore size. As has been recently clarified,29 the temperature depression for the freezing point depends on the surface-to-volume ratio of the pores, while that of the melting is defined by the mean curvature of the pore wall. Hence, NMR cryoporometry is capable of providing both pore size and pore shape information. Although the experiment is relatively timeconsuming (that is, compared to DSC thermoporometry), it is straightforward to perform. On the other hand, the obtained pore size distributions are very detailed and available for a wide range (1 nm to 1 µm) of pore sizes. In well-defined model materials, cryo- and thermoporometric methods provide pore size distributions that are very close to those obtained by gas sorption methods.21,24-26 In this work, we explore the porous films formed by anatase TiO2 powders synthesized with two different routes. We employ a combination of four techniques to characterize the pore size distribution: X-ray diffraction, transmission electron microscopy and, foremost, NMR-cryoporometry. The latter technique is also used to obtain information about pore morphology. Finally, the geometric pore data are correlated by network permeability information as provided by 1H NMR-based determination of the diffusion of pore-imbibed water. Experimental Section Preparation of the Porous TiO2 Films. Two series of TiO2 were prepared in two different routes, labeled either as acidic (A) or basic (B) and having different temperature treatments (see Table 1). The acidic route is as follows: a 600 mL solution of 0.15 M HNO3 in MilliQ water was prepared and 100 mL of titanium isopropoxide (Ti(OCH(CH3)2)4, 97% Aldrich) was added. The solution was heated to 80 °C under stirring at 650 rpm. When 80 °C was reached, the stirring was adjusted to 100 rpm, and the solution was kept at these conditions for 24 h. The solution was then diluted to 5 wt % with respect to TiO2 and transferred to an autoclave quartz container, and heated in a security autoclave (Parr Instrument, Model 4768) at 200 °C for 16 h. The resulting solution was then homogenized by
Figure 1. TEM micrographs of the particles prepared by the different procedures specified in the text. The scale bar in the lower corner of the TEM images measures 50 nm.
stirring and placed in an ultrasonic bath for 20 min. Sufficient solvent was then evaporated to reach a concentration suitable for preparing a “doctor-blading” paste (14-15 wt %, w r t TiO2). Finally, carbowax (PEG 20 000) was added in an amount of 50% of the weight of TiO2 (A1). The same procedure was repeated using the autoclave temperature of 230 °C (A2). The basic route was analogous, using 0.15 M ammonia instead of HNO3 with autoclave temperatures 200° (B1) and 220 °C (B2). To prepare the nanostructured TiO2 films, the colloidal solution was spread onto an objective glass with the doctorblading technique and sintered at 450 °C (far above the combustion temperature of carbowax) for 30 min in an air-flow. The absence of significant carbon residues from carbowax after sintering is routinely checked by gravimetry. The obtained film thickness was between 10 and 15 µm. For NMR cryoporometry, the films were then carefully scraped off and placed at the bottom of 5 mm NMR tubes. From the film thickness (measured by a Dektak profilometer), film area, and mass, we estimated the total porosity, that is, the volume fraction of pores in the total volume of the A1 film to 0.60-0.61. Electron Microscopy and Powder XRD. Samples for TEM analysis were prepared by diluting the TiO2 particle dispersion and spraying it onto an electron microscopy grid of copper, coated with a perforated polymer film. The micrographs (see example in Figure 1) were recorded on a Zeiss 9002 transmission electron microscope operating at 80 kV. The particle sizes were determined by zone counting where all of the particles in a specific zone were measured manually in an image analysis program and the corresponding average was calculated. The powder XRD patterns of the nanostructured TiO2 (Figure 2) were collected by a Panalytic X’Pert Pro diffractometer using the KR irradiation of Cu (1.5406 Å). Thin (10 µm) films of nanostructured TiO2 were prepared on optical glass (see scanning electron microscopy image in Figure 2) and analyzed in an angular range 4° < 2Θ < 70°. The particle sizes were determined from line broadening via the Scherrer equation, using
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Figure 3. Total NMR liquid intensity curves I(T) for the melting and freezing phase transitions of water in sample A1. The sharp transition of bulk water serves as internal temperature reference and the presence of extraporous ice suppresses supercooling when recording the freezing pathway.29 The arrows indicate the signal intensities whose fraction multiplied by the total mass of liquid added to the sample provides the amount of liquid imbibed in the nanoporous TiO2 sample.37
Figure 2. X-ray diffraction pattern for the B2 nanostructured TiO2 film (top) and a scanning electron microscopy (SEM) image of the film (recorded on a Leo Gemini microscope). The anatase structure is clearly identified where the most signifying peak is denoted in the graph. Traces of the brookite phase is seen at 2Θ ∼ 31°. The scale bar in the lower corner of the SEM image measures 1000 nm.
the XRD line width obtained in large crystals of BaTiO3 (2 µm, Ventron) as reference. NMR Experiments. Millipore water was added to the NMR tubes that contained, respectively, the four different samples of anatase (∼20 mg each). This material amount (corresponding to about 0.5-1 m2 total surface, see below) is up to 2 orders of magnitude less than that required for an analysis by gas sorption methods (20-50 m2).11 Centrifugation (10 h, 600 rpm) was used to eliminate possible air plugs within the pores. The amount of water was set to both fill the preliminarily estimated pore space and to provide bulk liquid excess where the role of the latter is to provide an in-sample temperature reference and to suppress supercooling in the pore freezing experiments. Water was chosen as the probe liquid because the surface of the TiO2 particles is hydrophilic. Note that different probe liquids such as cyclohexane,29 octamethylcyclotetrasiloxane,30 both of which contract upon freezing, and water,29 which expands upon freezing, typically provide very similar pore size distributions, and repeated experiments with water reveal minor damage to the pore structure by freezing.31 Cryoporometric 1H NMR measurements were carried out on a Bruker DMX 500 spectrometer with 500 MHz resonance frequency equipped with a standard 5 mm probe. NMR cryoporometry detects upon warming and/or cooling the temperature-dependent integral intensity of the liquid NMR signal I(T) that arises from pores where the material melted. The liquid and solid signals are distinguished on the basis of their different transverse relaxation times, T2 which is very short (∼10-20 µs) for ice, even when that is confined to small pores.32 Hence, a Carr-Purcell-Meiboom-Gill spin-echo sequence with 4 ms
total echo time suppressed the signal from ice while it kept the liquid signal that has a T2 that is several orders of magnitude longer than that for ice. A Bruker BVT3000 temperature controller was used to set and hold temperatures with an accuracy of (0.1 K. The temperature spread over the sample was estimated from the spread of the bulk melting transition of the excess water (see Figure 3) to ∼0.2 K. The correct absolute temperature scale was set by shifting the nominal temperatures so that the freezing/ melting point of the excess water (see above) coincides with 273.2 K. The temperature course was the same for all samples. They were first cooled to 260 K where all bulk and pore water was frozen and then warmed up to slightly below the bulk melting point T0; at this temperature, the excess bulk liquid was frozen while the pore water molten. The freezing branches of the cryoporometry experiments started at this point and proceeded with a 0.1 K temperature decrement and with a waiting time g10 min at each temperature which was sufficient to achieve thermal equilibrium.29 When there was no more detectable liquid signal, the melting commenced with the temperature step size and waiting time as above. The experiment finished by reaching the state where all liquid, pore and excess bulk, was molten. The resulting temperature-dependent intensity curves are presented in Figure 3-4. Note that these curves remain unchanged upon repeated experiments. We stress in particular that the freezing curves were continuous and reproducible which indicates a multi-connected pore space. 1H NMR diffusion experiments were performed in a Bruker DMX200 spectrometer equipped with a Bruker DIFF30 probe. All data were obtained by pulsed-field-gradient stimulated echo experiments. In order to suppress the effect of the internal magnetic field gradients in the pores, bipolar gradient pulses were used.33,34 All decays recorded in the porous films were significantly non-Gaussian. Hence, to obtain a measure of the average diffusion coefficient D, the initial parts (down to 50% of intensity) of the diffusional decays were fitted by the conventional Stejskal-Tanner expression.35 The thus obtained apparent average diffusion coefficients were normalized by the diffusion coefficient value D0 recorded in the same way in bulk water. The experiments for measuring D and D0 were performed at temperatures (270-273 K) where the bulk water was frozen; hence, they were performed in supercooled water below its bulk equilibrium freezing point. Note that in the indicated temperature range the bulk water diffusion coefficient is less than half the value obtained at room temperature.36
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Figure 4. NMR liquid intensity curves I(T) for the melting and freezing phase transitions of water imbibed in nanoporous TiO2 samples. Samples A1 and A2 were synthesized following an acidic route and B1 and B2 with a basic route.
Results and Discussion Particle Sizes. The diffraction peaks for the TiO2 samples reveals an almost pure anatase phase, see Figure 1. The mean particle sizes determined by XRD and TEM are close to each other (with the possible exception of sample B2, see Table 1) which indicates that a particle typically consists of a single crystalline domain. The TEM data reveal, though, a significant particle size distribution that is particularly large for the samples prepared on the basic route. The same route also results in larger mean particle diameter: 11 and 15 nm for samples A1 and A2 and 16 and 18 nm for samples B1 and B2, respectively. The polydispersity also increases with temperature which makes image analysis of the micrographs more sensitive to the actual selected region. Total Porosity. The total porosity is obtained by NMR cryoporometry as
φ)
1 1 + m/FVpore
(1)
where m is the mass of the porous material, F is the density of the matrix, that is, of TiO2 ()3.88 g/cm3), Vpore is the total pore volume, and (1 - φ) defines the packing density. As illustrated in Figure 3, this can be easily obtained37 by measuring the total amount of pore filling liquid. The values, collected in Table 2, are close to that obtained by the (assumedly less accurate) gravimetric procedure. Note that any large (V/S > 100 nm) voids do not contribute to the cryporometric φ value but may be taken into account by the gravimetric experiment. As is well-known, the porosity of hcp spheres is 0.26. For disordered impenetrable and monodisperse spheres, the thermalequilibrium limiting porosity (also defined as close random packing38) becomes higher, ∼0.36, whereas the equilibrium freezing transition occurs at φ ∼ 0.5.39 Any polydispersity is likely to decrease these latter numbers. Hence, our experimental porosities, in values similar to those obtained without compression in related systems,40-42 indicate that any of the present preparation processes create a jammed, nonequilibrium particle
TABLE 2: Porosity Characteristics from NMR Cryoporometry for the Two Investigated Series of TiO2
sample
total porosity
peak,a median,b and meanc pore size V/S (nm)
width of PSDd (nm)
morphology indicatore 〈2κV/S〉
A1 A2 B1 B2
0.62 (0.6f) 0.63 0.56 0.57
4.0/4.2/6.8 4.4/4.6/6.0 5.7/5.9/8.1 5.7/5.9/8.3
3.6-4.2 3.7-4.8 2.8-8.6 5.2-6.4
0.61 0.62 0.66 0.62
a Defined by the inflection point of the corresponding I(T) curve. Half of the total pore volume in pores smaller than the median pore size. Defined by the half-intensity point of the corresponding I(T) curve. c Operationally defined as V V V V pi S S i S i+1 S i V i ) S V V V pi S S i+1 S i i where i indexes the points in the corresponding pore size distribution in Figure 4. d 50% of pore volume within these limits defined at equal PSD height. e (0.02 from the experiments. f From gravimetry, on films prepared at 3 µm thickness. b
( )( ) [( ) ( ) ] 〈〉 ∑ ( )[( ) ( ) ] ∑
pack.39 Since the TEM images do not indicate any large difference between particle shapes produced by the different processes, it is (i) particle-particle interactions in part modulated by the polymers (PEG in the carbowax) and/or (ii) the kinetics of drying that define the jamming. Pore Size Distribution. Our cryoporometric results are analyzed using the recently established consistent form29 of the Gibbs-Thompson equation
∆Tm ) -
υγslT0 2κV 2κ ) ∆Tf ∆H S
(2)
where ∆Tf and ∆Tm are the freezing-point and melting-point depressions, respectively, γsl is the surface free energy of the crystal-liquid interface, υ is the molar volume, and ∆H is the melting enthalpy of water. S/V denotes the surface-to-volume
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Figure 5. Pore size distributions of TiO2 nanoparticles obtained via eq 3 from data of NMR signal intensity for the melting I(T) curves presented in Figure 4. Samples A1 and A2 were prepared with an acidic route and B1 and B2 with a basic route.
ratio of a particular pore within which κ is the mean curvature of the pore surface. The material parameters are typically expressed as k ) υγslT0/∆H and for water they yield k ) 25 K‚nm. The NMR liquid intensity curves I(T) are presented in Figure 4 for the acidic and basic TiO2 series. Both the melting and the freezing regions are >1 K broad which shows that they arise because of the distribution of pore size; recall that the temperature spread within the sample volume is only ∼0.2 K. Clearly, the basic samples exhibit a broader melting-freezing range and therefore a larger polydispersity (note the different scale for samples A and B). The quantitative pore size distribution (PSD) function, p(V/S) can be calculated from the freezing branches of the I(T) curves by numerical differentiation and rescaling as
p
(VS) ) Vk ∂I(T) (S) ∂T 2
(3)
If so defined, the resulting PSD provides the volume of pores with the given size range. Note that uniform (maximum frequency for the given experimental setup) sampling of the freezing/melting temperatures results in a nonuniform sampling of the size distribution. For this reason, any calculation of the mean pore size must account for the variable width of the size window (see Table 2). In contrast to the mean pore size, the median and peak sizes are simply provided by the half-intensity and inflection points of the corresponding I(T) curve, respectively. Recall that the pore size defined as V/S is equivalent to d/4 for cylindrical and d/6 for spherical pores with d as the diameter. Note that this procedure ignores the effect of the premolten surface layer on the pore size.43-45 Considering that the width of this layer is ca. twice the molecular size, the resulting error in pore dimensions is 1-2%. A qualitative analysis of pore shape can be obtained by evaluating
∆Tm V ) 2κ ∆Tf S
(4)
this morphology indicator is 2κV/S ) 2/3 for a spherical and 2κV/S ) 1/2 for a cylindrical pore. We obtained the average values of this quantity 〈2κV/S〉 ) 〈∆Tm〉/〈∆Tf〉 where the average freezing and melting temperatures are taken at the half-intensity points of the corresponding I(T) curves (see Table 2). Although originally derived for convex pore shapes, one can well assume that this morphology indicator is sensitive to changes of pore shape. Since 〈2κV/S〉 is invariant (∼0.6) to sample preparation, we conclude that the average morphology is the same for all samples and the average characteristics, that is, peak, median, and mean pore sizes, change from sample to sample by dominant scaling with the particle sizes (see Table 1). In contrast to pore morphology, the width of the pore size distribution seems to be very sensitive to the preparation method. This is not unexpected and is not unique46 to the current preparation method of TiO2 films. One interesting feature is the large “foot” of pore size distributions toward large pores. This is not an experimental artifact; in the I(T) curves, the presence of some large pores is more clearly visualized by the slow increase of the intensity up to the bulk transition temperature. Such behavior is absent in, e.g., controlled pore glasses which have a sharp pore size distribution.29 From the I(T) curves, one can estimate that these large pores may have up to 20% of total pore volume. Larger (V/S > 100 nm) voids, implicated by the difference between the gravimetric and cryoporometric total porosities, may constitute a continuation of the pore size distributions to even larger sizes. Pore Permeability. The apparent average self-diffusion coefficient of water confined in the porous network is presented in Figure 6; the units are relative to the diffusion coefficient of bulk water. To be able to measure diffusion within the liquidsaturated porous network, the experiments were performed at temperatures where the bulk water surrounding the flakes of the TiO2 film is frozen. One of the other two options is measuring at temperatures when that bulk water is molten; however, the diffusion behavior is then biased by that water. The other option is to fill the porous network with the amount of liquid that fills exactly the total pore volume although the
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Figure 6. Dependence of the average apparent diffusion coefficients for samples A1 (b,O), B1 (2,4), and B2 (9,0) on the diffusion time ∆. The open symbols represent results of experiments performed directly below the melting point of bulk water (see text) and therefore represent diffusion all over the porous network. The filled symbols represent results obtained at those temperatures below the bulk melting point where water in large pores representing ca. 20% of total pore volume were frozen (by 2.2, 1.1, and 1.5 K below bulk melting for samples A1, B1, and B2, respectively, measured from the upper edge of the bulk transition). The estimated error of the relative diffusion coefficients is ca (5 %.
result is very sensitive to volume errors and requires very accurate estimates of the total pore volume. The experiments were performed at two temperatures. The higher one was set at ca. 0.1 K below the temperature at which, considering our temperature spread, the bulk melting has certainly not commenced yet; in practice, these temperature points are the third or fourth ones from the right in Figure 4. Hence, at this temperature the liquid water within the pores was confined to the porous network by the ice that surrounds the flakes of the porous TiO2 film. The lower temperatures were defined by the point (see the temperatures given in Figure 6) where most of the “large” (ca V/S > 8 nm) pores present in the pore size distributions also contain ice. The obtained diffusion coefficient values vary with the diffusion time ∆ set in the stimulated echo experiment. Such a variation indicates that the diffusion is obstructed;47,48 upon increasing the diffusion time, the average displacement increases less than expected for a continuous morphology. The length scale L for those obstructions can be estimated from the apparent diffusion coefficient D and the diffusion time ∆ as L ∼ (2∆D)1/2. At this point, it should be recalled that in all of our experiments the water is confined, by the bulk ice around, to the porous network or parts of that within individual flakes (∼mm diameter) of the TiO2 film. Hence, water diffusion in the lateral directions of the flakes is free but obstruction may arise in the direction normal to the flake. Considering that the approximate film thickness is 10 µm and that the apparent diffusion coefficient is on the order of 0.5 × 10-9 m2/s, we expect those obstruction effects to be effective at diffusion times on the order of ∆ ) 100 ms. Indeed, at diffusion times of 40-200 ms the different samples seem to follow the same trend which we interpret as the effect of obstruction of diffusion in the direction normal to the flake. The three investigated samples present three very different transport scenarios. First of all, every sample shows signs of obstruction on the 10-20 ms time and, therefore, ∼2-3 µm length scales. These obstructions might arise from larger cracks formed during the drying of the films49-51 and which cracks are filled by ice under our experimental conditions. Under operational conditions in dye-sensitized solar cells, such liquidfilled cracks would not obstruct electrolyte diffusion but would, on the other hand, disrupt the electron-conducting TiO2 network.
Vargas-Florencia et al. On the other hand, the curves clearly level off at short (
