Thermal Stability and Optimal Photoinduced Hydrophilicity of

Article pubs.acs.org/JPCC

Thermal Stability and Optimal Photoinduced Hydrophilicity of Mesoporous TiO2 Thin Films Jinshu Wang,* Hui Li, Hongyi Li, Chen Zuo, and Hong Wang School of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, People's Republic of China ABSTRACT: Using the triblock copolymer Pluronic F127 (EO106PO70EO106) as the templating agent and Ti(OBun)4 as the titanium source, mesostructured TiO2 thin films were constructed through the sol−gel and evaporation-induced selfassembly method. The effect of the calcination temperature on the mesostructure and on the hydrophilicity of the obtained mesoporous TiO2 thin films was investigated. Small-angle and wide-angle X-ray diffractions, transmission electron microscopy, N2 adsorption−desorption, and contact angle measurements were used to characterize the as-synthesized TiO2 thin films. It was shown that the synthesized mesoporous TiO2 materials exhibited an excellent thermal stability and possessed pores with a diameter larger than 7 nm and a narrow pore-size distribution, and thick inorganic walls composed of nanocrystalline anatase. The calcination temperature affected the stability of the mesoporous structures. In the range of 450− 600 °C, the mesoporous framework was stable and the pore size was from 7.3 to 7.8 nm. Above 600 °C, however, the structure collapsed partially. On the basis of the film structure, a four-coordinate channel mode was proposed and the collapse criterion for the mesoporous structure was established through thermodynamic calculation. The synthesized mesoporous TiO2 thin films showed excellent hydrophilicity without light illumination; for example, the film obtained after being treated at 600 °C had a contact angle of about 22.5°, whereas the sample treated at 500 °C (the particle and pore sizes were 10.2 and 7.5 nm, respectively) showed the optimal photoinduced hydrophilicity, with the contact angle of about 9.5°.

1. INTRODUCTION The unique electronic, optical, and catalytic characteristics of crystalline TiO2 associated with the photoinduced electronic transfer behavior render their usefulness in superhydrophilic surfaces, photovoltaic devices, and photocatalysts.1 To further expand its applications in such fields, it is necessary to prepare TiO2 materials as thin films or coatings with high crystallinity and high surface areas.2,3 Since the discovery of periodically organized silica-based mesostructural materials,4 similar templating approaches have been extended to fabricate mesoporous transition-metal oxides.5−9 These mesoporous materials show higher surface areas and much more uniform and controllable pore sizes and morphologies and thus display unique electronic, magnetic, and catalytic properties. The evaporation-induced self-assembly (EISA) method was proposed by Brinker et al., which allows for regulating the inorganic condensation rate with the formation of an organized liquid-crystal template, and has been used for the construction of well-defined mesoporous materials.10,11 However, there are two main hurdles to be taken into account during the preparation of highly crystalline mesoporous TiO2 films depending on the EISA route:12 An alterative is the high reactivity of most of the titania inorganic precursors toward hydrolysis and condensation. One possible © 2012 American Chemical Society

strategy of controlling the instantaneous hydrolysis−condensation of the precursor is to perform the cooperative assembly process in nonaqueous media.13,14 Additionally, adding a suitable chelating agent into the reaction solution15−18 or carrying out the reaction under strong acidic conditions (pH < 1) can also control the reactivity of titania precursors.12,19−22 Another challenge is that the crystallization takes place at a temperature higher than 400 °C and it is always accompanied with the collapse of the mesostructure due to the extensive crystallization and nanocrystal growth.23,24 In an attempt to improve the thermal stability of the mesoporous TiO2 framework, some efforts have been carried out,25−27 in which post-treatments with ammonia or in supercritical carbon dioxide with the presence of tetraisopropoxide or tetramethoxysilane are required. However, apart from the complicated procedures, these postsynthesis strategies would introduce impurities into the mesoporous walls, which might affect the unique properties of single-component metal oxides and limit their applications. Using block copolymers as a supermolecular Received: December 13, 2011 Revised: April 4, 2012 Published: April 5, 2012 9517

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100 mA. The crystalline phases and crystallinity of the samples were measured by X-ray powder diffraction (WAXRD) analysis (SHIMADZU XRD-7000) using Cu Kα radiation (λ = 0.15418 nm) operated at 40 kV and 40 mA. A transmission electron microscopy (TEM) analysis was performed on a JEOL-2010 electron microscope with an acceleration voltage of 200 kV. Nitrogen adsorption−desorption isotherms at −196 °C were recorded using a Micromeritics ASAP2020 instrument. The Brunauer−Emmett−Teller (BET) equation was used to calculate the surface areas, and pore-size distributions were measured by the Barrett−Joyner−Halenda (BJH) method from the desorption branch of the isotherm. 2.4. Measurement of Water Contact Angle. The water contact angle on the surface of the synthesized mesoporous TiO2 thin films was measured by a video-based contact angle measuring device (Dataphysics OCA20, Germany) in an ambient environment. An ultraviolet (UV) lamp was employed as the light source. The intensity of the UV light striking on the film was about 2 mW·cm−2. To eliminate the influence of the photocatalytic decomposition of inorganic substrates on the surface of the films, the as-deposited TiO2 films were thoroughly cleaned with acetone, ethanol, and deionized water in advance. Before the contact angle measurement, these thin films were stored in the clean air and dark condition to prevent the adsorption of contaminants from the air. The sessile drop method was used for the contact angle measurements, and the precision is ±1°. Distilled water was used as the water source, and the volume of the droplet for the measurements was 5 μL. The samples were irradiated in an ambient environment for 5 min. It was found that the shape and size of the droplet became stable in 30 s. Accordingly, all the contact angles presented in this work referred to a water droplet 30 s after the droplet has contacted with the substrate. Water droplets were placed at five different spots on each sample, and the average value of the contact angles was taken.

templating agent has attracted much attention, because thicker walls and larger mesopores can be obtained in the framework.28,29One advantage of the thick inorganic walls is that domains of the nanocrystallinity can be produced in the frameworks, while maintaining the mesostructural integrities of the mesoporous materials, hence leading to the improvement in thermal stability of the network. Pluronic F127 (HO(CH 2 CH 2 O) 106 (CH 2 CH(CH 3 )O)70(CH2CH2O)106H) is a unique candidate as the templating agent due to its higher molecular weight coupled with long hydrophilic PEO blocks and hydrophobic PPO blocks.30−33 On the other hand, compared with other titania precursors (e.g., Ti(OBut)4, Ti(OPri)4, Ti(OEt)4, and TiCl4), Ti(OBun)434,35 has two important advantages: (i) it possesses a higher linearity and larger size and (ii) n-butanol can be in situ released, which acts as a swelling agent or cosurfactant. We have made a primary study on the synthesis of mesoporous TiO2 using the F127−Ti(OBun)4−EtOH−HCl system.36 It is well known that the characteristics of such materials are governed by the particle size and crystallinity. In this paper, the effect of the calcination temperature on the structural and textural parameters of the obtained mesoporous nanocrystalline TO2 thin films was studied. Furthermore, thermodynamic calculation for the mesoporous structure was carried out, and a four-coordinate channel mode was proposed. The hydrophilicity with and without UV illumination was also investigated.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Triblock copolymer Pluronic F127 (HO(CH 2 CH 2 O) 1 0 6 (CH 2 CH(CH 3 )O) 7 0 (CH 2 CH 2 O) 1 0 6 H, EO106PO70EO106, MW = 12 600) was purchased from BASF Corp. The other chemicals (A.R. in purity) were purchased from the Beijing Chemical Agents Company and used as received without further purification. 2.2. Synthesis. F127 and Ti(OBun)4 were used as the templating agent and inorganic precursor, respectively. In a typical synthesis process, 2 g of F127 was dissolved in 50 mL of absolute ethanol (EtOH) and concentrated HCl solution at room temperature under magnetic stirring for 30 min, obtaining the mixed F127/EtOH/HCl solution. Separately, 50 mL of absolute ethanol was added to the solution of Ti(OBun)4 and acetylacetone (AcAc) under vigorous stirring for 20 min, obtaining the mixed Ti(OBun)4/EtOH/AcAc solution. The mixed F127/EtOH/HCl solution was then added dropwise to the mixed Ti(OBun)4/EtOH/AcAc solution under vigorous stirring for 30 min, and the obtained sol was stirred for another 24 h at room temperature. The F127/Ti(OBun)4/ HCl/EtOH/AcAc molar ratio was 0.0008/0.0726/0.5036/ 19.928/0.1476. Uniform and transparent thin films were produced by spin-coating on the silicon wafer or indium tin oxide (ITO)-coated glass substrates at the constant spinning rate of 2500 rpm. The deposited films were aged at 28 °C and 30−50% relative humidity (RH) for 24 h. The as-prepared thin films were subsequently calcined at a heating rate of 1 °C·min−1 in an oxygen atmosphere from room temperature to 350, 450, 500, 600, or 700 °C and held at this temperature for 2.5 h. The corresponding powdered mesoporous TiO2 sample was prepared by scrapping the films from the substrate. 2.3. Characterization. The small-angle X-ray diffraction (SAXRD) patterns of the obtained samples were obtained by using a Rigaku D/max-rA diffractometer with a Cu Kα radiation source (λ = 0.15418 nm) operated at 40 kV and

3. RESULTS AND DISCUSSION 3.1. Small- and Wide-Angle X-ray Diffraction. Figure 1A shows the small-angle X-ray diffraction (SAXRD) patterns of the mesoporous TiO2 samples synthesized at different temperatures. The film calcined at 350 °C presented one intense diffraction peak, indicating that a well-organized mesostructure was formed, which was also confirmed by TEM micrographs (Figure 2A,B). No significant change was observed in the position of the (110) diffraction peak of the sample synthesized at 450 or 500 °C, strongly suggesting that the ordered mesostructure was maintained without obvious contraction during the condensation and crystallization of the films at or below 500 °C. Additionally, the small variation in both peak position and width indicated the highly thermal stability of the mesoporous thin films. Furthermore, the appearance of one weak and broad (110) peak for the film calcined at 600 °C implied that the framework was still maintained during the high-temperature treatment, although the mesoporous structure was contracted somewhat (Figure 1A, pattern d). The result was substantiated by the TEM micrographs, as shown in Figure 2. Treating the thin film at 700 °C, however, led to a serious deterioration of the mesostructure (Figure 1A, pattern e). The wide-angle X-ray diffraction (WAXRD) patterns of the samples are shown in Figure 1B. It could be clearly seen that all of the samples showed the presence of pure nanocrystalline anatase (JCPDS No. 21-1272) without other crystalline phases 9518

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(brookite or rutile) even at a calcination temperature of 700 °C, indicating the high stability of anatase within the scaffold.37 It is known that anatase will transform into rutile at ∼550 °C. The retarding of the phase transformation can be explained by the following reasons. First, during calcination, the adjacent crystallites would agglomerate and grow. The anatase phase in the inner region of the agglomerated TiO2 particles changed into the rutile phase more easily than that in the outer surface region of the agglomerated TiO2 particles.38 In this work, the mesoporous TiO2 frameworks had relatively thicker walls and a higher specific surface area with most crystallites in the outer surface of the mesostruture, which restrained the transformation from anatase into rutile. Second, according to the investigation of Pillai et al., the phase transformation process of anatase to rutile usually commenced with oxygen vacancy formation, which accelerated the Ti−O bond breaking and phase transition associated with the crystalline growth.39 Under usual preparation conditions, high-temperature treatment of titania always resulted in the formation of oxygen vacancies.40 During the high-temperature treatment, the Ti−O−Ti network weakened, and this facilitated the Ti−O bond breaking and a consequent structural rearrangement to a thermodynamically stable rutile phase. In our synthesis process, in order to remove the carbon residual completely, the titania sample was calcined at a pure oxygen atmosphere. This strategy could hinder the formation of the oxygen vacancies and retained the strength of the Ti−O−Ti network. The formed stronger Ti−O−Ti bonds hindered the Ti−O bond breaking at higher temperature, leading to the stabilization of the anatase phase. Figure 1B also displayed that, with increasing treatment temperature, these diffraction peaks became narrow and strong owing to the growth of crystallites and improvement of crystallinity. According to the Scherrer equation and using the (101) diffraction peak of anatase, the average crystallite sizes were calculated and are listed in Table 1. The crystallite size

Figure 1. (A) The SAXRD and (B) WAXRD patterns of the prepared mesoporous samples calcined at (a) 350, (b) 450, (c) 500, (d) 600, and (e) 700 °C.

Table 1. Textural and Structural Parameters and Crystal Phase of the Mesoporous TiO2 Thin Films Calcined at Different Temperatures calcination temperature (°C)

Dporea (nm)

SBETb (m2·g−1)

Pc (%)

Vd (cm3 g−1)

Dee (nm)

phase

350 450 500 600

4.8 7.8 7.5 7.4

145 119 101 70

37 44 40 30

0.1501 0.2085 0.1701 0.1141

7.6 9.0 10.2 12.7

anatase anatase anatase anatase

a

The average pore diameter is estimated using the desorption branch of the isotherm and the BJH model. bThe surface area was calculated by the BET method. cThe porosity (P) is estimated from the pore volume (V) determined using the desorption branch of the N2 isotherm curve at the P/P0 = 0.976 single point. P = V/(V + Vanatase). Herein, Vanatase, which is the theoretical volume of pure anatase per gram, is determined by anatase density (ρanatase): Vanatase = 1/ρanatase = 0.2604. dThe total pore volume is taken from the desorption branch of the nitrogen isotherm curve at the P/P0 = 0.976 single point. eThe crystalline size calculated by applying the Scherrer equation on the anatase (101) diffraction peak.

increased with the rise in calcination temperature. The good crystallization of the mesoporous TiO2 frameworks is important for their applications in antifogging, photocatalysis, and photovoltaic fields. When the calcination temperature was elevated to 700 °C, the crystallites grew to larger than 20 nm in size, exceeding the thickness of the pore walls (around 13 nm,

Figure 2. TEM and HRTEM images of the mesoporous TiO2 thin films calcined at 350 °C (A, B), 600 °C (C, D), and 700 °C (E). 9519

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estimated by the TEM images shown below). Therefore, the framework was severely destroyed. 3.2. TEM Analysis. The mesostructural evolution of the synthesized TiO2 thin films with the change in calcination temperature is shown in Figure 2. It could be seen from the TEM micrographs (Figure 2A) that a well-organized cylindrical pore structure was formed in the sample calcined at 350 °C. Its pore size estimated from the HRTEM image (Figure 2B) was about 4−6 nm. In the HRTEM images, almost no nanocrystallites were found in the channel walls, implying a low crystallinity of the sample. During the calcination process at 350 °C, the initial amorphous Im3m cubic structure transformed into the two-dimensional gridlike structure.41At this temperature, anisotropic crystallites grew within the geometry of the framework without obvious deformation or destruction of the cylindrical pore structure. The TEM image of the sample calcined at 600 °C (Figure 2C) also displayed a well-organized mesostructure. However, when the calcination temperature increased from 350 to 600 °C, the pore shape was transformed into an elliptical shape due to the growth of crystallites at high temperature (Figure 2C). The excessive growth of the crystallites, that is, exceeding the geometry of the inorganic framework, resulted in the distortion of pore walls to some degree; that is, the randomly orientated anatase particles occupied some space and led to the deformation of the pores. This was in agreement with the SAXRD results (Figure 1A). The HRTEM micrograph (Figure 2D) of the sample calcined at 600 °C clearly shows the formation of a crystalline structure. The wall thicknesses and pore sizes estimated from the HRTEM images were in the ranges of 9−13 and 6−9 nm, respectively. The thick walls of the framework were attributed to the excellent thermal stability of the framework. The d spacings determined from the diffraction rings of the SAED pattern (inset of Figure 2D) indicated that the film was composed of the crystalline anatase phase, which was coincident with the WAXRD results. In this case, the initial cooperative assembly of the mesoscopically ordered hybrid mesostructure with thick amorphous inorganic walls (as reflected from the WAXRD pattern) provided nucleation sites for nanocrystalline domains within the walls. A relatively high density of nanocrystallites could be produced within the thick walls, in which the partial crystalline structure effectively sustained the local strain caused by the crystallization and prevented the mesostructure from collapsing at a higher treatment temperature. From the image of the film calcined at 700 °C (Figure 2E), one can find that this sample has almost lost its initial well-defined mesostructure and transformed into a disordered porous framework. This is due to the overgrowth of the grains. 3.3. Nitrogen Adsorption Analysis. N2 adsorption− desorption isotherms of the mesoporous TiO2 samples calcined at various temperatures are shown in Figure 3. It is observed that all the samples calcined at different temperatures displayed a type IV isotherm curve, which was representative of mesoporous materials.42 However, the hysteresis loops of samples calcined at lower than 700 °C seemed to be the intermediate between type H1 and H2, which exhibited the isotherms with broad hysteresis loops, but without any dramatic differences in steepness of adsorption and desorption branches. Such a feature might be associated with the presence of uniform cagelike pores in the samples.43 In comparison, the hysteresis curves of the sample calcined at 700 °C can be classified into the type H1, which means the characteristic of materials with a

Figure 3. N2 adsorption−desorption isotherms for the synthesized samples calcined at 350, 450, 500, 600, and 700 °C. Vp = volume adsorption; P/P0 = relative pressure; V = pore volume.

cylindrical pore geometry. In addition, compared with other samples, the sample calcined at 350 °C displayed a different hysteresis loop, indicative of a different pore shape and network effect. The porosity of the sample calcined at 350 °C (deduced from the pore volume and determined by the adsorption branch of the N2 isotherm curve at P/P0 = 0.976 single point) was only 37%, whereas the sample calcined at 450 °C presented a porosity of 44%. This difference might be due to the incomplete decomposition of the template residues treated at 350 °C. It has been reported that the PEO−PPO block copolymer could be removed from the system at temperatures below 400 °C.44 The escape of PPO decomposition products from the framework resulted in the formation of pores and the unidirectional shrinkage of the framework, which induced part of the pores to heal up, and the pores became inaccessible to N2. A further rise in calcination temperature to 450 °C gave rise to the sample with all the pores being accessible. This might be attributed to a local migration of matter due to the faster diffusion at higher temperatures. On the other hand, the isotherms of all of the samples presented a sharp capillary condensation step, which implied a high degree of pore-size uniformity.43 The shift of the capillary condensation step at high relative pressures for the samples calcined above 450 °C indicated that the calcined samples had large channel-like mesopores, which was confirmed by the evolving pore-size distribution curves. Upon further increasing the calcination temperature to 500 or 600 °C, the obtained sample had a lower N2 adsorption amount, implying the decrease of surface area of the sample. When the calcination temperature was 700 °C, the obtained sample showed an isotherm different from those of the other samples, indicating the occurrence of a progressive deformation of the framework. On the basis of the desorption branches, the pore sizes of different samples were analyzed, and the results are listed in Table 1. Despite the rise in calcination temperature from 450 to 500 °C and further to 600 °C, no significant change in pore diameter was observed. This result demonstrated that the TiO2 thin films possessed good thermal stability. 3.4. Thermal Stability of TiO2 Mesoporous Structure. As shown above, highly thermally stable mesoporous TiO2 thin films with thick walls and a larger pore size were successfully synthesized in a F127−Ti(OBun)4−EtOH−HCl system. The formation of the robust mesoporous TiO2 framework could be attributed to the reasons as follows: First, the F127, acting as the templating agent, was the premise for the formation of the thick walls and larger pore diameters in the mesostructure. The F127 was a unique surfactant owing to its high molecular weight and long 9520

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3.5. Thermodynamic Study of the Thermal Stability of the Mesoporous Structure. It is widely accepted that the excess growth of crystallites causes the mesoporous structure to collapse.46,47 However, the mechanism on thermal stability of mesoporous structures has not been reported. We conducted the thermodynamic study of the collapse of the mesoporous structure. Taking the grid mesopores as orderly arranged pores surrounded by crystallites, and four crystallites, which have the cylindrical morphology with the base circle diameter of D and height D, connected to form a pore with the radius of R. The

hydrophilic PEO and hydrophobic PPO segments, which could offer the possibility of forming thicker walls and larger pore diameters in the mesostructure of the TiO2 thin films. The triblock copolymer micelle was composed of a core dominated by the PPO segments and a corona dominated by the PEO segments. The core of the micelles was believed to be free of water, whereas the corona was hydrated. The pore size was, to a large extent, dependent on the effective volume of the hydrophobic core (PPO) of the micelles. The wall thickness was determined mainly by the hydrophilic corona (PEO). As shown in Figure 2, the wall thickness of the obtained mesostructure was 9−13 nm (TEM results). It is well known that regulating the hydrolysis and condensation of transition-metal oxide precursors is of paramount importance for the formation of mesophases of most transition-metal oxides, owing to their high reactivity to precipitate and crystallize into bulk oxide phases directly in aqueous media. Here, we adopted a special procedure that could control the hydrolysis−condensation and cooperative procedures simultaneously. This strategy seems to be critical for the generation of solid and thick wall frameworks. This could be described as follows: (1) Using a nonaqueous solvent and Ti(OBun)4 as the inorganic precursor was very important since it could effectively restrain the hydrolysis and condensation rate of the metal species and prevented them from fast crystallization. The reaction system was carried out in a quasi-anhydrous medium, in which a small amount of water was only provided by air moisture and reagent. (2) The strong acidic conditions of the reaction system and the addition of the complexing agent AcAc in the system were also crucial. Blanchard et al. reported that the mean size and fractal dimension of the titanium oxo-polymers increased with increasing the hydrolysis ratio (H = [H2O]/[Ti]) and/or decreasing the inhibitor ratio (p = [H+]/[Ti], or a = [acacH]/ [Ti], acacH = acetylacetone).45 For a low H value and a high inhibitor ratio, tenuous titanium oxo-polymers could be obtained. In our case, the value of H (≤1), p (ca. 15), and a (ca. 2) were favorable parameters for the presence of lowweight oligermeric Ti-oxo species in solution. The high surfaceto-volume ratio of these small entities would make them ideal to be associated with the surfactant molecules. In the cooperative assembly process, these small entities preferentially interacted with the polar PEO moieties via a hydrogen-bonding manner. Upon a subsequent aging procedure and solvent evaporation, the cross-linking between the Ti-oxo species and the surfactants became dominant, and the microphase segregation was promoted, which resulted in the formation of a thick hybrid framework. The nanocrystallites could be produced within the thick framework walls upon calcination, whose partial crystalline structure would effectively sustain the local strain caused by the crystallization and prevent the mesostructure from collapsing during the calcination process. Finally, the n-butanol in situ released by Ti(OBun)4 was favorable for the formation of larger-sized mesopores. Because of the nonpolar nature, the n-butanol produced by Ti(OBun)4 inclined to penetrate the interface between the hydrophilic and hydrophobic domains of the micelles and located at the hydrophobic cores, which would act as a cosurfactant to swell the cores of the micelles. Because the pore size of the mesoporous network is mainly dependent on the hydrophobic core diameter, the in situ released n-butanol might play a pronounced role in the construction of large pore mesostructured TiO2 frameworks.

Figure 4. Schematic diagram of the TiO2 crystallites in the mesoporous structure.

schematic diagram of this model is shown in Figure 4. The stress imposed on the pores could be expressed as σ = σcomp − σtension (1) where σcomp and σtension are the compression stress and tension stress applied on the pores, respectively. The surface energy of crystallites produced the tension stress toward the outside from the pore center σtension = dEsurf /dA = γsurf

(2)

where Esurf is the surface energy, A is the area exposed to the pores, and γsurf is the specific surface energy. The interface energy between the crystallites provided the compression stress toward the center σcomp = dE interf /dA

(3)

where Einterf is the interface energy, and the A can be described as eq 4 A = πDpD

(4)

where Dp is the pore diameter. The interface energy could be written as E interf = nLDγinterf

(5)

where n is the coordinate number of the pore, L is the contact length between two crystallites, and γinterf is the interface energy. Combining eqs 3 and 5, we got 9521

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nLD nL = γinterf πDpD πDp

⎡ D ⎤ |J | = ⎢ eff ⎥|∇u| ⎣ ΩαkT ⎦

(6)

Combining eqs 1 and 6, then σ = σcomp − σtension

nL = γinterf − γsurf πDp

in which |J| is the absolute value of the particle flux across the unit cross-sectional area, Deff is the effective coefficient, Ωα is the volume of diffusion particles, k is the Boltzmann coefficient, T is the absolute temperature, and |∇u| is the chemical potential gradient. The chemical potential gradient |∇u| could be approximately defined as the chemical potential divided by the particle diffusion distance, which was equal to the distance between the pore center and the crystallite center. Therefore, |∇u| could be expressed as

(7)

On the basis of the TEM results (Figure 2), four crystallites connected to form one pore, indicating that the coordinate number of the pore was 4. From Figure 5, based on the geometrical rule, it is obtained (r − h)2 + l 2 = r 2

(13)

(8)

|∇u| = 2

Δu Dp + D

(14)

where Δu is the chemical potential, and it can be calculated by the compression stress multiplied by the volume of diffusion particles. Δu = σ Ωα

(15)

Combining expressions 14, 15, and 13 yields |J | = Figure 5. Sketch of the pore structure.

where l is one-half of L, R is the pore radius, r is the crystallite radius, and h is one-half of the contact height of two cylindrical crystallites. Combining eqs 8 and 9, we got l=

2r 2 − R2 2

−R +

J=

Since L = 2l, Dp = 2R, and D = 2r, then eq 11 could be written as L=

−Dp +

2D − Dp

(17)

⎡ 2 −Dp + 2D2 − Dp2 ⎢ 2Deff J= ⎢γ kT (Dp + D) ⎢ interf πDp ⎣

(

2

(11)

2

2σDeff kT (Dp + D)

It was apparent that, when J > 0, the particles would diffuse toward the pores, leading to the shrinkage of the pores. Substitution of eq 12 into expression 17 yields

(10)

2

(16)

From eq 16, it was obvious that, when compression stress was applied on the pores, particles could diffuse toward the pores. Taking the diffusion direction of the particles toward the pores as the positive direction, eq 16 became

(9)

l+R=r−h

2σDeff kT (Dp + D)

(18)

Inserting 11 into 7, we got

In the calculation, the morphology of crystallite was taken as a cylinder, while spherical crystallites were usually adopted for the crystallite size calculation. Although the morphologies of the crystallites were different, the volume of these two kinds of crystallites should be constant, namely

σ = σcomp − σtension

(

4 −Dp + = γinterf

2πDp

(

2 −Dp + = γinterf

2D2 − Dp2

2D2 − Dp2 πDp

⎤ ⎥ surf ⎥ ⎥⎦

) −γ

) −γ

surf

4π (De /2)3 ⎛ D ⎞2 = π⎜ ⎟ D ⎝2⎠ 3

) −γ

surf

(19)

(12)

Therefore,

The change of pore volume is equal to the diffusion flux of the particles (atoms, molecules) moving to these vacancies. The diffusion flux is a function of the effective diffusion coefficient and diffusion driving force (chemical potential gradient), which can be described as48

D = 0.67De

(20)

in which De is the diameter of spherical crystallites. Substitution of the above expression into eq 18 yields 9522

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(

Article

0.90De 2 − Dp2

results are illustrated in Figure 6. A significant decrease in the water contact angle occurred upon the rise in calcination

)

πDp

⎤ ⎥ − γsurf ⎥ ⎥⎦

(21)

The mesoporous structure stability could be predicted by the value of J. When J > 0, the particles would diffuse toward the pores, causing the collapse of the mesoporous structure. Otherwise, the mesoporous structure would be stable. The surface energy and interface energy of TiO2 are given by eqs 22 and 23, respectively.49 γsurf = 1.91 − 1.48 × 10−4(T − 298)

(22)

γinterf = 1.32 − 1.48 × 10−4(T − 298)

(23)

Figure 6. Variation of the water contact angle of the mesoporous thin films calcined at different temperatures: (A) without UV light illumination and (B) in the presence of UV light illumination for 5 min.

Therefore, J in eq 21 could be written as ⎡ J = ⎢2Deff ⎣

{(⎡⎢⎣2[1.32 − 1.48 × 10

−4

(−D + p

temperature. The mesoporous TiO2 thin film calcined at 350 °C showed low hydrophilicity, regardless of UV irradiation, a result due to the low crystallinity and organic residues. The low crystallinity would result in the recombination of the photogenerated electrons and holes, consequently leading to the lack of photoinduced hydrophilic conversion. The films calcined at temperatures above 450 °C exhibited higher hydrophilicity even without UV light illumination. The water contact angles decreased with increasing the calcination temperature. The contact angle for the film calcined at 600 or 700 °C was about 22°. These results were in good agreement with those obtained on the nanotubular TiO2 layers50,51and mesoporous TiO2 thin films,52 which exhibited high hydrophilicity in the absence of UV light irradiation. On the basis of the 3D capillary effect, Bico et al. proposed that the hydrophilicity of the film surface could be enhanced by the surface roughness.53 According to the mode, the porous surface was beneficial for the films to be hydrophilic. The thermally stable mesoporous TiO2 thin films presented here exhibited higher hydrophilicity than the traditional compact titania thin films (water contact angles, 50−60°).54−56 Except for the film annealed at 350 °C, the contact angles of the films calcined at higher temperatures became significantly decreased when they were illuminated by UV light for 5 min; especially, the film calcined at 500 °C exhibited the optimal photoinduced hydrophilicity. The contact angle was 9.5°, which might be due to the crystallite size range of 8−10 nm. Previous studies showed that the optimal crystallite size for the best photocatalytic activity was 8−10 nm .57,58 A smaller crystallite size favores the surface recombination, whereas larger crystallites exhibited low efficiency in surface recombination.59The increasing density of hydroxyl groups on the surface of the TiO2 thin film produced by UV light irradiation resulted in the improvement in hydrophilicity of the TiO2 thin film. In fact, the UV light photoinduced hydrophilicity resembled the 2D capillary phenomenon.60 Therefore, it can be concluded that the cooperation of 2D and 3D capillary effects resulted in the excellent hydrophilicity of the mesoporous TiO2 thin films. Furthermore, it is noticeable that the photoinduced hydrophilicity of the film calcined at 600 or 700 °C decreased somewhat compared with that of the sample calcined at 500 °C. This is probably due to the growth of the crystallites and the

(T − 298)]

⎤ 0.90De 2 − Dp2 ⎥⎦ /[πDp]

) ⎤ (T − 298)]}⎥⎦ )

− [1.91 − 1.48 × 10−4 /[kT (Dp + 0.67De)]

Using the data in Table 1 and eqs 22 and 23, the J value at different temperatures could be calculated, and the results are shown in Table 2. J was smaller than zero in the range of 450− Table 2. J Values and Other Parameters of the TiO2 Mesoporous Films Calcined at Different Temperatures T (°C)

Dp (nm)b

De (nm)b

γsurf

γinterf

J

350 450 500 600 700

4.8 7.8 7.5 7.4 7.6a

7.6 9.0 10.3 12.7 29.6

1.86 1.85 1.84 1.82 1.81

1.27 1.26 1.25 1.23 1.22