Pore Size Distribution Analysis of Mesoporous TiO2 Spheres by 1H

Sep 21, 2010 - Pore Size Distribution Analysis of Mesoporous TiO2 Spheres by 1H .... by the factor T/T0, where T0 = 280 K and T is the actual temperat...
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J. Phys. Chem. C 2010, 114, 17440–17445

Pore Size Distribution Analysis of Mesoporous TiO2 Spheres by 1H Nuclear Magnetic Resonance (NMR) Cryoporometry Su-Yeol Ryu, Dong Suk Kim, Jae-Deok Jeon, and Seung-Yeop Kwak* Department of Materials Science and Engineering, Seoul National UniVersity, 599 Gwanak-ro, Gwanak-gu, Seoul 151-744, Korea ReceiVed: June 15, 2010; ReVised Manuscript ReceiVed: September 6, 2010

Mesoporous TiO2 spheres with various pore sizes were prepared by varying the calcination temperature in the range of 300-700 °C. Increasing calcination temperature was found to increase the crystal size, decrease the surface area, and increase the pore size. The morphologies of mesoporous TiO2 spheres consist of welldefined spherical shapes of monodisperse sizes near 0.8 µm. To determine the pore size distributions (PSDs) of these mesoporous TiO2 spheres, 1H nuclear magnetic resonance (NMR) cryoporometry and BarrettJoyner-Halenda (BJH) analysis were conducted. NMR cryoporometry is based on the theory of the melting point depression (MPD) of a probe molecule confined within a pore, which is dependent on the pore diameter. MPD was determined by analyzing the variation of the NMR spin-echo intensity with temperature. From the resulting spin-echo intensity versus temperature (I-T) curves, it was found that the maximum MPD of a probe molecule confined within the pores of mesoporous TiO2 decreases with increasing calcination temperature; that is, the pore size increases with increasing calcination temperature. Because mesoporous TiO2 spheres consist of aggregates of nanocrystallite TiO2 and mesopores located at intercrystallites, an increase in the calcination temperature induces an increase in the crystallite size and, thus, in the pore size because the small pores collapse and the large pores increase in size. We also confirmed by BJH analysis that the pore size of mesoporous TiO2 increases with increasing calcination temperature. This trend is in agreement with our 1H NMR cryoporometry results. Overall, these findings indicate that NMR cryoporometry is a very effective method for determining the PSDs of mesoporous TiO2 spheres. Introduction Titanium dioxide (TiO2) exhibits useful electrical, optical, and photocatalytic behavior because of the powerful oxidation and reduction properties that arise in it as a result of the absorption of photon energy.1-3 These properties mean that TiO2 is useful in environmental remediation processes such as water and air purification, stain prevention, and sterilization.4,5 Mesoporous TiO2 is expected to exhibit outstanding photodegradation properties, because a TiO2 sample with a large surface area has many active sites, so substances can be adsorbed in large quantities onto the surface, and its porosity then facilitates pollutant access, adsorption, and decomposition.6-9 Thus, when developing a mesoporous TiO2 material for a sorption process, it is of prime importance to determine the size and size distribution of its pores as accurately as possible. In addition, smaller pores have better photocatalytic activity because the adsorption of substances onto the active sites of their walls is enhanced, so photocatalysts with small pore sizes decompose adsorbed substances more readily and effectively.10 Therefore, the precise measurement of the pore sizes and the pore size distributions of mesoporous TiO2 is a matter of great importance. Porous materials can be investigated with a variety of experimental techniques, including microscopic observation, the bubble pressure method, mercury intrusion porosimetry, permporometry, N2 adsorption-desorption, nuclear magnetic resonance (NMR) cryoporometry, NMR relaxometry, and differential scanning calorimetry (DSC) thermoporometry.11-21 These methods vary widely in applicability and sensitivity, as well as * Corresponding author. Tel.: +82-2-880-8365. Fax: +82-2-885-1748. E-mail: [email protected].

in the type of information that they yield. Because of the general complexity of three-dimensional porous networks, it is advantageous to combine several experimental techniques in the characterization of porous materials; the use of these techniques in combination can provide more information about pore structure than any single technique. During the past few years, 1H NMR cryoporometry, has been used by Strange et al.,22 Hansen et al.,23 and Petrov et al.24 to determine the pore size distributions (PSDs) of porous materials. This method determines the melting point depression (MPD), ∆Tm, of materials confined within the pores of the porous material. The theoretical basis of PSD analysis determined by MPD is the Gibbs-Thomson equation.21,24-27 This equation states that the difference between the bulk and depressed melting temperatures is inversely proportional to the linear dimension of the liquid confined within the pores. Strange et al.22 determined the PSDs of a variety of porous silicas using cyclohexane as the probe molecule. They found that the sensitivity of cyclohexane in these materials is approximately 3 times greater than that of water. However, when cyclohexane was used as a probe molecule, the PSDs of the porous materials could not be accurately determined because of differences in the magnetic susceptibility effects between the matrix and liquid as a function of temperature. Allen et al.28 determined the MPDs of cyclohexane confined within porous materials by using a spin-echo pulse sequence (90°-τ-180°-τ-echo). They found that pore susceptibility differences could be ignored when a spin-echo pulse sequence was used. With a pulse separation time of τ, the spin-echo intensity, I, from the liquid phase of cyclohexane confined within the pores was obtained as a

10.1021/jp105496h  2010 American Chemical Society Published on Web 09/21/2010

Pore Size Distributions of Mesoporous TiO2 Spheres function of temperature. The cyclohexane outside the sample behaves as bulk cyclohexane and provides a reference point for the changes in melting temperature arising from confinement. Using this technique, cryoporometry has been successfully applied to various porous materials, including uniform and nanoporous materials such as glasses, silica gels, sandstones, and membranes.17,21,22,24,29-32 In the present study, the main objective was to measure the PSDs of mesoporous TiO2 spheres by 1H NMR cryoporometry and Barrett-Joyner-Halenda (BJH) analysis. The latter technique was used to provide additional information about the PSDs of the mesoporous TiO2 spheres. We investigated five different sets of mesoporous TiO2 spheres with different calcination temperatures. The pore sizes and pore size distributions of mesoporous TiO2 spheres can be varied by altering the calcination temperature because of the resulting variation in the crystal size. The detailed results of this approach are presented and discussed herein. Experimental Section Materials. Titanium(IV) isopropoxide [TTIP, Ti(OPri)4], poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) (average MW ) 14600), 2,4-pentanedione (acetylacetone, AcAc), and cyclohexane were all purchased from Sigma-Aldrich and used as received without further purification. Other chemicals were of reagent grade, and highly deionized water with a resistivity of greater than 18.0 MΩ cm-1 was used throughout the experiments. Preparation of Mesoporous TiO2 Spheres. Mesoporous TiO2 spheres were synthesized by the sol-gel method using poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide), EO130PO60EO130 (Pluronic F108), as a triblock copolymer surfactant and titanium(IV) isopropoxide [Ti(OPri)4] mixed with 2,4-pentanedione (AcAc) in aqueous solution. In a typical eperiment, 14.6 g (1 mmol) of the surfactant was dissolved in 100 mL of deionized water at 40 °C. After the surfactant had dissolved sufficiently, 1.5 g (15.3 mmol) of sulfuric acid was added to the aqueous surfactant solution. Titanium(IV) isopropoxide (7.84 g, 27.6 mmol) was mixed with 2,4-pentanedione (2.76 g, 27.6 mmol) in a separate beaker and dropped slowly into the surfactant aqueous solution with vigorous stirring. The reaction was then carried out at 55 °C for 10 h without stirring. At first, there was no precipitation, but after several minutes, a light yellow powder was obtained. The resulting materials were treated hydrothermally at 90 °C for 10 h without stirring. The resulting powders were collected by filtration and thoroughly washed several times with deionized water and ethanol. To eliminate the residual surfactant, the powders were calcined at 300, 400, 500, 600, and 700 °C (the rate of temperature increase was 1 °C min-1) in air. In this article, MTx denotes a mesoporous TiO2 sphere calcined at x °C. Characterization. The surface features and morphologies of the MTx materials were investigated using field-emission scanning electron microscopy (FE-SEM, JEOL JSM-6330F) and high-resolution transmission electron microscopy (HR-TEM, JEOL JEM-2000 FX II). The crystallite structures of the MTx samples synthesized at the various calcination temperatures were investigated by analyzing the wide-angle X-ray diffraction (XRD) patterns obtained with a MAC/Sci MXP 18XHF-22SRA diffractometer equipped with a Cu KR radiation source (λ ) 0.514 nm) and a fixed power source (40 kV, 200 mA) at a step width of 0.02°. The crystallite sizes were calculated according to the Scherrer equation (Φ ) Kλ/β cos θ), where Φ is the

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17441 crystallite size, λ is 0.154 nm (the wavelength of the X-ray radiation), K is usually assumed to be 0.89, β is the full width at half-maximum intensity (fwhm), and θ is the diffraction angle of the (101) peak for anatase (2θ ) 25.3°). 1 H NMR cryoporometry was carried out on a Bruker mq20 spectrometer at 0.47 T and 19.95 MHz resonance frequency. The measurements for each MTx sample were performed over the temperature range from 200 to 285 K at an interval of 1 K using a Bruker BVT-3000 temperature control unit. During these measurements, the monitored temperature usually remained within (0.1 K of the target temperature. To prevent complications associated with supercooling or hysteresis, all measurements were recorded by increasing the temperature from a low initial temperature. Deionized water and cyclohexane were used as probe molecules in this study. Each MTx sample containing confined probe molecules was initially cooled to 200 K by using liquid nitrogen for complete freezing of the probe molecules confined within the pores of MTx. Then, the sample was warmed slowly while the NMR spin-echo intensities from the liquid phase of confined probe molecules were continuously measured until the confined probe molecules had completely melted. At each new temperature, the sample was allowed to equilibrate for at least 10 min before any measurements were obtained. All measurements were performed using a spin-echo pulse (90°-τ-180°-τ-echo) with a 90° pulse length of 2.14 µs and a 180° pulse length of 4.28 µs. The spin-echo amplitude was measured with a pulse separation time, τ, of 10 ms to ensure that the spin-echo signal was entirely due to the liquid-phase probe molecule. Because the nuclear magnetic transverse or spin-spin relaxation time (T2) of a frozen probe molecule is typically short, whereas the corresponding relaxation time of a liquid-phase probe molecule is long, only the liquid-phase probe molecule was detected. The NMR spin-echo intensity was corrected for temperature by implementing Curie’s law; that is, the observed signal intensity was multiplied by the factor T/T0, where T0 ) 280 K and T is the actual temperature. In addition, the specific surface areas and pore size distributions of the MTx samples were characterized by analyzing the N2 adsorption and desorption isotherms obtained at 77 K using a Micrometrics ASAP 2000 instrument. All of the MTx samples were degassed at 200 °C and 10-6 Torr for 10 h prior to these measurements. The surface areas were calculated according to the Brunauer-Emmett-Teller (BET) equation, and the poresize distributions were determined from the adsorption and desorption branches using the Barrett-Joyner-Halenda (BJH) formula. Results and Discussion Synthesis of Mesoporous TiO2 Spheres. A series of experiments were performed to find optimal conditions for the synthesis of mesoporous TiO2 spheres: concentration of surfactant (EO130PO60EO130, Pluronic F108) in deionized water, molar ratio of surfactant to titanium precursor [Ti(OPri)4], concentration of sulfuric acid, and reaction temperature. In varying molar ratios of surfactant to titanium precursor, the range between 1:20 and 1:60 was adequate to synthesize powders. The concentration of sulfuric acid ranging from 0.05 to 0.3 M was suitable to obtain the powder. A reaction temperature of at least 55 °C was good for the synthesis of powder. When the reaction temperature was decreased to below 40 °C, a lower yield of powder was obtained. The optimal conditions for the synthesis of mesoporous TiO2 spheres were found to be 14.6 wt % of the surfactant in deionized water, a molar ratio of surfactant to titanium precursor of about 1:30, a sulfuric acid

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Figure 1. Mechanism for the synthesis of mesoporous TiO2 spheres.

Figure 2. (a,b) FE-SEM images of MT400, (c) magnified FE-SEM image of a selected area of one particle, (d) HR-TEM image of mesoporous TiO2.

concentration of 0.15 M, and a temperature of 55 °C, as described in the Experimental Section. The surfactant forms micelles in the aqueous solution at 40 °C, because the PO block is more hydrophobic than the EO block under these conditions. Modified titanium precursor Ti(OPri)3AcAc formed from the titanium(IV) isopropoxide [Ti(OPri)4] and 2,4-pentanedione (AcAc) in a 1:1 molar ratio.33,34 When the Ti(OPri)3AcAc is dissolved in aqueous micelle solution, TiO2 nanoparticles slowly form through the hydrolysis of the Ti(OPri)3AcAc. TiO2 nanoparticles can be formed only at the EO block because the interactions between the hydroxyl groups of the TiO2 nanoparticles and the ether groups of the EO block can be attributed to hydrogen bonding.35-37 Continuous hydrolysis and condensation of the Ti(OPri)3AcAc leads to the growth of larger TiO2 nanoparticles. As the TiO2 nanoparticles continuously aggregate, the TiO2 particles form spheres. Finally, well-defined mesoporous TiO2 spheres are obtained by hydrothermal and calcination treatment (Figure 1). Characteristics of the Mesoporous TiO2 Spheres. Figure 2 shows the FE-SEM and HR-TEM images of MT400. The particles all have spherical morphologies with a diameter of 0.8 µm, as shown in Figure 2a. Figure 2b shows that the particles

Ryu et al. have a well-defined spherical shape and that they are well separated from each other; further, pores can be seen. Figure 2c shows a magnified image of one particle of mesoporous TiO2, in which the pores between the nanosized TiO2 primary particles are apparent. The pore structure consists of a wormhole-like pore array, and the wall of the mesoporous framework consists of aggregated TiO2 nanoparticles with a size of approximately 10 nm. A wormhole-like pore structure is also evident in the HR-TEM image shown in Figure 2d. The disordered channels are packed randomly and form a three-dimensional mesoporous framework; this result is consistent with the FE-SEM images. Spherical nanocrystalline particles with a size of approximately 10 nm are aggregated together, resulting in pore walls with disordered shapes, and this result is also consistent with the FE-SEM images. The sizes and morphologies of the other calcined samples (MT300, MT500, MT600, and MT700) are similar; however, the specific surface area and crystallite size vary with the calcination temperature. The surface areas gradually decrease with increasing calcination temperature. Figure S1 (Supporting Information) shows the BrunauerEmmett-Teller (BET) analyses for MT300, MT400, MT500, MT600, and MT700. The surface areas were found to be 337 m2 g-1 (MT300), 255 m2 g-1 (MT400), 177 m2 g-1 (MT500), 128 m2 g-1 (MT600), and 89 m2 g-1 (MT700); the surface areas decrease with increasing calcination temperature because of the resulting increases in crystallite size. To confirm that the crystallite size increases with increasing calcination temperature, the wide-angle X-ray diffraction (XRD) patterns of the samples were obtained. Figure S2 (Supporting Information) shows the X-ray diffraction peaks of MT300, MT400, MT500, MT600, and MT700. All of the samples have anatase structures. The average crystallite sizes (as shown in Table S1, Supporting Information) were calculated from the anatase peak (101) according to the Scherrer equation and found to be 6.0 nm (MT300), 6.7 nm (MT400), 7.5 nm (MT500), 10.6 nm (MT600), and 19.2 nm (MT700). These increases in crystallite size induce decreases in surface area and increases in pore size.6,7 To quantify the changes in pore size and pore size distributions (PSD), 1H NMR cryoporometry and BJH analysis were carried out. 1 H NMR Cryoporometry. The theoretical basis of PSD analysis determined by MPD is the Gibbs-Thomson equation,26 which describes the MPD of a liquid-phase probe molecule confined within a small pore, ∆Tm(D), as follows

∆Tm(D) ) Tm - Tm(D) )

4σslTm K ) D∆HfFs D

(1)

where σsl is the surface energy at the solid-liquid interface, Tm is the normal (bulk) melting point (280 K for cyclohexane) of the bulk material, Tm(D) is the melting point of the confined solid-phase probe molecule of dimension D, ∆Hf is the bulk enthalpy of fusion, Fs is the mass density of the crystalline solidphase probe molecule, and K is a constant depending solely on the physical properties of the liquid-phase probe molecule confined within the porous material. The value of K is a reliable indicator of its resolution to pore size. A larger K value means a larger melting point depression. Provided that K is known, the PSD can be estimated from measurements of the amount of liquid-phase probe molecule confined within the pores as a function of temperature. This equation indicates that the difference between the normal and depressed melting temperatures is inversely proportional to the linear dimension of the

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liquid-phase probe molecule confined within the pores. The spin-echo intensity provides a measure of the amount of probe molecules confined within the pores, V, that is in the liquid phase at a particular temperature T and, thus, of the volume of the pores that have a linear dimension equal to the pore diameter, D, in eq 1. The volume of the pores with pore diameters between D and D + ∆D is (dV/dD)∆D. If the pores are filled with liquidphase probe molecules, the PSD (dV/dD) can be determined from the derivative of the intensity-temperature (I-T) curve, given by

dI dV dV dTm(D) ) ) dD dD dTm(D) dD

(2)

From eq 1, dTm(D)/dD ) K/D2, and hence, eq 2 can be rewritten as

dV K dV ) 2 dD D dTm(D)

(3)

Thus, provided that K is known for the probe molecule, the PSD function can be determined from measurements of dV/ dTm(D). 1 H NMR cryoporometry was used to measure the volume of liquid-phase probe molecules confined within the pores as a function of temperature and thus to determine the PSDs of the MTx materials. The spin-spin relaxation time, T2, of a liquidphase probe molecule is easily distinguishable from that of a solid-phase probe molecule, because the liquid has a characteristically long T2 value, on the order of milliseconds, whereas the solid usually has a very short T2 value, on the order of microseconds. 1H NMR cryoporometry was performed using a spin-echo pulse sequence (90°-τ-180°-τ-echo). The 90° x pulse shifts the spins onto the y axis, where they start to recover but dephase during the experiment. After a pulse separation time of τ, the spins have dephased in the x-y plane. Applying a 180° y pulse rotates the spins about the y axis, causing them to rephase. The maximum signal is then measured at 2τ. This is known as a spin-echo, and the height of the echo is directly dependent on the volume of liquid-phase probe molecule in the sample. For a spin-echo pulse (90°-τ-180°-τ-echo), proper choice of τ is crucial. Petrov et al. studied the effect of the relaxation delay (∆ ) 2τ) on the NMR spin-echo intensity, I, and determined that using overly long values of relaxation delay resulted in a PSD skewed toward larger pores.24 In this study, the spin-echo amplitude was measured at time intervals τ of 10 ms (shorter than the T2 value of the liquid and longer than that of solid) to ensure that the spin-echo signal was entirely due to the liquid-phase probe molecule. This signal amplitude was measured as a function of temperature and should be proportional to the volume of the liquid-phase probe molecule confined within the pores of the samples. We used deionized water and cyclohexane as probe molecules. Deionized water is easily confined within hydrophilic pores. It has a much lower K value, for which K is approximately 50 K nm.39,42 Concerning damage to the pores, water expands upon freezing, and hence, freezing of the water confined within the pores could damage the pore structures over repeated freezing-melting cycles.28,39 On the other hand, Petrov et al. determined that such damage was not detected for nonrepeated freezing-melting cycles.43 In this work, when deionized water was used as the probe molecule at the beginning, water was

Figure 3. Relative NMR spin-echo intensities vs temperature (I-T curves) for cyclohexane confined within the pores of the MTx samples.

not confined in the pores of the MTx samples. The PSD curve of the non-UV-illuminated MT700, which was expected to have the largest pores among the MTx series, showed that its NMR spin-echo intensity was very weak and unreliable (as shown in Figure S3, Supporting Information). This means that water did not penetrate into the pores of non-UV-illuminated MT700. Because the surface of the MTx samples was contaminated by adsorbing some contaminants during calcination, the surface changed from hydrophilic to hydrophobic.44 To change the surface characteristics from hydrophobic to hydrophilic, the MT700 sample was illuminated by UV light for 1 day. After UV illumination, water was completely confined within pores of the MT700. For pores of diameter D ) 15 nm, water (K ) 50 K nm) provides a size resolution of about 4 nm in 1 K temperature interval (as shown in Figure S3, Supporting Information). Cyclohexane was also used as a probe molecule, because it has one of the highest K values, at approximately 178 K nm.40 It is an organic compound that comprises a ring molecule with a 6-fold-symmetrical structure.41 It is liquid at room temperature but forms a soft plastic crystalline phase below its melting point (approximately 280 K) that is less likely to damage the pore structures.42 The soft plastic crystalline phase is consisted of a rotationally disordered fcc lattice based on the random orientation of the molecules.30,38 To confine the cyclohexane in the pores completely, the MT700 samples were stored in a dark room for 7 days. Cyclohexane (K ) 178 K nm) provides a size resolution of about 1.5 nm in 1 K temperature intervals for pores of diameter D ) 15 nm (as shown in Figure 4, below). In our work, which was performed with an interval of 1 K temperature control, cyclohexane as the probe molecule was more appropriate for analyzing the pores that were several tens of nanometers in size because of the much larger K value, which means a larger melting point depression. Thus, cyclohexane was mainly used as the probe molecule. Figure 3 shows the NMR spin-echo intensity versus temperature (I-T) for cyclohexane confined within the pores of the MTx materials. For each sample, two separate melting peaks were observed: one at 280 K, corresponding to the melting of bulk cyclohexane between the powder grains, and one at lower temperatures, associated with the melting of cyclohexane confined within the pores of the MTx samples. These I-T curves show that the signal intensity increases smoothly as the temperature is increased from 210 to 285 K, consistent with the gradual melting of the frozen cyclohexane confined within the pores of the MTx samples. There is a marked difference

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TABLE 1: 1H NMR Cryoporometry and BJH Analysis Data for the MTx Materials 1

H NMR cryoporometry

BJH analysis of the desorption branch

sample

maximum melting point depression (K)

pore size distributiona (nm)

pore size distributionb (nm)

MT300 MT400 MT500 MT600 MT700

34 31 28 20 16

5.0-8.2 5.9-9.5 7.0-11.5 9.1-14.8 12.7-16.9

5.8-8.5 6.8-9.7 7.1-10.3 8.8-12.3 14.5-19.2

a Data obtained from the full width at half-maximum height (fwhm) in Figure 4. b Data obtained from the full width at half-maximum height (fwhm) in Figure 5.

Figure 5. Pore size distribution curves of the MTx samples obtained by BJH analysis from the desorption branches.

Figure 4. Pore size distribution curves of the MTx samples determined by 1H NMR cryoporometry.

between the signal intensities of the solid and liquid phases: the pure solid and liquid phases have relative signal intensities of 0 and 1, respectively. The I-T curves additionally confirm that the minimum melting points of cyclohexane confined within the pores of the MTx materials shift to lower temperatures with decreasing calcination temperature. The melting point depressions (MPDs) were determined from plots of dI/dT or dV/dT as a function of temperature, which were generated from the I-T curves. The maximum MPDs were estimated for each system from the difference between the minimum and normal melting points of cyclohexane confined within the pores of the MTx samples and are listed in Table 1. The maximum MPDs of the MTx materials decrease with increasing calcination temperature. Equation 1 indicates that the MPDs are inversely proportional to the linear dimension of the pore diameter. If the amount of cyclohexane confined within the pores of the MTx materials and the value of K are known, the PSDs can be estimated using eq 3. We assumed that, for cyclohexane, K ) 178 K nm to obtain the PSDs of the MTx materials.39 Figure 4 shows PSDs of the MTx samples obtained with 1H NMR cryoporometry. The pore sizes of the MTx samples increase with increasing calcination temperature (i.e., in the sequence MT300 < MT400 < MT500 < MT600 < MT700) in the range of 5-17 nm, as listed in Table 1. This trend is due to the increased crystal growth of the TiO2 nanoparticles and the aggregation of small pores that result from calcination at a higher temperature, and so the surface area decreases and the pore size increases.6,7 Overall, these results show that 1H NMR cry-

oporometry can be used to determine the PSDs of MTx materials with pores ranging from a few nanometers to tens of nanometers. These results are in partial similarity with previous findings reported by Vargas-Florencia et al.45 and Hansen et al.46 for other porous TiO2 and SiO2 materials, because those materials were essentially particle packs. However, this study has two distinctions compared to previous studies: selection of the proper probe molecule by considering the surface characteristics of the MTx material and the PSD determination of the MTx materials with wide pore size distributions using the chosen probe molecule. BJH Analysis. BJH analysis was used to determine the PSDs of the MTx samples by analyzing the variations of their N2 adsorption and desorption isotherms with calcination temperature. Figure S4 (Supporting Information) and Figure 5 show the PSDs of the MTx samples obtained by the BJH method from the adsorption and desorption branches. For all MTx samples, the pore size distribution obtained from the adsorption branch was found to be broader than that obtained from the desorption branch, as shown in Figure S4 (Supporting Information) and Figure 5, and the pore size obtained from the adsorption branch was found to be larger than that obtained from the desorption branch, as shown in Table S2 (Supporting Information) and Table 1. The results for the pore size distributions obtained from the desorption branches are similar to those obtained with 1H NMR cryoporometry. The PSD is calculated according to BJH analysis with the modified Kelvin equation. The Kelvin equation can be used to predict the pressure at which an adsorbed species will spontaneously condense and evaporate in a cylindrical pore of a given size. Condensation occurs in pores that already have some multilayer adsorption on the walls. The pore size can then be calculated from the Kelvin equation, and the selected statistical thickness (t-curve) equation. 1H NMR cryoporometry uses the differences between the solid and liquid phases of the probe molecule confined within the pores. Therefore, the PSDs obtained by BJH analysis and 1H NMR cryoporometry are expected to be somewhat different, as found in our measurements, but the variations of the PSD with calcination temperature obtained by the two methods are very similar. Furthermore, because the photocatalytic applications of mesoporous TiO2 spheres are usually in liquid solution, we believe that the PSD relevant to experimental conditions can be obtained with 1H NMR cryoporometry.

Pore Size Distributions of Mesoporous TiO2 Spheres Conclusions Monodisperse mesoporous TiO2 spheres were successfully synthesized with a sol-gel method from a mixture of a triblock copolymer and a titanium precursor in aqueous solution. The synthesized mesoporous TiO2 spheres had well-defined morphologies with particle sizes of approximately 0.8 µm. As the calcination temperature was increased, the surface areas decreased, the crystallite sizes increased, and so the pore sizes increased. To precisely investigate the pore sizes and pore size distributions of these samples, we conducted 1H nuclear magnetic resonance (NMR) cryoporometry and BarrettJoyner-Halenda (BJH) analysis. 1H NMR cryoporometry was carried out with a spin-echo pulse sequence (90°-τ-180°τ-echo) of the signal intensities, I, which were directly proportional to the nonfrozen volume fraction of the probe molecule confined within the pores, as a function of temperature, T. From the NMR spin-echo intensity versus temperature (I-T) curves, it was determined that the pore sizes of the mesoporous TiO2 spheres increased with increasing calcination temperature in the range of 5-17 nm (i.e., in the order MT300 < MT400 < MT500 < MT600 < MT700). The BJH analysis confirmed that the pore sizes of the mesoporous TiO2 spheres increased with increasing calcination temperature. This trend is in agreement with the results obtained with 1H NMR cryoporometry and is probably due to the increase in crystal growth of TiO2 nanoparticles during calcination at a higher temperature, which results in the aggregation of small pores, so that the surface area decreases and the pore size increases. In conclusion, 1H NMR cryoporometry provides an effective method for determining the PSDs of mesoporous TiO2 spheres. Acknowledgment. This research was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education, Science and Technology (R11-2005-065). SupportingInformationAvailable: N2 adsorption-desorption isotherms, XRD patterns, PSD curves obtained by the 1H NMR cryoporometry and BJH analysis from the adsorption branch, and crystallite size of the MTx materials as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Lu, Y.; Fan, H.; Stump, A.; Ward, T. L.; Rieker, T.; Brinker, C. J. Nature 1999, 398, 223–226. (2) Yi, G.-R.; Moon, J. H.; Manoharan, V. N.; Pine, D. J.; Yang, S.M. J. Am. Chem. Soc. 2002, 124, 13354–13355. (3) Eiden-Assmann, S.; Widoniak, J.; Maret, G. Chem. Mater. 2004, 16, 6–11. (4) Fujii, H.; Ohtaki, M.; Eguchi, K. J. Am. Chem. Soc. 1998, 120, 6832–6833. (5) Schattka, J. H.; Shchukin, D. G.; Jia, J.; Antonietti, M.; Caruso, R. A. Chem. Mater. 2002, 14, 5103–5108. (6) Peng, T.; Zhao, D.; Dai, K.; Shi, W.; Hirao, K. J. Phys. Chem. B 2005, 109, 4947–4952. (7) Kim, D. S.; Kwak, S.-Y. Appl. Catal. A 2007, 323, 110–118. (8) Cassiers, K.; Linssen, T.; Mathieu, M.; Bai, Y. Q.; Zhu, H. Y.; Cool, P.; Vansant, E. F. J. Phys. Chem. B 2004, 108, 3713–3721. (9) Sakatani, Y.; Grosso, D.; Nicole, L.; Boissie`re, C.; Soler-Illia, G. J. de A. A.; Sanchez, C. J. Mater. Chem. 2006, 16, 77–82.

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