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Porous Structure of Silica Colloidal Crystals Andrey V. Galukhin, Dmitrii Bolmatenkov, Alina Emelianova, Ilya Zharov, and Gennady Y. Gor Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03476 • Publication Date (Web): 12 Jan 2019 Downloaded from http://pubs.acs.org on January 13, 2019
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Porous Structure of Silica Colloidal Crystals Andrey Galukhin,1,* Dmitrii Bolmatenkov,1 Alina Emelianova,2 Ilya Zharov,1,3,4 and Gennady Y. Gor2 1
Alexander Butlerov Institute of Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA 3 Department of Chemistry, University of Utah, 315 S 1400 E, Salt Lake City, UT 84112, USA 4 Department of Materials Science & Engineering, University of Utah, 122 Central Campus Dr., Salt Lake City, UT 84112, USA 2
ABSTRACT: We prepared silica colloidal crystals with different pore sizes using isothermal heating evaporation-induced self-assembly in quantities suitable for nitrogen porosimetry and studied their porous structure. We observed pores of two types in agreement with the description of silica colloidal crystals as fcc packed structure containing octahedral and tetrahedral voids. We calculated the sizes of these pores using Derjaguin-Broekhoff-de Boer theory of capillary condensation for spherical pores. We also described the pore geometry mathematically and showed that the octahedral pore radii measured experimentally matched closely the radii of the spheres of the same pore volume. In the case of the tetrahedral pores the proposed approach underestimated the pore radius by ca. 40%. Overall, this simple geometrical description provides good representation of the porous system in silica colloidal crystals.
INTRODUCTION Silica colloidal crystals comprise a lattice of micrometer- and sub-micrometer- sized silica spheres in a close-packed face-centered cubic (fcc) arrangement. Because of their regular structure and size range of the silica spheres, synthetic silica colloidal crystals provide useful templates for the preparation of various materials, such as photonic1 and magnetic materials,2 porous polymer membranes3 and sensors.4 More recently, the structural features of synthetic colloidal crystals, specifically their ordered three-dimensional system of interconnected voids,5 drew attention in the area of inorganic nanoporous materials. For example, sintered6,7 silica colloidal crystals were used as nanoporous membranes with size selectivity for the transport of synthetic macromolecules8 and proteins.9 Sintered colloidal crystals were also used as porous supports for catalytic metal nanoparticles.10,11 Silica colloidal crystals are prepared by a welldeveloped self-assembly process12 of silica spheres,13 leading to materials with void sizes variable in a broad (10100 nm) range. Therefore, silica colloidal crystals may find other important applications where nanoporous materials are critical, such as in studying nanoconfinement effect.14 However, such applications require to better define the pore size and pore size distribution of colloidal crystals. These characteristics affect diffusion permeability,15,16 adsorption and other properties related to mass-transfer and heattransfer17,18 in porous systems. Ideal colloidal crystals are packed into a fcc lattice (Figure 1A) containing two types of voids: the octahedral and tetrahedral ones, formed by six (Figure 1B) and four (Figure 1C) touching spheres, respectively. These two types of pores are arranged into an interconnected threedimensional porous system19 with total porosity of 0.2596.20
Previously, the pore size in silica colloidal crystals was estimated based on their filtration cut-off.8,9 Such characterization assumed that the molecular transport through colloidal crystals prepared by vertical deposition of silica spheres and used as membranes occurs normal to the [111] plane of the fcc-packed structure. Thus, diffusing species would enter the crystal through the concave triangular openings between the silica spheres and the size of these openings can be estimated as the distance from the
Figure 1. The unit cell of face-centered cubic lattice (A). Octahedral (B) and tetrahedral (C) voids (colored orange) found in the colloidal crystal.
center of their projection to the nearest sphere surface, which is ca. 15% of the silica sphere radius.15 The validity of this estimation was confirmed experimentally by studying the transport of different species through the silica colloidal crystals,8,21-23 and using simulations.24 However, such characterization results in limited description of the porous system, because the octahedral pores are much larger than the tetrahedral pores, and the latter ones solely determine the size selectivity of the colloidal crystals. Thus, for applications of silica colloidal crystals as three-dimensional porous materials, the dimensions of both tetrahedral and octahedral voids are of critical importance. These dimensions can be described using straightforward
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1:1, 3:1) and deionized water. The dried silica spheres were then calcined in a furnace at 600 °C for 12 hours, desired temperature was achieved at a heating rate of 60 °C×hour-1. Silica spheres with radii of 53 ± 3 nm were prepared using the same approach. In the first stage solution of 3.4 ml of TEOS in 60 ml of ethanol and 2.25 ml of ammonia hydroxide and 21.6 ml of water were used. Then 9.2 ml of ammonia hydroxide was added to 140 ml of seeds solution. In the second stage the solution of 2 M NH3, 13.5 M H2O was used; other conditions and isolation procedure were the same. Silica spheres with radii of 285 ± 13 nm were prepared by classical Stöber synthesis by hydrolysis of TEOS in ethanol in the presence of water and ammonia.13 The final concentrations in reaction mixture were 0.4 M TEOS, 0.8 M NH3, and 13.0 M H2O. Silica particles were isolated by centrifugation at 4 000 rpm and calcined as described above.
geometrical considerations (see below), but the relationship of these dimensions to the pores sizes of silica colloidal crystals determined experimentally, has not been previously investigated. Usually, pore size distribution (PSD) of porous solids are studied experimentally by gas adsorption techniques (nitrogen, argon).25 However, until recently silica colloidal crystals have not been synthesized in an appreciable quantity and a systematic analysis of gas adsorption has not been performed for these materials. In the present work, we describe the determination of characteristic pore sizes is silica colloidal crystals using nitrogen adsorption, discuss the theory applicable to the adsorption-desorption data interpretation, and compare the obtained results to the geometrical description of the voids in a closed-packed array of colloidal spheres.
Preparation and morphology examination of silica colloidal crystals. Silica colloidal crystals were prepared by
EXPERIMENTAL SECTION
modified vertical deposition method based on isothermal heating evaporation-induced self-assembly (IHEISA) method.5 Silica particles were dispersed in ethanol by sonication and glass beaker containing the dispersion was placed in a homemade setup at 79.8˚ С as described in ref. 5. Obtained colloidal crystals were carefully removed from the beaker’s walls and calcined at 800 ˚С for 12 hours, desired temperature was achieved at a heating rate of 300 °C per hour.
Materials. Ammonium hydroxide solution (25% of NH3, GOST 24147-80), tetraethylorthosilicate (TEOS, >99.9%, Aldrich, Inc.) were purchased and used without additional purification. Absolute ethanol was obtained by consecutive distillations of 96% ethanol over CaO and CaH2. Deionized water (18.2 MΩ) was obtained by Arium mini instrument (Sartorius). Transmission electron microscopy (TEM) images were obtained using Hitachi HT7700 Excellence. 10 µL of the silica particles suspension in ethanol were placed on a Formvar™/carbon coated 3 mm copper grid and dried at room temperature. After drying the grid was placed in a transmission electron microscope using special holder for microanalysis. Analysis was held at an accelerating voltage of 80 kV in TEM mode. The particles size was estimated by measuring 100 individual particles. Scanning electron microscopy (SEM) measurements were carried out using field-emission high-resolution scanning electron microscope Merlin Carl Zeiss. Observation photos of colloidal crystals’ surface were obtained at accelerating voltage of incident electrons of 15 kV and current probe of 300 pA. The particle size in colloidal crystals was estimated by measuring 100 individual particles. UP200Ht ultrasonic homogenizer was used for all sonications. MF48 centrifuge (AWEL) was used for all centrifugations. LOIP LF-7/11-G1 furnace was used for calcination and sintering.
Nitrogen adsorption and desorption measurements. Nitrogen adsorption and desorption measurements at 77 K were carried out with ASAP 2020 MP instrument (Micromeritics). Before measurements samples were degassed by heating at 200 °C under vacuum (8 µmHg) for 2 hours. Adsorption and desorption isotherms contained about 200 points for each colloidal crystal sample. Specific surface areas of the silica colloid crystal samples were determined by applying the Brunauer−Emmett−Teller (BET) equation in a range of 0.05-0.30 P/P0. Total pore volume of the colloidal crystal sample was measured at P/P0=0.999.
RESULTS AND DISCUSSION Preparation of silica colloidal crystals. To study the pore sizes of silica colloidal crystals by nitrogen adsorptiondesorption measurements, their pores radii have to be below 35 nm. Thus, colloidal crystals suitable for these measurements have to be assembled using silica spheres with radii smaller than 55 nm (See Geometrical description of the pore system in the ideally packed colloidal crystal in Supporting Information). The lower limit of silica spheres radii is restricted by synthetic approach we used to obtain silica nanoparticles: to obtain spherical silica nanoparticles by controlled growth technique26 the seed size have to be at least 4 times smaller than that of final particles.5 Since we used seeds of radii ca. 10 nm, the lower limit for our particles is ca. 40 nm. In addition, in order to enable nitrogen adsorption measurements using commerciallyavailable porosimeters, a substantial amount of the material is required (0.5-1 g). For our pore size characterization study, we prepared two colloidal crystal samples with pore sizes in the suitable range: the first one made of silica spheres with radii of 53 ± 3 nm (Sample 1) and second one (Sample 2) made of silica spheres with radii of 473 nm. In addition, we prepared a macroporous reference sample
Preparation and morphology examination of silica spheres. Silica spheres with radii of 47 ± 3 nm were prepared by two-step controllable growth technique based on regrowth of silica seeds.26 As a first step dispersion of seeds was prepared by mixing a solution of 4.5 mL (20 mmol) of TEOS in 80 ml of absolute ethanol with the solution of 3.0 mL (40 mmol) of ammonium hydroxide solution, 34 ml (1.9 mole) of deionized water in 80 mL of absolute ethanol. The reaction was carried out at 60 °C with mixing for 24 hours. Obtained dispersion contained approx. 20 nm sized silica nanoparticles (See Supporting Information, Figure S1). In the second step, 3.75 mL (46 mmol) of ammonium hydroxide solution was added to the 100 ml of obtained seeds dispersion and then two solutions (270 mL of 1.5 M solution of TEOS in ethanol and 270 mL of 1.2 M NH3, 16 M H2O solution in absolute ethanol) were dosed by MasterFlex peristaltic pump (ColeParmer) during 5 hours. The reaction was carried out at 60 °C with stirring for 24 hours. Silica particles were isolated by centrifugation (10 000 rpm) and washed consecutively with ethanol, water-ethanol solutions (water to ethanol ratios were 1:3, 2
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(referred below as Sample R) using silica spheres with radii of 285 ± 13 nm, which was used as a reference in pore size determination (see below). Due to the similarity of the Samples 1 and 2, detailed description on morphology in the article body is presented here only for Sample 1. The detailed information on the morphology and nitrogen adsorption measurements for Sample 2 can be found in Supporting Information (Figures S2 and S3). Because of the amount of material needed for adsorptiondesorption measurements, we used isothermal heating evaporation-induced self-assembly (IHEISA) method to prepare the colloidal crystal samples.5 Compared to the two common approaches used for the fabrication of colloidal crystals from silica spheres, namely sedimentation27,28 and conventional vertical deposition,29-31 this method is more reproducible and less time-consuming, allowing to obtain well-ordered colloidal crystals on a large scale. Figure 2 shows the morphology of the Sample 1 (A and B) and of Sample R (C and D) as imaged by SEM. The absence of macroscopic defects, e.g. cracks, can be seen in the low magnificaiton images. On the other hand, some microscopic defects can be detected on [111] plane of the Sample 1 crystal. These defects can be the result of higher diffusion mobility of small silica spheres (r = 533 nm) in colloidal dispersion, compared with large spheres (r = 28513 nm), which may interfere the crystal packing process.
In contrast, the adsorption-desorption isotherms from Sample R (Figure 3B) do not form hysteresis loop, which means large macropores of this colloidal crystal cannot be detected by nitrogen porosimetry and Sample R might be used as a “non-porous” reference sample. BET surface area of Sample R is 5.9 ± 0.1 m² g-1.
Figure 3. Nitrogen adsorption (red line) and desorption (blue dashed line) isotherms at 77 K and BET plots (insets) for Sample 1 (A) and Sample R (B).
The widely used methods for the analysis of the nitrogen adsorption isotherms, such as BJH (Barrett, Joyner, and Halenda)33 and DFT (density functional theory)32 appear not suitable for the silica colloid crystal samples considered in the current work. The BJH method is based on the cylindrical pore model, which does not capture the geometry of the pores formed by the silica sphere assembly. The DFT method, while suitable for pores of different geometries (slit, cylindrical and spherical) has another limitation: the upper limits of available DFT kernels do not allow to calculate the pore size distributions for samples with particularly large mesopores.34 Thus, we used an alternative method to calculate the pore sizes in silica colloidal crystals, based on the DerjaguinBroekhoff-de Boer (DBdB) theory of capillary condensation.35-37 The DBdB theory describes the
Figure 2. SEM image of [111] planes for Sample 1 (A-B) and Sample R (C-D). Scale bars as shown.
Experimental and theoretical study of the porous structure of silica colloidal crystals. Adsorption and desorption isotherms for Sample 1 are presented on Figure 3A. It shows a Type IVa isotherm, with H1-type hysteresis loop between the adsorption and desorption branches, typical for silica materials with large mesopores.32 BET surface area of the crystal is 31.2±0.2 m² g-1 and its total pore volume is 0.25 cm3 g-1, which yields porosity of 0.34 (using skeletal density of the silica of 2.09 g cm-3). The difference between this porosity and that of an ideal colloidal crystal can be attributed to the presence of packing defects. 3
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adsorption as a formation and growth of a liquid film on the pore wall surface, describing the interaction between adsorbed film and the solid surface in the form of disjoining pressure Π(h) introduced by Derjaguin.35 DBdB theory gives the following equation for the chemical potential of the adsorbed liquid film of the thickness h in a spherical pore of the radius R:
(
𝜇 = 𝑅𝑔𝑇𝑙𝑛(𝑝/𝑝0) = ― 𝛱(ℎ) +
unit mass of a sample 𝑛𝑎𝑑𝑠 to the thickness ℎ of the adsorbed liquid film as: ℎ=
𝑛𝑎𝑑𝑠𝑉𝓁 𝑆𝐴
(3)
The p/p0 values were recalculated to the Π(h), and the resulting dependence was fit to the Eq. 2, giving FHH parameters k = 47.22 and 𝑚 = 2.53. The result of the fit is shown in Figure S4. Note that these values slightly differ from the parameter values k = 44.54 and m = 2.241 for nitrogen adsorption on silica which are usually used in such calculations.42,43 Next, we applied the following procedure for both adsorption and desorption branches of the isotherm. Two points of pressure were chosen at a part of the isotherm corresponding to the phase transition: the first point at the beginning of the transition line and the second at the end. Then, the average of these two values was calculated. The pore radius giving the isotherm with the transition point approximately equal to the average pressure value was considered to be the average pore size (Figure 4). The resulting pore sizes calculated for the spherical pore model for Sample 1 are 35±7 nm for the adsorption branch and 27±3 nm for the desorption branch, and for Sample 2 they are 29±7 nm and 23±2 nm, respectively. These two sizes should correspond to the octahedral and tetrahedral voids in the colloidal crystal.
)
2𝛾 𝑉 (1) 𝑅―ℎ 𝓁
Here Rg is the gas constant, T is the absolute temperature, p and p0 are the vapor pressure and the saturation value of the vapor pressure, and Vl is the molar volume of adsorbed fluid (assumed to be the same as for the bulk liquid). Points of capillary condensation during adsorption and of evaporation during desorption are determined by a balance of capillary and disjoining pressures. Π(h) is often represented in the form of Frenkel-Halsey-Hill (FHH) equation:38-40 𝛱(ℎ) =
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𝑅𝑔𝑇
𝑘 (2) 𝑉𝓁 (ℎ/ℎ0)𝑚
where k and m are dimensionless parameters, h0 = 1 Å. Those parameters can be derived from the reference adsorption isotherm – an isotherm measured for a macroporous sample with the same surface chemistry. More details on the calculation of adsorption isotherm using DBdB theory, including the expressions for the characteristic points determining the hysteresis, can be found in refs. 41 and 42. Importantly, It was shown that for pores above 7-8 nm in diameter, the predictions of DBdB theory match those of DFT.43 Due to the packing of silica spheres which is close to the ideal fcc lattice, the porous system in silica colloidal crystal can be described as large octahedral pores interconnected by small tetrahedral pores (see Figure 1). Such pore geometry is vastly different from the widely used cylindrical pore model and is better described by the spherical pore model.34 Moreover, the pores form an interconnected network with two distinct pore sizes, therefore the hysteresis loop on the adsorption isotherm can be described by an ink-bottle model, where the capillary condensation transition on the adsorption branch is determined by the size of the body, while the capillary evaporation is related to the size of the throat.37 Based on these assumptions and the DBdB theory, we calculated the pore sizes using the characteristic points of the nitrogen adsorption and desorption isotherms. In order to perform the quantitative analysis of the adsorption isotherms for Samples 1 and 2 based on DBdB theory, the parameters for solid-fluid interactions are needed, which are derived from the reference isotherm. We used the adsorption isotherm measured for the macroporous Sample R as a reference isotherm and derived the FHH parameters. First, we recalculated the amount adsorbed per
Figure 4. Nitrogen adsorption and desorption isotherms for Sample 1 (markers) and model DBdB isotherms (lines) calculated for the sizes giving the best match to the adsorption and desorption branches.
Our comparison of the model isotherms to the experimental isotherms is based exclusively on the capillary condensation and evaporation points, and shows a mismatch of the amount adsorbed before the hysteresis region (Figure 4 and Figure S5). In both cases, the experimental amount adsorbed slightly exceeds the theoretical predictions. This is a result of the two factors: first, the volumes of an octahedral and a tetrahedral pore obviously differ from the volume of the spherical pore. The concave “corners” of those pores would fill at relatively 4
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low vapor pressures, contributing to the amount adsorbed. Second, each of the theoretical isotherms represents one type of the pore. However, the experimental amount adsorbed is a result of the adsorption in the entire system of pores. Even an ideal fcc lattice provides a bimodal pore-size distribution; a lattice with defects would mean even more complex PSD. In order to get a match for the amount adsorbed in the entire range of vapor pressures, one would need to take into account the peculiarities of the pore geometries and the PSD, which is beyond the scope of this paper. One way to describe the pore size in colloidal crystal is by using the radii of spheres that fit inside octahedral and tetrahedral voids of a close-packed face-centered cubic (fcc) lattice of hard spheres. In this interpretation, the pore radius is 0.414 and 0.225 of the sphere radius for octahedral and tetrahedral pores, respectively. For Sample 1 these radii are ~22 and ~12 nm, and for Sample 2 they are ~19 and ~11 nm, significantly different compared to the values obtained from adsorption-desorption measurements. Thus, we
compared the experimentally measured pore sizes and the geometry of the voids in more detail. While the shapes of pores in colloidal crystal are quite complex, their volumes (Vp) can be expressed mathematically quite easily (See Geometrical description of the pore system in the ideally packed colloidal crystal in Supporting Information). Thus, we propose to use the radii of the spheres with volumes Vp as the size of the corresponding pores in the colloidal crystal (Equation 4). 3
4𝜋(𝑟𝑒𝑞) = 𝑉𝑝 (4) 3 Table 1 groups main calculated parameters of porous system of unit cell of close packed fcc array consisting of spheres with radii of r, namely volumes of octahedral and 𝑒𝑞 tetrahedral pores (Vo, Vt), their equivalent radii (𝑟𝑒𝑞 𝑜 , 𝑟𝑡 ), total free volume of the unit cell (Vfree), octahedral (𝜌𝑜), tetrahedral (𝜌𝑡) and total porosity (ρ), as well as their percentages (%𝑜 and %𝑡).
Table 1. Parameters of porous system of unit cell of close packed fcc array consisting of spheres with radii of r. Vo
Vt
𝑟𝑒𝑞 𝑜
𝑟𝑒𝑞 𝑡
Vfree
ρ
𝜌𝑜
𝜌𝑡
%𝑜
%𝑡
1.053r3
0.208r3
0.631r
0.368r
5.872r3
0.2596
0.1861
0.0735
71.7
28.3
spherical pores. We also described the pore geometry mathematically and showed that the octahedral pore radii measured experimentally matched closely the radii of the spheres of the same pore volume. In the case of the tetrahedral pores the proposed approach underestimated the pore radius by ca. 40%. Overall, this simple geometrical description provides good representation of the porous system in silica colloidal crystals. Further increase in accuracy might be reached by using models accounting for the exact shapes of the pores in the crystal. We hope our study will motivate the creation of DFT kernels suitable for the geometries more complex than the commonly used slit, cylinder and sphere models.
Table 2. Measured and calculated octahedral and tetrahedral pore radii (spherical shape model) for Samples 1 and 2. Sample
𝑟𝐷𝐵𝑑𝐵 , nm 𝑜
𝑟𝐷𝐵𝑑𝐵 , nm 𝑡
𝑟𝑒𝑞 𝑜 , nm
𝑟𝑒𝑞 𝑡 , nm
1
35±7
27±3
33
19
2
29±7
23±2
30
17
Next, we compared the experimentally found and the calculated pore sizes for Samples 1 and 2 (Table 2). It is clear that experimentally measured octahedral pore sizes match closely the theoretical values for both samples. However, the effective pore radii of tetrahedral pores are somewhat smaller than the experimental values for both samples. The possible reason of such discrepancy is that the octahedral pores possess more symmetry than tetrahedral pore, and thus can be more precisely described by the sphere model.
AUTHOR INFORMATION * Corresponding Author. E-mail:
[email protected].
ACKNOWLEDGMENT This work was supported by the Russian Science Foundation (Project № 18-13-00149). AG thanks Dr. Yuri Osin (Kazan Federal University, Interdisciplinary Center for Analytical Microscopy) for SEM measurements.
CONCLUSIONS We prepared silica colloidal crystals with different pore sizes and studied their porous structure using nitrogen porosimetry. We observed pores of two types in agreement with the description of silica colloidal crystals as fcc packed structure containing octahedral and tetrahedral pores. The sizes of these pores were calculated using DerjaguinBroekhoff-de Boer theory of capillary condensation for
ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. 5
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TEM image of silica seeds (Figure S1); SEM image of Sample 2 (Figure S2); nitrogen adsorption and desorption isotherms at 77 K and BET plots for Sample 2 (Figure S3); Fit of experimental adsorption data for Sample R to FHH equation (Figure S4); Comparison of nitrogen adsorption and desorption isotherms for Sample 2 and model DBdB isotherms (Figure S5); Detailed geometrical description of the pore system in ideally packed colloidal crystal and derivation of main equations. (PDF)
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TOC Graphic
Porous Structure of Silica Colloidal Crystals Andrey Galukhin,1,* Dmitrii Bolmatenkov,1 Alina Emelianova,2 Ilya Zharov,1,3,4 and Gennady Y. Gor2
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