Positron annihilation and N₂ adsorption for nanopore determination in silica-polymer composites

Abstract

Silica has two different, fragmented and smooth, visual appearances when deposited onto porous Amberlite polymer substrate from TEOS at acidic and basic pH, respectively. The low temperature N₂ adsorption isotherms on both materials seem to be a combination of Type 1 and Type 4 isotherms with H2 hysteresis, indicating the presence of both micro (D < 2 nm diameter) and meso (2 nm < D < 50 nm) pores. Their mesopore distributions, computed by both BJH and DFT methods, show maxima near D∼5 nm with a narrower pore size distribution range than the organic support alone. For comparison, pores were also tested by positron annihilation lifetime spectroscopy (PALS) which can scan the full micro to mezo size range in one measurement without cooling and using any adsorbate molecules. These PALS results indicated the presence of D∼0.5, 0.8 and 1.5 nm diameter micropores and an average D∼5 nm diameter mesopores in both the base and the acid set materials. When the organic substrate is burned out from the two differently made composites, the new adsorption isotherms, BET surface areas, and differently measured pore sizes became distinctly different both from each other and from those of the parent materials.

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1. Introduction

Nanoporous systems have many practical applications, most of which involve adsorption and diffusion of molecules.^1–4 To control and optimize the related transport phenomena, one has to know the precise size and shape of the pores. This is poorly satisfied however for many silica-polymer nanocomposites, which form an interesting group of complex nanoporous materials with numerous applications.^5–10 One reason for their unsatisfactory pore definition is that the routinely used nitrogen adsorption isotherms are often irreversible over these materials, which makes their interpretation unreliable. Moreover, these isotherms may exhibit H2 type hysteresis with continuously increasing adsorption and steep desorption steps, which hints at the presence of cavities or some sort of pore blocking.^11–13

A further, more general problem with the commonly used gas adsorption based pore characterization methods is that they rely on phase transitions in the narrow pores at temperatures near the boiling point of the adsorbates, most frequently N₂, Ar, or CO₂, because cooling to these very low temperatures can alter the fine molecular constitution of pore walls and the room temperature size of pores. The polar and quadrupolar character of CO₂ and N₂ might also cause Coulomb and/or chemical interference with atoms in the pore walls of polar materials, like many metal oxides, thereby deteriorating the system from pure physisorption. An additional problem is that the interpretation of adsorption isotherms assumes knowledge of the total adsorbed amount of gases as well as the formation sequence of an adsorbed multilayer preceding the total condensation of adsorbate molecules in the 2 nm < D < 50 nm diameter mesopores. One also has to assume in advance the type and shape of pores, e.g., straight cylindrical, slit like, micropore, and so on. The curvature of the meniscus is also guessed for the Kelvin equation based mesopore measurements, including the most popular Barrett, Joyner, Halenda¹⁴ or BJH method. Alternative interpretations of the adsorption data are based on molecular dynamics, Monte Carlo simulations, and Non-Local Density Functional Theory, NLDFT.^15–19 Separate high precision sorption measurements in the 10⁻⁶ < p/p₀ < 0.02 relative pressure range and adequate calculation algorithms are needed if the material contains D < 2 nm micropores.^20,21

In the course of the past few years, an entirely different, efficient approach, positronium annihilation lifetime spectroscopy (PALS) has been developed and used successfully for characterizing a wide range of pores simultaneously without using any adsorbate molecules or cooling the probe .^22–29 For positronium, when used as a probe molecule, the free volumes in solids look and physically indeed remain, empty. In principle the PALS probe can also be used at most practical temperatures, at which porous materials are employed. Hence their pore size data can be obtained at real conditions. To learn more about the accuracy of this method and its potential for accurate pore size measurements in silica-polymer nanocomposites, we used PALS to determine the pore sizes in mixed porous Amberlite/silica materials made by depositing silica gel onto the organic substrate at acidic and basic conditions. The same method was also used for porosity measurement on silica obtained from these nanocomposites after calcination, which are promising supports for bio-active substances in certain controlled drug release systems.^30,31 In this paper we compare their PALS based porosity data with those measured by conventional low temperature N₂ adsorption. It will be demonstrated that the differently made composites and pure silica gels possess distinctly different pore size distributions which can be adequately interpreted by the combined use of the adsorption and the PALS techniques.

2. Experimental section

2.1. Composite preparation

The preparation of organic/inorganic composite samples was started by thoroughly washing commercial, spherical Amberlite XAD7HP beads with distilled water as the manufacturer suggests (Rohm & Haas; today BASF). The washed beads were soaked thereafter into tetraethoxysilane (TEOS, Sigma-Aldrich, 98%), the amount of which was adjusted so that the beads just started to stick together but still preserved a loosely packed structure. This procedure caused the polymer beads to swell to more than 3 times of their dry volume. The TEOS saturated particles were transferred into aqueous ammonium hydroxide solution (200 cm³ 25% NH₄OH from Polish Chemical Reagents, POCH, was added to 17.5 g solid) and kept at room temperature for 24 h for gelation and ageing. Thereafter the solid spherical particles were filtered out, washed with 3 L water, and dried at 80 °C under vacuum for 12 h or longer. No aggregation among these particles was observed. This material, with silica gel made at basic conditions, was denoted as SiHP-B.

In order to remove the organic substrate and prepare pure inorganic SiO₂, the SiHP-B sample was calcined in air at 550 °C for at least 12 h. Thermogravimetric (TG) measurements demonstrated that fast polymer degradation starts at around 250 °C and at 600 °C this process is completed. The remaining incombustible porous silica residue, denoted as Si-B, equaled about 15% of the SiHP-B composite particles.

The above described procedure was also applied for precipitating silica from TEOS onto the Amberlite substrate at acidic conditions, for which we used pH = 0.44 HCl solution instead of NH₄OH. The dry acid set composite in this case was denoted as SiHP-A and its incombustible SiO₂ residue after calcination in air for at least 12 h was denoted as Si-A.

2.2. Pore size measurements

2.2.1 N₂ adsorption. Nitrogen adsorption and desorption isotherms were measured with ultrahigh purity N₂ at −196 °C using a Quantachrome 1CMS Autosorb gas sorption system in the p/p₀ relative pressure range from 5 × 10⁻⁷ to 1. Samples were outgassed overnight at 80 °C prior to adsorption measurements. The specific surface areas, S_BET, were calculated using the BET equation³² at p/p₀∼0.05 to 0.25 relative pressures. The total pore volumes were estimated from single point adsorption at p/p₀∼0.985. The pore size distribution in the mesopore range was calculated both by the BJH method¹⁴ and the NLDFT equilibrium model for cylindrical pore geometry using Quantochrome's proprietary Autosorb 1.51 software.

2.2.2 PALS experiments. PALS measurements were carried out by using a combined fast-fast (start signal branch) and fast-slow (stop signal branch) delayed coincidence spectrometer.³³ Such a setup is required for obtaining good linearity (flat background), which is very important in the measurement of long positron lifetimes with satisfactory resolution function. The scintillation annihilation-radiation detectors were equipped with BaF₂ crystals. The porous sample was placed inside of a capsule in the form of 4 mm thick layer of powder with a positron source (80 kBq ²²Na enclosed in a Kapton envelope) in its middle. This sample-source-sample sandwich was kept at 10⁻⁵ Pa in a vacuum chamber during the measurements to avoid ortho-para conversion of positronium on the paramagnetic atmospheric oxygen molecules and to keep the sample surface largely free of any adsorbate molecules. The energy window of the “stop” detector was wide in order to cover a large part of the continuous energy spectrum of three gamma annihilation quanta. The coincidence counting rate was about 1.35 × 10⁶ counts per hour. About 2.5 × 10⁷ counts (excluding background) per spectrum were collected for 20 h.

2.2.3 Principle of PALS calculations. PALS uses positronium (Ps), i.e., a bound state of a positron and an electron as a probe atom. This is an unstable particle due to the spontaneous annihilation possibility of the positron (e⁺) with the electron in its vicinity. The electron may originate from the positronium itself (intrinsic annihilation) or from the surrounding medium (pick-off process). The experimental positron lifetime spectra, like those shown in Fig. 1 (dots), represent the probability of positron annihilation at time t. Positron annihilation follows the law of radioactive decay, therefore these spectra can also be viewed as the sum of exponential decay components with shorter and longer lifetimes. The Ps lifetime distribution can be calculated by numerical methods from the spectra. We used the maximum entropy method in the MELT routine³⁴ to compute the distribution of intensity per lifetime, dI/dτ, over the positron lifetime τ as illustrated for the SiHP-A and Si-A materials in Fig. 2.

Fig. 1 The experimental positron lifetime spectra of SiHP-A (blue lower curve) and Si-A (red upper curve). The territory of longest-lived components of SiHP-A are marked by forward slashes and those for Si-A by backward slashes. The inset magnifies the short-lived part of the spectra.

Fig. 2 Intensity distribution of o-Ps lifetimes in SiHP-A (red; forward slash) and Si-A (blue; backward slash).

To determine the specific pore sizes, one has to consider that two states of Ps exist: the singlet state with antiparallel spins (para-positronium, p-Ps) and the triplet state with parallel spins (ortho-positronium, o-Ps). The lifetime of p-Ps is about 125 ps, three orders of magnitude lower than the lifetime of o-Ps. The probability of pick-off is significantly smaller than the probability of p-Ps intrinsic annihilation. Therefore p-Ps lifetime is almost independent on its surrounding. On the other hand, the lifetime of o-Ps in matter is determined by the pick-off probability, which is related to the size of free volume that o-Ps is trapped in. Thus often several components attributed to o-Ps are observed in the positron spectra. Each corresponds to a fraction of o-Ps trapped in differently sized free volumes.

The relation between the lifetime and the free volume, i.e. pore diameter, was approximated with the extended Tao-Eldrup (ETE) model,^35,36 using an EELViS computing routine.³⁷ The ETE model takes into account the excited states of a particle in the well (i.e. Ps), contrary to commonly used Tao-Eldrup model, in which only the ground state is considered. As a result, the lifetimes for free volumes with diameters larger than 2 nm are shortened in the ETE model compared to the lifetimes computed from the Tao-Eldrup model. The ETE model is less commonly used than the Rectangular Tao-Eldrup (RTE) model developed a few years later,³⁸ which uses easier calculations at the expense of assuming a less realistic cuboidal shaped free volume. The results of both the ETE and the RTE are similar to each other for pore sizes above 2–3 nm, but below this size differences can reach as high as 20%. In the present paper where both meso- and micropores are presented this might be even more significant since the micropores are not cuboidal. Therefore, we chose the more accurate ETE model.

Two assumptions were made: i) an empirical parameter, Δ, was selected to characterize the materials at hand (Δ = 0.166 nm for commonly used organic materials³⁹); ii) the geometric shape of the pores was assumed to be cylindrical. Note that one can use the Δ = 0.166 nm empirical parameter both for the polymer and the silica, but this might cause a systematic shift in results. Although this error is only a few percent in the micropore range (D < 2 nm) it can reach as high as 30% at the higher end of the mesopore range (D∼50 nm). Therefore, it is better to use Δ≈0.15 for porous polymers⁴⁰ and Δ≈0.19 for silica,^41,42 when one knows which part of the free volume belongs to the polymer and which one to the silica.

The volume per size distribution, dV/dD, versus the D pore diameter can be derived⁴³ from the equation:

Results for samples SiHP-A and Si-A are illustrated in Fig. 3. The same computing algorithms were applied to determine the porosity for every material reported in this paper.

Fig. 3 Normalized volume distribution over free volume in SiHP-A (red forward slash) and Si-A (blue backward slash). Inset: relation between the lifetime and free volume (solid line) and its derivative (dashed line) as obtained from the ETE model.

In order to verify the reliability of MELT calculations and the repeatability of obtained results, we analyzed two subsequent XAD-7 measurements. Results (Fig. 4) confirm the reliability of this data analysis. The tendency of splitting a wide pore distribution into a series of narrower ones is a known phenomenon.^44,45 It has to be taken into account during the interpretation of the results. All in all, this novel method to derive pore distribution from PALS data with only few and more realistic assumptions gives much more reliable results than any other method used thus far.

Fig. 4 Normalized volume distribution over free volume in XAD-7 obtained from two subsequent measurements.

2.3. SEM

SEM micrographs were taken using Quanta™ 3D FEG operating at 30.0 kV.

2.4. ²⁹Si NMR

Solid state ²⁹Si Magic-Angle Spinning (MAS) NMR spectra were obtained at 59.6 MHz resonance frequency on a Bruker Avance-300 spectrometer at room temperature using 4 mm zirconia rotors with 8 kHz spinning speed. Typically 8000 scans resulted in satisfactory signal-to-noise ratio. Spectra were recorded by the CP pulse program. The chemical shifts are referenced to Q₈M₈ as standard material.

3. Results and discussion

Amberlite polymer particles easily absorb TEOS and swell to about three times of their dry volume. The microscopic pictures in Fig. 5 illustrate that the physical appearances of gels deposited onto these particles from TEOS at acidic (SiHP-A) and basic (SiHP-B) conditions dramatically differ. The matching NMR spectra indicate that the smooth and fragmented gel structures are related to distinct molecular constitutions. This is a bit surprising, since gels are generally considered to have indistinguishably complex 3D siloxane ring structures hence their chemical constitutions have virtually never been considered as potential causes of differences in their physical properties. A recent research paper discusses these issues in details.⁴⁶

Fig. 5 Acid (SiHP-A) and base (SiHP-B) set silica gel on Amberlite beads. The respective ²⁹Si NMR spectra illustrate that different molecular constitutions cause the differences in physical appearance of silica gels. Spectra and pictures are from ref. 43 which also discusses the molecular structures of these and related silica gels in detail.

Here we focus on another aspect of these acid and base set composites, namely that their different visual appearances and molecular constitutions are also associated with different pore size distributions. Fig. 6 shows the relevant nitrogen adsorption and desorption isotherms for the composite samples SiHP-A and SiHP-B as well as for the original Amberlite XAD7HP support (blue isotherms). One cannot help but notice that only slight differences exist between the shapes of these three isotherms especially for composite samples. In this case one can observe a linearly increasing adsorption and a sharply decreasing desorption branch. For the first sight they all can be classified as Type 4 with H2 hysteresis according to the IUPAC nomenclature.⁴⁷ Such isotherms are frequent among inorganic oxide gels¹³ or polymers where openings of pores are smaller than pores located in particle interior.²⁷ However, a more careful look at the initial, p/p₀ < 0.02, part of these curves suggests that a significant portion of N₂ has already adsorbed in this range, i.e., in the micropores. This is followed by a gradual building up of the first monolayer in the mesopores with a B turning point at around p/p₀∼0.05–0.10. Thus, one can qualitatively deduct that these experimental curves are combined from Type 1 and Type 4 isotherms.

Fig. 6 Low-temperature nitrogen adsorption (solid symbols) and desorption (open symbols) isotherms of investigated samples. The meaning of sample names is the same as in “Composite preparation” chapter.

The resemblance of these three isotherms and hystereses suggests that the silica gels only slightly penetrated the mesopores of the organic substrate. Indeed, the numerical parameters in Table 1 show only slight changes in the total mesopore volume (V_p), average pore diameter (D_p), or BET surface area of the Amberlite after depositing the gels onto it under either acidic (SiHP-A) or basic conditions (SiHP-B).

Table 1 Parameters characterizing the porosity of samples obtained from nitrogen adsorption/desorption measurements at −196 °C. D_p = mean pore diameter; S_BET = BET surface area; V_p = total pore volume; D_p = 4V_p/S_BET; sample names are the same as those in “Composite preparation” chapter

Sample name	S BET (m^2 g^−1)	V p (cm^3 g^−1)	D p (nm)
Amberlite® XAD7HP	498	0.68	5.46
SiHP-A	393	0.45	4.58
SiHP-B	414	0.54	5.22
Si-A	1185	1.17	3.95
Si-B	169	1.15	27.22

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However, when the organic matrix was eliminated by calcining the base set SiHP-B composite sample at 550 °C in air, its surface area dramatically dropped, presumably due to the collapse of the smaller pores as data for sample Si-B indicate. After burning out the Amberlite support at the same conditions from the acid set SiHP-A, its total pore volume and BET surface area substantially increased without measurable changes in the average mesopore diameter as data for Si-A demonstrate in Table 1. This is only possible when the microporosity increases in this material which could not be determined from these N₂ adsorption data, but the roughly doubled N₂ adsorption at p/p₀ < 0.02 qualitatively supports this idea. In contrast, Fig. 6 also illustrates that the isotherm shape changes in the opposite way for the base set Si-B gel which acquired Type 3 or 5 characteristics in line with the macroporous nature of its fragmented structure (Fig. 3). Note that both pure silicas kept their spherical shape after calcination at 550 °C.

The mesopore size distributions (PSD) for every material investigated were computed both by BJH and NLDFT methods from the N₂ adsorption data. Results on the left side of Fig. 7 indicate that the two methods give similar average pore sizes with a maximum near D∼5 nm. In the same figure PSDs calculated from PALS spectra are given on the right side. Clearly, pore volume in the mesopore part is similar compared to the narrower channels in every sample except Si-A. This sample has a relatively uniform pore distribution with D∼3 nm diameter which is very close to the meso/micro pore border hence the mesopore based BJH and DFT calculations lose accuracy. As previously predicted from the sorption isotherms (Fig. 6), every other sample contains comparable total volumes of micropores and mesopores although their average mesopore size is D∼5 nm which was also measured with PALS. The total volume of micropores similar to the total volume of mesopores is even valid for sample Si-B although a substantial part of pore volume in Si-B presumably comes from macropores (D > 50 nm), which generates the Type 3 and/or Type 5 isotherm character. Beside the hysteresis phenomenon associated with the Type 5 isotherm,^47,48 its hysteresis might also hint at its minor mesopore content.

Fig. 7 Pore size distributions derived from low-temperature nitrogen adsorption/desorption data (left side) using NLDFT (solid lines) and BJH (dotted line) calculations and measured by the PALS method (right side). Samples are named the same way as in “Composite preparation” chapter.

The relative volume of D < 1.5 nm micropores in relation to mesopores found by PALS is definitely smaller for Si-A than for Si-B. This seemingly contradicts the high micropore ratio obtained from the N₂ adsorption isotherms for Si-A in Fig 6. Although it is possible that Ps migrates from smaller free volumes to larger ones if they are interconnected^49,50 that might result in underestimation of the volume of smaller free volumes in Si-A, it is more likely that the mentioned inaccurate pore saturation measurement in the large, D ~ 3 nm micropores causes this discrepancy. On the other hand the micropores in Si-B are probably closed, which makes them impenetrable for nitrogen, but let Ps in.

4. Summary

In summary, the variously measured data indicate that both the physical appearance and the pore size distribution are functions of the pH at which silica gels are synthesized combined with a porous organic substrate. The underlying difference in their molecular structures^43,46 predetermines how the different post-treatments, like for example calcination in air, affect their final pore sizes, specific surface areas, and other physical properties.

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