(669f) Pore Size Distribution of Silica Colloidal Crystals from Nitrogen Adsorption Isotherms
AIChE Annual Meeting
2020
2020 Virtual AIChE Annual Meeting
Separations Division
Characterization of Adsorbent Materials
Friday, November 20, 2020 - 9:40am to 10:00am
Silica colloidal crystals, often referred to as opals, are face-centered closely packed cubic crystals comprised of silica spheres. The voids between the spheres form a network of octahedral and tetrahedral pores. These pores have sizes that could vary in the range of tens to hundreds of nanometers and can be probed by nitrogen adsorption porosimetry.
Here, we used sphere diameters 93 nm, 106 nm, and 565 nm to prepare two mesoporous samples and a macroporous sample and then measured nitrogen adsorption and desorption isotherms for further characterization [1]. Furthermore, we modified the surface of the samples with organics and measured new adsorption isotherms [2]. The IUPAC recommendation for the calculation of pore-size distribution (PSD) from a nitrogen adsorption isotherm is a combination of the density functional theory (DFT) with the integral adsorption equation. Although the DFT works for different pore geometries, the libraries available with commercial software are rather limited and the DFT predictions for nitrogen adsorption on a silica surface are based on one reference silica material. Therefore, the application of this model for deriving the PSD of silica materials with modified surfaces can lead to incorrect PSD. Furthermore, often available kernels of DFT isotherms for spherical pore geometry in the libraries are limited to ca. 40 nm, [3] which is not sufficient to describe the characteristic pores of silica colloidal crystals samples, estimated to be ca. 60 nm [1].
To resolve this problem we proposed a straightforward procedure for calculation of the PSD of silica colloidal crystals from nitrogen adsorption isotherms requiring only three parameters to fit. The procedure is based on the adsorption integral equation solution with a kernel of theoretical isotherms, consistent with the procedure used for many other porous materials [4]. The solution is carried out using the non-negative least squares (NNLS) regression with Tikhonov regularization. The kernel of mesoporous isotherms is built on the basis of the macroscopic Derjaguin−Broekhoff−de Boer theory of capillary condensation considering the voids as a network of spheres. Application of our procedure for the analysis of the adsorption branches of experimental isotherms resulted in bimodal distributions, where the modes matched well with the sizes of the voids in the colloidal crystals face-centered cubic structure: the main mode corresponds to the octahedral voids and the second mode to the tetrahedral voids. The resulting pore-size distribution for the samples with the modified surface matched the original one quite closely. It demonstrates the procedure as a simple and efficient technique to estimate the pore-size distribution and justifies the spherical shape approximation for the voids in the silica colloidal crystals.
Here, we used sphere diameters 93 nm, 106 nm, and 565 nm to prepare two mesoporous samples and a macroporous sample and then measured nitrogen adsorption and desorption isotherms for further characterization [1]. Furthermore, we modified the surface of the samples with organics and measured new adsorption isotherms [2]. The IUPAC recommendation for the calculation of pore-size distribution (PSD) from a nitrogen adsorption isotherm is a combination of the density functional theory (DFT) with the integral adsorption equation. Although the DFT works for different pore geometries, the libraries available with commercial software are rather limited and the DFT predictions for nitrogen adsorption on a silica surface are based on one reference silica material. Therefore, the application of this model for deriving the PSD of silica materials with modified surfaces can lead to incorrect PSD. Furthermore, often available kernels of DFT isotherms for spherical pore geometry in the libraries are limited to ca. 40 nm, [3] which is not sufficient to describe the characteristic pores of silica colloidal crystals samples, estimated to be ca. 60 nm [1].
To resolve this problem we proposed a straightforward procedure for calculation of the PSD of silica colloidal crystals from nitrogen adsorption isotherms requiring only three parameters to fit. The procedure is based on the adsorption integral equation solution with a kernel of theoretical isotherms, consistent with the procedure used for many other porous materials [4]. The solution is carried out using the non-negative least squares (NNLS) regression with Tikhonov regularization. The kernel of mesoporous isotherms is built on the basis of the macroscopic Derjaguin−Broekhoff−de Boer theory of capillary condensation considering the voids as a network of spheres. Application of our procedure for the analysis of the adsorption branches of experimental isotherms resulted in bimodal distributions, where the modes matched well with the sizes of the voids in the colloidal crystals face-centered cubic structure: the main mode corresponds to the octahedral voids and the second mode to the tetrahedral voids. The resulting pore-size distribution for the samples with the modified surface matched the original one quite closely. It demonstrates the procedure as a simple and efficient technique to estimate the pore-size distribution and justifies the spherical shape approximation for the voids in the silica colloidal crystals.
References:
[1] A. Galukhin, D. Bolmatenkov, A. Emelianova, I. Zharov, G. Y. Gor, Langmuir, 35, 2230 (2019).
[2] M. A. Maximov, A. Galukhin, G. Y. Gor, Langmuir, 35, 14975 (2019).
[3] Quantachrome NOVAtouch brochure. https://www.quantachrome.com/pdf_brochures/novatouch_rev1.pdf
[4] J. Landers, G. Y. Gor, A. V. Neimark, Coll. Surf. A., 437, 3, (2013).