Pore Analysis of Cylindrical and Spherical Porous Carbon using Quenched Solid Density Functional Theory (QSDFT)

Applying techniques such as the non-local density functional theory (NLDFT) method to gas adsorption data has resulted in major advancements in the textural characterization of porous materials. NLDFT methods help in describing the adsorption and phase behavior in fluids on a molecular level and to obtain pore size information over the complete range of micro- and mesopores.

Quantachrome has commercialized a comprehensive library of NLDFT and Grand Canonical Monte Carlo (GCMC) simulation methods for interpreting experimental data and the calculation of pore size distributions for various types of materials.

Hence, the NLDFT method is now widely applied and is featured in the latest gas adsorption standard by ISO [ISO-15901-3].

NLDFT has been proven to be a reliable method for pore size characterization of a variety of nanoporous materials, however pore size analysis of carbons with heterogeneous surfaces provides a challenge.

The main drawback of standards NLDFT methods are that chemical and geometrical heterogeneity of the pore walls are not taken into account, assuming instead a structureless, chemically and geometrically smooth, surface model.

To address this and several other challenges, Quantachrome helped to pioneer the development of a QSDFT method for the pore size analysis of nanoporous carbons and, in 2009, commercialized such a method for carbons with slit-like pores.

QSDFT, in contrast to NDLFT, considers surface roughness in disordered carbons, which prevents the occurrence of layering transitions in the theoretical DFT isotherms and provides a much more realistic description of the experimental adsorption isotherm.

The new QSDFT kernels that have been implemented in Quantachrome’s software as of June 2011 are shown in Table 1.

Table 1. QSDFT kernels in Quantachrome's software

QSDFT Kernel Applicable Pore Width Range Examples
QSDFT, N2, carbon adsorption branch kernel at 77 K based on a cylindrical pore model 0.35 nm - 33 nm Micro-mesoporous carbons with heterogeneous surface chemistry such as CMK-3, carbon nanotubes, carbon aerogels, FDU-14, FDU-15, etc. Allows obtaining an accurate pore size distribution even in case of pore network effects such as pore blocking and cavitation which affect the desorption branch (i.e. materials with type H2 or H3 hysteresis).
QSDFT, N2, carbon equilibrium transition kernel at 77 K based on a slit-pore model(pore diameter < 2 nm) and a cylindrical pore model (pore diameter > 2 nm) 0.35 nm - 50 nm Micro-mesoporous carbons with heterogeneous surface chemistry (some CMKs), certain activated carbons.
QSDFT, N2, carbon adsorption branch kernel at 77 K based on a slit-pore model (pore diameter < 2 nm) and cylindrical pore model (pore diameter > 2 nm) 0.35 nm - 33 nm Micro-mesoporous carbons with heterogeneous surface chemistry (some CMKs), certain activated carbons, FDU-14, FDU-15. Allows obtaining an accurate pore size distribution even in case of pore network effects such as pore blocking and cavitation which affect the desorption branch (i.e. materials with type H2 or H3 hysteresis).
QSDFT, N2, carbon adsorption branch kernel at 77 K based on a cylindrical pore model (pore diameter < 5 nm) and spherical pore model (pore diameter > 5 nm) 0.35 nm - 50 nm Micro-mesoporous carbons with heterogeneous surface chemistry and cage-like/spherical mesopore structure such as hierarchically ordered carbons (i.e. carbons templated using nanoparticles, colloidal crystals, 3DOm carbons, FDU-16), etc. Allows obtaining an accurate pore size distribution even in case of pore network effects such as pore blocking and cavitation which affect the desorption branch (i.e. materials with type H2 or H3 hysteresis).
QSDFT, N2, carbon adsorption branch kernel at 77 K based on a slit-pore model (pore diameter <2 nm) and a cylindrical pore model (pore diameter 2-5 nm) and a spherical pore model (pore diameter > 5 nm) 0.35 nm - 50 nm Micro-mesoporous carbons with heterogeneous surface chemistry and cage-like/spherical mesopore structure such as hierarchically ordered carbons (i.e. carbons templated using nanoparticles, colloidal crystals, 3DOm carbons, FDU-16), etc. Allows obtaining an accurate pore size distribution even in case of pore network effects such as pore blocking and cavitation which affect the desorption branch (i.e. materials with type H2 or H3 hysteresis).

Model Validation and Applications

The above additional QSDFT methods applicable for nitrogen (77 K) adsorption in porous carbons with cylindrical and spherical pore geometries have been recently developed and validated by Quantachrome.

The developed QSDFT models consider that pore condensation is delayed due to the existence of a metastable adsorption film and hindered nucleation of liquid bridges.

Application of QSDFT models with Spherical Pore Geometry

New QSDFT models relevant for nitrogen (77 K) adsorption in spherical pore carbons have been applied to three-dimensionally ordered mesoporous (3DOm) carbons).

The QSDFT model, which has been developed and applied to these carbons is a hybrid model that assumes spherical pore geometry in the relative pressure range of hysteresis (P/P0 > 0.5)and cylindrical pore geometry in the low pressure region (P/P0 < 0.5).

For spherical pores, the desorption is often affected by a pore blocking mechanism and the pore size can only be obtained from the adsorption branch of the isotherm using a QSDFT model which correctly takes into account the delay in condensation in spherical carbon pores. For instance, two carbons templated from 20 and 40 nm silica nanoparticles were analyzed using nitrogen (77 K) adsorption and the pore size distributions were calculated using the QSDFT method for spherical mesopores as shown in Figure 1.

The pore size distributions for these two samples have pronounced peaks at 23.6 nm and 40.9 nm for the two carbons and these pore sizes match closely with what is expected from the size of the nanoparticle template and the pore sizes measured independently using SEM, confirming the accuracy of the QSDFT kernel.

Experimental isotherms

(a)

pore size distributions calculated using the QSDFT cylindrical/spherical adsorption kernel.

(b)

Figure 1. Nitrogen (77.4 K) adsorption data from [11]. (a) Experimental isotherms and (b) pore size distributions calculated using the QSDFT cylindrical/spherical adsorption kernel.

Figure 2 shows the pore size distribution, isotherm and QSDFT fit for a new 3DOm carbon template from 30 nm spherical nanoparticles. The theoretical isotherm matches well with the experimental isotherm in both the mesopore (Figure 2a) and micropore (Figure 2c) regime. In the past there was no DFT method for evaluating the pore size of carbons with spherical pores and this new QSDFT method now allows one to analyze these unique materials.

Experimental nitrogen (77.4 K) isotherm of a 3DOm spherical pore carbon together with a QSDFT adsorption branch theoretical isotherm

(a)

differential pore size distribution curve obtained by applying a QSDFT adsorption branch method to the isotherm shown in 2a

(b)

experimental nitrogen (77.4 K) isotherm together with the QSDFT adsorption branch fit plotted semilogarithmically to highlight the good agreement in the micropore region.

(c)

Figure 2. (a) Experimental nitrogen (77.4 K) isotherm of a 3DOm spherical pore carbon together with a QSDFT adsorption branch theoretical isotherm, (b) differential pore size distribution curve obtained by applying a QSDFT adsorption branch method to the isotherm shown in 2a, and (c) experimental nitrogen (77.4 K) isotherm together with the QSDFT adsorption branch fit plotted semilogarithmically to highlight the good agreement in the micropore region.

Application of QSDFT models with Cylindrical Pore Geometry

New QSDFT models valid for nitrogen (77 K) adsorption in cylindrical pore carbons have been developed and validated by application to the appropriate branch of CMK-3 isotherms. A CMK- isotherm is shown in Figure 3a, the QSDFT fit is shown in Figure 3b, and the pore size distributions calculated from the adsorption and desorption branches, along with the NLDFT pore size distribution are shown in Figure 3c.

Experimental isotherm with fit from QSDFT cylindrical adsorption and cylindrical equilibrium kernels

(a)

experimental isotherm and fit from QSDFT cylindrical equilibrium kernel (plotted semi-logarithmically)

(b)

pore size distributions from QSDFT cylindrical adsorption and equilibrium kernels derived from adsorption and desorption branches of experimental isotherms and from NLDFT cylindrical pore equilibrium kernel.

(c)

Figure 3. Nitrogen (77.4 K) adsorption on CMK-3 sample. (a) Experimental isotherm with fit from QSDFT cylindrical adsorption and cylindrical equilibrium kernels, (b) experimental isotherm and fit from QSDFT cylindrical equilibrium kernel (plotted semi-logarithmically), and (c) pore size distributions from QSDFT cylindrical adsorption and equilibrium kernels derived from adsorption and desorption branches of experimental isotherms and from NLDFT cylindrical pore equilibrium kernel.

Further Applications

Application of QSDFT models with hybrid Slit/Cylindrical Pore Geometry New QSDFT models appropriate for nitrogen (77.4K) adsorption in activated carbons with slit pores in the low pressure region (micropores) and cylindrical-like pores in the high pressure region (mesopores) have been applied to micromesoporous carbons with heterogeneous surfaces, such as micro-mesoporous carbon derived from lignocellulosic precursors (e.g. peach and olive stones), and FDU-14-15 carbons [8-11].

Such carbons reveal type H2/H4 hysteresis characteristic of cavitation induced evaporation indicating that some mesopores can only be accessed through more narrow entrances/necks. Corresponding nitrogen (77.4 K) and argon (87.3 K) adsorption isotherms are shown in Figure 4a.

A resulting pore size distribution histogram obtained from the nitrogen adsorption isotherm highlighting the mesopore size range is shown in Figure 4b.

Another example of micro-mesoporous carbon of type H2 hysteresis where the application of a slit/cylindrical pore geometry is appropriate is shown in Figure 5.  Figure 5a shows the experimental data and the QSDFT adsorption branch kernel theoretical fit, which agree well. Figure 5b shows the corresponding QSDFT pore size distribution obtained for this isotherm.

Nitrogen (77.4 K) and argon (87.3 K) adsorption in micro-mesoporous lignocellulosic carbons

(a)

QSDFT pore size distribution from the N2 isotherm adsorption branch applying the QSDFT model for slit/cylindrical pores.

(b)

Figure 4. (a) Nitrogen (77.4 K) and argon (87.3 K) adsorption in micro-mesoporous lignocellulosic carbons and (b) QSDFT pore size distribution from the N2 isotherm adsorption branch applying the QSDFT model for slit/cylindrical pores.

Experimental nitrogen (77.4 K) isotherm of an activated carbon together with a slit/cylindrical model QSDFT theoretical isotherm

(a)

differential pore size distribution curve obtained by applying a slit/cylindrical QSDFT method to the isotherm shown in 5a. The slit/cylindrical hybrid model is also suitable to obtain the micro-mesopore size distribution of so-called FDU-14 and FDU-15 materials.

(b)

Figure 5. (a) Experimental nitrogen (77.4 K) isotherm of an activated carbon together with a slit/cylindrical model QSDFT theoretical isotherm and (b) differential pore size distribution curve obtained by applying a slit/cylindrical QSDFT method to the isotherm shown in 5a. The slit/cylindrical hybrid model is also suitable to obtain the micro-mesopore size distribution of so-called FDU-14 and FDU-15 materials.

Conclusions

The results show the applicability of the QSDFT method for reliable pore size and pore volume analyses of micro-mesoporous carbon materials. The present work is an extension of the QSDFT method, initially suggested for PSD analysis of disordered carbons based on the slit-pore model, to ordered hierarchical micro-mesoporous carbons prepared via various templating techniques.

Hybrid QSDFT kernels have been developed and introduced for the first time enabling the accurate analysis of novel specialized carbons such as CMK-3, FDU-14, FDU-15, and others.

About Quantachrome Instruments

Quantachrome... renowned innovator of ideas for today's porous materials needs. For more than 35 years, Quantachrome's scientists have revolutionized measurement techniques and designed instrumentation to enable the accurate, precise, and reliable characterization of powdered and porous materials according to:

  • Gas Sorption Isotherms
  • Surface Area Measurement
  • Pore Size Distribution
  • Chemisorption Studies
  • Water sorption
  • Mercury Porosimetry
  • True Solid Density
  • Tapped Density

Whether you work with catalysts, pharmaceuticals, ceramics, carbons, building materials - or any other porous or divided solid - at some point you, your colleagues or your customers will need quantitative information about surface area, pore size, pore volume and density, or more specific properties such as active metal area and hydrophilic behaviour. Quantachrome offers more than thirty instruments to meet your exact requirements - and Quantachrome backs its quality products with worldwide service and renowned application support. Not only are Quantachrome products the instruments of choice in academia, but the technology conceived and developed by our scientific staff is applied in industrial laboratories worldwide, where research and engineering of new and improved porous materials is ongoing. Manufacturers also rely on porous materials characterization technology to more precisely specify bulk materials, to control quality, and to isolate the source of production problems with greater efficiency.

Quantachrome is also recognized as an excellent resource for authoritative analysis of your samples in our fully equipped state-of-the-art particle characterization laboratory.

This information has been sourced, reviewed and adapted from materials provided by Quantachrome Instruments.

For more information on this source, please visit Quantachrome Instruments.

Citations

Please use one of the following formats to cite this article in your essay, paper or report:

  • APA

    Quantachrome Instruments. (2018, July 06). Pore Analysis of Cylindrical and Spherical Porous Carbon using Quenched Solid Density Functional Theory (QSDFT). AZoM. Retrieved on October 18, 2019 from https://www.azom.com/article.aspx?ArticleID=9435.

  • MLA

    Quantachrome Instruments. "Pore Analysis of Cylindrical and Spherical Porous Carbon using Quenched Solid Density Functional Theory (QSDFT)". AZoM. 18 October 2019. <https://www.azom.com/article.aspx?ArticleID=9435>.

  • Chicago

    Quantachrome Instruments. "Pore Analysis of Cylindrical and Spherical Porous Carbon using Quenched Solid Density Functional Theory (QSDFT)". AZoM. https://www.azom.com/article.aspx?ArticleID=9435. (accessed October 18, 2019).

  • Harvard

    Quantachrome Instruments. 2018. Pore Analysis of Cylindrical and Spherical Porous Carbon using Quenched Solid Density Functional Theory (QSDFT). AZoM, viewed 18 October 2019, https://www.azom.com/article.aspx?ArticleID=9435.

Ask A Question

Do you have a question you'd like to ask regarding this article?

Leave your feedback
Submit