## Topics Covered

Micropore Size Analysis of Porous Carbons Using CO_{2} Adsorption at 273.15 K (0°C)

Main Advantages of CO_{2} Micropore Analysis at 0ºC Versus Nitrogen Analysis at 77 K

The pore size distribution (PSD) is a key factor characterizing porous materials. The PSD analysis can be useful in developing new porous materials for specific applications as well as for testing of the existing products. Traditionally, the PSD of a porous solid is evaluated from the analysis of nitrogen adsorption isotherms measured at ~77 K. It is well known, however, that at such cryogenic temperature diffusion of nitrogen molecules into carbon micropores is very slow. Moreover, it was pointed out that diffusional limitations at this temperature might influence adsorption in ultramicropores (pores smaller than 7 Å). For porous carbons, usually containing a wide range of pore sizes including ultramicropores, this leads to time-consuming measurements and may cause under-equilibration of measured adsorption isotherms, which will give erroneous results of the analysis. It has been long time recognized that problems of this type can be eliminated by using CO_{2} adsorption analysis at 0°C. The saturation pressure of CO_{2} at 0°C is very high (~26141 torr) [A], therefore low relative pressure measurements necessary for the micropore analysis are achieved in the range of moderate absolute pressures (1 – 760 torr). At elevated temperatures and under higher absolute pressures CO_{2} molecules can more easily access ultramicropores than N_{2} at ~77 K in spite of the fact that molecular critical dimensions of both gases are similar. This kind of measurements can therefore be carried out without high vacuum equipment and without low-pressure transducers (e. g.; 1 torr or 10 torr transducers). The CO_{2} adsorption isotherms measured under such conditions can be analyzed using modern molecular models such as Density Functional Theory (DFT) or Monte Carlo Simulations to provide detailed information about carbon micropore structure.

- Faster analysis. Due to higher diffusion rate equilibrium is achieved faster, which allows completing the isotherm measurement in a significantly shorter time: about 3 hours for CO
_{2} versus more than 30 hours for N_{2}.
- Faster diffusion to micropores ensures greater confidence that measured adsorption points are equilibrated.
- Range of analysis is extended to pores of smaller sizes that are accessible to CO
_{2} molecules but not to N_{2}.
- Technical simplification of instrumentation:
- No need for high vacuum systems with turbomolecular pump; 10
^{-3} torr vacuum is sufficient.
- No need for a low-pressure transducer; 1000 torr transducer is sufficient.

Both the NOVA and Autosorb series instruments can perform the analysis. Data reduction is supported by Quantachrome software, which includes a comprehensive library of classical and modern methods for the calculation of PSD. In contrast to the classical macroscopic thermodynamic methods, modern approaches allow to describe the configuration of the pore fluid on the molecular level. Such microscopic methods for PSD analysis are available. Briefly, modern approach to the evaluation of PSD is based on the statistical mechanical model calculations. The most important part of this approach is development of theoretical isotherms calculated for individual pores of a given adsorbate-adsorbent system, such as Carbon-CO_{2} These isotherms, which constitute the so-called kernel, are generated using Grand Canonical Monte Carlo (GCMC) simulations or the Non-Local Density Functional Theory (NLDFT). Both of these statistical mechanical methods utilize fundamental molecular parameters characterizing the gas-gas and gas-solid interactions of the adsorption system. In the case of porous carbons the model of slit pores with graphite- like parallel walls is utilized. Mathematical procedure used to calculate PSD can be described as fitting a combination of the theoretical isotherms to the experimental data. The obtained PSD represents volumetric contributions of pores with different sizes whose theoretical isotherms best fit the experimental data.

Recognizing advantages of the CO_{2} analysis Quantachrome Instruments introduced NLDFT / GCMC kernels for the PSD calculation from CO_{2} isotherms. For illustration of the method, the CO_{2} analysis results are compared with the results of well-established nitrogen DFT analysis for the two representative carbon samples. The PSDs are presented as histograms in Figure 1 for the activated carbon fiber ACF-10 (Nippon Kynol, Japan) and in Figure 2 for the coal based activated carbon F400 (Calgon Carbon). ACF-10 is a typical microporous carbon fiber with almost no mesopores while F400 has both micro and mesopores. Agreement between the results of the two methods is very good for both samples especially in the range of small micropores. The CO_{2} isotherms measured at 0ºC below 760 torr yield pore size distribution in the range up to about 15 Å. The isotherms that were used for the PSD calculations of ACF-10 are shown in Figure 3. It is important to note that for nitrogen, adsorption in carbon micropores begins at relative pressures well below 10^{-6} P/P_{0} (<0.001 torr). At 10^{-6} P/P_{0}, the adsorbed amount is already about 20% of total adsorption of this sample, so in order to measure the initial part of the isotherm much lower pressure is necessary. On the other hand, CO_{2} adsorption begins at about 10^{-4} which in terms of absolute pressure is significantly higher compared to the nitrogen experiment (~1 torr). It follows that the initial parts of adsorption isotherms are accessed more easily for CO_{2} than for N_{2}. This comparison clearly demonstrates that in order to follow and analyze adsorption in micropores it is more convenient and beneficial to use CO_{2} rather then N_{2}.

**Figure 1**. PSD histograms for ACF-10 activated carbon fiber. Analysis times: 3 hours for CO_{2} and 40 hours for N_{2}.

**Figure 2**. PSD histograms for F400 activated carbon.Analysis times: 3 hours for CO_{2}, and 35 hours for N_{2}.

Obviously, when the range of mesopores is of interest, the CO_{2} analysis may be combined with the classical nitrogen mesopore analysis. Combination of the two methods allows for the micro and mesopore characterization of carbons avoiding time consuming and more costly low-pressure nitrogen measurements at ~77 K.

**Figure 3**. Adsorption isotherms of N_{2} at ~77 K and CO_{2} at ~273 K on activated carbon fiber ACF-10.

Source: Micropore Size Analysis of Porous Carbons Using CO_{2} Adsorption At 273.15 K (0°C)

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