Comparison of textural information from argon(87 K) and nitrogen(77 K) physisorption

Abstract

Argon(87 K) and nitrogen(77 K) adsorption of three types of porous samples (microporous, microporous-mesoporous and mesoporous) was evaluated. The shapes of isotherms, specific surface areas, mesopore-, micropore- and net pore volumes, pore-size distributions (PSD) and positions of micropore and mesopore PSD’s maxima were compared to ascertain the credibility of individual adsorbates for the texture information estimation. The shapes of adsorption isotherms for Ar and N₂ of all samples are similar and the adsorbed amounts at relative pressure x = 0.975 differ slightly. For mesoporous samples some differences are observed between specific mesopore surface areas derived from nitrogen and argon isotherms. Radii of pore size maxima from Ar(87 K) PSD’s are on average systematically lower than from N₂(77 K) for all samples. The Saito-Foley approach for ZSM-5 samples gives consistently lower mean pore radius from N₂(77 K) adsorbate than from Ar(87 K). This difference probably arises from the multiplication factor, Ω, in the Saito-Foley equation which includes physical properties (magnetic susceptibility, polarizability etc. at 77 and 87 K) and is not easy to obtain with sufficient precision. The use of both adsorbates Ar(87 K) and N₂(77 K) possesses some advantages as well some disadvantages and the comparison of textural properties of individual samples must be evaluated with respect to adsorbate.

Appendix

Saito-Foley [11] relation between micropore radius, r, and relative pressure, x, at which spontaneous condensation in micropores takes place, r(x):

$\ln (x) = \frac{3}{4}{\frac{{\pi {\text{A}}}}{{{\text{R}}_{g} T}}}\,\,{\frac{\Upomega }{{{\text{d}}_{o}^{4} }}}\sum\limits_{k = 0}^{\infty } {\left[ {{\frac{1}{k + 1}}\left( {1 - {\frac{{{\text{d}}_{o} }}{r}}} \right)^{2k} \left\{ {\frac{21}{32}\alpha_{k} \left( {{\frac{{{\text{d}}_{o} }}{r}}} \right)^{10} - \beta_{k} \left( {{\frac{{{\text{d}}_{o} }}{r}}} \right)^{4} } \right\}} \right],}$where the interaction parameter, Ω, is defined as:

$$ \Upomega = N_{A} A_{A} + N_{S} A_{S} $$

$$ {\text{with}}\,\, A_{S} = {\frac{{6mc^{2} \alpha_{s} \alpha_{A} }}{{{\frac{{\alpha_{s} }}{{\chi_{s} }}} + {\frac{{\alpha_{A} }}{{\chi_{A} }}}}}} , \quad A_{A} = {\frac{{3mc^{2} \alpha_{A} \chi_{A} }}{2}}\quad{\text{and}}\quad{\text{d}}_{o} = \left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right)\left( {d_{A} + d_{s} } \right) $$

The coefficients α _k and β _k are given by recurrent relations:

$$ \begin{gathered} \alpha_{k} = \left( {{\frac{ - 4.5 - k}{k}}} \right)^{2} \alpha_{k - 1} ;\quad\alpha_{o} = 1.0 \hfill \\ \beta_{k} = \left( {{\frac{ - 1.5 - k}{k}}} \right)^{2} \beta_{k - 1} ;\quad \beta_{o} = 1.0 \hfill \\ \end{gathered} $$

Here, N denotes the surface number of adsorbate gas molecules or porous sample atoms, d is the diameter of adsorbate gas molecule or adsorbate surface atom, mc² stands for the kinetic energy of an electron (0.8183 × 10⁻⁶ erg), α is the polarizability of porous sample atom or adsorbate gas molecule and χ is the diamagnetic susceptability of porous sample atom or adsorbate gas molecule. The lower index S denotes the porous sample, A denotes the adsorbate surface atom.

The following values were used for calculations of interaction parameter, Ω:

	Zeolites (index ‘S’)	Argon (index ‘A’)	Nitrogen (index ‘A’)
d (A)	3.04	2.95	3.00
N (molecules/cm2)	3.75 × 1015	7.608 × 1013	6.71 × 1013
−χ (cm3)	1.94 × 10−29	3.22 × 10−29	3.6 × 10−29
α (cm3)	0.85 × 10−24	1.63 × 10−24	1.76 × 10−24

Interaction parameters, Ω (erg.cm⁴):

Adsorbate	Adsorbent: zeolite
Ar at 87 K	3.19 × 1043
N2 at 77 K	3.49 × 1043