Using classical methods to start quantum mechanical calculations for microporosity and mesoporosity
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Using classical methods to start quantum mechanical calculations for microporosity and mesoporosity James Condon1 Received: 1 June 2020 / Revised: 24 August 2020 / Accepted: 5 September 2020 / Published online: 15 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract One primary measurement of open porosity uses physical adsorption isotherm, amount adsorbed versus gas pressure. Classical treatments, including the BET, cannot fit the isotherm for its full range, therefore standard curves have been created from non-porous materials for comparison. This classical method yields three output parameters, two surface areas, pore and external, relative to the standard. The third output is moles of material needed to fill the pores. A modern treatment using quantum mechanics and thermodynamics, call χ/ESW, yields seven physical quantities. However, the calculation requires a non-linear least squares routine, with initial parameters to find a minimum. In this paper the possibility of using the answers from the classical method as a first approximation is explored, with no need for a standard since χ/ESW treatment is used as a self-standard. Within limits, this works well for microporosity but mesoporosity presents some problems with one of the parameters. Keywords Microporosity · Mesoporosity · Adsorption · Physical-adsorption · Quantum-mechanical-modeling · Physisorption
1 Introduction One of the major measurements of physical adsorption is the adsorption isotherm, that is, the dependence of amount adsorbed as a function of pressure. The dependence is usually described by the generalized equation:
𝜃 = 𝐅(P, T)
(1)
θ is usually the “coverage,” defined as the number of moles of molecules adsorbed on the surface, nads called the adsorbate, divided by a quantity that is a monolayer equivalent, nm. The quantity nm is defined as the moles of adsorbate molecules that are needed to completely cover the surface if they were all in direct contact with the surface. P is the pressure of the gas, called the adsorptive, that is, the source for the adsorbate. The solid material upon which adsorption occurs is called the adsorbent. For the isotherm, T is supposed to be held constant and the isotherm is dependent only upon P.
* James Condon [email protected] 1
Before 1980, theories for determining porosity were by themselves not very successful. Thus, the use of standard curves was proposed, first by deBoer (deBoer et al. (1965)), et. al. and by Cranston and Inkley (Carnston and Inkley 1957) and later by Sing (Bhambhani et al. 1972; Sing et al. 1974), and the latest IUPAC recommendations (Thommes et al. 2015). Unfortunately, the deBoer t-curve was not consistent with later data and it has been speculated that the sample temperature control was problematic. The Sing’s, et. al., α-s curves are still used today, especially for silica materials. There are many other standard curves for other adsorbents in the literature. The methodology, which will be referred to here is the classical treatment,
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