Localized adsorption without interactions

The Langmuir model is based on the assumption of ideal localized adsorption without interaction on a set of identical sites as outlined in Section 2.4. The special case of sorption of CH4 or Ar in sodalite was noted in Section 3.5 as an example of a system for which the basic assumptions of the Langmuir model are in fact fulfilled and for which the isotherms conform, as expected, to the Langmuir equation (Eq. (2.28)]. Sorption of normal tri- or tetradecane in 5A zeolite is another example of a zeolitic system in which each cage can accommodate only one sorbate molecule. Approximate conformity... 

For reasons which will become clear in the following, the Langmuir isotherm has played (and continues to play) a special role in the theory of adsorption. The Langmuir isotherm, which describes submonolayer localized adsorption without lateral interaction, is given by... 

Adsorption without lateral interactions is particularly interesting because the topographic structure of the surface does not affect the integral equation. Localized adsorption without lateral interactions is even more interesting because the Langmuir isotherm (19) has the following additional features ... 

The following derivation is modified from that of Fowler and Guggenheim [10,11]. The adsorbed molecules are considered to differ from gaseous ones in that their potential energy and local partition function (see Section XVI-4A) have been modified and that, instead of possessing normal translational motion, they are confined to localized sites without any interactions between adjacent molecules but with an adsorption energy Q. 

Consider, by way of example, the simple case of localized monolayer adsorption without lateral interaction. Let there be /V j sites of type j. Tliese sites are distinguishable in the present situation we do not yet have to discriminate between patchwise and random distribution of these sites, but this becomes important as soon as lateral interaction has to be accounted for. We have Ns = Sj sj If Is the number of molecules adsorbed on sites j in... 

There are B equivalent sites for localized adsorption in the first layer, interactions between molecules in the first layer being neglected. This is just Fowler s model for Langmuir adsorption on a uniform surface without interactions. 

The simplest model of adsorption on a surface is that in which localized adsorption takes place on an energetically uniform surface without any interaction between adsorbed molecules. When surface coverage or fractional filling of the micropore is 0 (=gfgo) and the partial pressure in the gas phase, p, which is to be replaced by C = pIRT) when the concentration in the fluid phase is used, the adsorption rate is expressed as Kp 1 — 0) assuming first order kinetics with desorption rate given as keff. Then equilibration of adsorption rate and desorption rate gives the equilibrium relation as... 

Statistical mechanics is not the xmique frame for the theory of adsorption. A description in kinetic terms of the equilibrium of the adsorbent with a gas was proposed by Jovanovic, who assuming desorption-hindering collisions as the unique cause for deviation from ideality of the gas and modeling the adphase as formed by localized molecules without lateral interactions, eventually obtained the equation... 

Let us. before giving illustrations, discuss some aspects of the statistical foundations. Model assumptions regarding the mode of adsorption (patchwise or random mobile or localized mono- or multilayer with or without lateral interaction ) are reflected in the natures of the local partition functions and in the way they combine to Q[N,N, T). Again, no general solution can be given models of different degrees of sophistication can be developed. 

We presented a novel quenched solid non-local density functional (QSNLDFT) model, which provides a r istic description of adsorption on amorphous surfaces without resorting to computationally expensive two- or three-dimensional DFT formulations. The main idea is to consider solid as a quenched component of the solid-fluid mixture rather than a source of the external potential. The QSNLDFT extends the quenched-annealed DFT proposed recently by M. Schmidt and cowoikers [23,24] for systems with hard core interactions to porous solids with attractive interactions. We presented several examples of calculated adsorption isotherms on amorphous and microporous solids, which are in qualitative agreement with experimental measurements on typical polymer-templated silica materials like SBA-15, FDU-1 and oftiers. Introduction of the solid density distribution in QSNLDFT eliminates strong layering of the fluid near the walls that was a characteristic feature of NLDFT models with smoodi pore walls. As the result, QSNLDFT predicts smooth isotherms in the region of polymolecular adsorption. The main advantage of the proposed approach is that QSNLDFT retains one-dimensional solid and fluid density distributions, and thus, provides computational efficiency and accuracy similar to conventional NLDFT models. 

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