Energy distribution functions condensation approximation

The HILDA method developed by House and Jaycock [100] may be considered a modified, numerical version of the iterative procedure proposed by Adamson and Ling [126]. An excellent short presentations of the method can be found in the review by House [127] or in the monograph by Rudzinski and Everett [6]. This procedure can be outlined as follows The form of local isotherm is assumed and the distribution function is evaluated by using the iterative routine for each iterative step appropriate adjustments in distribution are made to bring the calculated and experimental isotherms into the best possible coincidence the condensation-approximation is used to determine the first approximation of the distribution. The Adamson-Ling method was widely applied to evaluate the energy distribution function from the measmed adsorption isotherm [97,122,128-135]. 

A first estimate of the energy distribution function is obtained via the condensation approximation. 

We may recall that the attractive V (r) is negative, so that work must be done to create a new surface, so there is an increase in free energy when a molecule is taken from the bulk and placed in the surface, as we have already discussed in Section 3.2.4. Unfortunately the experimental determination of aa is extremely difficult and we have to rely on density distribution functions and statistical mechanics or some other assumptions. It is well known that the effects of molecular structure and shape are often large for any condensed system, but since we have no adequate tools for describing such effects in a truly fundamental way, the best we can do is to estimate these effects by molecular simulation using computers. As we have already mentioned in Section 3.4.3, the density of the neighbor molecules is not uniform locally it is rather a function of the distance r from the guest molecule, p = ffr). This function is known as the density distribution function which can be approximately modeled and used in computation (see Section 4.1). 

Distribution (31), compared with distribution (10), shows that in the high-energy range the distribution function of equilibrium surfaces strictly resembles the distribution function explaining, in the condensation approximation, the modified DR isotherm if B is identified with l/ksT xo-... 

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