Standard Curve Analysis using Distributions - Uninterpreted

Standard Curve Analysis Using Distributions - Uninterpreted 

In Chapter 3, the micropore analysis using a standard curve was presented. It was assumed that the system of pores was very simple in this analysis. The simphfication was that there is one energy of adsorption and one pore size. This is very unlikely to be the case, so in this section addition parameters will be introduced into the standard curve analysis. 

In principle, any standard curve may be used in this analysis provided the standard curve is descriptive of a homogeneous, non-porous material of identical surface composition. This is quite an order and there are only a few materials for which one could with some confidence say the standard curve 

The following analysis need not be interpreted in terms of physical quantities. Thus it yields an analytical form which one could use more easily with more traditional pore size analysis systems as well as x theory or DFT. Included in the traditional digital methods is the pore length method originated by Wheeler [7] and developed by Shull [8], the Barrett loyner and Halenda (BJH) [9] and the Cranston and Inkley [10]. It is, however, easier to visualize and it may be possible that once the parameters for a particular isotherm are obtained one could attach different meanings to them. Indeed, the x plot representation has been presented [11] as a method to empirically construct an analytical expression for the standard curves. 

For the curve fitting, it will be assumed that there is a distribution of energies, E s, and a distribution of pore sizes. Furthermore, some of the surface area is not inside the pores and is referred to as external. The pore radius is reflected in a cutoff in the standard curve or in terms of x there is a mean value (x for which the standard curve in the pores is terminated. The probability mass function (PMF) distribution will be used with the standard deviations for energy and pore size. Any reasonable distribution could be used and the parameters expanded, for example to include skewness, etc., but usually the experimental data would not justify this. Thus there are six parameters  

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