Additivity of Plots

One of the nice features of the % plots is that for several mixed surfaces the X plots add. This is quite obvious because the dependent variable in the X equation is amount adsorbed which, of course, must add experimentally. An important feature of the x theory is the unit step function in Eq. (107). If there are several surface planes of different energies they would simply add 

An additional step is taken to determine the second differential 

The usefulness of this last equation is that the sum of 3 functions is an expression of the distribution of and thus the distribution of the various energies of adsorption. This fact wiU be utilized when a distribution is detected, which is x plot feature 1. 

It is not common to find pure materials with more than two distinct energies of adsorption. It may be common to find energy distributions as will be illustrated below. A couple of examples of two distinct energies of adsorption are found with carbon and with some ceramics that have distinct crystallographic planes on the surface. 

45-47 show some examples of x plot where it appears that two or more energy surfaces are involved. These are vulcan and sterling FT carbon [12] and high-fired thoria [13]. The adsorption on thoria has an addition feature due to mesoporosity, which can be separated out from the simple surface adsorption. This separation will be used as an example in a later section. 

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