© A.W.Marczewski 2002
A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces
Correlation of adsorption energies of components
See also Energy correlations:
Calculation of energy distribution of a single component (χi(Ei) , i=1 .. 2) for a known 2-dimensional energy distribution, χ(2)(E12):
and
Average energies of components "1" and "2":
and
Squares of energy dispersions of components "1" and "2":
and
Calculation of distribution of energy differences of 2 components, E12, for a known 2-dimensional energy distribution, χ(2)(E12) :
E12 = E1 - E2 - difference of energies (competitive adsorption)
- distribution of E12
- square of dispersion of E12
Calculation of correlation coefficient of components' energies:
By assuming that there exists some functional dependence between energies of components:
and/or
We obtain (at least) non-linear correlation of components' energies.
If we transform our differential energy distributions, χi(Ei), into integral (cumulative) distributions, Fi(Ei) with corresponding inverse functions, i.e. energy profiles Ei(Fi), by using the above assumed energy dependencs we arrive at the possibility of using energy profiles, Ei(F) where F is common for all components (see extended discussion).
If we use the relative energy function z(F):
with corresponding relations:
and/or
then the square of individual components' energy dispersion will be:
for i = 1, 2
Then for a difference of energies we obtain:
and the relative energy difference function:
By using the above defined quantities, we obtain the square of dispersion of energy differences (i.e. also the square of dispersion of adsorption energy E12 in competitive adsorption "1+2", e.g. in liquid mixture):
where the correlation coefficient may be calculated as:
Legend for model pictures
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