© 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 (χ_{i}(E_{i}) , i=1 .. 2) for a known 2-dimensional energy distribution, χ_{(2)}(E_{12}):
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, E_{12}, for a known 2-dimensional energy distribution, χ_{(2)}(E_{12}) :
E_{12} = E_{1} - E_{2} - difference of energies (competitive adsorption)
- distribution of E_{12}
- square of dispersion of E_{12}
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, χ_{i}(E_{i}), into integral (cumulative) distributions, F_{i}(E_{i}) with corresponding inverse functions, i.e. energy profiles E_{i}(F_{i}), by using the above assumed energy dependencs we arrive at the possibility of using energy profiles, E_{i}(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 E_{12} 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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