A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Potential Curves for DR isotherm

NOTE
Characteristic micropore-filling concentration co is smaller than cs (concentration of saturated solution). Analogously, for vapours, po < ps.  Legend.   The course of Dubinin-Radushkevich (DR) isotherm corresponds to the typical shape of characteristic potential curve found for microporous solids. In the following pictures, the characteristic potential curves obtained for T = 293K and 3 different B2 values are presented ( B2 = 3e-9; 1e-8; 3e-8 - it corresponds to B2(RT)2 = 0.0178; 0.0593; 0.178 or - if one prefers to use log10 scaling - B2[ln(10) RT]2 = 0.0944; 0.315; 0.944 ). Rotated and scaled model potential curves, adsorbate volume (V/Vs) vs. A, adsorption potential [J], calculated for Dubinin-Radushkevich isotherm, T = 293K and 3 values of B2 parameter (see legend). Scaled model potential curves, A, adsorption potential [J] vs. adsorbate volume (V/Vs), calculated for Dubinin-Radushkevich isotherm, T = 293K and 3 values of B2 parameter (see legend). Scaled model potential curves, A, adsorption potential [J] vs. adsorbate volume (V/Vs), calculated for Dubinin-Radushkevich isotherm, T = 293K and 3 values of B2 parameter (the same B2 as above; in the picture the values of B2(RT)2 are shown) (see legend). Linear Dubinin-Radushkevich plot: log10(V) vs. [log10(ps/p)]2 , calculated for Dubinin-Radushkevich isotherm, T = 293K and 3 values of B2 parameter (in the picture the values of B2(ln10 RT)2 are shown) (see legend). One has to be always aware which form of DR equation is used. In evaluation of experimental data this decimal logarithms are often used, however such obtained values of (slope is = B2(ln10 RT)2 ) parameters are scaled when compared to natural logarithm plots (slope is = B2(RT)2 ). Sometimes DR equation is defined in such a way, that the "convoluted" parameter B = B2(RT)2 is used, however, it hides the fact that the structural parameter B2 is temperature independent.

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