Dubinin-Radushkevich and Dubinin-Astakov plots

The Dubinin-Radushkevich (DR) and Dubinin-Astakov (DA) plots are often used to determine the pore volume and the characteristic adsorption potential of adsorbent materials, in particular those of carbonaceous materials, such as activated carbons, carbon black or carbon nanotubes. It is also sometimes used for solution adsorption isotherms.

In pyGAPS, both the DR and DA plots are available with the dr_plot and da_plot functions. First we import the example isotherms.



In [1]:

    
%run import.ipynb









    



Selected 5 isotherms with nitrogen at 77K
Selected 2 room temperature calorimetry isotherms
Selected 2 isotherms for IAST calculation
Selected 3 isotherms for isosteric enthalpy calculation

Then we'll select the Takeda 5A isotherm to examine. We will perform a DR plot, with increased verbosity to observe the resulting linear fit. The function returns a dictionary with the calculated pore volume and adsorption potential.



In [2]:

    
isotherm = next(i for i in isotherms_n2_77k if i.material=='Takeda 5A')

pygaps.dr_plot(isotherm, verbose=True)









    



Micropore volume is: 0.484 cm3
Effective adsorption potential is : 5.843 kj/mol






    Out[2]:





{'pore_volume': 0.48394993000838316, 'adsorption_potential': 5.842533982350703}

We can specify the pressure limits for the DR plot, to select only the points at low pressure for a better fit.



In [3]:

    
pygaps.dr_plot(isotherm, limits=[0,0.1], verbose=True)









    



Micropore volume is: 0.448 cm3
Effective adsorption potential is : 5.999 kj/mol






    Out[3]:





{'pore_volume': 0.44804691858361767,
 'adsorption_potential': 5.9985146944259355}

An extension of the DR model is the DA plot. In the DA equation, the exponent can vary, and is usually chosen between 1 (for surfaces) and 3 (for micropores). For an explanation of the theory, check the function reference.

We then use the da_plot function and specify the exponent to be 2.3 (larger than the standard DR exponent of 2)



In [4]:

    
pygaps.da_plot(isotherm, limits=[0,0.1], exp=2.3, verbose=True)









    



Micropore volume is: 0.421 cm3
Effective adsorption potential is : 6.345 kj/mol






    Out[4]:





{'pore_volume': 0.4213627701439593, 'adsorption_potential': 6.345248838485782}

The DA plot can also automatically test which exponent gives the best fit between 1 and 3, if the parameter is left blank. The calculated exponent is returned in the result dictionary.



In [5]:

    
pygaps.da_plot(isotherm, limits=[0, 0.1], exp=None, verbose=True)









    



Exponent is: 3.00
Micropore volume is: 0.383 cm3
Effective adsorption potential is : 6.924 kj/mol






    Out[5]:





{'pore_volume': 0.38315730195208947,
 'adsorption_potential': 6.924262107300744,
 'exponent': 2.999995637113072}

More info about the method can be found in the reference.