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The \(\alpha_s\) method#

Very similar to the t-plot method, the \(\alpha_s\) method compares an isotherm on a porous material with one that was taken on a reference non-porous surface. The reference isotherm should be measured over a wide pressure range, to be able to compare loading values. First, make sure the data is imported notebook.

[1]:

# import isotherms
%run import.ipynb

# import the characterisation module
import pygaps.characterisation as pgc

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

Unfortunately, we don't have a reference isotherm in our data. We are instead going to be creative and assume that the adsorption on the silica (\(SiO_2\) sample) is a good representation of an adsorption on a non-porous version of the MCM-41 sample. Let's try:

[2]:

iso_1 = next(i for i in isotherms_n2_77k if i.material == 'MCM-41')
iso_2 = next(i for i in isotherms_n2_77k if i.material == 'SiO2')

print(iso_1.material)
print(iso_2.material)
try:
    results = pgc.alpha_s(iso_1, reference_isotherm=iso_2, verbose=True)
except Exception as e:
    print('ERROR!:', e)

MCM-41
SiO2
ERROR!: A value in x_new is below the interpolation range.

The data in our reference isotherm is on a smaller range than that in the isotherm that we want to calculate! We are going to be creative again and first model the adsorption behaviour using a ModelIsotherm.

[3]:

import pygaps

model = pygaps.ModelIsotherm.from_pointisotherm(iso_2, model='BET', verbose=True)

Attempting to model using BET.
Model BET success, RMSE is 0.474
../_images/examples_alphas_5_1.png

With our model fitting the data pretty well, we can now try the \(\alpha_s\) method again.

[4]:

results = pgc.alpha_s(iso_1, model, verbose=True)

For linear region 0
The slope is 0.004462 and the intercept is 0.001096, with a correlation coefficient of 0.9848
The adsorbed volume is 0.0381 cm3/g and the area is 270.1 m2/g
For linear region 1
The slope is 0.0005994 and the intercept is 0.008443, with a correlation coefficient of 0.9656
The adsorbed volume is 0.293 cm3/g and the area is 36.28 m2/g
../_images/examples_alphas_7_1.png

The results don't look that bad, considering all our assumptions and modelling. There are other parameters which can be specified for the \(\alpha_s\) function such as:

  • The relative pressure to use as the reducing pressure

  • The known area of the reference material. If this is not specified, the BET method is used to calculate the surface area.

  • As in the t-plot function, the limits for the straight line selection.

Read more about the theory in the documentation of the module and in the manual.