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Henry's constant calculations#

In this notebook we'll calculate the characteristic Henry's constant at zero loading. Unlike fitting the entire isotherm with a Henry model, these methods will attempt to fit a straight line only on the initial part of the isotherm. First, make sure the data is imported.

[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

Slope method#

The slope method of calculating Henry's fits a linear henry model to the isotherm points. If the model does not fit, it goes to progressively lower pressures until it finds a good fit. For data that is very non-linear, this fit might be between p=0 and the first isotherm point.

[2]:

# Slope method
isotherm = next(i for i in isotherms_n2_77k if i.material == 'MCM-41')
h1 = pgc.initial_henry_slope(isotherm, max_adjrms=0.01, logx=True, verbose=True)

isotherm = next(i for i in isotherms_n2_77k if i.material == 'UiO-66(Zr)')
h2 = pgc.initial_henry_slope(isotherm, max_adjrms=0.01, logx=True, verbose=True)

print(h1, h2)

Calculated K = 5.549e+04
Starting points: 42
Selected points: 2
Final adjusted RMSE: 5.32e-13
Calculated K = 6.977e+05
Starting points: 91
Selected points: 7
Final adjusted RMSE: 0.0061
55485.962663510676 697654.2592115065

../_images/examples_initial_henryc_3_1.png

../_images/examples_initial_henryc_3_2.png

Virial method#

The virial method uses a virial model to fit the data and then obtain the Henry constant from the value of the virial function at n=0. If the data is fitted well by a virial model, the resulting Henry constant will be very accurate.

[3]:

# Virial method
isotherm = next(i for i in isotherms_n2_77k if i.material == 'MCM-41')
h1 = pgc.initial_henry_virial(isotherm, verbose=True)

isotherm = next(i for i in isotherms_n2_77k if i.material == 'UiO-66(Zr)')
h2 = pgc.initial_henry_virial(isotherm, verbose=True)

print(h1, h2)

Attempting to model using Virial
Model Virial success, RMSE is 0.2174
Attempting to model using Virial
Model Virial success, RMSE is 0.494
194297.38100718585 1365637.221525526

../_images/examples_initial_henryc_6_1.png

../_images/examples_initial_henryc_6_2.png

../_images/examples_initial_henryc_6_3.png

../_images/examples_initial_henryc_6_4.png

More information about the functions and their use can be found in the manual.