Isotherm model fitting#
In this notebook we'll attempt to fit isotherms using the included models. First, make sure the data is imported by running the import notebook.
[1]:
%matplotlib inline
# import isotherms
%run import.ipynb
# Then the modelling module
import pygaps.modelling as pgm
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
Selecting models#
Instead of recreating isotherms, we'll fit PointIsotherms with the model_iso function. Let's select one of the isotherms and attempt to model it with the Double Site Langmuir model. It is worth noting that, if the branch is not selected, the model will automatically select the adsorption branch.
[2]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='UiO-66(Zr)')
model_iso = pgm.model_iso(isotherm, model='DSLangmuir', verbose=True)
print(model_iso.model)
Attempting to model using DSLangmuir.
Model DSLangmuir success, RMSE is 0.0235
DSLangmuir isotherm model.
RMSE = 0.02352
Model parameters:
n_m1 = 4.736
K1 = 243.3
n_m2 = 9.218
K2 = 5.912e+04
Model applicable range:
Pressure range: 6.04e-07 - 0.96
Loading range: 0.257 - 14.7
The original model is therefore reasonably good, even if there are likely microporous filling steps at low pressure which are not fully captured. It's important to note that the ModelIsotherm has almost all the properties of a PointIsotherm and can be used for all calculations. For example:
[3]:
import pygaps.characterisation as pgc
res = pgc.area_langmuir(model_iso, verbose=True)
Langmuir area: a = 1361 m2/g
Minimum pressure point is 0.0482 and maximum is 0.851
The Langmuir constant is: K = 738
Amount Langmuir monolayer is: n = 0.014 mol/g
The slope of the Langmuir fit: s = 71.7
The intercept of the Langmuir fit: i = 0.0971
Let's now apply the same model to another isotherm.
[4]:
isotherm = next(i for i in isotherms_n2_77k if i.material == 'SiO2')
try:
model = pgm.model_iso(
isotherm,
model='DSLangmuir',
verbose=True,
)
except Exception as e:
print(e)
Attempting to model using DSLangmuir.
Fitting routine for DSLangmuir failed with error:
The maximum number of function evaluations is exceeded.
Try a different starting point in the nonlinear optimization
by passing a dictionary of parameter guesses, param_guess, to the constructor.
Default starting guess for parameters:
[ 8.584125 18.63017335 8.584125 27.94526003]
We can increase the number of minimisation iterations manually, by specifying an optimisation_params dictionary which will be passed to the relevant Scipy routine. However, the model chosen may not fit the data, no matter how much we attempt to minimise the function, as seen below.
[5]:
isotherm = next(i for i in isotherms_n2_77k if i.material == 'SiO2')
try:
model = pgm.model_iso(
isotherm,
model='DSLangmuir',
verbose=True,
optimization_params=dict(max_nfev=1e3),
)
except Exception as e:
print(e)
Attempting to model using DSLangmuir.
Fitting routine for DSLangmuir failed with error:
The maximum number of function evaluations is exceeded.
Try a different starting point in the nonlinear optimization
by passing a dictionary of parameter guesses, param_guess, to the constructor.
Default starting guess for parameters:
[ 8.584125 18.63017335 8.584125 27.94526003]
Guessing models#
We also have the option of guessing a model instead. This option will calculate model fits with a selection of the available models, and select the one with the smallest root mean square. Let's try this on the previous isotherm.
[6]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='SiO2')
model = pgm.model_iso(isotherm, model='guess', verbose=True)
Attempting to model using Henry.
Model Henry success, RMSE is 0.102
Attempting to model using Langmuir.
Modelling using Langmuir failed.
Fitting routine for Langmuir failed with error:
The maximum number of function evaluations is exceeded.
Try a different starting point in the nonlinear optimization
by passing a dictionary of parameter guesses, param_guess, to the constructor.
Default starting guess for parameters:
[46.57543338 17.16825 ]
Attempting to model using DSLangmuir.
Modelling using DSLangmuir failed.
Fitting routine for DSLangmuir failed with error:
The maximum number of function evaluations is exceeded.
Try a different starting point in the nonlinear optimization
by passing a dictionary of parameter guesses, param_guess, to the constructor.
Default starting guess for parameters:
[ 8.584125 18.63017335 8.584125 27.94526003]
Attempting to model using DR.
Model DR success, RMSE is 0.134
Attempting to model using Freundlich.
Model Freundlich success, RMSE is 0.0977
Attempting to model using Quadratic.
Model Quadratic success, RMSE is 0.181
Attempting to model using BET.
Model BET success, RMSE is 0.0311
Attempting to model using TemkinApprox.
Model TemkinApprox success, RMSE is 0.0963
Attempting to model using Toth.
Model Toth success, RMSE is 0.102
Attempting to model using JensenSeaton.
Model JensenSeaton success, RMSE is 0.102
Best model fit is BET.
We can see that most models failed or have a poor fit, but the BET model has been correctly identified as the best fitting one.
Other options#
We can also attempt to model the desorption branch of an isotherm, and provide a manual list of models to attempt to guess, including specialised models which are not usually included in the guessing routine.
[7]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='Takeda 5A')
model = pgm.model_iso(isotherm, model=['GAB', 'BET', 'Langmuir'], branch='des', verbose=True)
Attempting to model using GAB.
Model GAB success, RMSE is 0.0569
Attempting to model using BET.
Model BET success, RMSE is 0.0569
Attempting to model using Langmuir.
Model Langmuir success, RMSE is 0.119
Best model fit is BET.
We can manually set bounds on fitted parameters by using a param_bounds dictionary, passed to the ModelIsotherm.
[8]:
isotherm = next(i for i in isotherms_n2_77k if i.material == 'UiO-66(Zr)')
model = pgm.model_iso(
isotherm,
model='Langmuir',
param_bounds={
"n_m": [0., 14],
"K": [0., 100],
},
verbose=True,
)
Attempting to model using Langmuir.
Model Langmuir success, RMSE is 0.247
Just because a the minimisation has successfully produced a model that does NOT mean that the model is accurate. For example, trying to model the MCM-41 sample with a Langmuir model does not throw any errors but it is obvious that the model is not representative of the mesoporous condensation in the pores.
[9]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='MCM-41')
model = pgm.model_iso(isotherm, model="DSLangmuir", verbose=True)
Attempting to model using DSLangmuir.
Model DSLangmuir success, RMSE is 0.0507
Creating ModelIsotherms#
ModelIsotherms do not need to be created from a PointIsotherm. They can also be created from raw data, or from pre-generated models. To create one from scratch:
[10]:
import pygaps as pg
model_iso = pg.ModelIsotherm(
material='carbon',
adsorbate='N2',
temperature=77,
pressure=[1,2,3,4],
loading=[1,2,3,4],
model='Henry',
)
model_iso.plot()
WARNING: 'pressure_mode' was not specified, assumed as 'absolute'
WARNING: 'pressure_unit' was not specified, assumed as 'bar'
WARNING: 'material_basis' was not specified, assumed as 'mass'
WARNING: 'material_unit' was not specified, assumed as 'g'
WARNING: 'loading_basis' was not specified, assumed as 'molar'
WARNING: 'loading_unit' was not specified, assumed as 'mmol'
WARNING: 'temperature_unit' was not specified, assumed as 'K'
Or if a model is to be created from pre-defined parameters, one can do:
[11]:
model = pgm.get_isotherm_model(
'Langmuir',
parameters={
"K": 20,
"n_m": 2
},
pressure_range=(0.01, 2),
)
model_iso = pg.ModelIsotherm(
material='carbon',
adsorbate='N2',
temperature=77,
model=model,
)
model_iso.plot()
WARNING: 'pressure_mode' was not specified, assumed as 'absolute'
WARNING: 'pressure_unit' was not specified, assumed as 'bar'
WARNING: 'material_basis' was not specified, assumed as 'mass'
WARNING: 'material_unit' was not specified, assumed as 'g'
WARNING: 'loading_basis' was not specified, assumed as 'molar'
WARNING: 'loading_unit' was not specified, assumed as 'mmol'
WARNING: 'temperature_unit' was not specified, assumed as 'K'
More info can be found in the manual section.