# Unifying Mixed Gas Adsorption in Molecular Sieve Membranes and MOFs using
Machine Learning

Subhadeep Dasgupta  Amal R S  Prabal K. Maiti

###### Abstract

Recent machine learning models to accurately obtain gas adsorption isotherms
focus on polymers or metal-organic frameworks (MOFs) separately. The
difficulty in creating a unified model that can predict the adsorption trends
in both types of adsorbents is challenging, owing to the diversity in their
chemical structures. Moreover, models trained only on single gas adsorption
data are incapable of predicting adsorption isotherms for binary gas mixtures.
In this work, we address these problems using feature vectors comprising only
the physical properties of the gas mixtures and adsorbents. Our model is
trained on adsorption isotherms of both single and binary mixed gases inside
carbon molecular sieving membrane (CMSM), together with data available from
CoRE MOF database. The trained models are capable of accurately predicting the
adsorption trends in both classes of materials, for both pure and binary
components. ML architecture designed for one class of material, is not
suitable for predicting the other class, even after proper training,
signifying that the model must be trained jointly for proper predictions and
transferability. The model is used to predict with good accuracy the CO2
uptake inside CALF-20 framework. This work opens up a new avenue for
predicting complex adsorption processes for gas mixtures in a wide range of
materials.

###### keywords:

Carbon capture , Molecular sieve membrane , Metal organic framework , Machine
learning

††journal: Separation and Purification Technology — Accepted on June 16, 2024

[inst1] organization=Department of Physics, Indian Institute of Science,
city=Bangalore, postcode=560012, state=Karnataka, country=India

##  1 Introduction

In recent times, the rapid design and manufacture of nanoporous materials has
sparked interest in the chemical industry as a means to replace existing
solvent-based filtration with highly selective adsorbent frameworks.
Adsorption-based filtration are positioned to provide higher yield, while also
consuming less energy during chemical separation processes [1]. Unlike other
extraction techniques, nanofiltration operates under moderate temperature and
pressure conditions, and increases safety during operations [2, 3]. Nanoporous
materials include a diverse range of materials, all having completely
different chemical structures leading to a wide range of physicochemical
properties. The most common categories include metal-organic frameworks (MOFs)
[4], porous organic cages (POCs) [5], covalent-organic frameworks (COFs) [6],
and zeolites [7, 8]. There has also been significant developments in
understanding formation of nanoporous membranes, making them another viable
choice for chemical filtration. Advances have been made in the fabrication of
nanochannels [9], polymers [10], and mixed matrix membranes [11]. MOFs are
currently the most studied class of porous crystalline materials, made up of
repeating units of small building units consisting of metal sites connected to
organic molecules. Polymeric membranes are fabricated from growing connections
of individual monomers. The connectivity of these monomers, their growth rate,
cross-linking, and chain length can greatly influence their structural
properties and adsorption trends [12, 13, 14, 15, 16, 17, 18]. Research is
also being carried out to fabricate MOF-based membranes for enhanced gas
separations [19]. The different stoichiometry involved during fabrication
gives rise to a diverse variety of membranes, each showing unique physical and
chemical properties. The vast zoo of materials allows us to find the perfect
candidate for a particular filtration task, on the basis of its affinity to
accept one type of gas penetrant from different gas mixtures.

The adsorption performance of complex materials can be evaluated using
computational techniques, allowing pre-screening of materials prior to
manufacture, greatly cutting production costs for industries. Molecular
dynamics (MD) simulations, help in understanding the formation of the
adsorbent material. Grand canonical Monte Carlo (GCMC) simulations of the
adsorbent kept in contact with a virtual reservoir of gas molecules provide
accurate prediction of the membrane gas uptake capacity. However, the
bottleneck of these simulations arise from their increasing system sizes.
Performing simulations (or experiments) to assess the performance on all
possible combinations of adsorbents and gas mixtures is thus still a
challenge. To overcome the computational limitations, predictive algorithms
powered by machine learning (ML) models, trained on available data, is
currently being explored to predict gas separation of newly discovered
materials [20, 21]. However, the vast majority of existing literature data
primarily focus on single component adsorption, thereby raising concerns on a
trained model’s ability to make accurate predictions for gas mixtures [22]. In
current times there has been a peak in industrial and academic interests of
using ML algorithms towards materials discovery and their prediction
capacities [23, 24, 25, 26]. Since the output of all such models are
correlated with the input dataset, training on MOFs alone restricts
predictions on polymer membranes and vice versa. Data driven techniques, such
as transfer learning [27], fine-tuning [28], and predicting with large
language models (LLMs) [29] are not applicable in such cases since the nature
of adsorption is inherently different in different classes of materials [30].
Additionally, there the available database for membranes is not as robust as
for MOFs, making it difficult to validate the predictions. The type of input
features used for MOFs (fingerprints) during training may not be available for
other nanomaterials, making it impossible for an existing model to be applied
on polymer membranes.

ML assisted workflows have been exceptionally powerful in performing high
throughput screening of millions of possible MOF for finding optimum thermal
and mechanical stability and also for targeted applications [31, 32, 33, 34].
Energy based descriptors have been used to rapidly model and understand MOFs
with exceptional H2 storage capacities [35, 36, 37]. Likewise, similar efforts
have resulted in identification of composite MOFs for use in CO2 storage in
harsh environmental setting of low to high pressures [38, 39, 40, 41, 42, 43].
The methodology has also proven to be useful for prediction gas adsorption in
general in MOFs [44, 45, 46]. The role of publicly available large databases
has also facilitated the study of nanopores in the structures which further
enriches the understanding of gas adsorption processes and aid in future
designing of MOFs [47, 48, 49, 50, 51, 52, 53]. Sophisticated state-of-the-art
tools like genetic algorithms, transfer learning and tailored ML models have
also been proposed for guided and intelligent choice of MOFs towards a variety
of use cases including CH4 sensing [54], accurate MOF forcefield development
[55] and gas separations [56, 57, 58, 59]. The success of the above techniques
in predicting material properties and molecular interactions have also been
utilized to study gas adsorption in polymeric membranes [60, 61]. ML has also
empowered predicting the gas diffusivities and permeabilities of a wide range
of materials [22, 62, 63] which otherwise requires performing careful
simulations, particularly for gas mixtures [64, 65, 66, 67]. Techniques have
also been developed to account for incomplete datasets during the training
process of an ML model [68], obtaining fractional free volume of membranes
[69], and predicting a given polymer membrane’s adsorption selectivity and
their performance towards gas separation [70, 71, 72, 73, 74, 75, 76].

Regardless of the vast number of advances, all ML algorithms are restricted by
their training data, limiting their scope of applicability. In this work, we
propose a solution addressing the transferability concerns of trained ML
model, by training on combined data of carbon molecular sieving membranes
(CMSMs) and MOFs. The input and output features allow for both single and
binary gas mixtures while also taking into consideration the presence of
moisture. The input features used are purely physical properties of a material
which can be easily obtained for any class of material. The methodology
section describes the database and techniques used to train the ML models,
followed by the results section which discusses our findings. In the
conclusion section, we discuss the implications and scope of this work.

##  2 Method

###  2.1 Data preparation

Figure 1:  Monomers (a) pyrrole and (b) pyridine used to build different
$6$F-CMSM polymers. Equilibrated morphologies of three representative
membranes. The inverse density $(1/\rho)$ of these membranes are (c) highest
$($0.86\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$, (d) average
$($0.79\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$, and (e) lowest
$($0.69\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$. The simulation
box lengths are in $\AA$ units. The bottom color legends show the constituent
elements in the polymer membrane.

Figure 2:  Unit cell structures of three MOFs in the dataset. The inverse
density $(1/\rho)$ values are (a) highest
$($6.41\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$, (b) average
$($1.22\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$, and (c) lowest
$($0.46\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{g}}^{-1}$)$. The unit cell
lengths of the MOFs are in $\AA$ units. The bottom color legends show the
constituent elements in the MOFs.

To obtain gas adsorption data for polymers we require datasets comprising
significant variations in the membrane’s structural properties. In our
previous work [14], we have shown that the physical properties of a carbon
molecular sieving membrane derived from 6FDA/BPDA-DAM polymer precursor [77]
($6\text{F-CMSM}$) is highly tunable, based on the chain length of individual
polymer strands. The 6F-CMSMs are built using pyrrole and pyridine monomers
(Figure 2a, 2b), distributed randomly throughout each polymer chain. Variation
in porosity of equilibrated membranes also explain the different gas
adsorption performances observed in experiments owing to pyrolisis of the
precursor at different temperatures. The bonded and non-bonded interactions
are computed using parameters of the modified Dreiding forcefield [78, 79].
The MD simulations to obtain the density equilibrated 6F-CMSM structures were
performed using compression-decompression algorithms using LAMMPS [80]
discussed in our earlier works [14, 79]. The TraPPE forcefield [81] is used to
compute the bonded and non-bonded interactions of the gases with each other
and the adsorbent framework. Lorentz-Berthelot mixing rule is used to compute
the interaction of different atom types. For equilibration, we follow a
simulation protocol comprising a series of compression-decompression
algorithms in NPT ensemble for $100\text{\,}\mathrm{ns}$ described in detail
in our previous work [14]. The final equilibrated system corresponds to
temperature $300\text{\,}\mathrm{K}$ and pressure of $1\text{\,}\mathrm{bar}$.
The equilibrated structures of 6F-CMSM are obtained using all-atom MD
simulations. Figure 2c to 2e shows three representative structures of the
membrane arranged in decreasing order of inverse density $(1/\rho)$. Different
physical properties such as gravimetric surface area (GSA), helium void
fraction $(\xi)$, density $(\rho)$, largest included sphere $(D_{i})$, and
largest free spheres $(d_{max})$ of the different 6F-CMSM are obtained using
the equilibrated MD structures using RASPA [82] and Zeo++ [83], enabling us to
create a dataset for adsorption of different gases at different temperature
$(T)$, pressure $(P)$, and vapor pressures. These quantities are used as input
features to describe the adsorbent material. GSA, $\rho,D_{i},d_{max}$ of the
equilibrated $6$F-CMSMs are computed using Zeo++ [83]. $\xi$ is obtained using
Widom insertion of helium atom in the membrane[82], as implemented in RASPA.

Table 1: Kinetic diameters, $d(\AA)$, of gas molecules studied in this work. Gas |  C6H6 |  C2H6 |  C3H8 |  Xe |  Kr |  CH4 |  N2 |  O2 |  Ar |  CO2 |  H2 |  H2O
---|---|---|---|---|---|---|---|---|---|---|---|---
$d(\AA)$ | $5.85$ | $4.443$ | $4.3$ | $3.96$ | $3.6$ | $3.758$ | $3.64$ | $3.46$ | $3.4$ | $3.3$ | $2.89$ | $2.65$

To obtain gas adsorption isotherms we perform a series of GCMC simulations in
the $\mu$VT ensemble, until the loading equilibrates, using RASPA [82]. The
membrane is kept rigid during GCMC adsorption simulation. Each GCMC step is
composed of insertion of a gas from reservoir into the pore of $6$F-CMSM,
deletion, translation, rotation, and swapping of two gas molecules, similar to
the protocol used in our previous work [14]. The number of gases inside the
membrane gradually increases starting from zero to its equilibrium value based
on the environmental condition of pressure
($0-$50\text{\,}\mathrm{b}\mathrm{a}\mathrm{r}$$) and temperature
($273\text{\,}\mathrm{K}$, $308\text{\,}\mathrm{K}$, and
$373\text{\,}\mathrm{K}$). Our GCMC simulations consist of both pure and
binary gas mixtures of varying mole fractions, which in turn will help our
model to predict for competitive adsorption processes as well. The kinetic
diameters of the different gases are given in Table 1. For binary gas mixtures
following compositions are studied: CO2:CH4 are studied for 50:50, and 10:90
mole fractions, and CO2:N2 for 20:80 mole fraction. The additional effects of
moisture on gas uptake is studied by introducing some amount of H2O molecules
in $\ce{CO2}:\ce{CH4}$ = 10:90 mixture. Data for MOFs were taken from the
Computation-Ready Experimental (CoRE) MOFs database [84], for which all of the
above physical properties as well as gas loading capacity are available in
literature [20]. The available data is thus a subset of the complete database,
containing the gases C2H6, Xe, Kr, CH4, N2, O2, and Ar. The chemical
structures of three representative MOFs from this dataset are shown in Figure
2, arranged in descending order of their inverse density. Figure 2 and Figure
2 showcase the diversity in the free volumes inside these nanostructures,
giving rise to their interesting physico-chemical properties. From our GCMC
simulations we obtain a set of 3180 adsorption data for the membrane, while
there are 1741 available data for MOFs comprising all required properties.

Figure 3: Correlation coefficients of input and output features.

###  2.2 Fingerprinting

Each gas molecule is identified using its kinetic diameters $(d)$, followed by
their mole fraction $(x)$ in the mixture. The fingerprint used to describe
each input parameter is,

$\displaystyle I=\big{\\{}$ $\displaystyle d_{A}(\AA),\enspace
d_{B}(\AA),\enspace x_{A},\enspace x_{B},$ $\displaystyle T(K),\enspace
P(bar),\enspace\text{GSA}(m^{2}g^{-1}),$
$\displaystyle\xi,\enspace\rho^{-1}(cm^{3}g^{-1}),\enspace D_{i}(\AA),\enspace
d_{max}(\AA)\big{\\}},$

where the subscripts A, B denote the two gases in a binary mixture. The output
features are the saturated gas uptake $(q)$ of the binary gas components,
given by

$\displaystyle O=\big{\\{}q_{A}(mol\enspace kg^{-1}),\enspace
q_{B}(mol\enspace kg^{-1})\big{\\}}$

The conditions $d_{B}=0$ and $q_{B}=0$ describe the cases for pure gas
adsorption. The correlation coefficients of the input and output features are
shown in Figure 3. Aside from $d$ and $x$, there is no strong correlation in
the parameters, making it a valid choice for fingerprinting the dataset.

###  2.3 Model Training

Figure 4:  Distribution of physical properties of the combined $6$F-CMSM and
MOF dataset.

To prevent overfitting and improve the generality of predictions, a common
strategy is to introduce randomness to the input feature, mimicking small
noises in the dataset [85]. We perturb the quantities in $I(T,\dots,d_{max})$
using small random Gaussian noise. The kinetic diameter and mole fraction of
gases are excluded during this perturbation since they uniquely identify a gas
molecule, and slight change in $d$ will inadvertently represent a completely
different gas molecule. Noise inherently appears in $q$ from fluctuations
during the steps of GCMC simulation. The distribution of the combined dataset
is shown in Figure 4. The combined dataset is normalized, shuffled, and split
for training (80%), validation (10%), and testing (10%) purposes. The training
data is fed into two ML models, artificial neural networks (ANN) in
TensorFlow[86], and XGBoost [87]. The ML models are kept blind to the data
kept aside for testing.

Each ML model is described by a set of hyper-parameters that affect how the
model learns. NN models are made up of different nodes and layers, each node
having different weights and biases to pass information to the next layer. For
NN the hyper-parameters investigated in this work include number of hidden
layers $(h)$, number of nodes in each layer $(n)$, training epochs $(e)$,
activation functions $(f)$, kernel initializers and regularizers, and loss
functions. We vary $n$ from $11$ to $600$. For each $n$, we explore $h$ from
$3$ to $9$. We also explore a set of $\\{n,h\\}$ where $n$ decreases down from
$\\{2^{h},\dots,2^{1}\\}$ for each subsequent layer. In this case, we vary $h$
from $3$ to $16$. Our set-up thus allows exploring shallow and deep neural
networks (DNNs). The training epochs $(e)$ are explored with and without
early-stopping. We investigate $f$ using ReLU and sigmoid functions, with
orthogonal initializers, and L1, L2 regularizers.

The XGBoost model is a random forest algorithm designed to quickly navigate
through the dataset, identify logical relations between input and output,
thereby creating a hierarchy of hyper-branched data, terminating at different
output points (leaf). For XGBoost, we perform a thorough grid-search involving
the parameters number of estimators, learning rate, depth of the tree and
branches, loss reduction, and regularizers. The performance of the models are
measured using mean squared error (MSE) and mean absolute error (MAE) metrics
against the testing data. The best performing models are identified based on
their training and validation losses of the output predictions w.r.t. testing
data which serves as our ground truth, which serves as the reference for
comparing the ML predictions.

##  3 Results and discussion

Figure 5:  Training and validation loss vs. epochs for a neural network having
$(n,h)=(160,7)$ using (a) MSE and (b) MAE metrics respectively.

Figure 6:  NN predictions with $(n,h)=(160,7)$ using (a) MSE and (b) MAE
metrics respectively. The different gas molecules are shown in different
symbols shown in the legend. The 100% agreement line is shown in black as a
guide to the eyes.

We explore the various configurations of the different NN hyper-parameters to
identify the optimum configuration of our model. We find that ReLU activation
function works better with our dataset. Including kernel regularizers in the
NN nodes also reduces the rate of convergence of the model. The training and
validation losses for two NN models are shown in Figure 6, both models have
ReLU activation function, without kernel regularizers. We find that using MSE
to compute the error leads to a faster convergence with significant less loss
compared to MAE. The fluctuations in the losses with epochs is also less when
using MSE in contrast to noticeable fluctuations when using MAE. This
phenomenon can be explained based on the diversity of our input dataset. When
using MSE as the loss function during training, the penalty imposed on $I$ is
higher, which leads to sharp changes in the weights of NN nodes in the layers.
The performance of the two types of models using MSE and MAE against the test
data is shown in Figure 6. The prediction accuracy for Kr, significantly
deviate from the agreement line when using MAE metric for the loss function.
The prediction accuracy for the other gases are similar using both MSE and MAE
metrics. We thus focus our work using MSE as the preferred loss function.

Figure 7: Comparison of gas loading (q) predictions using (a) NN with
$(n,h)=(2^{14},14)$ trained on the combined dataset and (b) NN with
$(n,h)=(2^{10},10)$ trained only using $6\text{F-CMSM}$ data.  Figure 8:
Comparison of gas loading (q) predictions (normalized) using (a) best
performing NN having $(n,h)=(240,3)$ and (b) XGBoost after hyper-parameter
optimization. The predictions of $q_{A}$ are for gas loading inside $6$F-CMSM
and MOFs. $q_{B}$ denotes the gas loading in cases of binary gas mixtures
inside $6$F-CMSM.  Figure 9: Prediction of CO2 uptake inside structured
CALF-20 framework at $T=$313\text{\,}\mathrm{K}$$. The red line corresponds to
the average prediction obtained from three different neural networks and the
shaded region corresponds to its standard deviation. The predictions are
compared against experimental data points available in literature [88].

When presented with a given dataset, there is no robust mechanism for deciding
what kind of ML architecture one would need to use. As such, even within an NN
model, one cannot ascertain the architecture of nodes and hidden layers a
priori. We highlight the importance of choosing a reasonable ML model
architecture by studying a set of DNNs having increasingly large $n$. DNNs
require significant computational resources during training and prediction,
which becomes their major drawback, and is thus important to use early-
stopping on the epochs, once the loss function converges. By training various
DNNs, we observe that the models fail to perform well when trained on the
combined polymer and MOF dataset (Figure 7a). In contrast, when presented with
gas adsorption data inside $6$F-CMSM only (Figure 7b), the predictions from
DNN are close to the ground truth. This shows that combining two datasets
without considering their architectures will lead unsatisfactory predictions.

We perform a thorough search of hyper-parameters for NN and XGBoost models and
obtain the best performing ML models as described in the previous section.
Among the trained neural networks, we observe that $(n,h)$ greatly affects,
the model’s performance. The best performing $(n,h)$ pairs for both pure and
binary gas mixtures are $(100,3)$, $(240,3)$, $(256,3)$, $(260,3)$, $(320,7)$,
$(330,5)$, and $(560,7)$. For all other combinations, the predictive
capabilities are restricted only to the single gas loadings. In Figure 8, we
compare the performance of a tuned NN model having $(n,h)=$ (240, 3) vs. tuned
XGBoost model. It is to be noted that the dataset contains Gaussian noise and
is thus not susceptible to overfitting. There is excellent agreement of the
XGBoost prediction against our test data. The NN predictions also have good
accuracy, lying very close to the 100% agreement line. Although the
predictions using XGBoost is closer to the test values, the random forest
model does not generate smooth adsorption isotherms for an input gas,
temperature, and pressure condition. The predictions from NN models thus
resemble physical processes, while also preserving reasonable accuracy. To
test the performance of our model on unknown data, we study the adsorption
isotherm of pure CO2 within the structured CALF-20 framework [88], at
$313\text{\,}\mathrm{K}$ temperature, which was not present in our training
dataset. The input physical properties for the structured CALF-20 are taken to
be $\rho=$0.57\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}$$ [89], GSA
$=$528\text{\,}{\mathrm{m}}^{2}\text{\,}{\mathrm{g}}^{-1}$$ [88], $\xi=0.35$,
$D_{i}=2.8\AA$, and $d_{max}=4.3\AA$ [90]. It is to be noted that CALF-20
shows a drastic increase in CO2 adsorption in the low pressure regime, unlike
the CMS membrane or majority of the MOFs available in our training data.
Despite the lack of such isotherms in training dataset, the models could learn
the details of the gas adsorption and could reproduce the uptake capacity with
good accuracy. The obtained isotherm is plotted in Figure 9 compared alongside
with experimental data available in literature [88].

##  4 Conclusion

Obtaining precise gas loading capacities by an adsorbent from gas mixtures is
important, since a slight deviation can drastically change their solubility
coefficients, changing its permeability, affecting the materials expected
separation performances. In this work we predict using machine learning
techniques, the gas adsorption isotherms for pure and binary mixtures inside
polymers and MOFs. We utilize only the physical properties of the system to
train the ML models on a relatively small dataset, obtained from our
simulations and literature. The ML predictions are in excellent agreement with
the available data on $6$F-CMSM and the available subset of the CoRE MOF
database. Moreover, the computational cost associated with training these
different ML models is less demanding than performing fully atomistic
simulations. The data sent to the ML model covers a wide range of possible
physical values, thereby providing a large range of inputs for the model to
predict on, without having to extrapolate. With available pure gas loadings
inside a material, the trained ML models can help map it to a set of input
features, which in turn can be used to easily predict the loading capacities
in gas mixtures. Our work thus demonstrates that input features trained only
on physical properties of adsorbent materials can predict the gas separation
performance of any given class of materials.

## Acknowledgement

The authors thank the Department of Science and Technology (DST), and Ministry
of Education (MOE), India, for providing funding and computational resources.
The authors also acknowledge Science and Engineering Research Board (SERB),
India and BRNS-DAE, Govt. of India, for financial support.

## Data availability

The data used in this work is made available in the Zenodo database
https://doi.org/10.5281/zenodo.11567899

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