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Licensed Unlicensed Requires Authentication Published online by De Gruyter November 21, 2023

A perspective on data-driven screening and discovery of polymer membranes for gas separation, from the molecular structure to the industrial performance

  • Eleonora Ricci

    Eleonora Ricci is a Marie Skłodowska-Curie postdoctoral fellow at the National Centre for Scientific Research “Demokritos”, Athens, Greece, working on the application of artificial intelligence methods in multiscale molecular simulation frameworks. She obtained an MSc in Chemical Engineering from the University of Bologna, Italy, and earned a PhD in 2020 from the same university. Her research interests include the thermodynamic, molecular, and data-driven modelling of polymeric materials, for the study of multicomponent phase equilibria and mass transfer in polymeric membranes.

     ORCID logo EMAIL logo     and Maria Grazia De Angelis

    Maria Grazia De Angelis is a professor of Institute for Materials and Processes, School of Engineering, University of Edinburgh, EH9 3FB Edinburgh, ScotlandDepartment of Civil, Chemical, Environmental and Materials Engineering (DICAM), Alma Mater Studiorum – University of Bologna, Bologna, Italy. Her expertise is in the multiscale modelling of the physical phenomena associated to fluid transport in solid polymeric materials, with application in membrane separation, fluid purification and packaging design. She elucidated the mechanism of sorption of pure and mixed gases in glassy, composite and semicrystalline membranes, and is pursuing the integration of different theories to enhance the predictive ability of modelling tools.

     EMAIL logo
From the journal Reviews in Chemical Engineering
https://doi.org/10.1515/revce-2023-0021

Abstract

In the portfolio of technologies available for net zero-enabling solutions, such as carbon capture and low-carbon production of hydrogen, membrane-based gas separation is a sustainable alternative to energy-intensive processes, such as solvent-based absorption or cryogenic distillation. Detailed knowledge of membrane materials performance in wide operative ranges is a necessary prerequisite for the design of efficient membrane processes. With the increasing popularization of data-driven methods in natural sciences and engineering, the investigation of their potential to support materials and process design for gas separation with membranes has received increasing attention, as it can help compact the lab-to-market cycle. In this work we review several machine learning (ML) strategies for the estimation of the gas separation performance of polymer membranes. New hybrid modelling strategies, in which ML complements physics-based models and simulation methods, are also discussed. Such strategies can enable the fast screening of large databases of existing materials for a specific separation, as well as assist in de-novo materials design. We conclude by highlighting the challenges and future directions envisioned for the ML-assisted design and optimization of membrane materials and processes for traditional, as well as new, membrane separations.

Keywords: data-driven modelling; diffusivity; permeability; polymer membranes; solubility
Corresponding authors: Eleonora Ricci, Department of Civil, Chemical, Environmental and Materials Engineering (DICAM), Alma Mater Studiorum – University of Bologna, Bologna, Italy; and Current address: National Centre for Scientific Research “Demokritos”, Athens 15310, Greece, E-mail: ; and Maria Grazia De Angelis, Institute for Materials and Processes, School of Engineering, University of Edinburgh, EH9 3FB Edinburgh, Scotland; and Department of Civil, Chemical, Environmental and Materials Engineering (DICAM), Alma Mater Studiorum – University of Bologna, Bologna, Italy, E-mail:

Funding source: Royal Society of Edinburgh

Award Identifier / Grant number: 2915

About the authors

Eleonora Ricci

Eleonora Ricci is a Marie Skłodowska-Curie postdoctoral fellow at the National Centre for Scientific Research “Demokritos”, Athens, Greece, working on the application of artificial intelligence methods in multiscale molecular simulation frameworks. She obtained an MSc in Chemical Engineering from the University of Bologna, Italy, and earned a PhD in 2020 from the same university. Her research interests include the thermodynamic, molecular, and data-driven modelling of polymeric materials, for the study of multicomponent phase equilibria and mass transfer in polymeric membranes.

Maria Grazia De Angelis

Maria Grazia De Angelis is a professor of Institute for Materials and Processes, School of Engineering, University of Edinburgh, EH9 3FB Edinburgh, ScotlandDepartment of Civil, Chemical, Environmental and Materials Engineering (DICAM), Alma Mater Studiorum – University of Bologna, Bologna, Italy. Her expertise is in the multiscale modelling of the physical phenomena associated to fluid transport in solid polymeric materials, with application in membrane separation, fluid purification and packaging design. She elucidated the mechanism of sorption of pure and mixed gases in glassy, composite and semicrystalline membranes, and is pursuing the integration of different theories to enhance the predictive ability of modelling tools.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors declare no conflicts of interest regarding this article.

  4. Research funding: The present work is partly supported by the RSE Research Workshop Autumn 2022 Award 2915 “A Machine Learning-Aided Modeling Platform for the design of Hydrogen-Ready materials”.

  5. Data availability: Not applicable.

Appendix A: Short introduction to machine learning

In general terms, machine learning is a subset of artificial intelligence, and it involves the development of models that learn to make predictions based on the data used to train them. There is an overlap in the classification between ML methods and non-ML statistical modeling techniques, for example in the case of linear regression analysis. Sometimes the “scale” of the task, i.e. the size of the dataset considered, is used to discriminate between ML and non-ML applications.

ML methods can be divided into three main categories: i) supervised learning, ii) unsupervised learning, and iii) reinforcement learning.

  1. Supervised learning involves training a model on a dataset where, for a set of given input properties (features) the values of the output properties (labels) are known. The model is trained by minimizing a penalty function (also called loss function) related to the accuracy of the predicted labels in comparison to the known values. Afterwards, the trained model is used to predict the labels of input features for which the labels were unknown.

    Supervised learning methods are further split into a) classification, used for predicting categorical values, and b) regression, used for predicting continuous values. Several ML methods can be applied both for classification and regression tasks. Supervised learning regression methods are the most frequently applied for the prediction of gas transport properties in membrane materials and include neural networks, decision trees, logistic regression, Gaussian processes, support vector machines, and several variants of these methods, which are defined in the Table below.

  2. Unsupervised learning involves training a model on an unlabeled dataset, where the desired output is not known. The aim is to identify patterns or structure in the data without a predefined categorization. Examples of unsupervised learning are clustering techniques and dimensionality reduction methods, such as principal component analysis.

  3. Reinforcement learning also does not make use of labeled data, but rather it involves training a model by providing it with a reward signal based on its performance, and the model learns to make decisions that maximize the reward. An example of foreseeable application for membrane separations would be process control: the model would receive a reward signal based on the target set point of the process and it would learn to adjust the operating conditions to minimize deviations from the set point, thus maximizing the reward signal. To the best of our knowledge, no applications of reinforcement learning methods were reported concerning gas transport properties predictions.

A recent short communication by Tayyebi et al. (2022), provides some useful model selection guidelines in their supporting information.

Glossary and references for machine learning methods and terminology

Name Acronym Definition References
Activation function – In artificial neural networks, activation functions are applied to the output of a neuron to modulate the response depending on the input values. E.g., different activation functions can be used to threshold the output of a neuron or introduce nonlinear relations between input and output. Russell and Norvig (2020)
Agglomerative clustering AC Clustering method in which initially each point forms a separate cluster and the clusters are progressively merged, based on the chosen similarity measure. Maimon and Rokach (2006)
(Artificial) neural network (A)NN A numeric-mathematical construction that can model complex non-linear relationships. Usually consisting of input, hidden (in the case of “deep” models), and output layers, each with a suitable number of nodes. The values assumed by each node are calculated from the connections with the nodes in the previous layer, expressed by weight and bias parameters that are tuned during the training of the model. The application of activation functions between each layers introduces nonlinearity into the model. Russell and Norvig (2020)
Adaptive neuro-fuzzy inference system ANFIS Model consisting of a series of fuzzy rules and appropriate membership functions, which, after initialization, are tuned to minimize the output error. Jang (1993)
Accelerated particle swarm optimization APSO Simplified variant of the PSO algorithm that does not use the “velocity” concept, thus speeding up convergence. Yang et al. (2012)
Bayesian linear regression BLR Modeling method that aims at determining the posterior probability distribution of the model parameters conditional upon the training inputs and outputs, which are typically sampled from a normal distribution. MacKay (1992)
Chaos-enhanced accelerated particle swarm optimization CEAPSO Improvement of the APSO algorithm that employs the Lorenze equations to generate a chaotic sequence for tuning the acceleration coefficients of the APSO method. Ru-Ting and Xing-Yuan (2015)
Committee machine intelligent system CMIS Model combining the responses of multiple ML models into a single response. Russell and Norvig (2020)
Cross validation – Test of the generalization capacity of an ML model, which consists of splitting the data into n portions and performing n tests in which every portion of the data is in turn left out of the training set and used for testing the obtained model. Russell and Norvig (2020)
Decision tree/Regression trees DT/RT Non-parametric supervised learning algorithm, which is utilized for both classification and regression tasks. It has a hierarchical, tree structure, consisting of a root node, branches and internal nodes, which are created to learn the paths between input and output. Decision trees where the target variable can take continuous values are called regression trees. Russell and Norvig (2020)
Double-population particle swarm optimization based on diffusion theory DP-DT-PSO Variation of the PSO algorithm, in which the iterative update function is inspired by diffusion theory. Mengshan et al. (2017a)
Extremely randomized trees ERT Variation of the random forest (RF) algorithm, which does not result in deterministic splits of the decision trees (DT). Geurts et al. (2006)
Fuzzy clustering FC Unsupervised clustering method in which each data point can belong to more than one cluster, with a membership grades value between 0 and 1 for each cluster. Abiyev (2011)
Fuzzy neural network FNN Neural network models that tune fuzzy rules and membership functions automatically from the input data. Russell and Norvig (2020)
Fuzzy logic FL A form of logic in which the value of “true” can correspond to any real number between 0 and 1, unlike Boolean logic, where only two integer values are considered, 0 or 1. Zadeh (1988)
Gaussian process regression GPR GPR is a probabilistic approach to regression analysis, in which the distribution of all possible functions relating input and output variables that could explain the observed data is considered. This distribution is a Gaussian process, which is defined by a mean function and a covariance function, which allows calculating the most likely values and associated uncertainties for the model predictions. Rasmussen and Williams (2005)
Genetic algorithms GA A type of optimization algorithm inspired by the process of natural selection and evolution: a population of candidate solutions is initially generated randomly and iteratively evolved over many generations, using a fitness function. The fittest individuals are then selected for reproduction, and combined to create new candidate solutions, iterating until a satisfactory solution is found or a maximum number of generations is reached. Koza (1994)
Genetic function approximation GFA Symbolic regression performed through genetic algorithm optimization. Rogers (1999)
Genetic programming GP A technique of creating programs fit for a specific task by “evolving” an initial random population through crossover and mutation of the population members to create new “generations” until the required accuracy criterion is satisfied. Koza (1994)
Hyperparameter – A parameter used to specify a characteristic of the ML model used (e.g., number of neurons in a neural network) or of the optimization algorithm (e.g., the learning rate). Yang and Shami (2020)
k-means clustering KM Unsupervised ML method for the partitioning of a dataset. Each data point is assigned to the cluster with the nearest mean distance. Russell and Norvig (2020)
k-harmonic means clustering KHM Center-based clustering algorithm considering the harmonic means of the distances from each data point to the centers as components to its object function. Zhang et al. (2001)
Kernel Ridge regression KRR Combination of Ridge regression (linear least squares with l2-norm regularization) with the kernel trick. The kernel trick is used to measure the similarity between two points in a higher-dimensional space, without actually computing the coordinates of the points in that space, thus implicitly mapping data from a low to a higher-dimensional space, without actually computing the transformed feature vectors. Burges (1998)
Least square SVM LSSVM While SVM separation hyperplanes are obtained through solving systems of inequality constraints, the least squares formulation involves equality constraints only. Suykens and Vandewalle (1999)
Multivariate imputation by chained equations MICE Multiple imputation method used to complete missing data values in a data set, under the assumption that they are missing at random. Buuren and Groothuis-Oudshoorn (2011)
Natural language processsing NLP AI techniques that focus on enabling computers to understand, interpret, and generate human language, leveraging elements of computer science and linguistics to analyze and process large amounts of natural language data. Applications of NLP include machine translation, speech recognition, and text mining.
Overfitting – Creation of a model that represents the training data with a very high accuracy but fails to generalize to unseen data, often because of the presence of too many model parameters with respect to training data set size. Russell and Norvig (2020)
Principal component analysis PCA Statistical method that applies an orthogonal transformation to convert the feature set into a set of linearly uncorrelated variables (principal components). Often applied for dimensionality reduction. Russell and Norvig (2020)
Particle swarm optimization PSO Group evolution optimization algorithm to solve problems that can be represented as a point or surface in a multi-dimensional space. In PSO, a “particle” is designed as a potential solution in the search space. A particle updates its “speed” and “position” iteratively, until converging to a solution. Kennedy and Eberhart (1995)
Polynomial regression PR Form of regression in which the relationship between the independent variable and the dependent variable is modelled as an nth degree polynomial function. Kleinbaum et al. (2013)
Random forest RF Ensemble model combining the prediction of multiple decision tree models. Russell and Norvig (2020)
Radial basis function neural network RBFNN NN model typically consisting of 3 layers: input, hidden, and output. In the hidden layer nodes, the input is transformed by the application of radial basis function (RBF). Training is performed in two steps. At first the parameters the RBF are tuned (e.g., centers and widths, if a Gaussian function is used), for example using unsupervised clustering algorithms, and at a second stage the connection weights between the hidden layer and the output layer are optimized. Elanayar and Shin (1994)
Stochastic gradient boosting SGB Improvement of the gradient boosting method, which consists of an ensemble of “weak” prediction models, typically decision trees, applied in sequence to minimize the residual error of the previous model. Mason et al. (1999)
Shapley additive explanations SHAP Calculation of the individual contribution of each feature to the predicted output of an ML model to increase the explainability of the results. Lundberg and Lee (2017)
Symbolic regression SR Search in the space of mathematical expressions to find the function that best fits a given dataset, both in terms of accuracy and simplicity. Billard and Diday (2002)
Support vector machines SVM Supervised learning models that construct hyperplanes in a multidimensional space to separate cases of different class labels. They can be applied to multiple continuous and categorical variables, thus allowing both classification and regression analysis. Russell and Norvig (2020)
Transfer learning TL Transfer learning consists of reusing parts of a previously trained model (usually trained on a large dataset) on a new model used for a different but similar problem, retraining only a smaller portion of the parameters on the dataset related to the new task. Russell and Norvig (2020)
Transformer – The transformer is a deep learning architecture used in natural language processing and other tasks, based on self-attention mechanisms. It is an embedding technique that converts input data, like words or sentences (or chemical formulas specifically), into dense numerical representations, capturing semantic meaning, and enabling efficient handling of long-range dependencies. Vaswani et al. (2017)

Glossary and references for gas separation with membranes terminology

Name Definition References
Diffusivity The diffusion coefficient gives the rate at which dilute gas molecules can move through the membrane according to the diffusive mechanism and it is related to diffusive flux and transmembrane concentration gradient across the membrane of thickness l according to Fick’s law. N = D   ∆ c l Matteucci et al. (2006)
Permeability The permeability coefficient ( P ) relates the diffusive flux to an applied partial pressure gradient of external gas phase (∆p): N = P   ∆ p l Matteucci et al. (2006)
Selectivity Membrane selectivity to a gas pair (i, j) is defined as in other separation processes as the ratio between the enrichment of the most permeable component (i) from the feed to the permeate stream, versus the same value calculated for the less permeable component (j) (y i P /y i F )/(y j P /y j F ). If the downstream side is at negligible pressure, this value coincides with the ratio between the permeability coefficient of i to that of j, P i P j . Matteucci et al. (2006)
Solubility Assuming that interphase equilibrium is valid at the membrane/gas contact surface, which is usually the case, solubility is given quantitatively by the equilibrium solubility coefficient of the gas in the polymer ( S ), i.e. the ratio of the concentration of gas dissolved in the polymer ( c ) to the pressure of gas (or partial pressure in the case of mixtures) in the contiguous gas phase (p): S = c p (gas fugacity is a better measure of the driving force for solubility if the gas is not ideal). Matteucci et al. (2006)
Solution-diffusion theory If Fick’s law and interfacial equilibrium are valid, the definition of permeability together with the corresponding physical laws imply that that permeability coefficient ( P ) of the gas in a polymer is the product of its solubility ( S ) and diffusivity ( D ) coefficients: = S ∙ D . Such a formula indicates that the permeation mechanism in nonporous membranes can be schematized as a sequence of steps: the gases dissolve into the membrane material, diffuse through it, and desorb on the other side. This description forms the backbone of the solution–diffusion theory. Wijmans and Baker (2006)
Swelling Gas-induced swelling in gas separation membranes refers to the phenomenon where certain gases, when sorbed into the membrane material, cause it to expand or swell, leading to changes in its structure and properties, and affecting gas permeation and separation performance. It is quantified as relative polymer volume increase, ΔV/V0, at a given gas pressure or concentration. If mixing volume effects are negligible, the volume increase of the polymer phase is equal to the volume of pure liquid penetrant absorbed. Matteucci et al. (2006)

Acronyms

CMS

carbon molecular sieve

CPEs

carboxylated polyesters

CPI

cardo-type poly-Imide

DEA

diethanolamine

HDPE

high-density polyethylene

LDPE

low-density polyethylene

NBR

nitrile butadiene rubber

PB

polybutadiene

PBS

polybutylene succinate

PBSA

poly(butylene succinate-co-adipate)

PC

polycarbonate

PCP

polychloroprene

PDMB

polydimethylbutadiene

PDMS

polydimethylsiloxane

PEM

polyethylmethacrylate

PES

polyethersulfone

PET

polyethylene terephthalate

PIB

polyisobutylene

PIP

cis-1,4-polyisoprene

PLGA

poly(D,L-lactide-co-glycolide)

PLLA

poly(L-lactide)

PMP

poly (4-methyl-1-pentane)

pNA

p-nitroaniline

POM

polyoxymethylene

POSS

octa-trimethylsiloxy polyhedral oligomeric silsesquioxane

PP

polypropylene (PP)

PPO

poly(2,6-dimethyl-1,4-phenylene ether) or poly(2,6-dimethyl-1,4-phenylene oxide)

PS

polystyrene

PSf

polysulfone

PTFE

polytetrafluoroethylene

PU

polyurethane

PVAc

poly(vinyl acetate)

PVC

polyvinylchloride

PVLA

polyacetyl lactone

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Received: 2023-04-17
Accepted: 2023-09-02
Published Online: 2023-11-21

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