2019, Vol.48, No.2

A database for 240 types of lithium-ion conducting solid polymer electrolytes was newly constructed and analyzed by machine learning. Despite the complexity of the polymer composites as electrolytes, accurate prediction was achieved by the appropriate learning model. Inspired by the analyses, poly(glycidyl ether) derivatives were synthesized to yield higher conductivity. Screening of single-ion conducting polymers with de novo design (>15000 candidates) was also conducted based on the established database.

Along with the significant development of machine learning technologies, exploring novel compounds by materials informatics has become one recent hot issue.16 Numerous studies have begun, mainly in the areas of small molecules and inorganic crystals (for medicines and electronics, respectively).4 The in-silico screening of a large number of chemical structures by simulation and machine learning will inspire and help chemists synthesize new materials.14,7

On the other hand, materials informatics often faces the problems of the rather small number of experimental data (e.g., 100 samples) for machine learning while the trending deep learning techniques (deep neural network, DNN), whose main targets are images, sounds, and texts, normally requires a much larger number of samples (>104).3 Further, measurements of feature values such as crystal structure, melting point, and permittivity for each material take a long time while investigators are not exactly sure whether those parameters are really important to describe the desired characteristics. Especially, polymers have been one of the important challenges for the informatics because of their impact on markets and complicated properties to describe.1,2,7 Polydispersity, higher-order structures, intermolecular interactions, amorphous states, and hysteresis are the main difficulties, which were normally ignored in previous reports.1,2,7 Further, for practical use, polymers are often composited with additives such as plasticizers, or treated with chemicals to improve their properties, which also adds complexity to the overall system.

To challenge the complexity of polymers as materials informatics, as a model study, we firstly predicted the conductivity of lithium-ion conducting solid polymer electrolytes, on the basis of the originally established database and machine learning (Figure 1a). The increasing demand for solid-state lithium-ion batteries requires the discovery of highly conductive and easily processable polymer electrolytes.811 A polymer electrolyte database was newly constructed, because the previously reported polymer databases1,7,12 focused on conventional polymers and their fundamental characteristics (e.g., mechanical properties). As the input data (X), the contained ratio and the fingerprints of each added chemical (e.g., polymer matrix, electrolyte salt, and other additives) in an electrolyte were entered. Other parameters, such as glass transition temperature (Tg) and Young’s modulus of the polymers were also recorded if available from the literature or by our experimental reexamination. The output (Y) could be ionic conductivity, σ, activation energy, Ea, permittivity, ε, and other desired parameters. Function f, determined by machine learning, calculates Y = f(X). It was recently shown that, with optimal tuning of the models, the inverse function, X = f−1(Y) can be even determined and used to propose chemical structures (X) having desired performances (Y).5,13,14

A new database was constructed by entering 240 types of previously reported lithium-ion conducting solid polymer electrolytes, by mainly referring to reviews.8,15 Single-ion conducting polymers (i.e., polyanions) and highly conductive electrolytes composited with plasticizers and metal oxides were selected preferentially. Conductivity at room temperature was selected as Y in this study. As a simple yet powerful approach, Mordred descriptors16 for repeating units of the polymers were used as their fingerprints (1825 scalars for one molecule). Although the descriptors did not calculate their accurate electronic structures or molecular dynamics, the method was sufficiently fast16 (ca. 20 polymers per second by a conventional quad-core CPU) to enable the facile and quick analysis of the database and the following compound screening. Degree of polymerization and polymer structures (e.g., single chain, cross-linked, or co-polymerized) were input as a scalar and one-hot vectors, respectively, while most previous reports assumed only sufficiently long, linear chain polymers.1,2 A composite electrolyte in the database can consist of four different polymers or monomers in maximum, whose amount was recorded by mol ratio. For inorganic metal oxides as additives, those types and amount in weight were recorded. The database can be used with most types of electrolytes, regardless of the polymer structures (monomer, homopolymer, and copolymer) and the composition (salt in polymer or polyelectrolyte).

A gradient boosting model17 was selected to predict the ionic conductivity from the input data, X (Figure 1b). The model had the advantages of both deep learning and classical regression techniques, that is, an accurate prediction could be expected even with the small amount of data.17 Here, 10% of samples randomly selected in the database were not used for the learning but only for the prediction (test data). Accurate predictions were obtained, as indicated by the large coefficient of determination between the experimental (σexp) and the predicted conductivity (σpred), R2 = 0.90 (for train data) and 0.81 (test). The prediction was valid regardless of the differences in conducting ions (single-ion for polyanions and dual ions for salt in polymer). The successful prediction suggested that, even for the complicated polymer composites, the machine learning can be used by appropriately selecting the essential parameters as input. Also, the machine learning could extract the important feature values for conductivity from X (Table S1). The analysis indicated that electronegativity and polarity of the monomer units, related to the solvation of cations,15 are the most dominant parameters to determine lithium-ion conductivity (>30% contribution to σ among all parameters). On the other hand, the degree of polymerization (or molecular weight) and higher-order polymer structures (e.g., linear chain or cross-linked) gave the smaller contribution of 1.6 and 1.9%, respectively, suggesting the higher importance of the chemical structures of the repeating units. We note that the major machine learning models such as DNN and support vector machine (SVM) did not yield good predictions for the database (commonly R2 < 0.3 for test data). The smaller R2 with the models meant that, for complex materials and composites, whose number of samples was limited (102) but input vectors were huge (1825 Mordred descriptors for each 4 molecule), selecting a proper learning model was crucially important.

Inspired by the polymer database and the learning model results, we synthesized and examined polyethers 13 as solid-state electrolytes (Scheme 1). Careful analysis of the database indicated that, for higher conductivity, higher polarity of molecules and lower Tg were required (the strategy was also consistent with the trends for the polymer electrolytes).15 We selected the polyether backbones, having oxygen atoms with large electronegativity and capability to solvate Li+ ions by their flexible chain conformation. As the functional pendant groups, lithium sulfonate and carbonate were introduced to yield 2 and 3, respectively. Only a few cases had been reported for the synthesis of functional polyethers, because of the difficulty in anionic ring-opening polymerization with the ionic pendant groups.1821 Here, the polymer reactions were conducted after the precise synthesis of poly(allyl glycidyl ether) (1) to yield 2 and 3.22 Low glass transition temperatures were obtained for the polymers (−3 and −13 °C for 2 and 3, respectively) while most methacrylate-, styrene-, and vinyl-backbone polymers are commonly brittle at room temperature (Tg ≫ r.t.).15,23 The conductivity (3 × 10−7 and 3 × 10−5 S/cm at room temperature for pristine 2 and 3/LiClO4 mixture ([O]/[Li] = 8/1), respectively) was higher than sulfonate polymers with vinyl and styrene backbones (10−8 S/cm).24,25 by virtue of the polyether structures. The estimated conductivity by machine learning (10−7 and 10−6 S/cm for 2 and 3/LiClO4 composite, respectively) was comparable to the experimental results, supporting the accuracy and the versatility of the learned model. For the polyanion 2, its temperature dependence of the complex impedance was studied (Figure 2a). The decrease in the impedance at an elevated temperature suggested the enhanced segmental motion of the polymer chains. The plateaus of Z′ around 104–105 Hz corresponded to the migration of ions. The increase of Z′ and −Z′′ at lower frequency was caused by the blocking response.26 The ionic conductivity was calculated using equivalent circuit fitting at different temperatures (Figure 2b). A quasi-linear relationship between 1/T (T: temperature) and logσ was observed. The apparent activation energy for ion transport, 13 kJ/mol, was much smaller than the conventional poly(ethylene oxide)-based electrolytes (>30 kJ/mol),27 presumably due to the rather long side chains and their facile movement in the polymer.28 Although the polymer had a low glass transition temperature, a self-standing film was easily obtained, due to the sufficiently high degree of polymerization (ca. 100).

Finally, to discover new chemical structures with higher conductivity, candidate polymers with de novo design were screened by the machine learning prediction. Over 15000 types of single-ion conductive polymers (containing B, C, N, O, Al, Si, P, S, and Se anions) were created randomly, based on the fragmentation algorithm (example structures are shown in Figure S2).29 The conductivity as an solid-state electrolyte was predicted with the composite of poly(ethylene oxide). Through Bayesian optimization,30 about 200 compounds were extracted to give the conductivity around 10−4 S/cm, which should be more than 10 times higher than previously reported single-ion conducting polymers (representative compounds were shown in Figure S3). Polymers containing a large number of heteroatoms with large electron negativity (N, O, S, and F) were selected as the electron withdrawing units. Further, in addition to the conventional anions (carboxylic acids, borates, sulfinic acids, and thioacetic acids), negatively charged aromatic rings could be considerable to reduce the interactions between Li+ and anions. Delocalized electrons in aromatic rings were recently reported to provide the exceptionally large diffusion coefficient of 10−4 cm2/s (Li+ in graphene),31 although the chemical stability, synthetic feasibility, and many other factors must be improved for lithium-ion batteries.

Developing a more accurate machine learning prediction model and extending the polymer database by (first-principle) calculation are our ongoing issue. Especially, calculating the intermolecular interactions (e.g., solvation of ions by polymer chains, complex conformation, impact on Lewis acidity/basicity of the atoms for salt dissociation15) will lead to more accurate and deeper insights into conduction processes. We are also trying to predict activation energy, mechanical strength, stability, and other parameters of the electrolytes based on the enhanced prediction approach.

This work was partially supported by Grants-in-Aid for Scientific Research (Nos. 17H03072, 18K19120, 18H05515, and 18H05983) from MEXT, Japan. K. H.-S. is grateful for financial support from FS research by JXTG Co. The work was also partially supported by Research Institute for Science and Engineering, Waseda University.

We acknowledge Dr. Takeo Suga and Dr. Takahito Nakajima for scientific discussion of polymer synthesis and machine learning.

Supporting Information is available on http://dx.doi.org/10.1246/cl.180847.

K. Oyaizu

K. Hatakeyama-Sato