Room temperature ionic liquids viscosity prediction from deep-learning models

Dataset extraction and preparation

In this work, all the viscosity datasets we used were gathered from the Ionic Liquids Database - ILThermo (v2.0.)^[45,46], which is a comprehensive database of thermophysical and thermodynamic properties of ILs in the field. According to the latest update (by 28th Dec 2022), the ILThermo contains 2,732 types of ILs and includes 5,177 compounds, with a total of 870,304 datapoints collected from 4,230 published works of literature. For pure ILs, the database has 2,332 IL systems with 145,602 datapoints related to thermodynamic, thermochemical, and transport properties. For this study, the room-temperature viscosity collected dataset contains 922 types of ILs and includes a wide range of IL families. For this wide range of IL candidates, predicting room-temperature viscosities accurately and understanding their useful structure-property relationship without depending on costly computational resources are important in practice. The details of data extraction, conversion, and post-processing of the ILThermo dataset can be found in our recent work^[47]. To account for an extensive description of molecular structure features of each individual IL in the dataset, all the 5,272 molecular descriptors based on chemoinformatic QSPR approach^[48,49], e.g., constitutional indices, topological indices, connectivity indices, walk and path counts, etc., were generated based on Dragon7 software^[48].

Prior to the ML study, it is important to remove the unnecessary data. During this process, all the molecular descriptor columns with low variance and those containing missing values or empty columns were removed. All the molecular descriptors and viscosity values were normalized using the Standard Scaler function from scikit-learn (scikit-learn 1.2.0)^[50]. To overcome the problem of overfitting, the dimension of the original molecule descriptors matrix was further reduced using the Pearson correlation. This helps us to further identify important molecular descriptors that exhibit a statistical significance with a high correlation to the viscosity of ILs. To achieve this goal, the molecular descriptors with low correlations (< 0.20) and high correlations (> 0.90) were further excluded from the dataset. Throughout this process, a set of important molecular structure features consisting of 179 molecular descriptors was identified. After the correlation feature selection and normalization of these molecular descriptors, the dataset was randomly split into training and testing datasets with a ratio of 80/20 (or 80% for training and 20% for testing) for the evaluation of our ML models. To improve the accuracy (i.e., R²) of our ML models in regression analysis, we have removed some of the outliers (i.e., 13 in total). These outliers are not restricted to particular cationic or anionic species. They are mostly ILs with high η (η ~ 150-2,030 mPa·s) and might not be very useful in batterie applications. Generally, all these outliers are large molecules and have large molecular weight (190 ≤ MW ≤ 583), large Bertz branching index (i.e., 11 ≤ BBI ≤ 52), and large Zagreb indices^[51,52](e.g., 44 ≤ ZM1 ≤ 176) due to their high complexity in molecular substructures (e.g., N,N,N-tributyloctan-1-aminium trifluoromethanesulfonate, decyldimethyl(4-vinylbenzyl)ammonium bis(trifluoromethanesulfonyl)amide), etc.). Therefore, for the η-prediction based on regression model of ML in the subsequent study (Section "Viscosity prediction from deep-learning (DL) models"), it will base on 909 types instead of 922 types of ILs found in this work.

Machine-learning model: deep-learning

In this work, we have considered two types of DL models, i.e., deep neural networks (DNN) and convolutional neural networks (CNN), which are based on the algorithms implemented in TensorFlow (i.e., TensorFlow 2)^[53], a popular ML framework that provides a high-level python API to construct and train DL models. DL is a subfield of ML and is an artificial neural network (ANN) that is essentially represented by multiple layers of neural networks. While a neural network with a single layer can still make approximate predictions, additional hidden layers can help to optimize and refine for accurate prediction^[39-41]. These neural networks attempt to mimic how the human brain processes information progressively with higher-level features from large data and are able to develop a hierarchy of learning processes based on a set of algorithms defined within each layer.

For a DL model, a multi-layer feedforward neural network is constructed with multiple hidden layers, of which each layer contains predefined numbers of neurons to capture the non-linear relationship between the input features (e.g., molecular descriptors of ILs) and the output viscosities. The network is trained using stochastic gradient descent with backpropagation to minimize the mean squared error between the predicted and actual viscosity values. Figure 1 shows a general structure of our DNN and CNN models, which consists of multiple layers, with each layer containing a different number of neurons. As shown in Figure 1A, our DNN model consists of one input layer (179 neurons), 1st hidden layer (128 neurons), 2nd hidden layer (64 neurons), 3rd hidden layer (32 neurons), 4th hidden layer (16 neurons), and output layer (1 neuron). In contrast, our CNN model [Figure 1B] is a neural network with basic building blocks/layers consisting of tensors except for the output layer. Specifically, Figure 1B features one input layer represented by 1D convolutional layer with tensor (179, 1), 1st hidden layer based on 1D convolutional layer with tensor (177, 32), 2nd hidden layer as flattened layer (5,664 neurons), 3rd hidden layer (180 neurons), 4th hidden layer (128 neurons), 5th hidden layer (64 neurons), 6th hidden layer (32 neurons), 7th hidden layer (16 neurons) and output layer (1 neuron). To update all the neural network weights or hyperparameters iteratively during the training of the DL model, an adaptive moment estimation (Adam) optimizer, a stochastic gradient descent method, is used to speed up the optimization process^[54]. To avoid an over-fitting problem during the training process of DL models (i.e., DNN and CNN), we have carried out a systematic study on the accuracy of data validation or error rates for a range of epochs through an iterative process. As shown in Supplementary Figure 1, an optimal number of epochs (i.e., epoch = 1,500) are identified when convergence is achieved (i.e., when the accuracy in the DL model stops improving). Thus, in this work, to fit the DNN and CNN with a training dataset, the number of iterations, i.e., epochs, is set to 1,500, and the batch size equal to 32 in each epoch is used throughout the process.

Figure 1. The schematic plot of the deep-learning (DL) models adopted in this work: (A) deep neural network (DNN) and (B) convolutional neural network (CNN).

Data consolidation and evaluation

In this work, we are only interested in the viscosity of pure ILs that are close to the room temperature (i.e., T = 298 ± 5 K) and at ambient pressure (i.e., P = 101 ± 2 kPa), a condition relevant to the operating condition of conventional batteries. By neglecting the binary and ternary mixtures, there are 2,119 entries of the viscosity dataset of pure ILs, which are within this room-temperature range collected from the ILThermo database^[45,46]. Among these experimentally measured η data reported by different authors at ILThermo^[45,46], we found that some entries are duplicated or belong to the same ILs. For these duplicated entries, it is noted that the collected η data reported by different authors do exhibit some small discrepancies or variations, which might be possibly related to impurities (e.g., water), differences in purification procedures, or experimental techniques employed in viscosity measurements. To reconcile with the discrepancies reported by different authors that belong to the same ILs, the reported η values, which are duplicated by different studies or duplicated entries, were averaged and retained only if the minimum and maximum reported values were within the average error (i.e., reported standard deviation) of the average value ($$\bar{\eta}$$), i.e., $$\bar{\eta}+\overline{\eta_{std}} < \eta_{max}$$ and $$\bar{\eta}-\overline{\eta_{std}} > \eta_{min}$$, where $$\bar{\eta}$$ is the average duplicated reported values, $$\overline{{\eta_{std}}}$$ is the average measurement error, and η_min and η_max are the minimum and maximum reported value for the duplicated values reported by different studies, respectively.

In this dataset, a wide diversity of structures and functional groups in ILs with various combinations of cations (e.g., imidazolium, ammonium, pyridinium, phosphonium, pyrrolidinium, etc.) and anions (e.g., bistriflimide (NTF2) derivatives, sulfonate, phosphate, hexafluorophosphate, borate, sulfate, acetate, dicyanamide, triazolide, etc.) families can be found and is highlighted in Figure 2. From this large dataset (922 types of ILs), a wide distribution of room temperature measured η can be found, whose viscosities vary from 2 to 97,000 (in mPa·s) based on various combinations of anionic and cationic families of ILs. Although the imidazolium-based cation is the dominant cationic family in this dataset [Figure 2], it covers a wide variety of ILs. Among the 320 types of ILs, those consisting of imidazolium-related cations exhibit a wide range of viscosity values, i.e., spanning from 1-ethyl-1H-imidazolium acetate to 1-(2-cyanoethyl)-3-(phenylmethyl)-1H-imidazolium chloride with η ~ 4-69,000 mPa·s. Meanwhile, for the imidazolium-based ILs that with viscosity < 50 mPa·s, there are only 77 candidates are found from 320, as shown in Figure 2. Similarly, a wide range of η ~ 12-20,100 mPa·s is also found among the dominant NTF2 anionic species [Figure 2] related ILs. Therefore, in our opinion, the issue of a strongly skewed IL dataset toward a narrow range of viscosities restricted to the dominant imidazolium cationic species or NTF2 anionic species should not be a major concern.

Figure 2. The schematic plot of the distribution of cationic (A) and anionic (B) families from various ILs in the dataset.

Viscosity prediction from deep-learning (DL) models

To measure the accuracy of the prediction from the DL models (i.e., DNN and CNN) described in Section "Machine-learning model: deep-learning", three metrics, such as the square coefficient of correlation (R²), the root mean square error (RMSE), and mean absolute error (MAE), were used to assess the performance of the DL models for the test dataset. Based on the selected 179 molecular descriptors for each IL (Section "Dataset extraction and preparation"), a summary of the performance of DL models on test dataset prediction can be found in Figure 3 and Table 1. As shown in Figure 3, a linear regression with high R² value [Table 1] can be found. Supported by the high R² value, the predicted viscosity values from both DNN and CNN models are found to be randomly distributed along the diagonal line with only a small deviation, compared with experimentally reported viscosity values at room temperature.

Figure 3. The DL model predicted viscosity values vs. experimentally measured viscosity values (both in mPa·s unit) in the test dataset, with (A) representing the DNN model and (B) representing the CNN model separately. The dataset used consists of 909 types of ILs with 179 molecular descriptors for each IL.

As shown in Table 1, we found that the accuracy of viscosity prediction is, in general, dictated by the sample size of distinct ILs (n), ML models, and the representation of structure features or molecular descriptors of ILs. Compared to the reported literature^[34,36-38], the test R² score and RMSE for the prediction of viscosity around room temperature (T ~ 298 K) reported in this work are found to be outstanding. Among the DL models we considered, the performance metrics obtained from CNN models are found to be among the best in reported literature, especially for the prediction of room-temperature viscosities (i.e., R² ~ 0.9980, RMSE ~ 45.27, MAE ~ 30.42) [Table 1]. For the DNN model, the prediction accuracy is also found to be excellent, i.e., R² ~ 0.9869, RMSE ~ 63.78, MAE ~ 41.68 [Table 1], compared to the reported literature, especially for the room-temperature viscosity prediction.

To further examine the influences of molecular descriptors on the performance of DL models, the top important molecular descriptors for these models were computed, and the top 20 most important molecular descriptors can be found in Supplementary Table 1. Based on Pearson correlation, these 20 descriptors are found to have important impacts on the room-temperature viscosity of ILs obtained from DNN and CNN models. For DNN models, the performance of metrics is found to be nearly similar (i.e., R² ~ 0.988, RMSE ~ 108.92 mPa·s,MAE ~ 65.96 mPa·s) compared to 179 molecular descriptors [Table 1] if only the selected top 20 molecular descriptors for each IL are used for test prediction [Supplementary Table 1]. Whereas for the CNN model, the performance of metrics based on the top 20 molecular descriptors [Supplementary Table 1] is found to be decreased slightly (i.e., R² ~ 0.963, RMSE ~ 195.2 mPa·s, MAE ~ 115.41 mPa·s) compared to the prediction based on 179 molecular descriptors [Table 1]. Therefore, this suggests that the performance metrics of our DNN and CNN models are very similar and robust if an optimum number of important molecular descriptors are used.

Prior to our study, a systematic study of IL viscosity prediction across a wide range of IL families based on the ILThermo dataset^[45,46] has been reported by Beckner et al. Based on the dataset, consisting of 723 distinct ILs for temperature range 273.15-373.15 K, pressure range of 60-160 kPa, and η range of 3.5-993 mPa·s, a reasonably good model of viscosity prediction can be obtained based on traditional ML models^[36]. According to Beckner et al., high accuracy of viscosity prediction (R² ~ 0.93, RMSE ~ 0.69 mPa·s) [Table 1] can be achieved based on feedforward ANN (FFANN)^[36]. For that work, the result is based on 11 molecular descriptors selected by the least absolute shrinkage and selection operator (LASSO) from 633 molecular structure descriptors of ILs using the QSPR model.

The ability to predict the viscosities of a wide range of ILs accurately using the QSPR model has inspired further studies of physicochemical properties of other ILs in combination with diverse ML methods and molecular representations derived from QSPR models. To achieve this goal, a large-scale benchmark study of QSPR models combining several ML methods (e.g., random forest regression, RFR; extreme gradient boosting, XGBoost; TransCNN, etc.) with different types of molecular representations to predict several key physical properties of ILs (i.e., electrical conductance, density, refractive index, melting point, viscosity, and surface tension) was reported by Baskin et al. recently^[37]. As shown by Baskin et al., it is possible to predict N different properties of ILs at the same condition simultaneously or the same property under N different conditions (e.g., temperature) simultaneously based on multi-task learning (MTL) models^[37]. From this MTL model, it was found that the accuracy, unfortunately, is low for viscosity prediction (R² = 0.69, RMSE = 0.40, MAE = 0.28) [Table 1] when making a prediction for five physical properties (i.e., electrical conductance, density, surface tension, viscosity, and refractive index) at T = 298 K during the test prediction. Whereas for MTL models in making a simultaneous prediction for viscosities at different temperatures within the range of T = 288-343 K, the performance metrics were found to be nearly similar (i.e., R² = 0.674, RMSE = 0.375, MAE = 0.265) [Table 1] during the cross-validation test prediction. Thus, this suggests that while more robust than a single-task QSPR model that only manages to predict one physical property at room temperature, how to systematically improve the accuracy of an MTL model capable of providing simultaneous predictions of several room-temperature properties or predicting a property at several different temperatures remains a challenge.

In addition to QSPR models adopted by Beckner et al., one of the best approaches reported in the literature was based on the GC method developed by Paduszyński et al.^[33,34,36]. Based on the GC method, the complex functional groups used to describe a diverse family of ILs can be represented as their cations and anions fragmented into a set of predefined molecular groups or fragments. And each group has a direct influence on the property (e.g., η(T) = η₀f(T) where η₀ denotes the viscosity at a reference temperature, T₀ = 298.15 K) value as a function of temperature (f(T)), and can be combined with ML algorithms (e.g., FFANN; stepwise multiple linear regression, LSSVM) for a systematic study. Based on an extensive IL dataset, the FFANN is found to be the best ML model^[34] to predict the viscosity at room temperature (η₀) with test accuracy of R² ~ 0.8637 and RMSE ~ 0.51 mPa·s. Based on the LSSVM best fitted f(T) with R² ~ 0.97, the overall prediction of η(T) with accuracy of R² ~ 0.91, RMSE ~ 203 mPa·s [Table 1] can be obtained modeled with FFANN and LSSVM. As noted by Paduszyński et al., the large RMSE is attributed to a wide range of IL datasets across wide temperature ranges (T ~ 290-410 K)^[34].

To improve upon the GC method inspired by Paduszyński et al.^[33,55-57], a newly improved GC fragmentation scheme has been proposed by Boualem et al. recently^[38]. This new GC scheme is capable of defining a large variety of ILs and is able to differentiate among the isomers. According to this scheme, the molecular structure of each IL can be considered as a collection of three separate groups, i.e., cationic, anionic, and substituent groups. The cationic and anionic groups are the constituent groups, representing charged components/fragments of ions, whereas the substituent groups are those representing neutral components/fragments of various types of side chains^[33,38,58]. With this new approach, it is possible to overcome the limitation related to structural representation that is not sufficiently described in a conventional GC scheme^[33,34]. With this new fragmentation scheme combined with SVM, the overall accuracy of the test prediction of η(T) reported by Boualem et al. was impressive, i.e., R² ~ 0.9859 with RMSE ~ 57.92 mPa·s, despite being the largest dataset considered to date [Table 1]^[38]. Thus, this suggests that besides the ML model itself, a systematic classification and robust identification of molecular structural features of ILs are also critical factors in improving the accuracy of the model.

Low- and high-viscosity binary classification prediction from deep-learning model

In addition to the room-temperature viscosity prediction (Section "Viscosity prediction from deep-learning (DL) models"), it is also necessary to investigate the important structure-property relationship that determines the low- or high-η of various ILs at room temperature based on a robust binary classification of ML models. It is noteworthy to point out that the extremely low-η (< 2-3 mPa·s) ILs at room temperature comparable to traditional solvents (e.g., water, ethanol) are very rare in the ILThermo (v2.0.) database^[45,46], i.e., only six candidates (i.e., from 2-methylpyridinium acetate to N-methyl-2-oxopyrrolidinium butanoate) out of 922 types of ILs are found in this work. Whereas for the ILs below the range of η ~ 10 mPa·s at room temperature, only about 19 types of ILs can be found (e.g., 2-methylpyridinium acetate, trihexylammonium hexanoate, 1-ethyl-3-methyl-1H-imidazolium tricyanomethanide, etc.). The very limited dataset makes ML model prediction, especially for the extremely low-η ILs (< 2-3 mPa·s or ≤ 10 mPa·s), becomes very difficult. According to a recent comprehensive review of room-temperature viscosities of ILs by Jiang et al., typical room-temperature low-to-medium viscosities of ILs were commonly found below 100 mPa·s, whereas for high-η, the η is generally larger than 100 mPa·s^[18]. In addition, it is also found that the most commonly used low-η ILs in metal-ion batteries at room temperature are within the range of η ~ 19-156 mPa·s^[59]. With this as a reference^[18,59], all the ILs studied in this work can be classified into two groups, i.e., low-η ILs (η ≤ 100 mPa·s) and and high-η ILs (η > 100 mPa·s), accordingly across a wide range of viscosities in our dataset [Figure 4A], which spans from two to 97,000 mPa·s based on various combinations of anionic and cationic families of ILs [Figure 4B]. Based on this low/high-η binary classification, there are 540 high-η and 382 low-η ILs can be found in the dataset.

Figure 4. (A) The schematic plot of the room-temperature viscosity distribution (in log(mPa·s) scale) that classifies the low-η(η ≤ 100 mPa·s) and high-η (η > 100 mPa·s) ILs from various types in the dataset. (B) A few randomly selected ILs that represent low-η and high-η ILs in the dataset.

To further identify the hidden correlation of the structure-property relationship of these low-η and high-η ILs, a DL model based on a DNN model is constructed [Supplementary Figure 2], which is similar to the DNN model discussed in Section "Machine-learning model: deep-learning". Based on the 179 selected molecular descriptors (M = 179 in Table 2), similar to our aforementioned viscosity prediction model (Section "Viscosity prediction from deep-learning (DL) models"), the overall accuracy of the low/high-η binary classification reaches 93% for test prediction, even with a skewed dataset (i.e., ~58.6% high-η ILs relative to ~41.4% low-η ILs). To better evaluate the performance of this DNN model in low/high-η binary classification, the positive precision (positive predictive value, PPV) (i.e., the accuracy of positive prediction/high-η prediction), negative precision (negative predictive value, NPV) (i.e., the accuracy of negative prediction/low-η prediction), recall for sensitivity of positive class (i.e., true positive rate, TPR), and recall for specificity of negative class (i.e., true negative rate, TNR) are used. These metrics are defined in the following equations^[60]:

positive precision = $$\frac{TP}{TP+FP}$$, where TP is the number of true positives (i.e., true high-η), and FP is the number of false positives (i.e., false high-η)

negative precision = $$\frac{TN}{TN+FN}$$, where TN is the number of true negatives (i.e., true low-η), and FN is the number of false negatives (i.e., false low-η)

recall (sensitivity) = $$\frac{TP}{TP+FN}$$, where FN is the number of false negatives (i.e., false low-η).

recall(specificity) = $$\frac{TN}{TN+FP}$$, where FP is the number of false positives (i.e., false high-η).

Based on the computed confusion matrix [Supplementary Figure 3], all the values of TP, TN, FP, and FN can be obtained. Based on the test sample (i.e., 20% of dataset), the overall performance metrics of DNN models [Supplementary Figure 2] in low/high-η binary classification are shown in Table 2. Despite the skewed dataset, a balanced accuracy in both negative (NPV ~ 91%) and positive precision (PPV ~ 95%) was found [Table 2] based on our DNN model. For positive (i.e., high-η) prediction, the TPR of 92% is slightly lower than TNR (i.e., 94%), even though a larger sample size in positive cases (high-η). To further examine the influence of the number of molecular descriptors on the DNN model performance in low/high-η binary classification, the top-ranking important molecular descriptors were computed. From the feature filtering and ranking scores [Figure 5] of DNN models, the important correlation among the top 20 molecular descriptors that are important in low/high-η binary classification of ILs was obtained using Pearson correlation. Based on the DNN model with only the top 20 molecular descriptors [Figure 5], the overall accuracy of the low/high-η binary classification is 90 % for test prediction and is slightly lower than the 179 selected descriptor-based test accuracy, i.e., 93%. As shown in Table 2, the overall performance metrics (i.e., PPV = 89%, NPV = 92%, TPR = 94%, TNR = 86%) of the DNN model with M = 20 are also generally lower than the accuracy obtained with M = 179. This suggests that the top 20 important molecular descriptors might not be sufficient to achieve the high accuracy anticipated in low/high-η binary classification prediction according to our current DNN model.

Figure 5. A Pearson correlation matrix comparing the viscosity with the top 20 important molecular descriptors for low/high-η binary classification of ILs based on DNN models. The numbers shown in the Pearson correlation matrix are the feature correlation coefficients among different molecular descriptors. A brief description of these molecular descriptors can be found in Supplementary Table 2.

Important molecular descriptors that determine viscosities of ILs

According to the DNN model, the top 20 important molecular descriptors that determine the low/high-η of ILs are highlighted in both Figure 5 and Supplementary Table 2. From Supplementary Tables 1 and 2, some common important molecular descriptors of ILs can be found in the findings of viscosity prediction [Supplementary Table 1] and low/high-η binary classification [Supplementary Table 2] using the DNN model, e.g., MPC10, piPC09, NdssC, etc., defined by chemoinformatics molecular descriptors^[48,49] of ILs. From these top ranked molecular descriptors [Supplementary Tables 1 and 2], the significant influences of both cations and anions of ILs are found to be closely related to the geometrical structures, shapes, or branching characters (e.g., piPC10, piPC09, MPC10). Besides, the molecular weights/sizes (e.g., ATS8m) of ILs, partial charges (e.g. ATSC7i), and functional groups and bonds (e.g., NdssC, B02[C-S], B04[N-S], B07[F-F], F05[S-F]) features of ILs are also found to be important factors that could possibly affect their viscosity due to the strong correlation of local bonding with molecular dipole/polarizability and electrostatic interaction (e.g., cation-cation, anion-anion, cation-anion interaction). In addition, the important structure features governing the intermolecular, hydrogen bonding, and van der Waals interactions of ILs can be captured based on the P-VSA and CATS2D-based molecular descriptors (e.g., P_VSA_ppp_L, CATS2D_03DA, CATS2D_07_DL) [Supplementary Tables 1 and 2].

To improve our basic understanding on how these top ranked molecular descriptors [Supplementary Table 2] determine the low/high-η of ILs, the distribution of low- and high-η ILs was analyzed based on the combination of two important descriptors selected from Supplementary Table 2. From the analysis of the distribution of low/high-η ILs using some of the best combinations of two top ranked molecular descriptors from Figure 5, we believe useful insights regarding design rules of IL viscosities can be found. In Figure 6, the unique interplay governed by the inherent structural features of the cations and anions of ILs that determine the distribution of low- and high-η ILs is obvious. From Figure 6, an opposite trend between the low- and high-η ILs represented by these molecular descriptors is evident. As shown in Figure 6A and C, the majority of low-η ILs favor the regime of smaller values in CATS2D_03_DA (i.e., CATS2D_03_DA = 0), MPC10 (i.e., MPC10 ≤ 3.25) or piPC10 (i.e., piPC10 ≤ 3). From the chemoinformatic model^[48,49,61], the CATS2D_03_DA is belonged to a CATS2D-based descriptor. It is a topological descriptor quantifying the number of hydrogen bond donor-acceptors (i.e., an integer) at a given topological distance (i.e., lag three) of an IL within the hydrogen-depleted molecular graph^[48,49,61]. As highlighted in Figure 6A and C, nearly all the low-η ILs (η ≤ 100 mPa·s) are found to have zero value (“0”) in CATS2D_03_DA values, whereas there is a substantial amount of high-η (η > 100 mPa·s) ILs are found to have nonzero (i.e., 1-6) values, despite some with zero values. Thus, this suggests that the majority of low-η ILs tend to have a minimal number of hydrogen bond donor-acceptors, whereas the high-η ILs tend to have a larger number of hydrogen bond donor-acceptors (e.g., 2-hydroxy-N-(2-hydroxyethyl)-N-methylethanaminium phosphate, 1-(2-hydroxyethyl)-3-methylimidazolium L-serinate, etc.).

Figure 6. The distribution of the IL viscosity that distinguishes the low-η (represented as 0) and high-η (represented as 1) using the combination of two important molecular descriptors selected from Pearson correlation matrix: (A) CATS2D_03_DA vs. MPC10; (B) P_VSA_ppp_L vs. ATSC7i; (C) CATS2D_03_DA vs. piPC10; and (D) ATSC7i vs. ATS8m. The yellow region highlights the dominance of high-η ILs, whereas the green region highlights the prevalence of low-η ILs in the distribution. For the ILs with very low η (η < 30 mPa·s) that could be potentially useful in battery electrolytes, they are mostly found in the red dotted region. For the complete list of these potentially useful ILs (η < 30 mPa·s), it can be found in File1.csv in the Supplementary Material.

Whereas for MPC10, it is a molecular path count (MPC) of order ten topological descriptors counting the total number of molecule paths of length m (in this case is ten). The length m of the path is the number of edges along the molecular path and is related to path order in an IL^[48,49,62]. This is complementary to piPC10, which quantifies multiple path counts. piPC10 is a descriptor that can capture bond order features (e.g., aromatic bonds) and belongs to the path count descriptor group^[48,49,63]. It is a count of molecular graph weighted paths of a given length (in this case is ten) in the molecular path, where each path is weighted by the product of the conventional bond order of the involved edges and, therefore, can account for multiple bonds in an IL^[48,49,63]. Large values in MPC10 imply large values in molecular branching or presence of long chain branches (e.g., 17-hydroxy-N-(17-hydroxy-3,6,9,12,15-pentaoxaheptadec-1-yl)-N-methyl-N-tetradecyl-3,6,9,12,15-pentaoxaheptadecan-1-aminium methyl sulfate) in ILs. Whereas larger values in piPC10 imply significant presence of multiple bonds (e.g., single, double, aromatic bonds) in molecular branches of ILs (e.g., L-phenylalanine benzyl ester bis(perfluoroethylsulfonyl)imide). For those ILs consisting of anionic and cationic species, this suggests that despite large molecular branching in IL cations, a reduced chain length or a minimal number of hydrogen bonds acceptor-donor in IL anions (e.g., low viscous trioctylammonium butanoate with η ~ 13 mPa·s, MPC10 = 3.1, CATS2D_03_DA = 0 in Figure 6A) helps reduce the IL viscosities, analogous to dicyanamide-based ILs^[18,64].

The P-VSA-like descriptors are the molecular descriptors that define the amount of van der Waals surface area (VSA) having a property in a certain range^[65]. According to P-VSA-based models^[48,49,65], P_VSA_ppp_L is the descriptor measuring the potential pharmacophore points of lipophilic, an important factor that estimates the level of lipophilicity. High-lipophilicity molecules tend to be hydrophobic or less polar, whereas for ATSC7i, it is a 2D autocorrelation descriptor [Supplementary Table 2] based on autocorrelation of a topological structure (ATS) that describes how a property is distributed along the topological structure^[48,49,66]. For ATSC7i, it is a descriptor measuring the centered Broto-Moreau autocorrelation of lag seven used to weigh all the contributions of the ionization potential of each different path length (lag) in the molecular graph. Smaller values of ATSC7i imply a strong tendency in the formation of cations. Therefore, from Figure 6B, it is found that the small values in both P_VSA_ppp_L and ATSC7i tend to yield low-η with highly ionic ILs (e.g., N-methyl-2-oxopyrrolidinium acetate with η ~ 2.4 mPa·s, P_VSA_ppp_L = 13.9, ATSC7i = 0 in Figure 6B). In contrast, for high-η ILs (e.g., trihexyl(tetradecyl)phosphonium chloride with η ~ 1,400 mPa·s, ATSC7i = 3.2, P_VSA_ppp_L = 148.6), large values in both P_VSA_ppp_L and ATSC7i are generally found, as shown in Figure 6B. In addition, it is also interesting to observe that low-η ILs tend to favor the regime of small values in both ATSC7i and ATS8m, as shown in Figure 6D (e.g., trimethylammonium hydrogen sulfate with η ~ 4.7 mPa·s, ATSC7i = 0, ATS8m = 0). Similar to ATSC7i, ATS8m belongs to 2D autocorrelation-based descriptors and represents a molecular feature that measures the centered Broto-Moreau autocorrelation of lag eight weighted by mass^[48,49,66]. Thus, ILs with small molecular sizes generally have small values in ATS8m. From Figure 6D, the trend suggests that heavier and less polar ILs with large molecular sizes tend to have high-η (e.g., tributyl(tetradecyl)phosphonium 2-dodecylbenzenesulfonate with η ~ 1,400 mPa·s, ATSC7i = 3.5, ATS8m = 4.0), and this observation is consistent with the observation that the presence or increase of alkyl group or alkyl chain (e.g., imidazolium cations) will increase viscosities of ILs due to increasing intermolecular van der Waals interactions^[18,35].

Thus, from the general trend of molecular descriptors for low/high-η ILs highlighted in Figure 6A-D, a set of useful design rules to tune the IL viscosity through molecular grafting can be obtained. Specifically for low-η ILs, small values in all these important descriptors, i.e., CATS2D_03_DA, MPC10, piPC10, P_VSA_ppp_L, ATSC7i, and ATS8m, are generally preferred (i.e., the red dotted region in Figure 6A-D and File1.csv in the Supplementary Material). From this observation, a list of 96 IL candidates with very low viscosities (i.e., below ~30 mPa·s), which might be potentially useful electrolytes in battery applications, can be identified [File1.csv in the Supplementary Material]. Thus, the observation [Figure 6] suggests that in order to reduce the IL viscosity, grafting IL cations into smaller sizes (e.g., smaller head rings) and short alkyl chains and reducing ionization potentials/energies will help. Meanwhile, for the same cations, further reducing anions in sizes, chain length, and hydrogen bonds [e.g., TFSI^-, N(CN)₂^-] might be useful to further help to reduce the viscosities. Thus, to fine-tune the IL viscosity, a synergistic effect to achieve an optimum design of both cations and anions in ILs is deemed necessary.