Optimizing the growth of vertically aligned carbon nanotubes by literature mining and high-throughput experiments

GAO Zhang-dan, JI Zhong-hai, ZHANG Li-li*, TANG Dai-ming*,ZOU Meng-ke2, XIE Rui-hong2, LIU Shao-kang2, LIU Chang*

（1. Shenyang National Laboratory for Materials Science, Institute of Metal Research (IMR), Chinese Academy of Sciences, Shenyang 110016, China;

2. School of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China;

3. Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan）

Abstract： Vertically aligned carbon nanotube (VACNT) arrays with good mechanical properties and high thermal conductivity can be used as effective thermal interface materials in thermal management. In order to take advantage of the high thermal conductivity along the axis of nanotubes, the quality and height of the arrays need to be optimized. However, the immense synthesis parameter space for VACNT arrays and the interdependence of structural features make it challenging to improve both their height and quality.We have developed a literature mining approach combined with machine learning and high-throughput design to efficiently optimize the height and quality of the arrays. To reveal the underlying relationship between VACNT structures and their key growth parameters, we used random forest regression (RFR) and SHapley Additive exPlanation (SHAP) methods to model a set of published sample data (864 samples). High-throughput experiments were designed to change 4 key parameters: growth temperature, growth time, catalyst composition, and concentration of the carbon source. It was found that a screened Fe/Gd/Al2O3 catalyst was able to grow VACNT arrays with millimeter-scale height and improved quality. Our results demonstrate that this approach can effectively deal with multi-parameter processes such as nanotube growth and improve control over their structures.

Key words: Vertically aligned carbon nanotube arrays；Controlled growth；Literature mining；Machine learning；High throughput

1 Introduction

The long phonon mean free path of carbon nanotubes (CNTs) lead to the excellent thermal properties[1]. Vertically aligned carbon nanotube (VACNT)arrays composed of numerous CNTs are highly ordered and tightly arranged, thus allowing better utilization of the high thermal conductivity along the axis of nanotubes[2]. The demand for mechanical flexibility and stability of thermal interface materials in practical applications also drives VACNT arrays to be one of the most ideal candidates. However, previous reports have shown that the actual thermal conductivity of VACNT arrays is much lower than predicted[3-4], due to the difficulties in increasing both array height[5]and quality (crystallinity and defect level of arrays)[6], which are highly sensitive to the complex and interdependent growth parameters.

In the last decade, the large number of publications on the synthesis of VACNT arrays results in a large amount of data on the process-structure-property interactions of VACNT arrays. However, as with most carbon materials, because of the vastness and complexity of the design variables, identifying the critical correlations between growth parameters and structure as well as properties is not straightforward[7].Significantly, text mining and data extraction from literature data have the potential to reveal hidden relationships that were not evident in the original investigations[8]. Meanwhile, machine learning (ML) tools have also been proposed for revealing difficult-to-access information and proposing solutions to complex problems[9]. These capabilities have proven to be useful for the screening of growth conditions for the synthesis of CNTs with high quality[10]or narrow diameter distribution[11]. Additionally, high-throughput methodology has been used in the field of catalyst synthesis for carbon nanomaterials because of the high efficiency to collect data[12-13]. These approaches lay the foundation for accelerating the structural modulation of VACNT arrays.

In this work, the chemical vapor deposition(CVD) process parameters and structure features from one of the most productive groups in the literature database of VACNT growth were manually mined.The VACNT growth data extracted from the literature were then parsed with an ML algorithm to understand the complex non-linear relationships between different variables. For the trained ML models, the SHAP analysis was conducted to assess important features and explore interactions between the VACNT structures and growth parameters. Based on the screened parameter space, a rigorous high-throughput method for rapidly optimizing the height and quality of VACNT arrays was used. The optimal synthesis target was achieved by delineating the critical region of growth in the reduced-dimensional space and mainly regulating the catalyst components. The workflow of this study is illustrated in Fig. 1. The structural optimization of VACNT arrays has been proven effective by text mining approach along with ML and high throughput methodology.

Fig. 1 Workflow for optimizing the height and quality of VACNT arrays by 4 main steps

2 Experimental

2.1 Literature data mining

Web of Science was employed as the search engine to systematically search for related literature on the controlled preparation of VACNT arrays. Since different research groups have different systems for growing VACNT arrays, the quality and consistency of data may vary greatly. For example, the Maruyama group focused on the preparation and physical properties of VACNT arrays with small diameters[14-19].Robertson group worked on the catalyst design and growth kinetics of VACNT arrays[20-24]. Hart group focused on the density modulation and growth mechanism of VACNT arrays[25-31]. Noda group focused on the height modulation of VACNT arrays. This study took into account the research content and the number of articles to artificially determine the research groups. The Noda group was finally selected to meet the data collection initiative.

Given the small number of papers (17 articles),this study directly used manual data mining to obtain data information within the literature. To avoid the limitations caused by the small sample size and inertia of human behavior during literature data mining,all process parameters involved were extracted from the papers. The process parameters of the CVD method and the growth results of the VACNT arrays extracted from the literature were recorded as the input and output parameters of the subsequent ML models,respectively. The input parameters include a total of 11 groups, such as annealing temperature, annealing atmosphere, primary catalyst, etc. The output parameters included array height and quality (the G/D intensity ratios from Raman spectra,IG/ID). Descriptive statistics of the data samples (input and output variables) used to formulate the models are shown in Table S1.

After data extraction, the units of the same parameter need to be kept consistent. Apart from the need for uniformity of the parameter units, the data-specific values need to be adjusted. There are 2 main cases:(1) when the statistical results of some data are range value, the median data is taken manually, (2) how to deal with missing value? If the parameter is not mentioned in the text, fill in the 0 value, otherwise, fill in the average of the data in the column. Details of the extracted data and the pre-processed data are included in Supporting Information.

2.2 Machine learning of the data set

In this paper, supervised linear regression (LR),support vector regression (SVR), and random forest regression (RFR) were used. Data samples were fed into the three machine learning models. The ratio of the training to the testing dataset was 8∶2. The process of optimizing and evaluating the performance of the model is mainly divided into 3 stages: (1) optimizing the hyperparameters of the model by Grid Search,(2) producing an overall measurement of the model by performing k-fold cross-validation (CV) on the training dataset, (3) evaluating the performance of a regression model through mean squared error (MSE),coefficient of determination score (R2) and mean absolute error (MAE). These metrics were calculated overall testing datasets to validate the developed prediction models’ adequacy and validity. The coefficient of determinationR2represents the accuracy of the prediction. Thus, forR2closer to 1, more prediction accuracy is obtained. The RMSE and the MAE are measures of the deviation between the predicted and true values. The higher the value of MSE, the greater the error and thus the worse the model.

2.3 High-throughput growth

2.3.1 Catalyst microarrays preparation

The methods used for physical combinational masks followed the general approach adopted earlier by Wang et al.[32]. The preparation of high-throughput catalyst arrays on a silicon wafer (with 300 nm of thermally grown SiO2) by the combinatorial masked deposition. Specifically, the Al2O3support layer was formed by depositing 10 nm Al on the marked silicon wafer and then exposing the layer to air. Ion-beamsputtered films of Fe, Gd and Cr were sequentially or separately prepared on Al2O3/SiO2/Si substrates under mask coverage. This quaternary combinatorial masking strategy enables the generation of thin-film catalyst libraries containing 64 different compositions or thicknesses on silicon wafers 1-centimeter square. The nominal thickness of Fe-Cr-Gd ternary catalyst is illustrated in Fig. S1.

2.3.2 Growth of VACNT arrays

The VACNT arrays were generated by the thermal CVD methodology in a horizontal quartz tube furnace. The reactor was heated to a target temperature range of 770-850 °C and the temperature was maintained at least for 0.5 h. Before the formation and reduction of catalyst particles, a vacuum pump was used to extract air from the furnace tube and then the reducing atmosphere (e.g., hydrogen and argon) was introduced to reach ambient pressure. After the pretreatment, the nucleation and growth of VACNT arrays were carried out by passing a gaseous mixture of ethylene and hydrogen (with argon as the carrier gas)through a heated reaction chamber.

2.3.3 Characterization

The height and quality (IG/ID) of each sample were measured using a Raman imaging system(WITEC alpha 300R) with a 532 nm excitation wavelength. The sample was placed on a flat stage.The Z-axis of the Raman imaging system was set to 0 on the Si substrate surface. The height of the VACNT array was obtained by reading the Z-axis value of the Raman system when the top side of the sample was clearly focused by the 532 nm laser. The corresponding Raman spectra obtained from different positions along the array cross-section show that theIG/IDratio in the tip of the forest has a higher value than the root.This trend arises because the growth of the VACNT arrays occurs in the tip-growth mode[33]. The bottom of the VACNT arrays has been exposed to amorphous carbon deposition for a longer period than the top of the VACNT arrays[34]. For this study, the crystallinity of the VACNT arrays was assessed using the ratio ofIGandIDpeak at the top of the sample. The morphology and detailed structure of the VACNT arrays were observed by high-resolution field emission scanning electron microscopy (SEM, FEI Nova NanoSEM 430) and transmission electron microscopy (TEM,FEI Tecnai F20). Surface topography and roughness of the annealed catalyst substrates were analyzed with atomic force microscopy (AFM, Bruker Multimode 8).

3 Results and discussion

3.1 VACNT structure and its correlation to growth parameters

Out of 17 original research articles published by the Noda group, data from 12 studies were retained.The data extracted from the selected literature included VACNT structural features corresponding growth parameters. Ultimately, data mining yielded a total of 845 VACNT arrays. The 13 process parameters and 2 structural data were statistically studied separately (Fig. S2). The carbon source of the Noda group was mainly C2H2and C2H4(Fig. S2a), and the general growth temperature increased from C2H2(600°C) to C2H4(800 °C). The film thickness of the dominant catalyst Fe ranged from 0 to 8 nm, with an average thickness of 1.5 nm (Fig. S2e). In the reducing gas environment (H2and Ar), the reduction time of the catalyst is typically 5 min (Fig. S2l). H2O was used as a promoter in some of the studies (Fig. S2j). From Fig. S2n-o, it can be seen that the height of VACNT arrays is mainly concentrated in 0.5±0.5 mm, and the mean value ofIG/IDis 6.3.

To be able to deal with the 2 structural features of VACNT arrays, namely, the height and quality, two mode data sets were created: A subset of data containing 787 VACNT arrays with known height and a subset of data containing 93 VACNT arrays with known crystallinity. To avoid the overfitting problem of the ML algorithm, a RFR model were used to roughly filter non-critical parameters for both datasets. The input parameters were ranked in order of importance and the top 10 items are retained (ESI). Several algorithms were built in an attempt to predict the height and crystallinity of VACNT, respectively. It is vital to evaluate the models’ performance and verify the prediction results’ accuracy. For the comparative analysis of the ML approaches on the new datasets, we performed the Grid Search hyperparameter optimization for several classical regression models (Table S2) and evaluated their performance (Table 1).

According to Table 1, linear approximations are not well suited for this prediction task, and SVR also performs significantly worse than the RFR model.This result is to be expected for 2 reasons. First, the strong relationship between height orIG/IDand growth parameters is non-linear. Second, LR and SVR models don’t perform as well with multicollinear predictor variables. Based on the performance metrics, the RFR method was selected due to its high performance both in height (R2= 0.90) andIG/ID(R2= 0.82).The height dataset was split into 10 folds andIG/IDdataset was split into 5 folds. The average k-fold CV scores for prediction height andIG/IDvalues using 3 different ML algorithms are shown in Table S3.

In order to evaluate the performance for reliable prediction of the RFR model, the predicted results and statistical datasets are compared with a simple linearregression. Fig. S3a shows that the height dataset and predicted values are almost close to each other, signifying a reliable RFR model. The predicted values in Fig. S3b are distributed over a wide range on both sides ofy=x. This is due to the small amount ofIG/IDdata, so the presence of the error is inevitable in the model.

Table 1 Regression model validation and performance evaluation

Identifying the main features affecting height andIG/IDvalues is essential for structural control of VACNT arrays. To establish clear parameter-structure relationships for VACNT arrays, interpretation methods can be used to provide a deeper understanding of the obtained models. Therefore, we utilized a supplemental technique known as SHAP, which enables enhanced analysis of the relative importance of each variable in a machine learning prediction, via game theory[35]. SHAP values derived from the RFR models are shown in Fig. 2, where the variables are ordered according to their overall importance (degree of influence on model output). Based on the mean absolute SHAP value, temperature (TEMP), growth time(t(G.)), thickness of Fe catalyst film (Fe), and concentration of C2H4are the top 4 critical synthesis parameters for the height of VACNT arrays (Fig. 2a).Similarly, thickness of Fe catalyst film, temperature,concentration of CH4and C2H2are the top four critical synthesis parameters for theIG/IDof VACNT arrays (Fig. 2b).

The SHAP values in Fig. 2 show that high temperatures and high carbon source concentrations (positive red symbols) increase the height and quality of VACNT arrays, whereas a high Fe catalyst thickness decreases the array quality. Gd catalyst (Fig. 2a) and CH4concentration (Fig. 2b) contribute significantly to the height and crystallinity of VACNT arrays, respectively. A retrospective of the original data revealed that Gd suppressed the interaction between Fe and C[36]and CH4prevents the coarsening of Fe particles[37],thus prolonging the catalyst lifetime in a CVD environment. The height and crystallinity of VACNT arrays can be improved by suppressing the lateral structure change of Fe nanoparticles. Therefore, the catalyst component is the main parameter for regulations in the subsequent high-throughput experiments.

Taken together, it can be found that growth temperature, growth time, thickness of Fe catalyst film,carbon source, and co-catalyst component are the top 5 main features affecting the height andIG/IDof VACNT arrays. Among them, the change in growth temperature possibly affected the ratio of active catalyst particles[38-39], which in turn affected the height and quality of VACNT arrays. Prolonged growth time was able to increase the height of VACNT arrays within the growth lifetime of the catalyst particles[40-41]. Therefore, the design of catalysts is crucial for the structural control of VACNT arrays. In this study, high-throughput experiments were first designed using pure Fe catalysts to achieve optimization of temperature, carbon source, and Fe catalyst film thickness studies. Since Fe catalysts dominate the multilayer catalyst system, studies on growth time and co-catalyst components were then carried out under optimal growth conditions for pure Fe catalysts.

Fig. 2 SHAP summary plots of the effects of growth parameters in the RFR models for (a) height, and (b) IG/ID values, in descending order. All of the variables in the database constitute each point in the image, the color of the point indicates the value of the input variable, and the horizontal location shows whether the effect of that value is associated with a higher or a lower prediction. t(G.) and t(A.) denote the growth time and annealing time, respectively

3.2 Optimizing synthesis parameters by highthroughput methods

Since Fe is the most used catalyst for VACNT growth and the major component of the catalyst used here, the growth of VACNT arrays from metallic Fe catalyst is the control experiment to optimize the temperature and carbon source concentration. According to the literature mining dataset, the thickness of Fe film ranged from 0-8 nm and the annealing temperature was kept in line with the growth temperature between 750-820 °C with ethylene as the carbon source. In this study, the settings of Fe catalyst film thickness, temperature, and carbon source concentration were shown in Table S4. Further details of synthesis are given in Section 2.3. In the CVD growth system, it’s confirmed that the production of VACNT arrays in a narrow range of Fe film is thickness of 0.45 nm≤tFe≤2.52 nm. The preferred conditions were 20.1% C2H4and 800 °C. The products show a negative correlation between forest height andIG/ID.

Many types of metal such as Fe-Mo[42], Fe-Gd[36,43-44], Fe-Ni-Cr[45], Co-Mo[46], and Ni-Cr[47], have been reported to successfully control the diameter or height of VACNT arrays by selecting mixtures of catalyst element. The structure of VACNT arrays may be influenced by the number of catalysts because of the synergistic effect of multilayer or binary catalyst systems. We first performed a wide range of growth condition modulations for mono-Fe catalysts with thickness gradients based on the main influencing factors obtained from the SHAP model. Then Gd and Cr were selected as co-catalysts for VACNT array growth.

Taking the growth results from the mono-Fe catalyst as a benchmark, those from Fe catalyst with the addition of Cr, or Gd of the thickness of 0.1, 0.2,and 0.3 nm were compared. Gd has a significant contribution to both height andIG/IDof VACNT arrays.When the thickness of Fe film is less than 1 nm, the addition of Cr has no significant effect on the array structure. However, Chen et al. have demonstrated that Cr could suppress the catalyst’s migration by acting as a dispersant[47]. To suppress catalyst particle coarsening and prolong catalyst lifetime, the Fe-Cr-Gd ternary catalysts was investigated.

After synthesis, theIG/IDand height of VACNT arrays were characterized and plotted as a function of each alloy in a ternary plot. Fig. 3 shows the Fe/Cr/Gd ternary diagram associated with (a) height and (b)IG/IDvalues of the VACNT arrays. The active region marked with an arrow in Fig. 3a has a corresponding height greater than 500 μm for the VACNT arrays,and theIG/IDof the corresponding VACNT arrays in the active region in Fig. 3b (marked by an arrow) is greater than 6. However, Fig. 3c revealed a strong dependence of the height on the catalyst composition.Pearson correlation coefficient[48]is used to measure the degree of association between changes in one continuous variable and changes in another continuous variable. The relationship was analyzed by calculating the Pearson correlationrvalue between the catalyst component and the VACNT height orIG/ID. The VACNT height has a strong negative correlation with Cr content (r= -0.7) and is moderately negatively correlated with the Gd content (r= -0.47). And theIG/IDvalue is weakly negatively correlated with the Cr content (r= -0.14), but weakly positively correlated with Gd content (r= 0.12). The growth results of ternary catalysts indicated that the increase of Cr content suppressed the array height and crystallinity, while Gd had an enhancing effect on the array crystallinity.

To investigate the role of Gd and Cr addition, the average nanoparticle size and their size distribution of different catalysts on the Al2O3support layer were investigated with AFM after reduction under H2and Ar at 800 °C for 10 min (Fig. S4). Compared with Fe-Cr and Fe-Cr-Gd, Fe-Gd has the smallest mean particle size and the lowest mean square deviation of the statistics. The addition of both Cr and Gd to 1.1 nm-Fe reduced the average particle size, indicating that they can inhibit the agglomeration of Fe catalyst particles during the reduction process.

Fig. 3 Fe-Cr-Gd ternary diagram associated (a) height and (b) IG/ID values of the VACNT arrays. Plots of (c) height and (d) IG/ID values of the VACNT arrays as a function of Gd and Cr content (weight %). The arrows are just to guide the eyes

3.3 Optimization of VACNT height and quality

Fig. 4 illustrates the height of VACNT grown from Fe and Fe-Gd catalysts as a function ofIG/ID, respectively. The crystallinity of the VACNT arrays grown from Fe-Gd has been improved compared with the growth results of Fe catalyst. The dual outcome correlation was analyzed using Pearson’s correlation coefficients. The height of VACNT arrays grown from both Fe (r= -0.59) and FeGd (r= -0.47) catalysts showed a moderate negative correlation withIG/ID[36,39,49]. The negative correlation between height and crystallinity was improved by the addition of Gd catalyst.

The structural characterization of the tallest VACNT samples grown from Fe and Fe-Gd catalysts is compared in Fig. 5. The Raman spectrum of Fig. 5a shows that 1.5 nm Fe/0.2 nm Gd enhanced theIG/ID.Meanwhile, the height of Fe-Gd is slightly higher than that of the Fe growth product as can be seen from the side view of the corresponding SEM images in Fig. 5b. From the TEM plots of Fig. 5c, d and their corresponding diameter distribution statistics, the average diameters of VACNT arrays were 7.5 nm (1.8 nm Fe) and 3.7 nm (1.5 nm Fe-0.2 nm Gd). Fig. S5 shows the wall number distributions of VACNT arrays grown from (a) 1.8 nm Fe catalyst and (b) 1.5 nm Fe-0.2 nm Gd catalyst. The addition of Gd to Fe reduced the wall number of VACNT arrays, resulting in higher quality, narrower diameter single-wall VACNT arrays.

Fig. 4 Height of VACNT arrays grown from Fe and Fe-Gd catalyst as a function of the IG/ID values

Fig. 5 Characterizations of VACNT arrays before and after optimization. (a) Comparison of Raman spectra taken from the top of the VACNT arrays using a wavelength of 532 nm laser; (b) Cross-sectional SEM images of the VACNT arrays; TEM images and the inserted diameter distribution of VACNT arrays grown from (c) 1.8 nm Fe catalyst and (d) 1.5 nm Fe-0.2 nm Gd catalyst

All growth data form a new dataset for the ML model, which is fed into the ML model as training and test data. Since the silicon wafer contains 64 different locations, the catalyst position is also used as an input parameter for the machine learning model. The optimized hyperparameters of RFR and SVR models obtained using the grid search method were shown in Table S5. From the average 10-fold cross-validation scores (Table S6) and their associated performance evaluation metrics (Table S7), it can be concluded that the RFR model has the highest accuracy for predicting height andIG/IDof VACNT arrays. Shap summary plots of the effects of growth parameters on height andIG/IDanalyzed using the RFR model were shown in Fig. S6, in descending order. Fe catalyst thickness and growth time were the major factors affecting the height and crystallinity of VACNT arrays,yet in opposite roles (Fig. S6). Within the range of Fe catalyst thickness (0～2.52 nm) and growth lifetime,increasing the Fe catalyst thickness and extending the growth time can promote the VACNT height while degrading the VACNT quality. These results revealed the paradoxical relationship between long-length and high-quality CNT forests.

4 Conclusions

In summary, machine learning-based literature mining and high-throughput experiments were combined to optimize the growth of VACNT arrays. From literature mining, the most influential growth parameters were identified to be the growth temperature,growth time, catalyst component, and carbon source concentration. Based on the predicted optimal conditions, the relationship between the growth parameters and the height and the crystallinity of the VACNT arrays was investigated. A moderate negative correlation between the height andIG/IDof VACNT arrays was identified. Analysis of the correlation between catalyst composition and growth results (height andIG/ID) by Pearson’s correlation coefficient allows us to identify trends in the modulation of catalyst composition that improves height or quality. With an optimized Fe-Gd-Al2O3catalyst, a VACNT array with a height of ～1.3 mm and anIG/IDof 5.0 could be obtained.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51802316,51927803, 52188101 and 52130209), the JSPS KAKENHI (JP20K05281 and JP25820336), Natural Science Foundation of Liaoning Province (2020-MS-009), Liaoning Revitalization Talents Program(XLYC2002037), Basic Research Project of Natural Science Foundation of Shandong Province, China(ZR2019ZD49).

Data availability statement

The data that support the findings of this study are openly available in Science Data Bank at https://www.doi.org/10.57760/sciencedb.j00125.00056 or https://resolve.pid21.cn/31253.11.sciencedb.j00125.00 056.