Measurement of properties of graphene sheets subjected to drilling operation using computer simulation
Graphical abstract
Introduction
Graphene is a two dimensional carbon based nanomaterial which has recently attracted significant interest in nanotechnology due to its remarkable mechanical and physical properties [1], [2]. The thickness of a single layer of graphene sheet is only about the diameter of carbon atom which makes it the thinnest material with a large specific surface area [3], [4]. This feature of graphene has resulted in materials scientists in exploring the diverse possible applications of graphene in real world. These include applications in electric circuits such as graphene-based integrated circuits (ICs), field effect transistors (FET) and solar cells [2], [5]. In addition, it is an ideal candidate for potential applications in biomedical, chemical and industrial processes enhanced or enabled by the use of new graphene materials [6], [7]. These applications of graphene requires it to be machined at nanoscale, leading to production of graphene based nanocomponents of complex geometry and functionality. The increasing demand to manufacture nanocomponents for applications in aerospace, defense and electronics is one of the major incentives to study the drilling process of graphene.
Numerous studies have been undertaken to predict the performance of graphene subjected to drilling process. Freedman et al. [8] characterized the drilling kinetics of graphene sheet using a thermionic electron source and various electron beam fluxes. In this study, the drilling process of graphene resulted in the formation of nanopores which is used for translocation of DNA analytes for bio-medical application. Liu et al. [9] and Zhao et al. [10] proposed a fast and controllable method for drilling nanopores in graphene sheet using a suspended SiN substrate. They proposed that individual graphene sheets be transferred precisely on an SiN substrate after which nanopores with different diameters from 3 to 20 nm were drilled using a transmission electron microscope. Theoretical studies on drilling process of graphene are a popular mode of research employing ab initio calculations or molecular dynamics (MD) simulation technique. Zhao et al. [11] employed MD simulations to study the mechanical properties of graphene sheet at elevated temperature. They found that graphene sheet exhibits excellent Young’s modulus even at high temperatures. Hence, theoretical models can be used as a viable alternative compared to time consuming and expensive experiments for monitoring machining process at nanoscale. However, the formulation of these models requires a thorough knowledge on the functionality and the configuration of the nanoscale system.
Application of soft computing methods such as evolutionary approach of multi-gene genetic programming (MGGP) and artificial neural networks (ANN) is on the rise [12], [13], [14], [15], [16], [17]. Several novel approaches of soft computing methods have been proposed such as hybridizing differential evolution algorithm with receptor editing property of immune system [18], [19], [20], artificial bee colony algorithm with Taguchi’s method [21], [22], differential algorithm with Taguchi’s method [23], cuckoo search algorithm (CS) [24] and immune algorithm with hill climbing local search algorithm [25], [26] to optimize the unit production cost of the machining operations of materials. These methods require input training data which can be obtained from the analytical tools such as MD simulations which is based on a specific geometry and temperature. Considering input data, the soft computing methods can then be able to generate meaningful solutions for the complicated problems [27], [28], [29]. Additionally, among the various soft computing methods described above, evolutionary approach method, namely, GP offers the advantage of a fast and cost-effective explicit formulation of a mathematical model based on multiple variables with no existing analytical models [30], [31]. It is to the best of author’s knowledge that limited or no work exists on the application of soft computing models on the performance prediction of the nanoscale system. Hence, soft computing techniques can be used as an alternative method for modeling the machining process of nanoscale materials such as graphene. Additionally, the potential future applications of graphene in electronics industry requires a thorough understanding and investigation of modeling of machining process (for e.g. drilling) of graphene.
Therefore, the main purpose of the present study is to investigate the mechanical response of graphene during a nanodrilling process. Standard MD simulation approach is employed to investigate the effect of temperature, drill bit velocity, and the feed rate of drill bit on the mechanical strength and drilling time of graphene sheet. Data generated from the MD simulations is fed into the paradigm of GP and ANN for the formulation of mathematical models. The performance of these models is evaluated against the data generated from the MD simulations.
Section snippets
MD simulation methodology
In this section, nanoscale drilling of single layer graphene sheet (hereafter referred to as ‘graphene work piece’) using MD simulation is briefly outlined. The data generated from the MD simulation is used to provide the input data to the soft computing cluster (Fig. 1) for training and generation of results. The Brenner’s second generation bond order function (REBO) [32] is used to describe the covalent bonding of the carbon atoms in graphene work piece which is described mathematically as,
Multi-gene genetic programming (MGGP)
For understanding the functioning of evolutionary algorithm MGGP, the basics about the GP is first outlined. GP uses principle of genetic algorithms (GAs) to evolve computer programs/models of varying sizes based on Darwinian Theory of “Survival of the fittest” [44]. Although both GP and GA share the same working principle but there exists difference between them. GP algorithm starts by generating the models randomly. The numbers of models generated is represented by the population size. The
Evaluation and comparison of models
The results obtained from the two prediction modeling methods MGGP and ANN are illustrated in Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16, Fig. 17, Fig. 18 on training and testing data of mechanical strength and drilling time respectively. The best prediction method that gives highest accuracy is determined by comparing these two modelling methods. Square of the correlation coefficient (R2) and relative error (%) between the predicted values and the actual values of the mechanical
Parametric and sensitivity analysis of the best model
In this section, the ‘‘Parametric and Sensitivity analysis about the mean’’ was conducted for the best prediction method. Results discussed in Section 4 reveals that MGGP outperforms the ANN method in prediction of the mechanical strength and drilling time. This analysis provides a measure of the relative importance among the inputs of the MGGP model and illustrates how the two model outputs vary in response to variation of an input. For this purpose, on the MGGP trained models, the first input
Conclusion
In this paper, an evolutionary approach, MGGP, is proposed for the prediction of mechanical strength and drilling time of graphene subjected to drilling process. The performance of the proposed MGGP model is compared to that of the ANN model. The statistical comparison in Section 4 concludes that the performance of the MGGP model is better than that of the ANN model. From the present work, several advantages of MGGP over ANN can be found. High performance of the MGGP model on the testing data
Acknowledgement
The authors extend their heartfelt gratitude to the Editor-in-Chief and anonymous reviewers for suggesting constructive guidelines to improve the literal and technical content of the paper.
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The first two authors made equal contribution in this work and are both equally considered as first author.