Elastic properties and buckling behavior of single-walled carbon nanotubes functionalized with diethyltoluenediamines using molecular dynamics simulations

Accepted Manuscript Elastic properties and buckling behavior of single-walled carbon nanotubes functionalized with diethyltoluenediamines using molecular dynamics simulations R. Ansari, S. Ajori, S. Rouhi PII: DOI: Reference:

S0749-6036(14)00408-X http://dx.doi.org/10.1016/j.spmi.2014.11.002 YSPMI 3477

To appear in:

Superlattices and Microstructures

Received Date: Accepted Date:

6 October 2014 1 November 2014

Please cite this article as: R. Ansari, S. Ajori, S. Rouhi, Elastic properties and buckling behavior of single-walled carbon nanotubes functionalized with diethyltoluenediamines using molecular dynamics simulations, Superlattices and Microstructures (2014), doi: http://dx.doi.org/10.1016/j.spmi.2014.11.002

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Elastic properties and buckling behavior of single-walled carbon nanotubes functionalized with diethyltoluenediamines using molecular dynamics simulations R. Ansari*1, S. Ajori1, S. Rouhi2 1

Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

2

Young Researchers Club, Langroud Branch, Islamic Azad University, Langroud, Guilan, Iran

Abstract Carbon nanotube (CNT) modification processes are of great importance for good dispersion of CNTs and load transfer issues in nanocomposites. Among these processes, polymer covalent functionalization is found to be an effective way to alter the mechanical properties and behavior of pristine CNTs. Therefore, the mechanical properties and buckling behavior of diethyltoluenediamines (DETDA) functionalized CNTs are investigated employing molecular dynamics (MD) simulations. The results demonstrate that as the polymer weight percentage increases, Young’s modulus and critical buckling load increase almost linearly for both regular and random polymer distributions, whereas critical strain decreases with different trends depending on the type of polymer distribution. Finally, the buckling mode shapes of the presented models are illustrated and it was revealed that there are some differences between the mode shapes of functionalized CNTs and those of pristine CNTs. Keywords: Functionalized carbon nanotubes; Diethyltoluenediamines; Mechanical properties; Buckling; Molecular dynamics

*

Corresponding author. Tel. /fax : +98 131 6690276. E-mail address: [email protected] (R. Ansari)

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1. Introduction Since the discovery of carbon nanotubes (CNTs) [1], their unique mechanical, electrical and structural properties have attracted much interest of researchers around the world. During the past two decades, it has been found that apart from the outstanding intrinsic properties of individual CNTs like extraordinary mechanical, optical and electrical properties, they demonstrate high potential applications in nanoelectronics, nanosensors, nanocomposites, energy storage systems and so on [2,3]. It was observed that CNTs can be used as a superlative reinforcer, together with polymers in a nanocomposite structure [4-6]. Practically, because of agglomeration tendency of CNTs to form bundles and also strong interaction between walls of tubes which result in limitation of their solubility and dispersion in a polymer matrix [3,7], CNTs applications in nanocomposites were restricted to a significant extent [8,9]. To overcome this, a great has been made to break these bundles in order to good dispersion and also improvement of load transfer in the desired matrices. In this regard, numerous investigations have been carried out for CNT modification in recent years [2,10-13]. Functionalization of CNTs is found to be an effective way of modification processes which in general is divided in two main categories: noncovalent

and

covalent

functionalizations

functionalization is on the basis of

[2,9,14-17].

Generally,

noncovalent

different interactions like van der Waals (vdW) and

electrostatic forces, hydrogen bonds and π stacking interactions [18-21] and includes surfactants [22], biomacromolecules [23]and wrapping with polymers [24,25]. This kind of functionalization takes the advantage of preserving the graphitic sp2structure compared to covalent functionalization. Besides, duo to π-orbitals of carbon atoms, CNTs are found to be reactive enough to form covalent bonds with other atoms [26]. By introducing the functional groups [27,28] to the CNTs, covalent functionalization can be formed based on two direct (covalent 2

sidewall functionalization) and indirect (defect functionalization) methods [2,29-31]. Apparently, covalent functionalization destroys the perfect structures of CNTs resulting in significant changes in the mechanical, electrical and physical properties of CNTs as expected. Covalent functionalization of polymer molecules, known as polymer grafting, possesses an important role in enhancement of polymer/CNT nanocomposites. To the best of authors’ knowledge, investigation on the mechanical properties and buckling behavior of an individual functionalized CNT has not been studied in the literature up to now. Hence, in this paper the elastic properties and

buckling behavior such as critical strength and strain of

diethyltoluenediamines (DETDA) functionalized single walled carbon nanotube (SWCNT) which is successfully produced recently through diazonium-based addition quite [32], are investigated. Additionally, the effect of weight percentage of DETDA polymer on the aforementioned properties is studied in both random and regular patterns of covalent functionalization.

2. Methodology In order to perform classical molecular dynamics simulations in this study, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [33] is employed. In all simulations, canonical ensemble (NVT) is chosen employing Amber force field [34] in order to calculate the energetics of corresponding nanostructure in the room temperature. Moreover, Nose-Hoover thermostat algorithm is implemented within the Velocity-Verlet integrator algorithm and time step of 1 fs is chosen to guarantee the stability and reduction of temperature fluctuation of simulation system [35-37]. Also, to minimize energy of simulation system and in order to reach sufficient minimum relative energies, conjugate gradient algorithm with an energy convergence norm is applied. To simulate axial load, a displacement of 0.01 Å in desired 3

direction for tension and compression is applied to the boundaries of functionalized CNT and then the structure is allowed to relax for 5 ps. It should be noted that in these explorations, the CNTs are taken to be long enough so that the effect of boundary conditions and chirality of CNTs on the computed values can be neglected. After relaxation, the energy of functionalized CNT in each step of loading is computed and the desired mechanical properties and buckling behavior are determined and also, the buckling mode shapes are illustrated.

3. Results and discussion In order to demonstrate the structure of functionalized CNTs, Fig.1 is presented. This figure illustrates DETDA polymer structure, a pristine (7,7) CNT with length of 110 Å and schematics of regular and random distributions of polymers which are covalently bonded to CNTs. At first, so as to determine Young’s modulus of pristine CNT, tensile load is applied up to 3% of strain and energy of CNT is computed during simulation. Using second derivation of strain energy with respect to the applied strain and employing curve fitting on the data sets as presented in Fig. 2,Young’s modulus is calculated around 0.66 TPa which is in good agreement with previously reported molecular dynamics investigations [38,39]. Considering the effect of random covalently bonded polymer to CNTs with weight percentages of 4.5%, 7.5%, 10.5% and 13.5% of polymer in Young’s modulus, Fig.3 is illustrated. It is observed that Young’s modulus increases linearly up to 7.5 % in the case of functionalized CNT with 13.5 % of polymer weight and reaches to 0.71 TPa. Performing similar calculations on CNTs with regular distribution of polymer reveals that type of polymer distribution on the sidewalls of CNTs does not change the pattern of Young’s modulus variation with polymer weight percentage. To explore the buckling behavior, compressive load is applied. Fig. 4 reveals the strain energystrain curve for a CNT in presence of compressive load in which as buckling occurs, the slight 4

drop of energy can be observed. The results of all models of functionalized CNTs show that the DETDA polymer functionalization of CNT increases the critical buckling load and in opposite reduces the critical strain. In order to study more precisely, functionalized CNT with regular pattern of distribution is considered. The effect of polymer weight percentage on the critical buckling load and strain is presented in Figs. 5 and 6, respectively. According to Fig. 5, it is seen that critical buckling force increases up to 83 nN which is significantly higher (around 9 times) than that of pristine CNT. Fitting a curve on data sets of critical buckling load demonstrates approximately a linear variation of critical buckling load with the polymer weight percentage. From Fig. 6, considerable reduction can be observed in the value of critical strain with the increase of polymer weight for DETDA functionalized CNTs. The computations reveal that in the pristine CNT, buckling occurs at the strain of 5.7% which reduces to 3.3% in a CNT with 13.5% of DETDA functionalization. Similar to critical buckling load, the variation of critical strain is approximately linear with polymer weight percentage. To make a more realistic model, CNTs with random distribution of covalent bonding of DETDA polymer are considered. Figs. 7 and 8 are given to show the influence of polymer weight percentage on the critical buckling force and strain in the case of random distribution. It is found that the effect of polymer weight percentage on the critical buckling load is almost identical for both random and regular distributions, qualitatively and quantitatively, as illustrated in Figs. 5 and 7. In view of the critical strain, the trend is totally different from other cases of polymer regular distribution. From Fig. 8, the considerable drop (27%) in the value of critical strain is observed in the presence of approximately 4.5% DETDA polymer functionalization which can be explained by unbalanced distribution of van der Waals forces formed by random distribution of polymer on CNTs. Increasing the polymer weight percentage, it is revealed that the critical strain rises smoothly and

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converges to a specific value which is 9% higher than minimum value and almost becomes constant after that point of 4.7%. To study buckling mode shape of the models, Figs. 9 to 11 are presented. In the case of pristine CNT(Fig. 9), it is observed that CNT buckles locally near the boundaries and center of tube symmetrically in the direction where bending takes place which is different from buckling mode shape of functionalized CNTs to some extent. In the case of functionalized CNT with random distribution of polymers(Fig. 10), the buckling mode shape is almost similar to buckling of pristine CNT in which in some cases the symmetry is approximately broken. Different from what occurs in the buckling behavior of functionalized CNT with random distribution of polymers, it is found that regular distribution of polymers causes that the buckling occurs in the direction perpendicular to bending direction as revealed in Fig. 11.

4. Conclusion Herein, the mechanical properties and buckling behavior of diethyltoluenediamines (DETDA) functionalized CNTs, such as Young’s modulus, critical buckling load and strain were calculated utilizing molecular dynamics simulations. The simulation models were divided into two categories including CNTs with random distribution of DETDA polymer grafted to and the ones with regular distribution pattern. It was found that Young’s modulus and critical buckling force increase approximately by an almost linear trend, with respect to polymer weight percentage in which the increase of critical buckling force is significant. By contrast, For both types of distribution, the critical strain reduces considerably with different trends, as the polymer weight percentage increases. Also, the buckling mode of DETDA functionalized CNT was shown to be different from that of pristine CNTs.

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Figure captions: Fig.1. Schematic representation of a) pristine CNT, b) DETDA polymer structure, c) functionalized CNT with regular distribution of polymers and d) functionalized CNT with random distribution of polymers. Fig.2. Strain energy variation with tensile strain up to 3%. Fig.3. Variation of Young’s modulus with polymer weight percentage for random polymer functionalization CNTs. Fig.4. Strain energy variation with compressive strain. Fig.5.Variation of critical buckling force with polymer weight percentage for regular polymer functionalization CNTs. Fig.6. Variation of critical strain with polymer weight percentage for regular polymer functionalization CNTs. Fig.7. Variation of critical buckling force with polymer weight percentage for random polymer functionalization CNTs. Fig.8. Variation of critical strain with polymer weight percentage for random polymer functionalization CNTs. Fig.9. Buckling mode of pristine CNT. Fig.10. Buckling mode of functionalized CNT with random distribution of polymers. Fig.11. Buckling mode of functionalized CNT with regular distribution of polymers.

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Fig.1. Schematic representation of a) pristine CNT, b) DETDA polymer structure, c) functionalized CNT with regular distribution of polymers and d) functionalized CNT with random distribution of polymers

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Fig.2. Strain energy variation with tensile strain up to 3%.

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Fig. 3. Variation of Young’s modulus with polymer weight percentage for random polymer functionalization CNTs.

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Fig.4. Strain energy variation with compressive strain.

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Fig.5. Variation of critical buckling force with polymer weight percentage for regular polymer functionalized CNTs

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Fig.6. Variation of critical strain with polymer weight percentage for regular polymer functionalization CNTs.

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Fig.7. Variation of critical buckling force with polymer weight percentage for random polymer functionalization CNTs.

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Fig.8. Variation of critical strain with polymer weight percentage for random polymer functionalization CNTs.

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Fig.9. Buckling mode of pristine CNT.

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Fig.10. Buckling mode of functionalized CNT with random distribution of polymers.

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Fig.11. Buckling mode of functionalized CNT with regular distribution of polymers.

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Highlights Mechanical properties of DETDA-functionalized CNTs are characterized. Buckling behavior of DETDA-functionalized CNTs is described. Effects of polymer weight percentage and its regular and random distribution are explored.

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