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Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Reactivity-Controlled Aggregation of Graphene Nanoflakes in Aluminum Matrix: Atomistic Molecular Dynamics Simulation Sunil Kumar,*,† Sudip K. Pattanayek,‡ and Suchandan K. Das† †

CSIR-National Metallurgical Laboratory, Jamshedpur 831007, India Department of Chemical Engineering, IIT, Delhi 110016, India

‡

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S Supporting Information *

ABSTRACT: Aluminum graphene nanoflakes composite depicts many useful properties such as excellent mechanical strength, lightweight, high electrical, thermal properties, etc. Aggregation and dispersion of graphene nanoflakes in aluminum matrix highly influence the above-mentioned properties. In this paper, aggregation of graphene nanoflakes in aluminum matrix has been studied using molecular dynamics simulation. During simulations, adaptive intermolecular reactive empirical bond order (AIREBO) and embedded atom method force field were used for graphene nanoflakes and aluminum, respectively. AIREBO potential is capable of reproducing sp2−sp2 (covalent) bond formation or breaking between the reactive edge of graphene nanoflakes. The reactive edges of graphene nanoflakes form covalent bond with the neighboring graphene that produces a unique interconnected network in aluminum matrix. However, reactivity of graphene edge exclusively depends on the interfacial interaction between graphene and aluminum. Further, interfacial interactions significantly influence the crystallization temperature of aluminum. The adaptive common neighbor analysis, radial distribution function, mean square displacement, solvent-accessible surface area, and potential energy evolution have been used to characterize the properties of aluminum graphene nanoflakes composite. The results of this study may provide a comprehensive understanding of the interfacial properties of graphene aluminum nanocomposites, which help to improve the performance of nanocomposites materials.

1. INTRODUCTION Aluminum graphene nanocomposite depicts excellent properties compared to pure aluminum, such as high mechanical strength,1−4 low density,5 good corrosion resistance,6 better thermal stability,7 good electrochemical properties,8 excellent optical properties,9 and so forth. These properties of nanocomposite mostly depend on the dispersion and aggregation of graphene into the aluminum matrix. Optimum dispersion of graphene nanoflakes enhances characteristics of aluminum due to various factors such as modifications of microstructures, enhancement of crystallization temperatures, stress transfer during load applications, and so forth.10−14 Investigation of dispersion and aggregation of graphene nanoflakes in aluminum matrix at various processing conditions is vital in the development of high-performance aluminum/graphene nanocomposite systems. In the literature, various experimental10−20 and theoretical investigations21−33 have been reported to describe various aspects for the development of high-performance aluminum graphene composite. Most of the experimental research works reveal that the dispersion of graphene and atomistic organization of aluminum atoms at graphene−aluminum interface are the main causes for enhancement of its properties. Li et al.10 investigated the mechanical properties of aluminum/graphene nanoflake composite synthesized by the cryomilling. They observed the enhancement © XXXX American Chemical Society

in the mechanical strength of nanocomposite compared to that of pure aluminum. Yolshina et al.12 developed a novel and unique method to prepare aluminum/graphene nanocomposite by the direct synthesis of graphene nanosheets within the aluminum matrix. They observed uniformly distributed graphene nanoflakes in the aluminum matrix, which results in the enhancement of mechanical properties. Despite a large number of experimental investigations, theoretical modeling including molecular dynamics simulation technique has also been used for the synthesis and prediction of properties of aluminum graphene nanocomposites, as reported in the literature.21−33 Molecular dynamics simulations are extensively used for the synthesis and characterization21−33 of various properties of aluminum graphene nanoflakes composite, such as phase transitions, evolution of the crystal structures, mechanical properties, stability of material at high temperature and pressure, buckling behavior of carbon nanotubes or graphene, etc. Rong et al.21 demonstrated the mechanism of strengthening of aluminum matrix nanocomposites reinforced with graphene nanoplatelets using large-scale molecular dynamics simulations. Silvestre et al.22 Received: April 3, 2019 Revised: June 30, 2019 Published: July 1, 2019 A

DOI: 10.1021/acs.jpcc.9b03101 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

generalized into the Hamiltonian form for the aluminum atoms, as given by eqs 4−8 ÄÅ ÉÑ ÄÅ ÉÑ1/2 Å ÑÑ ÅÅ ÑÑ ÑÑ ÅÅ Ñ 1 ÅÅÅÅ H = ÅÅ∑ ∑ pi ̂ pĵ V (rij)ÑÑÑ − d ∑ pi ̂ ÅÅÅ∑ pĵ ⌀(rij)ÑÑÑÑ Å Ñ Å ÑÑ 2 ÅÅ i ≠ j ÑÑÑ ÅÅÅ j ≠ i i (4) ÇÅ Ö Ç ÖÑÑ The site occupancy operators p̂i for the aluminum atoms are defined as follows

studied the mechanical properties of aluminum/single-wall carbon nanotube composite by molecular dynamics simulations. They found that the aluminum carbon nanotubes composites exhibit improved mechanical properties compared to pure aluminum. Choi et al.26 investigated the effect of single-wall carbon nanotube inclusion in the aluminum matrix on the mechanical properties using large-scale molecular dynamics simulation. They observed that the stress−strain response, Young’s modulus, and toughness increase significantly. In our previous investigations,29−33 we have studied organization of different metal atoms in the vicinity of graphene and singlewall carbon nanotube and its effect on the mechanical properties without consideration of the effect of aggregation or dispersion of graphene in metal matrix. The aggregation and dispersion of graphene in aluminum matrix have prime importance for the complete investigation of various properties of nanocomposite. To the best of my knowledge, the reactivitycontrolled aggregation and dispersion of graphene flakes in aluminum matrix using molecular dynamics simulations have not been reported in the literature. In the present investigation, we have studied the reactivitycontrolled aggregation of graphene nanoflakes in aluminum matrix during thermal processing by molecular dynamics simulation. The adaptive common neighbor analysis, radial distribution functions, variation in the energies, mean square displacement, solid volume, and surface area have been estimated to conduct an accurate characterization of aggregation of graphene nanoflakes in aluminum matrix. The choice of monoatomic metallic material such as aluminum allows the simulation that interacts mainly through van der Waals interaction potential with the graphene nanoflakes. Graphene nanoflakes have been chosen as a nanofiller because of their well-defined, regular hexagonal ring structure made of carbon atoms. The behavior of aluminum matrix on graphene nanoflakes is perhaps the simplest system that allows us to focus on the structural orientation of the atoms.

l o o1, if site i is occupied by a aluminium atom pi ̂ = m o o 0, otherwise n ÄÅ ÉÑn ÅaÑ V (r ) = εÅÅÅÅ ÑÑÑÑ ÅÇ r ÑÖ

ÅÄÅ a ÑÉÑm ⌀(r ) = εÅÅÅÅ ÑÑÑÑ ÅÇ r ÑÖ The constant parameter d is defined as

(7)

Various interactions involved in the carbon atom of the graphene nanoflakes have been implemented by the adaptive intermolecular reactive empirical bond order (AIREBO)38−40 potential during molecular dynamics simulations. The AIREBO potential includes reactive empirical bond order (EREBO) potential, nonbonded interactions as Morse potential (EMP), and an explicit four-body potential for various dihedral angle (ETORSION) terms as given below ÄÅ ÉÑ ÅÅÅ ÑÑ 1 TORSION Ñ ÑÑ E = ∑ ∑ ÅÅÅÅEijREBO + EijMP + ∑ ∑ Ekijl ÑÑ ÑÑ 2 i j ≠ i ÅÅÅ k≠i ,j l≠i ,j,k ÅÇ ÑÖÑ (9)

The EREBO term consists of both attractive and repulsive ij between the carbon atoms, as given below EijREBO = VijR (rij) + bijVijA(rij)

VRij

(10)

VAij

where and are the repulsive and attractive terms, respectively, and bij depicts the environment-dependent bond order term between atoms. As the REBO potential only accounts for interactions of carbon atoms within 2 Å of one another. The AIREBO potential also includes Morse potential (EMP) for distances 2 Å < r < cutoff. The AIREBO potential is best suited for fullerene, carbon nanotubes, and graphene during molecular dynamics simulations. AIREBO potential has been shown to precisely capture the bond−bond interaction between carbon atoms along with bond breaking and bond re-forming. The AIREBO potential has earlier been used successfully in studying the various properties of various carbon allotropes.41−49 The interatomic potential energy between aluminum and carbon atoms of graphene nanoflakes has been implemented through 12-6 Lennard-Jones potential as given in the following equation ÄÅ ÉÑ 12 ÅÅi σ σAl − G yz6ÑÑÑ y i Å Al − G j z j z − jj zz ÑÑÑ E LJ = 4εAl − GÅÅÅjj ÅÅk r z{ k r { ÑÑÑÖ (11) ÅÇ where εAl−G and σAl−G are the Lennard-Jones parameters for energy minimum or well depth and equilibrium interatomic distance at null potential energy for aluminum (Al) and carbon atom of graphene (G), respectively. The values of εAl−G and σAl−G are determined by the Lorentz−Berthelot (L−B) mixing

n

ij a yz ρi = ∑ jjjj zzzz jr z j ≠ i k ij {

(6)

(8)

d=ε×c

2. SIMULATION DETAILS Classical molecular dynamics simulation34−36 has been used to investigate the aggregation of graphene nanoflakes in aluminum matrix. Generalized Finnis and Sinclair37 form of embedded atom method (EAM) potential has been employed for the interatomic interactions for the aluminum atoms. The energy contribution from EAM potential for aluminum atoms, EAl−Al, is given by ÅÄÅ ÑÉÑ ÅÅ 1 ÑÑ Å EAl − Al = ∑ εÅÅÅ ∑ V (rij) − c ρi ÑÑÑÑ ÅÅ 2 ÑÑ i ÅÇÅ j ≠ i ÑÖÑ (1) ji a zy V (rij) = jjjj zzzz j rij z k {

(5)

(2) m

(3)

where ε and a denote the interaction energy and lattice constant, respectively; n, m, and c are the positive constants for the aluminum atoms; rij is the separation between ith and jth aluminum atoms; V(rij) is the pair potential between ith and jth aluminum atoms; and ρi is the local electron density associated with aluminum atom i. The above equations can be B


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Figure 1. Preparation of simulation system for the study of aggregation of graphene nanosheets in aluminum matrix: (a) 108 000 pure aluminum atoms in the liquid phase, (b) a nanocomposite system consisting of 92 480 aluminum atoms and 64 graphene sheets (7744 carbon atoms), (c) hexagonal 2D structure of graphene nanosheet (size: 15 Å × 25 Å), and (d) potential energy color coding of graphene nanosheet.

rule.34,79 According to the L−B mixing rule, the value of εAl−G can be obtained from the geometric average (εAl − G = εAl − Al × εG − G ) between εAl−Al and εG−G. However, the values σAl−G have been

(

obtained by the arithmetic average σAl − G =

σAl − Al + σG − G 2

2.1. Simulation System and Processing Steps. Two simulation systems have been considered: the first is pure aluminum and the second is aluminum graphene nanoflakes composite, as shown in Figure 1a−d. The first simulation system consists of 108 000 aluminum atoms in liquid phase (temperature T = 1500 K) as given in Figure 1a. The second simulation system depicts aluminum graphene nanoflakes composite, which consists of 92 480 aluminum atoms and 64 graphene sheets (7744 carbon atoms) as shown in Figure 1b. Figure 1c depicts the surface architecture of graphene nanoflakes prepared by the hexagonal arrangement of sp2-hybridized carbon atoms. Figure 1d shows the potential energy of each carbon atom of graphene nanoflake by color coding. From color coding, it has been demonstrated that the carbon atom at corner, edges, and middle of graphene nanoflake depicts high, moderate, and low potential energies, respectively. Thermal processing of aluminum graphene nanoflakes composite involves two steps. In the first step, molecular dynamics simulations were carried out at 1500 K for 20 ns to equilibrate the system. In the second step, the temperature of the aluminum graphene nanoflakes system decreases from 1500 to 300 K at a cooling rate of 0.1 K/ps, in which aluminum shows phase transition from liquid to solid. In contrast to the reported literature,62−66 comparatively lower cooling rate for the solidification of aluminum graphene nanoflakes composite system has been adopted in the present investigation, so as to efficiently capture the evolution of various nanocrystalline structures. In the reported literature,62−66 most of the molecular dynamics simulation studies used cooling rate ranging from 0.1 to 10 K/ps for the crystallization process of pure metals or metal matrix nanocomposite. 2.2. Radial Distribution Function g(χ). The probability of finding an aluminum or carbon atom of graphene at a distance χ from an average central atom has been calculated

) of

σAl−Al and σG−G. The values of 12-6 Lennard-Jones parameters50,51 for energy and interatomic separation of carbon atom of graphene and aluminum are εG−G = 0.00296 eV, σG−G = 3.407 Å and εAl−Al = 0.4157e, σAl−Al = 2.62 Å, respectively. The values of 12-6 Lennard-Jones parameter52 between aluminum and carbon of graphene can be found after geometric and arithmetic mean as εAl−G = 0.035 eV and σAl−G = 3.013 Å, respectively. However, for in-depth investigations, we have considered the values of εAl−G between 0.02, 0.03, 0.04, 0.06, 0.08, and 0.1 eV. The variations in the values of εAl−G will influence the adhesion behavior between aluminum and graphene nanoflakes. The interaction between graphene and aluminum atom may vary from 0.0309 to 0.185 eV depending on the lattice plane of aluminum and number of layers of both graphene and aluminum. The graphene−aluminum interaction is explained by LJ potential, and it can be fitted reasonably to the ab initio simulation results. Therefore, it is justified that 12-6 LJ potential is a reasonably good choice for molecular dynamics simulation of metal graphene composite system.80−82 Molecular dynamics simulations are carried out in an NPT ensemble in periodic boundary conditions. The Nosé−Hoover thermostat53−56 has been implemented to sustain the appropriate temperature and pressure of the simulation system. The position and velocity of atoms updated by the velocity Verlet57 algorithm with a time step (Δt) of 1 fs. Large Scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS),58 Open Visualization Tool (OVITO),59,60 and Visual Molecular Dynamics (VMD)61 software packages have been used for the molecular dynamics simulation, visualization, and analysis of output data. C


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Figure 2. Sequence of snapshots for the growth of the crystalline structure of aluminum during cooling from 1500 to 300 K. The green, brick red, and gray atoms represent fcc, hcp, and other structures, respectively. The red arrows illustrate the progress of the solidification process.

through the pair or radial distribution function g(χ)67 as defined by eq 12 g (χ ) =

V N2

N

∑ i=1

n(χ ) 4πχ 2 Δχ

(12)

where N and V are the total number of atoms and volume of the simulation system, respectively, and n(χ) is the number of atoms in a spherical shell of radius χ and thickness Δχ around the considered central atom. 2.3. Adaptive Common Neighbor Analysis. The adaptive common neighbor analysis (a-CNA)59,60 was used to distinguish the crystalline structure of aluminum graphene nanoflakes composite. The a-CNA has the capability to identify the atoms belonging to a variety of structure types such as hexagonal closed-packed (hcp), face-centered cubic (fcc), body-centered cubic (bcc), icosahedra (ico), and others using the position (x, y, and z coordinates) of each aluminum atom. In the a-CNA analysis, the crystal structure of aluminum atoms was recognized by the estimation of three integers (ncn, nb, and nlcb) for each central aluminum atom.64,68−70 Ncn is the number of aluminum atoms that are neighbors to both aluminum atoms in the pair, which is called common neighbors. Nb depicts the total number of bonds between ncn common neighboring aluminum atosm. Nlcb is the number of bonds in the longest continuous chain of the nb. For the perfect fcc structure of aluminum, all pairs depict the type (ncn, nb, and nlcb) = (4, 2, 1). Similarly, for the perfect hcp structure of aluminum, 50% integers have 422 type and other 50% integers have 421 type. Furthermore, bcc structures of aluminum are consisting of both 441 and 661 types. The above algorithm for the recognition of crystal structure is in-built in the Open Visualization Tool (OVITO) software. 2.4. Mean Square Displacement (MSD). The mean square displacement (MSD)34 of aluminum and graphene

Figure 3. Evolution of total energy, density, fcc, hcp, and others of aluminum during cooling from 1500 to 300 K. The arrows indicate the crystallization temperature (T = 570 K) of aluminum.

nanoflakes was calculated to quantify the atomic mobility during equilibration and cooling process. The MSD can be computed by eq 13 MSD = ⟨|r(t ) − r(0)|2 ⟩

(13)

where r(0) and r(t) are the position of aluminum or carbon atom of graphene at time t = 0 and t = t, respectively. The calculation of MSD has been performed by LAMMPS. D


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Figure 4. Snapshots for the aggregation of graphene nanoflakes at various times during equilibration process at fixed temperature (T = 1500 K) in the aluminum matrix. For clear visualization, aluminum atoms are not shown in the above snapshots, i.e., free space in the simulation box corresponds to aluminum matrix. The red arrow shows progress of equilibration process.

3. RESULTS AND DISCUSSION The results from the molecular dynamics simulations of pure aluminum and aluminum graphene nanoflakes composite have been discussed in the next three subsections. In the first subsection, evolution of various structures such as fcc, hcp, bcc, ico, and others in pure aluminum during cooling from 1500 to 300 K has been discussed. In the second subsection, aggregation of graphene nanoflakes in aluminum matrix has been discussed during equilibration and cooling process. Further, in the third subsection, we have investigated the effect of εAl−C over the aggregation of graphene nanoflakes and evolution of various crystallization structure of aluminum. 3.1. Solidification of Pure Aluminum. Figure 2 depicts the evolution of a nanocrystalline structure of pure aluminum during solidification as the temperature of system decreases from 1500 to 300 K with the rate of 0.1 K/ps. During solidification, pure aluminum depicts phase transitions from liquid to crystalline at temperature T ≈ 570 ± 10 K. Analogous solidification processes of pure aluminum are extensively carried out using molecular dynamics simulations, as reported in the literature.63,71−73 The percentages of atom with structures like fcc, bcc, hcp, ico, and other during solidifications are shown in

Figure 3. At high temperatures (T > 570 K), all of the aluminum atoms were randomly distributed, which is known as the amorphous phase. However, as temperature decreased (below 570 K), fcc and hcp structures of aluminum atoms evolved, and subsequently, the number of amorphous aluminum atoms decreased. It is observed that the hcp structure of aluminum atoms evolves during the early stage of crystal growth. The density of the pure aluminum increases during cooling from 1500 to 300 K; however, at 570 K, sudden increase in density depicts phase transition from liquid to crystalline. On the contrary, total energy of aluminum decreases during cooling process, and a sudden dip in energy at 570 K depicts phase transition. From the above analysis, it has been confirmed that the crystallization temperature of aluminum is T = 570 K. 3.2. Equilibration Process of Aluminum Graphene Nanoflakes Composite. Figure 4 shows the snapshots for the equilibration process of aluminum graphene nanoflakes composite at 1500 K. We have placed graphene nanoflakes in a regular manner in aluminum matrix. During equilibration, graphene nanoflakes mixed randomly with aluminum matrix. However, mixing of highly reactive graphene edges forms covalent bonds E


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observed in the snapshots. The phase transition of aluminum graphene nanoflakes is observed at temperature T ≈ 730 ± 10 K, which is significantly higher compared to the pure aluminum (T ≈ 570 ± 10 K), as we discussed in the previous sections. The phase transition temperature of metal matrix significantly increases in the presence of graphene nanoflakes because it facilitates crystal nucleation and growth. Similar observations about phase transition of metals in the vicinity of carbon nanotubes and graphene have been reported in our previous studies.30−32,66 Radial distribution function, g(χ), of aluminum atoms calculated during the cooling process as the temperature decreased from 1500 to 300 K, as shown in Figure 7. The g(χ) vs χ plot can distinguish amorphous and crystalline phases of aluminum matrix. In the amorphous phase, peaks of g(χ) evolved at χ ≈ 2.85 Å for the first nearest neighbor of aluminum atoms (e.g., first nearest neighbor of aluminum at a × √2/2 = 2.86 Å, where lattice constant a = 4.05 Å). However, at χ > 2.85 Å, distinct and identifiable peaks of g(χ) were not found at temperatures above 730 K. This indicated that the aluminum matrix depicts short-range ordered structures in the amorphous phase. For the fcc crystalline state, distinct and multiple peaks of g(χ) appeared at χ ≥ 2.85 Å for the first, second, and next nearest neighbors of the aluminum atoms with decreasing temperature (below 730 K), due to both shortand long-range ordered structures. The evolution of bcc, fcc, hcp, and other structures along with solid volume (V), surface

with the another neighboring graphene to minimize energy of the system. Due to the formation of covalent bonds between graphene nanoflakes, an interconnected network of graphene has been formed in aluminum matrix. A similar kind of covalent bond formation between reactive graphene edges has been extensively reported in the literature.43,73−78 Figure 5 shows

(

area (S), and dimensionless aspect ratio κ =

s3 V2

) of alumi-

num graphene nanoflakes composite as temperature decreases from 1500 to 300 K is shown in Figure 8. It is observed that crystalline structures like fcc, bcc, and hcp evolve at 730 K and correspondingly other atoms decrease. These variations in crystal structures confirm that the phase transition temperature of aluminum graphene composites is 730 K. Sudden decrease in solid volume corresponds to phase transition from amorphous liquid to crystalline solid. Dimensionless aspect

Figure 5. Variations in different energies like total energy (TE), interaction potential energy between aluminum and graphene (PEAl‑G), potential energy of aluminum (PEAl), potential energy of graphene (PEG), and mean square displacement (MSD) during equilibration process of aluminum graphene nanoflakes composite at 1500 K.

the variations in total energy (TE), interaction potential between aluminum and graphene (PEAl‑G), potential energy of aluminum (PEAl), potential energy of graphene (PEG), and mean square displacement of graphene (MSD) of aluminum graphene nanocomposite during equilibration process at 1500 K. During the early stage of equilibration process, total energy (TE) and potential energies (PEAl and PEG) of aluminum and graphene decrease due to the removal of unfavorable atomic positions of aluminum and graphene. On the contrary, interface potential energy between aluminum and graphene (PEAl‑G) increases due to the formation of new covalent bond (sp2−sp2) between neighboring graphene edges, which minimize interface sites. Mean square displacement (MSD) increases during early stage of equilibrations, and as further simulation precedes, it becomes stagnant due to the formation of interconnected aggregate of graphene. Various energies and MSD become stagnant nearly after 5 ns, which indicate that the simulation for 20 ns is much enough to reach the nanocomposite system in equilibrium. Figure 6 depicts a sequence of snapshots for the growth of crystalline structure of aluminum during cooling from 1500 to 300 K. At high temperature (T > 730 K), aluminum atoms are randomly distributed in the composite system and are known to be in the amorphous state. However, as temperature decreases below 730 K, aluminum depicts phase transition from amorphous to crystalline phase. Crystal nucleation of aluminum has been observed in the vicinity of graphene nanoflakes as

(

ratio κ =

S3 V2

) increases during phase transition and becomes

stagnant as temperature decreases further, which shows that phase transition happened only once and crystalline structure stabilize at temperature below 730 K. 3.3. Effect of εAl−G on Aggregation of Graphene Nanoflakes in Aluminum Matrix. The effect of interfacial interactions between graphene nanoflakes and aluminum, εAl−G, on the aggregation of graphene nanoflakes in aluminum matrix is shown in Figure 9a−e. It has been found that the value of εAl−G significantly influences the mode of aggregation of graphene nanoflakes in aluminum matrix. At εAl−G = 0.02 and 0.04 eV, graphene nanoflakes form aggregates with the interconnected edges, due to the formation of new covalent bonds between nearby reactive edges as shown in Figure 9a,b. However, as the values of εAl−G increase, parallel stacking of graphene nanoflakes is observed in aggregates with limited reaction (formation of new covalent bonds) between graphene edges, as shown in Figure 9c,d. Figure 10a shows the schematic of the organization of aluminum atoms near the graphene edges at the possible high and low values of εAl−G. At high values of εAl−G, the density of aluminum atoms near the graphene edges is expected to be higher compared to the lower values of εAl−G. Also, radial distribution function between aluminum and graphene, gAl‑G(χ), clearly depicts that the distribution of aluminum atom near the graphene increases with increase in F


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Figure 6. Sequence of snapshots for the growth of the crystalline structure of aluminum graphene nanocomposite during cooling from 1500 to 300 K. The green, brick red, and yellow atoms represent fcc, hcp, and graphene structures, respectively. The red arrows illustrate the progress of the cooling process. For clear visualization, aluminum with liquid phase is not shown in the above snapshots, i.e., free space in the simulation box corresponds to aluminum matrix.

Therefore, graphene aggregate consists of parallel stacks of graphene nanoflakes at higher εAl−G. Various components of potential energies of aluminum graphene nanoflakes composite during equilibration process at various values of εAl−G are shown in the Supporting Information as Figure S1a−d. During the early stage of the equilibration process, potential energy decreases in all cases except potential energy between aluminum and graphene at εAl−G = 0.02 eV due to the formation of the covalent bond between the graphene edges. Further, mean square displacements of graphene and density variations during equilibration process are shown in the Supporting Information as Figure S2a,b. Mean square displacement (MSD) of graphene increases during the early stage of the equilibration process. For εAl−G = 0.02 and 0.04 eV, MSD of graphene becomes stagnant after nearly 5 ns because it forms an interconnected network, which restricts thermal motion of graphene in aluminum matrix. On the contrary, the MSD of graphene continuously increases for εAl−G = 0.06, 0.08, and 0.1 eV because graphene forms stacking of parallel graphene aggregation and have sufficient thermal vibrations. Density of aluminum graphene nanocomposite systems depicts dependence on the values of εAl−G and is found to be higher for higher values of εAl−G, as shown in Figure S2b.

Figure 7. Radial distribution function, g(χ), of aluminum atoms in aluminum graphene composite during the cooling process as the temperature decreases from 1500 to 300 K. The first nearest neighbors of aluminum atoms are indicated by an arrow. Liquid and fcc crystalline phases are indicated by black/gray and green lines at their respective temperatures.

εAl−G, as shown in Figure 10b. It is expected that the higher density of aluminum atom near the graphene edge prevents the formation of new covalent bonds between the edges. G


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aluminum depicts phase transition from amorphous to crystalline phase. Crystal nucleation of aluminum has been observed in the vicinity of graphene nanoflakes. Figure S4 in the Supporting Information shows the variation in total energy of aluminum graphene nanocomposite at various values of εAl−G during cooling from 1500 to 300 K. Total energy of nanocomposite system decreases with temperature; however, total energy of the system steeply decreases during phase transitions. The actual temperature for the phase transition depends on the shape of graphene aggregates. Figure S5 in the Supporting Information shows the variations in pair potential energy between graphene and aluminum at various values of εAl−G during cooling from 1500 to 300 K. During phase transition, pair potential energy suddenly increases due to stretching of graphene. Figure 11 shows the change in solvent accessible surface area (ΔSASA) during equilibration process of graphene aluminum nanocomposite at various values of εAl−G. At a low value of εAl−G (i.e., εAl−G = 0.02 eV), ΔSASA decreases significantly due to formation of network of graphene nanoflake aggregate. On the contrary, for εAl−G = 0.1 eV, ΔSASA decreases slightly during the early stage due to parallel stacking of graphene nanoflakes. We have confirmed that at lower value of εAl−G, graphene nanoflakes aggregates have lower evolved surface area, which may impart an undesirable effect on the properties of metal matrix graphene nanocomposite. The dispersion and aggregation of graphene nanoflakes will influence the desired properties such as mechanical properties. In the literature,83,84 extensive investigations have been carried out to estimate the mechanical properties of metal graphene nanocomposite using molecular dynamics simulations. We believe that our result will enhance the understanding of researchers to design and synthesize metal matrix graphene nanocomposite.

Figure 8. Evolution of bcc, fcc, hcp, and other structures and solid volume (V), surface area (S), and dimensionless aspect ratio s3

(k = ) of aluminum graphene composite as temperature decreases V2

from 1500 to 300 K.

The sequence of snapshots for the growth of the crystalline structure of aluminum during cooling from 1500 to 300 K at εAl−G = 0.1 eV is shown in the Supporting Information as Figure S3. At high temperature (T > 735 K), aluminum atoms are randomly distributed in the composite system and are known to be in the amorphous state with the parallel stacking of graphene. However, as temperature decreases below 735 K,

Figure 9. Snapshots depicting the aggregation of graphene nanoflakes in aluminum matrix at various values of εAl‑G: (a) εAl‑G = 0.02 eV, (b) εAl‑G = 0.04 eV, (c) εAl‑G = 0.06 eV, (d) εAl‑G = 0.08 eV, and (e) εAl‑G = 0.1 eV. For clear visualization, aluminum matrix is not shown in the snapshots, i.e., free space in the simulation box corresponds to aluminum matrix. H


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graphene nanoflakes, which is capable of simulating sp2−sp2 (covalent) bond formation between reactive edge of graphene flakes in the aluminum matrix. The formation of new covalent bond between the neighboring edges of graphene facilitates interconnected network of graphene nanoflakes in aluminum matrix. The extent of reactivity of graphene edge exclusively depends on the interfacial interactions between carbon atom of graphene and aluminum. High interfacial interaction prevents the formation of new covalent bonds between the graphene edges. On the contrary, lower interfacial interaction facilitates the formation of covalent bond between the graphene edges, which leads to the formation of interconnected network of graphene nanoflakes. The results of this study may provide a comprehensive understanding of the interfacial properties of graphene aluminum nanoflakes composites, which help to improve the performance of nanocomposite materials.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03101.

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Figure 10. (a) Schematic of the organization aluminum near the graphene edges at high and low values of εAl‑G and (b) radial distribution function between aluminum and graphene atoms, gAl‑G.

Variations in potential energies mean square displacement and density of aluminum graphene nanoflakes composite at different temperature and interatomic interaction (εAl‑G) along with the snapshots during equilibration and cooling process (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]; [email protected] (S.K.). ORCID

Sunil Kumar: 0000-0003-2276-3087 Sudip K. Pattanayek: 0000-0001-9827-7232 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Chairman and members of i-PSG committee for providing the financial assistance under the project No. OLP-0320.

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REFERENCES

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Figure 11. Change in solvent accessible surface area (ΔSASA) of aggregate of graphene nanoflakes in aluminum matrix at various values of εAl−G.

4. CONCLUSIONS The aggregation of graphene nanoflakes in aluminum matrix is studied using molecular dynamics simulation. Simulation results explicitly explore the aggregation behavior of graphene nanoflakes at various processing conditions. It is found that the inclusion of graphene nanoflakes in aluminum matrix significantly increases the crystallization temperature from T = 570 K (pure aluminum) to T = 735 K (nanocomposite). The reactive AIREBO potential is used for various interactions in I


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