Molecular dynamics simulations of the aggregation behaviour of overlapped graphene sheets in linear aliphatic hydrocarbons

Full Terms b college of Science, china university of Petroleum, Qingdao, Pr china; c Department of chemistry, Mississippi State university, Mississippi State, MS, uSa; d Department of aerospace engineering, Mississippi State university, Mississippi State, MS, uSa ABSTRACT Molecular dynamics simulations were used to investigate the aggregation of two partially overlapped graphene sheets in hexane, dodecane and eicosane. When partially overlapped graphene sheets are adjacent to one another, they will expel the adsorbed layers of the solvent molecules on the graphene surface, and the amount of overlap will increase. When the overlapped regions of the graphene sheets are separated by solvent molecules, they cannot expel the adsorption layers between them, and so the sheets remain separated. The driving force for aggregation is the van der Waals interaction between the two graphene sheets, while the van der Waals interaction between the graphene sheets and the solvent molecules inhibits graphene aggregation. The diffusion rate of the hydrocarbon molecules with shorter chain lengths is higher. Thus, they diffuse faster during graphene aggregation, which leads to a higher rate of graphene overlapping in the shorter hydrocarbons. This work provides useful insights into graphene aggregation in linear hydrocarbon solvents of varying lengths at the nanoscale. 1. Introduction Since graphene was first discovered 1, composite materials filled with graphene have been widely studied due to the sig- nificant enhancement in the mechanical, electrical and thermal properties 28. However, van der Waals (vdW) attractions between graphene sheets are strong, leading to the aggregation and accumulation of graphene sheets during the preparation of composites 9,10. This aggregation significantly limits the per- formance of graphene-based composites 11,12. Konios et al. 13 added graphene oxide (GO) and chemi- cally reduced GO (rGO) into 18 different solvents to investigate graphene dispersion. They showed that the solubility and stability of graphene greatly depended on the reduction process. The dis- persions of GO in N-methyl-2-pyrrolidone (NMP), ethylene gly- col and water were more stable (solubility was about 8.7 g/mL for NMP), while after reduction, better rGO solubility occurred in 1,2-dichlorbenzene (about 9 g/mL) and acetonitrile (about 8.1 g/mL) 13. Kim et al. 14 prepared graphene/ polyurethane composites using solvent blending, melt compounding and in situ polymerisation. The graphene dispersion in polymer matrix using solvent-based blending was better than that using melt compounding. After solvent blending, the composites provided better conductive and tensile properties and lower N 2 permea- bility. Li et al. 15 obtained water-soluble graphene sheets from graphite by controlled chemical conversion, and these graphene sheets could form stable aqueous colloids without polymeric or surfactant stabilizers. The work of Y ang et al. 16 showed that the aggregation of graphene platelets could be significantly weakened by carbon nanotubes. Synergetic effects between these platelets and the carbon nanotubes improved epoxy composite mechan- ical properties and thermal conductivities. Graphene dispersion in water and many other solvents using surfactants, polymers and other dispersants was reviewed by Texter 17. Although many experimental studies have investigated ways to reduce graphene aggregation in a host matrix, it is difficult to study the mechanisms of graphene aggregation at the atomistic level using experimental methods. Computational simulations have been applied to study graphene dispersion in a matrix. T ang et al. 18 performed molecular dynamics (MD) simulations to study GO aggregation in water. Aggregation was a point-line- plane process, and five forces were involved: van der W aals attrac- tion, electrostatic interactions, hydrogen-bond interactions, - stacking and collision of water molecules. The dominant forces were different in different aggregation stages. They also studied the effects on aggregation of the GOs oxygen-containing func- tional groups. Zhao et al. 19 simulated graphene dispersion in ionic liquids (IL s) based on a vdW interaction model, finding that much larger barriers to dispersion existed when graphene plates aggregate in ILs than in water due to formation of metastable 2018 informa uK limited, trading as taylor aggregation; linear aliphatic hydrocarbons; composites; molecular dynamics simulations ARTICLE HISTORY received 22 January 2018 a ccepted 12 april 2018 CONTACT Shenghui chen ; Songqing Hu 2 S. CHEN ET AL. 2.2. Dynamics simulations In this work, all the simulations were conducted using the Condensed-Phase Optimised Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field 26 built into the Materials Studio software package. 1 The Ewald method 27 was chosen for the calculations of Coulomb interactions, and the atom-based method was chosen for the calculations of vdW interactions. The cut-off radius was set to 12.5 . The same sim- ulation protocol was used for all six systems. First, the Smart Minimizer method was used to conduct a 10,000 iteration opti- misation of the initial models. Before simulating sheet aggre- gation, an annealing MD simulation was carried out with the two graphene sheets frozen to ensure that the solvent molecules were fully relaxed. All atoms in the simulation box were then allowed to move freely. In order to obtain the potential aggre- gation process of the two graphene sheets, a subsequent MD simulation was run for an additional 11 ns at room temperature (300 K). The model of the separated graphene sheets in hexane was run an additional 12 ns, for a total simulation time of 23 ns at 300 K, as explained below. The NVT ensemble was used for all the MD simulations. 2.3. Calculating interaction energies To analyze the interaction between graphene and solvent mole- cules, the interaction energy (IE) was calculated. where E total refers to the total energy of the whole model (graphene and solvent). E sheets refers to the energy of the graphene sheets without solvent molecules. E solvent refers to the energy of the solvent molecules without graphene sheets. All the atom (1) states. Metastable states in IL s originated purely from the micro- scopic collective vdW interactions between the graphene and IL s. Shiu et al. 20 studied the effect of graphene dispersions on graphene/epoxy nanocomposites based on different graphene sheet formats. Nanocomposites with higher graphene dispersion exhibited better mechanical and thermal properties. The work of Shih et al. 21 revealed that the strong interactions between graphene sheets and solvent molecules played an important role in graphene dispersion stabilisation. They also conducted MD simulations of two nearby graphene sheets to quantify the sus- pended graphene lifetime. Strong vdW attraction between the sheets induced sheet aggregation within 5 ns. However, the pro- cess by which graphene aggregation occurred was not analyzed in their work. Other investigations have also focused on the parallel graphene model 2224, while partially overlapping graphene sheets have received little attention. Partially overlapping sheets are important intermediate configurations in graphene aggrega- tion. First, in real composites, two graphene sheets are not likely to be completely coincident. Therefore, many partially overlap- ping graphene sheets must exist in the composites. Second, par- tially overlapped graphene structures will be formed during the aggregation process. Thus, studying overlapped graphene during aggregation helps to understand this assembly process in a host solvent. The MD simulations presented here were used to study how the aggregation of two graphene sheets occurs in three different solvents. Two initial partially overlapped graphene sheet arrange- ments (directly adjacent sheets and sheets separated by a solvent layer) in three different linear aliphatic hydrocarbon solvents, hexane (C 6 H 14 ), dodecane (C 12 H 26 ) and eicosane (C 20 H 42 ), were analyzed to study why and how the aggregation process proceeds. Nonpolar linear alkanes were selected because their structures would allow these solvents to align next to the graphene sheets and interact along their entire molecular length. 2. Calculation models and methods 2.1. Simulation model Two kinds of overlapped graphene sheet models were built: adjacent graphene sheets and separated graphene sheets (Figure 1) where the perpendicular distances between the sheets were 3.4 and 6.8 , respectively. In both initial models, the length of graphene overlapped region was 7.4 (chosen to be in the x direction). Linear aliphatic hydrocarbon solvents with three different carbon chain lengths (hexane, dodecane and eicosane) were added to the two kinds of simulation cells after building the graphene sheets, giving a total of six models. In the adjacent sheet models (Figure 1(a), no solvent molecules existed in the interlayer spacing in the initial sheet structures. Conversely, the graphene sheets were separated by some solvent molecules in the initial structures of the separated graphene models (Figure 1(b). The simulation cell size was 91.0 38.3 40.0 3 for all six models. In the initial models, the density of the host matrix was set at 0.9 gcm 3 . Periodic boundary conditions were applied in the x, y and z directions. Two models of overlapped graphene sheets in dodecane were simulated in our previous work 25. To facilitate comparison, these two models were studied again, and more details were analyzed. Figure 1. (colour online) View of the adjacent sheets model (a) and the separated sheets model (b).MOLECULAR SIMULA TION 3 positions in the models were fixed when the interaction energy was calculated. 3. Results and discussion 3.1. Equilibrated structures Figure 2 shows the final structures of all six systems with the overlapped graphene in hexane, dodecane and eicosane after 11 ns of MD simulation at 300 K. When the two graphene sheets were directly adjacent initially, the sheetsheet contact region increased in all three solvents (Figure 2(ac) during the MD simulations. In hexane and dodecane, which have lower viscos- ities than eicosane, the two sheets were completely overlapped after the 11 ns MD simulation. In eicosane, overlap was not com - plete after 11 ns of simulation; instead the system was still in an intermediate stage of advancing overlap. In sharp contrast, when the two graphene sheets were initially separated with solvent in between the layers, they remained separated after the 11 ns MD simulations (Figure 2(df). In each case, a single layer of solvent was present between the sheets, both initially and throughout the MD simulations. In dodecane and eicosane, the overlap region between the sheets remained almost constant throughout the simulation with little to no increase of the overlap. In contrast, the overlap of the sheets in hexane increased, even though the sheets were still separated by a solvent layer (Figure 2(d). T o see if the sheets would become completely overlapped in the hexane system, the MD simulation was extended to a total of 23 ns of sim - ulation time. The final structure (Figure 3 ) shows that the sheets were completely overlapped at the end of this longer simulation, even though the hexane monolayer still remained between them. Figures 2 and 3 also show structure forming within the sol- vent adjacent to the sheets. At least two clear layers of solvent molecules formed parallel to the graphene sheets next to the outer surfaces. This behaviour was consistent with that seen in other simulations of graphene with linear hydrocarbon solvents 25,28,29. Figure 2. Final structures of overlapped-graphene models after 11 ns of MD simulation at 300 K. a, b, c: adjacent graphene in hexane, dodecane and eicosane, respectively; d, e, f: separated graphene in hexane, dodecane and eicosane, respectively.4 S. CHEN ET AL. 3.3. Energy analyses The energy of the graphene sheets (Figure 5) and the interaction energy between the graphene and the solvent molecules (Figure 6) were analyzed as a function of time to examine the driving force for this aggregation. The graphs begin after the initial 1 ns of equilibration. The trends in the adjacent graphene system energies were similar to those for the length of the overlapped region in Section 3.2. The energy of the graphene sheets decreased with time in all three solvents. The decrease in energy was the fastest in hex- ane and was the slowest in eicosane. When the graphene sheets were initially separated by 6.8 and with solvent intercalated in the intersheet gap, the energy decreases during the simula- tions were very small. A linear fit of the energies of the sepa- rated graphene sheets in hexane during the overlapping gave a slope of 2.69 kcal mol 1 ns 1 , showing that the energy was decreasing very slowly, consistent with the rate of graphene sheet overlapping. Hence, the reduction of the graphene sheet energy appeared to drive the rate and degree of graphene stacking. In other words, the graphenegraphene attractive interactions between the sheets led to the graphene sheets stacking. What role did the solvent molecules play in the stacking process? When the graphene sheets were initially adjacent, the interaction energy progressively became less negative (Figure 6). Thus, the net interaction between solvent and graphene weakened 3.2. The process of graphene aggregation To analyze the aggregation pathways in different solvents, the length of the graphene sheet overlapped region as a function of simulation time was calculated (Figure 4). In the adjacent systems, the length of the overlapped region increased during the simulation in all three solvents; by the end of the simulation, the two sheets completely overlapped in hexane and dodecane. In hexane, complete overlap occurred after 2.5 ns. The rate of graphene sheet overlap in dodecane was slower. The two sheets finished overlapping in dodecane at about 78 ns. In eicosane, the two sheets did not finish overlapping during the 11 ns simulation. The graphene sheet overlap rate was lowest in eicosane. However, the overlapped length in eicosane continued to increase during all 11 ns of the simulation time, indicating continued sheet stack - ing. The two sheets would likely eventually completely overlap if the simulation were extended. The rate of overlapping clearly decreased with increasing solvent molecule length. When the graphene sheets were initially separated by 6.8 in hexane, with a layer of hexane between them, the length of the overlapped region increased to about 20 during the 11 ns simu - lation. The sheets completed their stacking after about 23 ns. This rate was about a factor of ten slower than when the aggregating sheets were initially adjacent (initial separation of 3.4 ) with no solvent between them. V ery little increase in overlap occurred in dodecane and eicosane when the sheets were initially separated by 6.8 and a solvent layer. Figure 3. Final structures of the overlapped-graphene sheets in hexane after a total of 23 ns of MD simulation at 300 K. Figure 4. (colour online) l ength of the overlapped area in the six models with the simulation time. Figure 5. (colour online) energy of the two graphene sheets in all six models as a function of the simulation time. Figure 6. (colour online) interaction energy between the graphene sheets and solvent molecules in all six models as a function of the simulation time.MOLECULAR SIMULA TION 5 sheets were adjacent to each other, the sheetsheet interaction was energetically more favourable than the interaction between an equivalent area of graphene and the solvent. The models of adjacent graphene sheets in dodecane and eicosane gave the same results. When the graphene sheets were separated by 6.8 in the ini- tial structures (Figure 7(b), an adsorption layer formed not only around the graphene sheets but also between them. At the com- pletion of the MD simulation, the adsorbed solvent layer between the sheets remained in the interlayer space. The strength of the van der W aals attraction between the graphene sheets decreases with the sixth power of the intersheet distance. Hence, when the sheets were separated by the adsorbed solvent, the interactions between the graphene sheets at the longer distance were too weak to displace the adsorption layer. Obviously, then, an adsorption layer was able to inhibit the aggregation of graphene sheets when the sheets were separated. 3.5. Effects of solvent molecule length The initial structures of the graphene sheets in the three different solvents were the same, while the final structures were differ- ent. T o explain the effects of solvent molecules, the mean square displacements (MSD) of the solvent molecules in the adjacent and separated graphene models were analyzed (Figures 8 and 9). The MSDs of the solvent molecules in both models showed, as expected, that the hexane diffusion rate was highest, followed by dodecane and then eicosane. Figures 8 and 9 illustrate that the order of the diffusion rates was consistent with the rates of graphene sheet overlapping when the graphene sheets are adja- cent: hexane dodecane eicosane. Hexane molecules had the highest diffusion rate; they were most easily displaced as the directly adjacent graphene sheets stacked. The diffusion rate of eicosane was slowest, leading to much longer sheet overlap times. The attraction between the graphene sheets was much weaker in the separated graphene models. The low viscosity of hexane permitted the solvent to rearrange and the graphene to stack during the 23 ns simulation. The larger viscosities of dodecane and eicosane did not allow significant sheet movement on the time