Molecular Computer Simulations of Graphene Oxide Intercalated with Methanol: Swelling Properties and Interlayer Structure

Molecular Computer Simulations of Graphene oxide intercalated with methanol: Swelling Properties and Interlayer Structure

Taleb Baker Jader ([email protected]), Physics Department, Umeå University

April, 2017

Table of contents Abstract 3 1. Introduction 4 1.1 Graphite oxide 5 1.2 Simulation method and codes 6 2. Simulation systems 6 3. Detailing of simulation process 8 3.1 Simulation concepts 13 3.1.1 Periodic boundary conditions (PBC) 13 3.1.2 Short-range interactions 14 3.1.3 Long-range interactions 14 3.1.4 Temperature and pressure 14 3.1.5 Constraints 14 3.1.6 Cutoffs 15 4. Results and Discussion 16 4.1 Swelling curves 16 4.2. Solvation 23 4.3 The enthalpy 25 4.4 Interlayers distribution 25 5. Conclusion 29 6. References 31

Abstract Molecular dynamics (MD) simulations has emerged as a very useful technique to study many types of properties for layered nanomaterials, such as graphene oxide (GO), which is of broad interest in different areas such as biotechnology, nanoscience, biomedicine and so forth. Moreover, its physical, chemical, and electronic properties have attracted significant attention from researchers to investigate its properties. The purpose of the present work was to probe the expansion of GO by intercalation of methanol between GO Nano-layers using molecular computer simulations. Atoms and molecule trajectories and their mutual interaction were modelled on the length and time scales of nanometres and nanoseconds, using the GROMACS MD code computing all electrostatic and van der Waals interactions. Analysis of the MD simulations versus methanol loading revealed that graphite oxide’s layers could be intercalated with methanol. Subsequently, it changes the distance between graphene oxides interlayers, which have different functional groups, such as epoxy, and hydroxyl by oxidation. These properties revealed the apparent swelling that corresponds to solvation of the GO monolayers, which helps to illustrate the energetic origin of crystalline swelling processes in graphene oxide. The results will be valuable for researchers by increasing their knowledge about graphite oxides interlayer’s properties. The results will also help researchers to unravel the range and location of graphite oxides applications in our life. They can also serve the readers with new information about graphene oxides properties.

1. Introduction To be mindful about a material such as graphene oxide (GO), which has remarkable relevance in various fields, requires studying it under specific conditions. Because GO has unique structural and dynamic properties. Which can be used to investigate unanticipated physical or chemical properties of atoms and molecules as the present project with the graphene oxide (GO) molecule (it has many crystalline properties e.g. the phenomenon of swelling due to strong oxidation) under periodical boundary conditions1.

This study concerns molecular dynamics (MD) simulation of graphite oxide (GO) and how its interlayers change by intercalation of methanol as a solvent. Why graphite oxide? It has many interesting chemical and physical properties which encourage detailed investigations. To mention some of that explored properties, there are similarities between GO and clay material about their swelling behaviour in water and hydrophilic solvents because they are hydrophilic materials. Just as with clays, the modulation of the GO structure can be changed by the physicochemical environments properties (such as pH, salinity, etc.)2.

Solvation plays an important role in the regulation of the structural properties e.gs. the interlayer distance of GO increases when immersed in water3,4. In pure water both GO and graphite oxide membrane are solvated similarly5. The first layered material, which was showing powerful swelling with water at high- pressure level, was graphene oxide. Subsequently, phenomenon of hydrophilic was demonstrated6,7. Graphene oxide (GO) has a tuneable conductivity and electronic band gap, which opens possibilities for a huge number of potential applications. GO is chemically stable with a high surface area up to 2630 (m2/g)8. This plays a huge role in the field of absorption applications, i.e. it affects the heat transfer’s process during the porous material9. The interlayer limitation of graphite oxide’s membrane for absorption depends on the type of liquid as a solvent, chemical nature of the solutes, and interaction of dissolved species into the graphite oxide structure. Limitation of GO for Nano-filtrations application for some solution (basic salts, and amines etc.) showed a broad variation of results10,11 .

Moreover, the motivation behind the study was to know more about GO. To know how its interlayers structure changes, how its crystalline properties change by swelling, considering the effect of intercalation of methanol into GO interlayer structure. The aim of the study was to investigate swelling of graphene oxide layers and compute the solvation, immersion, and potential energy. Molecular dynamics (MD) simulation was used for this purpose. After building of six different systems with different ratios of –OH and -epoxide of GO functional groups and preparing a suitable environment factors, such as constant temperature, pressure, with periodic boundary conditions (PBC). The results are that we could show by swelling the possibility of intercalation of

graphene oxides interlayers structure12 of methanol and recognizing the solvation, immersion, and potential energy by analysis of the MD simulations13,14.

Why is this topic important? Graphene oxide displays a great role in the field of filtration. One of the greatest challenges, which people have just now in the world, is clean water. The population increases year after year, accordingly they need clean water. Such a challenge requires development and optimization of industrial processes aimed at filtering and desalinating (removing salt from seawater) using the most promising filtration technology. Graphene oxide acting as Nano-sponges (NS) has been prepared and intensively studied for this purpose. They can absorb many times its own weight, and can have both hydrophilic and hydrophobic properties, which are extremely useful to separate liquids like oil from water, e.g. when we treat oil spills in the oceans15. Additionally, nowadays, the expanding of chemical products in agriculture, the industry’s applications or in general the modern life leads to many new dangerous contaminants into our environment. Moreover, not long ago the removing of these contaminants such as bacteria, viruses and other natural organic matter (NOM) were difficult with the traditional absorbents e.g. ozone or ultraviolet light. That is because they were very expensive and not active. Therefore, it was and hitherto necessary to search after a new generation of absorbent materials and their properties which extend the limits of that removing materials and absorbents. As we explained above GO has an enormous role in the field of absorption applications. Therefore, the aim of this study is to discover something new about its properties, such as the immersion and solvation energy. We hence think our results will be a value in the field of adsorption16. 1.1. Graphite oxide According to the production method, there are two types of graphene oxide Brodie (B-GO membranes) and Hummer (H-GO powders). However, the type selected graphene model for the present project was inspired by Brodie. Studies have shown the same results about their absorption of polar organic solvent under constant temperature. Studying such property by different solvents and under specific conditions e.g. constant volume and pressure allows intercalation of graphene oxide interlayers by different molecules. Accordingly, producing information about properties of both solute and solvent17.

One study showed that the change in interlayer distance of both types is similar in pure water. However with intercalation of some aqueous liquids, such as ethanol, the interlayer of graphene will change. Moreover, the interlayers distance for H-GO powders will increase whereas for B-GO membranes decrease. That is because the solvent will contract the lattice and the permeation will slow down. Other studies have reported that the synthesized graphite oxide (Brodie and Hummer) is different in solvation and exfoliation18.

Shije et al. (2012) reported that there is a significant expansion of H-GO in alcohol with increasing temperature. Nevertheless at low temperature the phase transitions differs more for B-GO than H-GO. The reason behind GO becoming one of the most intensive subject of debate between researchers is the possibility to synthesize it in different types with various degrees and number of functional groups19. The possibility of intercalation of graphene oxide by alcohol (ethanol, and methanol etc.) in different temperature opens other possibilities to intercalate it by larger solvents; also producing varies composition of graphene oxide20. 1.2. Simulation method and codes A number of methods and programs have been used for molecular or particle simulation techniques. Molecular dynamics (MD) has been used in a wide range of the applications in both science and engineering, because it can be used for relatively large simulations on the molecular scale (Nano-scale) starting from simple gases and liquids to complex materials. In classical MD simulations, the system is described by Newton’s equation of motion, with the atom being the basic particle. That is why magnetic and electronic properties cannot be determined by this method, because interatomic potential will be used21. Typical programs for MD simulations are LAMMPS, AMBER, DL-POLY, CHARMM, and GROMACS, where the latter was utilized in this work22,23.

Another method is the Finite Element Analysis (FEA). In this method, the system is divided into many small elements. FEA provides solutions for very complex problems that have relation with material properties such as permeation24. A third method is Monte Carlo (MC) simulations, which uses random atomic movements accepted by a probability determined by the ratio of a random number and the Boltzmann factor (the Boltzmann factor indicates how probable is the new configuration), to solve problems and to find new configurations25,26. 2. Simulation systems To investigate the crystalline swelling properties of graphene oxide (GO) with intercalation of methanol as a solvent, molecular dynamics (MD) simulations were used. The simulations systems consisted of constant number of particles (N) inside a periodically replicated rectangular simulation box. The initial simulation box size was approx. (3.40, 2.95, 12) nm in the x, y and z-axis directions, respectively, based on a graphene unit cell with 8 C atoms, and x and y dimensions of 0.4254 and 0.4912 nm. This GO layer and box size was required to disallow the methanol molecules not to ‘see’ itself, even at the lowest methanol loading.

The simulation boxes contained four GO layers based on 8x6x1 unit cells of graphene, having the atom types C (opls_141), C_OH (opls_159), Ce (opls_183), epoxide Oe (opls_180), hydroxyl Oh (opls_154) and H (opls_155), These four GO layers were initially intercalated with 360 methanol molecules each. The z- axis is taken perpendicular to the interlayers, and thus it decreases in length when removing the methanol. Hence, the initial systems consisted of 8x6 graphene of GO unit cells, with a basal spacing of 3 nm. Five different systems of GO and methanol molecules were used, differing in their epoxide O (Oe) to hydroxyl O (Oh) ratio. Each system consisted of 146 O atoms and 384 C atoms per each layer of graphene oxide. For reference one pure graphene system was also modelled.

A) B) C)

D) E) F)

Figure 1. Representative snapshots from the MD simulations showing representative graphene and GO layers. From A-D the layers are: A) Graphene, B) 146 OH, C) 100 OH +46EpO, D) 146EpO, E) 73OH + 73EpO, and F) 46OH +100EpO.

Specifically, the five GO systems consisted of 146OH (Oe/Oh = 0), 146Epo (Oe/Oh = 1), 100OH+46Epo (Oe/Oh = 0.31), 73OH+73Epo (Oe/Oh = 0.50), and 46OH+100Epo (Oe/Oh = 0.69), where Oe represent epoxide O and Oh the hydroxyl O. The pictures for the systems Graphene, 146 OH, 100 OH+46EpO,

146EpO, 73OH + 73EpO and 46OH +100EpO, with dimensions of (2.898nm x 3.346nm), is shown in figure 1 as well as an example for the full system of 46OH+100EpO in figure 2. The short-range van der Waals and the electrostatics interactions were handled by the Lennard-Jones potential and Coulombs law, resp., using a cut-off of 1 nm, whereas long-range electrostatic interactions were treated with particle mesh Ewald (PME) method27,28.

Figure 2. Initial configuration for the 46OH+100EpO system with 360 methanol in each interlayer. 3. Details of the simulation process All-atom optimized potentials for liquid simulations using the OPLS/aa force field was used29. Before the simulation the system has to be equilibrated by finding a minimum point of the systems potential energy. The equilibration was performed first by energy minimization using the steepest descent algorithm, secondly under NVT conditions in the canonical ensemble i.e. constant number of particles, volume and temperature30. Volume optimization was performed under NPT conditions in the isothermal-isobaric ensemble.

GROMACS (5.1.2) was used for all simulations. The energy minimizing by this method started with steepest descent (an extension of Laplace's method for approximating an integral) algorithm for flexible and constrained bonds. It

takes a step in the direction of the force without depending on the building of the previous step. It adjusts the step size in order for the search to become faster. Although it is not an efficient algorithm for searching, it is strong, simple, and powerful to carry out31,32.

The time evolution of the particles interactions inside the simulation cell was calculated by integrating Newton’s equations of motion over discrete time steps. The initial velocities were assigned to the Maxwell-Boltzmann distribution corresponding to a temperature of 298K. The output trajectories were saved every 5 ps and the pressure was coupled to a Berendsen barostat.

Periodic boundary condition were used in all directions. The time step for each production run was 2.0 fs, and the total simulation time for each system was 60 x 5 ns

In MD simulations all atoms interact with each other thus, the forces act on particles are the negative derivatives of a potential energy.

휕퐸 퐹푖 = − (1) 휕푟푖

In molecular dynamics simulations the forces of the N particles with coordinates 푟푖 are described by

푑2푟 푚 푖 = 퐹 i = 1, ...... ,n 푖 푑푡2 푖 (2)

Where 푚푖 is the mass of particle i, and Fi is the force acting

Part of the total potential energy and interaction forces stem from the bonded intramolecular interactions, not just between pair interactions, but also between three and four atoms. The bonded interaction between two covalently bonded atoms is called bond stretching, between three atoms is bond angle, and between four atoms is called dihedral angle. There is also an improper dihedral which is a special type of dihedral interaction (torsions) used to maintain remaining atoms in a plane.

Electrostatic (long-ranged potential) and van der Waals interaction (short- ranged interactions potential) as a non-bonded energy between pairs interaction33. Figure 3 explains the non-bonded interactions between particles during simulation’s process.

Figure 3. Types of interaction forces between particles during molecular dynamics simulation which includes, bonded (bond stretching, angle, dihedral angle, and improper) and non-bonded interactions (electrostatic, and van der Waals) from http://www.verachem.com/products/vm2/.

As we mentioned above, the molecule has the following configuration of energy consists of the sum of bonding (퐸푏) and non-bond (퐸푛푏).

퐸푡표푡 = 퐸푏 + 퐸푛푏 (3)

The bonding energy is

퐸 = 퐸푏표푛푑 + 퐸푎푛𝑔 + 퐸푑푖ℎ + 퐸푡표푟푡ℎ (4)

Where 퐸푏표푛푑 is the potential energy corresponding to covalent bonds, 퐸푎푛𝑔is the energy of the angular bonds, 퐸푑푖ℎ is the energy of the dihedral bond’s angles which involving more than three atoms, and 퐸푡표푟푡ℎ is the energy of the torsion, which keep groups in planar.

The harmonic potential energy of the system due to covalent bonds, which is a function of the particle separation, is described by the following equations34.

Bond potential (interactions between pairwise particles)

1 U (푟 ) = ∑1, 2 pairs 퐾 (푏 -b0)2 (5) 푖푗 2 0 푖푗

Where b0 is the average bond length and K0 the bond spring constant.

Angle potential (interactions between three particles)

1 2 푈(휃 ) = ∑ 퐾 (휃 − 휃 ) (6) 푖푗푘 푎푛𝑔푙푒푠 2 휃 푖푗푘 0

Where 퐾휃 is the force constant, 휃 is the average bond angle.

Dihedral potential (interactions between more than three particles)

For dihedral potential (interactions between mor than three particles), or for torsion as it is symmetric beween (o-휋). For alkanes (methane, ethane, propane, and higher members), the Ryckaert-Bellemans potential is often used. An equivalent torsional potential is the Fourier cosine seriesexpansion35.

1 푈 (∅) = ∑ 푉푛 ( 1 + 푐표푠(푛∅ − 훿 ) (7) 푡표푟푠푖표푛 푛 2 푛

Where, Ø is diheral angle, Vn the torsional rotation, 훿푛 is the face factor and n is multipilicity force constant or the number of function minima under rotation of 2휋.

The non-bonded interaction energy (퐸푛푏 ) is the sum of van der Waals and Coulomb potential energy. Due to the complex of calculation of pairwise potential during simulation, the non-bonded interactions are the most time consuming task, since each particle in non-bonded interactions has a large number of interacting neighbours.

퐸푛푏 = 퐸푣푑푊 + 퐸푐표푙 (8)

The short-range van der Waals interactions energy between each pair of atoms which located within a cutoff distance (in this study taken as 1.2nm), is expressed by the Lennard-Jones potential energy.

12 6 휎푖푗 휎푖푗 퐸 ( 푟푖푗) = ∑푖,푗 4휀푖푗 [( ) − ( ) ] for rij < 1.2nm (9) 푟푖푗 푟푖푗 where rij is the distance between the pair of atoms, εij is the potential energy minimum (the maximum interaction strength) whereas σij represents the interatomic distance at which the potential U is zero36. The term 1/r6 describes the attraction and the term 1/r12 describes the repulsion term37.

As for the short-range electrostatic contribution to Enb, it is expressed by Coulomb’s law:

1 푞푖 푞푗 E(rij ) = (10) 4휋휀푟휀0 푟푖푗

Where 푞푖 and 푞푗 corresponds charges, 휀0 is the permittivity of space and 휀푟 the dielectric constant of the medium (here == 1). For efficiency reasons, the long-

range coulombic interactions beyond the cutoff distance are treated by Particle Mesh Ewald (PME) method.

Matter strives to the lower its energy state. The balance between attraction and repulsion of the particles will take place when they reach the distance of equilibrium38 as it is explained by Lennard Jones potential in the figure 4.

Figure 4. The Lennard Jones potential between two particles as a function of the separation r, displaying the attractive and repulsive contributions to the potential energy. From: http://www.talkchannels.com/lennard-jones-potential-equation/

The leap-frog (Verlet) algorithm was used to calculate atomic trajectories by integration of Newton’s equation of motion39. Its disadvantage is that the position and velocity will be obtained at different time step. Gathering errors produces fluctuations on the molecular dynamics simulation.

Figure 5. The leap-frog algorithm process between the position and velocity as function of time. From: https://www.physics.drexel.edu/students/courses/Comp_Phys/Integrators/ leapfrog/

The leapfrog algorithm is the standard MD integrator in Gromacs molecular dynamics simulations. The positions, velocities and accelerations of particles were be known at the same time step. Thus, it is stable, works perfect for both short and long time steps and the time is changeful and precise. Figure 5 shows the positions and velocities, which leap-frog algorithm over each other.

Leap-frog integration is a particular differential equation for the two-coupled first order which can be written:

Xn+1 – X n / Δ t = Vn+1 /2 → Xn+1 = X n + Vn+1 /2 Δ t (11)

Where, Δ t → 0. Χ is sampled at time points t = 0… n Δt and V is sampled at t = Δ t /2, 3t Δt/ 2 ,………… n Δt/2. When the time changes the position jumps over, so on for all other orders40. 3.1 Simulation concepts 3.1.1. Periodic boundary conditions (PBC) As mentioned above periodic boundary conditions were used during the simulations. The idea behind periodic boundary conditions is to decrease the number of interactions and to avoid edge artefacts (since the interactions between the particles at the edge of the box would be different from the other places). Another idea for of periodic boundary conditions is that when a particle leaves the simulation cell on the right, it will re-enter it as an image of itself on the left41 as it seems in figure 6 .

Figure 6. Explanation of how particles move under PBC, particle that leaves the domain at the right of the box will re-enter the domain from the left (dashed). From: https://astronomy.swin.edu.au/sao/guest/knebe/

In such situation, translated copies of itself will be surround the box, as it appears in figure 7, i.e. there will be no actual limiting boundaries of the system. Thus, implementation of molecular dynamics simulation requires a suitable simulation box in order to decrease the number of interaction between

particles, to be a suitable for the study number of particles in the box and to keep only track of the original image as a representative of all other images42.

Figure 7. Illustration of the particle images inside the simulations box. From: http://www.ch.embnet.org/MD_tutorial/pages/MD.Part3.html

3.1.2. Short-range interactions For calculation of short-ranged interactions between neighbouring simulation cells, the minimum image convention (MIC) combined with particle boundary conditions (PBC) are used in MD simulations, in such a way that only one image of each particle is considered for each pair interaction calculation. The role of the cut-off is to avoid inefficiency as it decreases the number of pairwise potentials that needs to be calculated43,44.

3.1.3 Long-range interactions The long-range electrostatic interactions are calculated in the reciprocal space using both PBC and PME. Using a cut-off for this version is to decrease errors produced from a large number of interactions between particles 45.

3.1.4. Temperature and pressure In general there are very few instances under which the micro canonical NVE- ensemble, i.e. constant number of particles N, volume V, and energy E usually are studied by molecular dynamics. It is often more relevant to study and probe other types of ensembles such as the canonical NVT ensemble, which corresponds to constant number of particles N, volume V and temperature T, or the isobaric-isothermal ensemble, having constant number of particles N, pressure P and temperature T, GROMACS supports all common baro-stats and thermostats46,47.

3.1.5 Constraints By applying constraints on the bond lengths and angles of the atoms, creates possibilities for removing the fastest motion (degree of freedom) from the system, and use of longer time steps and subsequently more efficient simulations. Because the fastest degree of freedom is that of to the light atoms,

here hydrogen atoms, which in fact cannot be well described by a harmonic oscillation, it is constrained using the so-called LINCS algorithm48.

Since the hydrogen bonds are important for efficiency of the simulations, we will mention some facts about them. Hydrogen bonds is an intermolecular bond formed between two different electronegative atoms, such as N, O, and F, via an intermediate H atom. Different geometric criteria for hydrogen bonds exist. In GROMACS it’s considered that when the angle between the donor-hydrogen- acceptor is less than 30° and the donor-acceptor distance is less than 0.35nm, they share enough electron density to make a hydrogen bond. In hydroxyl groups, the oxygen becomes negative charged because it takes electron density since it has more charge density around it compared to hydrogen49. Figure 8 is illustrated what mentioned above.

Figure 8. Shows hydrogen bond between two different molecules bond. From: https://www.khanacademy.org/science/biology/water-acids-and-bases/hydrogen-bonding-in- water/a/hydrogen-bonding-in-water.

Constraints in GROMACS can include: positions, angles, distances, orientations and dihedrals. They are based on the fixed lists and are useful when increasing the time step for molecular dynamics simulation. The most obvious constraint among them is the position constraints, which are used to avoid severe rearrangement when the system equilibrates 50.

3.1.6. Cut-offs To perform the simulations, the non-bonded van der Waals and Columbic forces in every atom have to be calculated. Particles within a cut-off radius (푅푐) and neighbour list (푟푙) considered for the force calculation as illustrated in figure 9. During the simulations, the number of solvent molecules should be somewhat small to reduce the computational cost. Due to the minimum-image convention (MIC), each particle only interacts with the nearest (image-) particles of the remaining system. Because of this the non-bonded interactions must have a cut- 51,52 off radius (푅푐) that does not exceed half of the box’s length (푅푐 ≤ L/2) , since else some atom-atom interactions would be accounted twice.

Figure 9. Illustration showing the particles that have to be accounted for when performing (MD) simulation those particles inside both the cut-off radius (푟푐) and neighbour list (푟푙), which in principle can be identical. From: htt://silas.psfs.mit.edu./22.15/lectures/chap 10 .xml

4. Results and Discussion 4.1. Swelling curves The properties of graphene oxide were investigated in order to compute the swelling energetics and layers spacing. Simulations were performed with six different energy systems. The basal spacing and the solvation, immersion and potential energies were calculated. The basal spacing for the graphene, 146OH, 100OH 46EpO, 73OH 73EpO, 46OH 100EpO and 146EpO systems are plotted in Figure 10. The curves except graphene show its first plateau approximately at one methanol layers per GO unit cell which identical start of swelling. The simulation reproduce that plateaus with very small spacing during the process. 4

3.5 +0.8 nm +0.6 +0.4 3 +0.2 +0.0 2.5

1.5

Basal [nm]spacingBasal 1 Graphene 146 OH

100 OH 46 EpO 73 OH 73 EpO 0.5 46 OH 100 EpO 146 EpO 0

0 2 4 6 8 Num. of MET per GO unit cell

Figure 10. Swelling curves from simulation between the number of methanol contents per GO

layer and basal spacing (d001) for the systems Graphene, 146OH, 100OH+46EpO, 73OH+73EpO, 46OH+100EpO, and 146EpO. Note that all GO curves were shifted for clarity. Error bars are

omitted since the block-averaged standard deviations of the d001 values were less than 1pm.

The computed basal spacing are functions of the methanol layer contents. From figure 10, it can be seen that the swelling curves of the GO systems increase monotonically above approx. 3 and sometimes 2 methanol layers per GO unit cell whereas the graphene system display a non-linear expansion up to much higher methanol loadings.

The density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the basal spacing values for the six systems can be observed in the figures (11-16), where the blue colour corresponds to low density, and yellow high density of Methanol. The basal spacing decrease when moving from left to wright.

Figure 11. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the 146OH system

Figure 12. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the 100OH+46Epo system

Figure 13. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the 73OH+73Epo system

Figure 14. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the 46OH+100Epo system

Figure 15. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the 146Epo system

Figure 16. Shows density maps in two and three dimensions for Methanol in two interlayers between GO layers as a function of the d001 values for the graphene reference system

4.2. Solvation In general the solvation energy comes from intercalation of solute by solvent that causes to change the layers and interlayers properties. Moreover, Solvation considers the change of GO swelling energy and reflect the energy of adsorbed methanol. The solvation energy can be defined by the following equation.

ΔU= (U (N) – U (0)/N (12)

Where, N is the number of the interlayer methanol molecules, U(N) is the ensemble average of the potential energy and U(0) is the potential energy of the dry GO respectively53.

The calculated solvation energy of GO for the graphene, 146OH, 100OH+46EpO, 73OH+73EpO, 46OH+100EpO and 146EpO systems is displayed in figure 17.

20 Graphene 146 OH 15 100 OH 46 EpO 73 OH 73 EpO 10 46 OH 100 EpO 146 EpO 5 X1/10 0 0 2 4 6 8 -5 -10 -15

Solvation energy [KJ/mol] energy Solvation -20 -25 -30 -35 Num. of MET per GO unit cell

Figure 17. Solvation energy, from simulation as a function of the number of methanol content per GO layers for the six systems.

For the GO systems the common feature is that when the methanol content per GO unit cells increases, the negative (i.e. favourable) solvation energies approach the less negative average bulk of methanol energy. Among the different GO systems, increased ratios of hydroxyl groups generally lower solvation energy. From figure 17, the solvation energy of the graphene system shows that the graphene does not swell since its solvation energy is positive.

The determination of immersion energy will supply a complementary and efficient method for investigation of discrete swelling properties. The immersion

energy was found to be most useful uncover an apparently global minimum in the enthalpy swelling energy and is displayed in figure 18, which shows many clear minima as a meta-stable points implying that there is an energetic stabilization of the discrete layers. These immersion energies data provide computational verification of discrete swelling process in GO. Many simulation’s processes for swelling have done without effecting of the pressure i.e. the pressure was constant, as in present study. However, the evidence for swelling process is the oscillation pressure inside the simulation box. The oscillation uncovers behaviour of methanol through layers and interlayers equilibration and formation of solvation.

350 Graphene 146 OH 300 100 OH 46 EpO 73 OH 73 EpO 46 OH 100 EpO 146 EpO 250

200

150

Immersion energy [J/g] energy Immersion 100 +80 J/g +60 50 +40 +20 0 +0 0 2 4 6 8 Num. of MET per GO unit cell

퐅퐢퐠퐮퐫퐞 18. Immersion energy, from simulation as a function of methanol content per layer of GO, which shows the stable points that do not tend to solvate, that have minimum immersion energy.

From figure 18, with increasing methanol content, all the GO systems show a decrease in the immersion energy, except 146EpO. Since it does want to solvate initially. For graphene, the fully desolvated state is by far the most stable which means also it does not tend to solvate at all, although several meta-stable minima are found at higher methanol loadings. The states of methanol content layers for the systems graphene, 146OH, 100OH+46EpO, 73OH+73EpO, 46OH+100EpO, and 146EpO, of above 0, 3, 3 or 4, 4, 3 and 3 or 3.5, respectively correspond to the global immersion energy minimum.

The maximum immersion energies values, for the 146OH, 100OH 46EpO, 73OH 73EpO, 46OH 100EpO, and 146EpO systems, calculated from the most stable

solvation state minus the value of starting point, were -186.5, -202.6, -205.0, - 200.6, and -213.9 (J/g). This suggests that the system 146OH has minimum immersion energy. Note that for graphene, the immersion energy would be positive upon solvation.

4.3. The enthalpy The enthalpy of the system equals the internal potential energy U and the smaller product of pressure and volume. As mentioned the driving forces for solvation GO depend on the deferential enthalpy. A plot between methanol contents layer and the immersion energy (Q) in figure 18 obviously shows the enthalpy minima. Q can be define by the equation:

0 0 푄 = ⟨푈(푁)⟩ − ⟨푈(푁 )⟩ − (푁 − 푁 ) 푈푏푢푙푘 (13)

Where, 〈U(N°)〉 is the average energy of the GO at some standard solvation state N° (usually taken from the minimum, i.e. the most stable solvation state) and (U) bulk = -10.432 KJ/mole is the mean bulk Methanol-Methanol interaction potential energy, obtained from corresponding bulk simulations.

If the dry state is taken to be the reference state the immersion and solvation energy will be related by the equation.

푄푑 = 푁 [훥 푈 (푁) − 푈푏푢푙푘] (14)

Where, d is the dry reference state of GO during immersion and the primary difference between 푄푑 and ∆U is the factor N; the solvation energy is expressed per mole of methanol while the immersion energy is expressed by J/g GO.

4.4. Interlayer distribution The distribution of solution’s layers and interlayers indicates interaction between the solvent and GO. As shown in Figure 12, the distribution of interlayers for all the systems except 146EpO is single-peaked at two-layer solute and splits into two smaller peaks at the four-layer solute etc. The splitting of the peaks distribution relate to solvation of methanol in different GO configuration.

Figure 19 shows the calculated potential energy for the different systems. The data show that the potential energy is a function of the methanol content. The changes of the curves (small plateaus) show swelling property of GO, especially graphene system.

Graphene 146 OH 100 OH 46 EpO 73 OH 73 EpO 46 OH 100 EpO 146 EpO 5000 4500 4000 3500 3000 2500 2000 1500 1000

Potential energy [KJ/mol] energy Potential 500 0 0 2 4 6 8 Num. of MET per GO unit cell

Figure 19. Graphene oxide potential energy from simulation, as a function of the number of methanol content per GO layers.

The calculated relative changes of x and y dimension for the graphene, 146OH, 100OH 46EpO, 73OH 73EpO, 46OH 100EpO, and 146EpO systems are presented in figures 20-25. All the plotted curves for the six systems are between the number of methanol content per GO layers and the norm size. For the graphene system shown in figure 20, and due to the plateaus of the curves, the expansion or oscillation of the system before 3 methanol per unit cell, the relative changes in x dimension (red) are higher than the y dimension (blue).

1.001 Graphene rel_X_dim 1.000 Graphene rel_Y_dim 1.000 1.000 1.000

1.000 Norm. size Norm. 0.999 0.999 0.999 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 20. The norm. Size for the relative changes in x (red) and y dimension (blue), as a function of the number of methanol molecules per GO unit cell for the graphene system.

1.003 146 OH rel_X_dim 1.002 146 OH rel_Y_dim 1.001

1.000

Norm. size Norm. 0.999

0.998

0.997 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 21. The norm. Size for the relative changes in x (red) and y dimension (blue), as a function of the number of methanol molecules per GO unit cell for the 146OH system.

From figure 21, due to the plateaus and minimum points of the relative changes in x and y dimension, the system oscillates regularly, except the last part after about 5.5 number methanol content per GO layer, the relative changes in y dimension (blue) are higher than x dimension.

1.003 100 OH 46 EpO 1.002 rel_X_dim 100 OH 46 EpO 1.001 rel_Y_dim

1.000

Norm. size Norm. 0.999

0.998

0.997 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 22. The norm. Size for the relative changes in x (red) and y dimension (blue), as a function of the number of methanol molecules per GO unit cell for the 100OH+46EpO system.

For the 100OH+46EpO system shown in figure 22, by comparing the relative changes in x and y dimension. Due to the plateaus and minimum points, the changes in x dimension are almost higher than y dimension during the simulation process.

1.009 73 OH 73 EpO rel_X_dim 1.007 73 OH 73 EpO rel_Y_dim

1.005

1.003

Norm. size Norm. 1.001

0.999

0.997 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 23. The norm. Size for the relative changes in x (red) and y dimension (blue), from simulation with the number of methanol content per GO layers for the 73OH+73EpO system.

The relative changes in x and y dimension for the 73OH+73EpO system are shown in figure 23. It is seen that the changes in x dimension (red) are higher than y dimension during the time of simulations. After 3 methanol molecules per GO unit cell, and due to the plateaus, the relative changes in y dimension are a straight line, which means the changes are monotonically.

1.003 46 OH 100 EpO rel_X_dim 1.002 46 OH 100 EpO rel_Y_dim 1.001

1.000

Norm. size Norm. 0.999

0.998

0.997 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 24. The norm. Size for the relative changes in x (red) and y dimension (blue), from simulation with the number of methanol content per GO layers for the 46OH+100EpO system.

Figure 24 show that the relative changes in x and y dimensions for the 46OH+100EpO system starts at the same point, and the plotted data show obvious differences in the y dimension (blue) after the first methanol molecule per GO unit cell are higher until number 4.5 of methanol content, after that the changes occur regularly.

1.003 146 EpO rel_X_dim 1.002 146 EpO rel_Y_dim 1.001

1.000

Norm. size Norm. 0.999

0.998

0.997 0 1 2 3 4 5 6 7 8 Num. of MET per GO layer

Figure 25. The norm. Size for the relative changes in x (red) and y dimension (blue), from simulation with the number of methanol content per GO layers for the 146EpO system.

The relative changes (oscillations) in x and y dimensions for the 146EpO system is shown in figure 25, displaying changes in both dimensions. With note due to the plateaus and minimum pointe (oscillation), it seems that the changes in x dimension (red) are higher during simulation.

Thus, from the results of the simulated basal spacings, the relative changes in x and y dimensions, solvation energy and the immersion energy, the latter perhaps best illustrates the solvation behaviour, and potential energy for the six different systems were calculated. From figure 18, among the GO systems, the 146EpO has minimum immersion energy. I think the curves in figure 18 show the swelling property of graphene more obviously among the other systems. Due to the curves carbon system does not like to solvate.

I think we could get better results by increasing the number of investigated systems. Search for the better interlayer distance (d001) larger or smaller than the one taken in this project (2.8 nm). Search for the most suitable size of simulation’s box. In order to prevent or decrease number of interactions between particles inside solvent with copies of neighbouring boxes (unite cells). Moreover, a longer time step for integration will give better results. 5. Conclusion Simulation of six different systems of pure graphene as well as graphene oxide (GO) layers (based upon a 384 atom graphene layer) denoted 146EpO, 46OH+100EpO, 73OH+73EpO, 100OH+46EpO, and 146OH were performed, where the numbers denote the amount of hydroxyl groups or epoxide groups per 384 carbon atoms. The graphene and GO layers were initially intercalated with 7.5 methanol molecules per GO unit cell (defined with 8 C atoms), which gradually were removed or ‘evaporated’ through 60 sequential simulations

steps. The interpretation of the association of methanol with GO stems from the presence of hydroxyl and epoxide groups.

The technique of MD simulations offers atomistic depiction of the GO oxide hydroxyl and epoxide groups, with the possibility to simulate them separately. The MD simulations allowed the determination of interlayers swelling without competition of any other effects or changes in the graphene/GO layers themselves. The subsequent post-analysis indicated an energetic origin for discrete swelling in graphene and GO, providing a unique computational verification for swelling of GO crystallite.

The swelling behaviour of GO will open new possibilities for intercalation or functionalization of this material, using different types of molecules and synthesis of new GO framework materials. Swelling is also a useful step for manufacturing functionalized graphene that can potentially facilitate better mechanical, thermal and electronically properties. The expansion of the GO layers thus supplies an opportunity for applications such as molecular filters with tuneable size, which adjusts to specific conditions during absorption processes.

Since different types of GO were investigated, the sorption of solvent to the different GO layers was as expected not the same. Accordingly, these results also lead to new possibilities to separate GO structures by inserting some other solvents. Thus, we explored the absorption or swelling properties of GO intercalated with methanol for the first time. We hope these results will help others in their research and serve the readers with new information about applications in nanoscience.

Acknowledgements

First and foremost my sincerest acknowledgements goes to my supervisor, Assistant Professor Michael Holmboe, for giving me the opportunity to work with the project, who has always made time to answer all my questions. I am so grateful to him for his kind guidance. I give my warmest thanks to my family, for their consistent support especially my sons Dolovan, Bahdin and Matin, which this work is dedicated to.

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