## 2.1.1 Molecular dynamics simulation

The MD simulation is a powerful computational approach used to simulate the behavior of atoms and molecules in nanostructures [26]. This method is widely employed in the field of nanotechnology to understand the dynamic properties of materials at the atomic level. By utilizing MD simulations, researchers can gain valuable insights into the structural, mechanical, and thermal characteristics of nanostructures, which are crucial for the design and development of advanced nanomaterials and devices. Computationally, this method predicts the time evolution of the system using Newton’s laws and formalism as below [27],

$${F}_{i}=\sum _{i\ne j}{F}_{ij}=-grad {V}_{ij}= {m}_{i}\frac{{d}^{2}{r}_{i}}{{dt}^{2}}$$

1

here, the \(F\)parameter is the atomic net- force, \({m}_{i }\)is the mass of atoms, \({r}_{i}\)is the position of atoms, and \(v\)is the atom’s velocity. This formalism is evaluated via the velocity Verlet algorithm to integrate Newton's formalism [28–30],

$$r(t+\varDelta t)=r\left(t\right)+v\left(t\right)\varDelta t+\frac{1}{2}a\left(t\right){\varDelta t}^{2} \left(2\right)$$

$$v(t+\varDelta t)=v\left(t\right)+\frac{1}{2}\left[a\right(t)+a(t+\varDelta t\left)\right]\varDelta t \left(3\right)$$

In Equations (2) and (3), the \(\alpha \left(t\right)\)parameter is the atomic acceleration and \(\varDelta t\)is the atomic time step. In MD simulations, the interactions between atoms and molecules are modeled using force fields, which are mathematical expressions that describe the potential energy of the system as a function of atomic positions [31]. In our MD simulation the interactions between various particles are described with DREIDING and TERSOFF force fields [32, 33]. Our modeled samples in the initial step of MD simulations are depicted in Fig. 1, which was rendered with OVITO software [34]. Computationally, the DREIDING force field is used to describe the interaction between magnetic water and magnetic water-graphene interactions. In the DREIDING force field, \(4\epsilon [{\left(\frac{\sigma }{{r}_{ij}}\right)}^{12}-{\left(\frac{\sigma }{{r}_{ij}}\right)}^{6})]\) and \({k}_{r}(r-{r}_{0})\) equations are implemented to describe non- bonds and simple- bond interactions between various particles [35, 36]. Furthermore, the \({k}_{\theta }(\theta -{\theta }_{0})\) relationship is implemented to describe angle- bonds inside samples. The TERSOFF force field also describes the atomic interactions between carbon atoms inside a pristine graphite sample. In TERSOFF formalism, possible energy for atoms arrangement is represented by a superposition of the interactions distance component. Theoretically, the common description of the TERSOFF force field is [33],

$$E=\frac{1}{2}\sum _{i}\sum _{i\ne j}{V}_{ij}$$

4

$${V}_{ij}={f}_{c}\left({r}_{ij}\right)\left[{f}_{R}\right({r}_{ij})+{b}_{ij}{f}_{A}({r}_{ij}\left)\right]$$

5

This formula's summations are over all neighbors \(j\)and \(k\)of atom \(i\)within a cutoff distance. In Eq. (5), \({f}_{R }\)is computationally a two-body term (repulsive), \({f}_{A }\)includes three-body (attraction) interactions, and \({f}_{c}\)is a smooth cutoff function that decreases from 1 to 0 values. The constant values for the TERSOFF force field in our MD simulations are reported in Table 1.

Table 1

The TERSOFF potential parameters for graphite sample simulation in current MD research [33].

Interaction Type | R (Å) | D (Å) | A (eV) | B (eV) | λ1 (1/ Å) | λ2 (1/ Å) |

C-C-C | 1.95 | 0.15 | 1393.6 | 346.7 | 3.4879 | 2.2119 |

In the current research, we describe a computational approach to introduce the atomic interaction between magnetic water and a pristine graphite matrix to design an effective method for graphene nanosheet synthesis. For this purpose, our MD simulations are done in two main phases. Firstly, the modeled sample (see Fig. 1) is equilibrated at 300 K for 1 ns. In this step the kinetic and potential energy changes of the system as a function of simulation time are calculated using the NVT ensemble and the Nose-Hoover thermostat with a 0.01 fs value for the time step [37, 38]. After equilibrium phase detection, the NVT ensemble is converted to NVE one and the atomic interaction between various particles is estimated to detect the graphene nanosheets created inside the computational box. In this step, H2O molecules are accelerated to collide with the target graphite sample. Our MD simulation settings in the current work are listed in Table 2.

Table 2

MD simulation settings in current computational research.

Simulation Parameter | Setting |

MD Box Length | 103×103×103 Å3 |

Number of Atoms | 19038 |

Boundary Condition | Periodic Boundary Condition [41] |

Initial Temperature | 300 K |

Time Step | 0.01 fs |

Computational Algorithm | NVT/NVE |

Damping Ratio of Temperature | 1 fs |

Equilibrium Time | 1 ns |

Total Simulation Time | 11 ns |