Molecular Dynamics Study of Nanoparticles/argon Atoms Size Effects on Atomic Aggregation Phenomena in Ideal Platinum Nanochannel Affected by the External Magnetic Field

11 In this paper, the computational method is used to describe the atomic behavior of Fe 3 O 4 12 nanoparticles size effect on these nanoparticles aggregation phenomena in ideal platinum 13 nanochannel and in the presence of outer magnetic major. In this work molecular dynamics (MD) 14 method used and argon atoms described as base fluid. Technically, for the interaction between 15 base fluid atoms, we used Lennard-jones (LJ) potential, while the nanochannel wall and 16 nanoparticle structures are simulated. To calculate the atomic behavior of simulated systems, we 17 report temperature, total energy, and distance of nanoparticles center of mass (COM) and time of 18 aggregation phenomena. Our MD simulation results show the Fe 3 O 4 nanoparticle size is an 19 important factor in aggregation phenomenon occur. Numerically, by enlarging the Fe 3 O 4 20 nanoparticle size, the aggregation time of Al 2 O 3 nanoparticles changes from 1.41 ns to 1.29 ns. 21 Further, the external magnetic field can be delayed this atomic phenomenon effectively. 22


Introduction
A nanostructure is a material of intermediate size between molecular and microscopic dimension.
Nanofluid is one of the promising structures in nanotechnology which used in various industrial applications [1][2][3][4].Technically, a nanofluid is a base fluid containing nanoparticles.These atomic structures are engineered atomic suspensions of nanostructures in a common base fluid [5][6].The nanostructures (nanoparticles) which used in nanofluids are made of metals, metal oxides, and etc.
Further, fluids such as water, oil and other liquid materials used as a base fluid in nanofluid structure [7].Nanofluids have a promising properties that make them appropriate in various aims such as heat conducting, nanoelectronics, fuel cells, pharmaceutical applications [8][9].These structures exhibit good thermal behavior and the optimized heat transfer process rather to the base fluids [10].Science of the atomic manner of nanofluids is found to be significant in planning for heat transfer applications [11][12].These atomic effect becomes more pronounced as concentration increases [13].These nanostructures are firstly used for their optimized thermal behavior as coolants in heat transfer applications such as heat exchangers, electronic cooling equipment and so heat transfer over plate has been described by various reports [14][15].Unlike the many excellent properties of nanofluids, some bad phenomenon can disrupt their benefits.One of the important disrupting phenomena is the aggregation of nanostructures in nanofluid mixtures.Previously, researchers reported the influence of nanostructures size on atomic behavior of common nanofluids.Nkurikiyimfura et al. [16] showed that nanoparticle aggregation phenomena disrupt the thermal behavior of nanofluids.Xuan et al. [17] reported the transmission electron micrograph picture of Cu/H2O nanofluid for the first time.They also done a simulation of nanoparticle aggregation phenomena in Cu/H2O nanofluid.They showed the irregular displacement of nanostructures was caused by Brownian motion.Murshed et al. [18] produce nanofluids with various atomic ratio of TiO2 nanoparticles and used the transmission electron micrograph to describe the morphology of nanostructures in base fluid.Song et al. [19] proposed a model which was based on modified population balance model of rheological law to describe the atomic properties of magnetic nanofluids.Based on their reports, they showed the atomic viscosity of nanofluids decreased with the aggregates size decreasing.Duan et al. [20] reported the viscosity value of Al2O3/H2O nanofluids.The gained outcomes express that the viscosity value was higher than that of nanofluids.In addition to experimental methods, theoretical approaches can be used to atomic study of various structures [21][22][23][24].Molecular Dynamics (MD) approach is widely implemented in the atomic and thermal behavior of nanostructures [25][26][27][28][29]. Technically, molecular systems consist of a vast number of atoms and it is impossible to describe the properties of such computationally huge structures, analytically.MD simulation solve this problem by using numerical methods.In this work we use of this computational approach to study of Fe3O4 spherical nanoparticles size effect on aggregation phenomena occur argon base fluid in presence of various magnetic field which arises from external source.The result of this innovative simulation can be used in heat transfer mechanism designing to increase their efficiency.

Computational method
In our MD study, atoms interact with each other in defined time steps (t = 1 fs) and these atomic procedure determines the physical properties of them.In our report, all MD simulations were done via LAMMPS (Large Scale Atomic Molecular Massively Simulator) MD box [30][31][32][33].This MD simulation package designing began in the 1995 in Sandia and LLNL laboratories.In this package various materials can be defined by atomic precession.So in this work, total atomic system simulated as Ar, Pt, Fe, and O atoms with all atoms method perfectly.To simulate atomic aggregation in Ar/Fe3O4 nanofluid, two Pt plate created as nanochannel in MD simulation box as shown in Fig. 1.Technically, this atomic structure depicted by Open Visualization Tool (OVITO) [34].Further, Initial simulated structures which shown in Fig. 1, designed via Packmol modeling package [35].Computationally, in our molecular dynamics simulations, periodic boundary condition was implemented in x and y directions and fix one used for z direction.NVT ensemble used in the molecular dynamics simulations to set the initial temperature of atomic systems.This computational ensemble (NVT) set to 300 K with 0.01 damping rate to reach equilibrium phase of structures.Time step in MD simulations is another important parameter which affected to simulation results.In this computational work, 1 fs rate set to each time step.Atomic potential is an important parameter in MD simulation approach.To simulate Ar base fluid and this structure interaction with Pt, Fe, and O atoms, we use Universal Force Field (UFF) [36].
In UFF, the atomic interactions were described by bonded and non-bonded forces.Non-bond force between various atoms defined by the Lennard-Jones (LJ) equation (see equation 1).This equation is a simple formula that describe the atomic force between various particles in MD simulation box.
Historically, John Lennard Jones defined this equation in 1924 as below [37,38]: In LJ equation ( 1), σ is the distance at which the potential is 0 and ε is the depth of the potential well, and rij is the distance between two simulated particles.These physical parameters selected with type of the atoms in MD simulation box.So, the σ and ε rates for various atoms in our simulated systems defined from table 1 [36].
Table 1.The length scale and energy parameters for LJ interaction in our molecular dynamics simulations [36].Atom Model (EAM) potential [38].The EAM potential energy of an atom, i, is expressed by [37,38]:

Element
After determining the appropriate force fields to simulated structures, MD study was fulfilled.
Then, to estimate the atoms evolution in MD simulation box, Newton's law's in atomic level is used as the gradient of simulation potential in below equations [39]: From ( 3) and ( 4) equations, the atomic momentum   can be defined as below [39]: Further, in common MD approach, Gaussian distribution is used for defining the temperature of structures that is described by equation ( 10) [39]: Finally, the instantaneous temperature variation is calculated from below equation [39]: (7) In this equation,   is the degree of freedom of the simulated atomic structures.Finally, according to the reported descriptions, MD simulations in this computational study carried out as fellow: Step 1: Ar/Fe3O4 nanofluid was simulated with UFF and EAM force field.For this purpose, atomic structures temperature is set at 300 K, initially.By set the initial physical properties in our MD simulation, atomic structures equilibrated for 1 ns.After, atomic structure reached to equilibrium phase, computational running was continued to 2 ns later.
Step 2: Next, magnetic field inserted to MD simulation package.The atomic structures equilibrated for 1 ns at 300 K with common nose-hoover thermostat [40][41].In our MD simulations the interaction between atoms done for 2 ns.Finally, to describe of Fe3O4 nanoparticle aggregation phenomena, physical parameters such as: time of aggregation phenomena and distance of nanoparticles were reported.

Equilibrium Phase of Simulated Structures
In the first step of this simulation, the atomic structure of ideal Pt nanochannel and fluid/nanofluid was described and accuracy of simulated atoms and used force fields studied.Our molecular dynamics simulations results displayed the initial coordination of atoms in fluid and nanochannel that recorded in later studies are adopted with UFF and EAM potentials.In our simulations, the atomic stability of fluid/nanochannel described by calculation of structures temperature and total energy at 300 K. Figures 2 and 3   In the next, the atomic structure of Ar/Fe3O4 nanofluid and Pt nanochannel was studied.Figure 4 shows the simulated nanofluid with difference size of Fe3O4 nanoparticles (r = 1 nm, 2 nm, and 3 nm).Our MD results showed the initial coordination of atoms in Ar/Fe3O4 nanofluid are adopted with UFF and EAM potentials.Figure 5 shows the total energy of nanofluids as a function of nanoparticles radius and MD simulation time.From this figure, we conclude the atomic mixture total energy converged after 1 ns.Further, the total energy magnitude increased by radius of nanoparticles enhancing from -785 eV to -999 eV.This atomic behavior shows that, by Fe3O4 nanoparticle adding to base fluid the stability of total structure increases and this atomic structure show better physical manner in various applications.

Time Evolution of Simulated Structures
After reaching to equilibration phase of Ar/Fe3O4 nanofluid and Pt ideal nanochannel, outer force with 0.002 eV/A implemented to simulated nanofluid and micro canonical ensemble used in our MD simulations for 2 ns.In MD simulations, a micro canonical ensemble is the statistical setting which used to represent the possible states of an atomic structure that has an exactly specified energy.The atomic system is assumed to be isolated in the sense and the atomic structure cannot exchange energy or atoms with its environment, so that the total energy of the simulated structure remains the same as simulation time goes on.For time evolution of simulated atomic structure, we calculate the center of mass (COM [38]) distance between Fe3O4 nanostructures, firstly.From Figure 6, we conclude the interatomic force between Fe3O4 nanofluid is attractive force.The distance of these nanoparticles varies from 50.00 Å to 11.01 Å at T=300 K. Further, this atomic parameter decreases by radius of nanoparticles increasing as reported in Table 2.This atomic manner of simulated nanofluids arises from increasing of total energy and attraction interaction between spherical nanostructures.In the next, the magnetic field from external source by equation ( 8) implemented to Ar/Fe3O4 nanofluid: In equation ( 8), q is atomic charge, v is atomic velocity, B is external magnetic magnitude, ω is external field frequency and t is the MD simulation time.By implementing of this magnetic force, the Fe3O4 nanoparticles aggregation phenomena affected.In Table 3 and 4 the distance of nanoparticles before aggregation phenomena (t = 1 ns) for various simulated structures with external magnetic field reported.By magnitude of this external field increasing, the aggregation phenomena of nanoparticles weakened.Further, with frequency increasing identical atomic manner can be seen and the atomic aggregation phenomenon weakened, too.These atomic behaviors of Ar/Fe3O4 nanofluid can be used for heat transfer optimization in industrial applications.Physically, by aggregation time increasing, we can say the attraction force between Fe3O4 nanoparticles decreases and so these atomic arrangements stay away from each other.The aggregation time of Fe3O4 nanoparticles in base fluid as a function of nanoparticles radius reported in Table 5.From figure 8 we can conclude the attraction interaction between simulated nanoparticles increases by radius of spherical Fe3O4 increasing.Numerically, by nanoparticles radius enhancing from 1 nm to 3 nm the aggregation time of these atomic structures decreases from 1.41 ns to 1.29 ns.The classic Navier-Stokes approach are usually used for the simulation of nanofluid flow and heat transfer; however the particle base methods like MD would show better performance at micro and nano scales levels [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].Based on present work achievements, we can say the nanoparticle radius variation is an important parameter for using of Ar/Fe3O4 atomic structure in various industrial applications.
, show the temperature and total energy of simulated base fluid as a function of molecular dynamics simulation time.From this figure we conclude the atomic structures temperature and total energy converged after 1 ns.

Figure 2 .
Figure 2. Temperature changes of Ar base fluid as a function of molecular dynamics simulation time.

Figure 3 .
Figure 3.Total energy changes of Ar base fluid as a function of molecular dynamics simulation time.

Figure 5 .
Figure 5.Total energy changes of Ar/Fe3O4 nanofluid as a function of nanoparticle radius and MD simulation time.

Figure 6 .
Figure 6.Time evolution of Ar/Fe3O4 nanofluid with MD simulation time in atomic aggregation procedure.

Figure 7 .
Figure 7. COM distance of Fe3O4 nanoparticles changes as a function of molecular dynamics simulation time.

Figure 8 .
Figure 8. Aggregation time of Fe3O4 nanoparticles as a function of nanoparticles radius in presence of external magnetic field (B=1 and ω=0.1).

Figures Figure 1
Figures

Figure 2 Temperature
Figure 2

Figure 3 Total
Figure 3

Figure 5 Total
Figure 5

Figure 6 Time
Figure 6

Figure 7 COM
Figure 7

Table 2 .
COM distance of Fe3O4 nanoparticles as a function of nanoparticle radius without external magnetic field after 1 ns.

Table 3 .
COM distance of Fe3O4 nanoparticles as a function of nanoparticle radius with external magnetic field (B=1 and ω=0.1) after 1 ns.

Table 4 .
COM distance of Fe3O4 nanoparticles as a function of external magnetic field magnitude and frequency after 1ns.After the first step of our MD simulations (equilibration process of Ar/Fe3O4 nanofluid and Pt nanochannel), the time of Fe3O4 aggregation phenomena calculated for report the radius of nanoparticles effect in atomic aggregation phenomena.The time of aggregation phenomena is appropriate for analysis of the spherical nanoparticles distribution around other nanoparticle.

Table 5 .
Aggregation time of Fe3O4 nanoparticles in Ar/Fe3O4 nanofluid as a function of nanoparticles radius.By enhancing the radius of Fe3O4 nanoparticle radius from 1 nm to 3 nm, the aggregation phenomena time decreases from 1.41 ns to 1.29 ns.Finally, we expected, these MD simulations results can be implemented in various industrial applications such as heat transfer mechanisms; so that thermal conductivity of Ar fluid was improved by adding nanoparticles.It implies the important roles of nanoparticles concentration and external magnetic field strength in designing the thermal systems. E.