The Study of Simulating Metaloxide Nanoparticles in Aqueous Fluid.

The Study of Simulating Metaloxide Nanoparticles in Aqueous Fluid.

Adil Loya

School of Engineering and Technology

University of Hertfordshire Hatfield, UK

Jacqueline L. Stair School of Pharmacy University of Hertfordshire Hatfield, UK

Guogang Ren

School of Engineering and Technology

University of Hertfordshire Hatfield, UK

Abstract Dynamics of nanoparticle dispersion in engineering fluids has a significant impact on the quality and performance of liquid based fluidic systems; such as in biomedical fluids, contaminated water system and its purifications. The dispersion dynamics of metaloxidenanoparticles in an aqueous fluidic system,wasstudiedusing large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) in this paper by using CuO particles as a targeting material in water (H2O)fluid system. Two major calculation parameters were selected for evaluating the system in the simulation: a) discrete particle dynamics (DPD), and b) smoothed particle hydrodynamics (SPH). Comparing experimental with the molecular dynamics (MD) simulation results showsgood correlationswith the MD viscosityas 1.44mPas at 313K and diffusion coefficient ofmetaloxidenanoparticle-H2O system was obtained as 1.03 x 10-8m2/s.

Keywords –Nanoparticle dispersion in fluids Molecular dynamics Diffusion simulations Copper oxide LAMMPS

I. INTRODUCTION

Nanoparticles provides large surface area to their volume ratio, which may reduce or enhance theirdiffusioncapabilities in a fluidic system, and specifically controlling of this diffusion proved to be a challenging task[1, 2]. Several studies have focused on nano particle dispersion and stabilization in a base fluid such as water, to establish an effective methodology for a thorough dispersion of nano particles influidic systems [3- 5]. The metal oxide nano particles(M Ox) are the widely used in biomedical devices, environmental and water contamination research due to their environmental stability, functionality[6], thermo-mechanical[7-9] and physio-chemicalproperties[10, 11]. These types of nanoparticles including CuO, ZnO, MgO,CaO, and many others, are increasingly used in applications such asbiomedical fluidic and water purification[12-14], asantibacterialadditivesand components andmostly the medical devices surface coating [6, 12, 15, 16]. Especially, in the water purification processes and biomedical applications, it is involving the releases of Cu2+, Zn2+and ironic particles that may result in disinfection of contaminations frombacteria pathogens[12-14].As the metal oxidessuch as CuO nanoparticles (CuO-NPs) are common atomic structures andthermally and physically stable and cost-effective,

therefore, this study concentratedoninvestigating the CuOnanoparticles dispersibility in water fluid system using molecular dynamics whichis not yet reported[3, 4].

Simulations as a major prediction of the mechanism of nanoparticles dispersion in engineering liquids, is a fast and cost-effective alternative parallel to the experimental works. A number of diffusion simulations of polymeric, ionic and mineral nanoparticles have been extensivelyreported[17-19]. Themajorparticle diffusion phenomena in these studies havebeencarried out is based on the Brownian dynamics (BD),targetingthe random motion of the nanoparticlein a water fluidic system. One of the most acceptedsimulationparametersforthe dispersion of metal oxide nanoparticlesina water system isthe discrete particle dynamic (DPD) potential, which is used for assessingthe power to disperse nanoclustersreflecting the phenomena of the Brownian dynamics [20, 21].Studiesusing DPD for complex fluidic systems [22-24] shown that the dispersion of nanoparticlesin water exhibits complex properties in simulation.

An initial selection of boundary conditions iscarriedoutwith a molecular dynamic simulator[25], working on cluster particle sizes, their force field interactions, diffusion in solvent, and physiochemical properties [26, 27]. Within the simulation system, force field is a mathematical parameter that governs the energies and potentials between interactive atomscontrolled by the pair potentials between atoms. The physiochemical settings of the system referred to the thermal, chemical and physical properties of the system such as initial temperature settings, charges and dynamics of the system.

1. Materials

   The CuO nanoparticleswere prepared by thermal plasma forming technology (TesmiaTM) by QinetiQ Nanomaterial Ltd (Farnborough, UK). The bulk density of CuO-NPs is 6.3-6.49 g/cm3. The measurement of theCuO-NPaverage crystal size mixture is 22.6 nm.

   The simulated CuO-NP configuration of crystal lattice was is 90°, is 99.54° and is 90° with a space group of C2/c that was generatred on a Material Studio software by Accelry Ltd.

2. Methodology

Experimental viscosity was measured in this work by using TA 1500Ex. The TA Instruments AR1500ex Rheometeris an advanced analyzer for measuring properties of rheology such as viscosity, shear rate, stress and strain.Theexperimental viscosityof CuO-water nanofluid system was measured to compareandsupport the MD results. The mixture of nanoparticlesin the experiments were measured and calculatedwitha volumetricfractionof ~2% vol.

1. Simulation conditions:nanoparticles dispersed in water fluids

   Metal oxidenanoparticlesin water fluidic media were simulated by using COMPASS force field oncondensed-phase optimized molecular Potential [26-29]. The COMPASS force field was used for computational energy calculations.This force field has been implemented for different molecular interactions from organics, inorganics, monomers, and polymers, to metals, metallic ions and metal oxides[26-29].Green-Kubo formulization was also used shown in Equation 5to extrapolate the system viscosity, which is a well-established method of computing the viscositybyautocorrelation functions equation 6. Later the results of the viscosity achieved through simulation are validated using stress autocorrelation function as shown in Fig.3.

   The Interactive parameters for the fluidic system used in thissimulationare DPD and SPH potential for composing the diffusion model of the CuO-NP-water fluidic system. The DPD factor is explained byEquation 1, whichcomposes of 3 force components, accounting for the particle random movement and momentum through the system.

   C D R

   f (F F F )rij

   (1)

   These three forces (i.e, Fc, Fd and FR) are comprised in DPD pair-style to execute the DPD actionsto perform the desired motion. The influence of the forces in particular directions is handled by ij .

2. Simulation

   The dispersingnanoparticles in water was simulated byusingLAMMPS [30-32]composed of 80000transferable intermolecular potential (TIP3P)water molecules[33].The nanoparticles used in this study are in 80000 TIP3P water molecular system.The system wassimulated with SPH and DPD potential in an imaginary orthogonal box (i.e., 100 Angstrom x 100 Angstrom x 100 Angstrom) shown in Fig.1.The initial simulation system was setup by using3320 CuO molecules, which were represented by 2 nanoclusters each carrying 1660 molecules bonded by compass force field. Therefore, the simulated particles in this work are in the nanometre scale between 4-6 nm. This is due to the limitations of current lab-based computers, which are impractical for simulating particles largerthan 10nm with particle volume fractionbetween1.5-2% equivalent to the volume fractionused in the experiments. Simulation trajectories were visualized using OVITO the code free availabe by Alexander Stukowski[34].

   Fig.1 Molecular system comparison with and without CuO- NPs: a) simulation results (control) of pure water molecules in an Orthogonal box of 100 Angstrom x 100 Angstrom x 100 Angstrom,the box contained 80000 TIP3P water molecules, where white is oxygen and blue is hydrogen. b). Molecular system of 80000 TIP3P water molecules with 2 CuO-NPs of 4nm in an Orthogonal box of 100 Angstrom x 100 Angstrom x 100 Angstrom, where white is oxygen, blue is hydrogen and red is representing CuO-NP, under NPT (NPT ensemble enables the system to keep the pressure constant but the volume is varied) conditions i.e. 1 bar pressure at the temperature of 303K.

   5 Results and Discussion

   The simulations were carried out by resembling the nanoparticle simulation in the water fluidic system. Although the particulate did not reach the actual nanoscalesizein the simulation, the results still proved valuable as it showed temperature effects on the systems viscosity and particle diffusion efficiency, which ismostly effected by the particle volume fraction[35].The diffusion coefficient is a measure of the number of atoms movement with the change in position; it is dependent on the viscosity, size and shape of molecules.However, viscosity isa measure ofresistance to the fluid flow and depends on the gradual deformation of shear stress. The equations used for calculating these variables, shown in Table1are the bases for analyzing and comparing the results with the experimental trends.The properties analysed using the MD simulation were dependent on the statistical mechanical calculation implemented by Green-Kubo. However, images shows a constant volume, whereas, during

   the simulation due to implementation of NPT ensemble caused the volume of simulation box to vary. The variable definition and further statistical formula has been presented in Table

   1.Where n is the number of atoms, T is the temperature, t is timeperiod, vi is velocity of particle iandp is the shear stress in Table 1.

   Table 1 Diffusion coefficient and viscosity variables, definitions and the statistical mechanical formula, and their equations.

   Property Variable Definition Statistical Mechanical formula

   (Green-Kubo)

   2

   1

   D d r (t) r (0) / dt

   n D (2)

   D

   Diffusion Coefficient

   x

   6

   i

   i

   (4)

   (5)

   (0) dt

   P (t)P

   3k T

   V

   (3)

   F U

   Viscosity

   x

   B 0 x y

   xy xy

   Where n is the diffusion flux, D is the diffusion coefficient and

   x is the concentration at a particular position as shown in equation 1;(mPas) is viscosity for the system V is the

   U Brownian volume fraction (Ã…3) of particles in the system, x Velocity in x direction, F is the magnitude of force in equation

   3; ri (t) radius of particle i at time t and ri (0) radius of particle i at starting time in equation 4; T is the temperature

   (K) of the system and Pxy is the stress component for atoms (atm), t is time (ps), KBBoltzmann constant in equation 5.

   Viscosity

   The simulated viscosity of CuO-NPdispersed in water is coherent to the experimental values. The Green Kubo method utilizes stress tensor to analyse the viscosity.This stress tensor Pxy is the stress component between molecules of the x-y direction.

   The viscosity from the TIP3P water model is decreasing with increasing temperature as shown in Figure 2. These simulation values are in good correlations withH.L. Tepper and Gonzalez results[36, 37], which were shown at temperatures around 298-300K giving the viscosity of TIP3P model as 0.321-0.311 mPas,whereas the experimental value obtained in this work was around 0.59 mPas.These values can furtherbe compared with Min-yiShen and Karl F. Freeds[38]achieved similar viscosity around 0.5 mPas at 300K using simulation technique of Langevin dynamics. The viscosity values obtainedin this workwereslightly higher due

   to the higher heat conduction through the system and dissipative particle dynamics potential.

   A decrease was seen for the viscosity of the TIP3P water model with the increasing temperature of the system.This is a usual phenomenon for any liquid when temperature is increased while molecules started to expand which leads to anomalous decrease in viscosity shown in Figure 2.

   High concurrenttrendofexperimental viscosity results [29] of dispersing CuO-NPs in deionized water were compared,withthealgorithm-neural network (GANN)method[39], which are shown in Fig.2to the trend ofmolecular dynamic simulation results.Some studies relate that particle size shows negligible effect over the viscosity [40]while others suggest that a decrease in particle size gives a viscosity increase[41-44] and vice versa for other researchers[35, 45, 46].The results of the system are averaged over the N number of particles in the system.

   Fig.2Viscosity (mPa.s) comparison of the fluidic systems of experimental, MD simulation of CuO-water system, pure water, and the algrothim results[39] and experimental [35].

   This size dependent system causes an increase in the number ofruns and equilibration time. Later improvement of the statistical precision is achieved by three off diagonal element of the stress tensor.

   Stress Autocorrleation function (SACF)

   The molecular dynamic viscosity was measured using the Green-Kubo method. This method uses an autocorrelation function to validate the results of viscosity. The viscosity validation is carried out using the stress autocorrelation function. This function uses three off-diagonal terms to analyse the system viscosity. These terms are Pxy, Pyz and Pxz related to pressure fluctuations in different directions. The stress tensors in between the angular brackets as shown in equation 6 computes averages of large number of samples.Where term Pxycomputes the stress in x-y direction. The sample quantities consist of duration the MD simulation will run for, t, and N number of particles in the system.

   The diffusion rate was calculated by the slope measurement oftrend linesandusing one-sixth of the slope which gives the self-diffusion coefficient. The calculated MSDisshown in Fig.4,by using the slope of theselines, the diffusion coefficient of CuO-NPsinwater suspension at different temperatures of 303K, 313K and 323K was found.Table 2 lists particular diffusion coefficients of CuO-NP water suspension and pure water system. Later,Fig.4 showsthe CuO-NP water suspension MSD at different temperatures.The diffusion coefficient reults obtained for this suspension model is similar with the result of CuO nano-rods diffusion coefficient in water by Cheong F.C et al.[47], they measured diffusion coefficient of CuO nano- rods with holographic video microscopy and obtained the value of 2.31E-7m2s-1 at 298K. However, there is a slight

   Cxy (t) Pxy (t)Pxy (0)

   x y

   (6)

   difference, this can be due to temperature and heat conduction through the system that causes the Brownian effect to change and concsequently altering the diffusion.

   In Figure 4there is a linear increase in the diffusion coefficient (m2/s) of the water with temperature increase and this has been correlated by other studies of TIP3P water molecules [48]. This study investigated TIP3P water molecular diffusion coefficient at 320 K is 2.272E10-9 m2/s, which is in a good agreement with achieved value in this work as shown in table 2,together withother experimental value obtained from previous literature [49]. It is also known that by implementation of DPD helped in decreasing the computing time step for equilibrium convergence and higher accuracy [50].

   Fig.3 Stress autocorrelation function graphs for validation of achieved viscosity of CuO-NPs in water from MD simulation at 303k.

   Further, the monotonic decay of the SACF relates to the successful achievement of rheologial quantity i.e. viscosity in our case. The SACF took 0.07 fs to completely settle for 303k viscosity reading, whereas, for other two temperature readings of 313k and 323k took 0.07-0.09 fs.

3. Mean Square Displacement (MSD)

Diffusion coefficient was measured for analyzing the diffusion rate of the CuO in water using Equation4, where D is diffusion coefficient (m/s2), r is the distance between consecutive particles and t is time (s).

Fig.4 MSD of CuO nanoparticles in water suspension a)303K, b)313K, c)323k.

Table 2Simulated diffusion coefficients of nanoCuO-water system and pure water system.

Fig.5CuO-NPs water suspension system at 303K;5a) 0.000 femtoseconds; 5b) 0.035 nanoseconds;and 5c) 0.070 femtoseconds.

Finally, the Fig.5 illustrates the simulation screen dumps of CuO water suspensionat 303K. The Fig. 5a shows the screen dump at 0fs, the initial condition when simulation was just started, no atomic movement can be found. Later Fig. 5b demonstrates the simulation at an interval of 0.035fs. Here the simulation is approaching the equilibrium level of convergence as shown in Fig.3 of SACF.Further, Fig. 5c shows the simulation at final stages or the time when the simulation has gained the equilibrium convergence.It can be seen in Fig. 5c that the nanoparticles structural shape has changed, this is due to the influence of hydrodynamic

boundary layer that forms around the nanoparticles while in a nanofluidic dispersion state. However, Brownian motion cannot be neglected here, since this influence on nanoparticles micro motions i.e. responsible for rotation and vibration of the particles in suspension.

The viscosity trends obtained through molecular dynamics simulation is in 4-6% contrast with experimental obtained values. The CuO-NPs simulated results of diffusion coefficientis found to be1.033×10-8 m2/s at 303K, this can be correlated with the data found from literature[47].

CONCLUSIONS

This studyhas demonstrated a simulative model prototype development,whichcan be used for different metal oxide nanoparticles dispersion in aqueous fluid in terms of the viscosity and diffusion coefficients. Reproductions of self- diffusion constant of TIP3P water model in the systemhasbeen givento provide a comparative base for the system with CuO nanoparticles indiffusion interactions. However, concurrent trendsand resultshave been achieved under the experimental and simulative conditions. It is investigated that the viscosity increment is dependent on

the volume fraction of particles rather than its size. It was seen that the molecular dynamic of 2% CuO nanoparticle suspension shows similar trend as 2% vol. of experimentally setup mechanism.

This study excavated the interactive dispersion mechanism of nanoparticles at molecular level in order toexploit the lab-based computersimulation capabilitiestowardsthe nanoparticles-water system in reflecting of some larger sized potential particles and multiple particle system for future considerations.

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Abbreviation Table and their units