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A molecular dynamic investigation of viscosity and diffusion coefficient of nanoclusters in hydrocarbon fluids
Computational Materials Science 99 (2015) 242–246
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
A molecular dynamic investigation of viscosity and diffusion coefficient of nanoclusters in hydrocarbon fluids Adil Loya a,⇑, Jacqueline L. Stair b, Ali R. Jafri a, Ke Yang c, Guogang Ren a,⇑ a
School of Engineering and Technology, University of Hertfordshire, UK Department of Pharmacy, University of Hertfordshire, UK c Institute of Metal Research, Shenyang, China b
a r t i c l e
i n f o
Article history: Received 4 April 2014 Received in revised form 21 November 2014 Accepted 23 November 2014
Keywords: Diffusion coefficient Nano-fluids Molecular dynamics Viscosity LAMMPS
a b s t r a c t Straight chain alkanes modified by metal oxide nanoclusters have gained wide recognition in applications in tribology, energy and thermal storage. This paper investigates the system’s rheological properties and diffusion coefficient in a reflection of the nanocluster’s nanofluidic dispersibility and stability in the domain of thermal and diffusive properties. A computational model working on CuO nanoclusters in an alkane (C20H44) fluidic system has been developed at an atomic-molecular level. The simulation results are used to assess the outcomes of the suspension’s fluidic stability and thermal diffusive capabilities. A COMPASS force field was employed, and periodic boundary conditions were defined to address the molecular dynamic (MD) simulation results in the dispersion system. The MD viscosity quantification using stress autocorrelation function shows a monotonic decay for 303–323 K temperatures. These results of autocorrelation calculations were used for validating viscosity results obtained from MD simulation. The viscosity of the CuO-Alkane system was found out to be 1.613 mPa s at 303 K. The diffusion coefficients were also calculated for the CuO-Alkane system using mean square displacement and it was found that at 303 K this system gives 4.302 E11 m2/s rate of diffusion. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Nano and subnanomaterials can be beneficial to fluids by enhancing the thermal capability and conductivity as phase change materials for thermal transformation, rheological modification and energy storage applications [1,2]. The preparation and characterization of nanoclusters in fluids as suspension additives demonstrated a modification of thermal transformation, di-electric enhancements, physiochemical stability, and rheological smoothness in subjected systems [3–7]. Before the availability of nanoclusters, fluids used for thermal transfer were enhanced mostly as a model by the uses of micrometer particles [8]. However, most of these nanoparticle suspensions give a high level of aggregation and precipitation, which has shown a high level of instability due to particle clogging caused by larger particle sizes [9–12]. Previous work shows that CuO nanoparticles in API-SF engine oil and base paraffin oils have enhanced wear performance and characteristics by reducing the worn scar depth by 17% and 78% and decreased friction coefficient by 18.4% and 6% respectively [13,14]. During the past decade, selected nanoparti⇑ Corresponding author. http://dx.doi.org/10.1016/j.commatsci.2014.11.051 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
cles have been modified by the uses of surface activating agents such as carboxylate and silanes [14]. These modified nanoparticles (such as CuO and ZnBO3) demonstrated better wear-resistant properties than those of micro-scaled particles for base lubricants and reduced the system’s friction remarkably [13–15]. Experimental studies have been carried out to investigate the underlying capabilities of the nanofluidic materials in the fluidic systems [5,7]. Thermal properties such as latent heat, thermal conductivity and thermal diffusivity are mainly investigated by experimental analysis, through using advanced facilities such as differential scanning calorimetry, and thermal conductivity analyzers [7,16,17]. The major challenges in collecting experimental data for a complex nanofluid material system is that the equipment can be expensive and high-quality data is difficult to obtain because some of the thermal properties of the fluidic samples are hard to determine until the sample could be homogeneously dispersed, in which the status and properties are incomprehensible. Therefore, it is necessary to proceed from the experimental mechanism of dispersion as a first step or as a base level, following the use of computational simulation to approach the physical parameters of the subjected solid–fluid systems in order for understanding,
A. Loya et al. / Computational Materials Science 99 (2015) 242–246
supporting and predicting of the performance of the nanoclusterfluidic system. The simulation on individual particle motion as a function of time in this paper addresses thermal–mechanical properties of nanocluster-fluidic system as a model system. This is considered often as a complementary to experiments performed on the actual system. The use of molecular dynamics (MD) as an emerging effective nanoscopic or sub-nanoscopic solid–fluid analysis technique, may overcome the challenges on obtaining the thermal properties of the suspension fluids, including the isothermal crystallization containing the metal nanocluster and nanoparticles [3]. MD simulations have been used in many solid–liquid systems to determine their rheological properties, i.e. for a solid particlehexadecane suspension system [18]. The use of MD simulation results were used to investigate the binding system [19], to obtain the self-diffusion coefficient in lattice models of zeolites solid solution [20]. Moreover, MD study was carried out for examining the ratio of volume with mutation relationship of temperature over a heptadecane and pentadecane fluidic system has reported by Que et al. [21]. In this study MD viscosity is determined by the use of the Green Kubo‘s (GK) viscosity formulation [22]. GK parameters were implemented through the use of LAMMPS molecular dynamic processing. However, as far as lubrication applications are concerned, the simulation can be the best technique for the solid–fluidic system modelling through non-equilibrium molecular dynamics (NEMD). As used by Cui et al. [18] for their simulation towards a liquid decane and an n-hexadecane system. Therefore, in this investigation, the basic simulation work was carried out by using the NEMD to achieve the rheological data analysis of a nanocluster-alkane fluidic system.
2. Materials, experimental and simulation methodology Simulation of viscosity and diffusion of atomic interaction was carried out by using LAMMPS [23,24]. The fluidic system was simulated with hybrid pair style, i.e. smoothed particle hydrodynamic (SPH) and discrete particle dynamics (DPD) potential in an imaginary domain. The initial simulation system was setup by use of 252 CuO molecules, which were represented by 7 nanoclusters each carrying 36 molecules bonded by COMPASS force field. Therefore, the simulated particles in this work are in the sub-nanometer scale between 0.2 and 0.6 nm [25]. The molar weight ratio of nanoclusters in alkane was calculated to be 2–3%. The initial equilibration time limit used for carrying out successful data quantification was about 50 ps for alkane simulation, whereas for alkane with nanoclusters required 4 ps. The complete equilibration process for alkanes took 300– 400 ps, whereas for alkane with nanocluster took 15–16 ps.
243
2.1.2. Diffusion coefficient The diffusion coefficient, D, was measured to explain the effect of diffusion rate with the system. The diffusion was measured using diffusion Eq. (2) [26–28].
D¼
E 1 D d ðr i ðtÞ r i ð0ÞÞ2 =dt 6N
ð2Þ
where D is diffusion coefficient, N is number of particles, ri(t) is the particle position corresponding to time period of t and ri(0) is the initial position of particle. Metal oxide nanoparticles in paraffin oil were reported to improve the rheological and thermal properties that played a significant role in enhancing the dielectric properties of the fluids. As far as the use of CuO sub-nanoparticles is concerned in paraffin/alkanes, high dielectric losses can be expected at around 1 MHz [3]. This is an important control variable at the time of over voltage spikes. This correlation was also analysed in the previous study on the TiO2 nanoparticles fluidic systems [29]. 2.2. Simulation method The system viscosities were analysed from a temperature increase of 303–323 K. The MD simulation of an alkane (Eicosane, i.e. C20H42) was acting as carrier constitute fluid and used as a control medium for the whole system. The dispersed CuO nanoclusters in base paraffin oil were simulated and were presented as shown in Fig. 1. A COMPASS forcefield was incorporated into the generated particle‘s fluid system [30]. This system was equilibrated from 303 to 323 K, with degree intervals of 10 K under atmospheric pressure. Using N (Number of particles), P (pressure), and T (temperature) ensemble (i.e. using Nose–Hoover style), the dynamics simulations were applied with a smoothed particle hydrodynamic (SPH) and a discrete particle dynamics (DPD) potential, which were employed because their functionalities enabled them to give a realistic effect to the system configuration. The CuO nanoclusters in alkane system were configured in random orientation providing the rheological transport analysis to be anisotropic. The system was equilibrated for different iteration levels until the stress autocorrelation was converged for viscosity calculations. There are also reports on Van der Waals and electrostatic interactions applied on to the atomic and molecular dynamic simulation [12], where time step length of 1 fs has been employed. The
2.1. Simulation data acquisition 2.1.1. Viscosity Viscosity was calculated by using GK formulae for a measurement method. The stress tensor for measuring viscosity was implemented by Eq. (1) [22]:
V g¼ 3kB T
Z 0
1
* + X Pxy ðtÞPxy ð0Þ dt
ð1Þ
x
where g is the viscosity, V is the volume of the system, T is the temperature, kB is the Boltzmann constant, and Pxy refers to an independent component of the stress in the xy direction.
Fig. 1. CuO nanoclusters in alkane fluid: The blue spheres represent n-Eicosane (C20H42), the red spheres represent Cu and the brown spheres represent oxygen connected to Cu. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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A. Loya et al. / Computational Materials Science 99 (2015) 242–246
COMPASS force field was implemented in the material studio. The Material Studio Discover module was employed to implant charges of force field. The combined system of nanocluster and alkanes has been shown in Fig. 1. For clearer visualization, the alkane radius has been decreased so that nanoclusters can be illustrated clearly.
Table 1 Diffusion coefficient of pure alkanes and alkanes with CuO nanoclusters. Temperature 303 K 313 K 323 K
Dc (alkanes)
Dc (alkane with nanoclusters) 2
7.376 e006 m /s 6.137 e006 m2/s 7.985 e006 m2/s
4.302 e011 m2/s 4.928 e011 m2/s 5.605 e011 m2/s
3. Results and discussion Paraffin is widely used in thermal, heat-transfer and potential coolant applications [7]. However, the thermal transfer capability of paraffin is very low due to its mononerma nature. The implementation of CuO nanoparticles in alkanes is expected to improve its heat-transfer capability, and enhance the thermal stability properties. 3.1. MD viscosity analysis The major fluidic property that is affected by nanoclusters addition to the system is the viscosity. The viscosity increment by addition of nanoclusters was compared to the pure alkane system. It was found that the viscosity of the alkane is 1.137– 0.812 mPa s from temperature of 293–323 K as shown in Fig. 2, while nanoclusters addition in the alkane system causes the viscosity to rise by 60–70% (i.e. from 1.305 to 1.815 at 293 K). This effect is caused by the nanocluster’s high surface area to volume ratio, which produced a significant change in the viscosity. The viscosity variation under a particular temperature point was found within 2–5% of accuracy as shown by the error bars in Fig. 2. Moreover, a simulation viscosity’s accuracy can be confirmed by stress autocorrelation as shown in Figs. 5 and 6. 3.2. Mean square displacement (MSD) The dispersed and aggregated state of fluids (interactions with nanocluster) can be described in a better way by using a diffusion coefficient. The slope of scattered lines of MSD helps in predicting the diffusion coefficient [31]. The diffusion coefficient of CuOnanoclusters in alkane at different temperatures demonstrated various effects of diffusion interactivity between additives and base fluidic system. The data achieved for gold nanoparticle absorption at liquid–liquid interface in literature [29] are from 3.70E10 to 5.70E13 m2/s, which are similar to the data obtained by the simulation work carried in this study, i.e. 4.03E11 m2/s as
Fig. 2. The results of the viscosity simulations showing viscosity of the pure alkane system and alkane system with nanoclusters against temperature rise.
Fig. 3. Diffusion coefficients of pure alkanes at different temperatures.
shown in Table 1. Fig. 3 shows the self-diffusivity of pure alkanes, where the diffusion rate at different temperatures from 303–323 K shows similar trends. This is due to less change in viscosity with low temperature variations. The molecular loading (number of atoms) increment causes collision between the alkane and nanoparticle to intensify, additionally giving rise in energy barriers in the way of diffusion. The governing diffusion coefficient decreases because of intensive collision of molecules. Coppens et al. [20] found in their study that a lattice Monte Carlo simulation on diffusion depends on the lattice topology. They observed a decrease in the diffusion coefficient with increasing the particle concentration, i.e. similar to the weakly connected lattice of silicates, the self-diffusivity decreases in a non-liner fashion [32]. This trend was also observed in these studies, the system with nanoclusters show a lower diffusion rate than a system without nanoclusters. This has been explained as the loading of nanocluster in the system is increased, this creates viscosity and collision to increase making the diffusivity to decrease [33]. The diffusion coefficient values obtained for the pure alkane and CuO based sub-nanofluidic system are listed in Table 1. There seems to be a decrease in the diffusivity of alkanes with added nanoparticles, which is due to the increasing viscosity and aggregation kinetics caused by coagulation. The MD analysis confirmed the changes in viscosity by the convergence data from the stress autocorrelations, relating to viscosity effects on molecular dynamics simulations, reflected in N (number of moles), P (pressure), and T (Temperature) ensembles, by which the temperature and pressure are controlled. Scaling the velocity accurately is a necessary practice in order to give a real physical effect to support the system to reach equilibrium. Molecular dynamic simulations were performed for calculating the viscosity of the system by the use of the Green–Kubo method [34]. As indicated in Fig. 4, the thermal autocorrelation explored the barriers behind the experimental court which justified the simulated results achieved. There are two major types of autocorrelation functions that define the convergences of the thermophysical quantities:
A. Loya et al. / Computational Materials Science 99 (2015) 242–246
Fig. 4. A schematic showing of equilibration convergence approach of autocorrelation functions.
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Fig. 6. Stress autocorrelation function of molecular dynamic simulations of alkanes with CuO nanoclusters.
The accuracy of the results equilibrated in the CuO nanocluster alkane system for measuring the viscosity of a system can be verified by the estimation of stress autocorrelation function as shown in Fig. 5. The graphical result in Fig. 4 explains the process of the integration of non-equilibrated system to equilibration at different steps: (a) The system starts with a thermodynamic equilibrium (initial setting conditions), but not in an equilibrium state; (b) The thermodynamic conditions are changed due to the implementation of the thermal ensemble, causing the system to go towards equilibrium; (c) The non-equilibrium system moves to the equilibrated level of convergence, at this level the system satisfies the convergences. This process is continued through the equilibration of the thermophysical quantities. The convergence timesteps (i.e. the time taken by the simulation for effectively showing a monotonic decaying trend of autocorrelation function) depend on the volume and quantity of the atoms in that system. For the larger system, a large amount of computational power and time step will be required for the convergence.
Fig. 5. Stress autocorrelation functions of alkanes at (a) 303 K; (b) 313 K; and (c) 323 K.
(a) Stress autocorrelation function (SACF), defines the achieved viscosity to be correct on the basis of its convergences; (b) Heat autocorrelation function defines the achieved thermal conductivity to be accurate based on it convergences of its results. This is the theory of MD for quantifying the thermal effective viscosity and diffusion, by the help of autocorrelation convergence.
The SACF has been used to quantify the shear viscosity in a system. Likewise, the SACF has three major stress tensors i.e. Pxy, Pxy and Pyz. The convergence of a tensor, estimates the accuracy of the obtained viscosity. The MD viscosity results of the alkane with nanoclusters calculated by GK method were in good agreement, based on the relaxation of the autocorrelation function. These viscosity results are also in good coherence to the data achieved by others [35] as listed in Table 2. To investigate the macroscopic shear viscosity, the estimated time taken for the simulation to acquire highly accurate results, the Dt values were used for viscosity equilibration and are given in Table 2 in column 4. Where Dt estimates the amount of durations approached within two consecutive steps of an interval. However, time interval used was so small, the convergence was impossible at higher values of Dt and the convergence does not decay monotonically at higher time. Therefore, the properties did not meet the convergence totally, specifically in the case of stress autocorrelation tensor i.e. Pyz as illustrated in Fig. 5. In the case of the nanocluster—alkane system the relaxation of the stress tensors, it took more time to monotonically come to zero than the pure alkane simulation.
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A. Loya et al. / Computational Materials Science 99 (2015) 242–246
Table 2 Viscosity of alkanes at different temperatures from our work in comparison with reference values. Temperature (K)
l (mPa s) Pure
l (mPa s) Pure
l (mPa s)
alkane this work
alkane Ref.[35]
Alkane + CuO (This work)
303 313 323
0.951 0.750 0.656
0.900–0.950 0.720–0.760 0.625–0.680
1.630 (Dt = 15.500 ps) 1.375 (Dt = 13.500 ps) 1.218 (Dt = 12.300 ps)
ever, the simulation methodology can be further expanded with the implementation of nano-meter scale solutions by increasing the sizes of nanoclusters with more molecular attachment to existing nanoclusters with high computational power needed. Acknowledgement This work was partly supported by the UK Royal Academy of Engineering (RAEng Ref. 1213RECI052). References
Table 3 Time taken by each simulation to evaluate viscosity of pure alkanes. Temperature (K)
se (ps)
303 313 323
250 325 375
The SACF results for relaxation of equilibration time have been shown in Table 3 and Fig. 5 estimates that the time taken for the results to converge to a reasonable accuracy is equivalent with the results investigated in 1992 by Harris and Wang [36]. A similar equilibration time limit was also used to integrate the results (i.e. 500–600 Ps around 300–400 K respectively, with molecular dynamics of n-eicosane). In the case of the alkanes modified by nanoclusters, it was hard to signify the detailed viscosity convergence due to the lack of computational power and longer time required; therefore, it provided only one stress flux tensor to fully decay as shown in Fig. 6. However, the results demonstrated clear quantification of viscosity increment. 4. Conclusion In this work, the COMPASS force field methodology was used, while the experimental boundary conditions were implemented for performing the molecular dynamics (MD) simulation of a targeted CuO nanocluster-alkane fluidic system. However, the conducted exploitation is an application of the NEMD simulation which is beneficial for understanding the rheological behaviour of the CuO nanocluster dispersion in alkane system. The results accurately estimated the viscosity trends, including the effects of rheology and thermophysical quantities over the Brownian diffusion and inter-kinetic actions of nanoclusters in hydrocarbon based fluids. This was achieved by predicting and comparing the simulation data change of the diffusion and viscosity under different thermal conditions plus comparison with literature values. It is obvious that investigated particles were much smaller in this MD simulation in comparison to that of nanoparticles. How-
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Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
A molecular dynamic investigation of viscosity and diffusion coefficient of nanoclusters in hydrocarbon fluids Adil Loya a,⇑, Jacqueline L. Stair b, Ali R. Jafri a, Ke Yang c, Guogang Ren a,⇑ a
School of Engineering and Technology, University of Hertfordshire, UK Department of Pharmacy, University of Hertfordshire, UK c Institute of Metal Research, Shenyang, China b
a r t i c l e
i n f o
Article history: Received 4 April 2014 Received in revised form 21 November 2014 Accepted 23 November 2014
Keywords: Diffusion coefficient Nano-fluids Molecular dynamics Viscosity LAMMPS
a b s t r a c t Straight chain alkanes modified by metal oxide nanoclusters have gained wide recognition in applications in tribology, energy and thermal storage. This paper investigates the system’s rheological properties and diffusion coefficient in a reflection of the nanocluster’s nanofluidic dispersibility and stability in the domain of thermal and diffusive properties. A computational model working on CuO nanoclusters in an alkane (C20H44) fluidic system has been developed at an atomic-molecular level. The simulation results are used to assess the outcomes of the suspension’s fluidic stability and thermal diffusive capabilities. A COMPASS force field was employed, and periodic boundary conditions were defined to address the molecular dynamic (MD) simulation results in the dispersion system. The MD viscosity quantification using stress autocorrelation function shows a monotonic decay for 303–323 K temperatures. These results of autocorrelation calculations were used for validating viscosity results obtained from MD simulation. The viscosity of the CuO-Alkane system was found out to be 1.613 mPa s at 303 K. The diffusion coefficients were also calculated for the CuO-Alkane system using mean square displacement and it was found that at 303 K this system gives 4.302 E11 m2/s rate of diffusion. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Nano and subnanomaterials can be beneficial to fluids by enhancing the thermal capability and conductivity as phase change materials for thermal transformation, rheological modification and energy storage applications [1,2]. The preparation and characterization of nanoclusters in fluids as suspension additives demonstrated a modification of thermal transformation, di-electric enhancements, physiochemical stability, and rheological smoothness in subjected systems [3–7]. Before the availability of nanoclusters, fluids used for thermal transfer were enhanced mostly as a model by the uses of micrometer particles [8]. However, most of these nanoparticle suspensions give a high level of aggregation and precipitation, which has shown a high level of instability due to particle clogging caused by larger particle sizes [9–12]. Previous work shows that CuO nanoparticles in API-SF engine oil and base paraffin oils have enhanced wear performance and characteristics by reducing the worn scar depth by 17% and 78% and decreased friction coefficient by 18.4% and 6% respectively [13,14]. During the past decade, selected nanoparti⇑ Corresponding author. http://dx.doi.org/10.1016/j.commatsci.2014.11.051 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
cles have been modified by the uses of surface activating agents such as carboxylate and silanes [14]. These modified nanoparticles (such as CuO and ZnBO3) demonstrated better wear-resistant properties than those of micro-scaled particles for base lubricants and reduced the system’s friction remarkably [13–15]. Experimental studies have been carried out to investigate the underlying capabilities of the nanofluidic materials in the fluidic systems [5,7]. Thermal properties such as latent heat, thermal conductivity and thermal diffusivity are mainly investigated by experimental analysis, through using advanced facilities such as differential scanning calorimetry, and thermal conductivity analyzers [7,16,17]. The major challenges in collecting experimental data for a complex nanofluid material system is that the equipment can be expensive and high-quality data is difficult to obtain because some of the thermal properties of the fluidic samples are hard to determine until the sample could be homogeneously dispersed, in which the status and properties are incomprehensible. Therefore, it is necessary to proceed from the experimental mechanism of dispersion as a first step or as a base level, following the use of computational simulation to approach the physical parameters of the subjected solid–fluid systems in order for understanding,
A. Loya et al. / Computational Materials Science 99 (2015) 242–246
supporting and predicting of the performance of the nanoclusterfluidic system. The simulation on individual particle motion as a function of time in this paper addresses thermal–mechanical properties of nanocluster-fluidic system as a model system. This is considered often as a complementary to experiments performed on the actual system. The use of molecular dynamics (MD) as an emerging effective nanoscopic or sub-nanoscopic solid–fluid analysis technique, may overcome the challenges on obtaining the thermal properties of the suspension fluids, including the isothermal crystallization containing the metal nanocluster and nanoparticles [3]. MD simulations have been used in many solid–liquid systems to determine their rheological properties, i.e. for a solid particlehexadecane suspension system [18]. The use of MD simulation results were used to investigate the binding system [19], to obtain the self-diffusion coefficient in lattice models of zeolites solid solution [20]. Moreover, MD study was carried out for examining the ratio of volume with mutation relationship of temperature over a heptadecane and pentadecane fluidic system has reported by Que et al. [21]. In this study MD viscosity is determined by the use of the Green Kubo‘s (GK) viscosity formulation [22]. GK parameters were implemented through the use of LAMMPS molecular dynamic processing. However, as far as lubrication applications are concerned, the simulation can be the best technique for the solid–fluidic system modelling through non-equilibrium molecular dynamics (NEMD). As used by Cui et al. [18] for their simulation towards a liquid decane and an n-hexadecane system. Therefore, in this investigation, the basic simulation work was carried out by using the NEMD to achieve the rheological data analysis of a nanocluster-alkane fluidic system.
2. Materials, experimental and simulation methodology Simulation of viscosity and diffusion of atomic interaction was carried out by using LAMMPS [23,24]. The fluidic system was simulated with hybrid pair style, i.e. smoothed particle hydrodynamic (SPH) and discrete particle dynamics (DPD) potential in an imaginary domain. The initial simulation system was setup by use of 252 CuO molecules, which were represented by 7 nanoclusters each carrying 36 molecules bonded by COMPASS force field. Therefore, the simulated particles in this work are in the sub-nanometer scale between 0.2 and 0.6 nm [25]. The molar weight ratio of nanoclusters in alkane was calculated to be 2–3%. The initial equilibration time limit used for carrying out successful data quantification was about 50 ps for alkane simulation, whereas for alkane with nanoclusters required 4 ps. The complete equilibration process for alkanes took 300– 400 ps, whereas for alkane with nanocluster took 15–16 ps.
243
2.1.2. Diffusion coefficient The diffusion coefficient, D, was measured to explain the effect of diffusion rate with the system. The diffusion was measured using diffusion Eq. (2) [26–28].
D¼
E 1 D d ðr i ðtÞ r i ð0ÞÞ2 =dt 6N
ð2Þ
where D is diffusion coefficient, N is number of particles, ri(t) is the particle position corresponding to time period of t and ri(0) is the initial position of particle. Metal oxide nanoparticles in paraffin oil were reported to improve the rheological and thermal properties that played a significant role in enhancing the dielectric properties of the fluids. As far as the use of CuO sub-nanoparticles is concerned in paraffin/alkanes, high dielectric losses can be expected at around 1 MHz [3]. This is an important control variable at the time of over voltage spikes. This correlation was also analysed in the previous study on the TiO2 nanoparticles fluidic systems [29]. 2.2. Simulation method The system viscosities were analysed from a temperature increase of 303–323 K. The MD simulation of an alkane (Eicosane, i.e. C20H42) was acting as carrier constitute fluid and used as a control medium for the whole system. The dispersed CuO nanoclusters in base paraffin oil were simulated and were presented as shown in Fig. 1. A COMPASS forcefield was incorporated into the generated particle‘s fluid system [30]. This system was equilibrated from 303 to 323 K, with degree intervals of 10 K under atmospheric pressure. Using N (Number of particles), P (pressure), and T (temperature) ensemble (i.e. using Nose–Hoover style), the dynamics simulations were applied with a smoothed particle hydrodynamic (SPH) and a discrete particle dynamics (DPD) potential, which were employed because their functionalities enabled them to give a realistic effect to the system configuration. The CuO nanoclusters in alkane system were configured in random orientation providing the rheological transport analysis to be anisotropic. The system was equilibrated for different iteration levels until the stress autocorrelation was converged for viscosity calculations. There are also reports on Van der Waals and electrostatic interactions applied on to the atomic and molecular dynamic simulation [12], where time step length of 1 fs has been employed. The
2.1. Simulation data acquisition 2.1.1. Viscosity Viscosity was calculated by using GK formulae for a measurement method. The stress tensor for measuring viscosity was implemented by Eq. (1) [22]:
V g¼ 3kB T
Z 0
1
* + X Pxy ðtÞPxy ð0Þ dt
ð1Þ
x
where g is the viscosity, V is the volume of the system, T is the temperature, kB is the Boltzmann constant, and Pxy refers to an independent component of the stress in the xy direction.
Fig. 1. CuO nanoclusters in alkane fluid: The blue spheres represent n-Eicosane (C20H42), the red spheres represent Cu and the brown spheres represent oxygen connected to Cu. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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COMPASS force field was implemented in the material studio. The Material Studio Discover module was employed to implant charges of force field. The combined system of nanocluster and alkanes has been shown in Fig. 1. For clearer visualization, the alkane radius has been decreased so that nanoclusters can be illustrated clearly.
Table 1 Diffusion coefficient of pure alkanes and alkanes with CuO nanoclusters. Temperature 303 K 313 K 323 K
Dc (alkanes)
Dc (alkane with nanoclusters) 2
7.376 e006 m /s 6.137 e006 m2/s 7.985 e006 m2/s
4.302 e011 m2/s 4.928 e011 m2/s 5.605 e011 m2/s
3. Results and discussion Paraffin is widely used in thermal, heat-transfer and potential coolant applications [7]. However, the thermal transfer capability of paraffin is very low due to its mononerma nature. The implementation of CuO nanoparticles in alkanes is expected to improve its heat-transfer capability, and enhance the thermal stability properties. 3.1. MD viscosity analysis The major fluidic property that is affected by nanoclusters addition to the system is the viscosity. The viscosity increment by addition of nanoclusters was compared to the pure alkane system. It was found that the viscosity of the alkane is 1.137– 0.812 mPa s from temperature of 293–323 K as shown in Fig. 2, while nanoclusters addition in the alkane system causes the viscosity to rise by 60–70% (i.e. from 1.305 to 1.815 at 293 K). This effect is caused by the nanocluster’s high surface area to volume ratio, which produced a significant change in the viscosity. The viscosity variation under a particular temperature point was found within 2–5% of accuracy as shown by the error bars in Fig. 2. Moreover, a simulation viscosity’s accuracy can be confirmed by stress autocorrelation as shown in Figs. 5 and 6. 3.2. Mean square displacement (MSD) The dispersed and aggregated state of fluids (interactions with nanocluster) can be described in a better way by using a diffusion coefficient. The slope of scattered lines of MSD helps in predicting the diffusion coefficient [31]. The diffusion coefficient of CuOnanoclusters in alkane at different temperatures demonstrated various effects of diffusion interactivity between additives and base fluidic system. The data achieved for gold nanoparticle absorption at liquid–liquid interface in literature [29] are from 3.70E10 to 5.70E13 m2/s, which are similar to the data obtained by the simulation work carried in this study, i.e. 4.03E11 m2/s as
Fig. 2. The results of the viscosity simulations showing viscosity of the pure alkane system and alkane system with nanoclusters against temperature rise.
Fig. 3. Diffusion coefficients of pure alkanes at different temperatures.
shown in Table 1. Fig. 3 shows the self-diffusivity of pure alkanes, where the diffusion rate at different temperatures from 303–323 K shows similar trends. This is due to less change in viscosity with low temperature variations. The molecular loading (number of atoms) increment causes collision between the alkane and nanoparticle to intensify, additionally giving rise in energy barriers in the way of diffusion. The governing diffusion coefficient decreases because of intensive collision of molecules. Coppens et al. [20] found in their study that a lattice Monte Carlo simulation on diffusion depends on the lattice topology. They observed a decrease in the diffusion coefficient with increasing the particle concentration, i.e. similar to the weakly connected lattice of silicates, the self-diffusivity decreases in a non-liner fashion [32]. This trend was also observed in these studies, the system with nanoclusters show a lower diffusion rate than a system without nanoclusters. This has been explained as the loading of nanocluster in the system is increased, this creates viscosity and collision to increase making the diffusivity to decrease [33]. The diffusion coefficient values obtained for the pure alkane and CuO based sub-nanofluidic system are listed in Table 1. There seems to be a decrease in the diffusivity of alkanes with added nanoparticles, which is due to the increasing viscosity and aggregation kinetics caused by coagulation. The MD analysis confirmed the changes in viscosity by the convergence data from the stress autocorrelations, relating to viscosity effects on molecular dynamics simulations, reflected in N (number of moles), P (pressure), and T (Temperature) ensembles, by which the temperature and pressure are controlled. Scaling the velocity accurately is a necessary practice in order to give a real physical effect to support the system to reach equilibrium. Molecular dynamic simulations were performed for calculating the viscosity of the system by the use of the Green–Kubo method [34]. As indicated in Fig. 4, the thermal autocorrelation explored the barriers behind the experimental court which justified the simulated results achieved. There are two major types of autocorrelation functions that define the convergences of the thermophysical quantities:
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Fig. 4. A schematic showing of equilibration convergence approach of autocorrelation functions.
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Fig. 6. Stress autocorrelation function of molecular dynamic simulations of alkanes with CuO nanoclusters.
The accuracy of the results equilibrated in the CuO nanocluster alkane system for measuring the viscosity of a system can be verified by the estimation of stress autocorrelation function as shown in Fig. 5. The graphical result in Fig. 4 explains the process of the integration of non-equilibrated system to equilibration at different steps: (a) The system starts with a thermodynamic equilibrium (initial setting conditions), but not in an equilibrium state; (b) The thermodynamic conditions are changed due to the implementation of the thermal ensemble, causing the system to go towards equilibrium; (c) The non-equilibrium system moves to the equilibrated level of convergence, at this level the system satisfies the convergences. This process is continued through the equilibration of the thermophysical quantities. The convergence timesteps (i.e. the time taken by the simulation for effectively showing a monotonic decaying trend of autocorrelation function) depend on the volume and quantity of the atoms in that system. For the larger system, a large amount of computational power and time step will be required for the convergence.
Fig. 5. Stress autocorrelation functions of alkanes at (a) 303 K; (b) 313 K; and (c) 323 K.
(a) Stress autocorrelation function (SACF), defines the achieved viscosity to be correct on the basis of its convergences; (b) Heat autocorrelation function defines the achieved thermal conductivity to be accurate based on it convergences of its results. This is the theory of MD for quantifying the thermal effective viscosity and diffusion, by the help of autocorrelation convergence.
The SACF has been used to quantify the shear viscosity in a system. Likewise, the SACF has three major stress tensors i.e. Pxy, Pxy and Pyz. The convergence of a tensor, estimates the accuracy of the obtained viscosity. The MD viscosity results of the alkane with nanoclusters calculated by GK method were in good agreement, based on the relaxation of the autocorrelation function. These viscosity results are also in good coherence to the data achieved by others [35] as listed in Table 2. To investigate the macroscopic shear viscosity, the estimated time taken for the simulation to acquire highly accurate results, the Dt values were used for viscosity equilibration and are given in Table 2 in column 4. Where Dt estimates the amount of durations approached within two consecutive steps of an interval. However, time interval used was so small, the convergence was impossible at higher values of Dt and the convergence does not decay monotonically at higher time. Therefore, the properties did not meet the convergence totally, specifically in the case of stress autocorrelation tensor i.e. Pyz as illustrated in Fig. 5. In the case of the nanocluster—alkane system the relaxation of the stress tensors, it took more time to monotonically come to zero than the pure alkane simulation.
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Table 2 Viscosity of alkanes at different temperatures from our work in comparison with reference values. Temperature (K)
l (mPa s) Pure
l (mPa s) Pure
l (mPa s)
alkane this work
alkane Ref.[35]
Alkane + CuO (This work)
303 313 323
0.951 0.750 0.656
0.900–0.950 0.720–0.760 0.625–0.680
1.630 (Dt = 15.500 ps) 1.375 (Dt = 13.500 ps) 1.218 (Dt = 12.300 ps)
ever, the simulation methodology can be further expanded with the implementation of nano-meter scale solutions by increasing the sizes of nanoclusters with more molecular attachment to existing nanoclusters with high computational power needed. Acknowledgement This work was partly supported by the UK Royal Academy of Engineering (RAEng Ref. 1213RECI052). References
Table 3 Time taken by each simulation to evaluate viscosity of pure alkanes. Temperature (K)
se (ps)
303 313 323
250 325 375
The SACF results for relaxation of equilibration time have been shown in Table 3 and Fig. 5 estimates that the time taken for the results to converge to a reasonable accuracy is equivalent with the results investigated in 1992 by Harris and Wang [36]. A similar equilibration time limit was also used to integrate the results (i.e. 500–600 Ps around 300–400 K respectively, with molecular dynamics of n-eicosane). In the case of the alkanes modified by nanoclusters, it was hard to signify the detailed viscosity convergence due to the lack of computational power and longer time required; therefore, it provided only one stress flux tensor to fully decay as shown in Fig. 6. However, the results demonstrated clear quantification of viscosity increment. 4. Conclusion In this work, the COMPASS force field methodology was used, while the experimental boundary conditions were implemented for performing the molecular dynamics (MD) simulation of a targeted CuO nanocluster-alkane fluidic system. However, the conducted exploitation is an application of the NEMD simulation which is beneficial for understanding the rheological behaviour of the CuO nanocluster dispersion in alkane system. The results accurately estimated the viscosity trends, including the effects of rheology and thermophysical quantities over the Brownian diffusion and inter-kinetic actions of nanoclusters in hydrocarbon based fluids. This was achieved by predicting and comparing the simulation data change of the diffusion and viscosity under different thermal conditions plus comparison with literature values. It is obvious that investigated particles were much smaller in this MD simulation in comparison to that of nanoparticles. How-
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