Hossein Tafrishia,
Sadegh Sadeghzadeh*b,
Fatemeh Molaeic and
Hossein Siavoshid
aSchool of Advanced Technologies, Iran University of Science and Technology, Tehran, Iran
bSchool of Advanced Technologies, Iran University of Science and Technology, Tehran, Iran. E-mail: sadeghzadeh@iust.ac.ir
cMining and Geological Engineering Department, University of Arizona, Arizona, USA
dMining and Geological Engineering Department, University of Arizona, Arizona, USA
First published on 14th April 2020
Octadecane is an alkane that is used to store thermal energy at ambient temperature as a phase change material. A molecular dynamics study was conducted to investigate the effects of adding graphene and a boron nitride nanosheet on the thermal and structural properties of octadecane paraffin. The PCFF force field for paraffin, AIREBO potential for graphene, Tersoff potential for the boron nitride nanosheet, and Lennard-Jones potential for the van der Waals interaction between the nanoparticles and n-alkanes were used. Equilibrium and nonequilibrium molecular dynamics simulations were used to study the nano-enhanced phase change material properties. Results showed that the nanocomposite had a lower density change, more heat capacity (except at 300 K), more thermal conductivity, and a lower diffusion coefficient in comparison with pure paraffin. Additionally, the nanocomposite had a higher melting point, higher phonon density of state and radial distribution function peaks.
Molecular dynamics simulations have been demonstrated to be a useful tool for researchers to study the thermal properties of paraffin molecules. Every molecule is explicitly considered in this technique. The interaction of each atom with others is calculated using an atomic force field, which is the gradient of the potential energy function.9 Babaei et al.10 designed and simulated octadecane (C18H38) using carbon nanotubes and graphene. They demonstrated that adding carbon nanotubes and graphene improved the thermal conductivity, and decreased the thermal resistance as well. Indeed, by modifying the molecular alignment, these nano additives can increase the heat conductivity. They fixed the nano-additives to survey just the pure paraffin thermal properties. The findings of the non-equilibrium molecular dynamics (NEMD) simulations indicated that the thermal conductivity of paraffin-CNT at 270 K and 300 K was 0.499 and 0.243 W mK−1, respectively. Moreover, this study showed that the thermal conductivity of paraffin–graphene was 0.560 and 0.249 W mK−1 at 270 K and 320 K, respectively, while the pure paraffin thermal conductivity was 0.3 and 0.164 W mK−1 at 270 K and 300 K, respectively. The eicosane system (C20H42) comprising boron nitride was carried out by Rao et al.11 Using an equilibrium molecular dynamics simulation to study the thermal conductivity and other thermal properties, they chose n-eicosane alkane as the paraffin. Two paraffin mixtures, including the boron nitride nanosheet (BNNS) and boron nitride nanotube (BNNT), were simulated. Results revealed that the latent heat of the composites was reduced, in comparison to pure paraffin, after the addition of BN nanostructures. Conversely, the nano-additives significantly improved the thermal conductivity of pure paraffin. As will be shown in this paper, some discrepant results have been observed in these different studies. These differences arose from using different force fields and potentials, calculating several parameters in a wide range of temperatures, and incorporating different nanoparticles in one system, among others. By and large, fixing the nanoparticles and not allowing them to move is not a valid method to calculate the thermal properties of all nanocomposite systems. Additionally, using the equilibrium method for calculating thermal conductivity will produce much higher values for the nano-enhanced PCMs. Therefore, we think this method is not true for these systems. Accordingly, in this paper, we used the nonequilibrium method for the thermal conductivity calculation.
This paper studies the effects of adding nano-additives of graphene and BNNS to n-octadecane paraffin (C18H38). To the best of our knowledge, this has not been studied experimentally or numerically before. The essential contributions of this paper are as follows:
(1) A novel nanocomposite containing graphene and a boron nitride nanosheet was introduced.
(2) Several structural and thermal properties were studied to deeply investigate the PCM and NEPCM behaviors at different temperatures.
(3) The proposed nanocomposite can be used as a NEPCM with better thermo-structural properties.
The rest of this paper is organized as follows: Section 2 explains the modeling structures, how they are built, simulation trends and computational techniques. Section 3 presents the outcomes (including heat capacity, mean square displacement, diffusion coefficient, radial distribution function, phonon density of state, density, and thermal conductivity) and discussion, and finally, Section 4 presents the findings.
Fig. 1 Structure of: (a) an octadecane molecule (C18H38), (b) graphene, and (c) boron nitride nanosheet (BNNS). |
The box size for pure paraffin was 65 × 65 × 65 Å3 for 500 octadecane molecules. For the nanocomposite, the size of the box was 75 × 75 × 75 Å3. The graphene and BNNS weight proportions in the composite mixture were approximately 4.9% and 5.1%, respectively. Simulated graphene and BNNS were 38 × 38 Å2. At the beginning of the simulations, the energy of the systems was minimized using the conjugate gradient algorithm.15 Fig. 2(a) indicates the structure of pure paraffin used in simulations after minimization. Fig. 2(b) illustrates the structure of the nano-enhanced PCM, which was used in simulations after minimization. Periodic boundary conditions were employed in all three directions. The number of atoms in each simulation system is reported in Table 1.
Fig. 2 Structures of: (a) the pure paraffin and (b) nano-enhanced PCM used in the simulations after minimization. |
System | # of atoms in paraffin | # of atoms in graphene | # of atoms in BNNS | # of all atoms |
---|---|---|---|---|
Pure octadecane | 28000 | — | — | 28000 |
Nanocomposite | 28000 | 576 | 576 | 29152 |
In the second step, all structures were simulated at 260, 270, 280, 290, 300, 310, 320, 330, and 340 K. The simulation process was such that under the NPT ensemble, all structures were equilibrated for 2 × 106 time steps of the corresponding temperature (at 1 atm). The output of this section led to various energy fluctuation plots and the final density of the system at the desired temperatures. Subsequently, simulations were followed at the desired temperature for 4 × 106 time steps under the NVT ensemble (the third step). The outputs of this step included the MSD (mean square displacement), D (diffusion coefficient), Cv (heat capacity at constant volume), RDF (radial distribution function), and PDOS (phonon density of state) at several temperatures for every two structures.
Lastly, the structures were simulated for 6 × 106 time steps (3 nanoseconds) under the NVE ensemble to account for their thermal conductivity in the fourth step. The box was divided into several plates along the X/Y/Z direction. Through the simulation box, the heat flux was introduced by adding heat to the molecules inside the heat source (a planar slab) in two regions of the box. The same amount of heat was then extracted from the molecules within another slab (thermal sink) in another region (in the middle of the box). The thermal conductivity of the material in the simulation box (subject to the periodic boundary condition) was calculated after achieving a steady state based on Fourier's law. These simulations were carried out at 280 K (solid-state), 300 K (octadecane melting point) and 320 K (fluid state).
Fig. 3 Kinetic and potential energy fluctuations of (a) the pure octadecane, (b) octadecane–graphene–BNNS nanocomposite under NPT equilibrium at 300 K. |
Temperature (K) | Applied method | Density (g cm−3) | Thermal conductivity (W mK−1) | Reference |
---|---|---|---|---|
280 | MD (PCFF) | 0.7356 | 0.1194 | Current study |
290 | MD (PCFF) | 0.7303 | — | Current study |
300 | MD (PCFF) | 0.7184 | 0.1227 | Current study |
310 | MD (PCFF) | 0.7130 | — | Current study |
320 | MD (PCFF) | 0.7024 | 0.1180 | Current study |
298.15 | MD (COMPASS) | — | 0.277–0.303 | Liu et al.29 |
270 | MD (NERD) | — | 0.30 | Babaei et al.10 |
290 | MD (NERD) | 0.86 | — | Babaei et al.10 |
300 | MD (NERD) | — | 0.164 | Babaei et al.10 |
310 | MD (NERD) | 0.75 | — | Babaei et al.10 |
293–297 (solid phase) | Experimental | 0.91 | — | Gülseren et al.30 |
301–308 (liquid phase) | Experimental | 0.778 | — | Gülseren et al.30 |
300 (liquid phase) | Experimental | — | 0.153 | Powell et al.31 |
275 (solid phase) | Experimental | — | 0.33 | Yarbrough et al.32 |
294–300 (solid phase) | Experimental | — | 0.1505 | Xia et al.33 |
(1) |
(2) |
Fig. 5 Mean square displacement with temperature for (a) pure octadecane and (b) the octadecane–graphene–BNNS nanocomposite. |
Fig. 5(a) demonstrates that by increasing the octadecane temperature, the slope of the MSD diagram increased. It seemed that the slope of the MSD curve for octadecane grew considerably, becoming more steep at temperatures of 300 K and above. According to the experiments, the melting point was 300 K and this finding was quite close to it.30 The curves in Fig. 5(b) describe how MSD changed in the octadecane–graphene–BNNS nanocomposite at different temperatures. The nanocomposite continued to be solid up to 300 K, and then was melted at 310 K. This result confirms that the nano-additives increased the paraffin melting point by approximately 10 K.
(3) |
(4) |
Fig. 8 shows the PDOS for pure paraffin, and the mixture at 260, 300, and 340 K. The PDOS of pure paraffin had some peaks between 20 to 45 THz and in 90 THz, which was inconsistent with ref. 35. Another peak for pure paraffin was between 0 to 5 THz. The existence of graphene and BNNS caused higher peaks and troughs, and also caused other new peaks between 0 to 55 THz. With increasing temperature in both pure paraffin and the nanocomposite, the peaks of PDOS also increased.
Fig. 8 Phonon density of state (PDOS) of (a) pure paraffin and (b) the nanocomposite at temperatures 260 K, 300 K, and 340 K. |
(5) |
It is a measure of the probability of finding a particle at a distance of r away from a given reference particle. The general algorithm involves determining how many particles are within a distance of r and r + dr away from a particle (particle at each bin). N denotes the number of total atoms, Ni represents the number of atoms corresponding to the chemical type i (α and β subscriptions indicate the different types of chemicals), x is the mole fraction of chemical type α and β, and ρ is the density of the atoms.
Fig. 9 depicts the RDF curve of the two structures, pure PCM and nano-enhanced PCM (NEPCM) at different temperatures. This figure illustrates the radial distribution function for all atoms relative to each other. The RDFs displayed relatively isolated peaks at low temperatures. It implies that there were constant distances between the two atoms of interest that were characteristic of a solid-state. On the other hand, they became smoother for liquid materials. The RDF of NEPCM had more peaks than PCM.
Fig. 9 Total radial distribution function (RDF) of (a) all pure octadecane atoms and (b) all octadecane–graphene–BNNS atoms. |
Fig. 10 A schematic diagram of the simulation box for calculating the thermal conductivity in the (a) x-direction, (b) y-direction, and (c) z-direction. |
The heat flux Q (0.01 kcal mol−1 fs−1 for pure paraffin and 0.03 kcal mol−1 fs−1 for the nanocomposite) was applied between the heat sources and sinks under the microcanonical ensemble. As the kinetic energy of the atoms of the hot slab increased and the kinetic energy of the atoms of the cold slab decreased, this energy transferred from warmer atoms to colder atoms. Simulations of the thermal conductivity under the microcanonical ensemble for 3 ns (6 million time steps) were performed. Using the temperature output for the atoms of each part of the box along the box length, the temperature-position profile was plotted, and the thermal conductivity was calculated using Fourier's law as follows:
(6) |
In this equation, is the rate of the heat addition to heat sources or the heat extraction from the heat sink. ‘A’ is the cross-sectional area of the simulation box perpendicular to the direction of the imposed heat flux, whereas and are the temperature gradients on the linear section of the temperature-position curve for the left section and right section of the curve. This means that the temperature of the hot and cold sections was not included in calculating the temperature gradient. The heat sink was in the middle of the box with a thickness of 2 nm and the heat sources were in the two sides of the box, which were joined together as a union region, with 2 nm thickness. This means the thickness of each hot region was 1 nm.
Fig. S1† illustrates the temperature profiles of the pure octadecane in the x-, y-, and z-directions at 280 K (solid phase). Fig. S2 and S3† show the temperature-position profiles at 300 K (melting point) and 320 K (liquid phase), respectively, in different directions of pure octadecane paraffin. Thermal conductivities of paraffin at various temperatures in the x-, y-, and z-directions were calculated according to the corresponding graphs, and are presented in Table 3. The highest thermal conductivity of paraffin was obtained at the melting point.
Temperature (K) | kx (W mK−1) | ky (W mK−1) | kz (W mK−1) | kmean (W mK−1) |
---|---|---|---|---|
280 | 0.11242 | 0.11921 | 0.12659 | 0.1194 |
300 | 0.12277 | 0.12246 | 0.12294 | 0.1227 |
320 | 0.11652 | 0.11681 | 0.12052 | 0.1180 |
Investigating the effects of adding graphene and the boron nitride nanosheet to paraffin and understanding the variation of thermal transport in different temperatures is the purpose of this section. Fig. S4–S6† display the temperature profiles of the octadecane–graphene–BNNS nanocomposite in the x-, y-, and z-directions at different temperatures. The thermal conductivity of the nanocomposite at various temperatures and directions is calculated according to the corresponding graphs, and are presented in Table 4. The nano-additives improve paraffin's thermal conductivity. With increasing temperature, the enhancement of the thermal conductivity increased. This may be because of the higher peaks of the phonon density of state at high temperatures.
Temperature (K) | kx (W mK−1) | ky (W mK−1) | kz (W mK−1) | kmean (W mK−1) | Mean kappa changes compared to pure paraffin |
---|---|---|---|---|---|
280 | 0.16054 | 0.15231 | 0.12793 | 0.1469 | +23.0% |
300 | 0.16857 | 0.15731 | 0.13957 | 0.1552 | +26.5% |
320 | 0.16054 | 0.16124 | 0.13026 | 0.1507 | +27.7% |
According to the results, the maximum thermal conductivity was observed for the nanocomposite at 300 K. In both systems, the highest thermal conductivity occurred at 300 K.
It was observed that with increasing temperature, the diffusion coefficient also increased. However, the diffusion coefficient of the nanocomposite was lower than that for pure paraffin. Studying the thermal conductivity of different structures revealed that the addition of the nano-additives increased the thermal conductivity of paraffin by about 23.0%, 26.5% and 27.7% at 280 K, 300 K, and 320 K, respectively. By adding the nano-additives, the heat capacity of the phase change material was enhanced at all temperatures, except for at 300 K.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra01847c |
‡ Polymer consistent force field. |
This journal is © The Royal Society of Chemistry 2020 |