Molecular Dynamics Simulation of the Effects of the CarbonâWater

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Molecular Dynamics Simulation of the Effects of the Carbon-Water Interaction Parameters on the Nanofluidic Energy Absorption System Sayed Hossein Ganjiani, and Alireza Hossein Nezhad J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00421 • Publication Date (Web): 18 May 2016 Downloaded from http://pubs.acs.org on May 23, 2016

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The Journal of Physical Chemistry

Molecular Dynamics Simulation of the Effects of the Carbon-Water Interaction Parameters on the Nanofluidic Energy Absorption System

Sayed Hossein Ganjiani1, Alireza Hossein Nezhad1* 1

Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran. *

Corresponding author. E-mail address: [email protected]. Phone number: +989151416792.

ACS Paragon Plus Environment


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Abstract In this paper, the effects of the energy (ε) and distance (σ) parameters of Lennard-Jones potential in carbon-water interaction on the nanofluidic energy absorption system (NEAS) are investigated using molecular dynamics simulation. These parameters show the strength of the interactions between carbon nanotube (CNT) and water. For this purpose, six values for each of ε and σ used in the previous works are considered. The results show that the hydrophobic intensity of CNT is decreased by increasing each of the interaction parameters. The CNT surface at (ε = 0.0599 Kcal/mol and ε = 0.06461 Kcal/mol) and ε = 0.1349 Kcal/mol, at all σ’s, is obtained as hydrophobic and hydrophilic, respectively. For ε between 0.06461 Kcal/mol and 0.1349 Kcal/mol, the CNT surface is changed from hydrophobic to hydrophilic by increasing σ from 3.126 Å to 3.835 Å. When CNT surface is hydrophobic, contact angle, infiltration pressure and absorbed energy is reduced by increasing each of the interaction parameters.

Keywords: Lennard-Jones potential, Energy conversion, Wettability, Infiltration pressure, Contact angle.

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1. Introduction A new field of nanoscience, which includes the infiltration and transport of fluid molecules in nanochannels is called nanofluidics, having different applications in biological transport, drug delivery, molecular detection, energy conversions, etc. The infiltration and transport of fluid molecules through the nanochannels strongly depend on the interactions between the fluid molecules and solid surface atoms. In molecular mechanics, inter- and intramolecular interactions are modeled by energy potentials. The most famous energy potential to model the van der Waals (vdW) interaction is Lennard-Jones (LJ) potential1:  s 12  s 6  = VLJ 4e   −     r    r 

1

where r is the distance between atoms. The strength of interaction depends on the parameters of energy (ε) and distance (σ). The NEAS is a mixture of numerous nanoporous material particles and functional liquids. The mixture is sealed in a cylinder-piston chamber. The system is taken under pressure by displacements of the piston. This system can be used in many applications such as vibration proof, car bumper, etc. In addition to the absorption energy; this system can be used for other applications of energy conversions such as energy actuation and energy harvesting. Initially, the liquid molecules cannot enter the nanopores of nanoporous particles, so an external pressure is needed to infiltrate them in nanopores. This pressure can be produced by displacements of the piston. The system is taken under a reciprocating motion in applications such as car bumper. Therefore, a back-and-forth motion of the piston is applied to a loading-unloading cycle of the system. 3



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The CNTs are used commonly in the nanofluidic systems. Since carbon atoms in the pristine CNT are electrically neutral, the only interaction between these and other atoms is vdW interaction. In many works, the carbon-water interaction has been modeled employing LJ potential with different carbon-water interaction parameters; due to the different methods used to determine these parameters2. Hummer et al3 employed molecular dynamics (MD) to simulate transport of water in a CNT (6,6) and used two different values for carbon-water interaction parameters. They showed that the small change in carbon-water interactions causes large changes in the occupied water in the CNT. Yi and Shunle4 investigated the effects of electrical charge in the center of a CNT on the flow of water in the CNT. The carbon-water LJ parameters used by Yi and Shunle4 are different from what considered by Hummer et al3. Zambrano et al5 investigated the transport of a water droplet in a CNT by the temperature difference in the two ends of a CNT. Three values of ε and one value of σ were considered. They showed that by increasing ε, the CNT surface changes from hydrophobic to hydrophilic, as a result, causing the change of radial density profile in the vicinity of the interface. Joly6 simulated the capillary filling of the CNT by the water molecules. Larger values of ε and σ were used to indicate stronger carbon-water interactions and permit water molecules to enter the CNT spontaneously. NEAS has been simulated in many works: Liu etal7 investigated water infiltration in carbon nanocones, Liu et al8 and Liu et al9 examined the thermal effects and the electrical charges on the water infiltration in the CNTs, respectively. Xu et al10 explored the temperature effects on the infiltration pressure, contact angle and surface tension in a CNT. In these works the values were adopted for these

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parameters indicate a weak interaction between CNT and water. Under these conditions, water molecules cannot enter the CNT spontaneously and require an external pressure. Liu and Cao11 simulated a NEAS under impact loading and adopted carbon-water LJ parameters larger than those used by Joly6. They stated that after the system reaches equilibrium, water molecules can infiltrate the CNT spontaneously. The above reviews show that infiltration and transport of the water molecules in the CNTs have been investigated in many works, in which different values of carbon-water interaction parameters have been used. Selecting different values of carbon-water interaction parameters has resulted in hydrophilic CNT surface in some works6 and hydrophobic one in others7. Because CNTs have many applications in NEAS and both types of wettability of the CNT have been used in these systems (hydrophobic CNT in Ref. 8 and hydrophilic CNT in Ref. 11), it is important to understand the parameters affecting the CNT wettability. However, to the best of author’s knowledge, the effects of carbonwater interaction parameters on the performance of the NEAS have not been investigated so far. Therefore, in this paper, using MD, the effects of the change of carbon-water interaction parameters on the wettability of the CNT and on the performance characteristics of a NEAS including infiltration pressure, radial density profile and the rate of absorbed energy are studied.

2. Model and computational method 2.1. Problem statement The selected geometry to model a NEAS includes a rectangular reservoir and a rigid CNT (Figure 1). The reservoir is bounded by two rigid graphene planes in top and bottom. 5



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The upper plane is fixed and the lower plane which acts like a piston is movable. The reservoir dimensions are 34.43×34.79×24.97 Å3. An (10,10) armchair CNT is attached to the upper plane. The radius and the length of the CNT are 6.78 Å and 50 Å, respectively. The upper CNT end is closed by a rigid graphene plug. 1000 water molecules are considered in the reservoir; thus, the density of water molecules is obtained as 1.0 g/cm3 which is equal to the density of bulk water at 300 K and 1 atm.

Figure 1. The geometry of the computational model: a reservoir and a 5 nm length segment of the (10,10) CNT.

2.2. Governing equations and boundary conditions The 12-6 Lennard-Jones and columbic potentials are used to model the vdW and electrostatic interactions between atoms, respectively, and harmonic potentials are used to model the bond stretching and the angle bending interactions in water molecules1:

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( )

= V rN

∑

k bond 2

bonds

( li − li,0 )

2

+

∑

angles

k angle 2

( qi − qi,0 )

2

  s 12  s 6  qiq j  ij ij     + ∑ ∑ 4e ij   −   +  r   4pe r    rij  0 ij i = 1 j= i +1  ij       N

N

2

where kbond and kangle are coefficients of the harmonic potentials of the bond stretching and angle bending in water molecules, respectively. li and li,0 are the bond length and the reference bond length of O-H bond in ith water molecules. θi and θi,0 are the angle and the reference angle between two O-H bonds in ith water molecules. rij is the distance between two atoms i and j; qi and qj are the electric charges of atoms i and j, respectively. εij and σij are the energy and distance parameters of LJ potential between two atoms i and j, respectively and ε0 is the vacuum permittivity. The TIP3P model is used for water molecules. The vdW interaction of the hydrogen atoms with others atoms is ignored in the TIP3P water model due to its weak interaction. Therefore, only the oxygen atoms in water molecules have vdW interaction with carbon atoms. To investigate the effects of carbon-water interaction parameters on the NEAS performance systematically, six values for each of these parameters as shown in table 1 are selected. The cases 1 to six shown on the table are those that have been reported as paired interaction parameters in the literature, and the others have been added for the systematic study of their effects.

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Table 1. The carbon-water interaction parameters. 0.06461

0.0599 (Kcal/mol)

5

(Kcal/mol)

0.09369 3

(Kcal/mol)

0.1143 5

(Kcal/mol)

0.126 3

(Kcal/mol)

0.1349 11

(Kcal/mol) 5

3.126 Å 2 3.19 Å 5

Case 1

Case 3

3.2751 Å 3 3.35 Å

Case 4

4

3.4138 Å 3 3.835 Å

Case 6

Case 2

11

Case 5

In order to model a real NEAS, periodic boundary conditions are applied on four lateral surfaces of the computational model. The MD simulations are carried out using LAMMPS code12 with NVT ensemble. Nose-Hoover thermostat is used to fix temperature at 300 K. The cutoff distance of LJ potential is set to 10 Å. The PPPM method with accuracy of 10-4 is used to calculate long-rang columbic potential in water molecules. The time step in all simulations is set to 1 fs. First, the CNT opening is kept closed by a lid to prevent water molecules entering the CNT. Water molecules are equilibrated in reservoir at about 50 ps; next, the lid is removed and the whole system is equilibrated about 200 ps; then, the piston begins to move upward stepwise to apply the pressure on the water molecules in reservoir. In order not to apply the dynamic loading on the system, the piston is displaced 0.1 Å at each step and then kept fixed about 50 ps to allow the system to reach a new equilibrium. This procedure is repeated until the final displacement of the piston becomes 10 Å. The piston is returned to its initial position in the same style; and by this way, the loading-unloading cycle is completed. 8


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3. Results and discussion In the following sections, 36 MD simulations with the different carbon-water interaction parameters are carried out to investigate the effects of the change of carbon-water interaction parameters on the wettability of CNT, infiltration pressure, radial density profile and the energy conversion. In all of the simulations, the number and initial positions of water molecules, as well as energy potentials and initial ambient conditions of the system including temperature, 300 K, and pressure, 1 atm, are the same.

3.1. Wettability of the CNT After initial equilibrium, the number of infiltrated water molecules in CNT versus σ at different values of ε is shown in Figure 2. As shown in Figure 2, no water molecules enter CNT at ε = 0.0599 Kcal/mol and ε = 0.06461 Kcal/mol at all values of σ. A few water molecules infiltrate the CNT at ε = 0.09369 Kcal/mol and ε = 0.1143 Kcal/mol at σ = 3.835 Å and (σ = 3.4138 Å and σ = 0.0835 Å), respectively. Water molecules do not enter CNT at ε = 0.126 Kcal/mol and σ = 3.126 Å. Water molecules infiltrate CNT at ε = 0.1349 Kcal/mol at all distance parameters. At interaction parameters that water molecules do not enter CNT at ambient conditions, the CNT surface is obtained as hydrophobic. At other interaction parameters, shown in Figure 2 by filled symbols, water molecules infiltrate the whole length of CNT spontaneously, thus the CNT surface is obtained as hydrophilic. For the remaining interaction parameters, shown by hollow symbols, water molecules freely occupy a portion of the length of CNT. In these situations,

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water molecules need an external pressure for more infiltration. Thus, the CNT surface is introduced as partly hydrophilic.

250 Number of water molecules

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0.0599 (Kcal/mol) 0.06461 (Kcal/mol) 0.09369 (Kcal/mol) 0.1143 (Kcal/mol) 0.126 (Kcal/mol) 0.1349 (Kcal/mol)

200 150 100 50 0 3.1

3.2

3.3

3.4

3.5 3.6 σ (Å)

3.7

3.8

3.9

Figure 2. Number of infiltrated water molecules in CNT at different values of carbon-water interaction parameters.

Figure 3 shows the positions of water molecules 200 ps after removal of the lid from the CNT opening in cases 1, 5 and 6. The positions of water molecules at other interaction parameters with hydrophobic, hydrophilic and partly hydrophilic CNT are similar to cases 1, 5 and 6, respectively. In case 1, water molecules do not enter the CNT at ambient conditions. But, in cases 5 and 6, some water molecules freely enter the CNT without applying pressure. In case 5, water molecules infiltrate the whole length of the CNT, while in case 6, they occupy a small portion of the length ofthe CNT.

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Figure 3. The equilibrium positions of water molecules in cases 1, 5 and 6.

3.2. Infiltration pressure A CNT with hydrophilic surface is not appropriate for the NEAS, because the water molecules occupy the entire length of the CNT before applying pressure. Therefore, the loading-unloading cycle is not performed at interaction parameters that result in CNT surface being obtained as hydrophilic. As the volume and number of water molecules in the reservoir change by the piston displacements; the density of water molecules change in the reservoir. The pressure of the reservoir can be determined in all time steps in terms of density by the following equation of state13:  r  7.15  P= P0 + 298   − 1  r 0    

3

where ρ is density, and ρ0 = 1 g/cm3 and P0 = 0.1 MPa are the initial density and pressure, respectively.

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Figure 4 shows the pressure variations in the reservoir versus the number of infiltrated water molecules in the loading-unloading cycle in cases 2 and 6. The infiltration curves at other interaction parameters that result in CNT surface being obtained as hydrophobic and partly hydrophilic are similar to cases 2 and 6, respectively. The loading process in the infiltration curve in case 2 includes three stages. First, water molecules are compressed in the reservoir, as seen in the initial part of the curve. Next, water molecules infiltrate the CNT, as observed in the mid-part of the curve. Finally, water molecules are compressed in the reservoir and CNT, as seen in the final part of curve. The unloading process in these stages overlaps with the loading process, and water molecules leave the CNT at the end of the unloading process completely. The infiltration curve in case 6 is different from those in cases 2. In case 6, a large number of the water molecules enter the CNT at the initial displacements of the piston in the loading process and causes the mass in the reservoir to decrease faster than the reservoir volume; therefore, density reduces to less than 1 g/cm3 and pressure in the reservoir becomes negative. After water molecules reach the end of the CNT; the pressure in the reservoir is increased with the increase of the displacements of the piston. Moreover, water molecules remain in the CNT after the unloading process in case 6, thus the system cannot be used again, meaning that it is not appropriate for the NEAS. Therefore, interaction parameters that result in partly hydrophilic CNT are not suitable for the NEAS. The threshold pressure after which the water molecules can infiltrate the CNT is called the infiltration pressure, Pin. This is the pressure at the beginning of the second stage of the loading process.

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900 800

Loading Unloading

800

Case 2

700 600 Pressure (MPa)

700 Pressure (MPa)

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600 500 400 300 200

Case 6

500 400 300 200 100

100 0

Loading Unloading

0 0

20 40 60 80 100 120 140 Number of infiltrated water molecules

160

-100 0

20 40 60 80 100 120 140 Number of infiltrated water molecules

160

Figure 4. Pressure variations in the reservoir versus the number of infiltrated water molecules in the loading-unloading cycle in cases 2 and 6.

Infiltration pressure versus σ at different values of ε that result in hydrophobic CNT surface are shown in Figure 5. It is observed that at all ε’s, infiltration pressure is decreased by increasing σ. Infiltration pressure at ε = 0.0599 Kcal/mol, ε = 0.06461 Kcal/mol, ε = 0.09369 Kcal/mol and ε = 0.1143 Kcal/mol is decreased 60 %, 59 %, 35 % and 33 %, respectively, when σ is increased from 3.126 Å to 3.835 Å. Also, infiltration pressure is decreased by increasing ε at constant σ. For example, infiltration pressure at σ = 3.126 Å is decreased 79 % when ε is increased from 0.0599 Kcal/mol to 0.126 Kcal/mol. The reason of reduction of infiltration pressure by increasing each of the interaction parameters is that the interaction between the water molecules and CNT becomes stronger; therefore, water molecules need less pressure to infiltrate the CNT.

13



160 0.0599 (Kcal/mol) 0.06461(Kcal/mol) 0.09369 (Kcal/mol) 0.1143 (Kcal/mol) 0.126 (Kcal/mol)

140 Pressure (MPa)

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120 100 80 60 40 20 3.1

3.2

3.3

3.4

3.5 3.6 σ (Å)

3.7

3.8

3.9

Figure 5. Infiltration pressure versus σ at different values of ε that result in hydrophobic CNT surface

3.3. Radial density profile The radial density profile (RDP) is used to examine the structure of the water molecules in the CNT13. The RDP is defined by gr = nr / 2πr∆rnin in which nr is the number of the water molecules distributed in a cylindrical annulus with the inner radius r and outer radius r + ∆r, and nin is the total number of the infiltrated water molecules into the CNT. The RDPs of water molecules in CNT at ε = 0.06461 Kcal/mol and different σ's are shown in Figure 6-a. Data is averaged when the piston has moved from 0.8 nm to 1.0 nm. When the piston moves from 0.8 nm to 1.0 nm, the pressure at σ = 3.126 Å, σ = 3.19 Å, σ = 3.2751 Å, σ = 3.35 Å, σ = 3.4138 Å and σ = 3.835 Å varies from 329.7 MPa to 777.2 MPa, 336.5 MPa to 779.1 MPa, 357.3 MPa to 821.5 MPa, 364.5 MPa to 836.7 MPa, 375.4 MPa to 852.1 MPa and 401.8 MPa to 883.7 MPa, respectively. As shown in Figure 6-a, there are two shells in RDPs: the first shell is near the CNT wall and the second one is 14


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near the CNT center. By increasing σ, the RDP in both shells is increased, and the RDP in the second shell becomes more than that in the first shell. Therefore, more water molecules approach the CNT center. The effective radius is the radial distance of the first shell from the CNT center. The effective radius at (σ = 3.126 Å and σ = 3.19 Å), (σ = 3.2751 Å, σ = 3.35 Å and σ = 3.4138 Å) and σ = 3.835 Å is obtained as 4.53 Å, 4.28 Å and 3.78 Å, respectively. Therefore, the effective radius is decreased by increasing σ. The reason is that when σ is increased, the repulsive force between water molecules and CNT occurs at larger distance, causing water molecules move away from the CNT wall and approach the CNT center. Figure 6-b shows the RDPs of water molecules in CNT at σ = 3.35 Å and different ε’s. Data at ε = 0.0599 Kcal/mol, ε = 0.06461 Kcal/mol, ε = 0.09369 Kcal/mol and ε = 0.1143 Kcal/mol is averaged when the piston has moved from 0.8 nm to 1.0 nm. In this displacement of piston, the pressure at ε = 0.0599 Kcal/mol, ε = 0.06461 Kcal/mol, ε = 0.09369 Kcal/mol and ε = 0.1143 Kcal/mol varies from 353.8 MPa to 844.4 MPa, 375.4 MPa to 852.2 MPa, 353.8 MPa to 806.5 MPa and 380.4 MPa to 862.3 MPa, respectively. Comparing the results at ε = 0.0599 Kcal/mol to ε = 0.1143 Kcal/mol, which the system is under pressure, with ε = 0.126 Kcal/mol and ε = 0.1349 Kcal/mol, which the system is not under pressure, shows that the RDPs are more non-uniform under pressure. As shown in Figure 6-b, the RDP in the second shell is much less than that in the first shell at ε = 0.126 Kcal/mol and ε = 0.1349 Kcal/mol. Thus, the number of the water molecules near the CNT wall is more than those near the CNT center. The infiltrated water molecules at ε = 0.1349 Kcal/mol are more than that at ε = 0.126 Kcal/mol; therefore, the RDP in the second shell at ε = 0.1349 Kcal/mol is more than that at ε = 0.126 Kcal/mol. The RDP at 15



first shell is increased by increasing ε; thus, by increasing the ε, water molecules approach the CNT wall, because the carbon-water interactions are stronger than that of water-water. The effective radius from ε = 0.0599 Kcal/mol to ε = 0.09369 Kcal/mol and from ε = 0.1143 Kcal/mol to ε = 0.1349 Kcal/mol is obtained as 4.28 Å and 4.03 Å, respectively.

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a

3.126 Å 3.19 Å 3.2751 Å 3.35 Å 3.4138 Å 3.835 Å

2

8 Second shell

6

First shell

4 2 0

b

10 2

10

Density (1/nm )

12

Density (1/nm )

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8 6

Second shell


First shell

4 2

0

1

2

3 4 5 Radial distance (Å)

6

0

7

0

1

2

3 4 5 Radial distance (Å)

6

7

Figure 6. Radial density profiles a) at ε = 0.06461 Kcal/mol and different σ’s. b) at σ = 3.35 Å and different ε’s.

3.4. Energy conversion Surface tension depends on the intermolecular interactions, according to the microscopic point of view. The solid-liquid, solid-vapor and liquid-vapor surface tensions depend on the interactions between solid and liquid atoms, solid atoms and liquid molecules, respectively14. In all the simulations, the values of ε and σ in the vdW interactions between water molecules do not change, thus the liquid-vapor surface tension remain constant. But due to changes of the parameters in the vdW interactions between carbon atoms and water molecules, the solid-liquid surface tension changes.

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The required energy to adhere the liquid to the solid surface is obtained by14: ASL = gSV + g LV − gSL

4

where γSV, γLV and γSL are the solid-vapor, liquid-vapor and solid-liquid surface tensions, respectively. This equation can be simplified by using Young’s law14 as follows: ASL − g LV = gSV − gSL = g LV cos q

5

where θ is contact angle. The hydrophilicity or hydrophobicity of a surface depends on the values of γSV and γSL. When γSL > γSV, θ > π/2, solid surface is hydrophobic. In these conditions, the interactions between liquid molecules are stronger than that of between solid surface atoms and liquid molecules. Therefore, the liquid molecules tend to remain in the liquid bulk. But if γSL < γSV, θ < π/2, solid surface is hydrophilic thereby the interactions between solid surface atoms and liquid molecules are stronger than that of between liquid molecules; therefore, the liquid molecules tend to adhere to the solid surface. The initial temperature and pressure of water molecules in the reservoir are similar to the bulk water at the ambient conditions, and in these conditions, γLV = 0.0717 j/m2 15. ASL is the solid-liquid attractions energy. In this work, ASL is the total interaction energy between carbon atoms of the CNT and the infiltrated water molecules per unit area of the CNT wall, when water molecules entered in the entire length of CNT. Variations of contact angle, θ, versus σ at different ε's are shown in Figure 7. At interaction parameters corresponding to θ > π/2, CNT is hydrophobic and water molecules cannot enter it spontaneously, as shown in Figure 2. Also at interaction parameters corresponding to θ < π/2, the CNT is hydrophilic or partly hydrophilic thereby water molecules infiltrate the CNT spontaneously. As shown

17



in Figures 2 and 7, the CNT surface at (ε = 0.0599 Kcal/mol and ε = 0.06461 Kcal/mol) and ε = 0.1349 Kcal/mol at all σ’s is hydrophobic and hydrophilic, respectively. Contact angle at (ε = 0.1349 Kcal/mol and σ = 3.835 Å) cannot be defined. In these interaction parameters (ASL − γLV) / γLV is obtained more than one which is not physical. Contact angle which represents hydrophobic intensity at all ε’s is decreased by increasing σ. For example, the CNT surface at energy parameters 0.09369 Kcal/mol, 0.1143 Kcal/mol and 0.126 Kcal/mol is changed from hydrophobic to hydrophilic. Also, contact angle at all σ’s is decreased by increasing ε. It is concluded that the hydrophobic intensity of CNT decreases by increasing ε and σ, leading to the decrease of infiltration pressure.

210 Contact angle (degree)

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180 150 120 90 60 30 3.1

3.2

3.3

3.4

3.5 3.6 σ (Å)

3.7

3.8

3.9

Figure 7. Variation of contact angle, θ, versus σ at different ε's

The absorbed energy in the NEAS is obtained by: = E Dg ⋅ A

6

18


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where ∆γ = |γSV − γSL| and A is the CNT wall surface area. Absorbed energy density is defined as the absorbed energy divided by the total mass of the carbon atoms of the CNT and is given in table 2 at different interaction parameters with hydrophobic CNT. It is observed that the absorbed energy density is reduced by increasing the interaction parameters. Also, order of magnitude of absorbed energy density obtained from calculations is more than that in conventional energy absorption systems, e.g. 0.1 J/g of TiNi alloy, 1-10 J/g of textile composites, etc.

Table 2. Absorbed energy density at different interaction parameters with hydrophobic CNT. 0.0599

0.06461

0.09369

0.1143

0.126

0.1349

(Kcal/mol)

(Kcal/mol)

(Kcal/mol)

(Kcal/mol)

(Kcal/mol)

(Kcal/mol)

3.126 Å

48.19

41.17

20.61

11.99

1.60

3.19 Å

44.32

39.11

15.67

7.54

3.2751 Å

40.73

37.93

12.57

2.07

3.35 Å

39.38

37.19

8.78

1.05

3.4138 Å

37.98

34.95

5.64

3.835 Å

24.01

22.62

4. Verification . The experimental works found in the literature have been performed to study energy absorption in the nanoporous systems under different conditions16-19. The loadingunloading cycles at different interaction parameters with hydrophobic CNT have fairly acceptable agreement with the experimental works

18-19

. The differences between cycles

obtained in the present work with those of these experimental works are explained as follows: 19



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1- The infiltration stage has a small slope in the experimental cycles, but it is flat in the cycles of the present work. This difference is due to non-uniform pore diameter distribution of the nanoporous particles used in the experimental works, leading to non-similar infiltration pressures7. In these experimental works water molecules infiltrate nanopores having different diameters, but in the present work in fact one nanopore (the CNT) has been used. 2- In the experimental works, the loading-unloading cycle have a hysteresis diagram, because of the friction exists in the nanopores. But in the present simulations, the unloading and loading-processes are overlapped, because the CNT is frictionless. Another numerical simulation has been performed by Liu et al8, assuming εco = 0.07471 Kcal/mol, σco = 3.194 Å according to Bojan et al20. In this simulation a (10,10) CNT and the SPC/E water model were used. The displacement step and final displacement of the piston were assumed as 0.05 Å and 6 Å, respectively. The time period between the displacement steps of the piston was considered 50 ps. In Figure 8 pressure variations in the reservoir versus the number of infiltrated water molecules in the CNT obtained from the present work is compared with that obtained from the work of Liu et al8. Figure 8 shows excellent agreement between these two works, with less than 1% difference. The obtained infiltration pressure from this simulation is 152 MPa.

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180 150 Pressure (MPa)

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120

Loading (Liu et al8) Unloading (Liu et al8) Loading (Present work) Unloading (Present work)

90 60 30 0

0

20 40 60 80 Number of infiltrated water molecules

100

Figure 8. The infiltration curve in accordance to the work of Liu et al8 and compare with data of Liu et al8.

5. Conclusion The effects of carbon-water interaction parameters on the NEAS were investigated by using MD simulation. For a systematic study, six values for each of the carbon-water interaction parameters used in the previous works were considered. The results showed that the solid-liquid attraction energy and the solid-liquid surface tension in CNT, which has great effect on the NEAS, change by the change of carbon-water interaction parameters. At ε = 0.1349 Kcal/mol, CNT is obtained as hydrophilic when σ changing from 3.126 Å to 3.835 Å. At these interaction parameters, water molecules infiltrate the CNT spontaneously, but at both ε = 0.0599 Kcal/mol and ε = 0.06461 Kcal/mol, the CNT surface is obtained as hydrophobic at all σ’s. Because, the difference between the solid-vapor surface tension and the solid-liquid surface tension is obtained negative. At ε = 0.09369 Kcal/mol, ε = 0.1143 Kcal/mol and ε = 0.126 Kcal/mol, the CNT surface is 21



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changed from hydrophobic to hydrophilic by increasing σ from 3.126 Å to 3.835 Å. The hydrophobic intensity of CNT is reduced by increasing ε and σ. Also when the CNT is obtained hydrophobic, water molecules require external pressure to infiltrate the CNT. When the CNT is obtained as hydrophobic, the infiltration pressure and the absorbed energy are reduced by increasing ε and σ, because the strength of the interaction between the water molecules and the CNT increases.

References (1) Leach, A. R. Molecular Modelling, Principles and Applications; Prentice hall, 2011. (2) Wu, Y.; Aluru, N. R. Graphitic Carbon−Water Nonbonded Interaction Parameters. J. Phys. Chem. 2013, 117, 8802–8813. (3) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water Conduction through the Hydrophobic Channel of a Carbon Nanotube. Nature 2001, 41, 188–190. (4) Yi, Z.; Shunle, D. Molecular Dynamics Simulation of Water Conduction within Carbon Nanotube. Chin. Sci. Bulletin 2013, 58, 59–62. (5) Zambrano, H. A.; Walther, J. H.; Koumoutsakos, P.; Sbalzarini, I. F. Thermophoretic Motion of Water Nanodroplets Confined Inside Carbon Nanotubes. Nano Lett. 2009, 9, 66–71. (6) Joly, L. Capillary Filling with Giant Liquid/Solid Slip: Dynamics of Water Uptake by Carbon Nanotubes. J. Chem. Phys. 2011, 135, 214705. (7) Liu, L.; Zhao, J.; Yin, C. Y.; Culligana, P. J.; Chen, X. Mechanisms of Water Infiltration into Conical Hydrophobic Nanopores. Phys. Chem. Chem. Phys. 2009, 11, 6520–6524. (8) Liu, L.; Zhao, J.; Culligan, P. J.; Qiao, Y.; Chen, X. Thermally Responsive Fluid Behaviors in Hydrophobic Nanopores. Langmuir 2009, 25, 11862–11868.

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(9) Liu, L.; Qiao, Y.; Chen, X. Pressure-Driven Water Infiltration into Carbon Nanotube: the Effect of Applied Charges. Appl. Phys. Lett. 2008, 92, 101927. (10) Xu, B.; Qiao, Y.; Park, T.; Tak, M.; Zhoud, Q.; Chen, X. A Conceptual Thermal Actuation System Driven by Interface Tension of Nanofluids. Energy Environ. Sci. 2011, 4, 3632–3639. (11) Liu, H.; Cao, H. Interaction between Mechanical Wave and Nanoporous Energy Absorption System. J. Phys. Chem. C. 2013, 117, 4245–4252. (12) Plimpton, S. J. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1–19. (13) Cao, G.; Qiao, Y.; Zhou, Q.; Chen, X. Water Infiltration Behaviours in Carbon Nanotubes under Quasi-Static and Dynamic Loading Conditions. Molecular Simulation 2008, 34, 1267–1274. (14) Marchand, A.; Weijs, J. H.; Snoeijer, J. H.; Andreotti, B. Why Is Surface Tension a Force Parallel to the Interface? Am. J. Phys. 2011, 79, 999–1008. (15) Vargaftik, N. B.; Volkov, B. N.; Voljak, L. D. International Tables of the Surface Tension of Water. J. Phys. Chem. Ref. Data 1983, 12, 817–820. (16) Han, A.; Punyamurtula, V. K.; Qiao, Y. Heat Generation Associated with Pressure-Induced Infiltration in a Nanoporous Silica Gel. J. Mater. Res. 2008, 23, 1902–1906. (17) Han, A.; Qiao, Y. Infiltration Pressure of a Nanoporous Liquid Spring Modified by an Electrolyte. J. Mater. Res. 2007, 22, 644–648. (18) Han, A.; Lu, W.; Punyamurtula, V. K.; Kim, T.; Qiao, Y. Temperature Variation in Liquid Infiltration and Defiltration in a MCM41. J. Appl. Phys. 2009, 105, 024309. (19) Han, A.; Kong, X.; Qiao, Y. Pressure Induced Liquid Infiltration in Nanopores. J. Appl. Phys. 2006, 100, 014308. (20) Bojan, M. J.; Steele, W. A. Interactions of Diatomic Molecules with Graphite. Langmuir 1987, 3, 1123–1127.

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Molecular Dynamics Simulation of the Effects of the CarbonâWater

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