Super Energy Absorption System Based on Nanofluidic Glycerol

Article pubs.acs.org/JPCC

Super Energy Absorption System Based on Nanofluidic Glycerol Solution Hailong Liu and Guoxin Cao* HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China ABSTRACT: Nanofluidic behavior has been used to produce a high energy absorption system which can transfer the mechanical work (done by impact or blast) into the solid−liquid interfacial energy. Increasing the liquid interface area by using nanoporous particles with high specific surface area is the typical way to increase the energy absorption density of system. In present work, we found that the energy absorption density is also highly sensitive to the species of liquid selected in a nanofluidic system. Using molecular dynamics (MD) simulations, the performance of nanofluidic energy absorption system (NEAS) based on glycerol solutions with different concentrations is investigated, and the effects of nanochannel size and loading rate on the system performance are also considered. With the increase of the concentration of glycerol (ϕ), the energy absorption density of NEAS can be significantly increased; e.g., when the liquid changes from water (ϕ = 0) to pure glycerol (ϕ = 1), the energy absorption density of NEAS can be increased by up to three times.

1. INTRODUCTION Because it has a small volume, is lightweight, and has a high energy damping/absorption efficiency, the nanoporous energy absorption system (NEAS) recently has attracted considerable research interest.1−6 The energy damping/absorption mechanism of NEAS is different from the conventional mechanism converting mechanical energy into plastic energy (e.g., honeycomb and metallic foam) or new surface energy (e.g., nanocomposites).7,8 NEAS is typically made by enclosing nanoporous particles (in micron size) in a nonwetting liquid environment. Under the normal condition, the liquid cannot fill in the nanopore since it is nonwetting, while under the external load (e.g., impact or blast), the liquid will be pushed into the nanopore. Thus, the work done by the external load can be converted into the solid−liquid interfacial energy. Additionally, it has been reported that liquids can transport much faster in nanopore than that predicted from conventional fluid-flow theory.9−14 Thus, the energy damping procedure of NEAS could be very fast, which makes it possible to effectively protect against the high speed impact or the blast wave. Currently, the experimental works of NEAS based on nanoparticles (including silica gel,3,15,16 amorphous carbon5 and zeolites2,4,17) and liquids (including water,3,18 electrolyte solution,6,16 glycerol,12,19 and liquid metal20) have been reported, while most of the numerical/theoretical studies of NEAS are based on carbon nanotubes (CNT) and water molecules.21−26 Because it has a smooth surface, uniform size, and electrical neutrality, CNTs have become an ideal nanopore model to study the pore size effect on the transport behavior of nanofluid, but they have not been successfully employed in experiments yet. Since water has a simple geometric structure and chemical © 2014 American Chemical Society

component, it is widely used in both experimental and theoretical works. In our recent work, 21,22,26 we investigated the fundamental working mechanism of NEAS under high speed loading conditions and studied the influences of both nanopore size and impact loading rate on the energy absorption density of NEAS as well as the infiltrated water structure. The energy absorption density of NEAS (made by CNTs and water) was estimated to be about 0.4 kJ/cm3, which is significantly higher than that of the conventional energy absorption materials. The energy absorption density of NEAS increases with the impact loading rate. In addition, there is a significant change of water structure inside the small tubes, whereas the corresponding change is not obvious for the large tubes. The energy absorption density of NEAS depends on the specific surface area of nanoparticles and the solid−liquid interfacial energy density which is mainly dependent on both the atomic types of nanopore and liquid. Joseph and Aluru9 compared the water transport behavior inside different channels (including CNTs, boron nitride tubes, and silicon tubes) and showed that water transports with a lower speed through silicon tubes which have more hydrophilic Lennard−Jones (LJ) parameters. The infiltration behavior of electrolyte solutions into a model SiO2 nanochannel27 and metal organic frameworks28 was investigated, and it was reported that a higher infiltration pressure is required to sustain the infiltration of the electrolyte solution with a smaller ionic size. In most of the above nanofluidic studies, although the different types of solid walls are Received: July 23, 2014 Revised: October 4, 2014 Published: October 9, 2014 25223

dx.doi.org/10.1021/jp507411w | J. Phys. Chem. C 2014, 118, 25223−25233

The Journal of Physical Chemistry C

Article

Figure 1. Computational model of glycerol solutions used in MD simulations: (a) the initial state of system; (b) CNTs filled by glycerol solutions (ϕ = 0.4) under impact loading. The inset figure is the structure of glycerol molecule. The glycerol and water molecules are displayed in blue and red color, respectively.

number of liquid molecules and the density of glycerol solution reservoir are displayed in Table 1.

tested, the liquid inside is mainly limited as water while other liquid phases is very few investigated.29 However, selecting a new liquid phase in NEAS might be a very effective way to increase the energy absorption density of NEAS, which has not been studied theoretically to the best of our knowledge. In the present work, we modify the liquid environment in NEAS by adding a new liquid, glycerol into water, and then to examine the performance of NEAS. Glycerol has been used in the experimental investigations of NEAS.15,19 Using molecular dynamics (MD) simulations, the performance of NEAS based on the glycerol solution with different concentrations and CNTs is investigated, and both the effects of tube size and loading rate are considered. We will show how the liquid environment affects the performance of NEAS under high speed loading conditions. The observations in this paper may provide an important insight for developing and optimizing the new generation NEAS.

Table 1. Number of Liquid Molecules and Density of Reservoir concentration ϕ

water

glycerol

ρ0 (g/cm3)

1 0.6 0.4 0.2 0.1 0

0 1618 2427 3236 3641 4045

1000 600 400 200 100 0

1.260 1.157 1.102 1.050 1.023 0.997

Similar to our previous works,22,26 the impact load is applied on the reservoir by the displacement controlled piston. Four different impact loading rates are selected as 100, 200, 500, and 1000 m/s. The final displacement of piston is set to 2 nm for all different loading rates. To consider the nanopore size effect on the energy absorption, three CNTs (including (10, 10), (15, 15) and (20, 20) CNTs with radii of 0.67 nm, 1.03 and 1.33 nm, respectively) are selected. The length of CNT segments is set to 10 nm, and the right end of CNTs is closed to simulate the end of nanopore. Typically, nanopores are embedded into nanoporous particles in NEAS, and the pore wall is constrained by the matrix material of the nanoparticle, which has a very low flexibility (e.g., the bulk moduli of silica and water are around 37 and 2 GPa, respectively). In addition, the pressure typically resisted by the NEAS is lower than 100 MPa, and thus, the elastic deformation of nanopore particles can be neglected. Therefore, we select the rigid CNT segment in the present work. The MD simulations are carried out using LAMMPS,30 which is a classical molecular dynamics software from Sandia National

2. COMPUTATION METHODS The computational cell includes a rigid CNT segment and a liquid reservoir, as shown in Figure 1a. The reservoir is bounded by two parallel carbon planes: the right plane is fixed and connected with CNT segment; the left plane is moveable to mimic a piston. The periodic boundary condition is applied on the lateral directions of computation cell to remove the boundary effect. The volume concentrations of glycerol solutions (ϕ) in reservoir are selected as 0% (pure water), 10%, 20%, 40%, 60%, and 100% (pure glycerol). The densities of glycerol and water are set to be 1.26 g/cm3 and 0.997 g/cm3, respectively. The pure glycerol reservoir includes 1000 glycerol molecules, and the reservoirs of other glycerol solutions are built by replacing the certain number of glycerol molecules (decided by the volume fraction ϕ) by water molecules with the same volume. The 25224



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Laboratory. The Class-2 force field (in LAMMPS)31 is used to describe the solid−liquid van der Waals (VDW) interaction (based on 9-6 Lennard−Jones (LJ) potential), which has been widely used to study the interaction between liquid and CNTs.15,27,32−34 The cutoff distance for the VDW interaction is set to be 1 nm, which is typically used in the MD simulations of water.9,12 The long-range Columbic potential is calculated using the particle−particle particle−mesh (PPPM) method.35 The modified TIP3P (transferable intermolecular potential 3P) model36 is used to simulate water molecules, which has been successfully used to describe the transport behavior of water through CNTs.11,12,37−39 The SHAKE program is used to constrain the internal geometry of water molecules.40 The LJ potential parameters of liquid molecules are displayed in Table 2.

The simulation is still running after the piston reaches its final displacement. After the reflected wave reaches the tube opening, the simulation will run for another several picosecond until the density of the infiltrated liquid is stable. Figure 1b shows that the CNTs have been fully filled by the glycerol solutions under the impact load, and the water molecules can be uniformly mixed with the glycerol molecules in both the reservoirs and CNTs. The size effect of the reservoir on the infiltration behavior has been checked based on two pure water reservoirs, which include 3500 (4.65 × 4.65 × 4.9 nm) and 6000 (4.65 × 4.65 × 8.4 nm) water molecules, respectively. The (20, 20) tube is used in the checking procedure. It is found that the transport behavior and the density of infiltrated water molecules do not depend on the reservoir size.

Table 2. VDW Interaction Parameters

3. RESULTS AND DISCUSSION The energy absorption mechanism of NEAS including pure water and CNTs has been studied in our recent work.21,26 Under impact load, the mechanical wave created by piston first introduces the kinetic energy into the liquid reservoir, and then the wave begins to compress the liquid to increase the potential energy of reservoir. When the wave reaches the opening of tube, the liquid molecules close to the opening of CNTs will first enter into CNTs activated by the kinetic energy and transport through the tube with the same speed as a wave, and more liquid molecules will be then pushed into CNTs by the increased reservoir pressure. When the molecules reach the end of tube, the forward mechanical wave also reaches the end of tube, which is then reflected by the tube end to change to the reflected wave. The reflected wave will transport from the tube end to the tube opening, during which it compresses the infiltrated molecules to sharply increase the density of liquid. The behavior of the reflected wave can be monitored by the axial flow rate and density of liquid. When the reflected wave transports to the tube opening, the density of all liquid inside tube is increased. Thus, based on the changes of the axial flow rate and density, two different structures (structure I and II) are defined for the infiltrated water molecules before and after compressed by the reflected wave, respectively. For pure water, the energy absorbed is mainly from the energy difference between bulk and infiltrated water molecules, and the contribution from the solid−liquid friction is very small, which can be neglected. In present work, we will investigate the effect of the different liquids (glycerol solutions) on the energy absorption procedure, including the density of the infiltrated liquids, the solid−liquid interfacial energy, the response to the mechanical wave, the infiltration speed, and the solid−liquid friction. 3.1. Density of Infiltrated Glycerol Liquids. The density of the liquid inside nanopore is one of the important factors related to the energy absorption density of NEAS. Because of the repulsive interaction of LJ potential between liquids and nanotube wall, the infiltrated liquid molecules will not occupy the whole tube. If the density of infiltrated liquid is calculated based on the whole nanotube volume, it will be significantly underestimated, and the underestimation is larger for the smaller nanotube. Thus, the density calculated from the true occupied volume of the infiltrated liquids should be more effective, which is defined as the effective density ρeff. Figure 2 shows the value of ρeff of infiltrated glycerol solution with structure I/II under the impact velocities of 100−1000 m/s, which are normalized by their bulk counterpart (ρ0) (see Table 1). The densities of structure I/II are displayed as the dashed/solid lines in the figure. ρeff is calculated by the following expression:

molecule

atom

σ (nm)

ε (kcal/mol)

q (e)

glycerola

C1 C2 O H1 H2 C O H

0.3870 0.3815 0.3580 0.1087 0.2878 0.3915 0.3840 0.1087

0.0748 0.068 0.096 0.008 0.023 0.068 0.0800 0.0080

0.054 0.107 −0.57 0.41 0.053 0.0 −0.8200 0.4100

CNT H2O a

Atom index is displayed in the inset plot of Figure 1.

The geometric intramolecular parameters of glycerol are displayed in Table 3, and the coefficients of potential function Table 3. Geometric Parameters of Glycerol

a

bond length

nm

bond angle

deg

O−C1 O−C2 C1−C2

0.1425 0.1425 0.1529

O−C1−C2 O−C2−C1 C1−C2−C1

111.27 111.27 112.8

Atom index is displayed in the inset plot of Figure 1.

used are from the Class-2 force field (COMPASS).31,41 Since the VDW interaction between C and H is very weak, it is neglected from the interaction between water/glycerol and CNTs. Using NPT ensemble, we calculated the densities of the bulk glycerol solutions (with different glycerol concentrations) based on the parameters shown in Tables 2 and 3. The calculated density is very close to its real value; e.g., the calculated density of pure glycerol is 1.236 g/cm3, which is about 2% lower than its real value (1.26 g/cm3). Similar to the pure water model employed in our previous work,22 the left end of CNT (connecting with the reservoir) is covered with a cap, and the reservoir is isolated from CNTs before applying impact load. The initial computational cell is equilibrated using NVT ensemble for 150 ps (displayed in Figure 1a). The Nose-Hoover thermostat is used to keep the temperature at 300 K, and the time integration step is set to 1 fs. After the system is equilibrated, the cap is removed and the impact load is applied (the piston begins to push the liquid reservoir). NVE ensemble is employed to investigate the impactinduced infiltration behavior. The constant impact velocity is applied by moving piston with a tiny distance in every 10 fs, and the magnitude of the distance moved is calculated by the impact velocity. The trajectories, velocities, and accelerations of the liquid molecules are monitored during the impact procedure. 25225



Article in ρeff = (Nwinm w + Ngly mgly )/(πR e 2L in)

(1)

where Nin and m are the number of infiltrated molecules and the molecular mass, and the subscripts w and gly represent water and glycerol, respectively, and Lin is the infiltrated length of liquid. The value of Lin is the largest axial position of the infiltrated liquid. After the liquid reaches the end of tube, the value of Lin is equal to the tube length. The effective occupied radius (Re) of infiltrated liquid used in eq 1 is calculated from the largest radial distance of the atoms of C and O of liquid molecules inside CNTs (H atoms are neglected since its atomic mass is much less than that of C or O). The value of Re is typically larger for structure II than structure I and slightly increases with the concentration of glycerol (the variation range of Re with ϕ is less than 1%). After interacting with the reflected mechanical wave, the value of ρeff will rapidly increase, and thus the density of structure II is much higher than that of structure I (ρeffI < ρeffII). Similar to the results of pure water, the values of ρeffI and ρeffII decrease with the tube radius R, and ρeffI is lower under a higher impact speed v, whereas ρeffII is less sensitive to v. With the increase of the concentration of glycerol (ϕ), the ratios of both ρeffI/ρ0 and ρeffII/ρ0 decrease. The variation range of ρeffI/ρ0 is smaller for a higher value of v (e.g., 5−10% for v = 1000 m/s and 15−25% for v = 100 m/s), whereas the variation range of ρeffII/ρ0 is essentially not sensitive to v; the variation ranges of both ρeffI/ ρ0 and ρeffII/ρ0 decrease with the increase of R. The dependence of the density of infiltrated liquid on the solution concentration ϕ is mainly caused by the molecule size of liquid. The water molecule is roughly considered to be spherical and with a radius of about 0.145 nm, while the glycerol molecule is in an ellipsoidal shape with a long radius of ∼0.6 nm and a short radius of ∼0.3 nm (estimated by MD simulations). In the present study, the tube size R = 0.67−1.337 nm. For a given nanotube, the smaller molecule will have a higher filling fraction than a larger molecule, and this effect decreases with the increase in tube size. Thus, ρeffII/ρ0 will decrease with the increase of ϕ and this variation decreases with the increase of tube size. When the driver for liquid infiltration is kinetic energy (i.e., v is large), the effect of ϕ on ρeffI/ρ0 is small (i.e., the kinetic energy effect is not related to the molecular size), whereas when the infiltration driver changes to the potential energy gradient (i.e., pressure), this effect increases because the smaller molecules is easier to reorganize their structures to reduce the potential energy. Figure 3 shows the glycerol concentration variation between the infiltrated solution and its bulk counterpart under two different impact velocities, displayed as the ratio of ηin/η0, where ηin = Ningly/Ninw and η0 = N0gly/N0w, the number of molecule ratio of glycerol to water of the infiltrated solution and its bulk counterpart, respectively. ηin is calculated when the reflected wave reaches the tube opening, which means that the density of infiltrated liquid becomes stable. The value of ηin/η0 is less than 1, and it is smaller for a smaller tube; it is essentially not sensitive to ϕ. Thus, the concentration of glycerol solution will be reduced after infiltrating into the nanopore, especially for small nanotubes. The main reason is that water molecules more easily enter into nanopores than glycerol because the molecular size of glycerol is roughly 3−4 times of water, and the molecular size effect is stronger for a smaller pore. Figure 4 shows the molecular structure distribution probability of the glycerol molecules at the opening of CNTs, displayed by α in the figure, which can show the manner in which glycerol molecules enter into CNTs. α is an angle between the long axis direction of glycerol (defined by the line connected two O atoms in a glycerol molecule) and the axial

Figure 2. Effective density of infiltrated glycerol solution in CNTs, display as ρeffI/ρ0 and ρeffII/ρ0, where ρeffI and ρeffII are the effective densities of infiltrated liquids with structure I and II, shown as dashed/ solid lines in the figure, and ρ0 is the liquid density in bulk phase: (a) (10, 10) tube, (b) (15, 15) tube, and (c) (20, 20) tube. 25226



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Figure 3. Concentration change of the infiltrated glycerol solutions into CNTs, displayed by ηin/η0, where ηin and η0 are the ratio of the number of glycerol molecules to the number of water molecules inside CNTs or in bulk solutions, respectively.

direction of the tube (as shown by the inset plot of Figure 4). When glycerol molecules enter into CNTs, the peak of α distribution is at α ≈ 35°, which is not adjusted for a smaller tube or a lower impact velocity. Thus, there is a larger repulsion for glycerol molecules entering into CNTs, especially for small tubes. 3.2. Structure of Infiltrated Glycerol Liquids. In our previous work,22 it is found that the impact energy is mainly absorbed in the reflected procedure of the mechanical wave, in which the density of infiltrated liquid is rapidly increased by the interaction between the reflected wave and the infiltrated liquid. Therefore, we mainly study the effect of the liquid concentration ϕ on structure II of the infiltrated liquid in the present work, which can be shown by the mass distribution function (MDF) of infiltrated liquids along the radial distance. Because glycerol solutions include two types of different molecules (water and glycerol), the MDF in the present work is calculated based on the mass density: λ(r) = mr(r)/(2πrΔrLin)/ρ0, where mr is the mass of solution molecules distributed inside CNTs within a tubular space with inner radius r and outer radius r + Δr. Figure 5 shows the MDF of the infiltrated glycerol solutions with different ϕ under two different impact velocities (v = 200, 1000 m/s, displayed as the dashed/solid lines, respectively). For clarity purposes, the reference of curves in the figure are shifted up by 0.6n (n = 0−3 for ϕ = 0.6, 0.4, 0.2 and 0, respectively). With the increases of ϕ, the peak of MDF becomes wider and lower because the number of water molecule (small size) decreases and the number of glycerol molecule (big size) increases, which also shows that the solid−liquid interaction is stronger for the solution with a lower ϕ. Similar to pure water, for the tube with a larger R, the magnitude of MDF of the solution molecules located far away from the tube wall approaches one; with the increase of the impact velocity, the peak value decreases and the peak position has a slight larger radial distance from center. These results also show that there is a larger structure difference between the infiltrated liquid molecules inside smaller tube or with a larger impact velocity and their bulk counterpart than those inside larger tubes or with a lower impact velocity. In

Figure 4. Structure distribution probability of glycerol molecules at the opening of CNTs, which shows how glycerol molecules enter into CNTs, displayed by α, an angle between the tube axis and the long axis of the glycerol molecule: (a) (10, 10) tube, (b) (20, 20) tube. The distribution probability is counted based on more than 3000 molecules (from more snapshots).

addition, the infiltrated glycerin molecules have a significant structure change compared with their bulk counterpart. Figure 6a shows the distribution probability of α of the infiltrated glycerin molecules (structure II), which shows the distribution peak is around 90° (i.e., perpendicular to the tube axis), while there is no clear peak for bulk glycerol (i.e., quite uniformly distributed), as shown in Figure 6b. The α distribution is not related to tube radius, impact velocity, or concentration. Because the system potential energy is directly related to its structure, there will be a larger increase in the system energy when liquids are pushed into a smaller tube or with a higher impact velocity or a higher concentration, which will be discussed in the next section. 3.3. Interfacial Energy of Infiltrated Glycerol Liquids. After liquids are infiltrated into CNTs, the potential energy of system will be increased because of the new created solid−liquid interaction energy (Uint) and the potential energy difference between nanophase liquid and its bulk counterpart (ΔUliquid). In 25227



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Figure 6. Structure distribution probability of glycerol molecules: (a) inside (20, 20) tube, (b) in bulk solution. The distribution probability is counted based on more than 10000 molecules (from more snapshots). 0 ΔUtot = ΔUliquid + Uint = Uliquid + CNT − UCNT − Uliquid

(2)

where Uliquid+CNT, UCNT, and U0liquid are the total energy of the filled nanotube by liquid, the potential energy of CNT and bulk liquid, respectively. Because both ΔUliquid and Uint are caused by the solid−liquid interaction (VDW interaction), we defined the value of ΔUtot as the interfacial energy. To consider the effect of nanotube radius, the interfacial energy density is also defined: γ = ΔUtot/S, where S is the solid−liquid interface area, and S = 2πReLin. As we have already discussed, the concentration of glycerol solution will be changed after infiltrated into nanotube, and thus it is more complicated to calculate the value of γ for glycerol solutions. For bulk glycerol solution, an effective potential energy per molecule can be defined as the weighted average of the molecular potentials of glycerol (u0gly) and water (u0w) molecules:

Figure 5. Mass distribution function (MDF) of the infiltrated glycerol solutions with structure II in different tubes: (a) (10,10) tube, (b) (15, 15) tube, and (c) (20, 20) tube (from more snapshots).

MD simulations, the potential energy change of system can be easily calculated by the following expression:21

0 u0′ = ugly ϕ + uw0(1 − ϕ)

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(3)



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The interaction energy between glycerol and water in bulk solution is assumed to be equally assigned to both glycerol and water molecules, and thus 0 0 0 0 ugly = (Ugly + 0.5Ugw )/Ngly , u w0 = (U w0 + 0.5Ugw )/Nw

(4)

U0gly,

U0w,

U0gw

where and are the potential energies of glycerol and water molecules, and the interaction energy between glycerol and water molecules in bulk glycerol solution, respectively. Ngly and Nw are the numbers of glycerol and water molecules in bulk glycerol solution, respectively. The values of u0gly and u0w are not related to the values of Ngly and Nw used in the present study, based on the computational cell size effect checking. Both the u0glyand u0w calculated by MD simulations slightly increase with the decrease of ϕ and the variation slope is higher for u0gly, as shown in Figure 7. The lines in the figure are linear fitting curves.

Figure 7. Effective potential energy per water/glycerol molecule in the bulk glycerol solution with various concentration ϕ.

After glycerol solutions are pushed into CNTs, the interfacial energy density can be estimated as in 0 γ = (Uliquid + CNT − Ngly ugly − Nwinu w0 )/S

Ningly

(5)

Ninw

where and are the number of infiltrated glycerol/water molecules, respectively. If Ningly reduces to zero, eq 5 will converge to the γ of pure water. Similar to the result of pure water, the γ increases with the impact velocity v and reaches the maximum value for the (15, 15) tube (R ≈ 1 nm) in the current study range; the γ of structure II is significantly higher than that of structure I of the infiltrated glycerol solutions. With the increase of ϕ, γ rapidly increases, as displayed in Figure 8; e.g., γ increases by up to 300% when the liquid changes from pure water to pure glycerol. This change is mainly caused by the different molecular size: For large molecule glycerol, the number of molecules inside CNTs (e.g., along the radial or circumferential directions of tube) will be lower than that of small molecule water, especially for small tube (10, 10), which leads to that the liquid−liquid interaction inside CNTs becomes weaker. This further causes a larger conformation difference between the infiltrated liquids and their bulk counterparts, and then a larger potential energy difference per liquid molecule will be created; on the other words, the nanoconfinement has a larger effect on the liquid

Figure 8. Interfacial energy density of infiltrated glycerol solutions inside different CNTs: (a) (10, 10) tube, (b) (15, 15) tube and (c) (20, 20) tube. 25229



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molecule with a larger size. Thus, the glycerol solutions with a higher ϕ will have a larger γ. 3.4. Transport Behavior of Infiltrated Glycerol Liquids. Figure 9 shows the infiltration length (Lin) of the glycerol solutions varying with the simulation time under different impact velocities, and the slope of lines in the figure actually represents the flow rate (vt) of solutions through CNTs. Under a higher impact velocity (e.g., v = 1000 m/s), liquid molecules are carried into nanotubes by the mechanical wave initiated by impact load, and they transport through CNTs with the same speed as the wave.21,22 Because of the high transport speed, the VDW interaction between solid wall and liquid molecules has a very weak effect on the liquid flow, and thus the flow rate is not sensitive to the tube radius, but only related to the density and bulk modulus of flow (the wave speed scales with (E/ρ)1/2, where E is the bulk modulus of liquid). The glycerol solution with a higher ϕ has a higher ratio of E/ρ (e.g., the E/ρ of pure glycerol is about 60% higher than that of pure water), and thus it leads to a higher flow rate (i.e., a larger slope in the figure). With a lower impact velocity (e.g., v = 100 m/s), liquid molecules are pushed into nanotubes by the reservoir pressure and transport through tube with a lower speed. The stronger solid−liquid VDW interaction in CNTs with a larger radius will have a larger resistance to the flow through CNTs, which leads to a lower flow rate in larger tubes (a smaller slope in the figure). Because glycerol molecule has a larger size and more complex configuration, it is more difficult to create a stronger solid− liquid VDW interaction by adjusting atomic positions, which leads to a lower flow resistance. This can be clearly shown by the MDF of infiltrated glycerol solutions (see Figure 5), in which the peak of MDF (representing the solid−liquid VDW interaction strength) decreases with the increase of ϕ. Thus, the glycerol solution with a higher ϕ has a higher flow rate under a lower impact velocity. For the infiltrated liquid flow, the solid−liquid VDW interaction will create a friction, which is also a contribution to the system energy absorption. In the present work, the 9-6 Lennard−Jones (LJ) potential is adopted to compute the friction force: ⎡ ⎛ r ⎞9 ⎛ r ⎞6 ⎤ U (r ) = ε ⎢ 2 × ⎜ 0 ⎟ − 3 × ⎜ 0 ⎟ ⎥ ⎝r⎠ ⎝r⎠ ⎦ ⎣

(6)

where r denotes the distance between two atoms, ε and r0 are the LJ parameters, respectively. The VDW force between two atoms is calculated as

fij⃗ = −

dUij(r ) dr ⃗

(7)

The friction force is regarded as the summation of all the VDW forces (axial component) acted on each infiltrated liquid molecule. Additionally, the hydrogen−carbon interaction is neglected because it is minor compared to the carbon−carbon, carbon−oxygen interactions. Note that the axial velocities of liquid molecules with structure II is almost zero, only structure I is considered for the friction calculation. It is found that the contribution of the friction force to the overall energy absorption is less than 1%. Thus, similar to the results of pure water, the work done by friction force for glycerol solutions is also very small compared to the interfacial energy, which can be neglected. 3.5. Energy Absorption Efficiency of Infiltrated Glycerol Liquids. The energy absorption density ξ is typically

Figure 9. Infiltration length (Lin) of the glycerol solutions varying with simulation time: (a) ϕ = 1 (pure glycerol), (b) ϕ = 0.6, and (c) ϕ = 0 (pure water). The slope of lines in the figure actually represents the flow rate (vt) of solutions through CNTs. 25230



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used to represent the energy absorption efficiency of energy absorption system/material, which is defined as22

ξ = A̅ γλ

(8)

where A̅ is the specific surface area of CNTs per unit volume, and λ = Re/R, the ratio of the effective radius of water inside CNTs to the CNT radius and λ converges to one when the tube radius R is large enough. Figure 10 shows the value of ξ of glycerol solutions,

Figure 10. Energy absorption density (ξ) of glycerol solutions with different concentration ϕ. The error bar shows the variation range of ξ caused by the different impact velocity v and a higher value of v causes a larger ξ.

where the error bar shows the variation range of ξ caused by the different impact velocities. When v increases from 100 to 1000 m/s, the value ξ can increase by up to 2.2−4.7 times for pure water in the present CNT radius range (the increase is larger for a larger tube). The variation of ξ with v is essentially not sensitive to the solution concentration ϕ, e.g., ξ increases by 2−4 times for pure glycerol in the present range of v. With the increase of ϕ from 0 to 1 (from pure water to pure glycerol), the value of ξ increases by up to about 3 times, which are actually not sensitive to the tube radius R or the impact velocity v. Therefore, the energy absorption density of NEAS can be significantly increased by selecting glycerol solutions as the liquid environment instead of using water. It should be noted that the work done by the piston (W) is different for the glycerol solutions with varying concentration ϕ (or impact velocity v) because the impact load is applied by displacement control, which is described as21 W = ab

∫0

l

P(x) dx

(9)

where a and b are the lateral sizes of piston, l is the final displacement of piston, and P is the pressure applied on the piston. The work done by piston can be easily calculated from the variation of system energy based on the NVE ensemble because the system energy will be a constant if there is no extra energy introduced into the system. The work W increases with the increase of v or the decrease of R for all liquids, e.g., the W of pure water can be increased by 4.5 times from one case (R = 1.37 nm and v = 100 m/s) to the other case (R = 0.67 nm and v = 1000 m/ s), as shown in Figure 11. For glycerol solutions, the W also

Figure 11. (a−c) Piston work applied on the NEAS under the different impact velocities.

increases with the concentration ϕ, e.g., the work W will increase by 2.8−4.8 time from ϕ = 0 (pure water) to ϕ = 1 (pure glycerol). 25231



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difference between the infiltrated liquid and its bulk counterpart, i.e., a higher potential energy difference. Thus, the interfacial energy density is higher for the glycerol solution with a larger ϕ; in the other words, a higher solution concentration ϕ will cause a higher energy absorption density. When water is replaced by pure glycerol in NEAS, the energy absorption density can be increased by up to 3 times. In addition, although the piston pressure increases with the solution concentration ϕ because the impact load is applied by displacement control, the infiltration behavior of liquids is not related to the piston pressure as long as this pressure is higher than the infiltration pressure of nanotube. This result can be validated by the density of infiltrated glycerol solutions, which is not sensitive to the piston pressure. Introducing glycerol solutions into NEAS can not only increase the energy absorption density but also can adjust the infiltration pressure of NEAS, which is related to the protection range of NEAS. Moreover, the glycerol solution has a much lower frozen point than water, which can make it possible to use NEAS under a low temperature condition. Therefore, the performance of NEAS can be greatly improved by changing the liquid system from water to glycerol solutions.

However, the high energy absorption density of glycerol solutions with a larger ϕ is not related to the high value of W. A much higher bulk modulus of glycerol than water (Eglycerol = 4.5 GPa and Ewater = 2.15 GPa) causes a larger piston pressure for glycerol solutions at the same displacement of piston, and thus, a higher W is introduced. The effect of pressure (P) on infiltration behavior can be clearly shown by its effect on the density of infiltrated liquids. From Figure 2, it is found that when v increases from 100 to 1000 m/s, the density of pure glycerol (ϕ = 1) slightly decreases (∼5% lower), whereas the piston pressure P increases by up to about 3.4 times. The similar results are obtained for pure water and other glycerol solutions. In addition, the value of W for pure glycerol (ϕ = 1) at a lower impact velocity (e.g., v = 100 m/s) is close to that for pure water (ϕ = 0) at a higher impact velocity (v ≥ 500 m/s) for the larger CNT (20, 20) (R = 1.337 nm). Although the piston pressure P is highly different for the glycerol solutions with various values of ϕ, it essentially does not affect the density of infiltrated liquids. Therefore, a higher energy absorption density of glycerol solution with a larger ϕ is not related to the higher piston work. Noted that the glycerol solutions with various ϕ should have the different infiltration pressure (Pcr, the threshold for liquid infiltration), and the energy absorption procedure will be performed only when the piston pressure P is larger than Pcr. Therefore, introducing glycerol solutions into NEAS can not only increase the energy absorption density but can also adjust the protection range of NEAS which is decided by the value of Pcr. In addition, the NEAS made by water will lose its functions when the temperature is lower than 0 °C because it is frozen, whereas the frozen point of glycerol solution is much lower than that of water,42 and thus the new NEAS made by glycerol solutions can be used in low temperature condition.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 086-01-62756284. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the financial support provided by the Ministry of Science and Technology of China (2013CB933702) and the National Natural Science Foundation of China (11172002).

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4. CONCLUSIONS The performance of nanoporous energy absorption system based on glycerol solutions and CNTs is investigated using molecular dynamics simulations, and the effects of the loading rate, CNT size, and solution concentration are also considered. It is found that the energy absorption density of NEAS can be significantly increased by increasing the concentration of glycerol in the liquid environment. To the best of our knowledge, this is the first simulation work to consider the effect of the different liquid environment on the energy absorption efficiency of NEAS. Similar to pure water, the energy absorption procedure also includes two stages: (I) liquid molecules are carried into CNTs by mechanical wave; (II) infiltrated liquid molecules are compressed by the reflected mechanical wave. The mechanical wave transports faster in glycerol solution than pure water because it has a larger ratio of E/ρ, which causes a faster glycerol solution flow through nanotube. Glycerol molecule has a larger size than water molecule, and thus it is more difficult to enter into CNTs, especially for the small tube (10, 10), which leads to a slight lower glycerol concentration inside CNTs than its bulk counterpart. In addition, the solid−liquid VDW interaction has a lower effect on the transport behavior of glycerol because it has a larger size and more complicated configuration. Therefore, the flow friction created by the solid−liquid interaction can be also neglected, and the energy absorbed by NEAS is mainly from the interfacial energy. Compared with smaller molecule (e.g., water), for a given nanotube, the number of infiltrated molecule is lower for the molecule with a larger size (e.g., glycerol), and thus the liquid− liquid interaction is weaker, which leads to a larger structure

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