Reusable Energy Absorption Performance Based on Nanofluidic

Feb 22, 2016 - ABSTRACT: Using molecular dynamics simulations, we inves- tigated the reusable performance of the nanofluidic energy absorption system ...
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Reusable Energy Absorption Performance Based on Nanofluidic Systems Hailong Liu and Guoxin Cao* HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China ABSTRACT: Using molecular dynamics simulations, we investigated the reusable performance of the nanofluidic energy absorption system (NEAS) to dissipate the impact energy created by a drop hammer (simulated by a carbon plate with an initial velocity and mass). The effects of nanopore flexibility and surface roughness on the reusable performance of NEAS are also considered. The results clearly shown that NEAS can only convert the mechanical energy into the solid−liquid interfacial energy (i.e., store it in the system) in the loading stage; the stored interfacial energy is gradually released and finally dissipated as heat by the solid−liquid interaction in the unloading stage. Therefore, the unloading response of NEAS decides whether or not the system can be reused for energy absorption, which is sensitive to the loading condition. Although NEAS behaves as a one-time used energy absorption material under quasi-static loading condition, it can be reused under dynamic loading condition. In addition, the nanopore surface roughness also affects the unloading behavior of NEAS. To the best of our knowledge, this is the first time to theoretically validate the reusable performance of NEAS.

1. INTRODUCTION Because of its potential applications in mitigating impact/blast loadings, NEAS has attracted considerable research interest, which mainly consists of two functional components: lyophobic nanoporous materials and nonwetting liquid.1−5 At ambient conditions, liquid molecules cannot infiltrate into nanopores spontaneously because of capillarity. Only when the applied external pressure is higher than the capillary pressure will liquid molecules intrude into nanopores,2,6−10 converting mechanical energy into the solid−liquid interfacial energy.11−13 Nanoporous materials commonly have an ultralarge specific surface area (100−2000 m2/g); thus, NEAS will have a much higher energy absorption density compared with traditional energy absorption materials. Moreover, the energy absorption mechanism of NEAS is mainly based on the interaction between nanopores and liquid, which makes it possible that NEAS may protect objects against periodic loadings and behave as a reusable energy absorption material.1,14 For the conventional energy absorption materials (used only once for energy absorption), the performance of energy absorption is only decided by the loading stage. However, due to the different energy absorption mechanism, it is possible for NEAS to realize the repeatable energy absorption, which highly depends on the system response in the unloading stage. The prerequisite of the repeatable energy absorption of NEAS is that the infiltrated liquid molecules can flow out of nanopores during the unloading stage. Actually for NEAS, the loading stage is only involved in the energy conversion (the impact work is converted into the interfacial energy stored inside of NEAS), but the unloading stage is related to the energy damping (the impact work is finally dissipated into heat by the © XXXX American Chemical Society

liquid/solid interface friction when the infiltrated liquid molecules flow out of nanopores). If liquid molecules cannot flow out of nanopores during unloading stage of the first loading period, there is no space for new water entering into nanopore in the next loading period, and thus the NEAS only behaves as a one-time used energy absorption material (i.e., will not protect against repeatable loadings). Therefore, the performance of the reusable NEAS not only is related to the system response in the loading stage but also closely depends on the unloading behavior. The quasi-static compression test (loading rates of 0.5−7.5 mm/min) of NEAS (based on liquid water) shows that most of the infiltrated water molecules cannot flow out of the nanopores during unloading,4,5 whereas it was also reported that adding electrolyte into water will facilitate the liquid to flow out during unloading procedure.14 In addition, Han et al.15 reported that the “non-outflow” phenomenon is not sensitive to the loading rate: the infiltrated glycerol molecules cannot flow out of the nanopores when the loading rate (v) increases from 1 to 90 mm/min. However, the opposite results were also reported that water molecules will stay inside nanopores during unloading if v < 1 mm/min, whereas water molecules gradually flow out of the nanopores with the increase of v and water molecules will spontaneously flow out of the nanopores when v reaches 50 mm/min.16 The “non-outflow” phenomenon might depend on the atomic types of nonwetting liquid and Received: January 6, 2016 Revised: February 18, 2016

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The Journal of Physical Chemistry C nanoporous materials selected in the system as well as the environment temperature.6,17 Following the experimental investigations, many theoretical or numerical studies have been developed to investigate the performance of NEAS.11−13,18 Since molecular dynamics (MD) simulation can provide the details about the infiltration procedure of liquid into nanopores under loading and the defiltration procedure under unloading (e.g., the critical infiltration pressure, the transport velocity of liquid through nanopores, and the structure and energy of infiltrated liquid molecules), it become a main tool to investigate the working mechanism of NEAS. Currently, most of the reported numerical/theoretical works of NEAS are focusing on the system response in the loading stage. For example, using MD simulations, the basic mechanism of impact energy conversion of NEAS was investigated;11,12 the interaction between impact wave and infiltrated liquid molecules and the difference between the structure of infiltrated water molecules inside nanoporous and their bulk counterpart were identified;12,18 and the effect of liquid environment on the energy absorption performance of NEAS is optimized.13 However, to the best of our knowledge, the response of NEAS in the unloading stage has not been systematically investigated yet. In addition, the displacement control load (e.g., simulated by a piston with a constant moving velocity) is typically used in the previous studies of the energy absorption performance of NEAS, whereas there is a significant difference between the real impact load and the one used in above numerical studies. Actually, a more realistic impact loading mode should be used in the numerical simulations in order to get the real energy absorption performance of NEAS. In this paper, using MD simulations, the response of NEAS to a drop hammer (with an initial velocity and a mass) is investigated and the reusable performance of energy dissipation of NEAS is further validated. In addition, the effects of loading condition, tube surface roughness, and tube flexibility on the unloading behavior of NEAS are also considered.

Figure 1. Computational models used in MD simulations: (a) the initial state of NEAS with a smooth tube; (b) the rough tube model.

end open (connecting with the reservoir) and another end closed. All MD simulations are carried out using LAMMPS,22 which is a classical molecular dynamics simulation software from Sandia National Laboratory. The short-range nonbond interactions between two atoms are modeled by the LennardJones (L-J) potential: ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ U = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝r⎠ ⎦ ⎣⎝ r ⎠

(1)

where r is the atomic distance and ε and σ are the energy and length parameters, respectively. The SPC/E water model23 is used to simulate water molecules. The SHAKE algorithm24 is used to constrain the internal geometry of water molecules (bond length and bond angle). The L-J parameters between O and C atoms are εOC = 0.074 93 kcal/mol and σOC = 0.319 nm corresponding to a hydrophobic CNT (contact angle of 110°).25 The C−H nonbond interaction is neglected because it is much weaker compared with the C−O nonbond interaction. The cutoff distance for the VDW interaction is set to be 1.2 nm which is considered to be accurately describing the VDW interaction of water in the MD simulations.26,27 The long-range Columbic interaction among water molecules is calculated using the particle−particle particle−mesh (PPPM) method.28 A time integration step is set to 1.0 fs. Initially, the tube opening is covered by a lid and water molecules cannot infiltrate into the CNT, and the water molecules in reservoir are equilibrated for about 200 ps using the NVT ensemble. The Nosé−Hoover thermostat29 is used to keep a constant temperature of 298 K. When the system reaches equilibrium, the lid is removed and the drop hammer then begins to impact the reservoir. In experiments, the NEAS are tested with both quasi-static and dynamic loading conditions,2,30 and thus, both of these two loading conditions are considered in the present simulations. For quasi-static loading conditions (controlled by displace-

2. COMPUTATION METHODS The computational model includes a carbon nanotube (CNT) and a water reservoir, as shown in Figure 1a. The reservoir (5.03 × 5.08 × 7.46 nm) includes 6000 water molecules (corresponding to a water density of 0.997 g/cm3 of the reservoir). The reservoir is bounded between two parallel rigid carbon atomic planes: the lower one is fixed and with a hole in the center, through which water molecules can be pushed into the CNT; the upper plane is moveable to mimic a drop hammer including Nh = 1008 carbon atoms. Periodic boundary conditions are applied along the lateral directions (x and y directions). The elastic modulus of the nanoporous materials used in NEAS is typically much larger than the bulk modulus of water, and thus, the deformation of nanoporous materials is commonly neglected in simulating the response of NEAS during the loading procedure (e.g., rigid CNTs are widely used to mimic nanopores).11,19−21 In addition, the working mechanism of NEAS is mainly based on converting mechanical energy to the liquid−solid interfacial energy,12,13 which is not sensitive to the flexibility of nanopores. However, the interfacial energy will be dissipated as heat by the solid−liquid interaction during the unloading procedure, which might be highly related to the flexibility of nanopore. Thus, both rigid and flexible CNTs are considered in the present work to simulate the nanopore of NEAS. The length of CNT L = 7.0 nm with one B

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The Journal of Physical Chemistry C ment), the hammer gradually moves downward with a constant displacement increment (0.03 nm), and the system is equilibrated for 1.2 ns with the temperature keeping at 298 K after one move. The external pressure P is calculated as P = F/ Ah, where Ah = lxly is the area of the hammer (lx and ly are the lateral sizes of drop hammer) and F is the total force applied on reservoir by the drop hammer: nh

F=

nw

∑ ∑ fij i=1 j=1

dzij drij

,

fij = −

dUij drij

(2)

where nh and nw are the numbers of hammer atoms and the water molecules inside the cutoff distance from hammer, f ij and Uij are the L-J interaction force and energy between atom i (hammer) and atom j (water), and zij is the projection of rij along the z-direction. After the CNT is fully filled with water molecules, the drop hammer moves back (the displacement increment of 0.03 nm) in the same way as the loading process until P reduces to zero. For dynamic loading conditions, a drop hammer impacts reservoir with varies initial velocities and masses and the whole impact procedure is simulated using NVE ensemble. After impacting the reservoir, the velocity of the drop hammer diminishes and then the hammer is bounced back, which is similar to the real impact. After the drop hammer bounces back, the interaction between the hammer and reservoir will be neglected, and then, the responses of infiltrated water molecules are monitored. The range of the molar mass of hammer is selected as m = 2−20 kg/mol (the total mass of drop hammer M = Nhm/NA, where NA = 6.02 × 1023, the Avogadro’s constant), and the initial velocity range of hammer is used as v = 50−90 m/s. In order to investigate the size effect of nanopore on the unloading behavior, three CNTs are studied in the present work, including (10, 10), (15, 15), and (20, 20) CNTs with the tube radii of 0.67, 1.0, and 1.34 nm, respectively.

Figure 2. Relationship between the external pressure and nominal volumetric strain of NEAS under quasi-static loading condition.

relationship between the external pressure (P) and the volumetric strain of water reservoir (η = ΔV/V0, where V0 is the initial reservoir volume and ΔV is the reservoir volume change). At the beginning of loading, water molecules cannot infiltrate into the CNT because the external pressure is lower than the capillary pressure (Pc), and consequently, the first linear part of the loading curve (curve AB) corresponds to the compressibility of bulk water. When P = Pc, water molecules infiltrate into the CNT, which corresponds to a plateau of the P−η curve (curve BC). When the CNT is filled with water molecules, P linearly increases with η again (curve CD). The unloading curve (DE) is also nearly a straight line, and there is a residual volumetric strain η = 0.07 when P reduces to zero (see Figure 2), which means that most of the infiltrated water molecules are locked inside nanotube after unloading (i.e., almost none of the infiltrated water molecules flows out). This “non-outflow” phenomenon indicates that NEAS can be used only once to absorb the mechanical energy under the quasistatic loading condition since no more water can infiltrate into the CNT in the next loading period. Under dynamic load (impact), the variation of the interfacial energy (ϕ) and the number of infiltrated water molecules (Nin) with the simulation time (t) are shown in Figure 3, where the initial impact velocity of the drop hammer is set as v = 60 m/s, the molar mass of the hammer atom is m = 5000 g/mol, and the impact work W = Mv2/2 = Nhmv2/2 = 1.507 × 10−17 J. After impacting the reservoir, the hammer bounces back and the unloading stage starts: The infiltrated water molecules start to flow out of the CNT. As shown in Figure 3, ϕ decreases with Nin, and the interfacial energy is fully released (ϕ = 0) when there are no water molecules inside the CNT (Nin = 0). The duration time of outflowing procedure (tout) is much longer than that of the intrusion procedure (tin): tin ≈ 45 ps and tout ≈ 5.5tin (about 250 ps) for the case shown in the figure. Since all infiltrated water molecules will flow out of the CNT in the unloading stage, the NEAS changes back to its original state and it is ready for the next loading period, which means that the NEAS can be reused to behave as the impact mitigation material under the dynamic loading conditions. The impact work can be quickly converted into the interfacial energy stored inside nanopores during loading, and then the stored interfacial

3. RESULTS AND DISCUSSION 3.1. Unloading Behavior of NEAS under the QuasiStatic and Dynamic Loading Conditions. The energy absorption procedure can be divided into the intrusion stage (loading stage) and the outflowing stage (unloading stage). During the loading stage, the hammer press the reservoir, pushing water molecules into the CNT, and the mechanical energy is converted into the interfacial energy (ϕ). ϕ can be described as the equation12 0 ϕ = ξA = UH2O + CNT − UCNT − NineBulk

(3)

where ξ is the interfacial energy density, A is the solid−liquid interface area, U0CNT is the potential energy of empty CNT, Nin is the number of infiltrated water molecules, and eBulk = −7.744 × 10−20 J is the effective potential energy per bulk water molecule. UH2O+CNT is the total potential energy of both CNT and the infiltrated water molecules: UH2O+CNT = Uint + Uw + UCNT, where Uint is the interaction energy between CNT and infiltrated water molecules, the energy of infiltrated water molecules Uw = Ninew (ew is average molecular energy per infiltrated water molecule), and UCNT is the potential energy of CNT after infiltration (U0CNT = UCNT for rigid CNT). Thus, ϕ increases with both ew and Nin; ϕ reaches the maximum (ϕtot) when Nin reaches the maximum value (Ntot). Under quasi-static load, the loading and unloading curves of NEAS are shown in Figure 2, which are described by the C

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Figure 3. Variation of the interfacial energy and the number of infiltrated water molecules inside (15, 15) CNT with simulation time under the dynamic loading condition.

Figure 4. Radial distribution functions of the infiltrated water molecules under quasi-static and dynamic loading conditions. The dashed line shows the position of the first solvation shell (FSS) under quasi-static loading.

energy is slowly released as heat during unloading. It should be noted that the heat will be dissipated by the thermal vibration of nanopores in the real condition, whereas the heat will be held as the higher random vibration velocity of water molecules in the present simulations since the present CNT is rigid. The above results show that the unloading behavior of NEAS strongly depends on the loading conditions. Under quasi-static load, infiltrated water molecules cannot flow out of the nanopore during unloading, whereas the infiltrated water molecules will flow out in the unloading stage under the dynamic load. The aforementioned simulation results can be further verified by the experimental results: On the basis of βzeolite and water system, Sun et al.30 showed that no water flows out of the nanopores during quasi-static compression test, whereas water can flow out of the nanopores spontaneously under the drop hammer impact test. Under the quasi-static loading condition, there is sufficient time for infiltrated water molecules to restructure themselves forming a new metastable structure inside CNTs (i.e., water molecules stay inside some local potential well created by the solid−liquid interaction). It means that even though the infiltrated water molecules have a higher absolute potential energy than that of their bulk counterpart, they still stay inside if there is no activation energy to overcome the potential barrier of potential well. Because of this potential barrier, the infiltrated water molecules will stay inside the CNT after unloading under the quasi-static loading condition. However, under dynamic loading conditions, it is difficult for water molecules to stay at their equilibrium positions (with the lowest potential position or the bottom of potential well) due to a higher kinetic energy, which can be shown by their radial distribution functions (RDFs). This result is the same for all different tube sizes, and for the simplicity purpose, we only show the result of the tube with R = 1 nm. Figure 4 shows the RDFs of infiltrated water molecules, in which the dash-dotted lines represent the RDFs of infiltrated water molecules at point C and point E (in Figure 2) under quasi-static loading condition, and the solid line represents the RDF of infiltrated water molecules under the impact velocity of 60 m/s when Nin = Ntot. Under dynamic loading condition, the peak position of the first solvation shell (FSS) of RDF is closer to the CNT wall than its quasi-static counterpart, which

indicates that the infiltrated water molecules deviate from the solid−liquid equilibrium positions. In addition, the water density inside CNT under dynamic impact (Nin = 503) is 12% higher than that under the quasi-static loading condition (Nin = 447, at point C) before outflow (this can be shown by a much higher peak value of FSS in Figure 4). Therefore, under dynamic impact, the potential energy of the infiltrate water molecules is much higher than that under the quasi-static loading condition, e.g., ϕ = 413 × 10−20 J under impact but ϕ = 119 × 10−20 J for quasi-static loading condition (decreased by about 70%). Consequently, under dynamic impact, the potential barrier is much lower than that under the quasi-static loading condition (i.e., a much lower activation energy is needed). 3.2. Effects of the Initial Velocity and Mass of Drop Hammer on the Unloading Behavior. In our previous works,12,13 the impact load is applied by the displacement control: a piston with a constant velocity impacts the reservoir, but the displacement of piston is arbitrarily set during the impact procedure which might cause a very high impact pressure (not true for the real impact). In the present work, the impact is applied based on the mechanical energy (or impact work) W = Mv2/2, which is quite close to the real impact. Figure 5 shows the impact pulse profile (reservoir pressure versus simulation time), and the impact intensity can be adjusted by varying either mass or initial velocity of the hammer. With the fixed m and increasing v, Nin slightly increases (Ntot is higher for a higher v) and reduces to zero after unloading for all cases (the Nin−t and ϕ−t relationships under different v are very similar to the results displayed in Figure 4), i.e., all water molecules flow out after unloading; the tube will be filled faster (Ntot is reached with a smaller tin), but the flow-out time (tout) is essentially not sensitive to v (e.g., tout is quite close with each other for the different cases). Ntot just slightly increases with v (e.g., Ntot only increase by 20% when v increases from 50 to 90 m/s). The ϕ is more sensitive to v than Nin since ew will increases with v, which agrees very well with our previous findings.18 If v is fixed and m increases, the Nin−t and ϕ−t relationships also show the similar trends as those determined D

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Figure 5. Variation of the reservoir pressure with simulation time under different impact velocities, v = 50−90 m/s.

with the fixed m and various v. Actually, it is found that even though the values of m and v are different, Ntot and ϕtot will be the same with the same value of W, which indicates that the values of Ntot and ϕtot only depend on the impact work W. In addition, with the decrease of m (v is fixed), tin is invariant but tout decreases. Thus, the filling time is only related to the initial velocity, whereas the flow-out time depends on both the kinetic energy of infiltrate water molecule (determined by v) and the value of Ntot. For a given v, a higher Ntot has a larger tout. These observations are also true for different tube sizes (R = 0.67 and 1.34 nm). Figures 6a and 6b show the relationships between Ntot and ϕtot with the impact work W created from different values of m and v, which clearly show that Ntot and ϕtot are only related to the value of W but not depend upon v or m separately. Ntot just slightly increases with W; e.g., Ntot only increases by 20% while W increases by about 5 times. This small increase in Ntot is caused by the structural deformation of liquid molecule created by a higher impact work. The variation trend of ϕtot with W is similar to that of Ntot with W but with a higher sensitivity since ϕtot depends on both Ntot and ew (also increases with W). It is found that the infiltrated water molecules will flow out for all dynamic cases studied in the present work, and thus, NEAS can successfully be a reusable energy absorption system to protect against the multiple-time impact loadings. 3.3. Effects of Channel Surface Roughness on Unloading Behavior. Although Xu et al.31 have reported that the effect of the surface roughness on the energy absorption behavior of NEAS (in the loading stage), its effect on the unloading response is still not clear. Since the water density inside tube is much higher in the unloading stage (flowout) than that in the loading stage (flow-in) (discussed in our previous work18), the surface roughness might have a much stronger effect on the unloading stage. The sinusoidal wall profile (along the z-direction) is selected to model a channel with a rough surface, which can be described by the function R = R0 + A sin(2πz/λ), where R0 = 1.0 nm is the average radius of tube, A is the amplitude of roughness, and λ is the wavelength of roughness, as shown in Figure 1b. The relative roughness of CNT can be characterized by two dimensionless parameters: A/R0 and λ/R0. A larger value of A/R0 (or a smaller λ/R0) gives

Figure 6. Variation of Ntot (a) and ϕtot (b) with impact work W created from the different values of m and v.

a higher roughness of CNTs. In the present work, A/R0 and λ/ R0 are chosen as A/R0 = 0.1, 0.2 and λ/R0 = 1, 2, 4. The variations of Nin and ϕ with simulation time (t) in a rough tube is shown in Figure 7, in which m = 5000 g/mol and v = 80 m/s, and for the reference purpose, the results of a smooth tube are also displayed in the figure. With the increase of surface roughness (λ/R0 decreases and A/R0 = 0.1), the water outflow is gradually slowed down but the outflow is stopped when λ/R0 = 1, which can be clearly seen from the variation of Nin with t in the unloading stage. If the surface roughness continually increases, the rough tube cannot even be fully filled during the loading stage (e.g., A/R0 = 0.2, λ/R0 = 1) under the present loading condition. Similar as smooth tubes, the variation trend of ϕ has a good agreement with that of Nin. Thus, the above result means that the NEAS cannot be repeatedly used if the nanopore surface roughness is too high. From Figure 7, there are a portion of water molecules flowing out in the unloading stage even with a very high tube surface roughness, and thus, the non-outflow phenomenon of the rough tube under the dynamic loading condition differs from that of the smooth tube under quasi-static loading condition. In the loading stage, water molecules have a very high transport velocity (due to the impact piston),11,18,31 which makes them much easier to overcome the surface roughness E

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of NEAS including the flexible CNTs is investigated in this section. As shown in Figure 8a, the flexibility of tube only slightly reduces the value of Ntot, e.g., ∼10% for the present case (v0 = 80 m/s, m = 5000 g/mol, and R = 1.0 nm); the unloading behavior is also not sensitive to the flexibility of tube: in the unloading stage, all of the infiltrated water molecules gradually flow out of the flexible CNTs, and the value of tout is similar to that of the rigid tube. However, the flexibility of tube has a stronger effect on ϕtot; e.g., ϕtot is ∼30% lower than that in a rigid CNT (as shown in Figure 8b), which means that the flexibility of tube will affect the water structure inside the CNT. Figure 8c shows the RDFs of the infiltrated water molecules in both rigid and flexible CNTs when Nin = Ntot. The RDF of water molecules inside the flexible CNT has a much lower and wider peak, which indicates that the tube flexibility reduces the confinement of CNT (or introduces a weaker solid−liquid interaction energy) on water molecules, and thus, the hydrogen bonds between water molecules are less deformed (or leading to a decrease of ew). Thus, ϕtot in a flexible tube is lower than that in a rigid tube; on the other hand, the energy barrier of the potential well inside tube is also lower, and thus water molecules can flow out of the flexible tube with lower activation energy. In order to evaluate the effect of the tube flexibility on the energy dissipation, a new reference system on the basis of the flexible CNT is built, which includes the same flexible tube and reservoir system, but the temperature of the flexible CNT is kept at 298 K by the direct scaling method and the rest system (including all water molecules and the CNT−water interaction) are still simulated using NVE ensemble. The kinetic energy removed from this reference system by direct scaling can be approximated as the energy dissipated as the heat by the solid− liquid interaction. By computing the total energy difference between this reference system and the original system (without temperature control for CNT), the dissipated energy in both loading and unloading state can be determined, as shown in Figure 9. The energy dissipated as heat is very low in the loading stage, but it is significantly increased during the unloading stage. The total dissipated energy (heat) in the whole energy absorption procedure is estimated as ∼700 × 10−20 J (mainly from the unloading stage), which is very close to the interfacial energy (see Figure 8). Therefore, the mechanical energy absorbed by NEAS (stored as the interfacial energy) can be fully dissipated as heat by the solid−liquid interaction in the unloading stage. To the best of our knowledge, this is the first time to show that the absorbed energy in NEAS can be fully dissipated in the unloading stage.

Figure 7. Variation of the number of infiltrated water molecules (Nin) (a) and the interfacial energy (ϕ) (b) with simulation time inside the rough CNTs.

(like a deeper potential well), whereas in the unloading stage, water molecules have lost their transport velocity (only with random vibration velocity); thus, the surface roughness will have a stronger effect on the unloading stage. In addition, the water molecules infiltrated into the rough tube in advance will experience a larger resistance than those entered later on since the resistance scales with the infiltration length which decreases in the filling process. However, when water molecules flow out of tube in the unloading stage, the water molecules located near the tube opening will experience a lower resistance than those stay deep inside in the tube since they have a much smaller transport distance to flow out. When the tube is rough enough, the friction difference will break the water flow: part of water molecules (near tube opening) will flow out but another part (deep inside) is locked inside, as shown in the inset plot of Figure 7a. 3.4. Effects of CNT Flexibility on Unloading Behavior. Although it is widely considered that the behavior of NEAS in the loading stage is not very sensitive to the flexibility of CNTs,19,32−34 the response of NEAS in the unloading stage as well as the energy dissipating procedure might be closely related to the flexibility of CNTs. Thus, the unloading behavior

4. CONCLUSIONS In this paper, the unloading behavior of NEAS (based on water and CNTs) is investigated using MD simulations, based on which the reusable performance of NEAS is verified. The reusable performance is closely related to the unloading response of NEAS, which depends on the loading conditions and the nanopore roughness. Under quasi-static loadings, the infiltrated water molecules cannot flow out of CNTs in the unloading stage even with a higher potential energy because they can create a metastable structure (with a potential barrier) inside tube thanks to the solid−liquid interaction. However, under dynamic loadings condition, it is more difficult for the infiltrated water molecules to be confined at the equilibrium positions by the solid−liquid interaction since they have a F

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Figure 9. Dissipated energy varying with simulation time for the flexible CNT model.

will flow out of nanopores spontaneously in the unloading stage, which makes it possible for NEAS to be reused. The roughness of nanopore surface also strongly affects the unloading response of NEAS: If the tube is rough enough, the liquid/solid interaction will stop the water outflow and hold a portion of water inside tube in the unloading stage, which causes the “partial outflow” under dynamic loading conditions. In addition, the water outflow in the unloading stage is not sensitive to the flexibility of tube; i.e., all water molecules can flow out after unloading. Actually, the solid−liquid interaction reduces for a flexible tube, which leads to a lower energy barrier for water molecules to flow out. Finally, on the basis of the flexible CNT models, we proved that the absorbed energy stored as the solid−liquid interfacial energy can be fully dissipated as heat during the unloading stage. Therefore, the whole working mechanism of NEAS can be described as follows: the impact work is converted into the solid−liquid interfacial energy stored inside nanopores in the loading stage; in the unloading stage, the interfacial energy is slowly released and dissipated as heat by the solid−liquid interaction.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel 086-01-62756284 (G.C.). 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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Figure 8. Variation of the number of infiltrated water molecules (a) and interfacial energy (b) with the simulation time inside flexible CNTs. (c) RDFs of infiltrated water molecules inside flexible CNTs. For the reference purpose, the results for the rigid tube are also displayed in the figures.

REFERENCES

(1) Eroshenko, V.; Regis, R. C.; Soulard, M.; Patarin, J. Energetics: A New Field of Applications for Hydrophobic Zeolites. J. Am. Chem. Soc. 2001, 123, 8129−8130. (2) Surani, F. B.; Kong, X. G.; Qiao, Y. Two-Staged Sorption Isotherm of a Nanoporous Energy Absorption System. Appl. Phys. Lett. 2005, 87, 251906. (3) Chen, X.; Surani, F. B.; Kong, X. G.; Punyamurtula, V. K.; Qiao, Y. Energy Absorption Performance of Steel Tubes Enhanced by a

higher kinetic energy, and thus, the energy barrier is very low and easily to be overcome. Thus, the infiltrated water molecules G

DOI: 10.1021/acs.jpcc.6b00162 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Nanoporous Material Functionalized Liquid. Appl. Phys. Lett. 2006, 89, 241918. (4) Surani, F. B.; Qiao, Y. An Energy-Absorbing Polyelectrolyte Gel Matrix Composite Material. Composites, Part A 2006, 37, 1554−1556. (5) Qiao, Y.; Punyamurtula, V. K.; Xian, G. J.; Karbhari, V. M.; Han, A. J. Conversion of Mechanical Work to Interfacial Tension in a Nanoporous Silica Gel. Appl. Phys. Lett. 2008, 92, 063109. (6) Kong, X.; Qiao, Y. Thermal Effects on Pressure-Induced Infiltration of a Nanoporous System. Philos. Mag. Lett. 2005, 85, 331−337. (7) Kong, X. G.; Surani, F. B.; Qiao, Y. Effects of Addition of Ethanol on the Infiltration Pressure of a Mesoporous Silica. J. Mater. Res. 2005, 20, 1042−1045. (8) Mo, J. W.; Li, L.; Zhou, J. F.; Xu, D. Y.; Huang, B. L.; Li, Z. G. Fluid Infiltration Pressure for Hydrophobic Nanochannels. Phys. Rev. E 2015, 91, 033022. (9) Cao, G. X.; Qiao, Y.; Zhou, Q. L.; Chen, X. Infiltration Behaviour of Water in a Carbon Nanotube under External Pressure. Philos. Mag. Lett. 2008, 88, 371−378. (10) Cao, G. X.; Qiao, Y.; Zhou, Q. L.; Chen, X. Water Infiltration Behaviours in Carbon Nanotubes under Quasi-Static and Dynamic Loading Conditions. Mol. Simul. 2008, 34, 1267−1274. (11) Cao, G. X. Working Mechanism of Nanoporous Energy Absorption System under High Speed Loading. J. Phys. Chem. C 2012, 116, 8278−8286. (12) Liu, H. L.; Cao, G. X. Interaction between Mechanical Wave and Nanoporous Energy Absorption System. J. Phys. Chem. C 2013, 117, 4245−4252. (13) Liu, H. L.; Cao, G. X. Super Energy Absorption System Based on Nanofluidic Glycerol Solution. J. Phys. Chem. C 2014, 118, 25223− 25233. (14) Kong, X.; Qiao, Y. Improvement of Recoverability of a Nanoporous Energy Absorption System by Using Chemical Admixture. Appl. Phys. Lett. 2005, 86, 151919. (15) Han, A. J.; Lu, W. Y.; Punyamurtula, V. K.; Chen, X.; Surani, F. B.; Kim, T.; Qiao, Y. Effective Viscosity of Glycerin in a Nanoporous Silica Gel. J. Appl. Phys. 2008, 104, 124908. (16) Sun, Y. T.; Li, P. H.; Qiao, Y.; Li, Y. B. Time-Dependent GasLiquid Interaction in Molecular-Sized Nanopores. Sci. Rep. 2014, 4, 6547. (17) Qiao, Y.; Punyamurtula, V. K.; Han, A. J.; Kong, X. G.; Surani, F. B. Temperature Dependence of Working Pressure of a Nanoporous Liquid Spring. Appl. Phys. Lett. 2006, 89, 251905. (18) Liu, H. L.; Cao, G. X. Effects of Impact Velocity on PressureDriven Nanofluid. J. Chem. Phys. 2013, 139, 114701. (19) Qiao, Y.; Cao, G. X.; Chen, X. Effects of Gas Molecules on Nanofluidic Behaviors. J. Am. Chem. Soc. 2007, 129, 2355−2359. (20) Liu, L.; Zhao, J. B.; Yin, C. Y.; Culligan, P. J.; Chen, X. Mechanisms of Water Infiltration into Conical Hydrophobic Nanopores. Phys. Chem. Chem. Phys. 2009, 11, 6520−6524. (21) Xu, B. X.; Qiao, Y.; Chen, X. Mitigating Impact/Blast Energy Via a Novel Nanofluidic Energy Capture Mechanism. J. Mech. Phys. Solids 2014, 62, 194−208. (22) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. J. Comput. Phys. 1995, 117, 1−19. (23) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269−6271. (24) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. NumericalIntegration of Cartesian Equations of Motion of a System with Constraints - Molecular-Dynamics of N-Alkanes. J. Comput. Phys. 1977, 23, 327−341. (25) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. On the Water-Carbon Interaction for Use in Molecular Dynamics Simulations of Graphite and Carbon Nanotubes. J. Phys. Chem. B 2003, 107, 1345−1352. (26) Joseph, S.; Aluru, N. R. Why Are Carbon Nanotubes Fast Transporters of Water? Nano Lett. 2008, 8, 452−458.

(27) Chen, X.; Cao, G. X.; Han, A. J.; Punyamurtula, V. K.; Liu, L.; Culligan, P. J.; Kim, T.; Qiao, Y. Nanoscale Fluid Transport: Size and Rate Effects. Nano Lett. 2008, 8, 2988−2992. (28) Hockney, R. W.; Eastwood, J. W. Computer Simulation Using Particles; CRC Press: 1988. (29) Hoover, W. G. Canonical Dynamics - Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695−1697. (30) Sun, Y. T.; Guo, Z. Y.; Xu, J.; Xu, X. Q.; Liu, C.; Li, Y. B. A Candidate of Mechanical Energy Mitigation System: Dynamic and Quasi-Static Behaviors and Mechanisms of Zeolite Beta/Water System. Mater. Eng. 2015, 66, 545−551. (31) Xu, B. X.; Li, Y. B.; Park, T.; Chen, X. Effect of Wall Roughness on Fluid Transport Resistance in Nanopores. J. Chem. Phys. 2011, 135, 144703. (32) Liu, L.; Zhao, J. B.; Culligan, P. J.; Qiao, Y.; Chen, X. Thermally Responsive Fluid Behaviors in Hydrophobic Nanopores. Langmuir 2009, 25, 11862−11868. (33) Zhao, J. B.; Liu, L.; Culligan, P. J.; Chen, X. Thermal Effect on the Dynamic Infiltration of Water into Single-Walled Carbon Nanotubes. Phys. Rev. E 2009, 80, 061206. (34) Xu, B. X.; Qiao, Y.; Zhou, Q. L.; Chen, X. Effect of Electric Field on Liquid Infiltration into Hydrophobic Nanopores. Langmuir 2011, 27, 6349−6357.

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DOI: 10.1021/acs.jpcc.6b00162 J. Phys. Chem. C XXXX, XXX, XXX−XXX