Working Mechanism of Nanoporous Energy Absorption System under

Mar 20, 2012 - The working mechanism of nanoporous energy absorption system (NEAS) under high speed impact loading conditions are explored using molec...
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Working Mechanism of Nanoporous Energy Absorption System under High Speed Loading Guoxin Cao* Department of Mechanics and Aerospace Engineering, and HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing, 100871, China ABSTRACT: The working mechanism of nanoporous energy absorption system (NEAS) under high speed impact loading conditions are explored using molecular dynamics simulations, and the effects of loading rate and tube size are also considered. The present NEAS is composed of a single-walled carbon nanotube (CNT) segment and water molecules. The work done by the impact load can be converted into three parts: (I) water molecules potential change due to nanoconfinement, (II) solid− liquid interaction energy, and (III) the heat dissipated by the solid−liquid surface friction. We found that with a small tube size, part III provides the main contribution to the overall energy absorption; with the increase of tube size, part III rapidly decreases, and part I begins to give the main contribution. This result is different with the reported mechanism in which part II is the main contributor. The energy absorption density of NEAS is much higher than that of the conventional energy absorption materials, which decreases with the tube size and slightly increases with the impact loading rate. In addition, water molecules can transport through CNTs very fast under the high loading rate, thus NEAS can meet the requirement of a very low response time to prevent against the high speed impact load. On the basis of our simulations, NEAS can be a very promising candidate to protect against high speed loading.

1. INTRODUCTION Energy absorption structures or materials are used to absorb/ damp the mechanical energy created by the external load (e.g., impact or blast wave) to protect human or important electrical/ mechanical parts against injury/damage, which typically include composite and cellular materials, such as honeycombs, metal foams, and sandwich structures.1−4 In order to meet the requirement for the lightweight, small-volume, and highefficiency energy absorption system, new materials and structures need to be developed. Recently, a new highperformance nanoporous energy absorption system (NEAS) has attracted considerable research interests.5−9 A basic model of NEAS includes two functional components: nanoporous material and nonwetting liquid environment as shown in Figure 1. Both experimental and numerical studies have reported about the response of NEAS to the quasistatic compressive loading: under the normal state, due to the nonwetting characteristic, it is energetically favorable for the liquid to stay outside of the nanopores; while under the external applied load (impact or blast wave), the potential energy of liquid increases with the liquid pressure, and when the liquid pressure is higher than some critical value (defined as the infiltration pressure Pcr), the liquid will be pushed into nanopores to reduce the overall potential energy; the liquid transports through nanopores to fill the whole pores.5,6,9−13 Typically, it is considered that the work done by external load can be partly transferred into the solid−liquid interfacial energy (proportional to the specific surface area A and the solid−liquid interface energy γsl) and the heat created by the © 2012 American Chemical Society

solid−liquid interfacial friction. Since nanoporous materials typically have a very high specific surface area A (∼1000 m2/ g),7 NEAS can be a good candidate for the new high-efficiency energy absorption/damping system. It is reported that the NEAS made by silica gel and distilling water can have the energy absorption density of about 15 J/g or 18 J/cm3,9,10 which is much higher than the conventional used energy absorption/damping materials, such as porous aluminum. The energy absorption efficiency of NEAS mainly depends on the wetting and infiltration behavior of nanopores. Because of the small length scale, neutral and smooth surface, the nanofluid behavior (wetting/infiltration) is mainly investigated based on carbon nanotubes (CNTs) and especially for numerical simulations.11,13−16 In order to further understand the polar effect of nanopores, the infiltration behaviors of liquids into zeolites and silica tubes are also investigated.12,17,18 However, most of these studies are based on quasistatic loading conditions, and very few studies begin to touch the infiltration behavior under dynamic loading conditions (impact/blast),19 unfortunately which is the main loading mode for NEAS to protect against under the realistic condition. An excellent energy damping system is required not only to absorb or dissipate a high amount of energy but also to have a high absorption/damping rate, especially for protecting against high strain rate loading (e.g., impact or blast). The energy Received: January 28, 2012 Revised: March 15, 2012 Published: March 20, 2012 8278

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Figure 1. Schematics of nanoporous energy absorption system (NEAS): (a) NEAS and (b) nanopore.

impact on the transport behavior was neglected in the present work, and we will consider it in our future work. The MD simulations are carried out using LAMMPS.26 The computational cell includes a rigid SWCNT segment with a length of 5.2 nm and 3735 water molecules confined in a reservoir, illustrated in Figure 2. The reservoir is made by two

dissipation rate of NEAS is mainly decided by the transport rate of liquid through nanopore. Currently, both experimental and numerical studies have been reported that liquids can flow extremely fast through CNTs, about several orders higher than what the classic hydrodynamics predicted.20−24 For the nanopores with a typical length ( 0), and there is a new carbon−water interaction energy (Eint) created. In addition, an internal friction force is generated when water molecules transport along the CNT wall, which can dissipate the part of impact energy as heat (Hf). Therefore, the energy absorbed by NEAS can be expressed as E tot = E int + ΔE H2O + Hf

E int = E H2O + ECNT − ECNT + H2O

(5)

where ECNT+H2O is the total potential energy of CNT and all water molecules inside, and EH2O and ECNT are the potential energies of water molecules inside CNT and pure CNT, respectively. Figure 5 shows the relationship between the solid−liquid interaction energy per water molecule (eint = Eint/Nin) and the number of infiltrated water molecules (Nin) for the CNTs with different sizes under the different loading rates. For all cases, eint initially decreases with the increase of Nin and then converges to some constant value when Nin is large enough. With a large Nin, eint is actually not sensitive to the loading rate v and increases with the decrease of the CNT radius R (summarized in Figure 6). The above results are mainly caused by the

(4)

Equation 4 is the main working mechanism of NEAS. In this section, we will discuss the effects of nanopore size and impact loading rate on the energy absorption efficiency of NEAS. 3.2.1. Potential Energy Change of Water Molecules. Figure 4 shows the relationship between the variation of potential energy per water molecule (ΔeH2O) and the number of water molecules infiltrated into the CNTs (Nin) with different sizes under the loading rates from 100 to 1000 m/s. ΔeH2O = eH2O − eHB 2O , where eH2O and eHB 2O are the potential energies per water molecule of water inside CNT and bulk water, respectively. eHB 2O is obtained by the MD simulation of the bulk water model, which can be simulated using a computational cell with the density of bulk water and the periodic boundary condition applied along all three directions of cell. The value of eHB 2O is calculated as ∼7.07 × 10−20 J/molecule. With the increase of Nin, ΔeH2O rapidly decreases initially, then gradually converges to some constant value (except for the highest loading rate of 1000 m/s). After reaching the convergence, ΔeH2O is higher for a higher loading rate v or a lower tube radius R (summarized in Figure 6). The result is mainly caused by the variation of water−water interactions: with the increase of Nin, the water molecules inside CNTs begin to interact with each other through hydrogen bonding (i.e., water−water interactions), which will decrease eH2O, and thus, ΔeH2O decreases. When Nin is large enough, a stable water structure is generated inside CNT, which will not be changed by adding more water molecules, and then, ΔeH2O essentially converges with Nin. Under a higher loading rate v, the infiltrated water molecules will easily deviate from their equilibrium positions due to a higher transport velocity of water molecules in CNTs, which results a less stable water structure than what is generated under a lower loading rate. Thus, the potential energy of water inside CNT is higher under a higher loading rate, especially for a small Nin. In addition, because of the distortion of hydrogen bonding, a small size along the radial direction also makes the water structure generated in smaller CNTs less stable than in larger CNTs, i.e., a smaller CNT has a higher ΔeH2O.

Figure 6. Relationship between the converged values of ΔeH2O and eint (shown in Figures 4 and 5, respectively) and the CNT radius under the different impact loading rates.

coupling effect between solid−liquid interactions and liquid− liquid interactions. When there are a few water molecules infiltrated into CNTs, the C−O interaction is dominant (C−H interaction is very weak and can be neglected), and the water− water interaction is weak (or none), and thus, each water molecule can find the position with the strongest binding energy eint. While there are more water molecules inside CNTs, the water−water interactions become stronger and will adjust the positions and orientations of water molecules, which results in the decrease of the C−O interactions. When Nin is large enough, a stable water structure generates inside CNT, especially for the water layer contacting the tube wall (boundary layer), which determines the strength of C−O interactions. The structure of the boundary layer will not be affected by the new entered water molecules, and thus, eint becomes constant. For a small CNT, water molecules cannot bind very tightly with CNT due to the curvature effect of CNT, which can be shown by a lower initial value of eint. However, we have already 8283

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shown in the above section that a smaller CNT with a higher ΔeH2O after enough water molecules entered the CNT (shown in Figure 4), and thus, eint is higher for a smaller tube based on eq 5. 3.2.3. Solid−Liquid Friction Force. Under a constant pressure gradient, we have already known that water can transport as a plug flow through CNT with a very high flow rate. It shows that the solid−liquid shearing stress sharply reduces with the decrease of the CNT radius R and is essentially not sensitive with the transport velocity (>100 m/ s).22,24 Thus, in the present work, we neglect the effect of loading rate on the solid−liquid friction. The solid−liquid interaction can be described using the L-J potential between water molecules (simplified by O atoms) and carbon atoms of CNT as follows: ⎡⎛ ⎞12 ⎛ ⎞6⎤ σ σ U (r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎝ ⎠ ⎝ r ⎠ ⎥⎦ ⎢⎣ r

(6)

where σ and ε are L-J potential parameters, and r is the distance between C and O atoms. The VDW force is calculated as fij = −

dUij(r ) dr

(7)

The solid−liquid friction force is defined as NCNT Nin

Ff =

∑ ∑ fij

i=1 j=1

(8)

where NCNT is the number of C atoms of CNT. Figure 7a shows the relationship between the solid−liquid friction force (Ff) and the length of water segment in CNT (Lin) for the tubes with different sizes. Figure 7b shows the relationship between the number of infiltrated water molecules (Nin) and the length of water segment in CNT (Lin). In Figure 7, the lines are linear fitting results of MD results. Similar to our previous work, Ff increases with the tube radius R. The interesting result is that Ff is essentially insensitive with Lin in the current study range (Lin = 1.5−4.5 nm), while Nin increases by up to 5 times in the same range of Lin. Thus, Ff is essentially insensitive with Nin, which looks inconsistent with eq 8 as well as our common understanding. Actually, the VDW repulse force between the C atoms of CNT and the infiltrated water molecules (f ij) does not always work as a friction to resist the flow. Only when the water molecules lag behind the C atoms (zO < zC), f ij acts as a friction to resist the flow forward; while the water molecules are ahead of the C atoms (zO < zC), f ij can act as a driving force to assist the flow forward. The VDW force (f ij) between two atoms will periodically vary from the resist force to the driving force, and this is also the reason for a large fluctuation of the solid−liquid friction as shown in Figure 7a. With the increase of Nin, both the driving force and the resist force increase, and thus, the overall solid−liquid friction may essentially not change when Lin is large enough. In our previous work, the shear stress for the equilibrium water flow inside CNT under a constant pressure gradient is about 0.05−0.15 MPa for the current tube size range (R = 0.6− 1.3 nm),22 which is much lower than what we obtained in the present work (about 0.5−1.0 MPa calculated from the friction force shown in Figure 7a. Therefore, the impact induced

Figure 7. (a) Relationship between the solid−liquid friction force (Ff) and the length of water segment in CNT (Lin) for the tubes with different sizes; (b) relationship between the number of infiltrated water molecules (Nin) and the length of water segment in CNT (Lin).

nonequilibrium infiltration behavior will cause a higher solid− liquid friction than the equilibrium flow. The solid−liquid friction Ff has two-sided effects on NEAS: a larger Ff can cause a higher energy dissipated as heat to improve the energy absorption efficiency; while a larger Ff will also reduce the liquid transport velocity (vtr) through the tube to increase the system's response time to external impact loading. The transport velocity (vtr) can be calculated by the first derivative of the displacement of water segment in CNT (u) respect to the loading time (t). The u value can be approximately fitted as a two-stage function of t including a linear part and a quadratic part, and thus, vtr can be also shown as a two-stage function of t including a constant part and a linear part. When a stable water structure has not been generated yet (the number of the infiltrated water molecules Nin is small), vtr is small and can be approximated as a constant lower than the loading rate v; when a stable water structure generates with a large Nin, vtr linearly increases with the piston displacement and is much higher than v. For example, with v = 100 m/s, vtr = 35−59 m/s during the constant stage, then vtr increases to 360−580 m/s after the linear stage at the piston 8284

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displacement x = 2 nm for different tubes, as shown in Figure 8. In the constant part, vtr is the lowest for R = 1 nm ((15,15)

The energy absorption efficiency of NEAS can be evaluated by the energy absorption density e = Etot/VCNT (the absorbed energy per volume). The energy absorption density and the contributions from different components are shown in Figure

Figure 8. Relationship between the transport velocity in CNT (vtr) and the piston displacement (Nin) for different tubes under the loading rate v = 100 m/s.

Figure 9. Energy absorption density of NEAS (the total absorbed energy per unit tube volume) and its different components varying with the CNT radius. The energy absorption density (e) is composed of the potential difference of water molecules after entering CNT (ρ*ΔeH2O), the solid−liquid interaction energy (ρ*eint) and the energy dissipated by the solid−liquid interface friction (hf). All of the above values are calculated based on per unit volume. e* is the recalibrated energy absorption density after considering the volume fraction of CNT in CNT bundles (e* = eϕ). The length of the bar on the symbol shows the variation range of ΔEH2O and e with the loading rate v = 100−400 m/s, and the symbol is the middle point of the range (since the number of infiltrated water molecule is not enough large for v = 1000 m/s, the energy components may be inaccurate, and thus, we did not include those data in Figure 7).

tube), which is caused by the coupling effects of the solid− liquid and liquid−liquid interactions; in the linear part, vtr has a higher slope for a smaller tube, which means a smaller tube has a higher acceleration, and vtr is higher for a higher v (the results under higher v are not shown here for simplicity). For a typical nanopore length of ∼10 μm, the response time (the time required to fill nanopores) can be estimated to be less than 1 μs. Therefore, when Nin is large enough, the water inside CNT can flow much faster than the requirement of the response time to protect against the high speed impact or blast load. Actually, we can further increase the energy absorption efficiency through slightly increasing the liquid−solid friction. 3.3. Energy Absorption Efficiency of NEAS. On the basis of ΔeH2O, eint, and Ff as well as the water density in CNTs, we can estimate the energy absorption efficiency of the NEAS including CNTs and water. The nominal water density in CNTs is defined as ρ* =

9: e = ρ*ΔeH2O + ρ*eint + hf, where the energy per volume dissipated by the solid−liquid friction force can be calculated as hf =

Nin πR2Le

where Le is the water segment length in CNT, which is calculated based on the average position of the first three water molecules of the segment; ρ* is estimated from the results with v = 100 m/s. ρ* is essentially a constant (shown in Table 1) when Nin is enough large since Nin linearly scales with Le as shown in Figure 7b. In the present work, the effect of the loading rate on the water density in CNT is neglected and will be discussed in our future work. Table 1. System Information of NEAS CNT type

(10,10)

(15,15)

(20,20)

0.671 19.12 0.58

1.003 22.24 0.66

1.337 24.03 0.71

πR2Le

=

Ff s πR2Le

(10)

where s is the displacement of the water segment in CNT, which can be calculated by the change of the geometry center of the infiltrated water segment along the flow direction. On the basis of our simulations, e decreases with the tube radius R and is about 0.8−1.7 kJ/cm3 for the CNT + water systems with R = 0.67−1.34 nm under the loading rate v = 100−400 m/s. The smallest tube has the highest energy absorption density. In addition, since ΔeH2O increases with v, e slightly increases with v. It should be noted that e is calculated based on the isolated single-walled CNTs here; while under the more realistic conditions, e should be evaluated based on the CNT bundles created by CNTs with the fixed center−center spacing d (d ≈ 2R + 0.34 nm, the carbon−carbon VDW distance is about 0.34 nm). The volume fraction of CNTs in CNT bundles is obtained by ϕ = πR2/(√3/4d2), shown in Table 1. The recalibrated energy absorption density e* = eϕ, shown as the filled circle in Figure 9, is still significantly higher than the conventional energy materials.

(9)

tube radius R (nm) effective water density ρ* (molecule/nm3) volume fraction in CNT bundles ϕ

Hf

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The solid−liquid interaction energy (Eint) is typically considered to be the main contributor for NEAS to absorb/ damp the mechanical energy.5−9 However, our MD simulation results show that the contribution from the solid−liquid interaction (ρ*eint) to the overall energy absorption density is much smaller than that of the other two components (ρ*ΔeH2Ohf) and ρ*eint/e ≈ 15% in the current study range of CNT radius (R = 0.671−1.336 nm), which is essentially insensitive to the tube radius R. With the increase of R, all three components decrease, but hf decreases much faster. Although hf shows the main contribution to e with a small R, its contribution sharply decreases with the increase of R, and ρ*ΔeH2O becomes the main contributor. Therefore, it is not correct that the solid−liquid interaction energy (Eint) is considered to be the main contribution to the energy absorption efficiency of NEAS.

bundles, the recalibrated energy absorption density of NEAS (e*) based on CNT bundles can still be up to about 0.95 kJ/ cm3, which is significantly higher than the conventional energy absorption materials. Therefore, NEAS can be a promising candidate for the new generation energy absorption materials.

4. CONCLUSIONS By using MD simulations, we study the working mechanisms of the nanoporous energy absorption system including CNTs and water molecules, and the effects of both loading rate and tube size are also considered. The work done by the external impact load can be converted into three parts: the liquid molecule potential change compared with the bulk liquid after being infiltrated into nanopores, ΔeH2O; the solid−liquid interaction energy, Eint; and the heat dissipated by the solid−liquid friction, Hf, when the liquid transports to the solid wall. To the best of our knowledge, this is the first time the complete mechanism of NEAS response to the high strain rate loading has been shown. In the most reported works about NEAS (mainly under the quasistatic loading), the first part ΔEH2O was neglected, and the main energy absorption mechanism is based on Eint and Hf, among which Eint is typically considered to be the main contributor. However, this is incorrect according to our simulation results. This is also the first time to quantitatively show the relationship among the different energy absorption components. In the system of CNT + water, on the basis of the unit volume, Eint is much smaller than ΔEH2O and Hf; for the small tube, Hf gives the main contribution to NEAS instead of Eint; with the increase of R, Hf sharply decreases and ΔEH2O begins to provide the main contribution. In the present study range, the contribution of Eint to the overall absorbed energy is only about 15%, which is essentially insensitive with the tube radius, R. In addition, because of the smoothness of the wall, similar to the transport behavior under the quasistatic loading conditions, water can transport very fast through CNTs under the higher loading rate, which means NEAS have a very short response time. Thus, NEAS can meet the requirement to resist the very high speed loading. Both the water potential change and the solid−liquid interaction energy per water molecule (eint and ΔeH2O) first decreases with the increase of the number of infiltrated water molecules (Nin) then gradually converges to a constant when Nin is large enough. After the convergence, both eint and ΔeH2O decrease with R; ΔeH2O increases with the loading rate v, but eint is insensitive to v. The energy absorption density e of the present NEAS can have the maximum value of about 1.7 kJ/cm3 with the smallest CNT radius R = 0.67 nm, which will decrease with the increase of R. After considering the volume fraction of CNT in the CNT

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I acknowledge the financial support provided by the National Science Foundation of China under grant no. 11172002.

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REFERENCES

dx.doi.org/10.1021/jp3009145 | J. Phys. Chem. C 2012, 116, 8278−8286