Water filling and electric field-induced enhancement in the mechanical property of carbon nanotubes

The effects of water filling and electric field on the mechanical property of carbon nanotubes (CNTs) are investigated with molecular dynamics simulations. The simulation results indicate that the water filling and electric field could enhance the elastic modulus but reduce the Poisson’s ratio of the CNTs. As for the buckling behaviors, a significant enhancement could be observed in the yield stress and average post-buckling stress of the CNTs. In particular, the enhancement in the yield stress induced by the water filling and electric field could be even higher than that resulted from the solid filling. Moreover, a transition mechanism from the rod instability to shell buckling is shown to explain the nonmonotonic variation of yield stress, and the critical diameter can be tuned through filling the water molecules and applying the electric field. The present findings provide a valuable route for the optimized design and application of the nanoscale functional devices based on the water-filled CNTs.

breathing mode frequencies of water-filled and empty CNTs at elevated pressures 12 . Based on the water filling, our previous works explored the enhancements in the mechanical property of the (12,12) CNT 13 and further revealed the reversible stretching of the pre-strained (12,12) water-filled CNTs controlled by the electric field 14 . In fact, for the different CNTs, the amount of the filling water molecules increases with increasing the diameter of CNTs. Hence, the mechanical property of water-filled CNTs may vary with the characteristic size of the CNTs. Moreover, as a nanoscale material with nearly perfect tubular structure and excellent mechanical property, CNTs are regarded as an ideal nanoscale carrier or container for nanoparticles, such as drug molecules, metal particles and so on [15][16][17][18] . Hence, the research on the mechanical property of the filled CNTs is rather important for the reliability and stability evaluation of these CNT-based systems. Furthermore, the CNTs are also considered as a promising candidate for the nanoscale functional devices due to their unique physical property. The filling could further improve the physical property of the CNTs and therefore expand their functionality to serve the need in various fields. As a novel material in laboratories, the water-filled CNTs possess great potential applications and have been of great interest. Therefore, the further investigation on the size-dependent mechanical property of water-filled CNTs could provide a better understanding on the reliability of drug delivery and nanoscale channel, and establish a solid foundation for the future development and applications.
In this paper, the mechanical property of water-filled CNTs is investigated via MD simulation of the compressive response, with a focus on the size effect. The five CNTs with different diameters are considered to examine the size dependence of the mechanical property. In addition, it has been proved that the electricity, the ubiquitous environment in biological molecules, could make an obvious effect on the water molecules inside the CNTs [19][20][21] . Therefore, the electric field is also taken into account in the MD simulation reported here. Figure 1 shows the variations of the stresses with the strains of the empty CNTs, the water-filled CNTs and the water-filled CNTs under the electric field of 0.5 V/Å, respectively. In this work, the stress σ is calculated by the classical definition: σ = F/A, in which F is the spring force and A is the initial sectional area of CNTs. In the calculation of the sectional area, the thickness of CNTs is adopted as 0.66 Å 22 . From the figure, it can be seen that the stress linearly increases as the compressive strain increases in the initial elastic stage. Subsequently, when the strain reaches the critical buckling strain, the stress sharply decreases and the CNTs begin to buckle. For the buckled CNTs, the stress slowly decreases with the increase in the strain, and the variation range of the stress in this stage is rather small even though the strain keeps growing up to ~26%. The final buckling modes and the distributions of strain energy of the (8,8) and (16,16) CNTs are inserted in Fig. 1. The computational results reveal that the CNTs always present the asymmetric buckling mode in the final stage, which is similar to the common rod buckling. As compared to the (8,8) CNTs, based on the global buckling deformation, some local wrinkles appear on the wall of the empty (16,16) CNTs. For the water-filled CNTs, the CNTs look plump due to the filling of water molecules, and the local wrinkles on the wall of (16, 16) CNTs reduces. When the axial electric field is applied, the local wrinkles on the wall of (16, 16) CNTs almost disappear. Moreover, we can find that the high strain energy is always located on the positions of the large bending deformations along the CNTs. The average strain energies per carbon atom of the empty (8,8) and (16,16) CNTs under the strain of ~23% are 0.10 and 0.08 eV, respectively. After filling with water molecules, the corresponding average strain energies increase to 0.12 and 0.11 eV. Considering the electric field with the intensity of 0.5 eV/Å, a slight increase can still be observed for the average strain energies of the two CNTs. It is implied that under the same compressive strain, the water filling and electric field may speed up the compressive failure of CNTs, which is significant for the drug release and provides a reference point for the CNTs serving as a nanoscale fluid container.

Results
The elastic moduli of the empty CNTs, the water-filled CNTs and the water-filled CNTs under the electric fields of 0.5 V/Å are given in Fig. 2. The elastic modulus is defined as the slope of the linear stress-strain relationship in the whole elastic stage. The five columns in the three groups correspond to the elastic moduli of the (6, 6), (8,8), (10,10), (12,12) and (16,16) CNTs, respectively. Here, the elastic modulus and Poisson's ratio are considered as the material properties which are independent on the characteristic size. For the empty CNTs, the average elastic modulus is 5.43 ± 0.21 TPa, which is consistent with 5.5 TPa as reported in the previous work based on the same CNT thickness 22 . As for the water-filled CNTs, the average elastic modulus is enhanced to be 5.56 ± 0.22 TPa, which is due to the additional support from the incompressible water. When the axial electric field is applied, the elastic modulus only has a small increase (5.60 ± 0.23 TPa). The results indicate that the filling of water molecules and the introduction of electric field could slightly enhance the elastic modulus of the CNTs. Fig. 3 displays the average Poisson's ratios of the three types of CNTs, i.e., the empty CNTs, the water-filled CNTs and the water-filled CNTs under the electric field. Here, the Poisson's ratio is calculated by the expression, ν = -ε r /ε z , where ε r and ε z are the circumferential and axial strains, respectively. The corresponding Poisson's ratios for the three CNTs are 0.177 ± 0.012, 0.173 ± 0.012 and 0.170 ± 0.013, respectively. The present Poisson's ratio of the empty CNTs is in the range of that obtained in the previous work (0.16 ~ 0.19) [22][23][24] . It can be seen that the water filling reduces the Poisson's ratio of the CNTs, and the electric field could result in a further decrease in the Poisson's ratio. The reason is because there has been a pre-strain in the circumferential direction for the water-filled CNTs as compared to the empty CNTs.  Thus, for the water-filled CNTs, the further enlargement in the circumferential deformation becomes more difficult. Hence, it appears from the MD simulation that the water could offer a stronger suppression for the circumferential deformation than for the axial deformation.
The yield stresses of the three types of the CNTs as a function of the diameter are plotted in Fig. 4. The yield stress reflects the critical value for the CNTs from the elastic to buckling deformations. For the empty CNTs (square samples), the yield stress has an increase for the (8,8) CNT relative to the (6, 6) CNT, and then it decreases with the increase in the diameter. The nonmonotonic variation can be attributed to the different buckling mechanisms of the CNTs with different slenderness ratios. Though the final buckling modes of all the CNTs could be seen as the global instability, the initial buckling types, at which the stress just exceeds the yield stress, are completely different. The initial buckling mode of the small-diameter CNTs (the (6, 6) and (8,8) CNTs) are the rod-like global buckling, as shown in the left two insets of Fig. 4. In the continuum theory, the yield stress in this case is in proportion to the square of diameter, i.e., σ π = ( ) /( ) E D L 2 rc 2 2 , in which E is the elastic modulus, and D and L are the diameter and length of the CNTs 22,25 . As for the CNTs with larger diameter, the local buckling appears symmetrically and persists for several picoseconds, which is similar to the shell buckling, as shown in the lower two insets of Fig. 4. Based on the shell theory, the yield stress is in inverse proportion to the diameter and can be expressed as , in which t and ν are the thickness and Poisson's ratio of the CNTs 22,25 . Based on the two equations as given above, a nonmonotonic trend of the yield stress can be obtained after identifying a transition diameter from the rod buckling to the shell buckling. As a result, the physics behind the present simulation results could be qualitatively explained although the average difference between the simulation results and the predictions from the continuum theory is about 20%. The turning point in the yield stress-diameter curve of the empty CNTs indicates that the transition diameter is in the range of 10.85 ~ 13.56 Å.  In addition, it could be observed that the water filling and electric field enhance the yield stress of the CNTs. For the (6,6) and (8,8) CNTs, the number of water molecules in the unit sectional area of the CNTs is very small. Hence, the enhancement in the yield stress induced by the water effect is not evident. As the diameter of the CNTs increases, however, the enhancement in the yield stress becomes obvious. As compared with the empty CNTs, the average enhancements of the last three CNTs induced by the water filling and the electric field of 0.5 V/Å are 23.1% and 36.6%, respectively. These enhancements are comparable to and even higher than those induced by the solid filling (5% ~ 33%), including C 60 , gold nanowires and metal 9,11 . Furthermore, the simulation results reveal that besides the enhancement in the yield stress, the water filling and electric field result in the change in the initial buckling mechanism of the (10, 10) CNT (the right two insets in Fig. 4), which implies the enlargement of the transition diameter of the rod and shell buckling deformations.
It should be noted from the stress-strain curves that the buckled CNTs can still withstand a small compressive force. The resistant stress of the buckled CNTs, which is defined to be the post-buckling stress, only slightly decreases as the strain increases. The average post-buckling stresses of the buckled CNTs are shown in Fig. 5. The results indicate that the average post-buckling stress decreases firstly and then increases with the diameter of the empty CNTs. The average of the five average post-buckling stresses (five square samples) is about 0.034 ± 0.007 TPa. For the water-filled CNTs, the corresponding average value is increased by ~41.2% (0.048 ± 0.006 TPa). When the axial electric field with the intensity of 0.5 V/Å is applied, the average post-buckling stress of the five water-filled CNTs is increased to 0.053 ± 0.004 TPa, and the improvement in this case is about 55.9%. The present results demonstrate that the buckled CNTs could play a weak mechanical role, and water filling and electric field can enhance the mechanical performance of the buckled CNTs. It has been shown that the CNT can well maintain its structure even under a large deformation 26,27 . Hence, this weak and controllable mechanical property of the buckled CNTs may be significant for designing the restorable CNT-based devices to perform overloading tasks.

Conclusion
In this work, the size-dependent mechanical property of water-filled CNTs is investigated by MD simulations. An electric field with the intensity of 0.5 V/Å is applied along the CNTs to further expand the influence of the internal polar water molecules. The simulation results reveal that all the CNTs in this study finally exhibit the global instability. Some local wrinkles can be observed on the wall of the CNTs with a large diameter, which can be reduced by the filling of water molecules and the introduction of electric field. Moreover, it is found that the water filling and electric field could slightly enhance the elastic modulus but reduce the Poisson's ratio of the CNTs. For the buckling behavior, relative to the empty CNTs, the yield stress and average post-buckling stress have obvious enhancements due to the water filling and electric field. The high enhancement on the yield stress is even comparable to those induced by the solid filling, which may be ascribed to the incompressibility of water and the uniform distribution of water molecules inside the CNTs. Furthermore, as the slenderness ratio of the CNTs decreases, the initial buckling mode of the CNTs undergoes a transition from the rod instability to shell one, and the transition diameter can be changed through filling the water molecules and applying the electric field. In summary, for water-filled CNTs, the present research provides a valuable reference for designing the nanodevices based on this novel material. In addition, it is conceivable that the mechanical property of water-filled CNTs can be further changed via adjusting the water density and the electric field intensity, which may be utilized to fabricate the nanoscale functional devices.

Methods
The MD method is adopted to study the mechanical property of water-filled CNTs under the compressive load. Fig. 6 illustrates the computational models. Five capped armchair CNTs, i.e., (6,6), (8,8), (10,10), (12,12) and (16,16) CNTs, are chosen as the water carriers. The bottom end of the water-filled CNTs is fixed on a rigid substance, and the top end is compressed by a spring. The spring is gradually compressed as 0.1 Å/ps and its length change is used to calculate the applied compressive force. Moreover, to examine the effect of loading rate, the stress-strain curves with a small spring velocity of 0.05 Å/ps is also extracted and presented in Supplementary Fig. S1 online. The consistent results demonstrate the rationality of the present loading rate. Without considering the boundary section, the effective lengths of the water-filled CNTs are about 100 Å. The filling density of water inside the CNTs is 1.0 g/cm 3 . The mechanical property of the CNTs is described by the reactive empirical bond-order (REBO) potential 28 . The water molecules are simulated by the TIP4P-EW model 29 , in which the bond lengths and angle degrees are constrained by the SHAKE algorithm to the initial values of 0.9572 Å and 104.52°, respectively. The atomic interactions between the carbon atoms of CNTs and the oxygen atoms of water molecules are calculated by the Lennard-Jones (LJ) potential, and the corresponding parameters are σ CO = 3.28218 Å and ε CO = 0.11831 = kcal/mol 30 . The particle-particle-particle-mesh method is adopted to compute the long-range Coulomb interactions between the polar water molecules. The cutoff distances of the LJ and Coulomb interactions are 12 Å and 10 Å, respectively. The position and velocity are updated through the canonical ensemble (NVT) with the integration time-step of 1 fs. The system temperature is maintained at room temperature (298 = K) by the Nosé-Hoover thermostat. In the present research, the effect of the electric field on the mechanical property of water-filled CNTs is also explored through applying an axial electric field along the CNTs. The electric field intensity is 0.5 V/Å, which is comparable to the average local electric field within the condensed phase of water 31 . Moreover, it can be found that this intensity is still in the range of high-intensity electric field in laboratories [32][33][34][35] . Initially, the relaxation times for the hollow and the water-filled CNTs are 100 and 300 ps, respectively. Subsequently, the spring is compressed by 1 Å and the system is equilibrated for 100 ps. To eliminate the influences of the initial configuration and velocity, the results below are the averages of six independent simulations for each case. The MD simulations are carried out by LAMMPS package 36 .