Nanojunction Effects on Water Flow in Carbon Nanotubes

We report on the results of extensive molecular dynamics simulation of water imbibition in carbon nanotubes (CNTs), connected together by converging or diverging nanojunctions in various configurations. The goal of the study is to understand the effect of the nanojunctions on the interface motion, as well as the differences between what we study and water imbibition in microchannels. While the dynamics of water uptake in the entrance CNT is the same as that of imbibition in straight CNTs, with the main source of energy dissipation being the friction at the entrance, water uptake in the exit CNT is more complex due to significant energy loss in the nanojunctions. We derive an approximate but accurate expression for the pressure drop in the nanojunction. A remarkable difference between dynamic wetting of nano- and microjunctions is that, whereas water absorption time in the latter depends only on the ratios of the radii and of the lengths of the channels, the same is not true about the former, which is shown to be strongly dependent upon the size of each segment of the nanojunction. Interface pinning-depinning also occurs at the convex edges.

The last term of the right side of Eq. (1) vanishes due to incompressibility of water. To evaluate the dissipation function by Eq. (1), we use the time-averaged fluid velocities. does not vanish due to the slope of the variation of the radius R with the axial position, '( ⁄ ' . Given that = 0 and neither nor depends on the angular variable θ, the expression for is simplified to, Consider Figure 8 of the main text of the paper. As described in the paper, a nanojunction consists of + short carbon nanotubes (CNTs) of decreasing (or increasing) radii (( ) whose axes are aligned with the direction. Hereafter, we refer to such short CNTs as rings. Thus, if , is the volume flow rate, then, Using the well-known lubrication approximation, we obtain an approximate expression for : where ∆3 is the time needed for a molecule with axial velocity ( ) to pass through the +th ring of a nanojunction. Assuming that both ∆( and ∆3 are small, we obtain, ∆3 = ∆ 4 and, therefore, Substituting for and in Eq. (2) and summing over all the + rings of a nanojunction yields, depends only on the slope ∆< ∆ , and 6 ′ = +Δ is the effective length of the transition zone. Here, 1 < ( 9 > = = 1 with ( > being the radius of the +th ring. This is equivalent to a pressure drop∆? @ , given by Δ? @ = 5 6′, ( A 9 (9) resulting from the change in the radius in the transition region, which is Eq. (4) of the main text of the paper.
Assessing the effect of the thermostat on the results. As described in the main text of the paper, our molecular dynamics (MD) simulations were performed in the(BCD) ensemble. When dealing with a dynamic phenomenon, however, a thermostat might give rise to spurious effects.
Thus, to ensure that the thermostat did not give generate any unphysical effect, we also carried   (ii) We also computed the flux 'B/'3, where B is the number of the water molecules. Figure S2 presents the results. After the simulation reached equilibrium in the ensemble, we estimated that, 'B/'3 ≈ 5100 ± 900, while 'B/'3 ≈ 5700 ± 700, in the (BCE) ensemble that followed the calculations in the (BCD) ensemble. The two estimates are completely consistent. Thus, the results presented in the paper, which were computed by carrying out the MD simulations in the (BCD) ensemble, were not affected significantly by the presence of the thermostat.
Calculation of the contact angle of water with the nanotube's wall. We also carried out MD simulations to estimate the contact angle (CA) of nanometer-size water droplets with the surface of the CNT, and its possible dependence on the tubes' geometry. To do so, we used the method proposed by Werder [1], which is based on the least square fits of the isochore lines, lines of constant density, to a circle (or sphere). In this method the equilibrium configurations of a water nanodroplet at the desired temperature are used to compute the isochore lines at various levels. After reaching equilibrium and ignoring a thin layer of adsorbed water molecules, as described by Bormashenko [2], the least-square fit of the isochore lines is superimposed on the figure, from which the CA is determined by a simple geometrical construction. This is shown in Figure S3.
Our calculations indicated that the CA in the (20,20) CNT is (in degrees) 55 ± 8; see the isochores shown in Figure S3. The CA in the (30,30) CNT turned out to be 54 ± 7. The relatively large fluctuations are due to the small radii of the CNTs. We also computed the CA in a converging configuration, shown in Fig. S4, with the corresponding isochore lines shown in Figure S5. The CA turned out to be 59 ± 8. Thus, the CAs for the various configurations are consistent with each other, and are also in agreement with what has been reported in the literature.
6 Figure S4: A snapshot of water droplet in the configuration that converges at the center. Figure S5: The isochors for water droplet, averaged over 3.5 ns, which correspond to Figure S4.