A schematic figure of the experimental results obtained by A. Varghese and S. Datta. 3 Two chambers containing Na2S and CdCl2 solutions are connected by anodised aluminium oxide (AAO) nanochannels. Cylinders of CdS with a pore along the axis of the cylinder are obtained on only one side of the AAO nano-channels growing out from the AAO-nanochannel ends. Our work tries to elucidate the mechanism of the formation of CdS nano-tubes as observed in experiments. Refer to Ref. 3 for SEM images of CdS nanotubes growing out of the ends of AAO nanochannels. In our simulations, we just model the part of the setup, which is encircled in the figure: the entry point of Cd+2 ions into the Na2S chamber.
(a) and (b) are snapshots of a C-particle (CdS) nanotube growing out of the end of (AAO) square nanochannel (not seen) of width 2r NC = 10a placed at the center of the y − z plane from two different angles. The snapshot in picture (c) is for a nanochannel with width 2r NC = 20a. C-particles are colored blue, A-particles are red, and B particles (not plotted) are all around the nano-tube. The parameters used are p A = 0.2, ρ B = 0.6/a 3, D A = 0.0125, D B = 0.25, D C = 0.0125, and p P = 0.3. Figure 1(d) shows the variation of density of C-particles with the radial distance r from the center of the nano-tube for varying widths of the nanochannel. The box size is L x × 2 L y × 2 L z = 8000a × 64a × 64a, and the axes in (a), (b), and (c) are not drawn to scale. Only 5% of the particles have been plotted for the ease of visualization.
Variation of the density of C particles with the distance r from the center of the nano-tube as a function of the densities and diffusivities of A,B,C particles. The density of C particles is not a parameter of the simulation. Except of the particular quantity varying in each plot, the default parameters are p A = 0.2, ρ B = 0.6/a 3, D A = 0.0125, D B = 0.25, D C = 0.0125. The data are for the growth of a single nanotube in a bath of B-ions. The box size is L x × 2L y × 2L z = 8000a × 50a × 50a and 2*r NC = 10a.
(a) and (b) are snapshots of 9 nanotubes growing out from the exits of 9 nano-channels arranged in a periodic lattice, with p A = 0.2 and p A = 0.05, respectively, and g = 0.3a/τ. The distance between centers of nano-channels is d c = 28a. Nanochannel width r NC = 5a for (a), (b), (c), and (d). Other parameters are ρ B = 0.6, D A = 0.0125, D B = 0.2, D C = 0.0125. Only 2.5% of the total number of particles have been plotted in the snapshots to keep the picture-file-size within reasonable limits. (c) and (d) show variation of the density ρ C (r) of C particles for ρ A = 0.2, ρ B = 0.6, D A = 0.0125, D B = 0.2, D C = 0.0125 with different values of d c (for fixed g = p P a/τ = 0.3a/τ) and for different values of p P (for fixed d c = 28a), respectively. The size of the lattices for (c) mentioned in the text. For (a), (b), and (d), the box size is 8000a × 84a × 84a. Well-formed cylinders were obtained for lower values of p A , i.e., plot (b).
(a) shows snapshot of growth of 9 nano-cylinders with a much slower growth-rate of g = 0.025a/τ with ρ A = 0.2a −3. All other parameters are the same as Figure 4(a) . A slower growth rate leads to the formation of improved quality of cylinders. In contrast, (b) shows that no cylinders are formed if g = 0.0 and hopping of A is +x direction is switched off, corresponding to switch-off of flow from the AAO nanochannel, all other conditions remain exactly the same as in snapshot (a). Only 50% of the particles have been shown and the perspective of (b) is 180° rotated from that of (a).
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