  We present investigate the self assembly and growth of an array of $CdS$
nanotubes: a consequence of a fine balance of directed motion, diffusion and
aggregation of reacting ${\rm Cd^{+2}}$ and ${\rm S^{-2}}$ ions. In a previous
communication [J. Kiruthiga, A. Chatterji, J. Chem. Phys., {\bf 138} 024905
(2013)], we identified the mechanism of a unexpected growth of a very uniform
$CdS$ nano-cylinder from the end of a nano-channel. Furthermore, the cylinder
had a pore along the axis but were closed at one end. This unique phenomenon of
self assembly of {\em monodisperse} CdS nano-cylinders had been observed in a
rather simple experiment where two chambers containing 0.1 M ${\rm Cd Cl_2}$
and 0.1 M ${\rm Na_2 S}$ solutions were joined by an array of anodized
aluminium oxide (AAO) nano-channels [A. Varghese, S. Datta, Phys. Rev. E., {\bf
85}, 056104 (2012)]. Our previous study identified the principles governing the
growth of a single nano-tube at the exit point of a single AAO-nano-channel. In
this communication, we identify factors affecting the self-assembly process for
nano-tubes growing out an array of closely spaced AAO nano-channel exits. Our
model is not $Cd^{+2}$ or $S^{2-}$ specific, the experimental scheme can be
extended to self assemble a general class of reacting-diffusing A and B ions
with A (${\rm Cd^{+2}}$) selectively migrating out from a nano-channel. In
particular, we note that after the initial prolonged growth of nanotubes, there
can arise a severe deficiency of B-ions (${\rm S^{-2}}$) ions near the
AAO-nano-channel exits, the points where the reaction and aggregation occurs to
form the $CdS$ nanotube, thus impeding further growth of uniform CdS
nano-tubes. Thereby we predict the necessary characteristics of reacting
systems which can be self assembled using suitable adaptations of previous
experiments.
