  Molecular dynamics simulations are used to study the occupancy and flow of
water through nanotubes comprised of hydrophobic and hydrophilic atoms, which
are arranged on a honeycomb lattice to mimic functionalized carbon nanotubes
(CNTs). We consider single-file motion of TIP3P water through narrow channels
of (6,6) CNTs with varying fractions (f) of hydrophilic atoms. Various
arrangements of hydrophilic atoms are used to create heterogeneous nanotubes
with separate hydrophobic/hydrophilic domains along the tube as well as random
mixtures of the two types of atoms. The water occupancy inside the nanotube
channel is found to vary nonlinearly as a function of f, and a small fraction
of hydrophilic atoms (f ~ 0.4) are sufficient to induce spontaneous and
continuous filling of the nanotube. Interestingly, the average number of water
molecules inside the channel and water flux through the nanotube are less
sensitive to the specific arrangement of hydrophilic atoms than to the
fraction, f. Two different regimes are observed for the water flux dependence
on f - an approximately linear increase in flux as a function of f for f < 0.4,
and almost no change in flux for higher f values, similar to the change in
water occupancy. We are able to define an effective interaction strength
between nanotube atoms and water's oxygen, based on a linear combination of
interaction strengths between hydrophobic and hydrophilic nanotube atoms and
water, that can quantitatively capture the observed behavior.
