Civil Engineering Reference
In-Depth Information
reactions like fl uorination, hydrogenation and cycloaddition can be possi-
ble. The fl uorine atoms of fl uorinated CNTs can be replaced through
nucleophilic substitution reaction, and thus, functional groups of alcohols,
amines and Grignard reagent, etc., can be successfully incorporated onto
the CNT sidewall.
So far we have been concerned mainly with the functionalization of the
sidewall and tip of CNTs. But the inner hollow cavity of CNTs offers tre-
mendous opportunity to materials scientists, chemists and engineers to do
excellent R&D in the nanoscale test tube. The critical issue is the wetting
properties of the CNTs. The wettability determines what liquid would fi ll
the tube by capillary action and cover the inner surface. The Young-Laplace
relation relates the pressure difference
P
across the liquid-vapour inter-
face in a capillary to the surface tension of the liquid (
Δ
γ
) and contact angle
(
θ
) between the solid and the liquid as shown by:
−
1
cos
Pr
=
2
γ
θ
[16.1]
where
r
is the radius of curvature of the meniscus. The contact angle
is an
indicator of the strength of the interaction between the liquid and the solid
interface relative to the cohesive forces in the liquid. If
θ
is smaller than
90°, the contact between the liquid and the surface is said to be wetting and
Δ
θ
P
is positive. Therefore the liquid will be pulled into the capillary sponta-
neously, as there is an energy gain in the wetting process. If
θ
is larger than
90°, the contact angle is said to be non-wetting and
Δ
P
will be negative.
Therefore, when
90°, the only way to introduce liquid into a capillary is
to apply pressure larger than
θ
>
P
.
Extremely high aspect ratios, molecularly smooth hydrophobic graphitic
walls, and nanoscale inner diameters of carbon nanotubes give rise to the
unique phenomenon of ultra-effi cient transport of water through these
ultra-narrow tubes. The idea of water occupying such confi ned hydrophobic
channels is somewhat diffi cult to comprehend, though experimental evi-
dence has confi rmed that water can indeed occupy these channels (Naguib
et al.
, 2004; Kolesnikov
et al.
, 2006). The proposed water transport mecha-
nism has a distinct similarity to the transport mechanisms of biological ion
channels. In recent years, numerous simulations (Hummer
et al.
, 2001; Kalra,
2003) of water transport through SWNT have suggested that fast molecular
transport takes place, far in excess of what continuum hydrodynamic theo-
ries would predict if applied on this length scale. There have been many
efforts to defi ne the boundary between bulk water and confi ned water
transport, and it was found sensible to set a threshold for the continuum
treatment of liquid as around 7.5 nm.
A no slip boundary condition is typically used in continuum fl uid dynam-
ics. It constrains a fl uid closest to a solid boundary to obtain the same
tangential velocity as the solid. When the tangential velocity of the fl uid
Δ
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