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150 Principles and Methods
The limitation of this method for determining nanoparticle contact angle
falls on the ability to successfully attach the nanoparticle to the end of
an AFM cantilever. Attaching increasingly smaller particles to AFM
cantilevers becomes problematic as the epoxy used to glue the two sur-
faces together may cover or alter the nanoparticle surface chemistry.
However, as expertise in this area continues to develop and the use of
other probes such as carbon nanotubes progresses, smaller nanoparti-
cles (d < 50 nm) may be investigated using this technique.
The relative hydrophobicity of nanoparticles may be determined by
measuring their propensity to partition into hydrophobic solvents. In
these measurements a particle suspension of known concentration is
prepared by dispersing the nanoparticles in water. This suspension is
then mixed with a volume of a hydrophobic solvent such as octanol or
dodecane. The two phases are mixed and subsequently allowed to phase
separate. The particle concentration in the water phase is measured. The
relative hydrophobicity may then be expressed in terms of the percent-
age of the initial nanoparticle concentration that has partitioned into
the hydrophobic phase. For octanol-water partitioning tests, the rela-
tive hydrophobicity is expressed in terms of the logarithm of the octanol-
water partition coefficient (log P), which is defined as:
C 0
log P 5 loga b (31)
C w
where C and C w are the nanoparticle concentrations in the octanol and
0
water phases after phase separation, respectively.
a c
Liquid phase
θ r D b
D b 0
b D d θ a
Liquid phase
Position (nm)
Figure 4.28 Illustration of the methods used to determine the (a) receding and (b)
advancing contact angle for a nanoparticle. (c) Determination of the zero-force position
in an AFM force plot.