Since atomic force microscopy (AFM) images are a
composite of probe and sample geometry, accurate
size determinations are problematic. A relatively straightforward
mathematical procedure for determining
tip radius of curvature (R
T) for an asymmetrical
tip was recently developed by Garcia et al. (Probe
Microsc.
1997, 1, 107). This study represents an
experimental test of that procedure for both silica (∼150 nm)
and
polystyrene (∼50 nm) nanospheres. The procedure can be
summarized by two steps: (1) tip characterization
assuming that the observed AFM height is a true measure of a spherical
particle's diameter and (2) use
of the tip shape to extract a calculated width. To ensure that AFM
heights were equivalent to the true
width, a direct comparison of individual particle sizes determined by
transmission electron microscopy
(TEM) and AFM was conducted. Heights measured from AFM images of
polystyrene nanospheres differed,
on average, less than 5% from widths measured by TEM. The quality
of R
T values was therefore
evaluated
by the magnitude of relative error in calculated particle widths with
respect to true widths. For the tip
used in this study a calculated R
T of 13 nm
resulted in excellent calculated widths for both
polystyrene
and silica spheres. While spherical particles whose diameter is
less than R
T (such as 5-nm Au
colloids)
can be used to characterize the tip apex, larger diameter spheres are
required to fully characterize the
tip. However, spheres much larger than R
T
predominantly interact with the walls of the tip and
therefore
yield artificially high R
T values. On the
basis of our analysis of the procedure developed by Garcia et
al.,
the best sphere size for full characterization of the tip (apex and
walls) is one in which both portions of
the tip interact with the sphere to similar extents (approximately:
R
T ≤ R
p ≤
2R
T, where R
p is the
particle
radius).