The size of GNPs with diameters smaller than 35 nm cannot
be determined using eq 10, and hence another method has to be
employed in this size range. Since, for decreasing particle size,
Aspr is increasingly damped relative to the absorbance at other
wavelengths, the ratio of the absorbance at different wavelengths
may be used to determine the particle size without knowledge of
the concentration. Figure 6a shows theoretical results for the ratio
of absorbance (A1/A2) of GNPs in dependence of the particle
diameter, where the wavelengths are stated in the figure; for
example, 450/600 refers to A1 at ì ) 450 nm divided by A2 at ì )
650 nm.
The most pronounced dependence of A1/A2 on d is found if
A2 is taken in the long-wavelength range. This is of course due to
the pronounced influence of the mean free path on the longwavelength
region of the optical functions (compare Figure 3). It
was found that in the long-wavelength range for some hydrosols
the calculated absorbance was not in good agreement with the
measured absorbance. This is probably due to the presence of
small amounts of oblate particles or particle aggregates in some
of the sols, which typically show strong absorbance at longer
wavelengths.14,20-22