From this viewpoint the ratios from Figure
6a, which have long-wavelength values in the denominator, can
be used to ascertain the quality of the gold hydrosol or monitor
aggregation of particles but are not suitable for the determination
of particle sizes.
However, a better agreement between theory and experiment
is found if the absorbance ratios are determined in the wavelength
region below 600 nm. Figure 6b shows the ratio of the absorbance
at the surface plasma resonance peak (Aspr) to the absorbance at
450 nm (A450) in dependence of the logarithm of the particle
diameter in the size range from 5 to 80 nm. The theoretical data
(circles) exhibit an excellent linearity (solid line in Figure 6b; R2
> 0.999), and hence the ratio Aspr/A450 should be particularly
suitable to calculate the particle diameter (in nanometers) from
Here, B1 is the inverse of the slope (m) of the linear fit in Figure
6b and B2 ) B0/m where B0 is the intercept. Agreement with the
experimental data is not perfect, and some spread is observed,
resulting in an error of 18% for the calculation of the particle
sizes if the best fit parameters are determined from the theoretical
data in Figure 6b (B1 ) 3.55; B2 ) 3.11). If the experimentally
determined fit parameters are used (B1 ) 3.00; B2 ) 2.20) the
calculation of particle diameters using eq 11 results in an improved
average deviation of 11%. Numerical data of d(Aspr/A450) which
allow the reader to determine the size of GNPs without the need
to perform calculations are presented in the Supporting Information.