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5) peaks at 400 nm, with the halfwidth about 40 nm. g. fumaric acid) promotes aggregation, and fractal colloid clusters (aggregates) are formed. 0cm3), the colloid's color changes through dark orange and violet to dark grey over ten hours. Following the aggregation, a large wing in the long wavelength part of the spectrum appears in the extinction, as seen in Fig. 5. Note that in calculations shown in Fig. 5, the data of Fig. 2 was used, where X and (~ are expressed in terms of A for silver particles.
This results from the fact that for fractals the dipole-dipole interactions are not long-range, and optical excitations are localized in small areas of a fractal aggregate. As mentioned, these areas have very different local structures and, accordingly, they resonate at different frequencies. In contrast, in compact nonfractal aggregates (with D = d = 3), the optical excitations (known also as dipolar collective modes) are delocalized over the whole sample, and their resonance frequencies lie in a relatively narrow spectral interval.
In contrast, the described model, although inexact, allows us to obtain the correct optical characteristics while remaining within the dipolar approximation - which is, of course, crucial for a complex random system, such as a fractal cluster consisting of thousands of particles. 2) takes an elegant form when written in matrix notation. , Ei,r We also define an orthonormal basis ]ia) in C aN, such that the Cartesian components of the dipole moments are expressed in this basis as die, = {iol]d).