Extinction coefficients of gold nanoparticles and their dimers. Dependence of optical factor on particle size

The generalized Mie theory has been employed to calculate extinction coefficients κ for isolated gold nanoparticles of different sizes (4–80 nm) and their dimers (κ₂) at the maximum of the short-wave plasmon resonance band. It has been found that the value of κ₂ essentially depends on both interparticle distance s and particle sizes R. According to the character of variations in the κ₂(s) dependence, three ranges of the distances are distinguished, i.e., large, intermediate, and small. In the first range, the κ₂ values slightly differ from doubled κ values. Nevertheless a tendency toward an increase in κ₂ is distinctly seen as the particles approach each other, and, within some range of s values and for particles with radii R < 15 nm, κ₂ is higher than 2κ. For dimers of larger particles, κ₂ < 2κ, with its value gradually decreasing with a reduction in the s value. The behavior changes when the particle sizes are of about 50 nm. In the range of small interparticle distances, κ₂ values slightly vary with the distance between the particles somewhat decreasing or oscillating with a small amplitude about some mean value. In this range, as the sizes of the gold particles grow, the extinction coefficients of dimers increasingly deviate from the sum of the extinction coefficients of the particles composing the dimers. For 20–80 nm nanoparticles, the size-dependence plotted for the extinction efficiency of dimers in logarithmic coordinates within the range of small interparticle distances is described by a straight line, the slope of which (1.036 ± 0.039) appears to be somewhat smaller than the slope of a corresponding line for individual gold particles (1.274 ± 0.014). The ratio between κ₂ and κ predetermines the character of variations in the optical factor as depending on the particle size and the interparticle distance and governs the behavior of the sol turbidity at the stage of nanoparticle dimerization.