Extended Maxwell-Garnett-Mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix

Abstract

The optical properties of metallic spherical nanoparticles embedded in host liquid matrix are studied. Extended Maxwell-Garnett-Mie formulation which accounts for size dispersion, the intrinsic confinement, and extrinsic size effect, is proposed for the calculation of the effective dielectric function and absorption coefficient of size dispersion of colloidal solution of Au and Ag nanoparticles in water. We demonstrate that the size distribution induces an inhomogeneous broadening and an increase of the amplitude of the plasmon band. A large redshift of the plasmon band is also observed for silver nanoparticles. Compared to the conventional Maxwell Garnett theory, we demonstrated that this model gives better description of the measured absorption spectra of colloidal gold solutions.

Experimental and theoretical determination of the plasmonic responses and shape distribution of colloidal metallic nanoparticles

“…(8) and (9) for several NP shape distributions. By considering that the NP size is higher than 5 nm, 17 the intrinsic confinement induced by the limitation of the electron mean free path can be neglected.…”

“…[13][14][15][16] This model was recently extended to describe the optical properties of spherical NPs distributed in size by averaging their polarizability. 17,18 However, preparation routes unavoidably conduct to NPs showing a shape distribution which induces drastic changes in the optical properties of NP assembly. [19][20][21][22] Indeed, by combining Gibbs free energy calculation to discrete dipole approximation, Noguez et al [23][24][25] have shown that the morphology and so the optical properties of NPs depend on the temperature used to synthesize them.…”

Determination of morphological characteristics of metallic nanoparticles based on modified Maxwell-Garnett fitting of optical responses

“…S1 mainly contains spherical NPs with a 8.4 nm mean diameter for which the intrinsic confinement can occur. 18 However, the model does not take into account this effect. The correlation matrix (not shown here) suggests that all the parameters are independent.…”

“…Effective medium theories, which approximate the composite material as a homogeneous medium, enable the calculation of the complex effective dielectric function and require few computing resources. The Maxwell Garnett theory 18 was recently extended to describe the optical properties of spherical NPs distributed in size by averaging their polarizability. An extension of the effective medium theory was proposed by Bohren and Huffman 19 to take into account the shape distribution of spheroidal NPs.…”

“…e np is the dielectric function of NPs while e m is the dielectric function of the surrounding medium. For gold NP diameter larger than 10 nm, 18 the intrinsic confinement can be neglected, and e np can be approximated by the bulk dielectric function. 23 hE m i, hE npo i, and hE npp i are the spatial average electric fields inside the matrix, oblate, and prolate NPs, respectively.…”