Dear Surbhi Sharma , there are plenty of articles describing metallic NP´s size effects on localized surface plasmon resonances (LSPR). As a rule of thumb you can consider that the larger the particle the more red-shifted will be the LSPR. A way to understand this is by considering the metallic NP as a resonance box, in a "tiny" NP the light will be bouncing up and down in a tiny space, so short wavelengths will be in resonance, while in "big" NP´s light could be bouncing in a "large" space and therefore in resonance with larger wavelengths.

Normally your NP´s are not monodispersed, so there is a size polydispersity, and therfore the response of your mixture will be a mixture of the response of your particles according to their distribution. Not just size matters, also the shape of NP´s have an effect on the SPR´s of NP´s, for instance, a rod-like NP will show a double peak or band spectrum, indicating the presence of two resonances, one in the short direction (tranverse) and another in the long one (longitudinal).

May be the following research works, could be illustrative of the literature about this tipic:

Article Size Effect of Ag Nanoparticles on Surface Plasmon Resonance

Article Size-Dependent Shifts of Plasmon Resonance in Silver Nanopar...

Article Gold nanoparticles: Optical properties and implementations i...

You even can choose the NP´s by their size or their SPR wavelength:

https://www.sigmaaldrich.com/ES/en/technical-documents/technical-article/materials-science-and-engineering/biosensors-and-imaging/gold-nanoparticles

RG let you search directly bibliography or questions already solved about any topic of your interest:

https://www.researchgate.net/post/What-effect-will-the-nanoparticle-size-have-on-surface-plasmon-resonance

Hope this helps. Good luck with your research work.

Addition： Shape- and Size-Dependent Refractive Index Sensitivity of Gold Nanoparticles

Article Size and Temperature Effects on the Surface Plasmon Resonanc...

https://www.sciencedirect.com/science/article/abs/pii/S0257897208004520

Chapter Effect of Size, Shape and Environment on the Optical Respons...

Dear Surbhi Sharma

i second the view of Manuel Gómez

In addition to the description given above one can also keep in mind that inherent material properties like inter-band transitions in nanoparticles, their size & shape and the dielectric constant of the surrounding medium significantly effects the surface plasmon resonance band. Also, the overall absorbance that we generally record in conventional absorption spectrophotometer instrument is not the true absorbance. It is the 'extinction' and its made up of 'absorption (losses in metals)' and the 'scattering'. Unlike simple organic molecule solutions (where only absorbance operates), in the case of nanoparticles, the scattering places a significant role.

So coming to your question, the red-shift that we observe as rightly mentioned by Manuel Gómez , for isotropic or spherical nanoparticles, is true as the size increases. But it is equally important to remember that the contribution from the scattering (of overall extinction) is significant for such bigger sized particles (and absorption losses are minimum). However, for anisotropic nanoparticles like rods or triangles or elongated assemblies of nanoparticles, the red shift observed is due to the longitudinal modes. All these discussions holds good for nanoparticles and is different for SPR of metal thin films.

One can take a look at the following recent works to get better insights.

Article Plasmon-Coupled Directional Emission from Soluplus-Mediated ...

Article Metal-Free, Graphene Oxide-Based Tunable Soliton and Plasmon...

Article Multifunctional Hybrid Soret nanoarchitectures for Mobile Ph...

Article Superior Resonant Nanocavities Engineering on Photonic Cryst...

Article Nanostructure effect on quenching and dequenching of quantum...

Article Femtomolar Detection of Spermidine Using Au Decorated SiO2 N...

Thanks!

It depends on the size range considered, and on the nature of the material considered. For very small particles (few nm and less), there are other effects resulting in resonance shifts (not necessarily following the "bigger particle= plasmon red-shift" picture). For instance, electronic confinement, which leads to a change of the particle's dielectric function with size, and thus to a resonance shift. Moreover, the "bigger particle=plasmon red shift" for larger particles works if the material has a Drude-like dielectric function. When it is not the case (transition metals, semi-metals, etc), the picture can be more complex. See for example the works by C. Langhammer.