Nanoparticles are kind of transient state of matter between molecular/atomic state and solid/condensed matter. In molecules we have well defined electronic states and spectra are linear. For infinite solid crystal we have long term order and well defined energy band structure and well defined spectral bands. Core of nanoparticles can be described as crystal with well-defined density of states and corresponding spectra. But surface atoms/molecules are not totally included into the lattice which has influence on bond energy, density of states, whatever . Partial fraction of surface atoms/molecules increases with decreasing of particle size. Thus we have increased width of spectral bands for smaller particles. It is very simplified description, sorry.
If the size polydispersity increases during the synthesis, you will observe peak broadening
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