Size and shape dependence of optical properties of nanostructures

A phenomenological model based on thermodynamical variables is used to analyze the optical properties of nanomaterials. The expression of cohesive energy given by Qi and Wang model is extended to study the variation of the energy band gap, vibrational frequency, and static dielectric constant with size for nanoparticles, nanowires, and nanofilms. The energy bandgap is observed to increase in nanostructures with a reduction in size while the reduction in the vibrational frequency of nanostructures is found with a decrease in size from model calculations. The dielectric constant is also found decreasing with the size reduction of the nanostructure to the nanoscale. As the number of surface atoms changes with change in the shape of the nanomaterial, the shape effect on optical properties is also studied. The size and shape effect are found prominent in nanostructures up to the size limit of approximately 30 nm; however, the effect of size and shape becomes less significant as the size is more than 30 nm. The model predictions are consistent with the available experimental and simulated trend which supports the validity of the model theory.