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The effective absorption cross-section of dye, and therefore, the efficiency of dye-sensitized solar cell can be increased by surface plasmon resonance (SPR) of metal nanoparticles with enhanced dephasing time. Further, the dephasing time is proportional to the enhancement factor of electric field in the vicinity of nanoparticle surface, and is governed by size, shape, and dielectric constant of surrounding medium. In this paper, we demonstrate that crystallinity of silver nanoparticles plays an important role in enhancing the dephasing time of SPR. Our theoretical formulation indicates that the dephasing time is higher for single crystalline silver nanoparticles as compared to that of polycrystalline nanoparticles, which is attributed to the presence of scattering centers in the latter. This suggests that single crystalline silver nanoparticles are interesting candidates for the enhancement of effective absorption cross-section of dyes. In order to validate our theoretical formulation, we have synthesized single crystalline and polycrystalline silver nanoparticles and studied their effect on absorption cross-section of N719 dye. We observed that dye incorporated with single crystalline silver nanoparticles showed a significant enhancement as compared to polycrystalline silver nanoparticles (24.42% in solution, 21.01% in thin film form in single crystalline silver nanoparticles while 8.52% in solution, 7.97% in thin film form in polycrystalline silver nanoparticles, respectively).

Schematic representing broadband enhancement in absorption cross-section of N719 dye using different anisotropic shaped single crystalline silver nanoparticles.

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The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin’s Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number $${\mathcal {R}}_0$$ R 0 is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of $${\mathcal {R}}_0$$ R 0 using the parameters value. In the numerical simulations, we concluded that reducing $${\mathcal {R}}_0$$ R 0 below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures.

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