Nanoparticle (NP) are promising agents to absorb external energy excitation and generate heat. Cluster of NPs or NP array heating have found essential roles for biomedical applications, diagnostic techniques and chemical catalysis. Various studies have shed light on the heat transfer of nanostructures and greatly advanced our understanding of NP array heating. However, there is a lack of analytical tools and dimensionless parameters to describe the transient heating of NP arrays. Here we demonstrate a comprehensive analysis of the transient NP array heating. Firstly, we developed analytical solution for the NP array heating and provide a useful mathematical description of the spatial-temporal evolution of temperature for 2D, 3D and spherical NP array heating. Based on this, we proposed the idea of thermal resolution that quantifies the relationship between minimal heating time, NP array size, energy intensity and target temperature. Lastly, we define a dimensionless parameter that characterize the transition from confined heating to delocalized heating. This study advances the in-depth understanding of nanomaterials heating and provides guidance for rationally designing innovative approaches for NP array heating.
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