Spatiotemporal Evolution of Temperature During Transient Heating of Nanoparticle Arrays.

Nanoparticles (NPs) are promising agents to absorb external energy and generate heat. Clusters of NPs or NP array heating have found an essential role in several 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 develop a set of analytical solutions 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 introduce the concept of thermal resolution that quantifies the relationship between minimal heating time, NP array size, energy intensity, and target temperature. Lastly, we define a set of dimensionless parameters that characterize the transition from confined heating to delocalized heating. This study advances the understanding of nanomaterials heating and guides the rational design of innovative approaches for NP array heating.