Universal scaling behavior of the temperature increase of a heat nanoparticle on a substrate

Knowledge of temperatures at the nanoscale is essential for studying and controlling the heat-induced local thermal responses. The temperature rise of a heated nanoparticle (NP) near the interface of two kinds of media with different thermal conductivities is numerically investigated. We find that the temperature rise becomes size independent if it is scaled by the temperature rise in the case where the particle-interface distance is zero and the distance is scaled by the equivalent radius of the NP. This universal scaling behavior can be understood with the principle of dimensional homogeneity. An empirical equation is retrieved to predict the actual particle temperature at a given position. Our results may benefit precise control of heat at the nanoscale with applications in plasmonic absorbers, immunotargeted photothermal cancer cell killing, etc.