Brownian Dynamics Simulation of Microscale Thermophoresis in Liquid

Microscale thermophoresis (MST) has garnered significant attention as a manipulation method for chemical species ranging from nanometers to micrometers in liquids. In particular, techniques for manipulating single nanometer-sized objects have been developed by driving MST through laser heating with near-infrared wavelengths focused down to submicron scales or via photothermal conversion of plasmonic nanoparticles. While MST simulations on a macroscopic scale can be addressed by solving the diffusion equation using the finite element method, alternative computational approaches are required to investigate thermophoretic behavior at the single-particle level. For this purpose, we have developed a numerical method for the thermophoresis of individual nanoparticles diffusing in a liquid by combining the finite element method for steady-state heat conduction with Brownian dynamics simulations. The scripts for the finite element method and Brownian dynamics calculations used in the present simulations are uploaded in the Supporting Information and freely available. The numerical results demonstrated satisfactory agreement with the experimental results of laser-induced thermophoresis performed on polystyrene nanoparticles with a diameter of 500 nm in water. This computational method is highly useful for controlling MST at the single-particle level, enabling the design of spatial temperature distributions and the evaluation of thermophoretic forces acting on individual nanoparticles.