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. Despite the substantial increase in experimental reports on MST, a comprehensive theoretical model remains elusive due to its intricate mechanism. Consequently, experimental research into MST faces two primary challenges: (i) predicting the outcomes of experiments before their execution at a practical level and (ii) quantitatively interpreting experimental results by comparing them with numerical calculation results, such as evaluating the thermophoretic force acting on nanomaterials. To address these challenges, 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 numerical method is expected to be invaluable for predicting and interpreting MST phenomena in liquids.