Generalised Einstein relation for hot Brownian motion

Abstract

The Brownian motion of a hot nanoparticle is described by an effective Markov theory based on fluctuating hydrodynamics. Its predictions are scrutinized over a wide temperature range using large-scale molecular dynamics simulations of a hot nanoparticle in a Lennard-Jones fluid. The particle positions and momenta are found to be Boltzmann distributed according to distinct effective temperatures T HBM and T k . For T HBM we derive a formally exact theoretical prediction and establish a generalised Einstein relation that links it to directly measurable quantities. * * *We gratefully acknowledge helpful discussions with Jean-Louis Barrat (Grenoble), Ramin Golestanian (Oxford), and Markus Selmke (Leipzig), and thank Hugo Brandao for a careful reading of the manuscript. This work was supported by the Alexander von Humboldt foundation, the Deutsche Forschungsgemeinschaft (DFG) via FOR 877 and, within the German excellence initiative, p-5

Motion of a hot particle in viscous fluids

“…[5]. More recently, the Brownian motion of a small heated sphere, a so-called hot particle, has been investigated [6,7]. The authors discovered that the particle diffusion has distinct features from the case of diffusion in isothermal systems.…”

“…To model experiments on the motion of a heated particle [7], the continuous spatial variation of viscosity was approximated by Chakraborty et al [6] using a set of spherical shells of monotonically changing but constant viscosity. Since the solution to the constant viscosity problem is straightforward, multiple such solutions can be stitched together.…”

Laser refrigeration of hydrothermal nanocrystals in physiological media

“…Given that the temperature of the trapped particle is significantly different from the temperature sufficiently far from the laser focus, the particle-trap system is not isothermal and behaves according to nonequilibrium dynamics. Thus, equating the experimental diffusion coefficient to nonisothermal Brownian dynamics necessitates the application of CBM, as derived by Chakraborty et al (25). The CBM diffusion coefficient is then related to the CBM temperature by…”

“…3 to obtain D CBM , which is subsequently compared with the experimental diffusion coefficient to determine the particle temperature T p [excluding the temperature discontinuity at the particle's surface from the Kapitza resistance (44)]. An alternative CBM temperature analysis using a semiphenomenological expression for D CBM that approximately accounts for higher-order terms in ΔT (equation 15 of the supporting online materials of Chakraborty et al (25)] yields consistent results, indicating that these higher-order corrections are negligible, for our purposes. For the experiments reported here, the VFT viscosity parameters were fit to experimental data and are as follows: VFT viscosity parameters for DI water, PBS (0.01M, pH 7.4; Sigma P5368), and DMEM (1×, high glucose, pyruvate; Life Technologies cat.…”

“…It has remained an open question whether these known cooling materials could act to refrigerate aqueous media and undergo hypothesized cold Brownian motion (CBM) (25,26), or whether solvent heating from the background absorption coefficient of water would overwhelm the cooling of individual YLF crystals. Furthermore, it is not obvious a priori that YLF crystals made through hydrothermal processing would have sufficiently low background impurity levels to achieve laser cooling (27,28).…”