Instantaneous ballistic velocity of suspended Brownian nanocrystals measured by upconversion nanothermometry

Brownian motion is one of the most fascinating phenomena in nature(1,2). Its conceptual implications have a profound impact in almost every field of science and even economics, from dissipative processes in thermodynamic systems(3,4), gene therapy in biomedical research(5), artificial motors(6) and galaxy formation(7) to the behaviour of stock prices(8). However, despite extensive experimental investigations, the basic microscopic knowledge of prototypical systems such as colloidal particles in a fluid is still far from being complete. This is particularly the case for the measurement of the particles' instantaneous velocities, elusive due to the rapid random movements on extremely short timescales(9). Here, we report the measurement of the instantaneous ballistic velocity of Brownian nanocrystals suspended in both aqueous and organic solvents. To achieve this, we develop a technique based on upconversion nanothermometry. We find that the population of excited electronic states in NaYF4: Yb/Er nanocrystals at thermal equilibrium can be used for temperature mapping of the nanofluid with great thermal sensitivity (1.15% K-1 at 296 K) and a high spatial resolution (< 1 mu m). A distinct correlation between the heat flux in the nanofluid and the temporal evolution of Er3+ emission allows us to measure the instantaneous velocity of nanocrystals with different sizes and shapes