Ballistic Hot Brownian Motion
Final Report Abstract
Within this project we have targeted the measurement of the instantaneous velocity of a heated Brownian particle in water. The experiments should give information on the theoretical prediction that the Brownian motion of a heated particle can be described by an effective temperature that is frequency-dependent and the instantaneous velocity is described by a different effective temperature than the long-time diffusive limit. For this purpose, we successfully have set up an optical tweezers that can capture the dynamics of the particle over time periods ranging from nanoseconds to 100 s, i.e., 11 orders of magnitude in time. The setup allows us to record displacements over 5 orders of magnitude down to values of 0.15 Angstrom. Therefore, our setup is one of the few in the world which can access this time and spatial regime. We have characterized the performance of this setup with extensive measurements on dielectric particles of different size and material suspended in water. The high time and spatial resolution allowed us to measure the mean squared displacement (MSD) of dielectric microparticles down to a regime where it carries out ballistic motion. The detected MSD also covering the regime of hydrodynamic memory is nicely fitted by available theories over the entire time range. We have been further able to reconstruct the Maxwell–Boltzmann velocity distribution of the microparticles, which is determined by the kinetic temperature. The obtained results are also capturing the theoretical predictions under isothermal conditions. To yield better signal-to-noise ratio especially in the ballistic regime, we have designed a home-built balanced photodiode which is able to withstand higher laser intensities in the detection. Yet this design could not be finalized yet, as the delivery of some parts has been delayed due to the COVID pandemic. To obtain information on the effective temperature of Hot Brownian Motion, we have identified suitable microparticles that are consisting of a polymer core that is decorated with gold nanoparticles at about 10% of its surface area. We have measured the size and the surface distribution of the gold nanoparticles by electron microscopy and used this data as input for numerical simulations of the surface temperature when heated with a 532 nm laser. The simulation results have been compared to measurements of the surface temperature by means of the nematic/isotropic phase transition of a liquid crystal (5 CB). The obtained results of simulation and measurement have been found in good agreement. We have used these AuNP decorated polymer particles to measure the Hot Brownian Motion in the long-time limit. Based on the temperature measurements and the measurements at various heating powers in the optical tweezers, we could confirm the predictions of the Hot Brownian Motion theory. Nevertheless, measurements of the dynamics of the heated particles have been difficult due to imperfections of the AuNP surface coverage of the particles as well as due to the loss of AuNP from the particle surface during the measurement, which made this part of the project considerably more time consuming. The measurements have finally been extended to the ballistic regime. To identify changes in the MSD of the heated Brownian particle we have calculated the ratio of the MSD under isothermal conditions to the one for the heated particle. The results provide indications that the dynamics of the heated particle is changed especially in the region of the hydrodynamic long-time tails. In the ballistic regime, we have first indications that the kinetic temperature is higher than the configurational temperature, which confirms current theory. To further consolidate these new results, we are currently setting up a new balanced photodiode, which has been delayed due to delivery shortages due to COVID.
Publications
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Fully Steerable Symmetric Thermoplasmonic Microswimmers. ACS Nano, 15(2), 3434-3440.
Fränzl, Martin; Muiños-Landin, Santiago; Holubec, Viktor & Cichos, Frank
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Towards Measuring the Maxwell–Boltzmann Distribution of a Single Heated Particle. Frontiers in Physics, 9.
Su, Xiaoya; Fischer, Alexander & Cichos, Frank
