The theory of Brownian motion is a cornerstone of modern physics. In this thesis, we introduce a nonequilibrium extension to this theory, namely an effective Markovian theory of the Brownian motion of a heated nanoparticle. This phenomenon belongs to the class of nonequilibrium steady states (NESS) and is characterized by spatially inhomogeneous temperature and viscosity fields extending in the solvent surrounding the nanoparticle.
The first chapter provides a pedagogic introduction to the subject and a concise summary of our main results and summarizes their implications for future developments and innovative applications.
The derivation of our main results is based on the theory of fluctuating hydrodynamics, which we introduce and extend to NESS conditions, in the second chapter. We derive the effective temperature and the effective friction coefficient for the generalized Langevin equation describing the Brownian motion of a heated nanoparticle. As major results, we find that these parameters obey a generalized Stokes–Einstein relation, and that, to first order in the temperature increment of the particle, the effective temperature is given in terms of a set of universal numbers.
In chapters three and four, these basic results are made explicit for various realizations of hot Brownian motion. We show in detail, that different degrees of freedom are governed by distinct effective parameters, and we calculate these for the rotational and translational motion of heated nanobeads and nanorods. Whenever possible, analytic results are provided, and numerically accurate approximation methods are devised otherwise.
To test and validate all our theoretical predictions, we present large-scale molecular dynamics simulations of a Lennard-Jones system, in chapter five. These implement a state-of-the-art GPU-powered parallel algorithm, contributed by D. Chakraborty. Further support for our theory comes from recent experimental observations of gold nanobeads and nanorods made in the the groups of F. Cichos and M. Orrit. We introduce the theoretical concept of PhoCS, an innovative technique which puts the selective heating of nanoscopic tracer particles to good use.
We conclude in chapter six with some preliminary results about the self-phoretic motion of so-called Janus particles. These two-faced hybrids with a hotter and a cooler side perform a persistent random walk with the persistence only limited by their hot rotational Brownian motion. Such particles could act as versatile laser-controlled nanotransporters or nanomachines, to mention just the most obvious future nanotechnological applications of hot Brownian motion.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-102186 |
| Date | 18 February 2013 |
| Creators | Rings, Daniel |
| Contributors | Universität Leipzig, Fakultät für Physik und Geowissenschaften, Prof. Klaus Kroy, Prof. Klaus Kroy, Prof. Ramin Golestanian |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | German, English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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