Rotational hot Brownian motion

Abstract

We establish an effective Markov theory for the rotational Brownian motion of hot nanobeads and nanorods. Compact analytical expressions for the effective temperature and friction are derived from the fluctuating hydrodynamic equations of motion. They are verified by comparison with recent measurements and with parallel molecular dynamics simulations over a wide temperature range. This provides unique insights into the physics of hot Brownian motion and an excellent starting point for further experimental tests and applications involving laser-heated nanobeads, nanorods and Janus particles.The popular Markovian theory of Brownian motion, as developed by Einstein, Langevin and Smoluchowski a century ago, has been the starting point and inspiration for innumerable applications [1,2]. However, the usual convenient formulation in terms of the centre-of-mass coordinates of particles only pertains to the special case of an isolated spherical particle. In the general case of interacting and/or anisotropic particles, both translational and rotational degrees of freedom couple, calling for a more elaborate mathematical description. This is most obvious for rod-shaped particles that have different mobilities for the movement parallel and perpendicular to their long axis [3], but in fact also holds for interacting spherical particles [4]. Due to the associated technical complications, the present theoretical understanding is still relatively incomplete [6], in particular with regard to micro-swimmers and other active or selfpropelled colloidal particles [7][8][9], for which the proper hydrodynamic description is even more subtle than for passive particles in external fields [10,11]. The directed motion for such selfpropelled particles from sperms [12] to Janus particles running on chemical fuel [13] is usually limited by (equilibrium or nonequilibrium) rotational Brownian motion. Besides, rotational Brownian motion is undoubtedly of interest for its own sake. It is accessible to spectroscopy [14] and has been the basis for the development of new microrheological techniques [15] and nanoscopic heat engines [16].In this paper, we are concerned with a specific type of rotational Brownian motion that occurs whenever the colloidal particles have an elevated temperature with respect to their solvent. In this case, we speak of rotational hot Brownian motion, in analogy to the better understood translational case [17]. Both intended [18][19][20][21][22] and unintentional [23,24] realizations of (rotational) hot Brownian motion are nowadays widespread in biophysical and nanotechnological applications, which often employ nanoparticles exposed to laser light as tracers, anchors and localized heat sources. Deliberate heating of nanoparticles is, for instance, common in photothermal therapy [25,26], but it also helps to enhance the optical contrast for detection [27] or in photothermal correlation spectroscopy [28]. Laser-heating is also a convenient way of supplying the energy for the self-thermophoretic propulsion of anisotropic parti...

Laser-induced rotation and cooling of a trapped microgyroscope in vacuum

“…2 is calculated using equation (1), implying a pressure-dependent Stokes rotational drag coefficient. The discrepancy between the model and experimental values at pressures below 10 Pa could be attributed to particle instability induced by heat because of light absorption2223, while the low pressure particle loss might be due to the large inertial forces experienced by the particle at high rotation rates.…”

Brownian Thermometry Beyond Equilibrium

“…One finds that rotation and translation, exciting different solvent flow fields, have their own effective temperatures. [16,72] Far from equilibrium, temperature is thus seen to loose its universal character and to become more of an interaction parameter between the particle and its solvent, akin to the equilibrium friction coefficients ζ, say, which also differ between rotation and translation. In general, the effective parameters are complicated functions of the molecular temperature and viscosity fields TðrÞ, hðrÞ, (their spatial distribution for a hot Brownian particle is shown in Figure 2) and the solvent velocity field excited by the particle motion.…”

“…For a hot particle in a cool solvent, the kinetic degrees of freedom are always hotter than the spatial ones, and for example rotation is hotter than translation. [72] Considering a weakly damped hot Brownian particle trapped in a harmonic potential -a situation of high practical interest e. g. for nanoparticles controlled by optical tweezers [50,57] -then leads to the fancy notion of "Brownian thermospectrometry". [33] The characterizing observable of the setup can be chosen to be the particle position xðtÞ and the confinement force is mw 2 0 xðtÞ.…”

Invited Article: Optical trapping of ultrasmooth gold nanoparticles in liquid and air

“…Thus linearly polarized beam traps may result in more a pronounced difference in stiffness between US and NS gold NPs. We note that as discussed by Seol et al and others, trap stiffness is subject to laser-induced heating of trapped gold NPs, 4,[17][18][19] which is modeled using COMSOL and described later in this paper. As a result of the relatively low optical power of 45 mW in our case, the expected particle temperature rise (∼10 • C for 100 nm gold NPs) should have but little effect on stiffness measurement.…”