Theory of Hot Brownian Motion

Rings, Daniel; Selmke, Markus; Cichos, Frank; Kroy, Klaus

doi:10.1039/c0sm00854k

Cited by 29 publications

(59 citation statements)

References 34 publications

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“…On the other hand, if this known mismatch is corrected manually, one may indeed expect the effective friction for a radially varying viscosity, which can be calculated analytically from eq 8, to provide an accurate approximation to the exact result, which would have to be obtained numerically for each particular parameter set of interest from eq 7. In the following, we pursue this approximate analytical route, 21 which turns out to be in very reasonable accord with our experimental results. To model the temperature dependence of the viscosity, we use the phenomenological expression log(η/η 0 ) ) B/(T -T K ) (9) with parameters η 0 ) 2.984 × 10 -5 mPa s, B ) 496 K, T K ) 150 K (Kauzmann temp.…”

Section: Theoreticalsupporting

confidence: 73%

Hot Brownian Particles and Photothermal Correlation Spectroscopy

Radünz¹,

Rings²,

Kroy³

et al. 2009

J. Phys. Chem. A

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We introduce a new technique to measure tracer dynamics, which is sensitive to single metal nanoparticles down to a radius of 2.5 nm with a time resolution of a few microseconds. It is based on a fluctuation analysis of a heterodyne photothermal scattering signal emanating from the hot halo around the laser-heated tracer. A generalized Stokes-Einstein relation for "hot brownian motion" is developed and verified. Exploiting the excellent photostability of gold nanoparticles, the developed method promises broad applications especially in the field of quantitative biomedical screening.

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Section: Theoreticalsupporting

confidence: 73%

Hot Brownian Particles and Photothermal Correlation Spectroscopy

Radünz¹,

Rings²,

Kroy³

et al. 2009

J. Phys. Chem. A

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“…Substantial deviations from the value 3/4 for a sphere, equation (20), only become apparent for eccentricities τ −1 0 0.95, corresponding to extreme aspect ratios L/(2R) 3.5. Note that the high power of the radial distance r in the denominator under the integral in equations (15) and (18) suggests that the effective rotational temperature and friction should (15) and [31] are represented by solid and dot-dashed lines for rotational and translational motion, respectively. Note that they differ by a heating-dependent kinematic factor, an effect that we neglect in the estimate equation (23), for slender rods.…”

Section: Theorymentioning

confidence: 99%

“…On this basis, we construct and validate a Markov model for the rotational Langevin dynamics of a hot Brownian particle with effective temperature and friction parameters, T θ HBM and ζ θ HBM . While the success of this strategy has already been demonstrated for the translational motion [17,31,32], recent experiments using heated nanorods [24] and hot Janus particles [18] underscore the need for a separate quantitative analysis of the rotational dynamics. Below, we derive T θ HBM and ζ θ HBM for the rotational Brownian motion of a hot particle and demonstrate that they differ from their analogues for translational motion.…”

mentioning

confidence: 99%

Rotational hot Brownian motion

Rings¹,

Chakraborty²,

Kroy³

2012

New J. Phys.

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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...

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“…If the diamond is not in thermal equilibrium with the surrounding liquid and is held at a higher or lower temperature, a radial temperature gradient in the liquid is established and the Brownian motion of the particle is modified. This modification is known in the literature as hot or cold Brownian Motion [50][51][52][53][54][55][56] . In particular, in the case of cold Brownian motion (CBM), the diffusion constant is related to the effective CBM temperature of the particle T CBM , and CBM Stokes drag γ CBM , via…”

Section: Measuring the Temperature Of The Diamond Crystalitementioning

confidence: 99%

Optical cryocooling of diamond

et al. 2017

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The cooling of solids by optical means only using anti-Stokes emission has a long history of research and achievements. Such cooling methods have many advantages ranging from no-moving parts or fluids through to operation in vacuum and may have applications to cryosurgery. However achieving large optical cryocooling powers has been difficult to achieve except in certain rare-earth crystals. Through study of the emission and absorption cross sections we find that diamond, containing either NV or SiV (Nitrogen or Silicon vacancy), defects shows potential for optical cryocooling and in particular, NV doping shows promise for optical refrigeration. We study the optical cooling of doped diamond microcrystals ranging 10−250 µm in diameter trapped either in vacuum or in water. For the vacuum case we find NV-doped microdiamond optical cooling below room temperature could exceed |∆T | > 10 K, for irradiation powers of Pin < 100 mW. We predict that such temperature changes should be easily observed via large alterations in the diffusion constant for optically cryocooled microdiamonds trapped in water in an optical tweezer or via spectroscopic signatures such as the ZPL width or Raman line.Optical refrigeration, or optical cryocooling, uses antiStokes emission in solids to deplete the phonon population within the solid, cooling it. First suggested by Pringsheim 1 , and initially demonstrated by Epstein et al in 19952 , the phenomena is observed when low entropy laser light is primarily absorbed at wavelengths slightly longer than the mean fluorescence wavelength (λ f ) of the material. The light is reemitted with a broadband fluorescence possessing a mean energy which is higher than the incident pump laser. The increase in energy is due to absorption of lattice phonons (vibrations), reducing the net temperature of the solid. Optical refrigeration has experimentally achieved temperatures of T ∼155K (from room temperature) using ytterbium-doped fluoride crystal (YLiF 4 : Yb 3+ ) 3 , T ∼250K (from 290K), for the semiconductor CdS 4 , and T ∼114K more recently using a multi-pass setup with Yb-doped crystals 5 . These temperatures outperform Peltier/thermoelectric coolers and reach into the defined cryogenic regime (<123K). Importantly they operate with no mechanical vibrations, magnetic/electric fields or moving mechanical/liquid/gas components and are ideal refrigeration solutions in many difficult/sensitive situations eg. optomechanical, space, sensing experiments 6-9 . In addition, spin properties of diamond defects have recently attracted much attention owing to their long spin coherence times T 2 . Since T 2 times increase at low temperatures, a new way of cooling diamond is important for applications where long spin relaxation times are needed. Microscopic diamond crystals are highly biocompatible and can be functionalised to attach to specific biologically important ligands 10 . Cryosurgery and cryotherapy is a method to destroy diseased or harmful tissues within the body and involves cyclic freezing and thawing of the ...

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Theory of Hot Brownian Motion

Cited by 29 publications

References 34 publications

Hot Brownian Particles and Photothermal Correlation Spectroscopy

Hot Brownian Particles and Photothermal Correlation Spectroscopy

Rotational hot Brownian motion

Optical cryocooling of diamond

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