Rotational Brownian Motion Research Articles

Role of Brownian motion and Néel relaxations in Mössbauer spectra of magnetic liquids

The absorption cross-section of Mössbauer radiation in magnetic liquids is calculated, taking into consideration both translational and rotational Brownian motion of magnetic nanoparticles as well as stochastic reversals of their magnetization in the absence of an external magnetic field. The role of Brownian motion in ferrofluids is considered in the framework of the diffusion theory, while for the magnetorheological fluids with large nanoparticles, it is done with the aid of Langevin's approach. For stochastic rotation, we derived the equation analogous to Langevin's one and found the corresponding correlation function. In both cases, simple rotational correlation functions are obtained in the approximation of small rotations during the lifetime of the excited Mossbauer nuclei. Influence of the Néel's relaxations is considered in the framework of the Blume - Tjon model.

Immunojanus Particles for low-volume and isolation-free unlabeled characterization of small Extracellular Vesicle in biofluids: Characterization of disease type by surface marker profiling.

Small extracellular vesicles (sEVs) are vital for cellular communication and serve as critical biomarker carriers for diseases such as cancer. However, quantifying and profiling sEV surface markers presents significant challenges due to the low concentration of specific sEV-bound proteins and interference by more abundant dispersed proteins. This paper presents Immunojanus Particles (IJPs), a new method that enables the direct detection of sEVs in less than an hour without isolation. The design of IJPs incorporates fluorescent and non-fluorescent halves, utilizing rotational Brownian motion to detect captured sEVs through the change in the blinking rate, without interference from the smaller dispersed proteins. We demonstrate a detection limit of 2E5 sEVs/mL with low sample volumes and the capability to characterize sEVs directly from plasma, serum, cell culture media, and urine. In a small pilot study involving 87 subjects, including individuals with colorectal cancer, pancreatic ductal adenocarcinoma, glioblastoma, Alzheimer's disease, and healthy controls, our method accurately identified the type of disease with high 0.90-0.99 AUC in a blind setting. Compared with an orthogonal ultracentrifugation plus surface plasmon resonance (UC+SPR) method that requires about 24 hours, the sensitivity and dynamic range of IJP are better by 2 logs.

Impact of ageing on structure of random sequential adsorption packings of discorectangles

The ageing processes in the systems of elongated particles (discorectangles) adsorbed on a plane was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was tested. The initial jammed state was produced using the random sequential adsorption (RSA) model. The transition from the jammed to equilibrium states were performed via translational and rotational Brownian motions. An aspect ratio of the particles (length-to-width ratio) was varied within the range ε=1−12 . At ɛ < 10 the relaxation into the isotropic state was always observed. In the intermediate range, 10⩽ε⩽11 , the relaxation transition into the states with ordered domains was observed. Particularly, for ɛ = 10 this transition was related with significant finite size scaling effects. For particles with ɛ = 12 formation of the large scale quasi-nematic domains and unlimited domain growth was observed. The impact of the relaxation on the domain structure, porosity, percolation connectivity and tracer particle diffusion in such barrier systems was also discussed.

Rotational and translational drags of a Janus particle close to a wall and a lipid membrane

HypothesisMeasuring rotational and translational Brownian motion of single spherical particles reveals dissipations due to the interaction between the particle and the environment. ExperimentsIn this article, we show experiments where the in-plane translational and the two rotational drag coefficients of a single spherical Brownian particle can be measured. These particle drags are functions of the particle size and of the particle–wall distance, and of the viscous dissipations at play. We measure drag coefficients for Janus particles close to a solid wall and close to a lipid bilayer membrane. FindingsFor a particle close to a wall, we show that according to hydrodynamic models, particle–wall distance and particle size can be determined. For a particle partially wrapped by lipid membranes, in absence of strong binding interactions, translational and rotational drags are significantly larger than the ones of non-wrapped particles. Beside the effect of the membrane viscosity, we show that dissipations in the deformed membrane cap region strongly contribute to the drag coefficients.

Brownian translation and rotation from the ballistic to the diffusive limit and derivation of the physical properties of dust agglomerates.

We analyzed the translational and rotational Brownian motion of aggregates of micrometer-sized silica spheres under microgravity conditions and in rarefied gas. The experimental data was collected in the form of high-speed recordings using a long-distance microscope as part of the ICAPS (Interactions in Cosmic and Atmospheric Particle Systems) experiment on board of the sounding rocket flight Texus-56. Our data analysis shows that the translational Brownian motion can be used to determine the mass and translational response time of each individual dust aggregate. The rotational Brownian motion additionally provides the moment of inertia and the rotational response time. A shallow positive correlation between mass and response time was found as predicted for aggregate structures with low fractal dimensions. Translational and rotational response times are roughly in agreement. Using the mass and the moment of inertia of each aggregate, we determined the fractal dimension of the aggregate ensemble. Slight deviations from the pure Gaussian one-dimensional displacement statistics were found in the ballistic limit for both the translational and rotational Brownian motion.

Effect of speed fluctuations on the collective dynamics of active disks.

Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate β. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of β, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.

Towards in vivo applications of 111Ag perturbed angular correlation of γ-rays (PAC) spectroscopy

111Ag-perturbed angular correlation of γ-rays (PAC) spectroscopy provides information on the nuclear quadrupole interactions, and thereby on the local structure and dynamics of the silver ion binding site. Brownian rotational motion, i.e. rotational diffusion, of 111Ag-labeled molecules will significantly affect the PAC spectra. Here we illustrate this effect, by simulating 111Ag PAC spectra for 111Ag-labeled molecules with molecular masses spanning from 102 to 106 g/mol, reflecting a span from fast (small molecules) to slow (large molecules) rotational diffusion on the PAC time scale. The simulated spectra are compared to 111Ag-PAC data obtained from a pilot study involving 111Ag(I) bound to a designed chelator exhibiting fast reorientation in solution, as well as to 111Ag-labeled species formed by 111Ag(I) in human serum, exhibiting slow (or no) reorientation on the PAC time scale. The simulated and experimental data illustrate typical PAC signals that are likely to be observed in vivo, when following the fate of 111Ag-labeled compounds. Potential in vivo applications are stability studies of 111Ag-radiopharmaceuticals, dissociation studies of 111Ag from the labeled molecule followed by binding to another (bio)molecule, or binding of 111Ag-labeled probes to larger carriers such as proteins.

Motion Analysis and Real‐Time Trajectory Prediction of Magnetically Steerable Catalytic Janus Micromotors

Chemically driven micromotors display unpredictable trajectories due to the rotational Brownian motion interacting with the surrounding fluid molecules. This hampers the practical applications of these tiny robots, particularly where precise control is a requisite. To overcome the rotational Brownian motion and increase motion directionality, robots are often decorated with a magnetic composition and guided by an external magnetic field. However, despite the straightforward method, explicit analysis and modeling of their motion have been limited. Here, catalytic Janus micromotors are fabricated with distinct magnetizations and a controlled self‐propelled motion with magnetic steering is shown. To analyze their dynamic behavior, a dynamic model that can successfully predict the trajectory of micromotors in uniform viscous flows in real time by incorporating a form of state‐dependent‐coefficient with a robust two‐stage Kalman filter is theoretically developed. A good agreement is observed between the theoretically predicted dynamics and experimental observations over a wide range of model parameter variations. The developed model can be universally adopted to various designs of catalytic micro‐/nanomotors with different sizes, geometries, and materials, even in diverse fuel solutions. Finally, the proposed model can be used as a platform for biosensing, detecting fuel concentration, or determining small‐scale motors’ propulsion mechanisms in an unknown environment.

Enhanced and Robust Directional Propulsion of Light-Activated Janus Micromotors by Magnetic Spinning and the Magnus Effect.

Advances in the versatile design and synthesis of nanomaterials have imparted diverse functionalities to Janus micromotors as autonomous vehicles. However, a significant challenge remains in maneuvering Janus micromotors by following desired trajectories for on-demand motility and intelligent control due to the inherent rotational Brownian motion. Here, we present the enhanced and robust directional propulsion of light-activated Fe3O4@TiO2/Pt Janus micromotors by magnetic spinning and the Magnus effect. Once exposed to a low-intensity rotating magnetic field, the micromotors become physically actuated, and their rotational Brownian diffusion is quenched by the magnetic rotation. Photocatalytic propulsion can be triggered by unidirectional irradiation based on a self-electrophoretic mechanism. Thus, a transverse Magnus force can be generated due to the rotational motion and ballistic motion (photocatalytic propulsion) of the micromotors. Both the self-electrophoretic propulsion and the Magnus force are periodically changed due to the magnetic rotation, which results in an overall directed motion moving toward a trajectory with a deflection angle from the direction of incident light with enhanced speed, maneuverability, and steering robustness. Our study illustrates the admirable directional motion capabilities of light-driven Janus micromotors based on magnetic spinning and the Magnus effect, which unfolds a new paradigm for addressing the limitations of directionality control in the current asymmetric micromotors.

Prediction of water relaxation time using near infrared spectroscopy

AbstractMolecular rotational relaxation time of water is believed to be an important parameter to evaluate the deterioration rate of biomaterial. In this work, we proposed and verified a method of using Fourier‐transform near infrared spectroscopy, which has advantages of non‐invasion, low‐cost, high spatial resolution as well as being time efficient, to predict the relaxation time of water in biomaterial. The Langevin equation of rotational Brownian motion of water dipole with double‐fold cosine potential barrier, solution of which gives the relaxation time as a function of potential barrier height, was applied to water–saccharide systems. We assumed that this potential barrier height is comparable to the increase of hydrogen bond strength of water in saccharide solution. The hydrogen bond strength values of pure water and saccharide solutions were calculated from the measured NIR absorbance band of water at 4500 –5500 cm−1. The relaxation times yielded by this method are in good agreement with those measured by dielectric spectroscopy.Practical ApplicationsWater plays important role in the investigation of long‐term preservation of biomaterials, since it is the medium of many chemical reactions which eventually lead to the deterioration. In principle, both cryopreservation and dry‐preservation involve the reduction of the mobility of water molecules to reduce chemical reaction rates. The rotational relaxation time as an indicator of molecular mobility of water was proved directly related to the protein deterioration rate. Compared with conventional methods of measuring water relaxation time such as dielectric spectroscopy or magnetic resonance, FT‐IR system has many advantages: low cost, non‐invasion, time efficient, and can provide spatial resolution up to μm level with infrared microscope. Therefore, our method may provide convenience to monitor crop growth and evaluate the quality of food in storage.

Development of a Self-Viscosity and Temperature-Compensated Technique for Highly Stable and Highly Sensitive Bead-Based Diffusometry.

Brownian motion, which is a natural phenomenon, has attracted numerous researchers and received extensive studies over the past decades. The effort contributes to the discovery of optical diffusometry, which is commonly used for micro/nano particle sizing. However, the analysis uncertainty caused by the coupling relationship among particle diameter, temperature, and fluid viscosity usually poses a barrier to precise measurement. Preventing random background noise becomes the key to achieving a high level of accuracy in diffusometry detection. Recently, Janus particles have become known as an ideal tool for resolving the rotational Brownian motion. Followed by our previous study, the rotational Brownian motion and the translational Brownian motion can be separately measured using the Janus particles. Accordingly, a simple self-viscosity and temperature-compensated technique based on the delicate removal of temperature and fluid viscosity variations through particle tracking was first proposed in this study. Consequently, the translational Brownian motion was expressed in terms of particle trajectory, whereas the rotational Brownian motion was expressed in terms of the blinking signal from the Janus particles. The algorithm was verified simulatively and experimentally in temperature (10 °C to 40 °C) and viscosity-controlled (1 mPa·s to 5 mPa·s) fields. In an evaluation of biosensing for a target protein, IFN-γ, the limit of detection of the proposed self-compensated diffusometry reached 0.45 pg/mL, whereas its uncertainties of viscosity and temperature were 96 and 15-fold lower than the pure the rotational Brownian motion counterpart, respectively. The results indicated the low-uncertainty and high-accuracy biosensing capability resulting from the self-viscosity and temperature-compensated technique. This research will provide a potential alternative to future similar bead-based immunosensing, which requires ultra-high stability and sensitivity.

Rate of Entropy Production in Stochastic Mechanical Systems.

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems.

Slip/Stick Viscosity Models of Nanoconfined Liquids: Solvent-Dependent Rotation in Metal-Organic Frameworks.

Artificial molecular machines are expected to operate in environments where viscous forces impact molecules significantly. With that, it is well-known that solvent behaviors dramatically change upon confinement into limited spaces as compared to bulk solvents. In this study, we demonstrate the utility of an amphidynamic metal-organic framework with pillars consisting of 2H-labeled dialkynyltriptycene and dialkynylphenylene barrierless rotators that operate as NMR sensors for solvent viscosity. Using line-shape analysis of quadrupolar spin echo spectra we showed that solvents such as dimethylformamide, diethylformamide, 2-octanone, bromobenzene, o-dichlorobenzene, and benzonitrile slow down their Brownian rotational motion (103-106 s-1) to values consistent with confined viscosity values (ca. 100-103 pa s) that are up to 10000 greater than those in the bulk. Magic angle spinning assisted 1H T2 measurements of included solvents revealed relaxation times of approximately 100-1000 ms over the explored temperature ranges, and MAS-assisted 1H T1 measurements of included solvents suggested a much lower activation energy for rotational dynamics as compared to those measured by the rotating pillars using 2H measurements. Finally, translational diffusion measurements of DMF using pulsed-field gradient methods revealed intermediate dynamics for the translational motion of the solvent molecules in MOFs.

Mode-coupling theory for tagged-particle motion of active Brownian particles.

We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.

Roughness induced rotational slowdown near the colloidal glass transition

HypothesisIn concentrated suspensions, the dynamics of colloids are strongly influenced by the shape and topographical surface characteristics of the particles. As the particles get into close proximity, surface roughness alters the translational and rotational Brownian motions in different ways. Eventually, the rotations will get frustrated due to geometric hindrance from interacting asperities. ExperimentsWe use model raspberry-like colloids to study the effect of roughness on the translational and rotational dynamics. Using Confocal Scanning Laser Microscopy and particle tracking, we simultaneously resolve the two types of Brownian motion and obtain the corresponding Mean Squared Displacements for varying concentrations up to the maximum packing fraction. FindingsRoughness not only lowers the concentration of the translational colloidal glass transition, but also generates a broad concentration range in which the rotational Brownian motion changes signature from high-amplitude diffusive to low-amplitude rattling. This hitherto not reported second glass transition for rough spherical colloids emerges when the particle intersurface distance becomes comparable to the roughness length scale. Our work provides a unifying understanding of the surface characteristics’ effect on the rotational dynamics during glass formation and provides a microscopic foundation for many roughness-related macroscale phenomena in nature and technology.

Feasibility of multi-particle collision dynamics for rod-like particles and its application to a change in the orientational regime of a hematite particle suspension

We have verified that the method of multi-particle collision dynamics (MPCD) is able to activate a physically reasonable level of random motion in the medium of virtual fluid particles and activate the translational, ordinary rotational and spin rotational Brownian motion of the magnetic rod-like particles. MPCD was then applied to a quasi-2D system of rod-like hematite particles. The particle Brownian motion was found slightly over-activated, but this tendency decreased with smaller simulation time steps. The deviation from the theoretical value in the present results may be regarded to be acceptable as a first approximation since the Brownian motion was activated without the addition of any special technique. The applied magnetic field strength is found to play a significant role to enhance the order of the alignment of the raft-like clusters along the direction of the applied magnetic field. A similar orientational regime change along the applied magnetic field may be accomplished by an increase in the volumetric fraction of magnetic particles. We have therefore concluded that both an applied magnetic field and the particle volumetric fraction may be feasible parameters for inducing a regime change in the ordering of the orientation of rod-like hematite particles.

Water accelerates the hydrogen-bond dynamics and abates heterogeneity in deep eutectic solvent based on acetamide and lithium perchlorate.

Deep eutectic solvents (DESs) have become a prevalent and promising medium in various industrial applications. The addition of water to DESs has attracted a lot of attention as a scheme to modulate their functionalities and improve their physicochemical properties. In this work, we study the effects of water on an acetamide based DES by probing its microscopic structure and dynamics using classical molecular dynamics simulation. It is observed that, at low water content, acetamide still remains the dominant solvate in the first solvation shell of lithium ions, however, beyond 10 wt. %, it is replaced by water. The increase in the water content in the solvent accelerates the H-bond dynamics by drastically decreasing the lifetimes of acetamide-lithium H-bond complexes. Additionally, water-lithium H-bond complexes are also found to form, with systematically longer lifetimes in comparison to acetamide-lithium complexes. Consequently, the diffusivity and ionic conductivity of all the species in the DES are found to increase substantially. Non-Gaussianity parameters for translational motions of acetamide and water in the DES show a conspicuous decrease with addition of water in the system. The signature of jump-like reorientation of acetamide is observed in the DES by quantifying the deviation from rotational Brownian motion. However, a notable decrease in the deviation is observed with an increase in the water content in the DES. This study demonstrates the intricate connection between H-bond dynamics and various microscopic dynamical parameters in the DES, by investigating the modulation of the former with addition of water.

Particle-Level Visualization of Hydrodynamic and Frictional Couplings in Dense Suspensions of Spherical Colloids

The rotational Brownian motion of colloidal spheres in dense suspensions reflects local hydrodynamics and friction, both key to non-linear rheological phenomena such as shear-thickening and jamming, and transport in crowded environments, including intracellular migration and blood flow. To fully elucidate the role of rotational dynamics experimentally, it is crucial to measure the translational and rotational motion of all spheres simultaneously. Here, we develop compositionally uniform colloidal spheres with an off-centre, fully embedded core with a different fluorophore to the particle body, allowing access to rotational motion for all particles at the single-particle level. We reveal interparticle hydrodynamic rotational coupling in charged colloidal crystals. We also find that higher local crystallinity in denser crystals enhances rotational diffusivity, and that nearly arrested particles exhibit a stick-slip rotational motion due to frictional coupling. Our method sheds new light on the largely-unexplored local rotational dynamics of spherical particles in dense colloidal materials.

Two-dimensional fluid viscosity measurement in microchannel flow using fluorescence polarization imaging

This study describes the development of a noncontact and two-dimensional fluid viscosity measurement technique based on fluorescence polarization microscopy. This technique exploits fluorescence depolarization due to rotational Brownian motion of fluorophores and determines fluid viscosity in microchannel flow by measuring steady-state fluorescence polarization. The main advantage of the technique is that planar distributions of fluid viscosity can be visualized by noncontact optical measurement, while commonly-used mechanical viscometers measure the viscosity of bulk liquids. Moreover, steady-state polarization measurements are realized using a simpler experimental setup compared to other noncontact techniques such as time-resolved fluorescence lifetime/polarization measurements. The relationship between the fluid viscosity (μ) and the fluorescence polarization degree (P) was experimentally obtained using casein molecules labeled with fluorescein isothiocyanate as a fluorescent probe. The fluid viscosity was controlled within the range of 0.7–3.0 mPa s, which is the range often encountered in biological materials, by mixing sucrose or glucose with the solution. The fluid temperature was maintained uniform at 30 °C during the measurement. The calibration result showed that 1/P linearly increased with 1/μ which qualitatively agreed well with the theoretical prediction. The measurement uncertainty was 7.5%–9.5% based on the slope of the calibration curve. The viscosity gradient generated by the mass diffusion between the two solutions co-flowing in the Y-shaped microchannel was clearly visualized under uniform temperature conditions by applying the calibration curve. Finally, the influence of the temperature change on P was experimentally evaluated. The results supported the applicability of the present technique for visualization of the viscosity distribution induced by temperature change. These results confirmed the feasibility of the present technique for analyzing microscale viscosity fields associated with mass transport or temperature change.

Thermal transport dynamics in active heat transfer fluids (AHTF)

We present results of molecular dynamics calculations of the effective thermal conductivity of nanofluids containing self-propelled nanoparticles. The translational and rotational dynamics observed in the simulations follow the behavior expected from the standard theoretical analysis of Brownian and self-propelled nanoparticles. The superposition of self-propulsion and rotational Brownian motion causes the behavior of the self-propelled nanoparticles to resemble Brownian diffusion with an effective diffusivity that is larger than the standard Brownian value by a factor of several thousand. As a result of the enhanced diffusion (and the convective mixing resulting from the motion), we observe a discriminable increase of the effective thermal conductivity of the solution containing self-propelled nanoparticles. While the increases we observe are in the range of several percent, they are significant considering that, without propulsion, the nanofluid thermal conductivity is essentially not affected by the Brownian motion and can be understood within the effective medium theory of thermal conduction. Our results constitute a proof of concept that self-propelled particles have the potential to enhance thermal conductivity of the liquid in which they are immersed, an idea that could ultimately be implemented in a broad variety of cooling applications.