Diffusion Coefficient For Brownian Motion Research Articles

Single-Particle Diffusion Characterization by Deep Learning

Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular movement by single-particle-tracking experiments has contributed to a growing body of evidence that many cellular systems do not exhibit classical Brownian motion but rather anomalous diffusion. Despite this evidence, characterization of the physical process underlying anomalous diffusion remains a challenging problem for several reasons. First, different physical processes can exist simultaneously in a system. Second, commonly used tools for distinguishing between these processes are based on asymptotic behavior, which is experimentally inaccessible in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables because different transport modes can result in the same diffusion power-law α, which is typically obtained from the mean-square displacements (MSDs). The outstanding challenge in the field is to develop a method to extract an accurate assessment of the diffusion process using many short trajectories with a simple scheme that is applicable at the nonexpert level. Here, we use deep learning to infer the underlying process resulting in anomalous diffusion. We implement a neural network to classify single-particle trajectories by diffusion type: Brownian motion, fractional Brownian motion and continuous time random walk. Further, we demonstrate the applicability of our network architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusion coefficient for Brownian motion on both simulated and experimental data. These networks achieve greater accuracy than time-averaged MSD analysis on simulated trajectories while only requiring as few as 25 steps. When tested on experimental data, both net and ensemble MSD analysis converge to similar values; however, the net needs only half the number of trajectories required for ensemble MSD to achieve the same confidence interval. Finally, we extract diffusion parameters from multiple extremely short trajectories (10 steps) using our approach.

Study on Nanoparticle Sizing Using Fluorescent Polarization Method with DNA Fluorescent Probe

Fluorescent polarization methods are used to detect complementary base pairing of DNA in biological fields. These methods work by measuring the rotational diffusion coefficient of Brownian motion of the fluorescent particles in solution. The rotational diffusion coefficient corresponds to the inverse third power of diameter according to the Debye-Stokes-Einstein equation for nanoparticles as hard spheres. We develop a novel method to measure the rotational diffusion coefficient using a fluorescent probe with a DNA spacer connected to a gold nanoparticle. We studied the physical characteristics of this probe to verify the feasibility of the proposed method. The rotational diffusion coefficients of gold nanoparticles with diameters ranging between 5–20 nm were measured using this developed system. In this manuscript we describe a novel fluorescent polarization method for nanoparticle sizing using a fluorescent DNA probe.

Length scale of polyisopirene and dynamic light scattering and structure of sodium-2-diethylhexyl sulfosuccinate/water/decane

The mixture of polyisopirene (PI) and sodium-2-diethylhexyl sulfosuccinate /decane/water microemulsion (ME) at AOT to water molar ratio (X = 30) and droplet mass fraction (mf,drop = 0.08) was studied with dynamic light scattering and small-angle X-ray scattering (SAXS). The light scattering was used to obtain the diffusion coefficient of Brownian motion of the nano-droplets at different polymer concentrations and molecular weights (1000 and 4700) in the ME. The dynamics of the nano-droplets decreased with the increase of molecular weight (from 1000 to 4700) and concentration (from 0.01 to 0.09) of PI. The study of the structure by SAXS showed that with increase of PI (MW = 1000) mass fraction from 0.01 to 0.09 at ME, the size of the droplets changes from 4.5 to 4.3 nm and with increase of PI (MW = 4700) concentration at ME, the size of droplets changes from 4.8 to 4.4 nm. The size ratio of droplets to polymer decreased with increase of concentration and molecular weight of polymer and also the interaction between the droplets increased with increase of polymer concentration.

High-Resolution Latex State 13C-NMR Spectroscopy: Part II. Effect of Particle Size and Temperature

Abstract Latex state C-NMR measurements were made for colloidal dispersions of polymer, using the observation conditions similar to those used in solution state measurement. The colloidal dispersion which showed broad and bimodal distributions in particle size was fractionated by centrifugation into four fractions with different volume mean particle diameter ranging from 0.121 to 1.31 µm with narrow and unimodal distributions. The signal to noise ratio, half width and intensity of each resolved carbon resonance for the fractionated dispersions were dependent upon the particle diameter. The intensity of the carbon resonances increased to 100% as the particle diameter decreased and temperature was raised. This is explained with respect to the increase in diffusion coefficient of Brownian motion of the particle. The intensity and the half width of the signals were superimposed against the diffusion coefficient of Brownian motion.

Experimental observations of non-Gaussian behavior and stringlike cooperative dynamics in concentrated quasi-two-dimensional colloidal liquids

We report, from direct observation of particle trajectories as a function of time, the presence of stringlike cooperative motion in a quasi-two-dimensional liquid. We have used digital video microscopy to study the equilibrium dynamics of suspensions of sterically stabilized uncharged poly(methylmethacrylate) spheres confined in a thin glass cell. Our experiments reveal the existence, in semidilute and dense liquid states, of a transition in the qualitative dynamical behavior of the system. At short times particles undergo unhindered Brownian motion, at intermediate times they undergo uncorrelated binary collisions, and at long times these one-particle self-diffusive modes are coupled to collective longitudinal acoustic modes of the fluid, the signature of which is local fluctuating domains of enhanced particle mobility. We study the properties of these domains by examining the density dependence of the van Hove self-correlation function and its deviation from Gaussian behavior. We observe that periods of non-Gaussian behavior correlate precisely with the timing of events involved in the relaxation of "caged" particles and their nearest neighbors. In contrast with relaxation processes in supercooled liquids, the lifetime of dynamical heterogeneities in a dissipative colloidal suspension is found to shift towards shorter time scales with increasing particle density. During time periods for which a quasi-two-dimensional system follows Gaussian behavior, we observe that, as predicted by Cichocki and Felderhof [J. Phys. Condens. Matter 6, 7287 (1994)], the time dependence of the evolution of the effective diffusion coefficient from its short time to its long time value has the form (ln t)/t. This last finding is true for all observed particle densities. To our knowledge, these results are the first experimental verification of the existence of microscopic cooperativity and the predicted temporal evolution of the diffusion coefficient for Brownian motion in concentrated quasi-two-dimensional liquids.

Self-diffusion in dilute quasi-two-dimensional hard sphere suspensions: Evanescent wave light scattering and video microscopy studies.

We report measurements of the diffusion coefficient of a dilute quasi-two-dimensional hard sphere colloidal suspension using two independent experimental techniques: evanescent wave dynamic light scattering (EWDLS) and digital video microscopy (DVM). The system studied consists of 1 \ensuremath{\mu}m sterically stabilized, uncharged, poly(methylmethacrylate) spheres in a very thin cell (\ensuremath{\sim}3 \ensuremath{\mu}m). In principle, EWDSL and DVM yield identical information about the system, albeit by different analyses. When both methods are used to study the same system it is possible to directly compare measurements of preaveraged statistical dynamical quantities with their microscopic counterparts. Our EWDLS measurements yield the effective diffusion coefficient as a function of wave number and the mean square particle displacement, for fixed wave number, as a function of time. The DVM measurements generate particle trajectories; Fourier decomposition of the trajectories yields the dynamic scattering function, which is found to be in quantitative agreement with the same function measured by EWDLS. Analysis of the observed intermediate scattering function indicates that, as predicted by Cichocki and Felderhof [J. Phys. Condens. Matter 6, 7287 (1994)], in this quasi-two-dimensional system the time dependence of the evolution of the effective diffusion coefficient from its short time value to its long time value has the form (lnt)/t. To our knowledge, these results are the first experimental verification of the predicted temporal evolution of the diffusion coefficient for Brownian motion in a quasi-two-dimensional liquid. \textcopyright{} 1996 The American Physical Society.

X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol.

We report x-ray photon correlation spectroscopy studies of the static structure factor and dynamic correlation function of a gold colloid dispersed in the viscous liquid glycerol. We find a diffusion coefficient for Brownian motion of the gold colloid which agrees well with that extrapolated from measurements made with visible light, but which was determined on an optically opaque sample and in a wave-vector range inaccessible to visible light.

Brownian motion in thin sheets of viscous fluid

The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity.

On the Einstein-Stokes diffusion coefficient for Brownian motion in two dimensions

It is shown that the application in two dimensions of Einstein's derivation of the Einstein-Stokes diffusion coefficient for Brownian motion, leads to an inconsistency.