Transition from fractional to classical Stokes–Einstein behaviour in simple fluids

Abstract

An optical technique for tracking single particles has been used to evaluate the particle diameter at which diffusion transitions from molecular behaviour described by the fractional Stokes–Einstein relationship to particle behaviour described by the classical Stokes–Einstein relationship. The results confirm a prior prediction from molecular dynamic simulations that there is a particle size at which transition occurs and show it is inversely dependent on concentration and viscosity but independent of particle density. For concentrations in the range 5 × 10−3 to 5 × 10−6 mg ml−1 and viscosities from 0.8 to 150 mPa s, the transition was found to occur in the diameter range 150–300 nm.

Limitations of Nanoparticles Size Characterization by Asymmetric Flow Field‑Fractionation Coupled with Online Dynamic Light Scattering

“…Coglitore et al found by tracking single monodispersed gold and polystyrene nanoparticles that, below a critical size and concentration, the diffusion coefficient of the nanoparticles was at least one order of magnitude smaller than the theoretical value predicted by Stokes-Einstein equation and was independent of nanoparticle size and density. The transition from the Stokes-Einstein diffusion regime to the slower diffusion regime has been reported to appear for concentration of particles in the range of 10 8 -10 9 particles m −1 [19,20].…”

Sedimentation-Diffusion Behaviour of Nanoparticles

“…The dynamic viscosity of DMEM with 10%FBS has been reported to be just 5% higher than the dynamic viscosity of pure water [34], which is not enough to have a significant impact on nanoparticle kinetics [23].…”

“…In this study we investigated the settling dynamics of different sized gold nanoparticles in water and cell culture medium at a range of different temperature exploiting the optical phenomenon of caustics [25] making the diffusion coefficient a function of the local concentration of nanoparticles, which is a factor that has been reported to influence the dynamics of nanoparticles in solution [23].…”

“…Kourki and Famili [27] observed the same decreasing trend of sedimentation velocity when investigating the sedimentation of silica nanoparticles. Coglitore et al [23] explained the low values of diffusion coefficient obtained from experiments by considering that, at low concentrations, nanoparticle motion is almost entirely controlled by collisions with fluid molecules and the particle-particle interaction can be neglected. Koening et al [28] reported a higher diffusion coefficient (of the same order of magnitude as the Stokes-Einstein prediction) using the same nanoparticles and solution but with a higher particle concentration.…”

“…where Dexp = 5 * 10 -13 m 2 s -1 is the experimental value of the diffusion coefficient measured at a low concentration of nanoparticles [23]. DStEin is the diffusion coefficient according to Stokes-Einstein equation, n 50 = 1.4 is the nanoparticle relative concentration at which the transition from the Stokes-Einstein diffusion mode to the low concentration diffusion mode happens, k = 20 is the slope of the transition (Fig.…”