Ionic liquid-based stable nanofluids containing gold nanoparticles

A one-phase and/or two-phase method were used to prepare the stable ionic liquid-based nanofluids containing same volume fraction but different sizes or surface states of gold nanoparticles (Au NPs) and their thermal conductivities were investigated in more detail. Five significant experiment parameters, i.e. temperature, dispersion condition, particle size and surface state, and viscosity of base liquid, were evaluated to supply experimental explanations for heat transport mechanisms. The conspicuously temperature-dependent and greatly enhanced thermal conductivity under high temperatures verify that Brownian motion should be one key effect factor in the heat transport processes of ionic liquid-based gold nanofluids. While the positive influences of proper aggregation and the optimized particle size on their thermal conductivity enhancements under some specific conditions demonstrate that clustering may be another critical effect factor in heat transport processes. Moreover, the remarkable difference of the thermal conductivity enhancements of the nanofluids containing Au NPs with different surface states could be attributed to the surface state which has a strong correlation with not only Brownian motion but also clustering. Whilst the close relationship between their thermal conductivity enhancements and the viscosity of base liquid further indicate Brownian motion must occupy the leading position among various influencing factors. Finally, a promisingly synergistic effect of Brownian motion and clustering based on experimental clues and theoretical analyses was first proposed, justifying different mechanisms are sure related. The results may shed lights on comprehensive understanding of heat transport mechanisms in nanofluids.     

Statistical mechanical theory for steady state systems. VIII. General theory for a Brownian particle driven by a time- and space-varying force

A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A fluctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation.     

Diffusing-wave spectroscopy and interferometry

Diffusing-wave spectroscopy and interferometry, the extensions of dynamic light scattering to materials which exhibit a very high degree of multiple scattering, have been used to measure the early-time, short length scale motion of Brownian particles. The transition from “ballistic” to “diffusive” motion is observed. In very dilute samples, this transition is described very well by theories which explicitly account for the time-dependent hydrodynamic interaction between a Brownian particle and the surrounding fluid. For particle volume fractions exceeding a few per cent, the data deviate from the theory for dilute suspensions, but exhibit a remarkable scaling with the suspension viscosity.     

Quantification of microstructures in stable and gelated suspensions from Cryo-SEM

It is shown that the microstructures of concentrated suspensions can be analyzed in a quantitative way from cryo-SEM images of high-pressure frozen samples, both in the electrostatically stabilized and in the flocculated state. Suspensions of spherical silica particles (40 vol%) in an aqueous solution were used. The average particle radius was 525 nm with a polydispersity of below 7%. The suspensions were high-pressure frozen, which resulted in a quenching of the configuration without apparent change in volume or crack formation. After fracturing the samples at liquid nitrogen temperature, the fracture surface was etched by controlled sublimation of the frozen aqueous phase, coated with 8 nm of platinum, and examined by stereo-cryo-SEM. The 3-dimensional positions of all the visible particles were determined from the SEM images. Assuming an isotropic particle configuration in the sample before cracking, it is possible to extract the 3-dimensional pair correlation function from the particle positions on the fracture surface. A comparison to recent results from Brownian Dynamics simulations shows good agreement between our experiments and the simulations.     

Thermally activated escape rate for a Brownian particle in a double-well potential for all values of the dissipation

The translational Brownian motion in a (2-4) double-well potential is considered. The escape rate, the position correlation function and correlation time, and the generalized susceptibility are evaluated from the solution of the underlying Langevin equation by using the matrix-continued fraction method. The escape rate and the correlation time are compared with the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. It is shown that in the low-temperature limit, the universal Mel'nikov and Meshkov expression for the escape rate provides a good estimate of both escape rate and inverse position correlation time for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and turnover regimes. Moreover, for low barriers, where the Mel'nikov and Meshkov method is not applicable, analytic equations for the correlation time in the VLD and VHD limits are derived.     

Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls

The diffusion tensor and velocity correlation function of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls are calculated in point approximation. The fluid is assumed to satisfy stick boundary conditions at the walls. It is found that the velocity correlation function decays asymptotically with a negative t(-2) long-time tail due to coupling to overdamped sound waves. The coefficient of the long-time tail is calculated and shown to be independent of fluid viscosity.     

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.     

Elastic coefficient of a single polymer chain by using Brownian dynamics analysis

The elastic coefficient of a single polystyrene chain has been experimentally evaluated by using Brownian dynamics analysis. The Brownian motion of the chain is probed using a particle trapped by optical tweezers with a negligibly small spring constant. The displacement of the particle due to Brownian motion is measured by an interferometer assembled using the same laser beam as the optical tweezers. Two methods are employed for Brownian dynamics analysis: (1) the analysis of the time course of the displacement of the particle and (2) the fitting of the power spectrum of Brownian motion with a Lorentzian. The elastic constant of a polystyrene chain in dichloromethane at 21 degrees C is estimated to be 6.4 x 10(-6) and 1.1 x 10(-5) N/m when methods (1) and (2) are employed, respectively. The elastic constant obtained by approximating the polystyrene chain to a freely jointed chain is in agreement with the experimentally evaluated elastic constant.     

Mobility matrix of a spherical particle translating and rotating in a viscous fluid confined in a spherical cell, and the rate of escape from the cell

The mobility matrix of a spherical particle moving in a spherical cavity, filled with a viscous incompressible fluid, and with no-slip boundary condition at the wall of the cavity, is evaluated from the Oseen tensor for the cavity by the method used by Lorentz for a particle near a planar wall. For the case that the particle is a rigid sphere with no-slip boundary condition the comparison with exact calculations shows that the approximation is quite accurate, provided the radius of the particle is small relative to that of the cavity, and provided the particle is not too close to the wall. The translational mobility is used to derive the diffusion tensor of a Brownian particle via an Einstein relation. The approximate result for the diffusion tensor is employed to estimate the rate of escape of a Brownian particle from a cavity with semipermeable wall.     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

Friction and diffusion of a Brownian particle in a mesoscopic solvent

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.     

Linear chains and chain-like fractals from electrostatic heteroaggregation

The internal structure of materials prepared by aggregation of oppositely charged polystyrene spheres (electrostatic heteroaggregation) is investigated by static light scattering, optical microscopy, and Brownian dynamics simulation. Light scattering indicates ultralow mass fractal dimensions, as low as 1.2. Such low fractal dimensions, approaching the theoretical limit of a linear object, imply a chaining mechanism. Optical micrographs reveal linear chains with the particle charge alternating down the chains. Brownian dynamics simulation gives additional support for a chaining mechanism. For the polystyrene system (120-nm primary particle diameters), the fractal dimension is found to increase from 1.2 to 1.7 as the background electrolyte is increased. In terms of electrostatic screening, the results match those reported recently for larger polystyrene spheres. The low fractal dimensions appear to represent a crossover from linear chains to a structure of diffusion-limited aggregates; however, experiments under density-neutral conditions imply that sedimentation plays an important role in the formation of ultralow fractal dimensions. The practical implication is that microcomposites with a locally uniform distribution of starting materials and almost any degree of branching can be prepared from oppositely charged particles.     

Thermodynamical approach to sympathetic cooling of neutral particles

We present a "toy" classical model for sympathetic cooling of the neutral Brownian particle in the frame of robust thermodynamical approach. The cooling time is expressed with the parameters of the Brownian particle and the particles from the cooling reservoir. Qualitative and numerical estimations of the model confirm that the sympathetic cooling can be efficient for heavy neutral molecules and clusters.     

Controlling the motion and placement of micrometer-sized metal particles using patterned polymer brush surfaces

In this paper, we show that silicon surfaces patterned with poly(methacrylic acid) brushes are able to control the Brownian motion of 2-3 μm iron particles, which sediment onto the surface in aqueous solution and experience differences in repulsive force depending upon their position. Differences in repulsion lead to different gravitational potential energies across the surface, which gives bias to the Brownian motion taking place. Three regimes have been identified depending upon the brush height: (i) no control of Brownian motion when the brush height is small, (ii) Brownian motion that is influenced by the polymer brush when the brush 17 height is intermediate, (iii) Brownian motion that is confined by polymer brush barriers when the brush height is greatest. The height of brush found necessary to significantly influence iron particle motion was small at 39 nm or 2% of the particle diameter.     

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.     

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in an asymmetrical double-well potential for all values of the dissipation

The Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov is used to evaluate the relaxation times and the dynamic susceptibility for the rotational Brownian motion of fixed axis rotators in an asymmetric double-well potential. An expression for the escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes is derived. It is shown that this expression provides a good asymptotic estimate of the inverse of the smallest nonvanishing eigenvalue lambda(1) of the underlying Fokker-Planck operator calculated by using the matrix-continued fraction method. For low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for the correlation time tau( parallel) of the longitudinal dipole correlation function in the VLD and VHD limits are derived and a simple extrapolating equation valid for all values of the damping is proposed.     

Structure and transport properties of polymer grafted nanoparticles

We perform molecular dynamics simulations on a bead-spring model of pure polymer grafted nanoparticles (PGNs) and of a blend of PGNs with a polymer melt to investigate the correlation between PGN design parameters (such as particle core concentration, polymer grafting density, and polymer length) and properties, such as microstructure, particle mobility, and viscous response. Constant strain-rate simulations were carried out to calculate viscosities and a constant-stress ensemble was used to calculate yield stresses. The PGN systems are found to have less structural order, lower viscosity, and faster diffusivity with increasing length of the grafted chains for a given core concentration or grafting density. Decreasing grafting density causes depletion effects associated with the chains leading to close contacts between some particle cores. All systems were found to shear thin, with the pure PGN systems shear thinning more than the blend; also, the pure systems exhibited a clear yielding behavior that was absent in the blend. Regarding the mechanism of shear thinning at the high shear rates examined, it was found that the shear-induced decrease of Brownian stresses and increase in chain alignment, both correlate with the reduction of viscosity in the system with the latter being more dominant. A coupling between Brownian stresses and chain alignment was also observed wherein the non-equilibrium particle distribution itself promotes chain alignment in the direction of shear.     

Scaling of the memory function and Brownian motion

It has been recently shown that the velocity autocorrelation function of a tracer particle immersed in a simple liquid scales approximately with the inverse of its mass. With increasing mass the amplitude is systematically reduced and the velocity autocorrelation function tends to a slowly decaying exponential, which is characteristic for Brownian motion. We give here an analytical proof for this behavior and comment on the usual explanation for Brownian dynamics which is based on the assumption that the memory function is proportional to a Dirac distribution. We also derive conditions for Brownian dynamics of a tracer particle which are entirely based on properties of its memory function.     

Estimating the viscoelastic moduli of complex fluids from observation of Brownian motion of a particle confined to a harmonic trap

A procedure is proposed to estimate the viscoelastic properties of a complex fluid from the behavior of the velocity autocorrelation function of a suspended Brownian particle, trapped in a harmonic potential. The procedure is tested for a model complex fluid with a given frequency-dependent shear viscosity. The analysis shows that the procedure can provide a rather accurate prediction of the viscoelastic properties of the fluid on the basis of experimental data on the velocity autocorrelation function of the trapped Brownian particle in a limited range of time.     

Effect of particle size distribution on the collection efficiency of Brownian particles

The main purpose of the present paper is to investigate the effect of the normal Gaussian size distribution on the deposition of Brownian particles onto a spherical collector, by applying the Brownian dynamic simulation method and the Kuwabara flow field model with different types of DLVO interaction energy curves and the shadow effect. The simulation results show that the collection efficiency of Brownian particles always increases with a wider particle size distribution region. The same increased tendencies are also observed for the case of increasing Reynolds number and for the case of increasing the particle size to the collector size ratio. When compared to the available experimental data, the present simulation method fits well with the experimental data when the specific deposit per collector is not large.