Investigation of short-time particle dynamics near an interface in the presence of nonadsorbed macro-ions

The optical technique of total internal reflection microscopy was used to study the normal Brownian motion of a single colloidal particle near an interface. The measurements were made using a recently developed technique in which the diffusion coefficient was determined by the variance of the short-time (Deltat --> 0) motion of the particle. Experiments were performed in solutions containing either silica nanospheres or clay platelets (Laponite RD) to investigate the effect of nonadsorbed material on the dynamics of near-contact particle motion. The change in the diffusion coefficient with separation distance between the particle and plate in solutions containing nonadsorbed macro-ions was well-described by the theory developed for simple fluids. These results suggest that, in dilute solutions of nonadsorbed material in which the bulk rheological properties remain similar to those of the pure fluid, the mobility and diffusion coefficient correction factors developed for simple fluids remain valid.     

A new approach for analyzing particle motion near an interface using total internal reflection microscopy

A new method was developed for analyzing the normal motion of a single colloidal particle near an interface. The optical technique of total internal reflection microscopy (TIRM) was used to determine the distribution of vertical displacements of a particle from a specific starting position as a function of time. At very small displacement times, the displacements are normally distributed with a variance that is proportional to the diffusion coefficient times the displacement time. The change in the diffusion coefficient with separation distance between the particle and plate was found to match that predicted by Brenner (Chem. Eng. Sci. 16 (1961) 242). As the sampling time becomes very large, the variance reaches a constant value determined strictly by the shape of the local potential energy profile holding the particle. A major advantage of this approach, relative to other measurement methods, is that the particle's spatially variant diffusion coefficient can be determined without any knowledge of the forces acting on the particle.     

Simultaneous measurement of structural and hydrodynamic forces between colloidal surfaces in complex fluids

An AFM study was performed to measure the effect of approach/retraction speed on the interaction force between a colloidal particle and a flat substrate in aqueous solutions containing silica nanospheres at concentrations of 4.5 and 6.5 vol.%. The total force consisted of contributions of electrostatic, depletion, structural and hydrodynamic forces. The hydrodynamic component of the force could be isolated by comparing the force profiles measured upon approach and retraction. It was found that when the hydrodynamic component was subtracted from the total force, the resulting force profiles measured at scan speeds of 80, 800, 2400, 4800 and 11,200 nm/s all overlaid, indicating that the surface forces (electrostatic, depletion and structural) were not affected by the scan speed. This result was further supported by an approximation of the rates of viscous and diffusive motion in the gap region. In addition, the variation of the hydrodynamic force with particle/plate separation distance agreed relatively well with a prediction made using the mobility correction factor developed for simple fluids, suggesting that the nanoparaticles do not alter the flow in the lubrication layer at these concentrations.     

Electrophoresis of a charge-regulated sphere normal to a large disk

The electrophoresis of a rigid, charge-regulated, spherical particle normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. We show that, although the presence of a charged disk does not generate an electroosmotic flow, it affects particle motion appreciably through inducing charge on its surface and establishing an osmotic pressure field. The competition between the hydrodynamic force and the electric force may yields a local extremum in mobility; it is also possible that the direction of particle movement is reversed. In general, if a particle remains at constant surface potential, a decrease in the thickness of double layer has the effect of increasing the electrostatic force acting on it so that its mobility increases. However, this might not be the case for a charged-regulated particle because an excess hydrodynamic force is enhanced. For a fixed separation distance, the influence of a charged disk on mobility may reduce to a minimum if the bulk concentration of hydrogen ion is equal to the dissociation constant of the monoprotic acidic functional groups on particle surface.     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.     

Evaluation of the dynamic properties of polymer latex particles interacting with quartz interface by evanescent wave dynamic light scattering

The diffusion behavior of polymer latex particles in dispersion near the quartz interface has been estimated by evanescent wave dynamic light scattering (EVDLS) technique. The diffusion coefficient of the particles was measured as a function of the distance between the particle and interface. The apparent diffusion coefficient estimated by EVDLS was small for particles near the interface and increased upon increasing the distance from the interface, and then saturated at a certain value which is close to the value expected for free-motion. The range of the distance over which diffusion was affected by interaction with the interface depended on the added salt concentration. This means that the diffusion of the particle is influenced by an electrostatic interaction between the particle and quartz interface in addition to the hydrodynamic effect near the wall. This range was found to be more than 800?nm at 0?M salt condition but about 400?nm at 10^-4 and 10^-3?M salt conditions. Hence it is appropriate to say that the hydrodynamic effect reaches up to 400?nm and the electrostatic effect is longer ranged, more than 800?nm, for the system studied here. The EVDLS technique is a very powerful tool for quantitative estimations of the dynamic behavior of the particle near the interface and for estimation of the range where the wall effect is dominant. EVDLS will give us an answer to the question of “where is the ‘interface’ and where is the ‘bulk’?”.     

Determination of the dynamic electrophoretic mobility of a spherical colloidal particle through a novel numerical solution of the electrokinetic equations

The standard equations developed to describe the electrophoretic motion of a charged particle immersed in an electrolyte subjected to an oscillating electric field are solved numerically with a new technique suitable for stiff systems. The focus of this work is to use this solution to determine the dynamic particle mobility, one of several quantities that can be extracted from these equations. This solution is valid from low frequencies to indefinitely high frequencies and has no restriction on zeta potential, double-layer thickness, or electrolyte composition. The solution has been used to calculate the dynamic electrophoretic mobility of a particle for a wide range of double-layer thicknesses and zeta potentials. The solution agrees with analytic approximations obtained previously by other authors under the conditions of a thin double layer and low zeta potential. The results are also consistent with calculations valid at frequencies where the ion diffusion length extends a significant distance beyond the double layer as obtained by another numerical technique.     

Self-diffusion in submonolayer colloidal fluids near a wall

Theoretical expressions are developed to describe self-diffusion in submonolayer colloidal fluids that require only equilibrium structural information as input. Submonolayer colloidal fluids are defined for the purpose of this work to occur when gravity confines colloids near a planar wall surface so that they behave thermodynamically as two dimensional fluids. Expressions for self-diffusion are generalized to consider different colloid and surface interaction potentials and interfacial concentrations from infinite dilution to near fluid-solid coexistence. The accuracy of these expressions is demonstrated by comparing self-diffusion coefficients predicted from Monte Carlo simulated equilibrium particle configurations with standard measures of self-diffusion evaluated from Stokesian Dynamics simulated particle trajectories. It is shown that diffusivities predicted for simulated equilibrium fluid structures via multibody hydrodynamic resistance tensors and particle distribution functions display excellent agreement with values computed from mean squared displacements and autocorrelation functions of simulated tracer particles. Results are obtained for short and long time self-diffusion both parallel and normal to underlying planar wall surfaces in fluids composed of particles having either repulsive electrostatic or attractive van der Waals interactions. The demonstrated accuracy of these expressions for self-diffusion should allow their direct application to experiments involving submonolayer colloidal fluids having a range of interaction potentials and interfacial concentrations.     

Peak broadening in capillary zone electrophoresis with electroosmotic flow: Dependence of plate number and resolution on charge number

Summary Based on the Einstein-Nernst equation, describing the relation between diffusion coefficient and ionic mobility, and expression for the plate height and plate number can be obtained which is independent of the diffusion coefficient. This approach was supported by experimental data, obtained from anionic and cationic solutes. An expression for the electrophoretic resolution is introduced that is also independent on diffusion coefficients. The effect of electro-osmotic flow on the separation of anions and cations based on the expressions derived for the plate number and the resolution is discussed.     

Particle size measurement of lipoprotein fractions using diffusion-ordered NMR spectroscopy

The sizes of certain types of lipoprotein particles have been associated with an increased risk of cardiovascular disease. However, there is currently no gold standard technique for the determination of this parameter. Here, we propose an analytical procedure to measure lipoprotein particles sizes using diffusion-ordered nuclear magnetic resonance spectroscopy (DOSY). The method was tested on six lipoprotein fractions, VLDL, IDL, LDL₁, LDL₂, HDL₂, and HDL₃, which were obtained by sequential ultracentrifugation from four patients. We performed a pulsed-field gradient experiment on each fraction to obtain a mean diffusion coefficient, and then determined the apparent hydrodynamic radius using the Stokes–Einstein equation. To validate the hydrodynamic radii obtained, the particle size distribution of these lipoprotein fractions was also measured using transmission electron microscopy (TEM). The standard errors of duplicate measurements of diffusion coefficient ranged from 0.5% to 1.3%, confirming the repeatability of the technique. The coefficient of determination between the hydrodynamic radii and the TEM-derived mean particle size was r ² = 0.96, and the agreement between the two techniques was 85%. Thus, DOSY experiments have proved to be accurate and reliable for estimating lipoprotein particle sizes.     

Planar optofluidic chip for single particle detection, manipulation, and analysis

We present a fully planar integrated optofluidic platform that permits single particle detection, manipulation and analysis on a chip. Liquid-core optical waveguides guide both light and fluids in the same volume. They are integrated with fluidic reservoirs and solid-core optical waveguides to define sub-picoliter excitation volumes and collect the optical signal, resulting in fully planar beam geometries. Single fluorescently labeled liposomes are used to demonstrate the capabilities of the optofluidic chip. Liposome motion is controlled electrically, and fluorescence correlation spectroscopy (FCS) is used to determine concentration and dynamic properties such as diffusion coefficient and velocity. This demonstration of fully planar particle analysis on a semiconductor chip may lead to a new class of planar optofluidics-based instruments.     

Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.     

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.     

Direct measurement of interaction forces between a single bacterium and a flat plate

A technique for precisely measuring the equilibrium and viscous interaction forces between a single bacterium and a flat surface as functions of separation distance is described. A single-beam gradient optical trap was used to micromanipulate the bacterium against a flat surface while evanescent wave light scattering was used to measure separation distances. Calibrating the optical trap far from the surface allowed the trapped bacterium to be used as a force probe. Equilibrium force-distance profiles were determined by measuring the deflection of the cell from the center of the optical trap at various trap positions. Simultaneously, viscous forces were determined by measuring the relaxation time for the fluctuating bacterium. Absolute distances were determined using a best-fit approximation to the theoretical prediction for the hindered mobility of a diffusing sphere near a wall. Using this approach, forces in the range from 0.01 to 4 pN were measured at near-nanometer resolution between Staphylococcus aureus and glass that was bare or coated with adsorbed protein.     

Diffusion of spherical particles in microcavities

The diffusive motion of a colloidal particle trapped inside a small cavity filled with fluid is reduced by hydrodynamic interactions with the confining walls. In this work, we study these wall effects on a spherical particle entrapped in a closed cylinder. We calculate the diffusion coefficient along the radial, azimuthal, and axial direction for different particle positions. At all locations the diffusion is smaller than in a bulk fluid and it becomes anisotropic near the container's walls. We present a simple model which reasonably well describes the simulation results for the given dimensions of the cylinder, which are taken from the recent experimental work.     

Method for viscosity measurements at high pressure

The technique of quasielastic light scattering is utilized to determine the viscosity of fluids subjected to large hydrostatic pressures. In this method, a small concentration of insoluble polystyrene spheres of known diameter, 0.109 μm, is added to the fluid. The high-pressure cell in which the fluid is contained has three optical windows. The laser light scattered from the suspended spheres is analyzed to determine the diffusion coefficient of the spheres. Since, by the Stokes law, the viscosity of the fluid is determined from the measured diffusion coefficient and known particle radius r. A small correction is required for the contraction of the spheres and for refractive-index change of the water under pressure. Results on the viscosity of water at 25°C up to pressures of 2.5 kbar are reported and compared with published results. This method is applicable to lubricants and polymer solutions where the viscosity is many orders of magnitude greater than that of water.     

Evanescent Wave Light Scattering A Fusion of the Evanescent Wave and Light Scattering Techniques to the Study of Colloids and Polymers Near the Interface

The evanescent wave light scattering technique, which is produced by a fusion of the evanescent wave technique and light scattering technique, is a very powerful and useful tool for investigation of colloidal particles and polymers near the surface and interfaces. We have developed two kinds of evanescent wave light scattering apparatuses. One is the evanescent wave dynamic light scattering (EVDLS) technique and the other is the evanescent wave light scattering microscope (EVLSM). By EVDLS, the diffusion behavior of a colloidal particle near the interface can be extracted quantitatively as a function of the distance from the interface. The diffusion coefficient was smaller than those for particles in bulk, reflecting electrostatic and hydrodynamic interactions. By EVLSM, the interaction potential profile between a colloidal particle and the surface in dispersion can be evaluated directly. EVLSM will play an important role in colloidal interaction studies, especially at a low ionic strength. It is also pointed out that a particle dynamics study is also possible by the EVLSM technique. A new field will be developed in colloid science and polymer science by application of the evanescent wave light scattering technique, i. e. a fusion of the evanescent light and a light scattering techniques.     

A method for determining electrophoretic and electroosmotic mobilities using AC and DC electric field particle displacements

We have developed a method for measuring the electrophoretic mobility of submicrometer, fluorescently labeled particles and the electroosmotic mobility of a microchannel. We derive explicit expressions for the unknown electrophoretic and the electroosmotic mobilities as a function of particle displacements resulting from alternating current (AC) and direct current (DC) applied electric fields. Images of particle displacements are captured using an epifluorescent microscope and a CCD camera. A custom image-processing code was developed to determine image streak lengths associated with AC measurements, and a custom particle tracking velocimetry (PTV) code was devised to determine DC particle displacements. Statistical analysis was applied to relate mobility estimates to measured particle displacement distributions.     

Comparison of dynamical heterogeneity in hard-sphere and attractive glass formers

Using molecular dynamics simulations, we have determined that the nature of dynamical heterogeneity in jammed liquids is very sensitive to short-ranged attractions. Weakly attractive systems differ little from dense hard-sphere and Lennard-Jones fluids. Particle motion is punctuated and tends to proceed in steps of roughly a single particle diameter. Both of these basic features change in the presence of appreciable short-ranged attractions. Transient periods of particle mobility and immobility cannot be discerned at intermediate attraction strength, for which structural relaxation is greatly enhanced. Strong attractions, known to dramatically inhibit relaxation, restore bimodality of particle motion. But in this regime, transiently mobile particles move in steps that are significantly more biased toward large displacements than those in the case of weak attractions. This modified feature of dynamical heterogeneity, which cannot be captured by conventional mode coupling theory, verifies recent predictions from a model of spatially correlated facilitating defects.     

Determination of the effective charge of individual colloidal particles

An optical method is presented that allows simultaneous determination of the diffusion constant and electrophoretic mobility of individual charged particles with radius down to 0.2 mum. By this method the size dependency of the effective charges and zeta potentials of individual particles can be investigated, as well as interparticle interactions and Brownian motion in confined geometries. The diffusion constant and mobility are determined from the power spectrum of the particle speed in a sinusoidal electrical field. The accuracy of the method was tested on PMMA spheres of known size in water. Experiments have been carried out on charged pigment particles with low concentration in a nonaqueous medium containing a charging agent. The mobility is found to be independent of the particle size.