Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

Hindered Diffusion near Fluid-Solid Interfaces: Comparison of Molecular Dynamics to Continuum Hydrodynamics

Studying the near-wall hindered diffusion of a particle suspended in a fluid is critical for understanding other more complex, confined systems. We provide a review of the previous experimental and simulation efforts trying to verify the classic calculations in hydrodynamics by Brenner and Faxén. We discuss some of the challenges of extracting the hindered diffusion constants from the mean squared displacements as often done in the literature. We demonstrate that the use of total force autocorrelation functions is a reliable alternative for calculating the diffusion constants without similar challenges for our molecular dynamics (MD) simulations. We find that the change in the diffusion constant in the perpendicular direction calculated in MD is roughly consistent with the hydrodynamic result by Brenner provided that they are normalized by the diffusion constant at the center between the two walls. However, the discrepancy grows large when the colloidal particle is very close to the wall where molecular details matter. Even though the agreement can be considerably improved when the attractions between the particles are made stronger to reduce slip to better fulfill the no-slip condition in MD, we report that there is an underlying difference between the range of the wall interactions with the colloidal particle predicted by MD and hydrodynamics.

Measurements of Particle-Surface Interactions in Both Equilibrium and Nonequilibrium Systems

Total internal reflection microscopy (TIRM) is a passive technique that measures colloidal interactions in aqueous solution. A traditional Boltzmann method requires that particles must fluctuate around equilibrium positions for a long time. A method based on multiparticle tracking and drift velocity method was developed to measure interactions in both equilibrium and nonequilibrium systems. This method relaxed the limitation of the traditional Boltzmann method and do not require any external force like optical tweezer. Theoretical predictions of particle sedimentation under the influence of various forces were investigated to determine the proper particle size and solution properties. We found that the polystyrene (PS) particle with a size of 2.1 μm took the longest time to finish sedimentation, and 5% (w/w) sucrose was chosen to suppress the Brownian motion. For single and ensemble particles in equilibrium, the experimental diffusion coefficients and potential energy profiles were consistent with the theoretical prediction. In nonequilibrium experiments, the van der Waals force between the bare/hybrid particles and flat surface was measured, and the silica shell acted to strengthen the van der Waals attraction. This method extends the application of TIRM to nonequilibrium systems without any active control. Moreover, the silica-coated PS core-shell hybrid particles facilitate surface modification with a variety of active chemicals. It would be a great advantage to measure all kinds of long-range interactions between surface-modified particles and surface in aqueous solution with TIRM.

Interfacial colloidal rod dynamics: Coefficients, simulations, and analysis

Colloidal rod diffusion near a wall is modeled and simulated based on a constrained Stokesian dynamic model of chains-of-spheres. By modeling colloidal rods as chains-of-spheres, complete diffusion tensors are computed for colloidal rods in bulk media and near interfaces, including hydrodynamic interactions, translation-rotation coupling, and all diffusion modes in the particle and lab frames. Simulated trajectories based on the chain-of-spheres diffusion tensor are quantified in terms of typical experimental quantities such as mean squared positional and angular displacements as well as autocorrelation functions. Theoretical expressions are reported to predict measured average diffusivities as well as the crossover from short-time anisotropic translational diffusion along the rod's major axis to isotropic diffusion. Diffusion modes are quantified in terms of closed form empirical fits to model results to aid their use in interpretation and prediction of experiments involving colloidal rod diffusion in interfacial and confined systems.

Shape-tailored polymer colloids on the road to become structural motifs for hierarchically organized materials

Anisometric polymer colloids are likely to behave differently when compared with centrosymmetric particles. Their study may not only shine new light on the organization of matter; they may also serve as building units with specific symmetries and complexity to build new materials from them. Polymer colloids of well-defined complex geometries can be obtained by packing a limited number of spherical polymer particles into clusters with defined configurations. Such supracolloidal architectures can be fabricated at larger scales using narrowly dispersed emulsion droplets as templates. Assemblies built from at least two different types of particles as elementary building units open perspectives in selective targeting of colloids with specific properties, aiming for mesoscale building blocks with tailor-made morphologies and multifunctionality. Polymer colloids with defined geometries are also ideal to study shape-dependent properties such as the diffusion of complex particles.

Self-consistent colloidal energy and diffusivity landscapes in macromolecular solutions

We report a dynamic analysis to simultaneously measure colloidal forces and hydrodynamic interactions in the presence of both adsorbed and unadsorbed macromolecules. A Bayesian inference method is used to self-consistently obtain the position-dependent potential energy (i.e., energy landscape) and diffusivity (i.e., diffusivity landscape) from measured colloidal trajectories normal to a wall. Measurements are performed for particles and surfaces with adsorbed polyethylene oxide (PEO) copolymer as a function of unadsorbed PEO homopolymer concentration. Energy landscapes are well described by a steric repulsion between adsorbed brushes and depletion attraction due to unadsorbed macromolecules. Diffusivity landscapes show agreement with predicted short-range permeable brush models and long-range mobilities determined by the bulk solution viscosity. Lower than expected mobilities in the vicinity of overlapping depletion layers are attributed to interactions of adsorbed and unadsorbed macromolecules altering nonconservative lubrication forces.

Anomalous silica colloid stability and gel layer mediated interactions

Total internal reflection microscopy (TIRM) is used to measure SiO2 colloid ensembles over a glass microscope slide to simultaneously obtain interactions and stability as a function of pH (4-10) and NaCl concentration (0.1-100 mM). Analysis of SiO2 colloid Brownian height excursions yields kT-scale potential energy vs separation profiles, U(h), and diffusivity vs separation profiles, D(h), and determines whether particles are levitated or irreversibly deposited (i.e., stable). By including an impermeable SiO2 "gel layer" when fitting van der Waals, electrostatic, and steric potentials to measured net potentials, gel layers are estimated to be ~10 nm thick and display an ionic strength collapse. The D(h) results indicate consistent surface separation scales for potential energy profiles and hydrodynamic interactions. Our measurements and model indicate how SiO2 gel layers influence van der Waals (e.g., dielectric properties), electrostatics (e.g., shear plane), and steric (e.g., layer thickness) potentials to understand the anomalous high ionic strength and high pH stability of SiO2 colloids.

Hydrodynamic force on a microparticle approaching a wall in a nanoparticle dispersion: observation of a separation-dependent effective viscosity

Colloid probe atomic force microscopy was used to measure the hydrodynamic force exerted on a 30-μm-diameter silica particle being moved toward or away from a silica plate in aqueous dispersions of 22-nm-diameter silica nanoparticles (6 or 8 vol %). Upon comparing the measured force to predictions made using the well-known expression of Cox and Brenner (Cox, R. G.; Brenner, H. Chem. Eng. Sci.1967, 22, 1753-1777) assuming a constant viscosity equal to that of the bulk dispersion, the measured drag force was found to become significantly less than that predicted at smaller particle-plate separation distances (e.g., <500 nm). A recent theoretical paper by Bhattacharya and Blawzdziewicz (Bhattacharya, S.; Blawzdziewicz, J. J. Chem. Phys.2008, 128, 214704) predicted that in a solution of dispersed nanoparticles the effective viscosity characterizing the hydrodynamic force on the particle should vary from that of the solvent at contact to that of the bulk dispersion at large separations. By adjusting the viscosity in the Cox and Brenner expression to make the predicted hydrodynamic force match that measured (i.e., the effective viscosity), a curve showing these exact characteristics was obtained. The effective viscosity profile was not a function of particle speed, and changes in the effective viscosity extended to separation distances of as large as 2 μm (nearly 100 times the hard diameter of the nanoparticles). These results suggest that in the range of typical colloidal forces (on the order of 100 nm), the dynamics of particle motion in such systems are determined by the viscosity of the solvent and not that of the bulk dispersion.

Direct measurement of anisotropic near-wall hindered diffusion using total internal reflection velocimetry

By applying the three-dimensional total internal reflection velocimetry (3D-TIRV) technique to freely suspended micron-sized fluorescent particles, we are able to simultaneously observe the three-dimensional anisotropic hindered diffusion for values of the gap-size-to-radius ratio much less than one. We demonstrate that the 3D-TIRV can be used to accurately track freely suspended 1.5-mum radius particles. The displacement measurements reveal that the hindered diffusion coefficients are in close agreement with the theoretical values predicted by the asymptotic solutions of Brenner [Chem. Eng. Sci. 16, 242 (1961)] and Goldman [Chem. Eng. Sci. 22, 637 (1967)] for gap-size-to-radius ratio much less than one, while hindered diffusion anisotropicity is simultaneously observed in all data sets.

Asymmetry in colloidal diffusion near a rigid wall

The three-dimensional motion of single colloidal particles close to a plane wall is measured by optical microscopy. In accordance with classical theoretical predictions, we find an asymmetric motion of the particles in the directions parallel and perpendicular to the wall. We also find that, close to the wall, the distribution functions of perpendicular steps are asymmetric, being shorter toward the wall and longer away from it.