Depletion potentials induced by charged colloidal rods

Parametric Study of Colloidal Particle Confinement near a Surface in the Presence of DLVO and Structural Interactions Using Brownian Dynamic Simulations

Total internal reflection microscopy (TIRM) has become a crucial technique for understanding the surface interactions and dynamics of Brownian colloidal particles near a surface. However, for select colloidal systems, experimental limitations associated with TIRM can occlude exploration of nano- and submicrometer colloids dispersed in complex or structured fluids. It should be possible to use Brownian dynamic simulations to quantify, explore, or circumvent these limitations to extend the TIRM technique further. A Brownian dynamics algorithm based on the Langevin equation was utilized to identify favorable colloidal systems for conducting TIRM experiments in electrolyte and nonadsorbing polyelectrolyte solutions. In electrolyte solution, the motion of polystyrene and silica particles of nanometer- and micrometer-sized radii was simulated near a glass slide in the presence of retarded van der Waals and electric double-layer forces to develop potential energy profiles. In the case of nonadsorbing polyelectrolyte solutions, a structural force was also implemented into the simulation, and the influence of structural interactions on particle confinement was explored as a function of particle size, particle density, and polyelectrolyte concentration. In electrolyte solutions, our results were able to identify the minimum particle size required for TIRM experiments as well as insight into particle selection based on material density. For structural or oscillatory forces, our results show that prior to conducting TIRM experiments, Brownian dynamics simulation can be used to select the appropriate particle size, material, and polyelectrolyte concentration range where the colloidal particle can sample multiple structural energy wells without confinement. These results provide insight into the colloidal system suitable to experimentally study near-surface particle diffusion dynamics for a range of separations in the presence of structural interactions.

Dimeric colloidal inclusion in a chiral active bath: Effective interactions and chirality-induced torque

Colloidal inclusions suspended in a bath of smaller particles experience an effective bath-mediated attraction at small intersurface separations, which is known as the depletion interaction. In an active bath of nonchiral self-propelled particles, the effective force changes from attraction to repulsion, an effect that is suppressed when the active bath particles are chiral. Using Brownian dynamics simulations, we study the effects of channel confinement and bath chirality on the effective forces and torques that are mediated between two inclusions that may be fixed within the channel or may be allowed to rotate freely as a rigid dimer around its center of mass. We show that the confinement has a strong effect on the effective interactions, depending on the orientation of the dimer relative to the channel walls. The active particle chirality leads to a force imbalance and, hence, a net torque on the inclusion dimer, which we investigate as a function of the bath chirality strength and the channel height.

In Situ Measurement of Depletion Caused by SDBS Micelles on the Surface of Silica Particles Using Optical Tweezers

Dual-trap optical tweezers have been used to directly measure the interaction forces between two silica particles upon controlling the concentration of the ionic surfactant sodium dodecylbenzenesulfonate (SDBS). By capturing two silica particles in one spot optical trap and one linear optical trap and controlling the linear trap to bring one particle to approach another sufficiently closer, the interaction forces between these two particles can be measured as the separation distance changes. Results showed that with increasing concentrations of SDBS, the interaction force between the two silica particles emerges at closer surface distance between two silica particles. Only repulsive force exists between silica particles below the critical micelle concentration (cmc) of SDBS and it could be well-fitted using the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. However, the depletion attraction force appears above the cmc of SDBS which is induced by the generation of SDBS micelles. By in situ measurement of the interaction force between two silica particles in the presence of different concentrations of SDBS, the depletion force can be quantitatively calculated.

Near wall dynamics of a spherical particle in crowded suspensions of colloidal rods - dynamic information from TIRM revisited

We performed total internal reflection microscopy (TIRM) experiments to determine the depletion potentials between probe spheres and a flat glass wall which are induced by long and thin, rod-shaped colloids (fd-virus), and probe the spatially resolved dynamics of the probe spheres. The dynamic information from the same raw TIRM intensity time traces is extracted in three different ways: by determining the spatially averaged diffusion constant of the probe sphere normal to the wall, by measuring the position dependence of the diffusion coefficient, and by measuring the particle's local drift velocity. Up to a concentration of about 6 times the overlap concentration of the rod-like colloids, the spatially averaged diffusion coefficient and the amplitude of the depletion potential are in surprisingly good agreement with theoretical predictions in which mutual interactions between the rods are neglected, that is, where the concentration is less than the overlap concentration. On increasing the depletant content even further, however, both the static and the averaged dynamic quantities begin to deviate from such theoretical predictions. In particular we find large deviations from the prediction by Mao, Cates, and Lekkerkerker [J. Chem. Phys., 1997, 106, 3721] based on the third order virial expansion for the rod concentration. It is shown that there are significant inaccuracies in TIRM measurements of diffusion coefficients due to the limited time range in which the mean squared displacements vary linearly in time, whereas mean displacements give much more accurate information concerning the probe sphere dynamics.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Effects of metal oxide nanoparticles on the stability of dispersions of weakly charged colloids

The stability behavior of dispersions of weakly charged silica colloids was studied in the presence of highly charged metal oxide nanoparticles. Experiments were performed using 5 nm zirconia as well as 10 nm alumina nanoparticles (both positively charged), which were added to 0.1 vol % suspensions of 1.0 μm silica microparticles at the silica IEP. Both types of nanoparticles provided effective stabilization of the silica; i.e., the silica suspensions were stabilized for longer than the observation period (greater than 12 h). Stability was observed at zirconia concentrations as low as 10(-4) vol % and at an alumina concentration of 10(-2) vol %. The nanoparticles adsorbed onto the microparticle surfaces (confirmed via SEM imaging), which increased the zeta-potential of the silica. Force profile measurements performed with colloidal probe atomic force microscopy showed that the adsorption was effectively irreversible.

Sphere to rod transitions in self assembled systems probed using direct force measurement

The influence of nanoparticle shape, in particular the sphere to rod transition, on surface forces and consequently the properties of colloidal fluids is an interesting but not well investigated phenomenon. Here, the surface force behaviour of concentrated surfactant solutions containing cetyltrimethylammonium bromide and sodium salicylate with micelle shapes varying from slightly prolate to high aspect ratio rods was measured. Atomic force microscopy (AFM) with both rigid particle and soft droplet probes was used with comparisons and analysis made using the Chan-Dagastine-White model. It is observed that small changes to the micelle shape result in no discernable differences to the surface force behaviour, however, once the micelles are elongated significantly, the long range forces adjust in nature from oscillatory to that of a single attractive force well. This highlights the importance that nanocolloid shape has on the behaviour and properties of emulsions and other colloidal fluids, specifically for emulsion flocculation and handling in systems of rod and worm like micelles.

Binary short-range colloidal assembly of magnetic iron oxides nanoparticles and fullerene (nC60) in environmental media

Colloidal assembly of nC60 fullerene with naturally abundant magnetic iron oxide NPs will affect their fate and transformation in environmental media. In solution, fullerene association to aggregating iron oxide NPs/clusters greatly enhanced the overall colloidal stability. Development of depletion-mediated structured fullerene layers between pure and surface modified γFe2O3 NPs possibly resulted in such stabilization. Here, we also report that on air-water interface, association of fullerene to pure and humic acid (HA7) coated γFe2O3 NPs led to the formation of ordered assemblies, e.g., binary wires and closed-packed "crystalline" and "glassy" structures in the presence and absence of electrolytes suggesting immobilization of the former. The interaction of fullerene to Fe3O4 NPs and clusters also produced ordered assemblies along with amorphous aggregates. Fullerene interaction with Fe3O4 NPs in low concentration of HA1 and Na(+) at pH 6 formed dendritic growth and polycrystalline circular assemblies on air-water interface. HRTEM study further revealed that the monolayer circular assemblies were highly ordered but structural degeneracy was evident in multilayers. Therefore, interfacial assemblies of fullerene with iron oxide NPs resulted in short-range periodic structures with concomitant immobilization and reduction in availability of the former, especially in soils or sediments rich in the latter.

Synergistic effects of nanoparticles and polymers on depletion and structural interactions

An experimental study was performed to investigate the synergistic effects of two different solution components on the depletion and structural forces between colloidal particles. Using silica nanoparticles and anionic poly(acrylic acid) polymer, it was found that the depletion and structural forces measured between a 30 μm diameter silica sphere and a flat silica plate (obtained using colloidal probe atomic force microscopy) were substantially greater than the sum of the forces obtained in systems containing only nanoparticles and only polymer. This result arises because the anionic polymer chains adsorb to the nanoparticles, creating a complex that is over twice as large as either component. Although the number density of depletants decreases with such complexation, the larger size results in much greater forces at longer ranges. In addition, the measured force profiles could be well described using a force model in which all components were treated as hard, charged spheres. The results clearly indicate that predicting the depletion force in systems with multiple depletant components, such as the one used here, can be much more complicated than simply adding the forces contributed from each component independently.

Shear-affected depletion interaction

We investigate the influence of flow fields on the strength of the depletion interaction caused by disc-shaped depletants. At low mass concentration of discs, it is possible to continuously decrease the depth of the depletion potential by increasing the applied shear rate until the depletion force is not perceivable experimentally. Above a threshold in the platelet mass concentration, the depletion potential can no longer be affected by flow in the accessible range of shear rates. While the observed decrease of depletion strength at low depletant concentration may be ascribed to flow alignment of the discs, it is not clear why the influence of flow is vanishing at high concentrations. In order to observe these effects, a modification of the established total internal reflexion microscopy (TIRM) technique is be implemented. We show the suitability of these modifications to measure particle-wall interaction potentials under non-equilibrium conditions for systems where particles are exposed to a shear.

Role of the electrostatic depletion attraction on the structure of charged liposome-polymer mixtures

The effect of adding charged nonadsorbing polymers to electrostatically structured suspensions of charged liposomes has been experimentally studied by means of light scattering techniques. The static structure factor of the mixtures is analyzed using two polymers of different sizes. As the polymer concentration increases, the main peak of the structure factor decreases and shows an important shift to larger values of the scattering vector. Such displacement is the consequence of the electrostatic-enhanced depletion attraction induced by the polymers that counteracts the electrostatic repulsion. For the shorter polymer, the system remains stable for all studied polymer concentrations. However, for the long polymer chains, the effective attraction induced at the highest polymer density studied is strong enough to destabilize the mixture. In this case, the aggregation of the liposomes leads to clusters of nearly linear morphology. The PRISM theory is employed to calculate the effective pair potential between liposomes. The theoretical predictions are able to support the experimental observations, and provide an explanation of the interplay between the electrostatic repulsive interaction and the depletion attraction. In particular, they show that the depletion attraction is especially long ranged, and is dominated by electrostatic effects rather than entropic.

Experimental verification of an exact evanescent light scattering model for TIRM

Total internal reflection microscopy (TIRM) is a method for the precise measurement of interaction potentials between a spherical colloidal particle and a wall. The method is based on single-particle evanescent wave light scattering. The well-established model used to interpret TIRM data is based on an exponential relation between scattering intensity and particle wall distance. However, applying this model for a certain range of experimental parameters leads to significant distortions of the measured potentials. Using a TIRM setup based on a two-wavelength illumination technique, we were able to directly measure the intensity distance relation revealing deviations from an exponential decay. The intensity-distance relations could be compared to scattering simulations taking into account exact experimental parameters and multiple reflections between a particle and the wall. Converging simulation results were independently obtained by the T-matrix method and the discrete sources method (DSM) and show excellent agreement with experiments. Using the new scattering model for data evaluation, we could reconstruct the correct potential shape for distorted interaction potentials as we demonstrate. The comparison of simulations to experiment intrinsically yields a new method to determine absolute particle-wall distances, a highly desired quantity in TIRM experiments.

Depletion interaction mediated by polydisperse rods

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.

Single-particle evanescent light scattering simulations for total internal reflection microscopy

We simulate and measure light scattering of a micrometer-sized spherical particle suspended in solution close to a glass substrate. The model, based on the discrete sources method, is developed to describe the experimental situation of total internal reflection microscopy experiments; i.e., the particle is illuminated by an evanescent light field originating from the glass-solvent interface. In contrast to the well-established assumption of a simple exponential decay of the scattering intensity with distance, we demonstrate significant deviations for a certain range of penetration depths and polarization states of the incident light.

Interactions between Colloidal Particles Induced by Polymer Brushes Grafted onto the Substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.

Mixtures of charged colloid and neutral polymer: Influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.