Aggregation of Charged Particles under Electrophoresis or Gravity at Arbitrary Péclet Numbers

Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime. This regime occurs when there is a large energy barrier in the interparticle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate. Copyright 2000 Academic Press.     

Theory for hierarchical assembly with dielectrophoresis and the role of particle anisotropy

Nonuniform electric fields cause polarizable particles to move through an effect known as dielectrophoresis (DEP). Additionally, the particles themselves create nonuniform fields due to their induced dipoles. When the nonuniform field of one particle causes another to move, it represents a path to hierarchical assembly termed mutual DEP (mDEP). Anisotropic particles potentially provide further opportunities for assembly through intense and intricate local field profiles. Here, we construct a theoretical framework for describing anisotropic particles as templates for assembly through mDEP by considering the motion of small nanoparticles near larger anisotropic nanoparticles. Using finite element analysis, we study eight particle shapes and compute their field enhancement and polarizability in an orientation-specific manner. Strikingly, we find a more than tenfold enhancement in the field near certain particle shapes, potentially promoting mDEP. To more directly relate the field intensity to the anticipated assembly outcome, we compute the volume experiencing each field enhancement versus particle shape and orientation. Finally, we provide a framework for predicting how mixtures of two distinct particle species will begin to assemble in a manner that allows for the identification of conditions that kinetically bias assembly toward specific hierarchical outcomes.     

pH-Dependent Control of Particle Motion through Surface Interactions with Patterned Polymer Brush Surfaces

In this Article, we show that inclined silicon surfaces patterned with poly(methacrylic acid) brushes are able to control the position and movement of 20 μm silica particles, which are propelled across the patterned surface by sedimentation forces. Three different types of behavior were observed depending on the angle between the direction in which a particle sedimented and the orientation of the polymer-brush silicon interface. At small angles, particles were found to sediment to the brush interface and then sediment following the direction of the brush interface. At larger angles, particles sedimented to the interface and then followed the direction of the brush interface, but then after a certain distance changed direction to pass over the interface. At the largest angles where the brush interface was approximately perpendicular to the motion of the particle, particles were found to travel over the interface unperturbed. This behavior was also found to be pH dependent, allowing the formation of pH responsive "gates", which allow particles to pass at low pH but not at high pH. It was also found that if patterned polymer brush surfaces were oriented in the correct way, they were able to control the number of particles present at specific locations.     

Nanoscavenger based dispersion preconcentration; sub-micron particulate extractants for analyte collection and enrichment

A new approach has been developed for the preconcentration of analytes from solution using nanoscavengers; monodisperse functionalised particles of sub-micron dimensions, that can be suspended as a quasi-stable sol in an aqueous solution, and quantitatively recovered with the analyte by conventional filtration. No external agitation of the sample is required as the particles move naturally through the sample by Brownian motion, convection and sedimentation. By careful choice and control of their particle size and surface chemistries, nanoscavengers can be designed to suit a number of different analytical problems. Surface modification of these nanometre-sized particles, through the grafting of complexing or partitioning functional groups, can produce nanoscavengers having affinities for specific analytes and operating through a wide range of mechanisms from covalent bonding to hydrophobic interaction. The approach is illustrated by the development of an extraction-based preconcentration of metals from solution that employs sub-micron St?ber-type silica spheres, the surfaces of which have been modified using chelating diamine and dithiocarbamate groups. The concept has potentially widespread applicability as it is neither limited to metal extractions, nor to the use of silica-based nanoscavengers. Minimal involvement of organic solvents make nanoscavengers a potentially environmentally benign ("green") alternative to many conventional solvent extraction techniques.     

Transport of a heated granular gas in a washboard potential

We study numerically the motion of a one dimensional array of Brownian particles in a washboard potential, driven by an external stochastic force and interacting via short range repulsive forces. In particular, we investigate the role of instantaneous elastic and inelastic collisions on the system dynamics and transport. The system displays a locked regime, where particles may move only via activated processes and a running regime where particles drift along the direction of the applied field. By tuning the value of the friction parameter controlling the Brownian motion we explore both the overdamped dynamics and the underdamped dynamics. In the two regimes we considered the mobility and the diffusivity of the system as functions of the tilt and other relevant control parameters such as coefficient of restitution, particle size, and total number of particles. We find that while in the overdamped regime the results for the interacting systems present similarities with the known noninteracting case, in the underdamped regime the inelastic collisions determine a rich variety of behaviors among which is an unexpected enhancement of the inelastic diffusion.     

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.     

Self‐Propelled Janus Mesoporous Silica Nanomotors with Sub‐100 nm Diameters for Drug Encapsulation and Delivery

The synthesis of an innovative self‐propelled Janus nanomotor with a diameter of about 75 nm that can be used as a drug carrier is described. The Janus nanomotor is based on mesoporous silica nanoparticles (MSNs) with chromium/platinum metallic caps and propelled by decomposing hydrogen peroxide to generate oxygen as a driving force with speeds up to 20.2 μm s^?1 (about 267 body lengths per second). The diffusion coefficient (D) of nanomotors with different H₂O₂ concentrations is calculated by tracking the movement of individual particles recorded by means of a self‐assembled fluorescence microscope and is significantly larger than free Brownian motion. The traction of a single Janus MSN nanomotor is estimated to be about 13.47×10^?15 N. Finally, intracellular localization and drug release in vitro shows that the amount of Janus MSN nanomotors entering the cells is more than MSNs with same culture time and particle concentrations, meanwhile anticancer drug doxorubicin hydrochloride loaded in Janus MSNs can be slowly released by biodegradation of lipid bilayers in cells.     

Dielectrophoretic manipulation of suspended submicron particles

Planar and three-dimensiònal multi-electrode systems with dimensions of 2 - 40 microm were fabricated by IC technology and used for trapping and aggregation of microparticles. To achieve negative dielectrophoresis (repelling forces) in aqueous solution, radiofrequency (RF) electric fields were used. Experimentally, particles down to 100 nm in diameter were enriched and trapped as aggregates in field cages and dielectrophoretic microfilters and observed using confocal fluorimetry. Theoretically, single particles with an effective diameter down to about 35 nm should be trappable in micron field cages. Due to the unavoidable Ohmic heating, RF electric fields can induce liquid streaming in extremely small channels (12 microm in height). This can be used for pumping and particle enrichment but it enhances Brownian motion and counteracts dielectrophoretic trapping. Combining Brownian motion with ratchet-like dielectrophoretic forces enables the creation of Brownian pumps that could be used as sensitive separation devices for submicron particles if liquid pumping is avoided in smaller structures.     

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.     

Brownian Motion and Large Electric Polarizabilities Facilitate Dielectrophoretic Capture of Sub-200 nm Gold Nanoparticles in Water

Dielectrophoresis can move small particles using the force resulting from their polarization in a divergent electric field. In liquids, it has most often been applied to micrometric objects such as biological cells or latex microspheres. For smaller particles, the dielectrophoretic force becomes very small and the phenomenon is furthermore perturbed by Brownian motion. Whereas dielectrophoresis has been used for assembly of superstructures of nanoparticles and for the detection of proteins and nucleic acids, the mechanisms underlying DEP of such small objects require further study. This work presents measurements of the alternating-current (AC) dielectrophoretic response of gold nanoparticles of less than 200 nm diameter in water. An original dark-field digital video-microscopic method was developed and used in combination with a microfluidic device containing transparent thin-film electrodes. It was found that the dielectrophoretic force is only effective in a small zone very close to the tip of the electrodes, and that Brownian motion actually facilitates transport of particles towards this zone. Moreover, the fact that particles as small as 80 nm are still efficiently captured in our device is not only due to Brownian transport but also to an effective polarizability that is larger than what would be expected on basis of current theory for a sphere in a dielectric medium.     

Microrheology and particle tracking in food gels and emulsions

Particle tracking microrheology, an emerging experimental technique, which utilizes the Brownian motion of embedded particles to probe local dynamics of soft materials, is presented. Particle tracking microrheology is a powerful technique that enables the measurement of viscoelastic responses in small sample volumes, which are inaccessible to macrorheology and to spatially map structural heterogeneities at a microlevel. Therefore, particle tracking microrheology has considerable potential in food emulsions and gels, since these systems are commonly inhomogeneous. Recent advances and achievements are discussed, including the basic principles, operating regimes and limitations of the technique. The application of the technique in the field of food gels and emulsions to study the evolving dynamics of inhomogeneous at microscale length systems and during sol–gel transition is highlighted.     

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a "virtual-move" Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific ("patchy") attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a "virtual" trial move. We determine which of its neighbors move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes and demonstrate its utility by applying it to a model of biological self-assembly.     

Preparation of composite fine particles by heterocoagulation

To prepare regular composite particles comprised of organic and inorganic compounds, based on heterocoagulation theory, the properties of the mixture of small amphoteric latices (2a=250 nm) and large spherical silica (2a=240–1590 nm) were investigated as a function of pH, particle number ratio, particle size ratio and electrolyte concentration in the medium. It is apparent that under suitable conditions, we may prepare a stable mixed suspension comprising uniform composite particles, which are made up of many latices regularly adsorbed on silica surfaces, and each composite particle is undergoing Brownian motion as an isolated unit. This new composite particle is very stable for electrolyte, base and acid medium, and its surface charges (sign and magnitude) can be controlled by changing the pH of the medium.     

Simultane Bestimmung von elektrophoretischer Beweglichkeit und Teilchengröße bei überlagerter Konvektion an Suspensionen und Emulsionen

With AWPS (Amplitude Weighted Phase Structuration), a new signal processing scheme is demonstrated for the simultaneous determination of zeta potentials and particle sizes. It allows the measurements of a small electrophoretic mobility in the presence of large particle diffusion and constant velocity, e. g. due to thermal convection. Laser light scattering techniques instead of the former methods determine electrophoretic velocity more objectively and precisely. The applicability of laser measurement techniques by analysis of the frequency spectrum is limited for particles ?50 nm or very low potentials, because of the broadening of the spectral peak by Brownian motion. In contrast to AWPS a separation of the various kinds of collective motion is not possible. The presented results demonstrate that this separation is of considerable significance in the acquisition of reliable values. Additionally the novel signal processing scheme allows a significant increase in sensitivity and therefore the application of an oscillating field (50–100 Hz) with a very small field strength. The system is feasible for particle sizes in the range of a few nm up to several μm. Its high resolution allows experiments with low fields or with small zeta potentials, even in the critical particles size range of a few nanometers.     

Colloidal crystallization in the quasi-two-dimensional induced by electrolyte gradients

We investigated driven crystal formation events in thin layers of sedimented colloidal particles under low salt conditions. Using optical microscopy, we observe particles in a thermodynamically stable colloidal fluid to move radially converging towards cation exchange resin fragments acting as seed particles. When the local particle concentration has become sufficiently large, subsequently crystallization occurs. Brownian dynamics simulations of a 2D system of purely repulsive point-like particles exposed to an attractive potential, yield strikingly similar scenarios, and kinetics of accumulation and micro-structure formation. This offers the possibility of flexibly designing and manufacturing thin colloidal crystals at controlled positions and thus to obtain specific micro-structures not accessible by conventional approaches. We further demonstrate that particle motion is correlated with the existence of a gradient in electrolyte concentration due to the release of electrolyte by the seeds.     

Determination of potential landscapes using video microscopy

Colloidal particles are used to characterize microscopic potential landscapes, which are defined on a sample surface and arise in ensembles of particles. The positions of the particles are recorded using video microscopy. Analysis of the positions, which the particles occupy during their Brownian motion, yields the exact shape of the surface potential, in which the particles move. The underlying principle of our measurements is well-known from measurements using total internal reflection microscopy; in contrast to these measurements, our scheme can be expanded to measurements of inter-particle interactions. As an example, we demonstrate the measurement of interactions between two magnetic particles, sedimenting towards a potential barrier in a tilted geometry.     

A computational study of the hydrodynamically assisted organization of DNA-functionalized colloids in 2D

We study computationally the self-organization of DNA-functionalized colloidal particles confined to two dimensions and subjected to a linear shear force. We show that hydrodynamic forces allow a more thorough sampling of phase space than thermal or Brownian forces alone. Two particle types are present in each of our dynamic simulations each signifying its own specific oligonucleotide sequence grafted to the particle surface: A-type and B-type. Particles are modeled as interacting via a type-specific DNA attraction where unlike-types have affinities for each other while like-types do not. The particles are small enough to feel Brownian motion while the shear adds motion to the particles. We find the formation of lines of A-type and B-type particles in simulations with an imposed shear. Simulations without imposed shear form a frustrated network with little or no linear order. An orientational distribution function, g2(r), quantifies the degree of linear order. A phase diagram is constructed, finding a linear dependence of the minimum DNA force necessary for line formation on the dimensionless shear rate. A force analysis performed on the structures shows that the lines orient perpendicular to the axis of the elongation component of the shear because it is this orientation that allows the DNA attraction to resist the shear.     

Limitations of differential electrophoresis for measuring colloidal forces: a Brownian dynamics study

Differential electrophoresis experiments are often used to measure subpiconewton forces between two spheres of a heterodoublet. The experiments have been interpreted by solving the electrokinetic equations to obtain a simple Stokes law-type equation. However, for nanocolloids, the effects of Brownian motion alter the interpretation: (1) Brownian translation changes the rate of axial separation. (2) Brownian rotation reduces the alignment of the doublet with the applied electric field. (3) Particles can reaggregate by Brownian motion after they break, forming either heterodoublets or homodoublets, and because homodoublets cannot be broken by differential electrophoresis, this effectively terminates the experiment. We tackle points 1 and 2 using Brownian dynamics simulations (BDS) with electrophoresis as an external force, accounting for convective translation and rotation as well as Brownian translation and rotation. Our simulations identify the lower particle size limit of differential electrophoresis to be about 1 microm for desired statistical accuracy. Furthermore, our simulations predict that particles around 10 nm in size and at ambient conditions will break primarily by Brownian motion, with a negligible effect due to the electric field.     

Switching between laser-induced thermophoresis and thermal convection of liquid suspension in a microgap with variable dimension

Phoretic motion of particles along a temperature gradient formed in a fluid, known as thermophoresis, often takes place under the influence of bulk motion caused by thermal convection. In this paper, using a laser heating method, the significance of two competing effects, that is, thermophoresis and thermal convection, for the particle transport in a liquid phase confined in a microgap is investigated experimentally by changing the gap size as a control parameter. It is found that there is a threshold of the gap size, above which the particles tend to accumulate around the heated spot, forming a ring-like particle distribution. On the contrary, if the gap size is below the threshold, the particles are depleted from the heated spot. Switching between these accumulation and depletion modes is expected to develop novel manipulation techniques.     

Calculating the hopping times of confined fluids: two hard disks in a box

The dynamical transition between the anomalous single file diffusion of highly confined fluids and bulk normal diffusion can be described by a phenomenological model involving a particle hopping time tau(hop). We suggest a theoretical formalism that will be useful for the calculation of tau(hop) for a variety of systems and test it using a simple model consisting of two hard disks confined to a rectangular box with hard walls. In the case where the particles are moving diffusively, we find the hopping time diverges as a power law in the threshold region with an exponent of -(3/2). Under conditions where the particles move inertially, transition state theory predicts a power law behavior with an exponent of -2. Molecular dynamics simulations confirm the transition state theory result for inertial dynamics, while Brownian dynamics simulations suggest the scaling exponent is highly sensitive to the details of the algorithm.