The trapping of diffusing particles by absorbing surface centers

The problem of the trapping of diffusing particles by nonoverlapping absorbing patches randomly distributed over a reflecting surface is considered. The suggested approach to its solution is based on the replacement of the inhomogeneous boundary condition on the surface by a radiation boundary condition with an effective rate of trapping the same at all surface points. An equation for the effective rate of the trapping of particles was obtained for absorbing round disks equal in size as reaction patches. The equation, which also described cooperative effects, was generalized to absorbing patches of different sizes and shapes. The possibility of finite absorption by reaction patches was included. The results obtained were in close agreement with computer simulation data obtained by the Brownian dynamics method.     

Communication: Clusters of absorbing disks on a reflecting wall: competition for diffusing particles

Trapping of diffusing particles by a cluster of absorbing disks on the otherwise reflecting wall is a manifestly many-body problem because of the disk competition for the particles. By replacing the cluster with an effective uniformly absorbing spot, we derive a simple formula for the rate constant that characterizes the trapping. The formula shows how the rate constant depends on the size and shape of the cluster.     

First-passage approach for permeable traps

Many reactive processes in complex materials involve absorption of diffusing molecules. Recently, there has been interest in particle interaction with partially absorbing (or permeable) traps. Here, we present a simple and efficient method for accounting for the non-diffusion-limited reaction of particles when the flux of particles to the trap is governed by surface permeability. The trapping probability is determined from a one-dimensional Green's function, which results in a simple algebraic expression. This expression, which applies in the region immediately adjacent to the trap, is then used with a first-passage approach far from the trap. When applied to a suspension of permeable traps, the method is seen to give accurate results over the concentration range. The method is applied to the competition of reactive particles in a suspension of permeable spheres with a reactive continuous phase.     

Time dependent diffusion in a disordered medium with partially absorbing walls: a perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick [J. Chem. Phys. 76, 4255 (1982)] we obtain a perturbative expansion for the time dependent particle density using volume fraction f of spheres as an expansion parameter. The exact single particle t operator for partially absorbing boundary condition is used to obtain a closed form time dependent diffusion coefficient D(t) accurate to first order in the volume fraction f. Short and long time limits of D(t) are checked against the known short time results for partially or fully absorbing boundary conditions and long time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be D(t)=5a(2)/(12fD(0)t)+O((D(0)t/a(2))(-2)) to the first order of perturbation theory. Here f is small but nonzero, D(0) the diffusion coefficient in the absence of spheres, and a the radius of the spheres. The validity of this perturbative result is discussed.     

Multistage adsorption of diffusing macromolecules and viruses

We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein insertion, cell signaling, and the infection of cells by virus particles. For example, viral entry into healthy cells is possible only after a series of receptor and coreceptor binding events occurs at the cellular surface. We couple the diffusion of particles in the bulk phase with the multistage surface kinetics and derive an effective, integrodifferential boundary condition that contains a memory kernel embodying the delay induced by the surface reactions. This boundary condition takes the form of a singular perturbation problem in the limit where particle-surface interactions are short ranged. Moreover, depending on the surface kinetics, the delay kernel induces a nonmonotonic, transient replenishment of the bulk particle concentration near the interface. The approach generalizes that of Ward and Tordai [J. Chem. Phys. 14, 453 (1946)] and Diamant and Andelman [Colloids Surf. A 183-185, 259 (2001)] to include surface kinetics, giving rise to qualitatively new behaviors. Our analysis also suggests a simple scheme by which stochastic surface reactions may be coupled to deterministic bulk diffusion.     

All-electron time-dependent density functional theory with finite elements: time-propagation approach

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.     

Contact angles of colloid silica and gold particles at air-water and oil-water interfaces determined with the gel trapping technique

We have used the recently developed gel trapping technique (GTT) to determine the three-phase contact angles of submicrometer silica particles partially coated with octadecyl groups. The particles were spread at air-water and decane-water surfaces, and the aqueous phase was subsequently gelled with a nonadsorbing polysaccharide. The particles trapped at the surface of the aqueous gel were lifted by molding with curable poly(dimethylsiloxane) and imaged with scanning electron microscopy (SEM) to determine the particle contact line diameter which allows their contact angle at the original air-water or oil-water interface to be estimated. We report for the first time the use of the GTT for characterizing the contact angle of individual submicrometer particles adsorbed at liquid interfaces. The SEM images also reveal the structure of the particle monolayer at the interface and the structure of adsorbed particle aggregates. We have also determined the contact angles of agglomerated gold powder microparticles at the air-water and the decane-water interfaces. It was found that agglomerated gold particles demonstrate considerably higher contact angles than those on flat gold-coated surfaces.     

Calculating quasi-bound rotation-vibrational states of HOCl using massively parallel computers

We calculate positions and predissociation widths for quasi-bound states of HOCl with total angular momentum of J=0 and J=3. An ab initio potential energy surface is used in conjunction with a complex absorbing potential (CAP). These calculations are performed by diagonalising a complex symmetric Hamiltonian using our discrete variable representation (DVR) based parallel code, PDVR3D, and a truncation and diagonalisation algorithm. The resonances are identified as those states in the continuum, which are stable with respect to CAP and basis set parameters. Test on the resonances are carried out using over 90 different absorbing potential heights. Resonances of both Feshbach (vibrational trapping) and shape (rotational trapping) are identified.     

Distribution of polymer chain lengths inside a spherical volume: Solution in terms of a diffusion problem

The probability W(t) that a given number t of segments of an infinite chain lie within a given sphere can be expressed in terms of the single-pass length probability and the probability of reentrance into the sphere. The problem of calculating these two probabilities is equivalent to that of a diffusing particle exiting or entering the sphere after a given time, when the surface of the sphere is an absorbing wall. It is shown that the boundary condition, c = 0, usually applied to an absorbing surface cannot be used for the present purpose. The boundary condition used instead is the so-called radiation condition ?c/?z = kc; it is shown that when k approaches infinity the final answer for W(t), which is given in the form of an infinite series, approaches the correct limit. In this same limit the ratio 〈t〉²/〈t〉² has the value 2.4     

Dynamic Photocontrol of the Coffee‐Ring Effect with Optically Tunable Particle Stickiness

When a colloidal drop dries on a surface, most of the particles accumulate at the drop periphery, yielding a characteristic ring‐shaped pattern. This so‐called coffee‐ring effect (CRE) is observed in any pinned evaporating drop containing non‐volatile solutes. Here, the CRE is dynamically controlled for the first time by using light, and an unprecedented reconfigurability of the deposit profile is demonstrated. This is achieved through a new mechanism where particle stickiness is optically tuned on demand, thus offering reliable modulation of the deposition pattern. The system consists of anionic nanoparticles and photosensitive cationic surfactants dispersed in water. It is shown that light‐dependent modulation of surfactant–particle interactions dictates particle attraction and trapping at the liquid–gas interface, which allows us to direct particle deposition into a wide range of patterns from rings to homogeneous disks. Patterning from single drops is photoreversible upon changing the wavelength whereas spatial control in multiple drop arrays is achieved using a photomask.     

Red blood cells do not attenuate the SPCE fluorescence in surface assays

We describe the positive effect of surface plasmon-coupled fluorescence emission (SPCE) on the detection of a signal from a surface immunoassay in highly absorbing or/and scattering samples. A model immunoassay using fluorescently labeled anti-rabbit antibodies that bind to rabbit immunoglobulin on a silver surface was performed, and the signal was detected in the presence of various highly absorbing and/or scattering solutions or suspensions, such as hemoglobin solution, plastic beads, and red blood cells. The results showed that a highly absorbing solution consisting of small molecules (dye, hemoglobin) attenuates the SPCE signal approximately 2-3-fold. In contrast, suspensions with the same absorption containing large particles (large beads, red blood cell suspension) attenuate the SPCE signal only slightly, approximately 5-10%. Also, a suspension of large undyed, highly scattering beads does not reduce the SPCE signal. The effects on the immunoassay signal of the sample background absorption and scattering, the size of the background particles, and the geometry of the experimental set-up are discussed. We believe that SPCE is a promising technique in the development of biosensors utilized for surface-based assays, as well as any assays performed directly in highly absorbing and/or scattering solutions without washing or separation procedures. Figure Red blood cells (unlike hemoglobin) do not attenuate the SPCE fluorescence in surface assays.     

On describing the steady absorption of brownian particles by a restricted random walk

This paper is concerned with idealizing brownian motion as a random walk, using the diffusion equation, and finding the boundary condition at an absorbing surface - all with an eye towards chemical kinetics. Three models of random walk (due to Smoluchowski, Fermi, and Lorentz) are considered, and it is concluded that the lorentzian model is the most appropriate.     

Chemically reactive thin diffusion barriers

We assess the degree of protection against diffusion of an environmental pollutant afforded by a thin, chemically reactive surface film on a slab or membrane. For the case of an irreversible quasi-unimolecular reaction in such a surface film we derive a modified radiation boundary condition which adequately describes the presence of such a film. We show that the two extra parameters which appear in this boundary condition, an effective surface conductivity and an effective ambient concentration can be found from the permeation steady state flux and time lag through such a membrane. We compare our approximate boundary condition with that obtained for a chemically passive thin film and a newly derived boundary condition which exactly describes the transport in the composite medium — reactive film and body (slab or membrane). In certain instances such a thin, reactive film is effective as a diffusion barrier.     

Emulsions stabilised by food colloid particles: role of particle adsorption and wettability at the liquid interface

We study the effect of the particle wettability on the preferred type of emulsion stabilised solely by food colloid particles. We present results obtained with the recently developed gel trapping technique (GTT) for characterisation of wettability and surface structuring of individual food colloid particles adsorbed at air-water and oil-water interfaces. This method allows us to replicate a particle monolayer onto the surface of polydimethylsiloxane (PDMS) without altering the position of the particles. By observing the polymer surface with scanning electron microscopy (SEM), we are able to determine the contact angle of the individual particles at the initial liquid interface. We demonstrate that the GTT can be applied to fat crystal particles, calcium carbonate particles coated with stearic acid and spray-dried soy protein/calcium phosphate particles at air-water and oil-water interfaces. Subsequently, we prepare emulsions of decane and water stabilised by the same food colloid particles and correlate the wettability data obtained for these particles to the preferred type of emulsions they stabilise.     

Particle trapping using dielectrophoretically patterned carbon nanotubes

This study presents the dielectrophoretic (DEP) assembly of multi‐walled carbon nanotubes (MWCNTs) between curved microelectrodes for the purpose of trapping polystyrene microparticles within a microfluidic system. Under normal conditions, polystyrene particles exhibit negative DEP behaviour and are repelled from microelectrodes. Interestingly, the addition of MWCNTs to the system alters this situation in two ways: first, they coat the surface of particles and change their dielectric properties to exhibit positive DEP behaviour; second, the assembled MWCNTs are highly conductive and after the deposition serve as extensions to the microelectrodes. They establish an array of nanoelectrodes that initiates from the edge of microelectrodes and grow along the electric field lines. These nanoelectrodes can effectively trap the MWCNT‐coated particles, since they cover a large portion of the microchannel bottom surface and also create a much stronger electric field than the primary microelectrodes as confirmed by our numerical simulations. We will show that the presence of MWCNT significantly changes performance of the system, which is investigated by trapping sample polystyrene particles with plain, COOH and goat anti‐mouse IgG surfaces.     

Sedimentation of concentrated spherical particles with a charge-regulated surface

The sedimentation of a concentrated colloidal dispersion is examined for the case of an arbitrary double-layer thickness. Here, a general mixed-type condition on particle surface is assumed, and the classic models, which assume constant surface properties, can be recovered as the special cases of the present analysis. In particular, the behavior of biological cells, which carry dissociable functional groups on their surfaces, and particles, which are capable of exchanging ions with the surrounding medium, can be simulated by the present model. The mixed-type boundary condition leads to several interesting results in both sedimentation velocity and sedimentation potential as double-layer thickness and the concentration of particles vary.     

Calculation of diffusion impedance in the terms of locally nonequilibrium diffusion

An equation for diffusion impedance is derived in the terms of the lattice diffusion model based on the assumption as to the local nonequilibrium distribution of diffusing particles across the sites of different types. This equation is valid at low lattice occupation. Unlike the multiple trapping model, all site types are interpreted symmetrically. In the boundary condition, it is assumed that there is a unique relationship between the electric potential variation, on one side of the interface and variation of the generalized particle activity on the other side.     

Adsorption on Heterogeneous Regular Surfaces

Quantifying the role of surface shape and physicochemical surface conditions on the interfacial reactivity of particles and substrates is fundamental to a multitude of natural and engineered surface adsorption phenomena. We consider continuum/jump regime adsorption at the gas or liquid interface of arbitrary regular solid surfaces with heterogeneous surface features. In particular, the 3-D boundary value problem (based on Laplace's diffusion equation) is converted into a 2-D integral equation for the adsorbate concentration at the particle surface. This accommodates numerical descretization via the implementation of 2-D Gauss-Legendre quadratures on an arrangement of high- and low-adsorption patch trace sites constructed to completely cover the particle surface. A generalized computer program is developed to solve the resulting linear algebra problem for the unkown local adsorption current densities. We investigate the role of various distributions of high- and low-adsorption sites for a generalized class of spheres which includes the DNA-like shaped twisted spheres. The biological implications of the role of surface curvature on interfacial adsorption/reactivity at particle surfaces are also discussed. Copyright 2001 Academic Press.     

On the electrophoretic mobility of a cylindrical soft particle

A previous theory for the electrophoresis of a cylindrical soft particle (that is, a cylindrical hard particle covered with a layer of polyelectrolytes) [7], which makes use of the condition that the electrical force acting on the polymer segments is balanced with a frictional force exerted by the liquid flow, is modified by replacing this condition with an alternative and more appropriate boundary condition that pressure is continuous at the boundary between the surface layer and the surrounding electrolyte solution. The general mobility expression thus obtained is found to reproduce all of the approximate analytic mobility expressions derived previously. Received: 20 July 2000/Accepted: 21 August 2000