Charged Macroparticles Research Articles

A perturbative density functional approach to the structure of colloidal suspension

A simple perturbative density functional approach which incorporates the three-body correlation in an approximate manner is used to study the structure of inhomogeneous as well as homogeneous colloidal suspension. The suspension is modeled as a one component fluid of charged macro particles interacting with the well known Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. We have calculated the density profiles of inhomogeneous colloidal suspension in front of a highly repulsive charged wall as well as in a planar slit consisting of two parallel planar charged walls. The radial distribution function g(r) of the homogeneous suspensions of charged colloidal particles has also been calculated by making use of the well known Percus identity which relates the density distribution of an inhomogeneous fluid to the g(r) of the corresponding homogeneous fluid when the external potential responsible for the inhomogeneity is the interparticle potential itself. The calculated results on the density profiles and g(r) obtained from the present approach are found to be in closer agreement with the simulation results and show a marked improvement over those obtained from perturbative as well as nonperturbative density functional theories presented in earlier works.

Ordered structures in a nonideal dusty glow-discharge plasma

The formation of ordered structures of charged macroparticles in a constant-current neon glow-discharge plasma is investigated. Experiments were performed with two types of particles: thin-walled glass spheres 50–63 μm in diameter and particles of Al2O3, 3–5 μm in diameter. Formation of quasicrystalline structures is observed in the standing strata and in an artificially created double electric layer. The formation of extended filamentary structures of macroparticles in the absence of visible stratification of the positive column has been observed for the first time. The influence of the discharge parameters on the formation of the ordered structures and their melting is examined. The form of the interaction potential between the charged macroparticles is considered, as well as changes in the conditions for maintaining the discharge in the presence of high concentrations of dust particles.

A Many-Bodied Interpretation of the Attraction between Macroions of Like Charge: Juxtaposition of Potential Fields

There has existed since the 1930s a dichotomy among practitioners in the field regarding the electrostatic interactions in colloidal suspensions and polyelectrolyte solutions, viz., whether the electrical free energy is attractive or repulsive. The well-known Derjaguin−Landau−Verwey−Overbeek (DLVO) theory views the electrostatic interactions between a pair of charged macroparticles as a repulsive interaction, whereas the many-bodied “salt-crystal” structure of colloidal suspensions of Langmuir gives rise to a net attractive electrostatic interaction. Experimental data likewise are not definitive regarding these two apparently opposite points of view on the role of electrostatic interactions in these complex systems. For example, recent digital video studies by Grier and co-workers on polystyrene latex spheres (PLS) indicate that the pairwise interaction potential is repulsive and of the Yukawa form, whereas a collection of PLS particles has a long-range attractive component. A method is described herein based on a chemical model and the juxtaposition of potential fields (JPF) for multibody interaction systems. The JPF method is based on a topological procedure for identifying chemical bonding in molecules by vector gradient mapping. Vector gradient mapping methods applied to the JPF method indicate the importance of the distribution of counterions in determining the stability of a system of highly charged spheres. It is this distribution of the counterions in response to the potential fields of the macroions that provides a “crossover” from a repulsive interaction between two isolated spheres (unstable structure) to an attractive interaction for a group of spheres (stable cluster). Salient features of the JPF approach to charged colloidal systems are that it (1) does not rely on a particular form of the interaction potential, (2) identifies the shortcoming of the pair potential in the describing many-body effects, and (3) provides three mechanisms for the stability of clusters of macroions of like charge.

Anomalous heating of a system of dust particles in a gas-discharge plasma

The coexistence of regions of negatively charged macroparticles with substantially different kinetic temperatures in a highly nonideal dusty plasma in a dc glow discharge has been observed experimentally. An explanation of the observed anomalous heating of the system of dust particles in a gas-discharge plasma is proposed on the basis of a molecular-dynamics model.

Anomalously high kinetic energy of charged macroparticles in a plasma

A number of recent experimental investigations of nonideal plasmas containing macroparticles have revealed an anomalous increase in that part of the kinetic energy of these macroparticles that corresponds to their random motion. In this paper a model is proposed for the dynamic motion of charged macroparticles that explains this phenomenon.Calculations based on this model are compared with experimental results.

Nonequilibrium macroparticle charging in low-density discharge plasmas

Nonequilibrium macroparticle (MP) charging was studied theoretically in the case of small MP radius to the Debye length ratio. The different cases were considered: 1) nonstationary MP charging in plasmas with large MP density to the ion density ratio /spl kappa/ and 2) MP charging in nonuniform plasmas. In the first case, the large fraction of plasma charges captured by MP's was taken into account. In the second case, the charging of MP's moving in plasmas with nonuniform density distributions was considered. It was obtained that the MP charge decreases with parameter /spl kappa/ and increases and saturates with radius (for MP radii larger than some critical radius R/sub cr/) and these effects strongly depend on the MP residence time in the discharge plasma. In the case of plasma density N/sub i/=10/sup 12/ m/sup -3/ and for /spl kappa/ in the range 10/sup -4/-10/sup -1/, the value of R decreases from 30 to 0.4 /spl mu/m if the MP residence time is t/spl sim/0.1 ms, and R/sub cr/ decreases from 20 to 0.1 /spl mu/m if t/spl sim/10 ms, while in the steady-state case, R/sub cr/ changes more significantly from 10 to 10/sup -2/ /spl mu/m. Qualitative agreement with experiments of MP charge behavior with the MP radius and the effect of MP charge saturation with the radius was obtained. MP's traveling through a nonuniform plasma, when the plasma density changed as N/sub i//spl sim/1/x/sup m/ (where m is the nonuniformity parameter) were considered. It was obtained that if the distance during which charging occurred is larger than the characteristic linear scale of the plasma density changes, the MP's may not have time to reach their equilibrium charge value at any location that they pass through. In the case of MP traveling in the plasma jet, the MP does not reach the equilibrium charge if m/spl ges/2 and /spl sim/1 cm.

Creation of ordered structures in a classical thermal plasma containing macroparticles: Experiment and computer simulation

We have compared experimental measurements of ordered structures in a thermal plasma containing macroparticles of CeO2 at atmospheric pressure and a temperature around 1700 K with the results of numerical Monte Carlo calculations for the Yukawa model. We describe several distinctive features of the way the experiments were done, including how the ordered macroparticle structures were detected. We discuss a theoretical model of the behavior of an equilibrium system of charged macroparticles in a plasma and the effective interaction potential between them. Good agreement between the experimental and numerical results is noted, and possible reasons for the observed discrepancies are discussed.

Rotational–translational electrolyte friction on nonspherical particles

We present and apply an approximate general theory for the effects of the direct interactions on the translational and rotational diffusion coefficients of a nonspherical Brownian particle interacting with other spherical particles diffusing around it. These results are specialized to a system formed by a charged axially-symmetric macroparticle that diffuses in an ionic solution, whose static properties are described within the Debye-Hückel approximation. In particular, we calculate the static friction coefficients of a Brownian point-dipole embedded in a hard-sphere, and of a charged hard-ellipsoidal tracer particle.

Cyclotron acceleration of macroparticles

The acceleration of charged macroparticles of lanthanum hexaboride by constant voltage pulses applied in synchronism with their orbital motion is considered. These macroparticles are confined on a circular path of constant radius by a radial electric field which increases as the square of the velocity of the macroparticles. Velocities above 300 km/s and initial impact temperatures in the range of 5 × 10 8 K are expected.

Application of the reference interaction site model theory to analysis on surface-induced structure of water

We consider the extended simple point charge (SPC/E) model water near uncharged and charged macroparticles. It is shown that the size of the macroparticle tested is sufficiently large and it acts in effect as a planar wall. The reference interaction site model (RISM) theory is employed, and a robust and very efficient algorithm has been developed for solving the basic equations. The algorithm is a hybrid of the Picard and Newton-Raphson methods. The Jacobian matrix is just part of the input data and need not be recalculated at all. Sufficiently accurate solutions are obtained in only 7 to 16 iterations. The reduced density profile of oxygen atoms near an uncharged macroparticle indicates significant dewetting and a clear contribution of the icelike structure. The surface potential calculated is positive but very small. When the macroparticle is charged, the number of water molecules in the close vicinity of the surface increases regardless of the sign of the charge. The interaction between uncharged macroparticles with sufficiently large sizes immersed in pure water is attractive and very strong at small separations. The interaction between negatively charged macroparticles is ‘‘more repulsive’’ than between positively charged macroparticles. On the whole, however, the asymmetry of the SPC/E water in responding to positively and negatively charged surfaces is not high. It has been shown that the results obtained from the RISM theory combined with the SPC/E water are in qualitative accord with those calculated by the reference hypernetted-chain (RHNC) theory for hard spheres with embedded dipoles and tetrahedral quadrupoles, in terms of reduced density profiles, surface potential, and macroparticle interactions.

Ion‐ion correlations and effective charges in electrolyte and macroion systems

AbstractVarious ion‐ion correlation mechanisms that affect double layer interactions between charged macroparticles in electrolyte solutions are reviewed and discussed. Such effects give rise to quantitative and sometimes qualitative deviation from the prediction of the Poisson‐Boltzmann theory. Special attention is given to the attractive double layer interactions that can appear between equally charged surfaces at short surface separations for aqueous systems with divalent counterions. The long‐range behaviour of the double layer interaction is also treated. It is efficiently described in terms of effective surface charge densities, which summarizes how the inner parts of the diffuse double layer affects the distant parts. The magnitude as well as the sign of the effective charge depends on the state of the system. Charge reversal can occur for aqueous systems with divalent counterions. A major objective of the paper is to describe and illustrate the mechanisms in a simple and graphical manner.

Behavior of Adhesive Charged Macroparticles Found from the MSA

The behavior of adhesive charged macroparticles was investigated on the basis of analytical solutions obtained using the mean spherical approximation. When ionic species regarded as point charges are added to a dispersed system of the macroparticles, this system, if they are sufficiently highly charged and the system is sufficiently dense, readily undergoes phase separation. However, when the macroparticles are not highly charged or the system is not sufficiently dense, it is difficult to observe this phenomenon even though a large quantity of the ionic species is added to the dispersed system. For this behavior, the contribution of the nonlinear condensation of the ionic species is considered.

Energy amplification in a DC linear accelerator of macroparticles for impact fusion

The acceleration to hypervelocities of charged macroparticles of lanthanum hexaboride by a high DC voltage is considered. Such a voltage is applied through a combination of resistance, capacitance, and inductance allowing one to enhance by a factor two or three the energy of the beam. Fusion reactions are expected when such a fast beam crosses a slow beam of uranium hydrides (UD 3, UT 3). The eventuality of a concomitant fission process is also considered.

Nonstationary macroparticle charging in an arc plasma jet

The charging of liquid metal macroparticles in the rarified part of a vacuum arc plasma jet is studied. The sheath in the vicinity of the macroparticle is collisionless and the problem with different Debye length to macroparticle radius ratios is analyzed. Maxwellian velocity distribution functions with different temperatures for the electrons and ions in an arbitrary ratio are allowed in the model. By solving the equation for the electric field together with the equation for ion and electron flux, the charging time and the near electric field of the macroparticles were calculated. The kinetics of the macroparticle charging are controlled by the ion and electron flux to the macroparticle, which depend on the potential distribution in the sheath. The potential falls off slower than 1/r/sup 2/ in the case of the large Debye length to macroparticle radius ratio, and falls off more rapidly than 1/r/sup 2/ in the other case. The charge which accumulates on a macroparticle at distances of about 10 cm from a 100-/spl Aring/ cathode is about 10/sup -16/ C and the charging time is about 10/sup -5/ s. The influence of the plasma drift velocity on the macroparticle charging is small. The model presented here agrees well with an experimental study of macroparticle repulsion from biased substrates.

Electrokinetic properties of a charged tracer in a time-dependent external field

In a previous paper [Cruz de León et al., Chem. Phys. Lett. 207, 294 (1993)], we have derived a formalism to calculate the dynamic friction function of a charged tracer macroparticle in a multicomponent ionic solution. Here we apply this theoretical scheme to describe the electrokinetic properties of a charged tracer immersed in a solution in the presence of a time-dependent external driving force. We derive analytic expressions for the self-diffusion coefficient and the electrophoretic mobility. We compute the Van Hove self-correlation function and compare it with previous results. As an example we compute the electrophoretic mobility in the presence of a time-independent external driving force within well-defined limits and approximations. We obtain complete results in the absence of hydrodynamic interactions. Our results derived here provide a framework to describe the dynamics of a charged tracer.

Brownian Motion in Polydisperse Charged Colloidal Suspensions

The effect of combined intrinsic size and charge polydispersity on the tracer diffusion in bimodal suspensions of strongly charged macroparticles is investigated both theoretically and experimentally. The measurable wavenumber-dependent mean squared displacement and the partial mean squared displacements are calculated based on a bimodal Schulz distribution for the particle sizes and charges, using both a single relaxation time approximation for the memory function (SEXP) and the multicomponent Brownian Dynamics (BD) simulation technique. It is found that intrinsic polydispersity has a significant effect on tracer diffusion. The partial static structure functions, which are required as an input for the single relaxation time approximation, are obtained by using the multicomponent hypernetted chain approximation. The predictions of the SEXP approximation and BD simulations are compared with data from large-wave-number dynamic light scattering (DLS) experiments on binary suspensions of strongly interacting polystyrene spheres. Good agreement between SEXP, BD, and DLS data is found within the experimentally scanned time window. However, at intermediate to large times, it is found that the mean squared displacements calculated from the SEXP approximation deviate significantly from results obtained from BD simulations, especially for systems with substantial polydispersity in macroion sizes and charges. We also discuss the range of validity for a simple extension of the substitutional model applicable to intrinsically polydisperse bimodal suspensions.

Correlations between macroions in mixtures of charged and uncharged macroparticles

Addition of uncharged or charged macroparticles to a solution of macroions and counterions significantly affects the macroion–macroion correlation function. This effect is studied using the hypernetted-chain integral equation. Two simple models are examined: (i) a multicomponent primitive model treats a solution as a mixture of charged and uncharged hard spheres, (ii) a one-component model where the electrostatic interactions are accounted for by the screened Coulomb potential and the effect of neutral macroparticles is given by an approximate ‘‘volume exclusion’’ potential. Both models ignore the molecular nature of solvent. The calculations presented here indicate that the one-component model is a poor representation of the actual interactions between macroions in the presence of the neutral macroparticles represented as hard spheres. In the second part of the work we study the mixtures of macroions (two positively charged macroions that differ in size) with a common counterion. The radial distribution functions are presented for systems containing mono- or divalent counterions for a range of macroion concentrations.

Electrostatic trapping of a colloidal monolayer near a charged wall

The structure of a model colloidal suspension in the vicinity of a charged wall is studied in the framework of the Derjaguin–Landau–Verwey–Overbeek interaction potential and the hypernetted-chain approximation. Here we consider the case of dilute suspension of highly charged macroparticles interacting with weakly repulsive, neutral, and attractive walls. As the wall–particle electrostatic interactions become successively less repulsive, the formation of a monolayer of colloidal particles, strongly adsorbed onto the surface, is predicted by our results. This monolayer of electrostatically confined particles mimic the effect of an effective surface charge distribution adjacent to the wall which, together with the bare wall surface charge, induces on the other, nonconfined, colloidal particles the same local-concentration profile as that in front of a highly charged and repulsive wall.

The interaction between macroparticles in molecular fluids

Potentials of mean force for pairs of charged and neutral macroparticles immersed in simple dipolar hard sphere and waterlike solvents are obtained using the reference hypernetted-chain theory. In general, the results depend rather strongly upon both the solvent and the size of the macroparticles. For smaller neutral macroparticles, the potential of mean force in both solvents is essentially a short-ranged hydrophobic interaction with very little structure. For larger neutral particles in water, short-ranged structural effects likely due to solvent ordering near the flatter surfaces are evident. For charged macroparticles, the potential of mean force is found to be essentially a superposition of three distinct contributions: a short-ranged structural contribution which clearly depends upon the granular nature of the solvent; a repulsive ‘‘cavity’’ term which decays asymptotically as r−4; and of course there is the long-ranged Coulombic interaction. At intermediate separations, this repulsion is the principal correction to Coulomb’s law and it is shown to be much more important in molecular solvents than predicted by comparable dielectric continuum calculations. Furthermore, it is shown that this contribution can be represented with reasonable accuracy by simple analytical approximations.

Steady state viscosity coefficients of charged colloidal systems

For a dispersion containing small charged macro-particles, the steady-state shear-viscosity and other viscosity coefficients are calculated. The deformation of the electrical double layer around the macro-particles is taken into account upto first order in the Péclet number. The viscosity coefficients are expressed as integrals over the (non-equilibrium) structure factor, and are thus valid up to “higher orders” in volume fraction. The deformation of the static structure factor due to the shear-flow is also discussed. It turns out that the structure factor is non-analytic in the shear-rate for small shear-rates.