Yukawa Particles Research Articles

Structures and dynamics of fine particles in fine particle plasmas under microgravity and friction between two-dimensional layers of charges

Low temperature structures and dynamics of fine (dust) particles in the ambient (background) plasma with the cylindrical symmetry are analyzed by numerical simulations and theory. Fine particles are modeled as Yukawa particles and the one- and two-component cases are considered. In the one-component case, particles form well-defined concentric cylindrical shells and the structures are expressed by simple interpolation formulas to a good accuracy. When we introduce the difference into charges of particles forming a shell, particles are separated into a smaller shell of larger charges and a larger shell of smaller charges. In the two-component Yukawa system, we usually have structures composed of charge-separated shells where larger and smaller charges appear alternately in the order of radius. When we have charge-dependent forces along the symmetry axis, shells of larger and smaller charges can move relative to each other keeping their own structures and the mobility for the relative motion can be defined. We give examples obtained for some combinations of parameters. It is found that, when appropriate conditions are satisfied, concentric shells form a kind of 'fine-particle (dust) screw' and the mobility is increased.

Structures of Yukawa and Coulomb particles in cylinders: Simulations for fine particle plasmas and colloidal suspensions

Low-temperature structures of Yukawa particles in systems with cylindrical symmetry are analyzed by numerical simulations. Particles are organized into well-defined thin concentric shells forming triangular lattices with defects on each shell and structural parameters are expressed by simple interpolation formulas including the limiting case of Coulomb particles. In outer shells, the local structure can be regarded as three-dimensional closest packing as in the case of the background of uniform spheres. These formulas can be directly compared with fine particle experiments in long cylindrical chambers under microgravity or colloidal suspensions in cylinders and may be useful as a basis of structural analyses in cylindrical systems.

Ion size effects upon ionic exclusion from dielectric interfaces and slit nanopores

A previously developed field-theoretic model (Coalson et al 1995 J. Chem. Phys. 102 4584)that treats core collisions and Coulomb interactions on the same footing is investigated inorder to understand ion size effects on the partition of neutral and charged particles atplanar interfaces and the ionic selectivity of slit nanopores. We introduce a variationalscheme that can go beyond the mean-field (MF) regime and couple in a consistent waypore-modified core interactions, steric effects, electrostatic solvation and image-chargeforces, and surface charge induced electrostatic potential. Density profiles of neutralparticles in contact with a neutral hard wall, obtained from Monte Carlo (MC) simulationsare compared with the solutions of mean-field and variational equations. A recentlyproposed random-phase approximation (RPA) method is tested as well. We show that inthe dilute limit, the MF and the variational theories agree well with simulation results, incontrast to the RPA method. The partition of charged Yukawa particles at a neutraldielectric interface (e.g. an air–water or protein–water interface) is investigated. It isshown that as a result of the competition between core collisions that push theions toward the surface, and repulsive solvation and image forces that excludethem from the interface, a concentration peak of finite size ions sets in close tothe dielectric interface. This effect is amplified with increasing ion size and bulkconcentration. An integral expression for the surface tension that accounts forexcluded volume effects is computed and the decrease of the surface tension withincreasing ion size is illustrated. We also characterize the role played by the ionsize in the ionic selectivity of neutral slit nanopores. We show that the complexinterplay between electrostatic forces, excluded volume effects induced by corecollisions and steric effects leads to an unexpected reversal in the ionic selectivity ofthe pore with varying pore size: while large pores exhibit a higher conductivityfor large ions, narrow pores exclude large ions more efficiently than small ones.

Yukawa particles confined in a channel and subject to a periodic potential: Ground state and normal modes

We consider a classical system of two-dimensional (2D) charged particles, which interact through a repulsive Yukawa potential $exp(-r/\lambda)/r$, confined in a parabolic channel which limits the motion of the particles in the $y$-direction. Along the $x$-direction, the particles are also subject to a periodic potential substrate. The ground state configurations and the normal mode spectra of the system are obtained as function of the periodicity and strength of the periodic potential ($V_0$), and density. An interesting set of tunable ground state configurations are found, with first and second order structural transitions between them. A magic configuration with particles aligned in each minimum of the periodic potential is obtained for V_0 larger than some critical value which has a power law dependence on the density. The phonon spectrum of different configurations were also calculated. A localization of the modes into a small frequency interval is observed for a sufficient strength of the periodic potential. A tunable band-gap is found as a function of $V_0$. This model system can be viewed as a generalization of the Frenkel and Kontorova model.

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule.

Two features at the two-dimensional freezing transitions

We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with short-ranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: (1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s(2), reaches -4.5±0.5 k(B). Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information.

Phase behaviour of the symmetric binary mixture from thermodynamic perturbationtheory

We study the phase behaviour of symmetric binary mixtures of hard core Yukawa (HCY)particles via thermodynamic perturbation theory (TPT). We show that all the topologies ofphase diagram reported for the symmetric binary mixtures are correctly reproducedwithin the TPT approach. In a second step we use the capability of TPT to bestraightforwardly extended to mixtures that are nonsymmetric in size. Starting frommixtures that belong to the different topologies of symmetric binary mixtures weinvestigate the effect on the phase behaviour when an asymmetry in the diameters ofthe two components is introduced. Interestingly, when the energy of interactionbetween unlike particles is weaker than the interaction between like particles, thepropensity for the solution to demix is found to increase strongly with size asymmetry.

Influence of Charged Nanoparticles on Colloidal Forces: A Molecular Simulation Study

We employ the grand canonical Monte Carlo simulation technique to investigate the influence of charged nanoparticles (macro-ions) on the force between colloidal objects. Specifically, the structure and osmotic pressure of a system of screened Coulomb (Yukawa) particles confined between charged planar walls are simulated. We observe osmotic pressure to oscillate with wall separation and these oscillations to correspond to changes in the number of nanoparticle layers present in the slit pore. Using the Derjaguin approximation, we estimate the overall force between a colloidal sphere and a flat surface and compare our predictions to recent atomic force microscopy (AFM) results (Tulpar, A.; Van Tassel, P. R.; Walz, J. Y. Langmuir 2006, 22, 2876-2883). In excellent agreement with experiment, we find the wavelength of the force versus distance oscillations to scale as c(nu), with c being the bulk nanoparticle concentration and nu = -0.31 +/- 0.01; that is, slightly lower in magnitude from the expected value -1/3 based on average molecule spacing. By considering an order parameter measuring the extent to which neighboring particles form hexagonal symmetry, we show structural order within confined nanoparticle systems to be significantly enhanced as compared to that of bulk systems, despite being quite insensitive to wall separation. Wavelength scaling and order parameter analysis together suggest the confined macro-ion systems to be somewhat glasslike.

Interfacial and wetting properties of a binary point Yukawa fluid

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler-Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e., we observe a thick film of fluid rich in species 2 adsorbed at the hard wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (prewetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the prewetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters.

Thermodynamics of strongly coupled repulsive Yukawa particles in ambient neutralizing plasma: Thermodynamic instability and the possibility of observation in fine particle plasmas

The thermodynamics is analyzed for a system composed of particles with hard cores, interacting via the repulsive Yukawa potential (Yukawa particulates), and neutralizing ambient (background) plasma. An approximate equation of state is given with proper account of the contribution of ambient plasma and it is shown that there exists a possibility for the total isothermal compressibility of Yukawa particulates and ambient plasma to diverge when the coupling between Yukawa particulates is sufficiently strong. In this case, the system undergoes a transition into separated phases with different densities and we have a critical point for this phase separation. Examples of approximate phase diagrams related to this transition are given. It is emphasized that the critical point can be in the solid phase and we have the possibility to observe a solid-solid phase separation. The applicability of these results to fine particle plasmas is investigated. It is shown that, though the values of the characteristic parameters are semiquantitative due to the effects not described by this model, these phenomena are expected to be observed in fine particle plasmas, when approximately isotropic bulk systems are realized with a very strong coupling between fine particles.

Disordering transitions and peak effect in polydisperse particle systems

We show numerically that in a binary system of Yukawa particles, a dispersity-driven disordering transition occurs. In the presence of quenched disorder this disordering transition coincides with a marked increase in the depinning threshold, known as a peak effect. We find that the addition of poorly pinned particles can increase the overall pinning in the sample by increasing the amount of topological disorder present. If the quenched disorder is strong enough to create a significant amount of topological disorder in the monodisperse system, addition of a poorly pinned species generates further disorder but does not produce a peak in the depinning force. Our results indicate that for binary mixtures, optimal pinning occurs for topological defect fraction densities from 0.2 to 0.25. For defect densities below this range, the system retains orientational order. We determine the effect of the pinning density, strength, and radius on the depinning peak and find that the peak effect is more pronounced in weakly pinning systems.

Defect fluctuations and lifetimes in disordered Yukawa systems

We examine the time-dependent defect fluctuations and lifetimes for a bidisperse disordered assembly of Yukawa particles. At high temperatures, the noise spectrum of fluctuations is white and the coordination number lifetimes have a stretched exponential distribution. At lower temperatures, the system dynamically freezes, the defect fluctuations exhibit a 1/f spectrum, and there is a power law distribution of the coordination number lifetimes. Our results indicate that topological defect fluctuations may be a useful way to characterize disordered systems.

Screening in Yukawa fluid mixtures

The effective pair potential between mesoscopic charged particles in a neutralizing background medium takes a Yukawa form exp(-lambda r)/r with screening length lambda(-1). We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length xi<lambda(-1) and show that the Yukawa interaction is screened if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length lambda(-1). However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened, i.e., the effective potential between the solute particles is equal to the bare potential at large particle separations.

Structure of spherical Yukawa clusters

Structure of clusters of Yukawa particles is analysed by simulations and theoretical approaches in an isotropic environment which can be realized under microgravity or by active cancellation of the effect of gravity. Yukawa particles model dust particles in dusty plasmas and such an environment is suitable to observe their inherent properties. At low temperatures, clusters are composed of spherical shells and, when scaled by the mean distance, the structure seems to depend almost only on the system size or the number of particles. The positions and populations of shells are given by simple interpolation formulae. It is shown that shells have an approximately equal spacing close to that of triangular lattice planes in the bulk close-packed structures. When the cohesive energy in each shell is properly taken into account, the shell model reproduces these structures of spherical Yukawa clusters to a good accuracy.

Structure of spherical Yukawa clusters: A model for dust particles in dusty plasmas in an isotropic environment

The structure of spherical clusters composed of Yukawa particles is analyzed by molecular dynamics simulations and theoretical approaches as a model for dust particles in dusty plasmas in the isotropic environment. The latter condition is expected to be realized under microgravity or by active cancellation of the effect of gravity on the ground. It is found that, at low temperatures, Yukawa particles form spherical shells and, when scaled by the mean distance, the structure is almost independent of the strength of screening including the case of the Coulomb interaction. The positions and populations of shells and the conditions for the change of the number of shells are expressed by simple interpolation formulas. Shells have an approximately equal spacing close to that of triangular lattice planes in the bulk close-packed structures. It is shown that, when the cohesive energy in each shell is properly taken into account, the shell model reproduces the structure of spherical Yukawa clusters to a good accuracy.

Influence of Solvent-Solvent and Solute-Solvent Interaction Propertieson Solvent-Mediated Potential**The project supported by National NaturalScience Foundation of China under Grant No. 20206033

A recently proposed universal calculational recipe for solvent-mediatedpotential is applied to calculate excess potential of mean force between twolarge Lennard–Jones (LJ) or hard core attractive Yukawa particles immersedin small LJ solvent bath at supercritical state. Comparison between thepresent prediction with a hypernetted chain approximation adopted forsolute-solute correlation at infinitely dilute limit and existing simulationdata shows high accuracy for the region with large separation, andqualitative reliability for the solute particle contact region. Thecalculational simplicity of the present recipe allows for a detailedinvestigation on the effect of the solute-solvent and solvent-solventinteraction details on the excess potential of mean force. The resultantconclusion is that gathering of solvent particles near a solute particleleads to repulsive excess PMF, while depletion of solvent particles awayfrom the solute particle leads to attractive excess PMF, and minor change of thesolvent-solvent interaction range has large influence on the excess PMF.

Umbrella sampling in non-equilibrium computer simulations

We describe the application of the umbrella sampling technique well known from equilibrium Monte Carlo to dynamical, non-equilibrium simulations. This method is used specifically to calculate the nucleation barrier of Brownian Yukawa particles in a homogeneous shear flow.

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations.

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.

Phase separation in mixtures of Yukawa and charged Yukawa particles from Gibbs ensemble Monte Carlo simulations and the mean spherical approximation.

The phase equilibrium of mixtures of Yukawa and charged Yukawa particles is studied by means of Gibbs ensemble Monte Carlo (GEMC) simulation method and the mean spherical approximation (MSA). The strength of the Coulomb energy compared to that of the Yukawa attraction is characterized by a coupling constant. For low coupling constants a classical vapor--liquid phase separation appears with a good agreement between GEMC and the MSA. For high coupling constant, a phase separation between a salt poor and a salt rich phase occurs that resembles the phase equilibrium behavior of the solvent primitive model.

Phase diagram of hard-core repulsive Yukawa particles with a density-dependenttruncation: a simple model for charged colloids

Using computer simulations we study the phase behaviour of hard spheres with repulsiveYukawa interactions and with the repulsion set to zero at distances larger than adensity-dependent cut-off distance. Earlier studies based on experiments and computersimulations in colloidal suspensions have shown that the effective colloid–colloid pairinteraction that takes into account many-body effects resembles closely this truncatedYukawa potential. We present a phase diagram for the truncated Yukawa system bycombining Helmholtz free energy calculations and the Kofke integration method. Comparedto the non-truncated Yukawa system we observe (i) a radical reduction of the stability ofthe body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the facecentred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly anyshift of the (FCC) melting line when compared with the (BCC) melting line forthe full Yukawa potential for sufficiently high salt concentrations, i.e. truncationof the potential does not affect the location of the solid–fluid line but replacesonly the BCC phase with the FCC at the melting line. We compare our resultswith earlier results on the truncated Yukawa potential and with results fromsimulations where the full many-body Poisson–Boltzmann problem is solved.