Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Weak and strong coupling theories for polarizable colloids and nanoparticles

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nanoparticles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far field. All the results are compared with the Monte?Carlo simulations, showing an excellent agreement between the theory and the simulations.     

Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

Nonequilibrium sedimentation of colloids on the particle scale

We investigate sedimentation of model hard-sphere-like colloidal dispersions confined in horizontal capillaries using laser scanning confocal microscopy, dynamical density functional theory, and Brownian dynamics computer simulations. For homogenized initial states we obtain quantitative agreement of the results from the respective approaches for the time evolution of the one-body density distribution and the osmotic pressure on the walls. We demonstrate that single-particle information can be obtained experimentally in systems that were initialized further out of equilibrium such that complex lateral patterns form.     

Coupling constant renormalization due to instantons in the O(3) non-linear sigma model

The renormalized lattice coupling constant for the O(3) non-linear sigma model is calculated, including instanton effects, and the correlation length estimated. The results are in good agreement with the Monte Carlo simulation of Shenker and Tobochnik. The topological charge density is also discussed in the light of recent Monte Carlo simulations.     

Computer simulations of structure, dynamics, and phase behavior of colloidal fluids in confined geometry and under shear

Using computer simulations, colloidal systems in different external fields are investigated. Colloid-polymer mixtures, described in terms of the Asakura-Oosawa (AO) model, are considered under strong confinement. Both in cylindrical and spherical confinement, the demixing transition of the three-dimensional AO model is rounded and, using Monte Carlo simulations, we analyze in detail the consequences of this rounding (occurrence of multi-domain states in cylindrical geometry, non-equivalence of conjugate ensembles due to different finite-size corrections in spherical geometry etc.). For the case of the AO model confined between two parallel walls, spinodal decomposition is studied using a combination of molecular dynamics simulation and the multiparticle collision dynamics method. This allows us to investigate the influence of hydrodynamic interactions on the domain growth during spinodal decomposition. For a binary glass-forming Yukawa mixture, non-linear active micro-rheology is considered, i.e. a single particle is pulled through a deeply supercooled liquid. The diffusion dynamics of the pulled particle is analyzed in terms of the van Hove correlation function. Finally, the Yukawa mixture in the glass state, confined between walls, is studied under the imposition of a uniform shear stress. Below and around the yield stress, persistent creep in the form of shear-banded structures is observed.     

A simple effective pair potential for the molecular simulation of the thermodynamic properties of ammonia

A new optimized effective pair potential model is proposed, which is appropriate for the prediction of thermodynamic properties of fluid ammonia including vapour—liquid coexistence data. The phase behaviour is determined using a recently developed version of the Gibbs ensemble Monte Carlo method. Furthermore, liquid structure characteristics, the dielectric constant and supercritical properties are determined by Monte Carlo simulations in the isothermal—isobaric ensemble. The second virial coefficient of the pair potential model is calculated over a broad range of temperature. All properties are compared with experimental data or results of a multi-parameter equation of state for ammonia. The new model is found to yield coexistence properties and second virial coefficients in good agreement with experimental data and the results of the equation of state, respectively.     

Interpretation of Light Scattering Spectra of Dispersions – A Hybrid Approach to Account for Interparticle Interactions

The problem of extracting quantitative information on individual particle properties from spectroscopic measurements conducted at concentrations where particle interactions become significant is of great industrial and theoretical importance. For dispersions of charged particles, this can happen at fairly low concentrations. The effect of the fluid (slurry) structure has to be taken into account to interpret the light scattering spectra of such dispersions. In this paper, a hybrid method that addresses the effect of the fluid structure is proposed. The hybrid approach describes the fluid structure by relating the “effective” Percus‐Yevick hard‐sphere parameters to the system parameters using empirical models. The feasibility of this approach is examined through a theoretical study with data generated by Monte Carlo simulations of a monodisperse dispersion of charged spherical particles using realistic interaction potentials under single scattering conditions.     

The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations

The chemical potential for a two-component Lennard-Jones fluid with associative interaction between opposite species promoting the formation of dimers is calculated using osmotic Monte Carlo (OMC) canonical ensemble simulations. Grand canonical Monte Carlo simulations also are performed to verify the accuracy of the OMC approach. The data from both methods agree very well for thermodynamic states with different degrees of dimerization. It follows that the OMC is a promising approach for the determination of the thermodynamics of and equilibria between associating and non-associating fluids and associating fluid mixtures.     

Investigation of nucleation and grain growth in 2-dimensional systems by using generalized Monte Carlo simulations

In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena.     

Phase coexistence and critical point determination in polydisperse fluids

Phase equilibria of fluids with variable size polydispersity have been investigated by means of Monte Carlo simulations. In the models, spherical particles of different additive diameters interact through Lennard-Jones and hard sphere Yukawa intermolecular potentials and the underlying distribution of particle sizes is a Gaussian. The Gibbs ensemble Monte Carlo technique has been applied to determine the phase coexistence far below the critical temperature. Critical points have been estimated by finite-size scaling analysis using histogram reweighting for NpT simulation data. In order to achieve efficient sampling in the vicinity of the critical points, the hyper-parallel tempering scheme has been utilized.     

Structure factor of a hard-core fluid with short-range Yukawa attraction: analytical FMSA theory against Monte Carlo simulations

ABSTRACT

Analytical solution of the first-order Ornstein–Zernike equation known as the first-order mean spherical approximation (FMSA) theory due to Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is used to write down a closed equation for the static structure factor of the hard-sphere fluid with a short-range Yukawa attraction. Calculations are performed for a Yukawa decay exponent that corresponds to a range of attraction that does not exceed the first coordination shell of Lennard-Jones-like simple fluids. By comparison with Monte Carlo simulation data it is shown that the analytical FMSA equation for the static structure factor is of the same or even of superior accuracy as that within the seminumerical mean spherical approximation theory.     

Liquid–vapour transition of the long range Yukawa fluid

Two liquid state theories, the self-consistent Ornstein–Zernike equation (SCOZA) and the hierarchical reference theory (HRT) are shown, by comparison with Monte Carlo simulations, to perform extremely well in predicting the liquid–vapour coexistence of the hard-core Yukawa (HCY) fluid when the interaction is long range. The long range of the potential is treated in the simulations using both an Ewald sum and hyperspherical boundary conditions. In addition, we present an analytical optimized mean field theory which is exact in the limit of an infinitely long-range interaction. The work extends a previous one by C. Caccamo, G. Pellicane, D. Costa, D. Pini, and G. Stell, Phys. Rev. E 60, 5533 (1999) for short-range interactions.     

Formation of plasma dust structures at atmospheric pressure

The formation of strongly coupled stable dust structures in the plasma produced by an electron beam at atmospheric pressure was detected experimentally. Analytical expressions were derived for the ionization rate of a gas by an electron beam in an axially symmetric geometry by comparing experimental data with Monte Carlo calculations. Self-consistent one-dimensional simulations of the beam plasma were performed in the diffusion drift approximation of charged plasma particle transport with electron diffusion to determine the dust particle levitation conditions. Since almost all of the applied voltage drops on the cathode layer in the Thomson glow regime of a non-self-sustained gas discharge, a distribution of the electric field that grows toward the cathode is produced in it; this field together with the gravity produces a potential well in which the dust particles levitate to form a stable disk-shaped structure. The nonideality parameters of the dust component in the formation region of a highly ordered quasi-crystalline structure calculated using computational data for the dust particle charging problem were found to be higher than the critical value after exceeding which an ensemble of particles with a Yukawa interaction should pass to the crystalline state.     

Heat capacities of the dipolar Yukawa model polar fluid

The Stockmayer fluid is often used to describe a polar fluid. The dipolar Yukawa (DY) fluid is also a useful model for such fluids and is convenient for theoretical applications. Here we use the mean spherical approximation (MSA) and perturbation theory (PT) to study the heat capacities of the DY fluid model of a polar fluid and compare these results with Monte Carlo simulations for this model polar fluid. We find that the DY fluid shows the same features as the Stockmayer fluid does; demonstrating the utility of the DY fluid and further finding that the MSA and PT approaches give reasonably accurate results for the heat capacity.     

Percolation cluster algorithm and scaling behaviour in the 4-dimensional ising model

The scaling behaviour of renormalized quantities and the validity of renormalized perturbation theory is tested numerically in the symmetric phase of the 4-dimensional Ising model. The high-precision Monte Carlo calculation is based on an efficient percolation cluster algorithm.     

Vapour-liquid equilibrium of the charged Yukawa fluid from Gibbs ensemble Monte Carlo simulations and the mean spherical approximation

A Gibbs ensemble Monte Carlo (GEMC) study supplemented by theoretical calculations using the mean spherical approximation (MSA) is reported for the charged Yukawa system. In this system the particles interact via an attractive Yukawa potential and a Coulomb potential. When the Coulomb potential is weak compared to the Yukawa attraction the results obtained for the vapour-liquid equilibrium from the GEMC and the MSA are very similar. On increasing the charge, the system becomes similar to the primitive model of electrolytes, and at high charges similar phenomena, such as ion association, are observed. At these charges, the MSA yields poorer results. Using both methods, an increase of the charge results in an increase of the critical temperature but a decrease of the critical density.     

A systematic Monte Carlo simulation and renormalized perturbation theoretical study of the dielectric constant of the polarizable Stockmayer fluid

A systematic Monte Carlo (MC) simulation and perturbation theory (PT) study is reported for the dielectric constant of the polarizable Stockmayer fluid. Our MC simulations apply the ‘pair approximation for polarization interaction’ procedure suggested by P?edota et al. The theoretical approach is based on our newly introduced equation (Valiskó et al., 2002, Molec. Phys., 100, 559) which is a density expansion for the dielectric constant using Wertheim's renormalized PT method. The agreement between our MC and PT results is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anisotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.