Soft-sphere Systems Research Articles

Dynamic equivalences in the hard-sphere dynamic universality class

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

Properties of liquid iron along the melting line up to Earth-core pressures

We report a molecular dynamics study of the transport coefficients and the infinite frequency shear modulus of liquid iron at high temperatures and high pressures. We observe a simultaneous rise of both the shear viscosity and the diffusion coefficient along the melting line and estimate whether liquid iron can vitrify under Earth-core conditions. We show that in the conditions of the model studied in our work iron demonstrates a moderate increase of viscosity along the melting line. It is also demonstrated that at the limit of high temperatures and high pressures the liquid iron behaves similarly to the soft sphere system with exponent n ≈ 4.6.

Molecular Dynamics Study of a Supercooled Binary Soft-Sphere System: Calculation of the Generalized Susceptibility in Supercooled and Glassy States

Molecular Dynamics Study of a Supercooled Binary Soft-Sphere System: Calculation of the Generalized Susceptibility in Supercooled and Glassy States

Role of Adsorbing Moieties on Thermal Conductivity and Associated Properties of Nanofluids

We probe the contributions of adsorbing moieties (surface active species) on thermal conductivity (k), rheology, density, contact angle, and refractive index of nanofluids. The role of surface morphology, initial thermal conductivity of solid particles and their number density on thermal property enhancement of nanofluids is also studied. Our studies on a model soft sphere system, consisting of micelles of an average size of 2.5–7 nm with different headgroup charges, show that the thermal conductivity of ionic surfactant micelles follows the effective medium theory of poor thermal conductors, i.e., 1 – 3φ/2 with the interfacial resistance tending to infinity, where φ is the volume fraction. The results suggest that the long alkyl chain group of nonionic surfactant micelles are poor thermal conductors at very low concentrations with large interfacial tension compared to their anionic counterparts. The k measurement in aqueous alumina, silica, and nonaqueous iron oxide nanofluids with particle size in the r...

Inelastic collapse in one-dimensional driven systems under gravity

We study inelastic collapse in a one-dimensional N-particle system when the system is driven from below under gravity. We investigate the hard-sphere limit of inelastic soft-sphere systems by numerical simulations to find how the collision rate per particle n(coll) increases as a function of the elastic constant of the sphere k when the restitution coefficient e is kept constant. For systems with large enough N>/~20, we find three regimes in e depending on the behavior of n(coll) in the hard-sphere limit: (i) an uncollapsing regime for 1≥e>e(c1), where n(coll) converges to a finite value, (ii) a logarithmically collapsing regime for e(c1)>e>e(c2), where n(coll) diverges as n(coll)~logk, and (iii) a power-law collapsing regime for e(c2)>e>0, where n(coll) diverges as n(coll)~k(α) with an exponent α that depends on N. The power-law collapsing regime shrinks as N decreases and seems not to exist for the system with N=3, while, for large N, the size of the uncollapsing and the logarithmically collapsing regime decreases as e(c1)=/~1-2.6/N and e(c2)=/~1-3.0/N. We demonstrate that this difference between large and small systems exists already in the inelastic collapse without external drive and gravity.

Thermodynamic scaling and corresponding states for the self-diffusion coefficient of non-conformal soft-sphere fluids

In this work, we explore transport properties of a special type of repulsive spheres that exhibit remarkable scaling of their thermodynamic properties. In order to accomplish that we propose a new way to derive and express effective hard-sphere diameters for transport properties of simple fluids. The procedure relies on mapping the system's transport properties, in the low density limit, to the hard-sphere fluid. We have chosen a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids and are an accurate representation of the effective repulsive potentials of real systems. The self-diffusion coefficient of the soft-sphere fluids is obtained by equilibrium molecular dynamics. The soft-sphere collision integrals of different systems are shown to follow quite simple relationships between each other. These collision integrals are incorporated, through the definition of the effective hard-sphere diameter, in the resulting equation for the self-diffusion coefficient. The approach followed exhibits a density rescaling that leads to a single master curve for all systems and temperatures. The scaling is carried through to the level of the mean-squared displacement.

Phase coexistence for charged soft dumbbell and ionic soft sphere systems via molecular dynamics simulation

Gas-liquid critical parameters of charged soft dumbbells (CSDs) as function of the site-to-site separation on the dumbbells, d, obtained on the basis of molecular dynamics computer simulation are presented. A mean field theoretical description is developed, which explains the results at small and large d, respectively. We note that in the limit d→0 the CSD system exhibits gas-liquid phase separation solely driven by repulsion and dipole-dipole interaction. If the dumbbell bond is eliminated the CSD system becomes similar to the restricted primitive model of ionic fluids with hard core repulsion replaced by soft repulsion. We obtain the gas-liquid critical parameters for this model and discuss their relation to the CSD system.

Dynamic equivalence between atomic and colloidal liquids

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids (Löwen H. et al., Phys. Rev. Lett., 70 (1993) 1557). We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the “hard-sphere”dynamic universality class.

Structural properties of thermoresponsive poly(N-isopropylacrylamide)-poly(ethyleneglycol) microgels

We present investigations of the structural properties of thermoresponsive poly(N-isopropylacrylamide) (PNiPAM) microgels dispersed in an aqueous solvent. In this particular work poly(ethyleneglycol) (PEG) units flanked with acrylate groups are employed as cross-linkers, providing an architecture designed to resist protein fouling. Dynamic light scattering (DLS), static light scattering (SLS), and small angle neutron scattering (SANS) are employed to study the microgels as a function of temperature over the range 10 °C ≤ T ≤ 40 °C. DLS and SLS measurements are simultaneously performed and, respectively, allow determination of the particle hydrodynamic radius, R(h), and radius of gyration, R(g), at each temperature. The thermal variation of these magnitudes reveals the microgel deswelling at the PNiPAM lower critical solution temperature (LCST). However, the hydrodynamic radius displays a second transition to larger radii at temperatures T ≤ 20 °C. This feature is atypical in standard PNiPAM microgels and suggests a structural reconfiguration within the polymer network at those temperatures. To better understand this behavior we perform neutron scattering measurements at different temperatures. In striking contrast to the scattering profile of soft sphere microgels, the SANS profiles for T ≤ LCST of our PNiPAM-PEG suspensions indicate that the particles exhibit structural properties characteristic of star polymer configurations. The star polymer radius of gyration and correlation length gradually decrease with increasing temperature despite maintenance of the star polymer configuration. At temperatures above the LCST, the scattered SANS intensity is typical of soft sphere systems.

Dynamic heterogeneity in hard and soft sphere colloidal glasses

The nature of dynamic correlations in glasses and jammed soft matter remains a puzzle. Despite the strong increase in viscosity, hard-spheres exhibit only moderate increase of dynamic correlations at the glass transition, while recent experiments on soft-spheres suggest that in these systems, correlations grow to macroscopic length. Here, we present a direct real-space analysis of dynamic correlations in hard and soft-sphere glasses. The motion of the particles is imaged directly with confocal microscopy, and the maximum dynamical susceptibility is determined systematically over a range of probe length and time scales. We elucidate the displacement vector field, and analyze correlations in the particles' direction of motion. This allows us to demonstrate the different nature of relaxations in hard and soft-sphere systems. We find that the deeply jammed soft sphere suspension shows by far longer-range dynamic correlations that are characterized by small, remarkably coherent displacements. These observations provide direct evidence of the internal elasticity that governs long-range relaxation modes in soft systems.

Thermodynamic properties of non-conformal soft-sphere fluids with effective hard-sphere diameters

In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids.

A generalized Karnahan-Starling approach for molecular systems with a positive definite potential of interaction between particles

A new method for obtaining the well-known Karnahan-Starling equation for systems of hard spheres and its generalization for the case of any number of precisely known virial coefficients is proposed. The efficiency of the method for the construction of the statistical thermodynamics of a system of soft spheres, where an analytical expression for free energy and equations of state that agree well with the data of the computer experiment are found, is shown. The considered approach is generalized for systems with a positive definite potential of interaction between particles.

Density-Temperature-Softness Scaling of the Dynamics of Glass-Forming Soft-Sphere Liquids

We employ the principle of dynamic equivalence between soft-sphere and hard-sphere fluids [Phys. Rev. E 68, 011405 (2003)] to describe the interplay of the effects of varying the density n, the temperature T, and the softness (characterized by a softness parameter ν(-1)) on the dynamics of glass-forming soft-sphere liquids in terms of simple scaling rules. The main prediction is the existence of a dynamic universality class associated with the hard-sphere fluid, constituted by the soft-sphere systems whose dynamic parameters depend on n, T, and ν only through the reduced density n*≡nσ(HS)(T*,ν). A number of scaling properties observed in recent experiments and simulations involving glass-forming fluids with repulsive short-range interactions are found to be a direct manifestation of this general dynamic equivalence principle.

Gas-liquid coexistence in a system of dipolar soft spheres

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Here we compute the gas-liquid critical point in a system of dipolar soft spheres subject to an external electric field using molecular dynamics computer simulation. Tracking the critical point as the field strength is approaching zero we find the following limiting values: T(c)=0.063 and ρ(c)=0.0033 (dipole moment μ=1). These values are confirmed by independent simulation at zero field strength.

Hidden slow time scale of correlated motions in supercooled liquids: Multi-time correlation function approach

A three-time correlation function of particle displacements is introduced and numerically calculated by performing molecular dynamics simulations of binary soft-sphere supercooled systems. It is found that the two-dimensional representations of the three-time correlation function reveal couplings of particle motions that exist over a wide range of time scales. Furthermore, it is demonstrated that the systematic change in the second time interval in the three-time correlation function enables us to analyze how the correlations in mobility decay with time. From this analysis, the characteristic time scale of dynamical heterogeneity is quantified. We find that the dynamical heterogeneity time scale becomes much slower than the α-relaxation time as the temperature decreased.

Phase equilibrium of colloidal suspensions with particle size dispersity: A Monte Carlo study

We have studied the crystalline-amorphous coexistence for systems of polydisperse soft spheres that interact via a purely repulsive power law potential. Potential softness quantified by the exponent of the potential was a primary input in our simulations. Simulations were performed in the isobaric semigrand statistical ensemble, i.e., the composition of the parent distribution was not fixed in our systems. Gibbs-Duhem integration was used to trace the coexistence pressure as a function of potential softness for monodisperse systems. A second Gibbs-Duhem integration, initiated from the monodisperse coexistence curve, was employed to determine coexistence pressure versus imposed variance of the activity distribution. Amorphous-crystalline coexistence densities and volume fractions were determined to be monotonically increasing functions of the breadth of particle size dispersity. Semigrand ensemble simulations testified to the existence of a terminal diameter dispersity, i.e., a dispersity above which no amorphous-crystalline phase coexistence was observed. At the terminus size dispersity increases from 5.8% to 6.1% to 6.4% and to 6.7% and 6.5% for the crystalline phase as the steepness parameter n, takes on smaller values: from 100 to 50 to 12 to 10 and 8, respectively. In sharp contrast to the crystalline phases' enhanced, by potential softness, allowable size dispersity the amorphous phase exhibits an opposite trend, as potential interactions soften. Furthermore, amorphous phases accommodate, on average, smaller particles than those of the ordered (fcc) phase. Contrary to widely accepted intuition crystalline phases composed of size-disperse particulates exhibit a higher degree of local order than their monodisperse counterparts, admittedly at differing thermodynamic conditions.

Field-induced layering of confined ferromagnetic nanoparticles: the role of attractive interactions

We present Molecular Dynamics simulation results for confined ferromagnetic nanoparticles (film geometry) under the influence of strong, homogeneous magnetic fields. We focus on the role of short-ranged attractive interactions between the particles for the structure formation in thin films consisting of four to five monolayers. To this end we compare simulation results for Stockmayer particles (Lennard-Jones plus dipolar interactions) with corresponding results for dipolar soft spheres, where the short-ranged potential is purely repulsive. At moderate and large average densities, both systems exhibit pronounced layering. Based on the corresponding normal pressure oscillations we show that the field-induced effects on the layer formation in this density range are essentially independent of the short-range interactions. The dipolar soft sphere system merely has a stronger tendency to form a crystal-like lateral structure upon application of a parallel field. More pronounced differences occur at lower densities and not too high dipolar coupling strengths within the vapour–liquid region of the confined, zero-field Stockmayer system. Applying a perpendicular field, the Stockmayer system develops a blob structure absent in the corresponding repulsive system. Finally, for very large values of both, dipolar coupling parameter and field strength of a perpendicular field, we find evidence for a field-induced in-plane crystallisation of the layered systems.

Glass transition in soft-sphere dispersions

The concept of dynamic equivalence among mono-disperse soft-sphere fluids is employed inthe framework of the self-consistent generalized Langevin equation (SCGLE) theory ofcolloid dynamics to calculate the ideal glass transition phase diagram of modelsoft-sphere colloidal dispersions in the softness–concentration state space. The slowdynamics predicted by this theory near the glass transition is compared withavailable experimental data for the decay of the intermediate scattering function ofcolloidal dispersions of soft-microgel particles. Increasing deviations from this simplescheme occur for increasingly softer potentials, and this is studied here using theRogers–Young static structure factor of the soft-sphere systems as the input of the SCGLEtheory, without assuming a priori the validity of the equivalence principle above.

Elastic properties of the fcc crystals of soft spheres with size dispersion at zero temperature

AbstractElastic constants of soft sphere systems, interacting through n ‐inverse‐power potential and exhibiting aperiodicity, caused by the size dispersion of the spheres, are determined at zero temperature by computer simulations. It is shown that, at a fixed number density of the spheres, the Poisson's ratio, as well as other elastic constants, increase with increasing disorder in the system. Properties of two types of systems, polydisperse spheres and binary mixture of spheres, are compared to determine the influence of various size distribution types on the system elastic properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Preface: phys. stat. sol. (b) 245/3

Preface: phys. stat. sol. (b) 245/3