Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

Models to predict configurational adiabats of Lennard-Jones fluids and their transport coefficients

A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid-vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid-vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid-vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity.

Aggregation behavior of nanoparticles: Revisiting the phase diagram of colloids

Surface functionalization of metal nanoparticles (NPs), e.g., using peptides and proteins, has recently attracted a considerable attention in the field of design of therapeutics and diagnostics. The possibility of diverse functionalization allows them to selectively interact with proteins, while the metal core ensures solubility, making them tunable therapeutic agents against diseases due to mis-folding or aggregation. On the other hand, their action is limited by possible self-aggregation, which could be, however, prevented based on the full understanding of their phase diagram as a function of the environmental variables (temperature, ionic strength of the solution, concentration) and intrinsic characteristics (size, charge, amount, and type of functional groups). A common modeling strategy to study the phase behavior is to represent the NPs as spheres interacting via effective potentials implicitly accounting for the solvation effects. Their size put the NPs into the class of colloids, albeit with particularly complex interactions including both attractive and repulsive features, and a consequently complex phase diagram. In this work, we review the studies exploring the phases of these systems starting from those with only attractive or repulsive interactions, displaying a simpler disperse-clustered-aggregated transitions. The phase diagram is here interpreted focusing on the universal aspects, i.e., those dependent on the general feature of the potentials, and available data are organized in a parametric phase diagram. We then consider the potentials with competing attractive short range well and average-long-range repulsive tail, better representing the NPs. Through the proper combination of the attractive only and repulsive only potentials, we are able to interpret the appearance of novel phases, characterized by aggregates with different structural characteristics. We identify the essential parameters that stabilize the disperse phase potentially useful to optimize NP therapeutic activity and indicate how to tune the phase behavior by changing environmental conditions or the NP chemical–physical properties.

Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations

A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to lattice vectors of a cuboidal unit cell. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy where the interaction is described by a Lennard-Jones (LJ) interaction potential or a sticky hard-sphere (SHS) model with a r^{-n} long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging Bessel function series. Applying the whole range of lattice parameters for the SHS and LJ potentials we prove that the bcc phase is unstable (or, at best, metastable) toward distortion into the fcc phase in the low temperature and pressure limit. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.

Entropy of simple fluids with repulsive interactions near freezing

Among different thermodynamic properties of liquids, the entropy is one of the hardest quantities to estimate. Therefore, the development of models allowing accurate estimations of the entropy for different mechanisms of interatomic interactions represents an important problem. Here, we propose a method for estimating the excess entropy of simple liquids not too far from the liquid-solid phase transition. The method represents a variant of cell theory, which particularly emphasizes relations between liquid state thermodynamics and collective modes properties. The method is applied to calculate the excess entropy of inverse-power-law fluids with ∝r^-n repulsive interactions. The covered range of potential softness is extremely wide, including the very soft Coulomb (n = 1) case, much steeper n = 6 and n = 12 cases, and the opposite hard-sphere interaction limit (n = ∞). An overall reasonably good agreement between the method's outcome and existing "exact" results is documented at sufficiently high fluid densities. Its applicability condition can be conveniently formulated in terms of the excess entropy itself. The method is also applied to the Lennard-Jones potential but demonstrates considerably lower accuracy in this case. Our results should be relevant to a broad range of liquid systems that can be described with isotropic repulsive interactions, including liquid metals, macromolecular systems, globular proteins, and colloidal suspensions.

Body centered tetragonal nanoparticle superlattices: why and when they form?

Body centered tetragonal (BCT) phases are structural intermediates between body centered cubic (BCC) and face centered cubic (FCC) structures. However, BCC ↔ FCC transitions may or may not involve a stable BCT intermediate. Interestingly, nanoparticle superlattices usually crystallize in BCT structures, but this phase is much less frequent for colloidal crystals of micrometer-sized particles. Two origins have been proposed for the formation of BCT NPSLs: (i) the influence of the substrate on which the nanoparticle superlattice is deposited, and (ii) non-spherical nanoparticle shapes, combined with the fact that different crystal facets have different ligand organizations. Notably, none of these two mechanisms alone is able to explain the set of available experimental observations. In this work, these two hypotheses were independently tested using a recently developed molecular theory for nanoparticle superlattices that explicitly captures the degrees of freedom associated with the ligands on the nanoparticle surface and the crystallization solvent. We show that the presence of a substrate can stabilize the BCT structure for spherical nanoparticles, but only for very specific combinations of parameters. On the other hand, a truncated-octahedron nanoparticle shape strongly stabilizes BCT structures in a wide region of the phase diagram. In the latter case, we show that the stabilization of BCT results from the geometry of the system and it does not require different crystal facets to have different ligand properties, as previously proposed. These results shed light on the mechanisms of BCT stabilization in nanoparticle superlattices and provide guidelines to control its formation.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

Universal Effect of Excitation Dispersion on the Heat Capacity and Gapped States in Fluids

The change in dispersion of high-frequency excitations in fluids, from an oscillating solidlike to a monotonic gaslike one, is shown for the first time to affect thermal behavior of heat capacity and the q-gap width in reciprocal space. With in silico study of liquified noble gases, liquid iron, liquid mercury, and model fluids, we established universal bilinear dependence of heat capacity on q-gap width, whereas the crossover precisely corresponds to the change in the excitation spectra. The results open novel prospects for studies of various fluids, from simple to molecular liquids and melts.

Exploring the connection between the density-scaling exponent and the intermolecular potential for liquids on the basis of computer simulations of quasireal model systems

In this paper, based on the molecular dynamics simulations of quasireal model systems, we propose a method for determination of the effective intermolecular potential for real materials. We show that in contrast to the simple liquids, the effective intermolecular potential for the studied systems depends on the thermodynamic conditions. Nevertheless, the previously established relationship for simple liquids between the exponent of the inverse power law approximation of intermolecular potential and the density-scaling exponent is still preserved when small enough intermolecular distances are considered. However, our studies show that molecules approach each other at these very short distances relatively rarely. Consequently, only sparse interactions between extremely close molecules determine the value of the scaling exponent and then strongly influence the connection between dynamics and thermodynamics of the whole system.

Influence of Softness on the Stability of Binary Colloidal Crystals

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB₄ phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.

Transformations of body-centered cubic crystals composed of hard or soft spheres to liquids or face-centered cubic crystals

The monodispersed hard-sphere system is one of the simplest models for the study of phase transitions. Despite intensive studies of crystallization and melting of hard-sphere face-centered cubic (FCC) crystals, the phase transformations of hard-sphere body-centered cubic (BCC) crystals have not been explored because hard spheres cannot form a stable BCC lattice. In fact, unstable BCC hard-sphere crystals and their related phase transformations can be experimentally achieved. Here, we measured the kinetics of the melting and solid-solid transformations of BCC hard-sphere crystals at various volume fractions via molecular dynamics simulations. When the volume fraction ϕ < 0.494, the system melts catastrophically. At ϕ > 0.545, the BCC crystal transforms to a metastable polycrystal consisting of FCC and hexagonal close-packed (HCP) domains, which is different from those crystallized from supercooled liquids, and then slowly equilibrates toward the FCC crystal. At 0.494 < ϕ < 0.545, the BCC crystal transforms to an intermediate-order metastable state consisting of BCC and non-crystal particles without FCC and HCP symmetries and then equilibrates toward the coexistence of the FCC crystal and liquid. We further studied the melting and BCC-FCC transitions of crystals composed of soft spheres with potential u(r) = ϵ(r/σ)^-n . The unstable BCC crystals at n = 12, 9, 8 exhibit similar melting and BCC-FCC transitions as hard-sphere BCC crystals, while the metastable BCC crystals at n = 5, 6, 7 melt quickly at low densities but take very long time for the BCC-FCC transition at high densities. We also estimate the BCC-FCC interfacial energy and critical nucleus size. These results cast light on the melting and solid-solid transformations of atomic BCC crystals, which exist widely in nature.

The effect of molecular architecture on the physical properties of supercooled liquids studied by MD simulations: Density scaling and its relation to the equation of state

Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement results obtained for real materials. One of the examples is an intriguing problem within the density scaling idea that has attracted attention in recent decades due to its hallmarks of universality, i.e., the fact that the difference between the density scaling exponent and the exponent of the equation of state is observed for real materials, whereas it has not been reported for the model system. In this paper, we use new model molecules of simple but anisotropic architecture to study the effect of molecular anisotropy on the dynamic and thermodynamic properties of the system. We identify the applicable range of intermolecular interactions for a given physical process, and then we explain the reason for observed differences between the behavior of the model and real systems. It demonstrates that the new model systems open broad perspectives for simulation and theoretical research, for example, into unifying concepts in the glass transition physics.

Thermodynamic curvature of soft-sphere fluids and solids

The influence of the strength of repulsion between particles on the thermodynamic curvature scalar R for the fluid and solid states is investigated for particles interacting with the inverse power (r^{-n}) potential, where r is the pair separation and 1/n is the softness. Exact results are obtained for R in certain limiting cases, and the R behavior determined for the systems in the fluid and solid phases. It is found that in such systems the thermodynamic curvature can be positive for very soft particles, negative for steeply repulsive (or large n) particles across almost the entire density range, and can change sign between negative and positive at a certain density. The relationship between R and the form of the interaction potential is more complex than previously suggested, and it may be that R is an indicator of the relative importance of energy and entropy contributions to the thermodynamic properties of the system.

Uhlenbeck-Ford model: Phase diagram and corresponding-states analysis

Using molecular dynamics simulations and nonequilibrium thermodynamic-integration techniques we compute the Helmholtz free energies of the body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed, and fluid phases of the Uhlenbeck-Ford model (UFM) and use the results to construct its phase diagram. The pair interaction associated with the UFM is characterized by an ultrasoft, purely repulsive pair potential that diverges logarithmically at the origin. We find that the bcc and fcc are the only thermodynamically stable crystalline phases in the phase diagram. Furthermore, we report the existence of two reentrant transition sequences as a function of the number density, one featuring a fluid-bcc-fluid succession and another displaying a bcc-fcc-bcc sequence near the triple point. We find strong resemblances to the phase behavior of other soft, purely repulsive systems such as the Gaussian-core model (GCM), inverse-power-law, and Yukawa potentials. In particular, we find that the fcc-bcc-fluid triple point and the phase boundaries in its vicinity are in good agreement with the prediction supplied by a recently proposed corresponding-states principle [J. Chem. Phys. 134, 241101 (2011)JCPSA60021-960610.1063/1.3605659; Europhys. Lett. 100, 66004 (2012)EULEEJ0295-507510.1209/0295-5075/100/66004]. The particularly strong resemblance between the behavior of the UFM and GCM models are also discussed.

Density-functional theory for fluid-solid and solid-solid phase transitions

We develop a theory to describe solid-solid phase transitions. The density functional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials u(r)=ε(σ/r)^{n}, where parameter n measures softness of the potential. We find that for 1/n<0.154 systems freeze into the face centered cubic (fcc) structure while for 1/n≥0.154 the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.

Diabat Interpolation for Polymorph Free-Energy Differences

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations

The Uhlenbeck-Ford (UF) model was originally proposed for the theoretical study of imperfect gases, given that all its virial coefficients can be evaluated exactly, in principle. Here, in addition to computing the previously unknown coefficients B₁₁ through B₁₃, we assess its applicability as a reference system in fluid-phase free-energy calculations using molecular simulation techniques. Our results demonstrate that, although the UF model itself is too soft, appropriately scaled Uhlenbeck-Ford (sUF) models provide robust reference systems that allow accurate fluid-phase free-energy calculations without the need for an intermediate reference model. Indeed, in addition to the accuracy with which their free energies are known and their convenient scaling properties, the fluid is the only thermodynamically stable phase for a wide range of sUF models. This set of favorable properties may potentially put the sUF fluid-phase reference systems on par with the standard role that harmonic and Einstein solids play as reference systems for solid-phase free-energy calculations.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

Simple liquids' quasiuniversality and the hard-sphere paradigm

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.

The relationship between local density and bond-orientational order during crystallization of the Gaussian core model

Whether nucleation is triggered by density or by bond-orientational order is one of the most hotly debated issues in recent investigations of the crystallization process. Here, we present a numerical study of the relationship between them for soft particles within the isothermal-isobaric ensemble. We compress the system and thus obtain the fluid-solid transition. By investigating locally dense-packed particles and particles with a relatively high bond-orientational order in the compressing process, we find a sharp increase of the spatial correlations for both densely packed particles and highly bond-orientational ordered particles at the phase transition point, which provide new characterization methods for the liquid-crystal transition. We also find that it is the bond-orientational order rather than density that triggers the nucleation process. The relationship between the local density and the bond-orientational order parameter is strongly affected by the characterization methods used. The local bond order parameter (q6) shows clear correlation with the local density (ρ) in the fluid stage, while the coarse-grained form (q[combining macron]6) does not correlate with ρ at all, owing to the comparable spatial scales of q6 and ρ. Nevertheless, q[combining macron]6 shows an obvious advantage in distinguishing between solid and liquid particles in our work. These results may elevate our understanding of the mechanism of the crystallization process.

Equilibrium and nonequilibrium dynamics of soft sphere fluids

We use computer simulations to test the freezing-point scaling relationship between equilibrium transport coefficients (self-diffusivity, viscosity) and thermodynamic parameters for soft sphere fluids. The fluid particles interact via the inverse-power potential (IPP), and the particle softness is changed by modifying the exponent of the distance-dependent potential term. In the case of IPP fluids, density and temperature are not independent variables and can be combined to obtain a coupling parameter to define the thermodynamic state of the system. We find that the rescaled coupling parameter, based on its value at the freezing point, can approximately collapse the diffusivity and viscosity data for IPP fluids over a wide range of particle softness. Even though the collapse is far from perfect, the freezing-point scaling relationship provides a convenient and effective way to compare the structure and dynamics of fluid systems with different particle softness. We further show that an alternate scaling relationship based on two-body excess entropy can provide an almost perfect collapse of the diffusivity and viscosity data below the freezing transition. Next, we perform nonequilibrium molecular dynamics simulations to calculate the shear-dependent viscosity and to identify the distinct role of particle softness in underlying structural changes associated with rheological properties. Qualitatively, we find a similar shear-thinning behavior for IPP fluids with different particle softness, though softer particles exhibit stronger shear-thinning tendency. By investigating the distance and angle-dependent pair correlation functions in these systems, we find different structural features in the case of IPP fluids with hard-sphere like and softer particle interactions. Interestingly, shear-thinning in hard-sphere like fluids is accompanied by enhanced translational order, whereas softer fluids exhibit loss of order with shear. Our results provide a systematic evaluation of the role of particle softness in equilibrium and nonequilibrium transport properties and their underlying connection with thermodynamic and structural properties.

Soft repulsive interactions, particle rearrangements and size selection in the self-assembly of nanoparticles at liquid interfaces

In the adsorption of nanoparticles at liquid interfaces, soft and short ranged repulsive effective interactions between the nanoparticles at the interface may eventually induce crowding, slow dynamics and jamming at high surface coverage. These phenomena can interfere during the adsorption process, significantly slowing down its kinetics. Here, by means of numerical simulations, we find that modifying the effective interactions, which can be achieved for example by grafting differently functionalized polymer shells on the bare nanoparticles, may qualitatively change such interplay. In particular our results suggest that, in the presence of ultrasoft particle interactions such as the ones described by a Gaussian Core Model potential, a small size polydispersity can be sufficient to decouple the adsorption kinetics from the slow dynamics that develops at the interface, due to a qualitative change from an irreversible adsorption controlled by particle rearrangements at the interface to one dominated by size selection mechanisms. These findings may be useful to achieve higher surface coverages and faster adsorption kinetics.

On the jamming phase diagram for frictionless hard-sphere packings

We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities φ (for monodisperse packings φ = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities φ(J) for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φ(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. φ(RCP) depends on the polydispersity and is ∼ 0.64 for monodisperse packings. For φ > 0.52, φ(J) increases with φ; the available phase space is dominated by basins of attraction that we associate with glass. When φ reaches the ideal glass transition density φ(g), φ(J) reaches the ideal glass density (the glass close packing limit) φ(GCP), so that the available phase space is dominated at φ(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φ(GCP) ≈ 0.655 and φ(g) ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φ(m) and ends at the crystallization offset density φ(off). For monodisperse packings, φ(m) ≈ 0.54 and φ(off) ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φ(g).

Thermodynamic properties and entropy scaling law for diffusivity in soft spheres

The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.

Particle segregation in a sedimenting bidisperse soft sphere system

We study the sedimentation process of a binary colloidal soft sphere system where significant overlaps of the particles are possible. We employ estimates of the equation of states in the small and large pressure limit in order to predict the final states of the sedimentation process. Furthermore, Brownian dynamics simulations were performed in order to confirm the predictions and to explore the dynamics of the sedimentation. We observe that the segregation process due to gravity usually consists of multiple steps. Instead of single particles moving upwards or downwards we usually observe that first local segregation occurs, then clusters consisting of particles of one species are formed that finally sink towards their equilibrium position within the final sedimentation profile. The possible final states include complex phases like a phase consisting of large particles on the top and the bottom of the system with small particles in between. We also observe metastable network-like structures.

Correlation functions in liquids and crystals: free-energy functional and liquid-to-crystal transition

A free-energy functional for a crystal that contains both the symmetry-conserved and symmetry-broken parts of the direct pair-correlation function has been used to investigate the crystallization of fluids in three dimensions. The symmetry-broken part of the direct pair-correlation function has been calculated using a series in ascending powers of the order parameters and which contains three- and higher-body direct correlation functions of the isotropic phase. It is shown that a very accurate description of freezing transitions for a wide class of potentials is found by considering the first two terms of this series. The results found for freezing parameters including the structure of the frozen phase for fluids interacting via the inverse power potential u(r)=ε(σ/r)(n) for n ranging from 4 to ∞ are in very good agreement with simulation results. It is found that for n>6.5 the fluid freezes into a face-centered cubic (fcc) structure while for n≤6 the body-centered cubic (bcc) structure is preferred. The fluid-bcc-fcc triple point is found to be at 1/n=0.158, which is in good agreement with simulation result.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.

Determination of the solid-fluid coexistence of the n - 6 Lennard-Jones system from free energy calculations

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T∗ = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.

Communication: Universality of the melting curves for a wide range of interaction potentials

We demonstrate that the melting curves of various model systems of interacting particles collapse to (or are located very close to) a universal master curve on a plane of appropriately chosen scaled variables. The physics behind this universality is discussed. An equation for the emerging "universal melting curve" is proposed. The obtained results can be used to approximately predict melting of various substances in a wide range of conditions.

Role of the prestructured surface cloud in crystal nucleation

For the homogeneous crystal nucleation process in a soft-core colloid model, we identify optimal reaction coordinates from a set of novel order parameters based on the local structure within the nucleus, by employing transition path sampling techniques combined with a likelihood maximization of the committor function. We find that nucleation is governed by solid clusters that consist of an hcp core embedded within a cloud of surface particles that are highly correlated with their nearest neighbors but not ordered in a high-symmetry crystal structure. The results shed new light on the interpretation of the surface and volume terms in classical nucleation theory.

Predicting freezing for some repulsive potentials

We propose a simple method to approximately predict the freezing (fluid-solid) phase transition in systems of particles interacting via purely repulsive potentials. The method is based on the striking universality of the freezing curve for the model Yukawa and inverse-power-law interactions. This method is applied to draw an exemplary phase diagram of complex plasmas. We suggest that it can also be used to locate freezing transition in other substances with similar properties of interaction.