Core-softened Potentials Research Articles

How Dimensionality Affects the Structural Anomaly in a Core-Softened Colloid

The interaction between hard core–soft shell colloids are characterized by having two characteristic distances: one associated with the penetrable, soft corona and another one corresponding to the impenetrable core. Isotropic core-softened potentials with two characteristic length scales have long been applied to understand the properties of such colloids. Those potentials usually show water-like anomalies, and recent findings have indicated the existence of multiple anomalous regions in the 2D limit under compression, while in 3D, only one anomalous region is observed. In this direction, we perform molecular dynamics simulations to unveil the details about the structural behavior in the quasi-2D limit of a core-softened colloid. The fluid was confined between highly repulsive solvophobic walls, and the behavior at distinct wall separations and colloid densities was analyzed. Our results indicated a straight relation between the 2D- or 3D-like behavior and layer separation. We can relate that if the system behaves as independent 2D-layers, it will have a 2D-like behavior. However, for some separations, the layers are connected, with colloids hopping from one layer to another, thus having a 3D-like structural behavior. These findings fill the gap in the depiction of the anomalous behavior from 2D to 3D.

Analytical treatment of the structure for systems interacting via core-softened potentials

We consider a double ramp (DR) model of the family of core-softened potentials which possess a liquid–liquid critical point when the energy parameter h is negative, as in the Jagla potential [E. A. Jagla, Phys. Rev. E 63, 061501–5 (2001)]. Our model offers the possibility of gradually passing from an attractive potential to a purely repulsive potential by varying the energy parameter h. Using a mean field density functional theory and the MC simulation, we determine the structure factor of the DR model for different values of the parameters. We show that the DR model belongs to the class of adaptable potentials continuously evolving between waterlike and hard sphere (HS) systems. The HS structure factor necessary for the analytical treatment is defined in terms of the effective HS diameter σe which is a function of temperature and density, and which makes it possible to predict the structure as a function of temperature with fairly good precision.

Facile equilibration of well-entangled semiflexible bead-spring polymer melts.

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40Ne and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 106 time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓK and entanglement length Ne.

Waterlike anomalies in hard core–soft shell nanoparticles using an effective potential approach: Pinned vs adsorbed polymers

In this work, a two dimensional system of polymer-grafted nanoparticles is analyzed using large-scale Langevin dynamics simulations. Effective core-softened potentials were obtained for two cases: one where the polymers are free to rotate around the nanoparticle core and a second where the polymers are fixed, with a 45° angle between them. The use of effective core-softened potentials allows us to explore the complete system phase space. In this way, the PT, Tρ, and Pρ phase diagrams for each potential were obtained, with all fluid and solid phases. The phase boundaries were defined analyzing the specific heat at constant pressure, system mean square displacement, radial distribution function, and discontinuities in the density–pressure phase diagram. Also, due to the competition in the system, we have observed the presence of waterlike anomalies, such as the temperature of maximum density (TMD)—in addition with a tendency of the TMD to move to lower temperatures (negative slope)—and the diffusion anomaly. Different morphologies (stripes, honeycomb, and amorphous) for each nanoparticle were observed. We observed that for the fixed polymer case, the waterlike anomalies are originated from the competition between the potential characteristic length scales, while for the free to rotate case, the anomalies arise due to a smaller region of stability in the phase diagram, and no competition between the scales was observed.

Core-softened potentials, multiple liquid–liquid critical points, and density anomaly regions: An exact solution

The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.

Random pinning elucidates the nature of melting transition in two-dimensional core-softened potential system

Despite about forty years of investigations, the nature of the melting transition in two dimensions is not completely clear. In the framework of the most popular Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young (BKTHNY) theory, 2D systems melt through two continuous Berezinskii–Kosterlitz–Thouless (BKT) transitions with intermediate hexatic phase. The conventional first-order transition is also possible. On the other hand, recently on the basis of computer simulations the new melting scenario was proposed with continuous BKT type solid–hexatic transition and first order hexatic–liquid transition. However, in the simulations the hexatic phase is extremely narrow that makes its study difficult. In the present paper, we propose to apply the random pinning to investigate the hexatic phase in more detail. The results of molecular dynamics simulations of two dimensional system having core-softened potentials with narrow repulsive step which is similar to the soft disk system are outlined. The system has a small fraction of pinned particles giving quenched disorder. Random pinning widens the hexatic phase without changing the melting scenario and gives the possibility to study the behavior of the diffusivity and order parameters in the vicinity of the melting transition and inside the hexatic phase.

A simple model for solute–solvent separation through nanopores based on core-softened potentials

We propose an effective model for solute separation from fluids through reverse osmosis based on core-softened potentials. Such potentials have been used to investigate anomalous fluids in several situations under a great variety of approaches. Due to their simplicity, computational simulations become faster and mathematical treatments are possible. Our model aims to mimic water desalination through nano-membranes through reverse osmosis, for which we have found reasonable qualitative results when confronted against all-atoms simulations found in the literature. The purpose of this work is not to replace any fully atomistic simulation at this stage, but instead to pave the first steps towards coarse-grained models for water desalination processes. This may help to approach problems in larger scales, in size and time, and perhaps make analytical theories more viable.

New structural anomaly induced by nanoconfinement.

We explore the structural properties of anomalous fluids confined in a nanopore using molecular dynamics simulations. The fluid is modeled by core-softened (CS) potentials that have a repulsive shoulder and an attractive well at a further distance. Changing the attractive well depth of the fluid-fluid interaction potential, we studied the behavior of the anomalies in the translational order parameter t and excess entropy s(2) for the particles near to the nanopore wall (contact layer) for systems with two or three layers of particles. When the attractive well of the CS potential is shallow, the systems present a three to two layers transition and, additionally to the usual structural anomaly, a new anomalous region in t and s(2). For attractive well deep enough, the systems change from three layers to a bulk-like profile and just one region of anomaly in t and s(2) is observed. Our results are discussed on the basis of the fluid-fluid and fluid-surface interactions.

Effect of attractive interactions on the water-like anomalies of a core-softened model potential

It is now well established that water-like anomalies can be reproduced by a spherically symmetric potential with two length scales, popularly known as core-softened potential. In the present study we aim to investigate the effect of attractive interactions among the particles in a model fluid interacting with core-softened potential on the existence and location of various water-like anomalies in the temperature-pressure plane. We employ extensive molecular dynamic simulations to study anomalous nature of various order parameters and properties under isothermal compression. Order map analyses have also been done for all the potentials. We observe that all the systems with varying depth of attractive wells show structural, dynamic, and thermodynamic anomalies. As many of the previous studies involving model water and a class of core softened potentials have concluded that the structural anomaly region encloses the diffusion anomaly region, which in turn, encloses the density anomaly region, the same pattern has also been observed in the present study for the systems with less depth of attractive well. For the systems with deeper attractive well, we observe that the diffusion anomaly region shifts toward higher densities and is not always enclosed by the structural anomaly region. Also, density anomaly region is not completely enclosed by diffusion anomaly region in this case.

Silicalike sequence of anomalies in core-softened systems

We present a simulation study of density, structural, and diffusion anomalies in a core-softened system, a remarkable model liquid that exhibits anomalous properties seen in tetrahedral liquids such as silica and water. It is widely believed that core-softened potentials demonstrate waterlike sequence of anomalies. Here, we show that the order of the region of anomalous diffusion and the regions of density and structural anomalies are inverted with increasing depth of the attractive part of the potential and have silicalike sequence. We also show that the Widom line slope is negative as in water.

Relation between occupation in the first coordination shells and Widom line in core-softened potentials

Three core-softened families of potentials are checked for the presence of density and diffusion anomalies. These potentials exhibit a repulsive core with a softening region and at larger distances an attractive well. We found that the region in the pressure-temperature phase diagram in which the anomalies are present increases if the slope between the core-softened scale and the attractive part of the potential decreases. The anomalous region also increases if the range of the core-softened or of the attractive part of the potential decreases. We also show that the presence of the density anomaly is consistent with the non-monotonic changes of the radial distribution function at each one of the two scales when temperature and density are varied. Then, using this anomalous behavior of the structure we show that the pressure and the temperature at which the radial distribution function of one of the two length scales equals the radial distribution function of the other length scales identify the Widom line.

Multiple liquid-liquid critical points and density anomaly in core-softened potentials

The relation between liquid-liquid phase transitions and waterlike density anomalies in core-softened potentials of fluids was investigated in an exactly solvable one-dimensional lattice model and in a three-dimensional fluid with a Fermi-like potential, the latter by molecular dynamics. Both systems were shown to present three liquid phases, two liquid-liquid phase transitions closely connected to two distinct regions of anomalous density increase. We propose that an oscillatory behavior observed on the thermal expansion coefficient as a function of pressure can be used as a signature of the connection between the liquid-liquid phase transition and density anomaly.

High-order jamming crossovers and density anomalies.

We demonstrate that particles interacting via core-softened potentials exhibit a series of successive density anomalies upon isothermal compression, leading to oscillations in the diffusivity and thermal expansion coefficient, with the latter reaching negative values. These finite-temperature density anomalies are then shown to correspond to zero-temperature high-order jamming crossovers. These occur when particles are forced to come into contact with neighbours in successive coordination shells upon increasing the density. The crossovers induce anomalous behavior of the bulk modulus, which oscillates with density. We rationalize the dependence of these crossovers on the softness of the interaction potential, and relate the jamming crossovers and the anomalous diffusivity via the properties of the vibrational spectrum.

Thermodynamic, dynamic, structural, and excess entropy anomalies for core-softened potentials

Using molecular dynamic simulations, we study three families of continuous core-softened potentials consisting of two length scales: a shoulder scale and an attractive scale. All the families have the same slope between the two length scales but exhibit different potential energy gap between them. For each family three shoulder depths are analyzed. We show that all these systems exhibit a liquid-liquid phase transition between a high density liquid phase and a low density liquid phase ending at a critical point. The critical temperature is the same for all cases suggesting that the critical temperature is only dependent on the slope between the two scales. The critical pressure decreases with the decrease of the potential energy gap between the two scales suggesting that the pressure is responsible for forming the high density liquid. We also show, using the radial distribution function and the excess entropy analysis, that the density, the diffusion, and the structural anomalies are present if particles move from the attractive scale to the shoulder scale with the increase of the temperature indicating that the anomalous behavior depends only in what happens up to the second coordination shell.

Core-softened fluids, water-like anomalies, and the liquid-liquid critical points

Molecular dynamics simulations are used to examine the relationship between water-like anomalies and the liquid-liquid critical point in a family of model fluids with multi-Gaussian, core-softened pair interactions. The core-softened pair interactions have two length scales, such that the longer length scale associated with a shallow, attractive well is kept constant while the shorter length scale associated with the repulsive shoulder is varied from an inflection point to a minimum of progressively increasing depth. The maximum depth of the shoulder well is chosen so that the resulting potential reproduces the oxygen-oxygen radial distribution function of the ST4 model of water. As the shoulder well depth increases, the pressure required to form the high density liquid decreases and the temperature up to which the high-density liquid is stable increases, resulting in the shift of the liquid-liquid critical point to much lower pressures and higher temperatures. To understand the entropic effects associated with the changes in the interaction potential, the pair correlation entropy is computed to show that the excess entropy anomaly diminishes when the shoulder well depth increases. Excess entropy scaling of diffusivity in this class of fluids is demonstrated, showing that decreasing strength of the excess entropy anomaly with increasing shoulder depth results in the progressive loss of water-like thermodynamic, structural and transport anomalies. Instantaneous normal mode analysis was used to index the overall curvature distribution of the fluid and the fraction of imaginary frequency modes was shown to correlate well with the anomalous behavior of the diffusivity and the pair correlation entropy. The results suggest in the case of core-softened potentials, in addition to the presence of two length scales, energetic, and entropic effects associated with local minima and curvatures of the pair interaction play an important role in determining the presence of water-like anomalies and the liquid-liquid phase transition.

Water-like anomalies in the core-softened systems: Dependence on the trajectory in density-temperature plane

We show that the existence of the water-like anomalies in kinetic coefficients in the core-softened systems depends on the trajectory in ρ – T plane along which the kinetic coefficients are calculated. In particular, it is shown that the diffusion anomaly does exist along the isotherms, but disappears along the isochors. We analyze the applicability of the Rosenfeld entropy scaling relations to the systems with the core-softened potentials demonstrating the water-like anomalies. It is shown that the validity of the Rosenfeld scaling relation for the diffusion coefficient also depends on the trajectory in the ρ – T plane along which the kinetic coefficients and the excess entropy are calculated. In particular, it is valid along isochors, but it breaks down along isotherms.

Effects of the attractive interactions in the thermodynamic, dynamic, and structural anomalies of a two length scale potential

Using molecular dynamic simulations, we study a system of particles interacting through a continuous core-softened potentials consisting of a hard core, a shoulder at closest distances, and an attractive well at further distance. We obtain the pressure-temperature phase diagram of this system for various depths of the tunable attractive well. Since this is a two length scale potential, density, diffusion, and structural anomalies are expected. We show that the effect of increasing the attractive interaction between the molecules is to shrink the region in pressure in which the density and the diffusion anomalies are present. If the attractive forces are too strong, particle will be predominantly in one of the two length scales and no density of diffusion anomaly is observed. The structural anomalous region is present for all the cases.

Thermodynamic, dynamic, and structural anomalies for shoulderlike potentials

Using molecular dynamic simulations we study a family of continuous core-softened potentials consisting of a hard core, a shoulder at closest distances, and an attractive well at further distance. The repulsive shoulder and the well distances represent two length scales. We show that if the first scale, the shoulder, is repulsive or has a small well, the potential has a region in the pressure-temperature phase diagram with density, diffusion, and structural anomalies. However, if the closest scale becomes a deep well, the regions in the pressure-temperature phase diagram where the three anomalies are present shrink and disappear. This result helps in defining two length scales potentials that exhibit anomalies.

Which mechanism underlies the water-like anomalies in core-softened potentials?

Using molecular dynamics simulations we investigate the thermodynamics of particles interacting with continuous and discrete versions of a core-softened (CS) intermolecular potential composed by a repulsive shoulder. Dynamical and structural properties are also analyzed by the simulations. We show that in the continuous version of the CS potential the density at constant pressure has a maximum for a certain temperature. Similarly the diffusion constant, D, at a constant temperature has a maximum at a density ρ D max and a minimum at a density ρ D min < ρDmax, and structural properties are also anomalous. For the discrete CS potential none of these anomalies are observed. The absence of anomalies in the discrete case and its presence in the continuous CS potential are discussed in the framework of the excess entropy.

Progression of phase behavior for a sequence of model core-softened potentials

A series of phase diagrams is obtained in three dimensions for a smooth pair potential with an outer well and a repulsive inner shoulder. Condensed phase boundaries are located using free energy calculations. Liquid-vapor equilibria are obtained with multicanonical methods. As the depth of the outer well is increased, a simple-hexagonal to close-packed transition appears in the solid, leading to a discontinuity in the slope of the melting curve. For deeper wells the simple hexagonal melting temperature exhibits a maximum with respect to pressure. The onset of the predicted metastable isostructural transition is also studied.