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.     

Structural anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations we investigate the structure of a system of particles interacting through a continuous core-softened interparticle potential. We found for the translational order parameter t a local maximum at a density rho(t-max) and a local minimum at rho(t-min)>rho(t-max). Between rho(t-max) and rho(t-min), the t parameter anomalously decreases upon increasing pressure. For the orientational order parameter Q(6) a maximum was observed at a density rho(t-max)相似文献   

Core-softened system with attraction: trajectory dependence of anomalous behavior

In the present article we carry out a molecular dynamics study of the core-softened system and show that the existence of the water-like anomalies in this system depends on the trajectory in P-ρ-T space along which the behavior of the system is studied. For example, diffusion and structural anomalies are visible along isotherms as a function of density, but disappears along the isochores and isobars as a function of temperature. On the other hand, the diffusion anomaly may be seen along adiabats as a function of temperature, density, and pressure. It should be noted that it may be no signature of a particular anomaly along a particular trajectory, but the anomalous region for that particular anomaly can be defined when all possible trajectories in the same space are examined (for example, signature of diffusion anomaly is evident through the crossing of different isochors. However, there is no signature of diffusion anomaly along a particular isochor). We also analyze the applicability of the Rosenfeld entropy scaling relations to this system in the regions with 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 P-ρ-T space along which the kinetic coefficients and the excess entropy are calculated.     

How short-range attractions impact the structural order, self-diffusivity, and viscosity of a fluid

We present molecular simulation data for viscosity, self-diffusivity, and the local structural ordering of (i) a hard-sphere fluid and (ii) a square-well fluid with short-range attractions. The latter fluid exhibits a region of dynamic anomalies in its phase diagram, where its mobility increases upon isochoric cooling, which is found to be a subset of a larger region of structural anomalies, in which its pair correlations strengthen upon isochoric heating. This "cascade of anomalies" qualitatively resembles that found in recent simulations of liquid water. The results for the hard-sphere and square-well systems also show that the breakdown of the Stokes-Einstein relation upon supercooling occurs for conditions where viscosity and self-diffusivity develop different couplings to the degree of pairwise structural ordering of the liquid. We discuss how these couplings reflect dynamic heterogeneities. Finally, we note that the simulation data suggest how repulsive and attractive glasses may generally be characterized by two distinct levels of short-range structural order.     

Waterlike hierarchy of anomalies in a continuous spherical shouldered potential

We investigate by molecular dynamics simulations a continuous isotropic core-softened potential with attractive well in three dimensions, introduced by Franzese [J. Mol. Liq. 136, 267 (2007)], that displays liquid-liquid coexistence with a critical point and waterlike density anomaly. Besides the thermodynamic anomalies, here we find diffusion and structural anomalies. The anomalies, not observed in the discrete version of this model, occur with the same hierarchy that characterizes water. We discuss the differences in the anomalous behavior of the continuous and the discrete model in the framework of the excess entropy, calculated within the pair correlation approximation.     

Thermodynamic and dynamic anomalies in a one-dimensional lattice model of liquid water

We investigate the occurrence of waterlike thermodynamic and dynamic anomalous behavior in a one dimensional lattice gas model. The system thermodynamics is obtained using the transfer matrix technique and anomalies on density and thermodynamic response functions are found. When the hydrogen bond (molecules separated by holes) is more attractive than the van der Waals interaction (molecules in contact) a transition between two fluid structures is found at null temperature and high pressure. This transition is analogous to a 'critical point' and intimately connects the anomalies in density and in thermodynamic response functions. Monte Carlo simulations were performed in the neighborhood of this transition and used to calculate the self diffusion constant, which increases with density as in liquid water.     

Complex phase behavior of the system of particles with smooth potential with repulsive shoulder and attractive well

We report a detailed simulation study of the phase behavior of core-softened system with attractive well. Different repulsive shoulder widths and attractive well depths are considered which allows to monitor the influence of repulsive and attractive forces on the phase diagram of the system. Thermodynamic anomalies in the systems are also studied. It is shown that the diffusion anomaly is stabilized by small attraction.     

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.     

Inversion of sequence of diffusion and density anomalies in core-softened systems

In this paper we present a simulation study of water-like anomalies in core-softened system introduced in our previous papers. We investigate the anomalous regions for a system with the same functional form of the potential but with different parameters and show that the order of the region of anomalous diffusion and the region of density anomaly is inverted with increasing the width of the repulsive shoulder.     

Observation of two diffusive relaxation modes in microemulsions by dynamic light scattering

Water-in-oil microemulsions stabilized by AOT and dispersed in n-alkane oils with a constant molar water-to-surfactant ratio were studied by dynamic light scattering. A dilution series (in the range of volume fraction of water plus surfactant, phi approximately 0.02-0.52) was used, which allowed us to extract information about droplet sizes, diffusion coefficients, interactions, and polydispersity from experimental data. We report the observation of two diffusive relaxation modes in a concentrated microemulsion (0.20 < phi < 0.5) due to density (collective diffusion) and concentration or polydispersity (self-diffusion) fluctuations. Below this concentration it was difficult to resolve two exponentials unambiguously, and in this case one apparent relaxation mode was observed. It was found that for a given composition self-diffusion is more pronounced in apparent relaxation mode for a shorter chain length alkane. The concentration dependence of these diffusion coefficients reflects the effect of hard sphere and the supplementary attractive interactions. It was observed that the attractive part becomes more pronounced in the case of a large alkane chain oil at a given temperature. This explains the shift of the region of microemulsion stability to lower temperatures for higher chain length alkanes. Increase in hydrodynamic radius, Rh, obtained from the diffusion coefficient extrapolated to infinite dilution was observed with increase of alkane chain length. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least 3 orders of magnitude longer than the estimated time between droplet collisions.     

A computational investigation of thermodynamics, structure, dynamics and solvation behavior in modified water models

We investigate the properties of geometrically modified water models by performing molecular dynamics simulations of perturbations of the extended simple point charge (SPC/E) model of water over a wide range of temperatures at 1 bar. The geometric modification consists of altering the H-O-H angle in SPC/E. The dipole moment is held constant by altering the O-H bond length, while the electrostatic charges are left unchanged. We find that a H-O-H angle of at least 100 degrees is necessary for the appearance of density anomalies and of solubility extrema with respect to temperature for small apolar solutes. We observe the occurrence of two incompatible types of structural order in these models: Tetrahedral, with waterlike translational order for bent models with H-O-H angles in excess of 100 degrees ; and linear, with Lennard-Jones-like orientationally averaged translational order for smaller H-O-H angles. Increasing the H-O-H angle causes the density to increase, while at the same time shifting waterlike anomalies to progressively higher temperatures. For bent models with H-O-H angle greater than SPC/E's, we observe arrest of translational motion at 300 K (115 degrees) and 330 K (120 degrees).     

Multicomponent diffusion in nanosystems

We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely, kinetic and density functional theory and their implementation as an effective numerical method via the lattice Boltzmann approach. By combining the first two methods, it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a self-consistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with short-range hard-core repulsion between particles of unequal sizes and weak attractive long-range interactions. As a result, the attractive part of the potential does not contribute explicitly to viscosity but to diffusivity and the thermodynamic properties. Finally, we obtain a practical scheme to solve the kinetic equations by employing a discretization procedure derived from the lattice Boltzmann approach. Within this framework, we present numerical data concerning the mutual diffusion properties both in the case of a quiescent bulk fluid and shear flow inducing Taylor dispersion.     

X-ray and neutron reflectometry for the investigation of polymer diffusion

Summary X-ray and neutron reflectometry are novel tools for the investigation of polymer interfaces. For this method we demonstrate the high resolution on the vertical length scale which is normally better than 1 nm and the ideal applicability for the analysis of polymer diffusion by showing both simulations and measurements. The limits and difficulties are discussed. We look at the broadening of the interface between two polystyrene films during interdiffusion slightly above the glass transition temperature. For short times we prove two distinct time regimes for polymer diffusion. This is achieved with a double layer system consisting of a deuterated and a protonated polystyrene film. The roughness of the individual films is well below 1 nm.     

Diffusion at the liquid-vapor interface

Recently, the intrinsic sampling method has been developed in order to obtain, from molecular simulations, the intrinsic structure of the liquid-vapor interface that is presupposed in the classical capillary wave theory. Our purpose here is to study dynamical processes at the liquid-vapor interface, since this method allows tracking down and analyzing the movement of surface molecules, thus providing, with great accuracy, dynamical information on molecules that are "at" the interface. We present results for the coefficients for diffusion parallel and perpendicular to the liquid-vapor interface of the Lennard-Jones fluid, as well as other time and length parameters that characterize the diffusion process in this system. We also obtain statistics of permanence and residence time. The generality of our results is tested by varying the system size and the temperature; for the latter case, an existing model for alkali metals is also considered. Our main conclusion is that, even if diffusion coefficients can still be computed, the turnover processes, by which molecules enter and leave the intrinsic surface, are as important as diffusion. For example, the typical time required for a molecule to traverse a molecular diameter is very similar to its residence time at the surface.     

Hydrogen bonded structure and dynamics of liquid-vapor interface of water-ammonia mixture: an ab initio molecular dynamics study

We have carried out ab initio molecular dynamics simulations of a liquid-vapor interfacial system consisting of a mixture of water and ammonia molecules. We have made a detailed analysis of the structural and dynamical properties of the bulk and interfacial regions of the mixture. Among structural properties, we have looked at the inhomogeneous density profiles of water and ammonia molecules, hydrogen bond distributions, orientational profiles, and also vibrational frequency distributions of bulk and interfacial molecules. It is found that the interfacial molecules show preference for specific orientations so as to form water-ammonia hydrogen bonds at the interface with ammonia as the acceptor. The structure of the system is also investigated in terms of inter-atomic voids present in the system. Among the dynamical properties, we have calculated the diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational spectral diffusion in bulk and interfacial regions. It is found that the diffusion and orientation relaxation of the interfacial molecules are faster than those of the bulk. However, the hydrogen bond lifetimes are longer at the interface which can be correlated with the time scales found from the decay of frequency time correlations.     

Structural precursor to freezing: an integral equation study

Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard spheres at densities close to freezing and which is associated with local crystalline ordering in the dense fluid. We address this structural precursor to freezing using an inhomogeneous integral equation theory capable of describing local packing constraints to a high level of accuracy. The addition of a short-range attractive interaction leads to a well known broadening of the fluid-solid coexistence region as a function of attraction strength. The appearance of a shoulder in our calculated radial distribution functions is found to be consistent with the broadened coexistence region for a simple model potential, thus demonstrating that the shoulder is not exclusively a high density packing effect.     

On the corresponding states law of the Yukawa fluid

We have analyzed the currently available simulation results as well as performed some additional Monte Carlo simulation for the hard-core attractive Yukawa fluid in order to study its corresponding state behavior. We show that the values of reduced surface tension map onto the master curve and a universal equation of state can be obtained in the wide range of the attractive Yukawa tail length after a certain rescaling of the number density. Some comparisons with other nonconformal potentials are presented and discussed.     

Memory formalism in the passive diffusion across highly heterogeneous systems

In this note, we present an extension of the Fick’s second law by introducing a memory formalism based on derivatives of fractional order to take into account the passive diffusion process across two different membranous systems, i.e., a biological membrane, where its structural complexity suggests the introduction of a space-dependent diffusion constant, and a heterogeneous highly porous system at a macroscopic level, composed of an impenetrant matrix and pores across which the solute diffuse. This approach has been employed to describe some recent experimental results concerning the transdermal diffusion of drugs through human stratum corneum and the flux of water observed across a sand layer under a constant hydrostatic pressure difference. Despite the two examples we report concern with deeply different heterogeneous systems at a different scale length, a reasonable good agreement is obtained in both the two cases.     

On the curvature dependence of the interfacial tension in a symmetric three-component interface

We consider a symmetric interface between two polymers A(N) and B(N) in a common monomeric solvent S using the mean-field Scheutjens-Fleer self-consistent field theory and focus on the curvature dependence of the interfacial tension. In multi-component systems there is not one unique scenario to curve such an interface. We elaborate on this by keeping either the chemical potential of the solvent or the bulk concentration of the solvent fixed, that is we focus on the semi-grand canonical ensemble case. Following Helfrich, we expand the surface tension as a Taylor series in the curvature parameters and find that there is a non-zero linear dependence of the interfacial tension on the mean curvature in both cases. This implies a finite Tolman length. In a thermodynamic analysis we prove that the non-zero Tolman length is related to the adsorption of solvent at the interface. Similar, but not the same, correlations between the solvent adsorption and the Tolman length are found in the two scenarios. This result indicates that one should be careful with symmetry arguments in a Helfrich analysis, in particular for systems that have a finite interfacial tension: one not only should consider the structural symmetry of the interface, but also consider the constraints that are enforced upon imposing the curvature. The volume fraction of solvent, the chain length N as well as the interaction parameter chi(AB) in the system can be used to take the system in the direction of the critical point. The usual critical behavior is found. Both the width of the interface and the Tolman length diverge, whereas the density difference between the two phases, adsorbed amount of solvent at the interface, interfacial tension, spontaneous curvature, mean bending modulus as well as the Gaussian bending modulus vanish upon approach of the critical point.     

Entropy, diffusivity, and structural order in liquids with waterlike anomalies

The excess entropy, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is studied as a function of density and temperature for liquid silica and a two-scale ramp potential, both of which are known to possess waterlike liquid state anomalies. The excess entropy for both systems is evaluated using a fairly accurate pair correlation approximation. The connection between the excess entropy and the density and diffusional anomalies is demonstrated. Using the pair correlation approximation to the excess entropy, it can be shown that if the energetically favorable local geometries in the low and high density limits have different symmetries, then a structurally anomalous regime can be defined in terms of orientational and translational order parameters, as in the case of silica and the two-scale ramp system but not for the one-scale ramp liquid. Within the category of liquids with waterlike anomalies, we show that the relationship between the macroscopic entropy and internal energy is sufficient to distinguish between those with local anisotropy and consequent open packings at low densities and those with isotropic interactions but multiple length scales. Since it is straightforward to evaluate the pair correlation entropy and internal energy from simulations or experimental data, such plots should provide a convenient means to diagnose the existence as well as type of anomalous behavior in a range of liquids, including ionic and intermetallic melts and complex fluids with ultrasoft repulsions.