Monatomic Liquids Research Articles

Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions

The effect of interfacial slip on steady-state and time-periodic flows of monatomic liquids is investigated using non-equilibrium molecular dynamics simulations. The fluid phase is confined between atomically smooth rigid walls, and the fluid flows are induced by moving one of the walls. In steady shear flows, the slip length increases almost linearly with shear rate. We found that the velocity profiles in oscillatory flows are well described by the Stokes flow solution with the slip length that depends on the local shear rate. Interestingly, the rate dependence of the slip length obtained in steady shear flows is recovered when the slip length in oscillatory flows is plotted as a function of the local shear rate magnitude. For both types of flows, the friction coefficient at the liquid-solid interface correlates well with the structure of the first fluid layer near the solid wall.

Application of Phase Transition Theory to a Glass-Forming System

We have investigated the crystallization of a monatomic simple liquid in equilibrium, where the constituents interact through the Lennard-Jones-Gauss (LJG) potential. By incorporating a perturbation expansion into a density functional approach, we obtain a phase diagram covering a wide range of the parameter space. The phase diagram agrees qualitatively with that obtained by molecular dynamics (MD) simulations. The MD simulations show that the system cannot be crystallized, even if the temperature is sufficiently low, in a certain region of the parameter space. In this parameter region, we find that the coexisting density of the fcc crystal is unexpectedly high owing to a decrease in the free energy and show that the third-nearest-neighbor site of the fcc crystal coincides with the second minimum in the LJG potential.

Free surface effects on thermodynamics and glass formation in simple monatomic supercooled liquids

Free surface effects on the thermodynamics and glass formation in simple monatomic supercooled liquids with the Lennard-Jones-Gauss interaction potential were studied by the molecular dynamics simulations. Glass with two free surfaces was obtained by cooling from the melt. We found the following important new results: Free surfaces significantly enhance atomic mobility in the system compared to that of the bulk and induce the formation of so-called layer structure of the interior of both liquid and glassy states. A mobile surface layer in the system exists for a wide temperature range; i.e., the thickness of the mobile surface layer and the discrepancy between atomic mobility in the surface and that in the interior have a tendency to increase with temperature. The atomic mechanism of glass formation in supercooled liquids with free surfaces exhibits heterogeneouslike behavior, unlike the homogeneous behavior observed in the bulk; i.e., the solidlike domain initiates/enhances in the interior and simultaneously grows outward to the surface to form a glassy solid phase. The interior of glass with free surfaces exhibits a stronger local icosahedral order compared to that of the bulk, and it may lead to higher stability of the glassy state compared to that of the latter. In contrast, the surface shell has a more porous structure and contains a large number of undercoordinated sites.

Molecular versus tissue liquids: an atomic length?

For the monatomic classical liquids like Ar, Kr and Xe, it has long been known that near the triple point, the product of surface tension σ and isothermal compressibility KT , having dimensions of length, is less than 1 Å. More recently, a similar result has been established from experimental data on some 20 organic liquids. The purpose of this article is to raise a possibly interesting question with experimentalists working on complex molecular liquids as well as biological cell assemblies. Thus, we first draw attention to measurements of the compressibility of some 25 proteins in water. Can complementary measurements of surface tension be carried out on at least some of these systems? And is the product σKT a length of order of an Å or so? Second, we note existing measurements of surface tension σ on five embryonic tissues and ask essentially the same question as to whether or not the product σKT is of atomic dimensions. Finally, via a biopsy of a tumour which might provide material to yield an approximately spherical aggregate of the cancerous cells, is σKT measurable and if so, is this product dependent on the presence of the tumour?

Glass Formation and Thermodynamics of Supercooled Monatomic Liquids

Atomic mechanism of glass formation of a supercooled simple monatomic liquid with Lennard-Jones-Gauss (LJG) interatomic potential is studied by molecular dynamics (MD) simulation. Supercooled and glassy states are obtained by cooling from the melt. Glassy state obtained at low temperatures is annealed for very long time, on the order of microsecond, and we find that glassy state remains unchanged and that the long-lived glassy state of a simple monatomic system in three dimensions is realized. We analyze the spatiotemporal properties of solid-like and liquid-like atoms that are defined by the Lindemann-like freezing criterion. The number of solid-like atoms, distributed throughout the liquid, increases with decreasing temperature toward glass transition and they form clusters. In the deeply supercooled region, almost all solid-like atoms form a single percolation cluster and its characteristic size increases sharply on further cooling. Glass formation in supercooled liquid occurs when a single percolation cluster of solid-like atoms involves a majority of atoms to form a relatively rigid solid phase. We also obtain several physical quantities of the system, including temperature dependence of mass density, Lindemann ratio, incoherent intermediate scattering function, α-relaxation time, evolution of radial distribution function, and local bond-pair orders detected by Honeycutt-Andersen analysis. We identify three characteristic temperatures related to the vitrification: a temperature at which crossover from liquid-like to solid-like dynamics occurs on cooling, the glass transition temperature, and the Vogel-Fulcher-Tammann temperature. Behavior of liquid-like atoms in glassy state has been analyzed and discussed.

Investigation of the particular features of the structure factor of liquid Al-based alloys

We study the structure of liquid binary and ternary alloys of aluminum with transition metals (Al–TM) obtained by Reverse Monte Carlo (RMC) and Molecular Dynamics (MD) simulation methods. Two distinctive features of their structure factor are discussed: the shoulder on the second peak and the prepeak on the left side of the main peak. The quadruples of mutually neighboring atoms (Delaunay simplexes) with a shape close to a regular tetrahedron's (quasi-regular tetrahedra) have been selected in the models and examined. They combine into clusters of different morphology (polytetrahedra) forming a polytetrahedral order (PTO), and there are no compact clusters of these tetrahedra similar to icosahedron in our alloys. It is discussed that the second peak feature of the structure factor is associated with PTO, and does not require for its explanation the presence of icosahedral short-range order (ISRO) in the liquid alloys. The prepeak is caused by the chemical short-range order (CSRO). In our models it is observed mainly on the subsystem of atoms which is complementary to the subsystem of the polytetrahedra. Simulation of the CSRO was performed on a model of monatomic liquid. A new length scale responsible for the prepeak has been obtained in this simulation.

Modeling Multiple Time Scales during Glass Formation with Phase-Field Crystals

The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase-field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass formation over multiple time scales. Agreement with mode coupling theory is demonstrated for underdamped liquids at moderate supercoolings, and a rapidly growing dynamic correlation length is found to be associated with fragile behavior.

Crystallization of the Lewis–Wahnström ortho-terphenyl model

Crystallization is observed during microsecond long molecular dynamics simulations of bent trimers, a molecular model proposed by Lewis and Wahnström for ortho-terphenyl. In the crystal, the three spheres that make up the rigid molecule sit near sites of a body centered cubic lattice. The trimer bond angle is almost optimal for this structure. The crystal exhibits orientational disorder with the molecules aligned randomly along the three Cartesian axis, i.e., cubatic orientational order. The rotational and translational mobilities exhibit only modest decreases on crystallization, by factors of 10 and 3, respectively. The rotational relaxation does change from Debye-like in the liquid to large angle jumps in the crystal. We consider the origin of the superior glass forming ability of the trimer over the monatomic liquid.

Some regularities of the behavior of the thermodynamic properties of systems with three-body intermolecular interactions

The effect of three-body intermolecular interactions on the behavior of different thermodynamic properties of monatomic liquids (pressure, internal energy, chemical potential) and conditions of the vaporliquid phase equilibrium is studied. The systems in which two-body intermolecular interactions were described by the Lennard-Jones potential and three-body ones were described by the Axilrod-Teller potential are considered. The Monte Carlo method and the method of partial distribution functions are used to solve the problem. Data obtained by means of these methods agree well.

Atomic mechanism of glass formation in supercooled monatomic liquids

Atomic mechanism of glass formation in supercooled monatomic liquids is monitored via analyzing the spatial arrangement of solid-like atoms. The supercooled states are obtained by cooling from the melt using molecular dynamics (MD) simulation. Solid-like atoms, detected via Lindemann-like freezing criterion, are found throughout the liquid. Their number increases with decreasing temperature and they form clusters. In the deeply supercooled region, all solid-like atoms form a single percolation cluster which spans throughout the system. The number of atoms in this cluster increases steeply with further cooling. Glass formation in supercooled liquids occurs when a single percolation cluster of solid-like atoms involves the majority of atoms in the system to form a relatively rigid glassy solid. By analyzing the temperature dependence of static and dynamic properties, we identify three characteristic temperatures of glass formation in supercooled liquids including the Vogel–Fulcher temperature.

Some properties of the structure factor S(q) in two-dimensional classical liquids near freezing

We explore general properties of the main peak of the structure factor S(q) near the melting temperature T melt in liquids confined in two dimensions, especially for the one component plasma model and for monatomic liquids interacting through inverse twelfth-power potentials. Those properties are the height of the peak, S(q m), where q m is the position of maximum in the peak, and the ratio between S(q m) and q m/Δq, where 2Δq is the width of the peak. The results obtained are then compared with those for similar systems in three dimensions. Other magnitude that we use to compare two-dimensional and three-dimensional simple liquids is r m/Δr, where r m is the position of the main peak in the pair distribution function g(r) and 2Δr is the width of that peak.

Statistical mechanics model for the transit free energy of monatomic liquids

In applying vibration-transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small (approximately 10%) transit contribution. Toward this goal, an analysis of the available high-temperature experimental entropy data for elemental liquids was recently completed [D. C. Wallace, E. D. Chisolm, and N. Bock, Phys. Rev. E 79, 051201 (2009)]. This analysis yields a common curve of transit entropy vs T/thetatr, where T is temperature and thetatr is a scaling temperature for each element. In the present paper, a statistical mechanics model is constructed for the transit partition function, and is calibrated to the experimental transit entropy curve. The model has two scalar parameters, and captures the temperature scaling of experiment. The calibrated model fits the experimental liquid entropy to high accuracy at all temperatures. With no additional parameters, the model also agrees with both experiment and molecular dynamics for the internal energy vs. T for Na. With the calibrated transit model, V-T theory provides equations subject to ab initio evaluation for thermodynamic properties of monatomic liquids. This will allow the range of applicability of the theory, and its overall accuracy, to be determined. More generally, the hypothesis of V-T theory, which divides the many-atom potential energy valleys into random and symmetric classes, can also be tested for its application beyond monatomic systems.

Predicting the Effective Temperature of a Glass

We explain the findings by Di Leonardo et al. [Phys. Rev. Lett. 84, 6054 (2000)10.1103/PhysRevLett.84.6054] that the effective temperature of a Lennard-Jones glass depends only on the final density in the volume and/or temperature jump that produces the glass. This is not only a property of the Lennard-Jones liquid, but a feature of all strongly correlating liquids. For such liquids data from a single quench simulation provide enough information to predict the effective temperature of any glass produced by jumping from an equilibrium state. This prediction is validated by simulations of the Kob-Andersen binary Lennard-Jones liquid and shown not to apply for the nonstrongly correlating monatomic Lennard-Jones Gaussian liquid.

A Generalized-Yvon−Born−Green Theory for Determining Coarse-Grained Interaction Potentials

The present work introduces a generalized-Yvon−Born−Green (YBG) theory for calculating coarse-grained (CG) force fields directly from structure ensembles. The method is noniterative and determines the CG potentials from a system of coupled linear integral equations that are expressed in terms of structural correlation functions for the CG sites. The force field obtained by solving these linear equations provides a variationally optimal approximation to the many-body potential of mean force determined by the atomistic model and the CG mapping. The generalized-YBG theory is equivalent to the conventional YBG equation when applied to monatomic liquids but also correctly treats the many-body structural correlations present in more complex molecular systems. Additionally, this work introduces an analogous version of the theory for determining discrete force field parameters. Numerical calculations for a CG model of a propane−propanol mixture illustrate the method.

Ab initiomethod for locating characteristic potential-energy minima of liquids

It is possible in principle to probe the many-atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids by Wallace [Phys. Rev. E 56, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential-energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid molecular dynamics configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations.

Vitrification of a monatomic 2D simple liquid

Abstract A monatomic simple liquid in two dimensions, where atoms interact isotropically through the Lennard-Jones-Gauss potential [M. Engel, H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid cooling technique in a molecular dynamics simulation. Transformation to a crystalline state is investigated at various temperatures and the time-temperature-transformation (TTT) curve is determined. It is found that the transformation time to a crystalline state is the shortest at a temerature 14% below the melting temperature T m and that at temperatures below T v ≡ 0:6T m the transformation time is much longer than the available CPU time. This indicates that a long-lived glassy state is realized for T ≤ T v.

The importance of the three-particle correlation function in the theory of monatomic classical liquids like argon

The present study was motivated by the work of Fortov et al. (2008) on the use of experimental methods of analysis of spatial correlation of dust particles in plasma. Here, we therefore focus on the importance of the three-particle correlation function g 3 in the theory of monatomic classical liquids like argon, in the framework of two-body central forces. We cover (i) the asymptotic relation of g 3 to the Ornstein–Zernike direct correlation function c(r); (ii) the use of g 3 to determine the specific heat difference c P − c V ; and (iii) g 3 related to the pressure dependence of the pair correlation function.

Improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of +/-2% among elemental liquids and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of +/-0.1% to the available experimental high-temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/theta_{0}) , where T is temperature and theta_{0} is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/theta_{tr}) , where theta_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived in a single formula applying to normal and anomalous melting alike. An ab initio calculation of theta_{0} , based on density-functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.

Structural model for octagonal quasicrystals derived from octagonal symmetry elements arising inβ-Mncrystallization of a simple monatomic liquid

While performing molecular-dynamics simulations of a simple monatomic liquid, we observed the crystallization of a material displaying octagonal symmetry in its simulated diffraction pattern. Inspection of the atomic arrangements in the crystallization product reveals large grains of the $\ensuremath{\beta}\text{-Mn}$ structure aligned along a common fourfold axis, with $45\ifmmode^\circ\else\textdegree\fi{}$ rotations between neighboring grains. These $45\ifmmode^\circ\else\textdegree\fi{}$ rotations can be traced to the intercession of a second crystalline structure fused epitaxially to the $\ensuremath{\beta}\text{-Mn}$ domain surfaces, whose primitive cell has lattice parameters $a=b=c={a}_{\ensuremath{\beta}\text{-Mn}}$, $\ensuremath{\alpha}=\ensuremath{\beta}=90\ifmmode^\circ\else\textdegree\fi{}$, and $\ensuremath{\gamma}=45\ifmmode^\circ\else\textdegree\fi{}$. This secondary phase adopts a structure which appears to have no known counterpart in the experimental literature, but can be simply derived from the ${\text{Cr}}_{3}\text{Si}$ and ${\text{Al}}_{3}{\text{Zr}}_{4}$ structure types. We used these observations as the basis for an atomistic structural model for octagonal quasicrystals, in which the $\ensuremath{\beta}\text{-Mn}$ and the secondary phase structure unit cells serve as square and rhombic tiles (in projection), respectively. Its diffraction pattern down the octagonal axis resembles those experimentally measured. The model is unique in being consistent with high-resolution electron microscopy images showing square and rhombic units with edge-lengths equal to that of the $\ensuremath{\beta}\text{-Mn}$ unit cell. Energy minimization of this configuration, using the same pair potential as above, results in an alternative octagonal quasiperiodic structure with the same tiling but a different atomic decoration and diffraction pattern.

Liquid boron: X-ray measurements andab initiomolecular dynamics simulations

We report results of a comprehensive study of liquid boron with x-ray measurements of the atomic structure and dynamics coupled with ab initio molecular dynamics simulations. There is no evidence of survival into the liquid of the icosahedral arrangements that characterize the crystal structures of boron but many atoms appear to adopt a geometry corresponding to the pentagonal pyramids of the crystalline phases. Despite similarities in the melting behavior of boron and silicon, there is little evidence of a significant structural shift with temperature that might suggest an eventual liquid-liquid phase transition. Relatively poor agreement with the observed damping of the sound excitations is obtained with the simple form of mode-coupling theory that has proved successful with other monatomic liquids, indicating that higher-order correlation functions arising from directional bonding and short-lived local structures are playing a crucial role. The large ratio of the high frequency to the isothermal sound velocity indicates a much stronger viscoelastic stiffening than in other monatomic liquids.