Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.     

Solid-liquid transitions of sodium chloride at high pressures

We investigate solid-liquid transitions in NaCl at high pressures using molecular dynamics simulations, including the melting curve and superheating/supercooling as well as solid-solid and liquid-liquid transitions. The first-order B1-B2 (NaCl-CsCl type) transition in solid is observed at high pressures besides continuous liquid structure transitions, which are largely analogous to the B1-B2 transition in solid. The equilibrium melting temperatures (T(m)) up to megabar pressure are obtained from the solid-liquid coexistence technique and the superheating-supercooling hysteresis method. Lindemann's vibrational and Born's mechanical instabilities are found upon melting. The Lindemann frequency is calculated from the vibrational density of states. The Lindemann parameter (fractional root-mean-squared displacement) increases with pressure and approaches a constant asymptotically, similar to the Lennard-Jones system. However, the Lindemann melting relation holds for both B1 and B2 phases to high accuracy as for the Lennard-Jonesium. The B1 and B2 NaCl solids can be superheated by 0.18T(m) and 0.24T(m), and the NaCl liquid, supercooled by 0.22T(m) and 0.32T(m), respectively, at heating or cooling rates of 1 K/s and 1 K/ps. The amount of maximum superheating or supercooling and its weak pressure dependence observed for NaCl are in accord with experiments on alkali halides and with simulations on the Lennard-Jones system and Al.     

Molecular dynamics simulations of the melting of aluminum nanoparticles

Molecular dynamics simulations are performed to determine the melting points of aluminum nanoparticles of 55-1000 atoms with the Streitz-Mintmire [Phys. Rev. B 1994, 50, 11996] variable-charge electrostatic plus potential. The melting of the nanoparticles is characterized by studying the temperature dependence of the potential energy and Lindemann index. Nanoparticles with less than 850 atoms show bistability between the solid and liquid phases over temperature ranges below the point of complete melting. The potential energy of a nanoparticle in the bistable region alternates between values corresponding to the solid and liquid phases. This bistability is characteristic of dynamic coexistence melting. At higher temperatures, only the liquid state is stable. Nanoparticles with more than 850 atoms undergo a sharp solid-liquid-phase transition characteristic of the bulk solid phase. The variation of the melting point with the effective nanoparticle radius is also determined.     

高压下MgO熔化特性的分子动力学模拟

Molecular dynamics simulation was used to study the melting of MgO at high pressures. The melting temperature of MgO was accurately obtained at elevated temperature and high pressure after corrections based on the modern theory of melting. The calculated melting curve was compared with the available experimental data and other theoretical results at the pressure range of 0-135 GPa. The corrected melting temperature of MgO is in good agreement with the results from Lindemann melting equation and the twophase simulated results below 15 GPa.     

Dynamics and structural changes of small water clusters on ionization

Despite utmost importance in understanding water ionization process, reliable theoretical results of structural changes and molecular dynamics (MD) of water clusters on ionization have hardly been reported yet. Here, we investigate the water cations [(H₂O)_{n = 2–6}⁺] with density functional theory (DFT), Möller–Plesset second‐order perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. The complete basis set limits of interaction energies at the CCSD(T) level are reported, and the geometrical structures, electronic properties, and infrared spectra are investigated. The characteristics of structures and spectra of the water cluster cations reflect the formation of the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. Although most density functionals fail to predict reasonable energetics of the water cations, some functionals are found to be reliable, in reasonable agreement with high‐level ab initio results. To understand the ionization process of water clusters, DFT‐ and MP2‐based Born‐Oppenheimer MD (BOMD) simulations are performed on ionization. On ionization, the water clusters tend to have an Eigen‐like form with the hydronium cation instead of a Zundel‐like form, based on reliable BOMD simulations. For the vertically ionized water hexamer, the relatively stable (H₂O)₅⁺ (5sL4A) cluster tends to form with a detached water molecule (H₂O). © 2013 Wiley Periodicals, Inc.     

Molecular dynamics simulations of melting and the glass transition of nitromethane

Molecular dynamics simulations have been used to investigate the thermodynamic melting point of the crystalline nitromethane, the melting mechanism of superheated crystalline nitromethane, and the physical properties of crystalline and glassy nitromethane. The maximum superheating and glass transition temperatures of nitromethane are calculated to be 316 and 160 K, respectively, for heating and cooling rates of 8.9 x 10(9) Ks. Using the hysteresis method [Luo et al., J. Chem. Phys. 120, 11640 (2004)] and by taking the glass transition temperature as the supercooling temperature, we calculate a value of 251.1 K for the thermodynamic melting point, which is in excellent agreement with the two-phase result [Agrawal et al., J. Chem. Phys. 119, 9617 (2003)] of 255.5 K and measured value of 244.73 K. In the melting process, the nitromethane molecules begin to rotate about their lattice positions in the crystal, followed by translational freedom of the molecules. A nucleation mechanism for the melting is illustrated by the distribution of the local translational order parameter. The critical values of the Lindemann index for the C and N atoms immediately prior to melting (the Lindemann criterion) are found to be around 0.155 at 1 atm. The intramolecular motions and molecular structure of nitromethane undergo no abrupt changes upon melting, indicating that the intramolecular degrees of freedom have little effect on the melting. The thermal expansion coefficient and bulk modulus are predicted to be about two or three times larger in crystalline nitromethane than in glassy nitromethane. The vibrational density of states is almost identical in both phases.     

Multipolar electrostatics for proteins: Atom–atom electrostatic energies in crambin

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom‐atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom‐atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ?_A+ ?_B + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom‐atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug‐cc‐pVTZ and MP2/aug‐cc‐pVTZ levels are only slightly larger than those calculated at HF/6‐31G(d,p) level. This convergence behavior is transferable to the well‐known amyloid beta polypeptide Aβ_1–42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance. © 2013 Wiley Periodicals, Inc.     

Vibrational density of states and Lindemann melting law

We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter delta(L) (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of delta(L) with pressure is non-negligible: delta(L) is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for delta(L), these values are about 0.067 (+/-0.002) and 0.084 (+/-0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of delta(L) suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.     

Lindemann measures for the solid-liquid phase transition

A set of Lindemann measures, based on positional deviations or return distances, defined with respect to mechanically stable inherent structure configurations, is applied to understand the solid-liquid phase transition in a Lennard-Jones-type system. The key quantity is shown to be the single-particle return distance-squared distribution. The first moment of this distribution is related to the Lindemann parameter which is widely used to predict the melting temperature of a variety of solids. The correlation of the single-particle return distance and local bond orientational order parameter in the liquid phase provides insights into mechanisms for melting. These generalized Lindemann measures, especially the lower order moments of the single-particle return distance distribution, show clear signatures of the transition of the liquid from the stable to the metastable, supercooled regime and serve as landscape-based indicators of the thermodynamic freezing transition for the Lennard-Jones-type system investigated.     

Grcarma: A fully automated task‐oriented interface for the analysis of molecular dynamics trajectories

We report the availability of grcarma, a program encoding for a fully automated set of tasks aiming to simplify the analysis of molecular dynamics trajectories of biological macromolecules. It is a cross‐platform, Perl/Tk‐based front‐end to the program carma and is designed to facilitate the needs of the novice as well as those of the expert user, while at the same time maintaining a user‐friendly and intuitive design. Particular emphasis was given to the automation of several tedious tasks, such as extraction of clusters of structures based on dihedral and Cartesian principal component analysis, secondary structure analysis, calculation and display of root‐mean‐square deviation (RMSD) matrices, calculation of entropy, calculation and analysis of variance–covariance matrices, calculation of the fraction of native contacts, etc. The program is free‐open source software available immediately for download. © 2013 Wiley Periodicals, Inc.     

Structures and electronic properties of the small rubidium‐doped silicon RbSin (n = 1–12) clusters

The geometries, relative stabilities, and electronic properties of small rubidium‐doped silicon clusters RbSi_n (n = 1–12) have been systematically investigated using the density functional theory at the B3LYP/GENECP level. The optimized structures show that lowest‐energy isomers of RbSi_n are similar with the ground state isomers of pure Si_n clusters and prefer the three‐dimensional for n = 3–12. The relative stabilities of RbSi_n clusters have been analyzed on the averaged binding energy, fragmentation energy, second‐order energy difference, and highest occupied molecular orbital‐lowest unoccupied molecular orbital energy gap. The calculated results indicate that the doping of Rb atom enhances the chemical activity of Si_n frame and the magic number is RbSi₂. The Mulliken population analysis reveals that the charges in the corresponding RbSi_n clusters transfer from the Rb atom to Si atoms. The partial density of states and chemical hardness are also discussed. © 2014 Wiley Periodicals, Inc.     

Simulations of the solid, liquid, and melting of 1-n-butyl-4-amino-1,2,4-triazolium bromide

Molecular dynamics simulations are used to study the solid and liquid properties and to predict the melting point of 1-n-propyl-4-amino-1,2,4-triazolium bromide ([patr][Br]) using a force field based on the one developed by Canongia Lopes et al. (J. Phys. Chem. B 2004, 108, 2038) for dialkyl substituted imidazolium salts, which was modified by including terms from the general AMBER force field. Electrostatic charges for the intermolecular interactions were determined from gas-phase ab initio electron structure calculations of the triazolium cation. Simulations of the solid state at 100 K reproduced the experimental density to within 4%. Simulations from 100 K to the melting point and the liquid from 333 to 500 K were performed to determine the temperature dependence of the densities of the two phases. The structures of the solid and liquid phases are characterized with radial distribution functions, which show that there are strong spatial correlations among neighboring ion pairs in liquid [patr][Br]. The dynamic behavior of the ions in the liquid state is also studied by computing velocity autocorrelation functions and the mean-square displacements between the ions. The melting point is determined by simulating void-induced melting. Changes in the density, intermolecular energy, and Lindemann index are used as indicators of the melting transition. The computed melting point is 360 +/- 10 K, which is within 10% of the experimental value 333 K.     

The glass transition temperature of polymer melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.     

自由表面的Ni原子团簇的熔化

采用分子动力学模拟技术研究了不同尺寸的Ni原子团簇的熔化过程.团簇的最初构型为FCC结构.研究结果表明,原子团簇的熔化温度与原子团簇中原子的个数有关,团簇的熔化首先从表面开始,当外层原子成为液态后,整个团簇的熔化从液态层开始,直至核心区域.该熔化过程可以被称为非均质熔化,自由表面充当非均质形核位置.作为对比,对无自由表面的大块固态Ni的熔化过程也进行了模拟,其熔化温度高于实验温度约400 K.表明对无自由表面的大块固态的熔化过程,液相形成无非均质形核位置,熔化的本质过程受均质形核机理控制.     

Size dependent melting mechanisms of iron nanoclusters

Molecular dynamics simulations were used to study the change in the mechanism of iron cluster melting with increasing cluster size. Melting of smaller clusters (e.g., Fe₅₅ and Fe₁₀₀) occurs over a large temperature interval where the phase of the cluster repeatedly oscillates between liquid and solid. In contrast, larger clusters (e.g., Fe₃₀₀) have sharper melting points with surface melting preceding bulk melting. The importance of the simulation time, the force field and the definition of cluster melting is also discussed.     

Pressure‐induced amorphization and disordering on cooling in semi‐crystalline polymers: calorimetric evidence for inverse melting in one component system

We report some unusual phase behaviour, of general implication for condensed matter, on the polymer poly‐4‐methyl pentene‐1 (P4MP1) induced by changes in pressure (P) and temperature (T), as observed by in‐situ X‐ray diffraction and high pressure DSC. Upon increasing pressure beyond a threshold value, the polymer, crystalline at ambient conditions, looses its crystalline order isothermally. The process is reversible. This behaviour is observed in two widely separated temperature regions, one below the glass transition temperature (< 50°C) and one close to the melting temperature (250°C), thus showing solid state amorphization and inversion in the melting temperature with increasing pressure. This further suggests inverse melting, i.e. re‐entrant of the two widely separated liquid and amorphous phases along the T‐axis at fixed P. This is confirmed experimentally as disordering in the crystalline structure on cooling. The inverse melting in P4MP1 raises the possibility of exothermic melting and endothermic crystallization as anticipated by Tammann (1903), see reference 1. The anticipated exothermic melting and endothermic crystallization is confirmed experimentally in the one component system P4MP1. We are observing similar features in a range of polymers.     

Metal clusters that freeze into high energy geometries

Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.     

Exact statistical mechanical lattice model and classical Lindemann theory of melting of inert gas solids

A modified form of Lindemann’s model shows that the melting points of the heavy inert gases and other effectively spherical molecular species are proportional to the depths of their diatomic potential wells. The success of the model when compared with experiment seems to rely on the almost constant value of the ratio of the fractional volume and entropy changes during fusion. The Lindemann proposal can be incorporated into an exactly treated statistical mechanical lattice model utilising expandable clusters which reproduces the solid–liquid melting phenomenon for argon with a realistic volume change and melting line.