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.     

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [Nature (London) 381, 137 (1996)], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity.     

Configurational entropy of binary hard-disk glasses: nonexistence of an ideal glass transition

We study the thermodynamics of a binary hard-disk mixture in which the ratio of disk diameters is kappa=1.4. We use a recently developed molecular dynamics algorithm to calculate the free-volume entropy of glassy configurations and obtain the configurational entropy (degeneracy) of the supercompressed liquid as a function of density. We find that the configurational entropy of the glasses near the kinetic glass transition is very close to the mixing entropy, suggesting that the degeneracy is zero only for the phase-separated crystal. We explicitly construct an exponential number of jammed packings with densities spanning the spectrum from the accepted "amorphous" glassy state to the phase-separated crystal, thus showing that there is no ideal glass transition in binary hard-disk mixtures. This construction also demonstrates that the ideal glass, defined as having zero configurational entropy, is not amorphous, but instead is nothing more than a phase-separated crystal. This critique of the presumed existence of an ideal glass parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)]. We also perform free-energy calculations to determine the equilibrium phase behavior of the system. The calculations predict a first-order freezing transition at a density below the kinetic glass transition. However, this transition appears to be strongly kinetically suppressed and is not observed directly. New simulation techniques are needed in order to gain a more complete understanding of the thermodynamic and kinetic behavior of the binary disk mixture and, in particular, of the demixing process during crystallization.     

Inherent structures for soft long-range interactions in two-dimensional many-particle systems

We generate inherent structures, local potential-energy minima, of the "k-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the k-space overlap potential are stealthy (i.e., completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform (i.e., infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom χ that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of the inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat along the directions sampled, with wide shallow local minima and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the k-space overlap potential belongs.     

Gaussian excitations model for glass-former dynamics and thermodynamics

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter model to the experimental data on excess entropy and heat capacity shows that "fragile" behavior, indicated by a sharply rising excess heat capacity as the glass transition is approached from above, occurs in anticipation of a first-order transition--usually hidden below the glass transition--to a "strong" liquid state of low excess entropy. The distinction between fragile and strong behavior of glass formers is traced back to an order of magnitude difference in the Gaussian width of their excitation energies. Simple relations connect the excess heat capacity to the Gaussian width parameter, and the liquid-liquid transition temperature, and strong, testable, predictions concerning the distinct properties of energy landscape for fragile liquids are made. The dynamic model relates relaxation to a hierarchical sequence of excitation events each involving the probability of accumulating sufficient kinetic energy on a separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and the known correlation of kinetic with thermodynamic fragility, both follow from the way the rugged landscape induces fluctuations in the partitioning of energy between vibrational and configurational manifolds. A relation is derived in which the configurational heat capacity, rather than the configurational entropy of the Adam-Gibbs equation, controls the temperature dependence of the relaxation times, and this gives a comparable account of the experimental observations without postulating a divergent length scale. The familiar coincidence of zero mobility and Kauzmann temperatures is obtained as an approximate extrapolation of the theoretical equations. The comparison of the fits to excess thermodynamic properties of laboratory glass formers, and to configurational thermodynamics from simulations, reveals that the major portion of the excitation entropy responsible for fragile behavior resides in the low-frequency vibrational density of states. The thermodynamic transition predicted for fragile liquids emerges from beneath the glass transition in case of laboratory water and the unusual heat capacity behavior observed for this much studied liquid can be closely reproduced by the model.     

Validation of Markov state models using Shannon's entropy

Markov state models are kinetic models built from the dynamics of molecular simulation trajectories by grouping similar configurations into states and examining the transition probabilities between states. Here we present a procedure for validating the underlying Markov assumption in Markov state models based on information theory using Shannon's entropy. This entropy method is applied to a simple system and is compared with the previous eigenvalue method. The entropy method also provides a way to identify states that are least Markovian, which can then be divided into finer states to improve the model.     

Voronoi cell volume distribution and configurational entropy of hard-spheres

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume vf, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2gamma) or a three-parameter (3gamma) gamma distribution. The free parameter m in both the 2gamma and 3gamma models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of vf. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.     

Geometrical properties of the potential energy of the soft-sphere binary mixture

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K versus temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K versus energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.     

Waterlike structural and excess entropy anomalies in liquid beryllium fluoride

The relationship between structural order metrics and the excess entropy is studied using the transferable rigid ion model (TRIM) of beryllium fluoride melt, which is known to display waterlike thermodynamic anomalies. The order map for liquid BeF2, plotted between translational and tetrahedral order metrics, shows a structurally anomalous regime, similar to that seen in water and silica melt, corresponding to a band of state points for which average tetrahedral (q(tet)) and translational (tau) order are strongly correlated. The tetrahedral order parameter distributions further substantiate the analogous structural properties of BeF2, SiO2, and H2O. A region of excess entropy anomaly can be defined within which the pair correlation contribution to the excess entropy (S2) shows an anomalous rise with isothermal compression. Within this region of anomalous entropy behavior, q(tet) and S2 display a strong negative correlation, indicating the connection between the thermodynamic and the structural anomalies. The existence of this region of excess entropy anomaly must play an important role in determining the existence of diffusional and mobility anomalies, given the excess entropy scaling of transport properties observed in many liquids.     

Ab initio molecular orbital analysis of acetaldehyde dimers.: Thermodynamic properties

The surface of the acetaldehyde dimer was studied by MP2/6-31+G^* ab initio calculations and some of the minima thus located were used in subsequent optimizations and single-point calculations at the B3-LYP/6-311+G(2d,p), MP2/6-311+G(2d,p), MP2/aug-cc-pDVZ and MP2/aug-cc-pTVZ levels. An overall of six minima in two distinct groups were detected, one group consisting of planar configurations and the other of more stable, non-planar (spatial) configurations of the two monomers. Some of the dimer thermodynamic properties were calculated from its harmonic frequencies and a comparison between the experimental values for the thermodynamic properties and the calculated values is discussed.     

A thermodynamic approach to the fragility of glass-forming polymers

We have connected the dynamic fragility, namely, the steepness of the relaxation-time variation upon temperature reduction, to the excess entropy and heat capacity of a large number of glass-forming polymers. The connection was obtained in a natural way from the Adam-Gibbs equation, relating the structural relaxation time to the configurational entropy. We find a clear correlation for a group of polymers. For another group of polymers, for which this correlation does not work, we emphasize the role of relaxation processes unrelated to the alpha process in affecting macroscopic thermodynamic properties. Once the residual excess entropy at the Vogel temperature is removed from the total excess entropy, the correlation between dynamic fragility and thermodynamic properties is reestablished.     

Modelling of the phase transition of nanoscale confined liquid crystal

By dividing the bulk melting entropy, a simple thermodynamic model without any adjustable parameter for the size-dependent melting transition temperature has been extended to interpret the melting and freezing transitions of liquid crystals (LCs) confined in nanopores. The results show that as the size of the nanopore decreases, the melting, clearing and freezing transition temperatures of LCs drop. The transition temperatures directly depend on the density of hydrogen bond at the interface between inner pore wall and LC molecules. The model predictions agree well with the corresponding experimental results of LCs p-azoxyanisole and 4-pentyl-4′-cyanobiphenyl confined in nanopores.     

An interaction potential to study the thermal structure evolution of a thermoelectric material: β‐Cu2Se

An interaction potential model has been developed, for the first time, for β‐Cu₂Se using the ab initio derived data. The structure and elastic constants of β‐Cu₂Se using the derived force‐field are within a few percent of DFT derived structure and elastic constants and reported experimental structure. The derived force‐field also shows remarkable ability to reproduce temperature dependent behavior of the specific heat and thermal expansion coefficient. The thermal structure evolution of the β‐Cu₂Se is studied by performing the molecular dynamic simulations using the derived force‐field. The simulation results demonstrate that the Cu ions moves around the equilibrium lattice position within the temperature range of 500–800 K. However, at a temperature > 800 K, the Cu ions starts diffusing within the material, while the Se ions remains in their lattice position. The evaluated thermodynamic properties such as free energy and excess entropy, show that the increased Cu–Se interaction with the temperature makes the system more thermodynamically stable. © 2017 Wiley Periodicals, Inc.     

Freezing-in and production of entropy in vitrification

Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.     

Thermodynamic study of Ag<Subscript>8</Subscript>GeSe<Subscript>6</Subscript> by EMF with an Ag<Subscript>4</Subscript>RbI<Subscript>5</Subscript> solid electrolyte

The Ag–Ge–Se system was studied in the range of compositions Ag₂Se–GeSe₂–Se by measuring the EMF of the concentration (relative to the silver electrode) circuits with a solid electrolyte Ag₄RbI₅ in the temperature range 290–430 K. The polymorphic transition temperature of Ag₈GeSe₆ (320 K) was determined and the partial molar functions of silver were calculated for both crystal modifications of this compound based on the EMF measurements. The thermodynamic functions of formation and entropy of both modifications of Ag₈GeSe₆ and the thermodynamic functions of its polymorphic transition were calculated.     

Correlations among residual multiparticle entropy, local atomic-level pressure, free volume and the phase-ordering rule in several liquids

A modified Wang-Landau density-of-states sampling approach has been performed to calculate the excess entropy of liquid metals, Lennard-Jones (LJ) system and liquid Si under NVT conditions; and it is then the residual multiparticle entropy (S(RMPE)) is obtained by subtraction of the pair correlation entropy. The temperature dependence of S(RMPE) has been investigated along with the temperature dependence of the local atomic-level pressure and the pair correlation functions. Our results suggest that the temperature dependence of the pair correlation entropy is well described by T(-1) scaling while T(-0.4) scaling well describes the relationship between the excess entropy and temperature. For liquid metals and LJ system, the -S(RMPE) versus temperature curves show positive correlations and the -S(RMPE) of liquid Si is shown to have a negative correlation with temperature, the phase-ordering criterion (based on the S(RMPE)) for predicting freezing transition works in liquid metals and LJ but fails in liquid Si. The local atomic-level pressure scaled with the virial pressure (σ(al)/σ(av)) exhibits the much similar temperature dependence as -S(RMPE) for all studied systems, even though simple liquid metals and liquid Si exhibit opposite temperature dependence in both σ(al)/σ(av) and -S(RMPE). The further analysis shows that the competing properties of the two effects due to localization and free volume on the S(RMPE) exist in simple liquid metals and LJ system but disappear in liquid Si, which may be the critical reason of the failure of the phase-ordering criterion in liquid Si.     

Entropy studies in interface science: An ageless tool

It is possible to obtain (excess) interfacial entropies from the temperature dependence of some characteristic surface parameter. Such excess entropies contain much valuable information. Their studies lead to deeper insight into the interfacial properties. In some cases, quite unexpected results are obtained. In the present paper, we shall consider three illustrations: (1) the surface excess entropy of the electrical double layer on silver iodide, (2) the surface excess entropy of the interface between air and electrolyte solutions and (3) the surface excess entropy of Langmuir polymeric monolayers. Their analysis starts with defining this characteristic parameter and measuring its temperature dependence, followed by a brief thermodynamic analysis to obtain the sought entropy.Given the generality of this methodology, its applicability is likely to be extended to a variety of other interfacial properties, in particular when competition between electric and non-electric forces plays a role as in self-assembly, hydrophobic bonding and polyelectrolytes.     

Prediction of excess thermodynamic functions and activity coefficients of some polymeric liquid mixtures using a new equation of state

In this work, the excess thermodynamic properties, namely excess molar Gibbs energy, excess molar enthalpy, excess molar entropy, excess molar internal energy, and excess molar Helmholtz energy for four polymer mixtures and blends at different temperatures, pressures, and compositions have been calculated using the GMA equation of state. We have also calculated the activity coefficient for these polymeric mixtures using the GMA equation of state. The values of statistical parameters between experimental and calculated properties show the ability of this equation of state in reproducing and predicting the excess thermodynamic functions and activity coefficients for studied polymeric mixtures.