Can experiments select the configurational component of excess entropy?

Configurational entropy is frequently used to rationalize the structural dynamics of glass-forming liquids. The main problem with this concept is that it is not directly accessible to experiments. We introduce a procedure to estimate the configurational component of the excess entropy of a liquid --specifically, the configurational-entropy contribution from the structural relaxation process-- through a combined investigation of dynamic and thermodynamic properties as functions of temperature and pressure. We test our method on orthoterphenyl, salol, and glycerol, and find that the fraction of excess entropy that arises from structural configurations is about 70% for all three materials.Received: 29 April 2004, Published online: 29 June 2004PACS: 64.70.Pf Glass transitions - 78.35. + c Brillouin and Rayleigh scattering; other light scattering - 77.22.Gm Dielectric loss and relaxation     

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamic and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the local minima energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.     

Temperature dependence of the configurational entropy of undercooled melts and the nature of glass transition

The configurational entropy as well as other related thermodynamic properties of a (poly)disperse glass-forming polymer melt have been calculated exactly in terms of a lattice-hole model and within the framework of the mean field approximation (MFA). One of the main results of the calculation, in which the average “stiffness” and the mean degree of polymerization (association) of the melt appear as temperature-dependent entities, is that for the first time a single analytical expression for the configurational entropy has been established which predicts a noncatastrophic behavior of the undercooled liquid. For certain, “realistic,” values of the energy parameters obtained, the results are consistent with previous theoretical and experimental investigations, although the entropy curve in the region of the supposed second-order phase transition (Gibbs and Di Marzio [1]) is considerably leveled off, and no abrupt changes of its derivatives are to be expected. Qualitative agreement with existing data is good, and ways for further refinement of the model are also discussed.     

Correlation of fragility with mechanical moduli in double-well potential for glass-forming liquid

The shoving model and the Vogel-Fulcher relation are employed to derive correlation of the fragility with the mechanical moduli for glass-forming simple liquids. The result shows that a liquid with smaller fragility will have larger ratio of K_∞/G_∞ in dilute liquid system. Based on radial distribution function with the Lennard-Jones potential modified by the Gaussian potential with a second minimum, fragility of the supercooled simple liquid is derived from the correlation between viscosity and shear modulus via configurational entropy. The results demonstrate that the fragility is determined by two parts: thermodynamic components and mechanical moduli. For a weak Gaussian potential liquid, the fragility is proportional to the T_g, while for a strong one, the fragility is inversely proportional to the T_g, and the Gaussian potential will increase fragility.     

Negative heat capacity of Ar55 cluster

The solid–liquid phase transitions of Ar₅₅ cluster was simulated by the microcanonical molecular dynamics and microcanonical parallel tempering methods using Lennard–Jones potential, and thermodynamic quantities were calculated. The caloric curve of cluster has S-bend. To understand this behaviour, configurational and total entropies were evaluated, and the dents on the entropy curves were noticed as the sign of negative heat capacity. The heat capacities were evaluated by using configurational entropy data. The potential energy distributions have bimodal behaviour in the given range at the melting temperature. At the same time by using configurational entropy canonical caloric curve and canonical heat capacity were calculated. To obtain entropy change upon melting, total entropy were calculated from the caloric curve. The microcanonical results melting temperature, latent heat and entropy change upon melting values were reported and compared with the values reported in the literature and the values calculated from the thermodynamic relations offered for bulk matter, consistent values were found.     

The relationship between kinetic and thermodynamic fragilities in metallic glass-forming liquids

The correlation between the temperature dependence of the kinetic and thermodynamic properties of a series of metallic glass-forming liquids is investigated using the concept of fragility. The results indicate a correlation between the kinetic fragility and thermodynamic fragility in these liquids. The correlation depends critically on the approach used to evaluate the thermodynamic fragility. Two distinct correlation lines are found for the metal–metalloid and for the all-metallic-constituents glass-forming liquids. For the same thermodynamic fragility the metal–metalloid liquids exhibit a distinctively larger kinetic fragility than the pure-metallic liquids. From the evaluation of the Gibbs free-energy difference between the undercooled liquid and the crystalline phase mixture, a correlation between the kinetic fragility and the driving force for nucleation is found, showing that for glass formation in metallic alloys the thermodynamic and kinetic contributions act together.     

Perturbation theory for non-axial molecular fluids

The thermodynamic perturbation theory in which all angle-dependent interactions are considered as a perturbation of the central potential is applied to study the equilibrium properties of a fluid composed of non-axial molecules. The influence of a large number of anisotropic pair and three-body non-additive interactions have been taken into account. Using the same set of force parameters the calculation is made for gaseous pressure second and third virial coefficients and liquid phase thermodynamic properties (Helmholtz free-energy, configurational energy, pressure and entropy). It is shown that the non-axial approximation is an improvement over the axial one. Excellent agreement between theory and experiment is obtained for ethylene.     

Potential energy landscape equation of state

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.     

Configurational entropy of systems with non-additive lateral interactions

The configurational entropy per site of a lattice gas model with non-additive interactions between adsorbed particles for square, triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the canonical ensemble by following the algorithm of parallel tempering and the thermodynamic integration method the configurational entropy per site has been calculated. By analyzing the behavior of the configurational entropy per site, the different low-temperature-ordered phases are described. The dependency of the critical temperature of the system as a function of characteristic parameters of the model is established.     

Anelastic to plastic transition in metallic glass-forming liquids

The configurational properties associated with the transition from anelasticity to plasticity in a transiently deforming metallic glass-forming liquid are studied. The data reveal that the underlying transition kinetics for flow can be separated into reversible and irreversible configurational hopping across the liquid energy landscape, identified with beta and alpha relaxation processes, respectively. A critical stress characterizing the transition is recognized as an effective Eshelby "backstress," revealing a link between the apparent anelasticity and the "confinement stress" of the elastic matrix surrounding the plastic core of a shear transformation zone.     

Conformational temperature characterizing the folding of a protein

The time sequences of the molecular dynamics simulation for the folding process of a protein is analyzed with the inherent structure landscape which focuses on the configurational dynamics of the system. Time-dependent energy and entropy for inherent structures are introduced, and from these quantities a conformational temperature is defined. The conformational temperature follows the time evolution of a slow relaxation process and reaches the bath temperature when the system is equilibrated. We show that the nonequilibrium system is described by two temperatures, one for fast vibration and the other for slow configurational relaxation, while the equilibrium system is described by one temperature. The proposed formalism is applicable widely for systems with many metastable states.     

Thermodynamic aspects of the glass transition of silicates

The marked increase in second-order thermodynamic properties observed at the glass-transition signals the onset of configurational changes in viscous liquids. Experimental determinations in the glass-transition range will illustrate this point for thermal expansivity and demonstrate that the kinetics of volume, enthalpy and structural relaxation are identical for silicate liquids. Within the framework of the Adam–Gibbs theory, heat capacity and viscosity data may be combined to calculate configurational entropies and gain insights into the potential energy barrier to viscous flow. Finally, the considerable effect of water on the glass transition temperature of geologically relevant silicates is presented.     

Structural phase transition in a large cluster

The effect of a phase transition between structures in a large cluster with a pair interatomic interaction on the thermodynamic parameters of the cluster is analyzed. The statistical parameters of a cluster consisting of 923 atoms are determined for an icosahedron and a face-centered cubic (fcc) structure. The specific heat and entropy of this cluster are calculated in the case when the transition between the icosahedron and fcc structures has the greatest effect on these parameters, so that at zero temperature this cluster has the structure of an icosahedron, and as the temperature increases to the melting point it assumes an fcc structure. Even with this, the contribution of the excitations of the atomic configurations to the thermodynamic parameters of a cluster is small compared with the excitation of vibrations in the cluster. The contribution of a configurational excitation in the thermodynamic parameters of a cluster becomes substantial for the liquid state of clusters.     

Diversity in liquid supercooling and glass formation phenomena illustrated by a simple model

The opportunity to map condensed-phase inherent structures (potential energy minima) approximately onto the vertices of a high-dimensional hypercube provides simple conceptual and numerical modeling for first-order melting-freezing transitions, as well as for liquid supercooling and glass formation phenomena. That approach is illustrated here by examination of three interaction examples that were selected to demonstrate the diversity of thermodynamic behavior possible within this hypercube modeling technique. Two of the cases behave, respectively, as "strong" and "fragile" glass formers, at least as judged by their heat capacities. The third presents a "degenerate glass," wherein full equilibration of the supercooling liquid (i.e., no kinetic arrest) leads to (a) residual entropy in the limit of absolute zero temperature, and (b) a linear temperature dependence of heat capacity in the same limit. None of the three cases displays a positive-temperature ideal (intrinsic) glass transition.     

Correlation between liquid structure and glass forming ability in glassy Ag-based binary alloys

The atomic structures of liquid Ag-based binary alloys have been investigated in the solidification process by means of X-ray diffraction. The results of liquid structure show that there is a break point in the mean nearest neighbor distance r1 and the coordination number Nmin for glass-forming liquid, while the correlation radius rc and the coordination number Nmin display a monotone variational trend above the break point. It means glass-forming liquids have a steady changing in structure above liquidus a...     

The Rise and Fall of Anomalies in Tetrahedral Liquids

The thermodynamic liquid-state anomalies and associated structural changes of the Stillinger-Weber family of liquids are mapped out as a function of the degree of tetrahedrality of the interaction potential, focusing in particular on tetrahedrality values suitable for modeling C, H₂O, Si, Ge and Sn. We show that the density anomaly, associated with a rise in molar volume on isobaric cooling, emerges at intermediate tetrahedralities (e.g. Ge, Si and H₂O) but is absent in the low (e.g. Sn) and high (e.g. C) tetrahedrality liquids. The rise in entropy on isothermal compression associated with the density anomaly is related to the structural changes in the liquid using the pair correlation entropy. An anomalous increase in the heat capacity on isobaric cooling exists at high tetrahedralities but is absent at low tetrahedralities (e.g. Sn). Structurally, this heat capacity anomaly originates in a sharp rise in the fraction of four-coordinated particles and local tetrahedral order in the liquid as its structure approaches that of the tetrahedral crystal.     

Possible link of the V-shaped phase diagram to the glass-forming ability and fragility in a water-salt mixture

Water is a very poor glass former, but its link to the thermodynamic and kinetic anomalies remains elusive. We experimentally reveal that the glass-forming ability and fragility of a water-salt mixture are closely related to its equilibrium phase diagram. We propose that frustration between local and global orderings controls both the glass-forming ability and the fragility. Relying on the same role of salt and pressure, which commonly break tetrahedral order, we apply this idea to pure water under pressure. This scenario not only explains unusual behavior of water-type liquids such as water, Si, and Ge but also provides a mechanism for a link between the equilibrium phase diagram, glass-forming ability, and fragility for various materials including oxides, chalcogenides, and metallic glasses.     

Reverse Monte Carlo study on structural order in liquid and glassy AlFe alloys

This paper reports that anomalous local order in liquid and glassy AlFeCe alloy has been detected by x-ray diffraction measurements. The addition of the element Ce has a great effect on this local structural order. The element Ce favours interpenetration of the icosahedra by sharing a common face and edges. It argues that frustration between this short-range order and the long-range crystalline order controls the glass-forming ability of these liquids. The obtained results suggest that a system having a stronger tendency to show local icosahedral order should be a better glass-former. This scenario also naturally explains the close relationship between the local icosahedral order in a liquid, glass-forming ability, and the nucleation barrier. Such topological local order has also been analysed directly using the reverse Monte Carlo method. It also estimated the fraction of local ordered and disordered structural units in a glassy AlFeCe alloy.