Anomalous Thermodynamics Research Articles

An entropy trap model of thermodynamic anomalies for dual-amorphous water undergoing liquid-liquid phase transition

Water displays numerous anomalously thermodynamic behaviors. However, the working principles behind these anomalies are not well understood, and the liquid-liquid phase transition (LLPT) is often regarded as the potential reason. In this study, we developed an entropy trap model to characterize the thermodynamic LLPT in dual-amorphous water, i.e. having both low-density and high-density liquid water. From the Adam-Gibbs model and free-volume theory, thermodynamic behaviors of water have been described using the proposed model, in which the constitutive relationships among density, heat capacity, thermal expansivity and glass transition temperature have been formulated. Moreover, the glass transition and its connection to thermodynamic behaviors were also investigated for dual-amorphous water. Finally, experimental data reported in the literature were used to verify effectiveness of the proposed model. This study is expected to provide a physical insight into the anomalous thermodynamics of dual-amorphous water undergoing the LLPT.

Statistical-mechanical liquid theories reproduce anomalous thermodynamic properties of explicit two-dimensional water models.

We have developed an analytical theory for a simple model of liquid water. We apply Wertheim's thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the rose model, which is among the simplest models of water. The particles interact through rose potentials for orientation dependent pairwise interactions. Modifying both the shape and range of a three-petal rose function, we construct an efficient and dynamical mimic of the two-dimensional (2D) Mercedes-Benz (MB) water model. The particles in 2D MB are 2D Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz logo. Both models qualitatively predict both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation functions at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

Anomalous thermodynamics in a mixed spin-1/2 and spin-1 hexagonal nanowire system

The mixed spin-1/2 Ising model and spin-1 Blume–Capel model in an hexagonal nanowire structure under the presence of crystal field is considered. The free energy is obtained through the transfer matrix technique, which is solved numerically. Our main result lies in the presence of pseudo-transition in low temperature region near the ferrimagnetic/ferromagnetic boundary, due to the influence of a crystal field. The evidence of a pseudo-transition is observed in several quantities. Free energy first derivative quantities like entropy and internal energy show an abrupt but continuous jump, whereas quantities associated with second derivatives of the free energy like the specific heat exhibit a strong sharp peak, quite similar to a second order phase transition. We also investigate magnetization patterns and do not find evidence of spontaneous magnetization. Nevertheless, assuming a small magnetic field, we can induce a magnetization which resembles a spontaneous magnetization at a pseudo-critical temperature.

A quantum magnetic analogue to the critical point of water.

At the liquid-gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point1, a concept ubiquitous in statistical thermodynamics2. In correlated quantum materials, it was predicted3 and then confirmed experimentally4,5 that a critical point terminates the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions6 have been controlled by pressure7,8, applied magnetic field9,10 and disorder11, but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu2(BO3)2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model12-14 and displays exotic phenomena including magnetization plateaus15, low-lying bound-state excitations16, anomalous thermodynamics17 and discontinuous quantum phase transitions18,19. Here we control both the pressure and the magnetic field applied to SrCu2(BO3)2 to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure-temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods17,20-22. These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties23,24 that are useful for spintronic applications.

Anomalous thermodynamics in homogenized generalized Langevin systems

We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where one or more of the inertial time scale(s), the memory time scale(s) and the noise correlation time scale(s) of the systems are taken to zero. We find that, unless one restricts to special situations that do not break symmetry of the Onsager matrix associated with the fast dynamics, it is generally not possible to express the effective evolution of these functionals solely in terms of trajectory of the homogenized process describing the system dynamics via the widely adopted Stratonovich convention. In fact, an anomalous term is often needed for a complete description, implying that convergence of these functionals needs more information than simply the limit of the dynamical process. We trace the origin of such impossibility to area anomaly, thereby linking the symmetry breaking and area anomaly. This hold important consequences for many nonequilibrium systems that can be modeled by generalized Langevin equations. Our convergence results hold in a strong pathwise sense.

Anomalous thermodynamics of a quantum spin system with large residual entropy

In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds $J_1$ and competing antiferromagnetic basal bonds $J_2$. At a quantum phase transition point $|J_2/J_1|=1/2$, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value $\lim_{T\to\infty} S(T)/N = \ln2$. In the present paper we study in detail the role of the spin quantum number $s$ and the magnetic field $H$ in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to $N=20$ lattice sites and the finite-temperature Lanczos method up to $N=36$ sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to $N=36$ allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin $s=1/2$, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.

Compaction-induced strengthening of intercalation within RNA double helices at high ionic strength of the medium: Spectral elucidation and anomalous thermodynamics

The present contribution attempts to unveil the interaction of a potential chloride channel- blocker, 9-methyl anthroate (9-MA) with double-stranded torula yeast RNA at varying ionic strength of the medium from spectroscopic and calorimetric standpoints. An intercalative mode of binding of the probe within the RNA duplex; the respective proportion of the intercalated probe and the corresponding affinity of association being functions of the ionic strength of the medium are ascertained from spectroscopic results. However, the straightforward exothermic thermodynamic profile of the probe-RNA interaction in aqueous buffer develops notable complexity at a high ionic strength of the medium, revealing the presence of two radically different thermodynamic affairs. Although the exothermic event seems readily attributable to the intercalation phenomenon itself, the unexpected endothermic signature has been argued to be the proliferation of the compaction and/or aggregation of the RNA at a high ionic strength of the medium.

Water anomalous thermodynamics, attraction, repulsion, and hydrophobic hydration.

A model composed of van der Waals-like and hydrogen bonding contributions that simulates the low-temperature anomalous thermodynamics of pure water while exhibiting a second, liquid-liquid critical point [P. H. Poole et al., Phys. Rev. Lett. 73, 1632 (1994)] is extended to dilute solutions of nonionic species. Critical lines emanating from such second critical point are calculated. While one infers that the smallness of the water molecule may be a relevant factor for those critical lines to move towards experimentally accessible regions, attention is mainly focused on the picture our model draws for the hydration thermodynamics of purely hydrophobic and amphiphilic non-electrolyte solutes. We first focus on differentiating solvation at constant volume from the corresponding isobaric process. Both processes provide the same viewpoint for the low solubility of hydrophobic solutes: it originates from the combination of weak solute-solvent attractive interactions and the specific excluded-volume effects associated with the small molecular size of water. However, a sharp distinction is found when exploring the temperature dependence of hydration phenomena since, in contrast to the situation for the constant-V process, the properties of pure water play a crucial role at isobaric conditions. Specifically, the solubility minimum as well as enthalpy and entropy convergence phenomena, exclusively ascribed to isobaric solvation, are closely related to water's density maximum. Furthermore, the behavior of the partial molecular volume and the partial molecular isobaric heat capacity highlights the interplay between water anomalies, attraction, and repulsion. The overall picture presented here is supported by experimental observations, simulations, and previous theoretical results.

Hydrophobicity and thermodynamic response for aqueous solutions of amphiphiles

The anomalous behavior of aqueous solutions of amphiphiles in the water-rich region is analyzed via a phenomenological approach that utilizes the isobaric heat capacity Cp as an experimental probe. We report extensive data for solutions of 14 amphiphiles as a function of temperature at atmospheric pressure. Beyond that, Cp data but also isobaric thermal expansivities and isothermal compressibilities for three solutions of tert-butanol as a function of both temperature and pressure are presented. Results rule out the possibility that the observed phenomenology is associated with the anomalous thermodynamics of pure water. Indeed, our Cp data, quantitatively consistent with recent spectroscopic analyses, suggest that water-mediated interactions between the nonpolar parts of amphiphiles are at the origin of anomalies, with the effects of such “hydrophobic aggregation” being observed at mole fractions as small as 0.01. Physicochemical details like the size, the electronic charge distribution and the geometry of amphiphile molecules as well as third-order derivatives of the Gibbs energy and the associated Koga lines support the above claims while they further contribute to characterizing the role of hydrophobicity in these phenomena. Progress with a view to gain a deeper, more concrete understanding remains.

Entropic phase transitions and accompanying anomalous thermodynamics of matter

Thermodynamic consequences of subdivision for all first-order phase transitions (PT) into enthalpy- and entropy-driven ones (H-PT and S-PT), proposed previously [arXiv:1403.8053], are under discussions. Key-value for proposed discrimination is main benefit (decreasing) in enthalpy or (nega)entropy in spontaneous phase decomposition, i.e. the sign of latent heat of PT and consequent slope of its P(T)-dependence. The main driving mechanism for many isostructural S-PT is the decay (delocalization) of some kind of bound complexes, e.g. atoms, molecules etc. Thermodynamic features of H-PT and S-PT differ significantly. Entropic PT are always the part of more general thermodynamic anomaly—domain where great number of usually positive second cross derivatives (e.g. Grüneisen parameter, thermal pressure coefficient etc.) became negative simultaneously. This domain is restricted (in the case of isostructural S-PT) by remarkable bound, where all mentioned second derivatives are equal to zero. Isostructural S-PT has more complicated topology of stable, metastable and unstable states and their boundaries—binodals and spinodals in comparison with ordinary enthalpic PTs. Two new thermodynamic objects accompany isostructural S-PT: (i) appearance of third (additional) region of metastable states with positive compressibility, isolated from the regions of stable states; (ii) appearance of new additional spinodal, topped with a new singular point, separating metastable and unstable states. These additional spinodal and singular point obey to relation (∂P/∂V)T = ∞. All thermodynamic anomalies of entropic PTs correspond to conclusive and transparent geometrical feature of such PTs: multilayered structure of thermodynamic surfaces for temperature, entropy and internal energy as pressure- density functions U(P, V), S(P, V) and T(P, V).

Phase diagram of neutron-rich nuclear matter and its impact on astrophysics

Dense matter as it can be found in core-collapse supernovae and neutron stars is expected to exhibit different phase transitions which impact the matter composition and the equation of state, with important consequences on the dynamics of core-collapse supernova explosion and on the structure of neutron stars. In this paper we will address the specific phenomenology of two of such transitions, namely the crust-core solid-liquid transition at sub-saturation density, and the possible strange transition at super-saturation density in the presence of hyperonic degrees of freedom. Concerning the neutron star crust-core phase transition at zero and finite temperature, it will be shown that, as a consequence of the presence of long-range Coulomb interactions, the equivalence of statistical ensembles is violated and a clusterized phase is expected which is not accessible in the grand-canonical ensemble. A specific quasi-particle model will be introduced to illustrate this anomalous thermodynamics and some quantitative results relevant for the supernova dynamics will be shown. The opening of hyperonic degrees of freedom at higher densities corresponding to the neutron stars core modifies the equation of state. The general characteristics and order of phase transitions in this regime will be analyzed in the framework of a self-consistent mean-field approach.

Hydrophobic Segregation, Phase Transitions and the Anomalous Thermodynamics of Water/Methanol Mixtures

When water and methanol are mixed, the entropy of mixing decreases, whereas mixing simple liquids normally leads to an increase in entropy. One speculation on the origin of the anomaly involves formation of water icebergs next to the hydrophobic methanol group, while more recent theories point to nanoscale clustering of methanol molecules. To elucidate the origin of this effect, we carried out extensive molecular dynamics calculations on water/methanol mixtures ranging from 0 to 100% and applied the 2PT method to extract the entropy and free energy changes of each component as a function of concentration. We find that water molecules lose at most 1/35 of their liquid entropy in mixtures. Methanol molecules, on the other hand, lose 3 times as much entropy as the water molecules, and their rotational entropy contains the signature of the entropic loss. We find that methanol has a discontinuous specific heat profile in these mixtures with a maximum at 40% methanol. These results do not support the iceberg model of immobilized waters and instead suggests a molecular mechanism of hydrophobic segregation at low methanol concentration where ordering of the methanol molecules bury the hydrophobic group away from the water phase. For higher methanol concentrations, there is insufficient water to accomplish this effect, and the system freely mixes and transitions to one better described as water dissolved into methanol.

Structural transformation in supercooled water controls the crystallization rate of ice

One of water's unsolved puzzles is the question of what determines the lowest temperature to which it can be cooled before freezing to ice. The supercooled liquid has been probed experimentally to near the homogeneous nucleation temperature, T(H) ≈ 232 K, yet the mechanism of ice crystallization-including the size and structure of critical nuclei-has not yet been resolved. The heat capacity and compressibility of liquid water anomalously increase on moving into the supercooled region, according to power laws that would diverge (that is, approach infinity) at ~225 K (refs 1, 2), so there may be a link between water's thermodynamic anomalies and the crystallization rate of ice. But probing this link is challenging because fast crystallization prevents experimental studies of the liquid below T(H). And although atomistic studies have captured water crystallization, high computational costs have so far prevented an assessment of the rates and mechanism involved. Here we report coarse-grained molecular simulations with the mW water model in the supercooled regime around T(H) which reveal that a sharp increase in the fraction of four-coordinated molecules in supercooled liquid water explains its anomalous thermodynamics and also controls the rate and mechanisms of ice formation. The results of the simulations and classical nucleation theory using experimental data suggest that the crystallization rate of water reaches a maximum around 225 K, below which ice nuclei form faster than liquid water can equilibrate. This implies a lower limit of metastability of liquid water just below T(H) and well above its glass transition temperature, 136 K. By establishing a relationship between the structural transformation in liquid water and its anomalous thermodynamics and crystallization rate, our findings also provide mechanistic insight into the observed dependence of homogeneous ice nucleation rates on the thermodynamics of water.

Anomalous thermodynamics of the doped Mott-Hubbard insulators

The concentration dependence of the entropy of doped Mott-Hubbard insulators has been considered within the t-J model. It has been shown that a change in the type and statistics of charge carriers as compared to the Fermi gas leads to a radical change in the entropy s, in particular, to the giant growth of the entropy upon doping. The quantity ∂s/∂x ≈ kB is approximately consistent with the experimental data for HTSC cuprates in the pseudogap phase.

Small-angle scattering and the structure of ambient liquid water

Structural polyamorphism has been promoted as a means for understanding the anomalous thermodynamics and dynamics of water in the experimentally inaccessible supercooled region. In the metastable liquid region, theory has hypothesized the existence of a liquid-liquid critical point from which a dividing line separates two water species of high and low density. A recent small-angle X-ray scattering study has claimed that the two structural species postulated in the supercooled state are seen to exist in bulk water at ambient conditions. We analyze new small-angle X-ray scattering data on ambient liquid water taken at third generation synchrotron sources, and large 32,000 water molecule simulations using the TIP4P-Ew model of water, to show that the small-angle region measures standard number density fluctuations consistent with water's isothermal compressibility temperature trends. Our study shows that there is no support or need for heterogeneities in water structure at room temperature to explain the small-angle scattering data, as it is consistent with a unimodal density of the tetrahedral liquid at ambient conditions.

Anomalous thermodynamics and phase transitions in neutron star matter

The presence of the long-range Coulomb force in dense stellar matter implies that the total charge cannot be associated with a chemical potential, even if it is a conserved quantity. As a consequence, the analytical properties of the partition sum are modified, changing the order of the phase transitions and affecting the possible occurrence of critical behaviors. The peculiar thermodynamic properties of this system can be understood introducing a model Hamiltonian where each charge is independently neutralized by a uniform background of opposite charge. Some consequences on the characteristics of mixed-phase structures in neutron star crusts and supernova cores are discussed.

Raman spectroscopy of aqueous methanol solutions under pressure

Recently, Dixit et al. (2002) used neutron diffraction to probe the molecular-scale structure of a concentrated methanol–water mixture (7:3 molar ratio) under ambient conditions. Their results suggest that the anomalous thermodynamics of water–alcohol systems arises from incomplete mixing at the molecular level, i.e. most of the water molecules exist as small hydrogen-bonded strings and clusters in a fluid of close-packed methyl groups. The application of high hydrostatic pressure together with Raman spectroscopy is a powerful technique to detect such structural changes in associated systems. In this work, we present measurements of Raman spectra of water–methanol mixtures under pressure at room temperature. We have used an anvil cell device with sapphire anvils to generate pressures up to 10 kbar. Our results allow us to suggest important changes on the cluster distribution as a function of pressure.

Thermodynamics of volume-collapse transitions in cerium and related compounds

We present a non-linear elastic model of a coherent transition with discontinuous volume change in an isotropic solid. The model reproduces the anomalous thermodynamics typical of coherent equilibrium including intrinsic hysteresis (for a pressure driven experiment) and a negative bulk modulus. The novelty of the model is that the statistical mechanics solution can be easily worked out. We find that coherency leads to an infinite-range density–density interaction, which drives classical critical behavior. The pressure width of the hysteresis loop shrinks with increasing temperature, ending at a critical point at a temperature related to the shear modulus. The bulk modulus softens with a 1/2 exponent at the transition even far from the critical point. Many well known features of the phase diagram of Ce and related systems are explained by the model.

Thermodynamic behavior of a model covalent material described by the environment-dependent interatomic potential

Using molecular-dynamics simulations we study the thermodynamic behavior of a single-component covalent material described by the recently proposed environment-dependent interatomic potential (EDIP). The parametrization of EDIP for silicon exhibits a range of unusual properties typically found in more complex materials, such as the existence of two structurally distinct disordered phases, a density increase upon melting of the low-temperature amorphous phase, and negative thermal-expansion coefficients for both the crystal (at high temperatures) and the amorphous phase (at all temperatures). Structural differences between the two disordered phases also lead to a first-order transition between them, which suggests the existence of a second critical point, as is believed to exist for amorphous forms of frozen water. For EDIP-Si, however, the unusual behavior is associated not only with the open nature of tetrahedral bonding but also with a competition between fourfold (covalent) and fivefold (metallic) coordination. The unusual behavior of the model and its unique ability to simulate the liquid/amorphous transition on molecular-dynamics time scales make it a suitable prototype for fundamental studies of anomalous thermodynamics in disordered systems.

Molecular segregation observed in a concentrated alcohol-water solution.

When a simple alcohol such as methanol or ethanol is mixed with water, the entropy of the system increases far less than expected for an ideal solution of randomly mixed molecules. This well-known effect has been attributed to hydrophobic headgroups creating ice-like or clathrate-like structures in the surrounding water, although experimental support for this hypothesis is scarce. In fact, an increasing amount of experimental and theoretical work suggests that the hydrophobic headgroups of alcohol molecules in aqueous solution cluster together. However, a consistent description of the details of this self-association is lacking. Here we use neutron diffraction with isotope substitution to probe the molecular-scale structure of a concentrated alcohol water mixture (7:3 molar ratio). Our data indicate that most of the water molecules exist as small hydrogen-bonded strings and clusters in a 'fluid' of close-packed methyl groups, with water clusters bridging neighbouring methanol hydroxyl groups through hydrogen bonding. This behaviour suggests that the anomalous thermodynamics of water alcohol systems arises from incomplete mixing at the molecular level and from retention of remnants of the three-dimensional hydrogen-bonded network structure of bulk water.