Connection between dynamics and thermodynamics of liquids on the melting line

Linking excess entropy and acentric factor in spherical fluids

Introduced by Pitzer in 1955, the acentric factor (ω) has been used to evaluate a molecule's deviation from the corresponding state principle. Pitzer devised ω based on a concept called perfect liquid (or centric fluid), a hypothetical species perfectly adhering to this principle. However, its physical significance remains unclear. This work attempts to clarify the centric fluid from an excess entropy perspective. We observe that the excess entropy per particle of centric fluids approximates -kB at their critical points, akin to the communal entropy of an ideal gas in classical cell theory. We devise an excess entropy dissection and apply it to model fluids (square-well, Lennard-Jones, Mie n-6, and the two-body ab initio models) to interpret this similarity. The dissection method identifies both centricity-independent and centricity-dependent entropic features. Regardless of the acentric factor, the attractive interaction contribution to the excess entropy peaks at the density where local density is most enhanced due to the competition between the local attraction and critical fluctuations. However, only in centric fluids does the entropic contribution from the local attractive potential become comparable to that of the hard sphere exclusion, making the centric fluid more structured than acentric ones. These findings elucidate the physical significance of the centric fluid as a system of particles where the repulsive and attractive contributions to the excess entropy become equal at its gas-liquid criticality. We expect these findings to offer a way to find suitable intermolecular potentials and assess the physical adequacy of equations of state.

Theory of melting lines

Our understanding of the three basic states of matter (solids, liquids, and gases) is based on temperature and pressure phase diagrams with three phase transition lines: solid-gas, liquid-gas, and solid-liquid lines. There are analytical expressions P(T) for the first two lines derived on a purely general-theoretical thermodynamic basis. In contrast, there exists no similar function for the third, melting, line (ML). Here, we develop a general two-phase theory of MLs and their analytical form. This theory predicts the parabolic form of the MLs for normal melting, relates the MLs to thermal and elastic properties of liquid and solid phases, and quantitatively agrees with experimental MLs in different system types. We show that the parameters of the ML parabola are governed by fundamental physical constants. In this sense, parabolic MLs possess universality across different systems.

Connecting Entropy Scaling and Density Scaling

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent appears to be related to the two-body interactions in the dilute-gas limit.

Synthesis and DFT Investigation of New Low-Melting Supramolecular Schiff Base Ionic Liquid Crystals

Supramolecular, low-melting (near or below 0.0 °C) ionic liquid crystals with two rings of Schiff bases were prepared and studied. The Schiff bases were synthesized using 4-substituted aniline derivatives and 4-pyridine carbaldehyde and then mixed in equimolar amounts with linear 1-bromoalkanes of different chain lengths, namely C6, C8, and C14. The mesomorphic behavior and thermal properties of the compounds were determined by polarized optical microscopy (POM) and differential scanning calorimetry (DSC). Only the ionic liquids analogous with 1-bromotetradecane exhibit mesomorphic behavior. All, except the smectic A (SmA) monomorphic fluorine-substituted complex, show dimorphic enantiotropic mesophases, namely SmA followed by nematic (N) mesophases depending on the temperature rise. The DSC and POM results for the induced mesophases were then treated with density functional theory calculations (DFT). The results showed that both the polarity of the polar groups and the length of the alkyl groups strongly influence the mesomorphic properties of the ionic liquids.

Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes

In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.

On the experimental determination of the repulsive component of the potential from high pressure measurements: What is special about twelve?

In this paper, we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent γ and argue that it exhibits the limiting behavior γ → 4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r) ∝ r^-n, γ has been found to be related to the exponent n via the relation γ = n/3. Therefore, this limiting behavior for γ would suggest that a large number of molecular systems may be described by a common repulsive potential U(r) ∝ r^-n with n ≈ 12.

Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry

Aspects of isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry are comparatively discussed on the basis of the Lennard-Jones potential. The first two approaches approximate the high-density fluid state well when the repulsive interparticle interactions become dominant, which is typically the case close to the freezing line. However, previous studies of Rosenfeld-Tarazona scaling for the isochoric heat capacity and its relation to isomorph theory reveal deviations for the temperature dependence. It turns out that a definition of a state region in which repulsive interactions dominate is required for achieving consistent results. The Riemannian thermodynamic scalar curvature R allows for such a classification, indicating predominantly repulsive interactions by R>0. An analysis of the isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona temperature scaling show that these approaches are consistent only in a small state region.

Communication: Effect of density on the physical aging of pressure-densified polymethylmethacrylate

The rate of physical aging of glassy polymethylmethacrylate (PMMA), followed from the change in the secondary relaxation with aging, is found to be independent of the density, the latter controlled by the pressure during glass formation. Thus, the aging behavior of the secondary relaxation is the same whether the glass is more compacted or less dense than the corresponding equilibrium liquid. This equivalence in aging of glasses formed under different pressures indicates that local packing is the dominant variable governing the glassy dynamics. The fact that pressure densification yields different glass structures is at odds with a model for non-associated materials having dynamic properties exhibited by PMMA, such as density scaling of the relaxation time and isochronal superposition of the relaxation dispersion.

The equation of state of polymers. Part III: Relation with the compensation law

The properties of amorphous polymers and of organic compounds under pressure are interpreted in the framework of the modified Van der Walls Equation of State (mVW-EOS) the Vogel-Fulcher-Tamann (VFT) law and of the compensation law. We have shown recently that polymers and organic compounds in amorphous liquid and crystalline states verify the mVW-EOS which depends on three parameters, [Formula: see text] [Formula: see text] and [Formula: see text]. In this paper we compare the characteristic pressure [Formula: see text] of the mVW-EOS to the various pressures [Formula: see text] deduced from thermodynamic and kinetic properties of polymers in the liquid and solid states. [Formula: see text] and [Formula: see text] are: a) the enthalpy and volume change at the melting and glass transitions (the glass being isotropic or oriented and annealed below [Formula: see text] at various aging conditions); b) the activation parameters of individual [Formula: see text] and cooperative [Formula: see text] motions in crystalline liquid and amorphous polymers studied by dielectric or mechanical spectroscopy; and c) the activation parameters of amorphous (solid and liquid) polymers submitted to a deformation depending on the time frequency temperature and strain rate. For a same material, whatever its state and whatever the experimental properties analyzed (dielectric and mechanical relaxation, viscosity, auto-diffusion, yielding under hydrostatic pressure), we demonstrate that [Formula: see text], ([Formula: see text] Grüneisen parameter, [Formula: see text] compressibility). In all polymers and organic compounds (and water), these pressures, weakly dependent on T and P near [Formula: see text] and [Formula: see text] at low pressure are characteristic of the H-H inter-molecular interactions. It is shown that the two empirical Lawson and Keyes relations of the compensation law can be deduced from the mVW-EOS.

A test for the existence of isomorphs in glass-forming materials

We describe a method to determine whether a material has isomorphs in its thermodynamic phase diagram. Isomorphs are state points for which various properties are invariant in reduced units. Such materials are commonly identified from strong correlation between thermal fluctuations of the potential energy, U, and the virial W, but this identification is not generally applicable to real materials. We show from molecular dynamic simulations of atomic, molecular, and polymeric materials that systems with strong U-W correlation cannot be pressure densified, that is, the density obtained on cooling to the glassy state and releasing the pressure is independent of the pressure applied during cooling.

Freezing and melting line invariants of the Lennard-Jones system

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of isomorph theory. First the freezing/melting lines of the LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phases. The structure is probed by the radial distribution function and the structure factor and dynamics are probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties with reference to isomorph theory explains why the known single-phase melting criteria hold, e.g., the Hansen-Verlet and the Lindemann criteria, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.

The Lennard-Jones melting line and isomorphism

The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.

The Modified VFT law of glass former materials under pressure: Part II: Relation with the equation of state

The dynamical properties of glass formers (GFs) as a function of P, V, and T are reanalyzed in relation with the equations of state (EOS) proposed recently (Eur. Phys. J. E 37, 113 (2014)). The relaxation times τ of the cooperative non-Arrhenius α process and the individual Arrhenius β process are coupled via the Kohlrausch exponent n S(T, P). In the model n S is the sigmoidal logistic function depending on T (and P, and the α relaxation time τ α of GFs above T g verifies the pressure-modified VFT law: log τ α ∼ E β /nsRT, which can be put into a form with separated variables: log τ α ∼ f(T)g(P). From the variation of n S and τ α with T and P the Vogel temperature T 0 (τ α → ∝, n S = 0) and the crossover temperature (also called the merging or splitting temperature) T B (τ α ∼ τ β, n S ∼ 1) are determined. The proposed sm-VFT equation fits with excellent accuracy the experimental data of fragile and strong GFs under pressure. The properties generally observed in organic mineral and metallic GFs are explained: a) The Vogel temperature is independent of P (as suggested by the EOS properties), the crossover is pressure-dependent. b) In crystallizable GFs the T B (P) and Clapeyron curves T m(P) coincide. c) The α and β processes have the same ratio of the activation energies and volume, E*/V* (T- and P-independent), the compensation law is observed, this ratio depends on the anharmonicity Slater-Grüneisen parameter and on the critical pressure P* deduced from the EOS. d) The properties of the Fan Structure of the Tangents (FST) to the isotherms and isobars curves log τ versus P and T and to the isochrones curves P(T). e) The scaling law log τ = f(V (Λ) ) and the relation between Γ and γ. We conclude that these properties should be studied in detail in GFs submitted to negative pressures.

Hidden scale invariance in condensed matter

Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.

Phase-dependent premelting of self-assembled phosphonic acid multilayers

Melting and premelting phenomena in self-organized organic systems have been extensively explored in the literature, exploring distinct behaviors of different molecule lengths and morphologies. Nevertheless, the influence of the supramolecular assembly configuration on the occurrence of premelting remains poorly explored. Here we use phosphonic acids as model systems for self-organized molecular assemblies. These molecules exhibit long-range order on different types of substrates. The balance between chain-to-chain and head-to-head interactions leads to distinct types of stackings. Although their structural configurations are well understood, very little is known about their behavior near the melting transition. We show here that premelting occurs in lamellar structures and that its behavior depends directly on the ordered configuration assumed in the studied multilayers. Two molecules with different chain lengths were investigated: octadecyl phosphonic and octyl phosphonic acids. Although almost no dependence on the molecule length was observed, the occurrence of premelting is strongly influenced by their lamellar packing configuration. For tilted packings premelting is unfavored while in straight configurations, where alkyl chain interactions are weakened with respect to head-to-head interactions, strong premelting is observed. We find that the onset of premelting occurs at the domain boundaries with straight lamellar configurations and the domain sizes exhibit power law temperature dependences.

Viscosity of methane to 6 GPa and 673 K

A rolling-sphere technique has been used to measure shear viscosities of (supercritical) fluid methane in a diamond-anvil cell between temperatures of 294 and 673 K, up to a pressure of 6 GPa. A correlation between a reduced viscosity and reduced residual entropy is shown to give a good account of much of the extant data, both from this study and the literature.