Freezing Line Research Articles

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.

Freezing lines of colloidal Yukawa spheres. II. Local structure and characteristic lengths.

Using the Rogers-Young (RY) integral equation scheme for the static pair correlation functions combined with the liquid-phase Hansen-Verlet freezing rule, we study the generic behavior of the radial distribution function and static structure factor of monodisperse charge-stabilized suspensions with Yukawa-type repulsive particle interactions at freezing. In a related article, labeled Paper I [J. Gapinski, G. Nägele, and A. Patkowski, J. Chem. Phys. 136, 024507 (2012)], this hybrid method was used to determine two-parameter freezing lines for experimentally controllable parameters, characteristic of suspensions of charged silica spheres in dimethylformamide. A universal scaling of the RY radial distribution function maximum is shown to apply to the liquid-bcc and liquid-fcc segments of the universal freezing line. A thorough analysis is made of the behavior of characteristic distances and wavenumbers, next-neighbor particle coordination numbers, osmotic compressibility factor, and the Ravaché-Mountain-Streett minimum-maximum radial distribution function ratio.

Factors controlling the ice nucleating abilities of α‐pinene SOA particles

AbstractThe ice nucleation abilities of fresh, water‐soluble, internally mixed, and photochemically oxidized α‐pinene secondary organic aerosol (SOA) particles were investigated at cirrus cloud temperatures in a continuous flow diffusion chamber. SOA sampled from a flow tube (SOA‐fresh‐FT) mimicked freshly generated particles, while the water‐soluble organic compound fraction from a FT and smog chamber (SOA‐WSOC‐FT, SOA‐WSOC‐SC) mimicked cloud‐processed particles. SOA‐fresh‐FT, SOA‐WSOC‐FT, and SOA‐WSOC‐SC particles were not highly active at nucleating ice between 233 K and 213 K, with activation onsets (i.e., 0.1% of particles forming ice) at or slightly above the theoretical homogeneous freezing line. A significant increase in the O/C of SOA‐WSOC‐SC via aqueous phase OH oxidation did not modify the ice nucleation abilities, indicating that the detailed composition of the particles is not of paramount importance to their ice nucleating abilities. Instead, precooling the SOA‐WSOC‐FT and SOA‐WSOC‐SC particles to 233 K dropped their ice nucleation onsets by up to 20% relative humidity with respect to ice, with lower temperatures likely driving the particles to be more viscous and solid‐like. However, it is possible that preactivation contributed to the reduction of the ice nucleation onsets. Particles composed of both SOA‐WSOC and ammonium sulfate (AS) were significantly less active in the deposition nucleation mode than pure, solid AS particles.

Beyond Clausius–Clapeyron: Determining the second derivative of a first-order phase transition line

We obtain an expression for the second derivative of the line in a PT diagram denoting a first-order phase transition for a pure hydrostatic system. Our result goes beyond the classical Clausius–Clapeyron equation, which provides only the first derivative of the pressure with respect to the temperature along the transition line. We present two pedagogical derivations suitable for an undergraduate thermodynamics class; the first one uses derivatives of the entropy while the second one uses derivatives of the enthalpy. The final expression for the second derivative involves only standard thermodynamic quantities such as the specific heats, the isothermal compressibilities, and the coefficients of thermal expansion of the two phases at the transition line. As an illustration, we compute the second derivatives of the freezing and vaporization lines of water at atmospheric pressure, and show that at this pressure the freezing line is concave down (negative second derivative) while the vaporization line is concave up (positive second derivative).

Arctic Ocean Water Mass Transformation in S–T Coordinates

AbstractIn this paper, water mass transformations in the Arctic Ocean are studied using a recently developed salinity–temperature (S–T) framework. The framework allows the water mass transformations to be succinctly quantified by computing the surface and internal diffusive fluxes in S–T coordinates. This study shows how the method can be applied to a specific oceanic region, in this case the Arctic Ocean, by including the advective exchange of water masses across the boundaries of the region. Based on a simulation with a global ocean circulation model, the authors examine the importance of various parameterized mixing processes and surface fluxes for the transformation of water across isohaline and isothermal surfaces in the Arctic Ocean. The model-based results reveal a broadly realistic Arctic Ocean where the inflowing Atlantic and Pacific waters are primarily cooled and freshened before exiting back to the North Atlantic. In the model, the water mass transformation in the T direction is primarily accomplished by the surface heat flux. However, the surface freshwater flux plays a minor role in the transformation of water toward lower salinities, which is mainly driven by a downgradient mixing of salt in the interior ocean. Near the freezing line, the seasonal melt and growth of sea ice influences the transformation pattern.

Freezing lines of colloidal Yukawa spheres. I. A Rogers-Young integral equation study

Using the Rogers-Young (RY) integral equation scheme for the static structure factor combined with the one-phase Hansen-Verlet (HV) freezing rule, we study the equilibrium structure and two-parameter freezing lines of colloidal particles with Yukawa-type pair interactions representing charge-stabilized silica spheres suspended in dimethylformamide (DMF). Results are presented for a vast range of concentrations, salinities and effective charges covering particles with masked excluded-volume interactions. The freezing lines were obtained for the low-charge and high-charge solutions of the static structure factor, for various two-parameter sets of experimentally accessible system parameters. All RY-HV based freezing lines can be mapped on a universal fluid-solid coexistence line in good agreement with computer simulation predictions. The RY-HV calculations extend the freezing lines obtained in earlier simulations to a broader parameter range. The experimentally observed fluid-bcc-fluid reentrant transition of charged silica spheres in DMF can be explained using the freezing lines obtained in this work.

The role of soil ice in land-atmosphere coupling over the United States: A soil moisture–precipitation winter feedback mechanism

[1] We perform two 23 year simulations using a regional climate model coupled with the National Center for Atmospheric Research Community Land Model version 3.5 (RegCM-CLM) to investigate land-atmosphere coupling in the continental United States during the cold season (October–April) and the role of soil water phase. One simulation allows the land surface to interact freely (RunI) while the other simulation uses monthly climatological soil moisture (soil liquid plus soil ice) to represent an uncoupled land surface (RunC). A winter land-atmosphere coupling signal occurs slightly south of the freezing line, indicating that the freezing line could be regarded as a temporally varying transition zone similar to the dry-to-wet transition zone identified in prior studies during boreal summer. Warmer soil temperatures in RunI translate into additional available surface energy (sum of latent and sensible heat) producing locally elevated moist static energy in the atmosphere. Additionally, warmer temperatures and greater moist static energy increase both large-scale (6–30% increase, March) and convective precipitation (>100% increase, April). As a result of the increased liquid precipitation during transition months, soil liquid water increases thereby warming winter ground and air temperatures in the interactive run and enhancing the potential for subsequent liquid precipitation. While RunC includes more persistent soil ice than is likely present in the real land-atmosphere system, this precipitation-soil moisture feedback underscores the role of soil moisture phase and variability as an important surface parameter in the winter months.

Melting and freezing lines for a mixture of charged colloidal spheres with spindle-type phase diagram

We have measured the phase behavior of a binary mixture of like-charged colloidal spheres with a size ratio of Γ=0.9 and a charge ratio of Λ=0.96 as a function of particle number density n and composition p. Under exhaustively deionized conditions, the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective one-component pair energy accounting for number weighted effective charge and screening constant. Using this description, we find that within experimental error the location of the experimental melting points meets the range of melting points predicted for monodisperse, one-component Yukawa systems made in several theoretical approaches. We further discuss that a detailed understanding of the exact phase diagram shape including the composition dependent width of the coexistence region will need an extended theoretical treatment.

A New “Polar” Program: Third Pole Environment (TPE) Workshop; Beijing, China, 14–16 August 2009

The highland core of Asia—the Qinghai‐Tibetan Plateau and the mountain ranges that surround it—has a large and complex cryosphere, which alone would earn it the title the “Third Pole” and justify greater attention. Like the other two poles, a geographic shift in the freezing line will drastically change the cryosphere, the water cycle, and the biosphere. Unlike the other two poles, the Third Pole is inhabited, and a considerable fraction of humanity in South Asia and East Asia depends on its resources, especially its water. To launch an international research program to study this important region, the Chinese Academy of Sciences Institute of Tibetan Plateau Research (ITP) hosted the Third Pole Environment (TPE) Workshop in Beijing. Approximately 70 scientists from 15 different countries attended the workshop.

Phase behavior of a de-ionized binary mixture of charged spheres in the presence of gravity

We report on the phase behavior of an aqueous binary charged sphere suspension under exhaustively de-ionized conditions as a function of number fraction of small particles p and total number density n. The mixture of size ratio Gamma=0.557 displays a complex phase diagram. Formation of bcc crystals with no compositional order dominates. We observe a region of drastically decreased crystal stability at 0.55<p<0.95 with the minimum located at p=0.8+/-0.05 at densities above n=26 microm(-3). A peaked region of enhanced stability is observed at p=0.4. Further light scattering experiments were conducted to characterize the crystallization time scales, the density profiles, and the composition of formed phases. For 0.82>p>0.95 crystal formation is partially assisted by gravity, i.e., gravitational separation of the two species precedes crystal formation for samples in the coexistence range. In the composition range corresponding to the decreased crystal stability only lower bounds of the freezing and melting line are obtained, but the general shape of the phase diagram is retained. At p=0.93 and n=43 microm(-3) two different crystalline phases coexist in the bulk, while at p=0.4 additional Bragg peaks appear in the static light scattering experiments. This strongly suggests that we observe an eutectic in the region of decreased stability, while the enhanced stability at p=0.4 seems to correlate with compound formation.

Residual multiparticle entropy does not generally change sign near freezing

The residual multiparticle entropy (RMPE) of two- and three-dimensional fluids changes sign near the freezing line, providing a quasiuniversal "one-phase" rule for the location of the liquid-solid transition. We present new simulation results for d-dimensional hard-sphere fluids (d=1-5) which show, however, that this freezing criterion fails in other spatial dimensions. The results also call into question the idea that a change in sign of the RMPE implies the emergence of a new kind of local structural order in the fluid.

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

Thermodynamic Properties of Compressed Liquid Methanol in the Vicinity of the Freezing Line

We present direct measurements of the isothermal compressibility (κT) and thermal expansion coefficient (αp) of liquid methanol using an expansion technique. The measurements of κT were carried out along six isotherms from (208.17 to 298.16) K at pressures up to 101 MPa. For αp, we have measured four isobars from (0.59 to 80.03) MPa from 195 K up to 300 K. Our experimental results of αp(T) for the 0.59 MPa isobar exhibit a minimum around 224 K. A clear shift of the minimum to higher temperatures is observed as the pressure increases along the different isobars. Interestingly, the minima for the isobars of αp(ρ) take place within a narrow range of densities, around 26.5 mol·dm-3 (about 3.15 times the critical density).

Freezing line of the Lennard-Jones fluid: A phase switch Monte Carlo study

We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.

Thermodynamic Stability of Fluid−Fluid Phase Separation in Binary Athermal Mixtures: The Role of Nonadditivity

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.

Liquid carbon: structure near the freezing line

We present a detailed analysis of the structure of liquid carbon near the freezing line. Theresults are obtained by molecular simulation using a recently developed state-of-the-artbond order potential. We find that along the melting line the liquid is predominantlythreefold coordinated up to pressures far beyond the liquid–graphite–diamond triple point.We find no sign of a first-order liquid–liquid phase transition when, at 10 500 K and∼300 GPa, the local structure of the liquid along the melting line changes dominant coordinationfrom three- to fourfold.

Segregation in aqueous methanol enhanced by cooling and compression

Molecular segregation in methanol-water mixtures is studied across a wide concentration range as a function of temperature and pressure. Cluster distributions obtained from both neutron diffraction and molecular dynamics simulations point to significantly enhanced segregation as the mixtures are cooled or compressed. This evolution toward greater molecular heterogenity in the mixture accounts for the observed changes in the water-water radial distribution function and there are indications also of a change in the topology of the water clusters. The observed behavior is consistent with an approach to an upper critical solution point. Such a point would appear to be "hidden" below the freezing line, thereby precluding observation of the two-fluid region.

Solid–liquid transition of charge-stabilized colloidal dispersions: a single-component structure-function approach

We have extended the Raveché–Mountain–Streett one-phasecriterion that governs the freezing of Lennard-Jones systems to a hard-core repulsive Yukawa-model (HCRYM) system. We find in the framework of the Rogers–Young (RY) approximation for an Ornstein–Zernike integral equation that an HCRYM fluid freezes when the ratio α = g(rmin)/g(rmax), where rmax is the distance corresponding to the maximum in the radial distribution function g(r) and rmin is the distance corresponding to the subsequent minimum in g(r), is approximately 0.215. To describe the freezing of charge-stabilized colloidal dispersions in electrolytes, which consist of colloidal macroions,electrolyte small ions, and solvent molecules, we employ the single-component model in which the colloidal particles interact through the effective screened Coulomb potential of Belloni. Whenthe macroion surface effective charge number is taken as an adjustable parameter, the theoretical freezing line predicted by the RY g(rmin)/g(rmax) = 0.215 Raveché–Mountain–Streett one-phase criterion is in very good agreement with the corresponding experimental data.PACS Nos.: 61.25.Em, 61.20.Gy

Influence of strain on transport in dense Lennard-Jones systems.

We study the shear stress relaxation and temperature dependence of the diffusion coefficient, viscosity, and thermal conductivity along a high-density Lennard-Jones isochore of the reduced density of 1.0, as it crosses the freezing and melting lines, in equilibrium and under constant strain.

Theoretical description of phase coexistence in model C60.

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.