Fluid-solid Phase Transition Research Articles

The Enskog–Vlasov equation: a kinetic model describing gas, liquid, and solid

The Enskog–Vlasov (EV) equation is a semi-empiric kinetic model describing gas–liquid phase transitions. In the framework of the EV equation, these correspond to an instability with respect to infinitely long perturbations, developing in a gas state when the temperature drops below (or density rises above) a certain threshold. In this paper, we show that the EV equation describes one more instability, with respect to perturbations with a finite wavelength and occurring at a higher density. This instability corresponds to fluid-solid phase transition and the perturbations’ wavelength is essentially the characteristic scale of the emerging crystal structure. Thus, even though the EV model does not describe the fundamental physics of the solid state, it can ‘mimic’ it—and, thus, be used in applications involving both evaporation and solidification of liquids. Our results also predict to which extent a pure fluid can be overcooled before it definitely turns into a solid.

Investigating the release and flow of snow avalanches at the slope-scale using a unified model based on the material point method

Snow slab avalanches start with a failure in a weak snow layer buried below a cohesive snow slab. After failure, the very porous character of the weak layer leads to its volumetric collapse and thus closing of crack faces due to the weight of the overlaying slab. This complex process, generally referred to as anticrack, explains why avalanches that release on steep slopes can be triggered from flat terrain. On the basis of a new elastoplastic model for porous cohesive materials and the Material Point Method, we investigate the dynamics of mixed-mode anticracks, the subsequent detachment of the slab and the flow of the avalanche. In particular, we performed two and three dimensional slope scale simulations of both the release and flow of slab avalanches triggered either directly or remotely. We describe the fracture and flow dynamics on a realistic topography and focus on the volumetric plastic strain, stress invariants, propagation speed and flow velocity. Our simulations reproduce typical observations of “en-echelon” fractures and the propagation speed reached up to three times that measured in field experiments. In addition, slab fracture always started from the top in the Propagation Saw Test while it systematically initiated at the interface with the weak layer at the crown of slope-scale simulations in agreement with limited field observations. During the avalanche flow, snow granulation, erosion and deposition processes were naturally simulated and do not need additional implementations. Our unified model represents a significant step forward as it allows simulating the entire avalanche process, from failure initiation to crack propagation and to solid-fluid phase transitions, which is of paramount importance to forecast and mitigate snow avalanches.

Equations of the state of hard sphere fluids based on recent accurate virial coefficients B5-B12.

By using the recently published simulation data for the compressibility factor (M. N. Bannerman, L. Lue and L. V. Woodcock, J. Chem. Phys., 2010, 132, 084507; S. Pieprzyk, M. N. Bannerman, A. C. Branka, M. Chudak and D. Heyes, Phys. Chem. Chem. Phys., 2019, 21, 6886) and the recently published numerical virial coefficients B5-B12 (R. J. Wheatley, Phys. Rev. Lett., 2013, 110, 200601; C. Zhang and B. M. Pettitt, Mol. Phys., 2014, 112, 1427; A. J. Schultz and D. A. Kofke, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2014, 90, 023301) of hard sphere fluids, we herein report the updated versions of the equations of the state of hard sphere fluids based on the asymptotic expansion method (J. Tian, H. Jiang, Y. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2009, 11, 11213), the Padé approximants (N. Clisby and B. McCoy, J. Stat. Phys., 2006, 122, 15) and the exponential approximants (N. S. Barlow, A. J. Schultz, S. J. Weinstein and D. A. Kofke, J. Chem. Phys., 2012, 137, 204102) and compare them with other recently published equations. It is found that the so-called mKLM equation describes the relation of the compressibility factor versus the packing fraction with the highest accuracy. The asymptotic expansion method based equation Z(-5, 2) is recommended to well describe both the virial coefficients and the compressibility factor.

Fluid–Solid Phase Transition in Molecular Layers Adsorbed on a Smooth Surface: A New Insight from Molecular Simulations

Two-dimensional (2D) phase transitions in molecular layers adsorbed on various surfaces have attracted much research attention over the past decades. Special attention is paid to the solidification...

Practical formula for the shear viscosity of Yukawa fluids

A simple practical formula for the shear viscosity coefficient of Yukawa fluids is presented. This formula allows estimation of the shear viscosity in a very extended range of temperatures, from the melting point to ≃ 100 times the melting temperature. It demonstrates reasonable agreement with the available results from molecular dynamics simulations. Some aspects of the temperature dependence of the shear viscosity and diffusion coefficients on approaching the fluid-solid phase transition are discussed.

Dynamic anticrack propagation in snow

Continuum numerical modeling of dynamic crack propagation has been a great challenge over the past decade. This is particularly the case for anticracks in porous materials, as reported in sedimentary rocks, deep earthquakes, landslides, and snow avalanches, as material inter-penetration further complicates the problem. Here, on the basis of a new elastoplasticity model for porous cohesive materials and a large strain hybrid Eulerian–Lagrangian numerical method, we accurately reproduced the onset and propagation dynamics of anticracks observed in snow fracture experiments. The key ingredient consists of a modified strain-softening plastic flow rule that captures the complexity of porous materials under mixed-mode loading accounting for the interplay between cohesion loss and volumetric collapse. Our unified model represents a significant step forward as it simulates solid-fluid phase transitions in geomaterials which is of paramount importance to mitigate and forecast gravitational hazards.

Study of the hard-disk system at high densities: the fluid-hexatic phase transition

Integral equations of uniform fluids have been considered unable to predict any characteristic feature of the fluid-solid phase transition, including the shoulder that arises in the second peak of the fluid-phase radial distribution function, RDF, of hard-core systems obtained by computer simulations, at fluid densities very close to the structural two-step phase transition. This reasoning is based on the results of traditional integral approximations, like Percus-Yevick, PY, which does not show such a shoulder in hard-core systems, neither in two nor three dimensions. In this work, we present results of three Ansätze, based on the PY theory, that were proposed to remedy the lack of PY analytical solutions in two dimensions. This comparative study shows that one of those Ansätze does develop a shoulder in the second peak of the RDF at densities very close to the phase transition, qualitatively describing this feature. Since the shoulder grows into a peak at still higher densities, this integral equation approach predicts the appearance of an orientational order characteristic of the hexatic phase in a continuous fluid-hexatic phase transition.

Biological tissue-inspired tunable photonic fluid

Inspired by how cells pack in dense biological tissues, we design 2D and 3D amorphous materials that possess a complete photonic bandgap. A physical parameter based on how cells adhere with one another and regulate their shapes can continuously tune the photonic bandgap size as well as the bulk mechanical properties of the material. The material can be tuned to go through a solid-fluid phase transition characterized by a vanishing shear modulus. Remarkably, the photonic bandgap persists in the fluid phase, giving rise to a photonic fluid that is robust to flow and rearrangements. Experimentally this design should lead to the engineering of self-assembled nonrigid photonic structures with photonic bandgaps that can be controlled in real time via mechanical and thermal tuning.

Early years of Computational Statistical Mechanics

Evidence that a model of hard spheres exhibits a first-order solid-fluid phase transition was provided in the late fifties by two new numerical techniques known as Monte Carlo and Molecular Dynamics. This result can be considered as the starting point of computational statistical mechanics: at the time, it was a confirmation of a counter-intuitive (and controversial) theoretical prediction by J. Kirkwood. It necessitated an intensive collaboration between the Los Alamos team, with Bill Wood developing the Monte Carlo approach, and the Livermore group, where Berni Alder was inventing Molecular Dynamics. This article tells how it happened.

Generalization of exactly-solvable model to exhibit solid-fluid phase transition in crystal structures with two particles in a primitive cell

In our previous paper (Komatsu 2015 J. Stat. Mech. P08020), we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation. However, we could treat only simple lattice structures in which more than one stable point exists in a primitive cell such as the triangular or face-centered cubic lattice. In the present paper, we generalize our previous scheme to more complicated lattice structures with two particles in a primitive cell. Generalization to more complicated lattice structures is straightforward.

Entropic patchiness drives multi-phase coexistence in discotic colloid\u2013depletant mixtures

Entropy–driven equilibrium phase behaviour of hard particle dispersions can be understood from excluded volume arguments only. While monodisperse hard spheres only exhibit a fluid–solid phase transition, anisotropic hard particles such as rods, discs, cuboids or boards exhibit various multi–phase equilibria. Ordering of such anisotropic particles increases the free volume entropy by reducing the excluded volume between them. The addition of depletants gives rise to an entropic patchiness represented by orientation–dependent attractions resulting in non–trivial phase behaviour. We show that free volume theory is a simple, generic and tractable framework that enables to incorporate these effects and rationalise various experimental findings. Plate-shaped particles constitute the main building blocks of clays, asphaltenes and chromonic liquid crystals that find widespread use in the food, cosmetics and oil industry. We demonstrate that mixtures of platelets and ideal depletants exhibit a strikingly rich phase behaviour containing several types of three–phase coexistence areas and even a quadruple region with four coexisting phases.

Premelting, solid-fluid equilibria, and thermodynamic properties in the high density region based on the Lennard-Jones potential.

The Lennard-Jones potential is used to study the high density fluid and face centered cubic solid state region, including solid-fluid equilibria. Numerous thermodynamic properties are considered, elucidating the behavior of matter in this poorly studied region. The present molecular simulation results are extensively compared to the latest and most accurate equation of state models for fluid and solid phases. It is shown that current models do not cover the thermodynamics of the system adequately near the solid-fluid phase transition. Furthermore, thermodynamic stability is analyzed, indicating that published solid-fluid coexistence data may not be correct at high temperatures. Particular attention is paid to the premelting zone, a range of states close to the melting line, which is characterized by strong variations of several thermodynamic properties. Because the underlying microscopic mechanisms are not yet fully understood, it is hoped that these data may contribute to the development of a theoretical framework for describing premelting effects.

Density-functional theory for fluid-solid and solid-solid phase transitions.

We develop a theory to describe solid-solid phase transitions. The density functional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials u(r)=ε(σ/r)^{n}, where parameter n measures softness of the potential. We find that for 1/n<0.154 systems freeze into the face centered cubic (fcc) structure while for 1/n≥0.154 the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.

Lipid organization and stratum corneum thickness determined in vivo in human skin analyzing lipid–keratin peak (2820–3030 cm−1) using confocal Raman microscopy

While the intercellular lipid structure of the stratum corneum (SC) plays an important role in the skin barrier function, the depth‐dependent profile of the intercellular lipids contributes decisively to deepen the understanding of the skin barrier function, drug penetration, development of skin diseases and their medication. The depth‐dependent profile of the lipids' chemico‐physical properties, such as the solid–fluid phase transition and the order–disorder transition, can exclusively be measured in human skin in vivo by means of confocal Raman microscopy. In the present paper, the lipid–keratin peak (2820–3030 cm−1) was investigated. The lipid‐related Raman peaks centered at 2850 cm−1 and 2880 cm−1 were deconvoluted using Gaussian functions and investigated for their depth‐dependent shape and positional changes. Different fitting procedures show that even an additional Gaussian function cannot be used to fully characterize the lipid's polymethylene chains around 2880 cm−1, which justifies the introduction of the sharpness of the peak centered near 2880 cm−1. The results show that the 2880 cm−1 peak sharpness might be used for determining the SC thickness. The concentration of the lipids with long‐chain carbon backbone (free fatty acids and ceramides) semi‐quantitatively decreases from 10 µm to 20 µm (SC thickness is 19.8 µm). The maximum position and broadness of the Gaussian peak centered at 2850 cm−1 show that near the surface and in the deeper layers of the SC, the state of the lipids is more fluid and disordered compared to the medium layers of the SC. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

We compute several ground state properties and the dynamical structure factor of a 0-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path integral ground state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of ground state properties and collective excitations of 2D-SC and 4He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in 4He. This result is in contrast with the view that the roton is the soft mode of the fluid-solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short range order as quantified by the height of the first peak of the static structure factor.

Note: Sound velocity of a soft sphere model near the fluid-solid phase transition.

The quasilocalized charge approximation is applied to estimate the sound velocity of simple soft sphere fluid with the repulsive inverse-power-law interaction. The obtained results are discussed in the context of the sound velocity of the hard-sphere system and of liquid metals at the melting temperature.

Examination of the phase transition behavior of nano-confined fluids by statistical temperature molecular dynamics.

The fluid-solid phase transition behavior of nano-confined Lennard-Jones fluids as a function of temperature and degree of nanoconfinement has been studied via statistical temperature molecular dynamics (STMD). The STMD method allows the direct calculation of the density of states and thus the heat capacity with high efficiency. The fluids are simulated between parallel solid surfaces with varying pore sizes, wall-fluid interaction energies, and registry of the walls. The fluid-solid phase transition behavior has been characterized through determination of the heat capacity. The results show that for pores of ideal-spacing, the order-disorder transition temperature (T(ODT)) is reduced as the pore size increases until values consistent with that seen in a bulk system. Also, as the interaction between the wall and fluid is reduced, T(ODT) is reduced due to weak constraints from the wall. However, for non-ideal spacing pores, quite different behavior is obtained, e.g., generally T(ODT) are largely reduced, and T(ODT) is decreased as the wall constraint becomes larger. For unaligned walls (i.e., whose lattices are not in registry), the fluid-solid transition is also detected as T is reduced, indicating non-ideality in orientation of the walls does not impact the formation of a solid, but results in a slight change in T(ODT) compared to the perfectly aligned systems. The STMD method is demonstrated to be a robust way for probing the phase transitions of nanoconfined fluids systematically, enabling the future examination of the phase transition behavior of more complex fluids.

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions.

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension ϕ, we can determine ϕ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using ϕ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on ϕ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

Practical expressions for the internal energy and pressure of Yukawa fluids.

Simple practical expressions that allow estimation of thermodynamic properties of Yukawa fluids in a wide range of coupling, up to the fluid-solid phase transition, are presented. These expressions demonstrate excellent agreement with the available results from numerical simulations. The approach provides simple and accurate tools to estimate thermodynamic properties of Yukawa fluids and related systems in a broad range of parameters.

Simulation study of the permeability of a model lipid membrane at the fluid-solid phase transition.

When a range of lipid bilayers are melted to the disordered fluid phase from the (much less permeable) ordered gel phase, their permeability to a variety of permeants shows a peak at the transition temperature and drops off with increasing temperature, rather than just rising as melting proceeds. To explore this anomalous behavior, a simulated coarse-grained lipid membrane model that exhibits a phase transition upon expansion or compression was studied to determine how the permeation rate of a simple particle depends on the phase composition in the two-phase region and on particle size. The permeation rate and each phase's area fraction and area density could be directly calculated, along with the probability that the permeant would cross in either phase or in interfacial regions. For large permeants and system sizes, conditions could be found where permeability increases upon compression of the bilayer. Permeation was negligible in the gel phase and, in contrast to the predictions of the "leaky interface" hypothesis, was not enriched in interfacial regions. The anomalous effect could instead be attributed to an increase in the area per lipid of fluid-phase domains. This result motivated a model for the decrease in effective permeability barrier through fluid-phase domains arising from a decrease in the length of the gel/fluid interface at the midpoint of a permeation event.