Special Issue "Statistical Mechanics and Thermodynamics of Liquids and Crystals"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (31 March 2021).

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A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Santi Prestipino
E-Mail Website
Guest Editor
Department of Mathematical and Computer Sciences, Physical Sciences, and Earth Sciences, University of Messina, 98166 Messina, Italy
Interests: liquid–solid transition; crystal nucleation; crystal roughening; confined liquids; liquids and crystals of softly-repulsive particles; superfluid–supersolid transition
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Special Issue Information

Dear Colleagues,

The thermodynamic and structural properties of liquids and crystals are a traditional subject of research in statistical mechanics. Especially liquid–solid transition has been the focus of much theoretical and computational work in recent decades, with countless variations since the discovery of an entropy-driven freezing transition in a fluid of hard spheres in the late 1950s. The ideas and methods developed in these investigations have shaped the entire field of statistical physics: Even the now popular topic of topological phases and phase transitions, deviating from the usual framework of Landau theory, has its foundation in the study of two-dimensional melting. Meanwhile, complex liquids and exotic crystals (like, for instance, patchy particles, cluster crystals, and crystalline membranes) have found their way into the field, with further types of self-assembling structures beyond conventional crystals.

In spite of the enormous effort spent in characterizing the huge variety of condensed phases, many questions remain open. To name but a few, a comprehensive understanding of the onset and growth of the crystal from the supercooled liquid, and of one crystal from another, requires going beyond a merely equilibrium description. Similarly, new guiding principles need to be explored aiming at a better control of self-assembly processes in complex liquids. This Special Issue aims to emphasize new research results in the application of statistical thermodynamics to liquids and crystals. Original manuscripts highlighting the various topics in this area, both traditional and novel, are welcome.

Prof. Santi Prestipino
Guest Editor

Manuscript Submission Information

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Keywords

  • Theory of the liquid structure
  • Liquid–solid transition
  • Translational and bond-angle correlations in dense liquids
  • Anisotropic liquids and their ordered phases
  • Supercooled liquids and crystal nucleation
  • Water
  • Crystal polymorphism in soft matter
  • Self-assembly of complex liquids
  • Liquid and crystalline membranes
  • Quantum liquids and crystals

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Published Papers (9 papers)

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Editorial

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Editorial
Statistical Mechanics and Thermodynamics of Liquids and Crystals
Entropy 2021, 23(6), 715; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060715 - 04 Jun 2021
Cited by 1 | Viewed by 722
Abstract
Thermodynamic phases are the most prominent manifestation of emergent behavior [...] Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)

Research

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Article
Self-Assembled Structures of Colloidal Dimers and Disks on a Spherical Surface
Entropy 2021, 23(5), 585; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050585 - 09 May 2021
Cited by 4 | Viewed by 628
Abstract
We study self-assembly on a spherical surface of a model for a binary mixture of amphiphilic dimers in the presence of guest particles via Monte Carlo (MC) computer simulation. All particles had a hard core, but one monomer of the dimer also interacted [...] Read more.
We study self-assembly on a spherical surface of a model for a binary mixture of amphiphilic dimers in the presence of guest particles via Monte Carlo (MC) computer simulation. All particles had a hard core, but one monomer of the dimer also interacted with the guest particle by means of a short-range attractive potential. We observed the formation of aggregates of various shapes as a function of the composition of the mixture and of the size of guest particles. Our MC simulations are a further step towards a microscopic understanding of experiments on colloidal aggregation over curved surfaces, such as oil droplets. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
The Molecular Theory of Liquid Nanodroplets Energetics in Aerosols
Entropy 2021, 23(1), 13; https://0-doi-org.brum.beds.ac.uk/10.3390/e23010013 - 24 Dec 2020
Cited by 1 | Viewed by 636
Abstract
Studies of the coronavirus SARS-CoV-2 spread mechanisms indicate that the main mechanism is associated with the spread in the atmosphere of micro- and nanodroplets of liquid with an active agent. However, the molecular theory of aerosols of microdroplets in gases remains poorly developed. [...] Read more.
Studies of the coronavirus SARS-CoV-2 spread mechanisms indicate that the main mechanism is associated with the spread in the atmosphere of micro- and nanodroplets of liquid with an active agent. However, the molecular theory of aerosols of microdroplets in gases remains poorly developed. In this work, the energy properties of aerosol nanodroplets of simple liquids suspended in a gas were studied within the framework of molecular theory. The three components of the effective aerosol Hamiltonian were investigated: (1) the interaction energy of an individual atom with a liquid nanodroplet; (2) the surface energy of liquid nanodroplet; and (3) the interaction energy of two liquid nanodroplets. The size dependence of all contributions was investigated. The pairwise interparticle interactions and pairwise interparticle correlations were accounted for to study the nanodroplet properties using the Fowler approximation. In this paper, the problem of the adhesion energy calculation of a molecular complex and a liquid nanodroplet is discussed. The derived effective Hamiltonian is generic and can be used for the cases of multicomponent nano-aerosols and to account for particle size distributions. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres
Entropy 2020, 22(12), 1338; https://0-doi-org.brum.beds.ac.uk/10.3390/e22121338 - 25 Nov 2020
Cited by 1 | Viewed by 814
Abstract
Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths [...] Read more.
Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths 0.2λB*<2, densities 0.1ρN*0.925). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson–Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (ρN*=0.9, 0.925). This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems). Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Ultracold Bosons on a Regular Spherical Mesh
Entropy 2020, 22(11), 1289; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111289 - 13 Nov 2020
Cited by 3 | Viewed by 528
Abstract
Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (“Platonic mesh”) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is [...] Read more.
Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (“Platonic mesh”) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Structural and Thermodynamic Peculiarities of Core-Shell Particles at Fluid Interfaces from Triangular Lattice Models
Entropy 2020, 22(11), 1215; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111215 - 26 Oct 2020
Cited by 2 | Viewed by 517
Abstract
A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground [...] Read more.
A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential—one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns—for example clusters or stripes—occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Entropy Multiparticle Correlation Expansion for a Crystal
Entropy 2020, 22(9), 1024; https://0-doi-org.brum.beds.ac.uk/10.3390/e22091024 - 13 Sep 2020
Cited by 1 | Viewed by 816
Abstract
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given [...] Read more.
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Time Evolution Features of Entropy Generation Rate in Turbulent Rayleigh-Bénard Convection with Mixed Insulating and Conducting Boundary Conditions
Entropy 2020, 22(6), 672; https://0-doi-org.brum.beds.ac.uk/10.3390/e22060672 - 17 Jun 2020
Cited by 1 | Viewed by 885
Abstract
Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar [...] Read more.
Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t/τ < 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t/τ = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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Article
Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures
Entropy 2020, 22(4), 469; https://0-doi-org.brum.beds.ac.uk/10.3390/e22040469 - 20 Apr 2020
Cited by 2 | Viewed by 1093
Abstract
New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact [...] Read more.
New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated. Full article
(This article belongs to the Special Issue Statistical Mechanics and Thermodynamics of Liquids and Crystals)
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