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Cerdeiriña CA, Troncoso J. Ising Paradigm in Isobaric Ensembles. ENTROPY (BASEL, SWITZERLAND) 2024; 26:438. [PMID: 38920447 PMCID: PMC11203012 DOI: 10.3390/e26060438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Revised: 05/17/2024] [Accepted: 05/20/2024] [Indexed: 06/27/2024]
Abstract
We review recent work on Ising-like models with "compressible cells" of fluctuating volume that, as such, are naturally treated in NpT and μpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on "compressible cell gases" (CCG), namely, lattice gases with fluctuating cell volumes, and "compressible cell liquids" (CCL) with singly occupied cells and fluctuating cell volumes. CCGs contemplate singular diameters and "Yang-Yang features" predicted by the "complete scaling" formulation of asymmetric fluid criticality, with a specific version incorporating "ice-like" hydrogen bonding further describing the "singularity-free scenario" for the low-temperature unusual thermodynamics of supercooled water. In turn, suitable CCL variants constitute adequate prototypes of water-like liquid-liquid criticality and the freezing transition of a system of hard spheres. On incorporating vacant cells to such two-state CCL variants, one obtains three-state, BEG-like models providing a satisfactory description of water's "second-critical-point scenario" and the whole phase behavior of a simple substance like argon. Future challenges comprise water's crystal-fluid phase behavior and metastable states.
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Troncoso J, Cerdeiriña CA. Ising model for the freezing transition. Phys Rev E 2024; 109:014123. [PMID: 38366505 DOI: 10.1103/physreve.109.014123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 12/10/2023] [Indexed: 02/18/2024]
Abstract
We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics. This fairly accurate qualitative description plausibly renders mean-field theory a reasonable approach for freezing in three dimensions. At the same time, our mean-field treatment itself suggests freezing to persist in infinitely many dimensions, as advanced from recent simulations [Charbonneau et al., Eur. Phys. J. E 44, 101 (2021)10.1140/epje/s10189-021-00104-y].
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Affiliation(s)
- Jacobo Troncoso
- Instituto de Física e Ciencias Aeroespaciais da Universidade de Vigo and Unidad MSMN Asociada al CSIC por el IQF Blas Cabrera, Ourense 32004, Spain
| | - Claudio A Cerdeiriña
- Instituto de Física e Ciencias Aeroespaciais da Universidade de Vigo and Unidad MSMN Asociada al CSIC por el IQF Blas Cabrera, Ourense 32004, Spain
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Zhou Z, Cai J, Hu Y. A self-consistent renormalisation group theory for critical asymmetry of one-component fluids. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1987541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Zhiyu Zhou
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai, People’s Republic of China
| | - Jun Cai
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai, People’s Republic of China
| | - Ying Hu
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai, People’s Republic of China
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Abdulagatov IM, Skripov PV. Thermodynamic and Transport Properties of Supercritical Fluids: Review of Thermodynamic Properties (Part 1). RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2021. [DOI: 10.1134/s1990793120070192] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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Drozd-Rzoska A, Rzoska SJ, Kalabiński J. Impact of Pressure on Low-Molecular Weight Near-Critical Mixtures of Limited Miscibility. ACS OMEGA 2020; 5:20141-20152. [PMID: 32832768 PMCID: PMC7439374 DOI: 10.1021/acsomega.0c01772] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
Near-critical mixtures of limited miscibility are significant for chemical physics, soft matter physics, and a variety of challenging applications. Their basic properties can be tuned by compressing or a systematic change of one of the components. This report addresses these issues, based on experimental studies in nitro-compound (nitrobenzene, o-nitrotoluene, and 1-nitropropane) and n-alkane (from pentane to eicosane) critical mixtures. Studies reveal new patterns for the evolution of the critical consolute temperature (T C) and concentration (x C, mole fraction) within the tested homologous series: T C(n) ∼ n 2 and x C(n) ∼ n 1/2. They also show two paths of the high-pressure impact: (i) dT C(P)/dP > 0 and overlapping of normalized T C(P) dependences and (ii) the crossover dT C(P)/dP < 0 → dT C(P)/dP > 0 with increasing n-alkane length. The consistent parameterization of all T C(P) dependencies is introduced. Supplementary nonlinear dielectric effect studies indicate a possible molecular origin of the phenomenon. The coexistence curve under high pressure is in the agreement with the isomorphism postulate for critical phenomena but with a surprisingly strong distortion from the Cailletet-Mathias law of the rectilinear diameter. The new and reliable method for estimating the critical concentration and temperature is proposed. It explores the analysis of relative volumes occupied by coexisting phases.
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Abstract
We use the recently-proposed compressible cell Ising-like model to estimate the ratio between thermal expansivity and specific heat (the Grüneisen parameter Γs) in supercooled water. Near the critical pressure and temperature, Γs becomes significantly sensitive to thermal fluctuations of the order-parameter, a characteristic behavior of pressure-induced critical points. Such enhancement of Γs indicates that two energy scales are governing the system, namely the coexistence of high- and low-density liquids, which become indistinguishable at the critical point in the supercooled phase. The temperature dependence of the compressibility, sound velocity and pseudo-Grüneisen parameter Γw are also reported. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Man’s Land regime, and indicates possible applications of this model to other systems. In particular, an application of the model to the qualitative behavior of the Ising-like nematic phase in Fe-based superconductors is also presented.
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Cerdeiriña CA, Troncoso J, González-Salgado D, Debenedetti PG, Stanley HE. Water’s two-critical-point scenario in the Ising paradigm. J Chem Phys 2019; 150:244509. [DOI: 10.1063/1.5096890] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Claudio A. Cerdeiriña
- Departamento de Física Aplicada, Universidad de Vigo—Campus del Agua, Ourense 32004, Spain
| | - Jacobo Troncoso
- Departamento de Física Aplicada, Universidad de Vigo—Campus del Agua, Ourense 32004, Spain
| | - Diego González-Salgado
- Departamento de Física Aplicada, Universidad de Vigo—Campus del Agua, Ourense 32004, Spain
| | - Pablo G. Debenedetti
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - H. Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Mitigating Complexity: Cohesion Parameters and Related Topics. I: The Hildebrand Solubility Parameter. J SOLUTION CHEM 2018. [DOI: 10.1007/s10953-018-0821-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Cerdeiriña CA, Stanley HE. Ising-like Models with Energy-Volume Coupling. PHYSICAL REVIEW LETTERS 2018; 120:120603. [PMID: 29694060 DOI: 10.1103/physrevlett.120.120603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Revised: 02/05/2018] [Indexed: 06/08/2023]
Abstract
We consider a regular assembly of singly occupied cells with two accessible volumes. Coupled to cell volumes are interaction energies between nearest neighbors that lead to a phase transition with a critical point. We find that these compressible cell models can serve as Ising-like prototypes of the one-component liquid-liquid and isostructural solid-solid phase transitions that originate in the short-range features of the intermolecular potential. The mean-field solutions provide hints concerning the analytical form of the equation of state of liquid water.
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Affiliation(s)
- Claudio A Cerdeiriña
- Departamento de Física Aplicada, Universidad de Vigo-Campus del Agua, Ourense 32004, Spain
| | - H Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Garrabos Y, Lecoutre C, Marre S, Beysens D, Hahn I. Liquid-vapor rectilinear diameter revisited. Phys Rev E 2018; 97:020101. [PMID: 29548230 DOI: 10.1103/physreve.97.020101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 11/07/2022]
Abstract
In the modern theory of critical phenomena, the liquid-vapor density diameter in simple fluids is generally expected to deviate from a rectilinear law approaching the critical point. However, by performing precise scannerlike optical measurements of the position of the SF_{6} liquid-vapor meniscus, in an approach much closer to criticality in temperature and density than earlier measurements, no deviation from a rectilinear diameter can be detected. The observed meniscus position from far (10K) to extremely close (1mK) to the critical temperature is analyzed using recent theoretical models to predict the complete scaling consequences of a fluid asymmetry. The temperature dependence of the meniscus position appears consistent with the law of rectilinear diameter. The apparent absence of the critical hook in SF_{6} therefore seemingly rules out the need for the pressure scaling field contribution in the complete scaling theoretical framework in this SF_{6} analysis. More generally, this work suggests a way to clarify the experimental ambiguities in the simple fluids for the near-critical singularities in the density diameter.
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Affiliation(s)
- Y Garrabos
- CNRS, ICMCB, UMR 5026, F-33600 Pessac, France.,Université Bordeaux, ICMCB, UMR 5026, F-33600 Pessac, France
| | - C Lecoutre
- CNRS, ICMCB, UMR 5026, F-33600 Pessac, France.,Université Bordeaux, ICMCB, UMR 5026, F-33600 Pessac, France
| | - S Marre
- CNRS, ICMCB, UMR 5026, F-33600 Pessac, France.,Université Bordeaux, ICMCB, UMR 5026, F-33600 Pessac, France
| | - D Beysens
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS PSL-ESPCI-Sorbonne Université-Sorbonne Paris Cité, 10 rue Vauquelin, F-75005, Paris, France
| | - I Hahn
- Jet Propulsion Laboratory, California Institute of Technology, California 91109, USA
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Cerdeiriña CA, Orkoulas G. Compressible cell gas models for asymmetric fluid criticality. Phys Rev E 2017; 95:032105. [PMID: 28415250 DOI: 10.1103/physreve.95.032105] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Indexed: 11/07/2022]
Abstract
We thoroughly describe a class of models recently presented by Fisher and coworkers [Phys. Rev. Lett. 116, 040601 (2016)]PRLTAO0031-900710.1103/PhysRevLett.116.040601. The crucial feature of such models, termed compressible cell gases (CCGs), is that the individual cell volumes of a lattice gas are allowed to fluctuate. They are studied via the seldom-used (μ, p, T) ensemble, which leads to their exact mapping onto the Ising model. Remarkably, CCGs obey complete scaling, a formulation for the thermodynamic behavior of fluids near the gas-liquid critical point that accommodates features inherent to the asymmetric nature of this phase transition like the Yang-Yang (YY) and singular coexistence-curve diameter anomalies. The CCG_{0} models generated when volumes vary freely reveal local free volume fluctuations as the origin of these phenomena. Local energy-volume coupling is found to be another relevant microscopic factor. Furthermore, the CCG class is greatly extended by using the decoration transformation, with an interesting example being the Sastry-Debenedetti-Sciortino-Stanley model for hydrogen bonding in low-temperature water. The magnitude of anomalies is characterized by a single parameter, the YY ratio, which for the models so far considered here ranges from -∞ to 1/2.
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Affiliation(s)
- Claudio A Cerdeiriña
- Departamento de Física Aplicada, Universidad de Vigo, Campus del Agua, Ourense 32004, Spain
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Midya J, Das SK. Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition. J Chem Phys 2017; 146:044503. [PMID: 28147549 DOI: 10.1063/1.4974506] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model has been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories.
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Affiliation(s)
- Jiarul Midya
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Abdulagatov IM, Bazaev AR, Bazaev EA, Dzhapparov TA. PVT properties of 1-propanol in the critical and supercritical regions. J Supercrit Fluids 2016. [DOI: 10.1016/j.supflu.2016.06.017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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