1
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Stepanov GO, Penkov NV, Rodionova NN, Petrova AO, Kozachenko AE, Kovalchuk AL, Tarasov SA, Tverdislov VA, Uvarov AV. The heterogeneity of aqueous solutions: the current situation in the context of experiment and theory. Front Chem 2024; 12:1456533. [PMID: 39391834 PMCID: PMC11464478 DOI: 10.3389/fchem.2024.1456533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2024] [Accepted: 09/12/2024] [Indexed: 10/12/2024] Open
Abstract
The advancement of experimental methods has provided new information about the structure and structural fluctuations of water. Despite the appearance of numerous models, which aim to describe a wide range of thermodynamic and electrical characteristics of water, there is a deficit in systemic understanding of structuring in aqueous solutions. A particular challenge is the fact that even pure water is a heterogeneous, multicomponent system composed of molecular and supramolecular structures. The possibility of the existence of such structures and their nature are of fundamental importance for various fields of science. However, great difficulties arise in modeling relatively large supramolecular structures (e.g. extended hydration shells), where the bonds between molecules are characterized by low energy. Generally, such structures may be non-equilibrium but relatively long-lived. Evidently, the short times of water microstructure exchanges do not mean short lifetimes of macrostructures, just as the instability of individual parts does not mean the instability of the entire structure. To explain this paradox, we review the data from experimental and theoretical research. Today, only some of the experimental results on the lifetime of water structures have been confirmed by modeling, so there is not a complete theoretical picture of the structure of water yet. We propose a new hierarchical water macrostructure model to resolve the issue of the stability of water structures. In this model, the structure of water is presented as consisting of many hierarchically related levels (the stratification model). The stratification mechanism is associated with symmetry breaking at the formation of the next level, even with minimal changes in the properties of the previous level. Such a hierarchical relationship can determine the unique physico-chemical properties of water systems and, in the future, provide a complete description of them.
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Affiliation(s)
- German O. Stepanov
- Department of General and Medical biophysics, Medical Biological Faculty, N.I. Pirogov Russian National Research Medical University, Moscow, Russia
- Research and Development Department, OOO "NPF "Materia Medica Holding", Moscow, Russia
| | - Nikita V. Penkov
- Institute of Cell Biophysics RAS, Federal Research Center “Pushchino Scientific Center for Biological Research of the Russian Academy of Sciences”, Pushchino, Russia
| | - Natalia N. Rodionova
- Research and Development Department, OOO "NPF "Materia Medica Holding", Moscow, Russia
| | - Anastasia O. Petrova
- Research and Development Department, OOO "NPF "Materia Medica Holding", Moscow, Russia
| | | | | | - Sergey A. Tarasov
- Research and Development Department, OOO "NPF "Materia Medica Holding", Moscow, Russia
| | - Vsevolod A. Tverdislov
- Department of Biophysics Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
| | - Alexander V. Uvarov
- Department of Molecular Processes and Extreme States of Matter, Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
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2
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Förster M, Ukoji N, Sahle CJ, Niskanen J, Sakrowski R, Surmeier G, Weis C, Irifune T, Imoto S, Yavas H, Huotari S, Marx D, Sternemann C, Tse JS. Generating interstitial water within the persisting tetrahedral H-bond network explains density increase upon compressing liquid water. Proc Natl Acad Sci U S A 2024; 121:e2403662121. [PMID: 39284048 PMCID: PMC11441526 DOI: 10.1073/pnas.2403662121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 07/16/2024] [Indexed: 10/02/2024] Open
Abstract
Despite its ubiquitous nature, the atomic structure of water in its liquid state is still controversially debated. We use a combination of X-ray Raman scattering spectroscopy in conjunction with ab initio and path integral molecular dynamics simulations to study the local atomic and electronic structure of water under high pressure conditions. Systematically increasing fingerprints of non-hydrogen-bonded H[Formula: see text]O molecules in the first hydration shell are identified in the experimental and computational oxygen K-edge excitation spectra. This provides evidence for a compaction mechanism in terms of a continuous collapse of the second hydration shell with increasing pressure via generation of interstitial water within locally tetrahedral hydrogen-bonding environments.
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Affiliation(s)
- Mirko Förster
- Fakultät Physik/DELTA, Technische Universität Dortmund, Dortmund44227, Germany
| | - Nnanna Ukoji
- Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SKS7N 5E2, Canada
| | | | - Johannes Niskanen
- Department of Physics and Astronomy, University of Turku, Turun yliopistoFI-20014, Finland
| | - Robin Sakrowski
- Fakultät Physik/DELTA, Technische Universität Dortmund, Dortmund44227, Germany
| | - Göran Surmeier
- Fakultät Physik/DELTA, Technische Universität Dortmund, Dortmund44227, Germany
| | - Christopher Weis
- Fakultät Physik/DELTA, Technische Universität Dortmund, Dortmund44227, Germany
| | - Tetsuo Irifune
- Geodynamics Research Center, Ehime University, Matsuyama790, Japan
| | - Sho Imoto
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum44780, Germany
| | - Hasan Yavas
- Deutsches Elektronen-Synchrotron, Hamburg22607, Germany
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA94025
| | - Simo Huotari
- Department of Physics, University of Helsinki, HelsinkiFI-00014, Finland
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum44780, Germany
| | | | - John S. Tse
- Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SKS7N 5E2, Canada
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3
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Kimmel GA. Isotope effects in supercooled H2O and D2O and a corresponding-states-like rescaling of the temperature and pressure. J Chem Phys 2024; 160:194508. [PMID: 38767262 DOI: 10.1063/5.0207719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Accepted: 04/30/2024] [Indexed: 05/22/2024] Open
Abstract
Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H2O and D2O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations-with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a "corresponding-states-like" rescaling for water properties in three classical water models that all exhibit a liquid-liquid transition and critical point [Uralcan et al., J. Chem. Phys. 150, 064503 (2019)], the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H2O and D2O is investigated here. Utilizing previously published data and equations-of-state for H2O and D2O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid-liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water's anomalies.
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Affiliation(s)
- Greg A Kimmel
- Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA
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4
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Donkor ED, Offei-Danso A, Rodriguez A, Sciortino F, Hassanali A. Beyond Local Structures in Critical Supercooled Water through Unsupervised Learning. J Phys Chem Lett 2024; 15:3996-4005. [PMID: 38574274 DOI: 10.1021/acs.jpclett.4c00383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/06/2024]
Abstract
The presence of a second critical point in water has been a topic of intense investigation for the last few decades. The molecular origins underlying this phenomenon are typically rationalized in terms of the competition between local high-density (HD) and low-density (LD) structures. Their identification often requires designing parameters that are subject to human intervention. Herein, we use unsupervised learning to discover structures in atomistic simulations of water close to the liquid-liquid critical point (LLCP). Encoding the information on the environment using local descriptors, we do not find evidence for two distinct thermodynamic structures. In contrast, when we deploy nonlocal descriptors that probe instead heterogeneities on the nanometer length scale, this leads to the emergence of LD and HD domains rationalizing the microscopic origins of the density fluctuations close to criticality.
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Affiliation(s)
- Edward Danquah Donkor
- The Abdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy
| | - Adu Offei-Danso
- The Abdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy
| | - Alex Rodriguez
- The Abdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
- Dipartimento di Matematica, Informatica e Geoscienze, Università degli studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Università di Roma, P. le Aldo Moro 5, 00185 Rome, Italy
| | - Ali Hassanali
- The Abdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
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5
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Maturi F, Raposo Filho RS, Brites CDS, Fan J, He R, Zhuang B, Liu X, Carlos LD. Deciphering Density Fluctuations in the Hydration Water of Brownian Nanoparticles via Upconversion Thermometry. J Phys Chem Lett 2024; 15:2606-2615. [PMID: 38420927 PMCID: PMC10926164 DOI: 10.1021/acs.jpclett.4c00044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Revised: 02/14/2024] [Accepted: 02/16/2024] [Indexed: 03/02/2024]
Abstract
We investigate the intricate relationship among temperature, pH, and Brownian velocity in a range of differently sized upconversion nanoparticles (UCNPs) dispersed in water. These UCNPs, acting as nanorulers, offer insights into assessing the relative proportion of high-density and low-density liquid in the surrounding hydration water. The study reveals a size-dependent reduction in the onset temperature of liquid-water fluctuations, indicating an augmented presence of high-density liquid domains at the nanoparticle surfaces. The observed upper-temperature threshold is consistent with a hypothetical phase diagram of water, validating the two-state model. Moreover, an increase in pH disrupts the organization of water molecules, similar to external pressure effects, allowing simulation of the effects of temperature and pressure on hydrogen bonding networks. The findings underscore the significance of the surface of suspended nanoparticles for understanding high- to low-density liquid fluctuations and water behavior at charged interfaces.
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Affiliation(s)
- Fernando
E. Maturi
- Phantom-g,
CICECO - Aveiro Institute of Materials, Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal
- Institute
of Chemistry, São Paulo State University
(UNESP), 14800-060 Araraquara, SP, Brazil
| | - Ramon S. Raposo Filho
- Phantom-g,
CICECO - Aveiro Institute of Materials, Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal
| | - Carlos D. S. Brites
- Phantom-g,
CICECO - Aveiro Institute of Materials, Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal
| | - Jingyue Fan
- Department
of Chemistry, National University of Singapore, Singapore 117543
| | - Ruihua He
- Department
of Chemistry, National University of Singapore, Singapore 117543
| | - Bilin Zhuang
- Harvey
Mudd College, 301 Platt
Boulevard, Claremont, California 91711, United States
| | - Xiaogang Liu
- Department
of Chemistry, National University of Singapore, Singapore 117543
| | - Luís D. Carlos
- Phantom-g,
CICECO - Aveiro Institute of Materials, Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal
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6
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Foffi R, Sciortino F. Identification of local structures in water from supercooled to ambient conditions. J Chem Phys 2024; 160:094504. [PMID: 38436442 DOI: 10.1063/5.0188764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 02/09/2024] [Indexed: 03/05/2024] Open
Abstract
Studies of water thermodynamics have long been tied to the identification of two distinct families of local structures, whose competition could explain the origin of the many thermodynamic anomalies and the hypothesized liquid-liquid critical point in water. Despite the many successes and insights gained, the structural indicators proposed throughout the years were not able to unequivocally identify these two families over a wide range of conditions. We show that a recently introduced indicator, Ψ, which exploits information on the hydrogen bond network connectivity, can reliably identify these two distinct local environments over a wide range of thermodynamic conditions (188-300 K and 0-13 kbar) and that close to the liquid-liquid critical point, the spatial correlations of density fluctuations are identical to those of the Ψ indicator. Our results strongly support the idea that water thermodynamic properties arise from the competition between two distinct and identifiable local environments.
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Affiliation(s)
- Riccardo Foffi
- Department of Civil, Environmental and Geomatic Engineering, Institute for Environmental Engineering, ETH Zürich, Laura-Hezner-Weg 7, 8093 Zürich, Switzerland
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Rome, Italy
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7
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Finney JL. The structure of water: A historical perspective. J Chem Phys 2024; 160:060901. [PMID: 38341786 DOI: 10.1063/5.0182665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/11/2024] [Indexed: 02/13/2024] Open
Abstract
Attempts to understand the molecular structure of water were first made well over a century ago. Looking back at the various attempts, it is illuminating to see how these were conditioned by the state of knowledge of chemistry and physics at the time and the experimental and theoretical tools then available. Progress in the intervening years has been facilitated by not only conceptual and theoretical advances in physics and chemistry but also the development of experimental techniques and instrumentation. Exploitation of powerful computational methods in interpreting what at first sight may seem impenetrable experimental data has led us to the consistent and detailed picture we have today of not only the structure of liquid water itself and how it changes with temperature and pressure but also its interactions with other molecules, in particular those relevant to water's role in important chemical and biological processes. Much remains to be done in the latter areas, but the experimental and computational techniques that now enable us to do what might reasonably be termed "liquid state crystallography" have opened the door to make possible further advances. Consequently, we now have the tools to explore further the role of water in those processes that underpin life itself-the very prospect that inspired Bernal to develop his ideas on the structure of liquids in general and of water in particular.
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Affiliation(s)
- John L Finney
- Department of Physics and Astronomy and London Centre for Nanotechnology, Gower Street, London WC1E 6BT, United Kingdom
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8
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Foffi R, Sciortino F. Correlated Fluctuations of Structural Indicators Close to the Liquid-Liquid Transition in Supercooled Water. J Phys Chem B 2022; 127:378-386. [PMID: 36538764 PMCID: PMC9841516 DOI: 10.1021/acs.jpcb.2c07169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Multiple numerical studies have unambiguously shown the existence of a liquid-liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of near-critical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.
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Affiliation(s)
- Riccardo Foffi
- Institute
for Environmental Engineering, Department of Civil, Environmental
and Geomatic Engineering, ETH Zürich, 8093Zürich, Switzerland
| | - Francesco Sciortino
- Dipartimento
di Fisica, Sapienza Università di
Roma, Piazzale Aldo Moro
5, I-00185Rome, Italy,E-mail:
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9
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Tsochantaris E, Muthachikavil AV, Peng B, Liang X, Kontogeorgis GM. Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water. AIChE J 2022; 68:e17891. [PMID: 36591369 PMCID: PMC9787682 DOI: 10.1002/aic.17891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Revised: 06/29/2022] [Accepted: 08/15/2022] [Indexed: 01/04/2023]
Abstract
Modern thermodynamic models incorporate the concept of association (hydrogen bonding) and they can describe very satisfactorily many properties of water containing mixtures. They have not been successful in representing water's anomalous properties and this work provides a possible explanation. We have analyzed and interpreted recent experimental data, molecular simulation results, and two-state theory approaches and compared against the predictions from thermodynamic models. We show that the dominance of the tetrahedral structure implemented in modern thermodynamic models may be the reason for their failure for describing water systems. While this study does not prove the two-state theories for water, it indicates that a high level of tetrahedral structure of water is not in agreement with water's anomalous properties when used in thermodynamic models.
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Affiliation(s)
- Evangelos Tsochantaris
- Department of Chemical and Biochemical Engineering, Center for Energy Resources EngineeringTechnical University of DenmarkLyngbyDenmark
| | - Aswin V. Muthachikavil
- Department of Chemical and Biochemical Engineering, Center for Energy Resources EngineeringTechnical University of DenmarkLyngbyDenmark
| | - Baoliang Peng
- Research Institute of Petroleum Exploration & Development (RIPED), PetroChinaBeijingChina
| | - Xiaodong Liang
- Department of Chemical and Biochemical Engineering, Center for Energy Resources EngineeringTechnical University of DenmarkLyngbyDenmark
| | - Georgios M. Kontogeorgis
- Department of Chemical and Biochemical Engineering, Center for Energy Resources EngineeringTechnical University of DenmarkLyngbyDenmark
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10
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On the relationship between volume fluctuations in liquids and the Gibbs free energy of cavity formation. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119845] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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11
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Faccio C, Benzi M, Zanetti-Polzi L, Daidone I. Low- and high-density forms of liquid water revealed by a new medium-range order descriptor. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.118922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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12
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Offei-Danso A, Hassanali A, Rodriguez A. High-Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning. J Chem Theory Comput 2022; 18:3136-3150. [PMID: 35472272 DOI: 10.1021/acs.jctc.1c01292] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free-energy landscape of water starting from encoding the water environment using local atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy under ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space, which we characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates. We demonstrate that a combination of both types of variables is needed in order to adequately capture the complexity of the fluctuations in the hydrogen bond network at different length scales both at room temperature and also close to the critical point of water. Our results provide a general framework for examining fluctuations in water under different conditions.
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Affiliation(s)
- Adu Offei-Danso
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.,SISSA─International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
| | - Ali Hassanali
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Alex Rodriguez
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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13
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Terban MW, Billinge SJL. Structural Analysis of Molecular Materials Using the Pair Distribution Function. Chem Rev 2022; 122:1208-1272. [PMID: 34788012 PMCID: PMC8759070 DOI: 10.1021/acs.chemrev.1c00237] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Indexed: 12/16/2022]
Abstract
This is a review of atomic pair distribution function (PDF) analysis as applied to the study of molecular materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorganic crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to molecular materials such as carbons, pharmaceuticals, polymers, liquids, coordination compounds, composites, and more. Here, an overview of applications toward a wide variety of molecular compounds (organic and inorganic) and systems with molecular components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material preparation, high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful reference to practitioners for PDF applications in a wide realm of molecular sciences, and help new practitioners to get started with this technique.
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Affiliation(s)
- Maxwell W. Terban
- Max
Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Simon J. L. Billinge
- Department
of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
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14
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Ibagon I, Furlan AP, Oliveira TJ, Dickman R. Phase diagram and critical properties of a two-dimensional associating lattice gas. Phys Rev E 2021; 104:064120. [PMID: 35030842 DOI: 10.1103/physreve.104.064120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 12/01/2021] [Indexed: 06/14/2023]
Abstract
We revisit the associating lattice gas (ALG) introduced by Henriques et al. [Phys. Rev. E 71, 031504 (2005)PLEEE81539-375510.1103/PhysRevE.71.031504] in its symmetric version. In this model, defined on the triangular lattice, interaction between molecules occupying nearest-neighbor sites depends on their relative orientation, mimicking the formation of hydrogen bonds in network-forming fluids. Although all previous studies of this model agree that it has a disordered fluid (DF), a low-density liquid (LDL), and a high-density liquid (HDL) phase, quite different forms have been reported for its phase diagram. Here, we present a thorough investigation of its phase behavior using both transfer matrix calculations and Monte Carlo (MC) simulations, along with finite-size scaling extrapolations. Results in striking agreement are found using these methods. The critical point associated with the DF-HDL transition at full occupancy, identified by Furlan et al. [Phys. Rev. E 100, 022109 (2019)2470-004510.1103/PhysRevE.100.022109] is shown to be one terminus of a critical line separating these phases. In opposition to previous simulation studies, we find that the transition between the DF and LDL phases is always discontinuous, similar to the LDL-HDL transition. The associated coexistence lines meet at the point where the DF-HDL critical line ends, making it a critical-end-point. Overall, the form of the phase diagram observed in our simulations is very similar to that found in the exact solution of the model on a Husimi lattice. Our results confirm that, despite the existence of some waterlike anomalies in this model, it is unable to reproduce key features of the phase behavior of liquid water.
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Affiliation(s)
- I Ibagon
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, C.P. 702, 30123-970, Belo Horizonte, Minas Gerais-Brazil
| | - A P Furlan
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, C.P. 702, 30123-970, Belo Horizonte, Minas Gerais-Brazil
| | - T J Oliveira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, Minas Gerais, Brazil
| | - R Dickman
- Departamento de Física and National Institute of Science and Technology for Complex Systems, ICEx, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, Minas Gerais-Brazil
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15
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Drewitt JWE. Liquid structure under extreme conditions: high-pressure x-ray diffraction studies. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:503004. [PMID: 34544063 DOI: 10.1088/1361-648x/ac2865] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 09/20/2021] [Indexed: 06/13/2023]
Abstract
Under extreme conditions of high pressure and temperature, liquids can undergo substantial structural transformations as their atoms rearrange to minimise energy within a more confined volume. Understanding the structural response of liquids under extreme conditions is important across a variety of disciplines, from fundamental physics and exotic chemistry to materials and planetary science.In situexperiments and atomistic simulations can provide crucial insight into the nature of liquid-liquid phase transitions and the complex phase diagrams and melting relations of high-pressure materials. Structural changes in natural magmas at the high-pressures experienced in deep planetary interiors can have a profound impact on their physical properties, knowledge of which is important to inform geochemical models of magmatic processes. Generating the extreme conditions required to melt samples at high-pressure, whilst simultaneously measuring their liquid structure, is a considerable challenge. The measurement, analysis, and interpretation of structural data is further complicated by the inherent disordered nature of liquids at the atomic-scale. However, recent advances in high-pressure technology mean that liquid diffraction measurements are becoming more routinely feasible at synchrotron facilities around the world. This topical review examines methods for high pressure synchrotron x-ray diffraction of liquids and the wide variety of systems which have been studied by them, from simple liquid metals and their remarkable complex behaviour at high-pressure, to molecular-polymeric liquid-liquid transitions in pnicogen and chalcogen liquids, and density-driven structural transformations in water and silicate melts.
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Affiliation(s)
- James W E Drewitt
- School of Physics, University of Bristol, H H Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
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16
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Corsaro C, Fazio E. From Critical Point to Critical Point: The Two-States Model Describes Liquid Water Self-Diffusion from 623 to 126 K. Molecules 2021; 26:molecules26195899. [PMID: 34641442 PMCID: PMC8512083 DOI: 10.3390/molecules26195899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 09/23/2021] [Accepted: 09/26/2021] [Indexed: 12/02/2022] Open
Abstract
Liquid’s behaviour, when close to critical points, is of extreme importance both for fundamental research and industrial applications. A detailed knowledge of the structural–dynamical correlations in their proximity is still today a target to reach. Liquid water anomalies are ascribed to the presence of a second liquid–liquid critical point, which seems to be located in the very deep supercooled regime, even below 200 K and at pressure around 2 kbar. In this work, the thermal behaviour of the self-diffusion coefficient for liquid water is analyzed, in terms of a two-states model, for the first time in a very wide thermal region (126 K < T < 623 K), including those of the two critical points. Further, the corresponding configurational entropy and isobaric-specific heat have been evaluated within the same interval. The two liquid states correspond to high and low-density water local structures that play a primary role on water dynamical behavior over 500 K.
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17
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Zakhvataev VE, Kompaniets LA. On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover. Sci Rep 2021; 11:5417. [PMID: 33686146 PMCID: PMC7940660 DOI: 10.1038/s41598-021-84277-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 02/04/2021] [Indexed: 11/11/2022] Open
Abstract
The problem of large-density variations in supercooled and ambient water has been widely discussed in the past years. Recent studies have indicated the possibility of nanometer-sized density variations on the subpicosecond and picosecond time scales. The nature of fluctuating density heterogeneities remains a highly debated issue. In the present work, we address the problem of possible association of such density variations with the dynamics of terahertz longitudinal acoustic-like modes in liquid water. Our study is based on the fact that the subpicosecond dynamics of liquid water are essentially governed by the structural relaxation. Using a mode coupling theory approach, we found that for typical values of parameters of liquid water, the dynamic mechanism coming from the combination of the structural relaxation process and the finiteness of the amplitude of terahertz longitudinal acoustic-like mode gives rise to a soliton-like collective mode on a temperature-dependent nanometer length scale. The characteristics of this mode are consistent with the estimates of the amplitudes and temperature-dependent correlation lengths of density fluctuations in liquid water obtained in experiments and simulations. Thus, the fully dynamic mechanism could contribute to the formation and dynamics of fluctuating density heterogeneities. The soliton-like collective excitations suggested by our analysis may be relevant to different phenomena connected with supercooled water and can be expected to be associated with some ultrafast biological processes.
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Affiliation(s)
- V E Zakhvataev
- Federal Research Center "Krasnoyarsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences", 660036, Krasnoyarsk, Russia.
- Siberian Federal University, 660041, Krasnoyarsk, Russia.
| | - L A Kompaniets
- Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences, 660036, Krasnoyarsk, Russia
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18
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Vibrational resonant inelastic X-ray scattering in liquid acetic acid: a ruler for molecular chain lengths. Sci Rep 2021; 11:4098. [PMID: 33602972 PMCID: PMC7893077 DOI: 10.1038/s41598-021-83248-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 02/01/2021] [Indexed: 11/08/2022] Open
Abstract
Quenching of vibrational excitations in resonant inelastic X-ray scattering (RIXS) spectra of liquid acetic acid is observed. At the oxygen core resonance associated with localized excitations at the O-H bond, the spectra lack the typical progression of vibrational excitations observed in RIXS spectra of comparable systems. We interpret this phenomenon as due to strong rehybridization of the unoccupied molecular orbitals as a result of hydrogen bonding, which however cannot be observed in x-ray absorption but only by means of RIXS. This allows us to address the molecular structure of the liquid, and to determine a lower limit for the average molecular chain length.
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19
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Perakis F, Gutt C. Towards molecular movies with X-ray photon correlation spectroscopy. Phys Chem Chem Phys 2021; 22:19443-19453. [PMID: 32870200 DOI: 10.1039/d0cp03551c] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.
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Affiliation(s)
- Fivos Perakis
- Department of Physics, AlbaNova University Center, Stockholm University, S-106 91 Stockholm, Sweden.
| | - Christian Gutt
- Department Physik, Universität Siegen, D-57072 Siegen, Germany.
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20
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Bachler J, Fidler LR, Loerting T. Absence of the liquid-liquid phase transition in aqueous ionic liquids. Phys Rev E 2021; 102:060601. [PMID: 33466086 DOI: 10.1103/physreve.102.060601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 11/18/2020] [Indexed: 11/07/2022]
Abstract
The anomalies of supercooled water may be explained by an underlying liquid-liquid phase transition (LLPT) between high- and low-density states. Recently, its observation at 185 K was inferred using solutions containing aqueous ionic liquids at a solute mole fraction of x=0.156 [Woutersen et al., Science 359, 1127 (2018)10.1126/science.aao7049]. We employ x-ray diffraction, calorimetry, and dilatometry on these hydrazinium trifluoroacetate solutions at x=0.00-0.40 to show that the transition at 185 K is not related to a genuine LLPT of water. Continuous densification upon compression, continuous changes of halo position, and absence of thermal signatures for a high- to low-density transition rule out the possibility of an LLPT for x≥0.13. The data show that employing sophisticated solutions adds a layer of complexity that hampers extrapolation of the LLPT concept from one- to two-component systems. The possibility of an LLPT can only be probed for pure water or sufficiently dilute aqueous solutions.
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Affiliation(s)
- Johannes Bachler
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Lilli-Ruth Fidler
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Thomas Loerting
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
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21
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Mendonça BHS, Ternes P, Salcedo E, de Oliveira AB, Barbosa MC. Water diffusion in carbon nanotubes: Interplay between confinement, surface deformation, and temperature. J Chem Phys 2020; 153:244504. [PMID: 33380079 DOI: 10.1063/5.0031084] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
In this article, we investigate, through molecular dynamics simulations, the diffusion behavior of the TIP4P/2005 water confined in pristine and deformed carbon nanotubes (armchair and zigzag). To analyze different diffusive mechanisms, the water temperature was varied as 210 ≤ T ≤ 380 K. The results of our simulations reveal that water presents a non-Arrhenius to Arrhenius diffusion crossover. The confinement shifts the diffusion transition to higher temperatures when compared with the bulk system. In addition, for narrower nanotubes, water diffuses in a single line, which leads to its mobility independent of the activation energy.
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Affiliation(s)
- Bruno H S Mendonça
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil
| | - Patricia Ternes
- School of Geography, University of Leeds, Leeds LS2 9NL, United Kingdom
| | - Evy Salcedo
- Coordenadoria Especial de Física, Química e Matemática, Universidade Federal de Santa Catarina, Araranguá, SC 88905-120, Brazil
| | - Alan B de Oliveira
- Departamento de Física, Universidade Federal de Ouro Preto, Ouro Preto, MG 35400-000, Brazil
| | - Marcia C Barbosa
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil
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22
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Kringle L, Thornley WA, Kay BD, Kimmel GA. Reversible structural transformations in supercooled liquid water from 135 to 245 K. Science 2020; 369:1490-1492. [DOI: 10.1126/science.abb7542] [Citation(s) in RCA: 45] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Accepted: 07/28/2020] [Indexed: 11/02/2022]
Abstract
A fundamental understanding of the unusual properties of water remains elusive because of the limited data at the temperatures and pressures needed to decide among competing theories. We investigated the structural transformations of transiently heated supercooled water films, which evolved for several nanoseconds per pulse during fast laser heating before quenching to 70 kelvin (K). Water’s structure relaxed from its initial configuration to a steady-state configuration before appreciable crystallization. Over the full temperature range investigated, all structural changes were reversible and reproducible by a linear combination of high- and low-temperature structural motifs. The fraction of the liquid with the high-temperature motif decreased rapidly as the temperature decreased from 245 to 190 K, consistent with the predictions of two-state “mixture” models for supercooled water in the supercritical regime.
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Affiliation(s)
- Loni Kringle
- Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA
| | - Wyatt A. Thornley
- Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA
| | - Bruce D. Kay
- Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA
| | - Greg A. Kimmel
- Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA
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23
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Debenedetti PG, Sciortino F, Zerze GH. Second critical point in two realistic
models of water. Science 2020; 369:289-292. [DOI: 10.1126/science.abb9796] [Citation(s) in RCA: 99] [Impact Index Per Article: 24.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 05/27/2020] [Indexed: 12/20/2022]
Abstract
The hypothesis that water has a second
critical point at deeply supercooled conditions
was formulated to provide a thermodynamically
consistent interpretation of numerous experimental
observations. A large body of work has been
devoted to verifying or falsifying this
hypothesis, but no unambiguous experimental proof
has yet been found. Here, we use histogram
reweighting and large-system scattering
calculations to investigate computationally two
molecular models of water, TIP4P/2005 and
TIP4P/Ice, widely regarded to be among the most
accurate classical force fields for this
substance. We show that both models have a
metastable liquid-liquid critical point at deeply
supercooled conditions and that this critical
point is consistent with the three-dimensional
Ising universality class.
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Affiliation(s)
- Pablo G. Debenedetti
- Department of Chemical and Biological
Engineering, Princeton University, Princeton, NJ,
USA
| | | | - Gül H. Zerze
- Department of Chemical and Biological
Engineering, Princeton University, Princeton, NJ,
USA
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24
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Montes de Oca JM, Sciortino F, Appignanesi GA. A structural indicator for water built upon potential energy considerations. J Chem Phys 2020; 152:244503. [PMID: 32610982 DOI: 10.1063/5.0010895] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a parameter-free structural indicator to classify local environments of water molecules in stable and supercooled liquid states, which reveals a clear two-peak distribution of local properties. The majority of molecules are tetrahedrally coordinated (T molecules), via low-energy hydrogen bonds. The minority component, whose relative concentration decreases with a decrease in the temperature at constant pressure, is characterized by prevalently three-coordinated molecules, giving rise to a distorted local network around them (D molecules). The inter-conversion between T and D molecules explains the increasing specific heat at constant pressure on cooling. The local structure around a T molecule resembles the one found experimentally in low-density amorphous ice (a network structure mostly composed by T molecules), while the local structure around a D molecule is reminiscent of the structural properties of high-density amorphous ice (a network structure composed by a mixture of T and D molecules).
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Affiliation(s)
- Joan M Montes de Oca
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale A. Moro 5, Roma 00185, Italy
| | - Gustavo A Appignanesi
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
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25
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Stopper D, Hansen-Goos H, Roth R, Evans R. Remnants of the disappearing critical point in chain-forming patchy fluids. J Chem Phys 2020; 152:111101. [DOI: 10.1063/1.5141059] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Daniel Stopper
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Hendrik Hansen-Goos
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 ITL, United Kingdom
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26
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Piskulich ZA, Thompson WH. The dynamics of supercooled water can be predicted from room temperature simulations. J Chem Phys 2020; 152:074505. [DOI: 10.1063/1.5139435] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zeke A. Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
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27
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Chen M, Zhou H, Zhu R, Lu X, He H. Closest-Packing Water Monolayer Stably Intercalated in Phyllosilicate Minerals under High Pressure. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:618-627. [PMID: 31886678 DOI: 10.1021/acs.langmuir.9b03394] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The directional hydrogen-bond (HB) network and nondirectional van der Waals (vdW) interactions make up the specificity of water. Directional HBs could construct an ice-like monolayer in hydrophobic confinement even in the ambient regime. Here, we report a water monolayer dominated by vdW interactions confined in a phyllosilicate interlayer under high pressure. Surprisingly, it was in a thermodynamically stable state coupled with bulk water at the same pressure (P) and temperature (T), as revealed by the thermodynamic integration approach on the basis of molecular dynamics (MD) simulations. Both classical and ab initio MD simulations showed water O atoms were stably trapped and exhibited an ordered hexagonal closest-packing arrangement, but OH bonds of water reoriented frequently and exhibited a specific two-stage reorientation relaxation. Strikingly, hydration in the interlayer under high pressure had no relevance with surface hydrophilicity rationalized by the HB forming ability, which, however, determines wetting in the ambient regime. Intercalated water molecules were trapped by vdW interactions, which shaped the closest-packing arrangement and made hydration energetically available. The high pressure-volume term largely drives hydration, as it compensates the entropy penalty which is restricted by a relatively lower temperature. This vdW water monolayer should be ubiquitous in the high pressure but low-temperature regime.
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Affiliation(s)
- Meng Chen
- CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Institutions of Earth Science , Chinese Academy of Sciences (CAS) , Guangzhou 510640 , China
| | - Huijun Zhou
- CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Institutions of Earth Science , Chinese Academy of Sciences (CAS) , Guangzhou 510640 , China
- University of Chinese Academy of Sciences , Beijing 100049 , China
| | - Runliang Zhu
- CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Institutions of Earth Science , Chinese Academy of Sciences (CAS) , Guangzhou 510640 , China
| | - Xiancai Lu
- State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering , Nanjing University , Nanjing 210093 , China
| | - Hongping He
- CAS Key Laboratory of Mineralogy and Metallogeny/Guangdong Provincial Key Laboratory of Mineral Physics and Materials, Guangzhou Institute of Geochemistry, Institutions of Earth Science , Chinese Academy of Sciences (CAS) , Guangzhou 510640 , China
- University of Chinese Academy of Sciences , Beijing 100049 , China
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28
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Gallo P, Loerting T, Sciortino F. Supercooled water: A polymorphic liquid with a cornucopia of behaviors. J Chem Phys 2019; 151:210401. [DOI: 10.1063/1.5135706] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Paola Gallo
- Department of Mathematics and Physics, University Roma Tre Via della Vasca Navale 84, I-00146 Rome, Italy
| | - Thomas Loerting
- Institute of Physical Chemistry, University of Innsbruck Innrain 52c, A-6020 Innsbruck, Austria
| | - Francesco Sciortino
- Department of Physics, Sapienza Universitá di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy
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29
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Soper AK. Through the looking glass and into the liquid. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1649497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Alan K. Soper
- ISIS Facility, UKRI-STFC Rutherford Appleton Laboratory, Didcot, UK
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