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Li DZ, Huang WJ, Yao Y, Yang XB. Exact results for the residual entropy of ice hexagonal monolayer. Phys Rev E 2023; 107:054121. [PMID: 37329040 DOI: 10.1103/physreve.107.054121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Since the problem of the residual entropy of square ice was exactly solved, exact solutions for two-dimensional realistic ice models have been of interest. In this work, we study the exact residual entropy of ice hexagonal monolayer in two cases. In the case that the external electric field along the z-axis exists, we map the hydrogen configurations into the spin configurations of the Ising model on the kagome lattice. By taking the low temperature limit of the Ising model, we derive the exact residual entropy, which agrees with the result determined previously from the dimer model on the honeycomb lattice. In another case that the ice hexagonal monolayer is under the periodic boundary conditions in the cubic ice lattice, the residual entropy has not been studied exactly. For this case, we employ the six-vertex model on the square lattice to represent the hydrogen configurations obeying the ice rules. The exact residual entropy is obtained from the solution of the equivalent six-vertex model. Our work provides more examples of the exactly soluble two-dimensional statistical models.
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Affiliation(s)
- De-Zhang Li
- Department of Physics, South China University of Technology, Guangzhou 510640, China
| | - Wei-Jie Huang
- Department of Physics, South China University of Technology, Guangzhou 510640, China
| | - Yao Yao
- Department of Physics, South China University of Technology, Guangzhou 510640, China
| | - Xiao-Bao Yang
- Department of Physics, South China University of Technology, Guangzhou 510640, China
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2
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Khosravi A, Lasave J, Koval S, Tosatti E. Ring population statistics in an ice lattice model. J Chem Phys 2021; 155:224502. [PMID: 34911305 DOI: 10.1063/5.0076719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We calculate the distribution probability of hexagonal six-site rings in the disordered state of a cubic or hexagonal ice lattice model with ice rules perfectly obeyed. The mean-field distribution obtained is in significant agreement with those, slightly different among them, obtained by Monte Carlo simulations of the cubic or hexagonal model. The results are discussed in connection with the equilibrium and non-equilibrium transition from disorder to ferroelectric proton order.
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Affiliation(s)
- Ali Khosravi
- International School for Advanced Studies (SISSA), I-34136 Trieste, Italy
| | - Jorge Lasave
- The Abdus Salam International Centre for Theoretical Physics, I-34151 Trieste, Italy
| | - Sergio Koval
- Instituto de Física Rosario, CONICET and Universidad Nacional de Rosario, 2000 Rosario, Argentina
| | - Erio Tosatti
- International School for Advanced Studies (SISSA), I-34136 Trieste, Italy
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Matsumoto M, Yagasaki T, Tanaka H. On the anomalous homogeneity of hydrogen-disordered ice and its origin. J Chem Phys 2021; 155:164502. [PMID: 34717348 DOI: 10.1063/5.0065215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Pauling's successful estimation of the residual entropy of hydrogen-disordered ice was based on the homogeneity of the binding energy of individual water molecules in ice. However, it has not been explained why the binding energies are homogeneous although the pair interaction energy of hydrogen-bonded dimers distributes widely. Here, we provide a rationale for this phenomenon. The topological constraints imposed by the ice rules, in which water molecules form directed cyclic paths of hydrogen bonds, cancel out the variability of local interactions. We also show that the cancellation mechanism does not work due to some imperfect cyclic paths on the surface of ice. Such water molecules do not enjoy homogeneity in the bulk state and suffer from a wide spectrum in the binding energy.
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Affiliation(s)
- Masakazu Matsumoto
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Takuma Yagasaki
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
| | - Hideki Tanaka
- Toyota Physical and Chemical Research Institute, Nagakute 480-1192, Japan
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4
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Hayashi T, Muguruma C, Okamoto Y. Calculation of the residual entropy of Ice Ih by Monte Carlo simulation with the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method. J Chem Phys 2021; 154:044503. [PMID: 33514077 DOI: 10.1063/5.0038157] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We estimated the residual entropy of Ice Ih by the recently developed simulation protocol, namely, the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method. We employed a model with the nearest neighbor interactions on the three-dimensional hexagonal lattice, which satisfied the ice rules in the ground state. The results showed that our estimate of the residual entropy is in accordance with various previous results. In this article, we not only give our latest estimate of the residual entropy of Ice Ih but also discuss the importance of the uniformity of a random number generator in Monte Carlo simulations.
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Affiliation(s)
- Takuya Hayashi
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
| | - Chizuru Muguruma
- Faculty of Liberal Arts and Sciences, Chukyo University, Toyota, Aichi 470-0393, Japan
| | - Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
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Affiliation(s)
- Jiří Kolafa
- Department of Physical Chemistry, University of Chemistry and Technology, Prague, Praha 6, Czech Republic
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Hayashi T, Okamoto Y. Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method. Phys Rev E 2019; 100:043304. [PMID: 31770876 DOI: 10.1103/physreve.100.043304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2019] [Indexed: 11/07/2022]
Abstract
By combining two generalized-ensemble algorithms, the replica-exchange Wang-Landau (REWL) method and the multicanonical replica-exchange method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model using the three methods, namely REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by REWL-MUCAREM is more accurate than that is estimated by the two methods separately.
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Affiliation(s)
- Takuya Hayashi
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
| | - Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,Structural Biology Research Center, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan.,Information Technology Center, Nagoya University, Nagoya, Aichi 464-8601, Japan.,JST-CREST, Nagoya, Aichi 464-8602, Japan
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7
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Kolafa J. Free Energy of Classical Molecular Crystals by Thermodynamic Integration from a Harmonic Reference. J Chem Theory Comput 2019; 15:68-77. [PMID: 30461278 DOI: 10.1021/acs.jctc.8b00674] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and models of rigid molecules, and use it to obtain the harmonic free energy of a crystal. The anharmonic correction is then calculated by the conventional thermodynamic integration over temperature in the NVT ensemble. Attention is paid to finite-size errors, tail corrections, thermostat choice, ergodicity, and other sources of inaccuracies. The calculated free energy of ice XIV modeled by the TIP4P/2005 potential agrees with the previously reported value and is by one order more accurate.
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Affiliation(s)
- Jiří Kolafa
- Department of Physical Chemistry , University of Chemistry and Technology , Technická 5 , 166 28 Praha 6 , Czech Republic
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Tsimpanogiannis IN, Economou IG. Monte Carlo simulation studies of clathrate hydrates: A review. J Supercrit Fluids 2018. [DOI: 10.1016/j.supflu.2017.12.017] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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9
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Abstract
We calculated the residual entropy of ice III as a function of the occupation probabilities of hydrogen positions α and β assuming equal energies of all configurations. To do this, a discrete ice model with Bjerrum defect energy penalty and harmonic terms to constrain the occupation probabilities was simulated by the Metropolis Monte Carlo method for a range of temperatures and sizes followed by thermodynamic integration and extrapolation to N = ∞. Similarly as for other ices, the residual entropies are slightly higher than the mean-field (no-loop) approximation. However, the corrections caused by fluctuation of energies of ice samples calculated using molecular models of water are too large for accurate determination of the chemical potential and phase equilibria.
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Affiliation(s)
- Jiří Kolafa
- Department of Physical Chemistry, University of Chemistry and Technology, 166 28 Prague 6, Czech Republic
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Corsetti F, Matthews P, Artacho E. Structural and configurational properties of nanoconfined monolayer ice from first principles. Sci Rep 2016; 6:18651. [PMID: 26728125 PMCID: PMC4700474 DOI: 10.1038/srep18651] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2015] [Accepted: 11/23/2015] [Indexed: 12/13/2022] Open
Abstract
Understanding the structural tendencies of nanoconfined water is of great interest for nanoscience and biology, where nano/micro-sized objects may be separated by very few layers of water. Here we investigate the properties of ice confined to a quasi-2D monolayer by a featureless, chemically neutral potential, in order to characterize its intrinsic behaviour. We use density-functional theory simulations with a non-local van der Waals density functional. An ab initio random structure search reveals all the energetically competitive monolayer configurations to belong to only two of the previously-identified families, characterized by a square or honeycomb hydrogen-bonding network, respectively. We discuss the modified ice rules needed for each network, and propose a simple point dipole 2D lattice model that successfully explains the energetics of the square configurations. All identified stable phases for both networks are found to be non-polar (but with a topologically non-trivial texture for the square) and, hence, non-ferroelectric, in contrast to previous predictions from a five-site empirical force-field model. Our results are in good agreement with very recently reported experimental observations.
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Affiliation(s)
- Fabiano Corsetti
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Department of Materials and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | | | - Emilio Artacho
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Basque Foundation for Science Ikerbasque, 48011 Bilbao, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
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Moustafa SG, Schultz AJ, Kofke DA. Effects of Finite Size and Proton Disorder on Lattice-Dynamics Estimates of the Free Energy of Clathrate Hydrates. Ind Eng Chem Res 2014. [DOI: 10.1021/ie504008h] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sabry G. Moustafa
- Department
of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - Andrew J. Schultz
- Department
of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
| | - David A. Kofke
- Department
of Chemical and
Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, United States
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