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Kalyuzhnyi YV, Patsahan T, Holovko M, Cummings PT. Phase behavior of patchy colloids confined in patchy porous media. NANOSCALE 2024; 16:4668-4677. [PMID: 38305436 DOI: 10.1039/d3nr02866f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
A simple model for functionalized disordered porous media is proposed and the effects of confinement on self-association, percolation and phase behavior of a fluid of patchy particles are studied. The media are formed by randomly distributed hard-sphere obstacles fixed in space and decorated by a certain number of off-center square-well sites. The properties of the fluid of patchy particles, represented by the fluid of hard spheres each bearing a set of the off-center square-well sites, are studied using an appropriate combination of the scaled particle theory for the porous media, Wertheim's thermodynamic perturbation theory, and Flory-Stockmayer theory. To assess the accuracy of the theory a set of computer simulations have been performed. In general, predictions of the theory appeared to be in good agreement with the computer simulation results. Confinement and competition between the formation of bonds connecting the fluid particles, and connecting fluid particles and obstacles of the matrix, gave rise to a re-entrant phase behavior with three critical points and two separate regions of the liquid-gas phase coexistence.
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Affiliation(s)
- Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
| | - Taras Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
- Lviv Polytechnic National University, 12 S. Bandera Street, UA-79013 Lviv, Ukraine
| | - Myroslav Holovko
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
| | - Peter T Cummings
- School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
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2
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Ogrin P, Urbic T. Thermodynamics perturbation theory for solvation of nonpolar solutes in rose model. Phys Rev E 2023; 108:054135. [PMID: 38115497 DOI: 10.1103/physreve.108.054135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
A simple model of water, called the rose model, is used in this work. The rose model is a very simple model that can provide insight into the anomalous properties of water. In the rose water model, the molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. We have recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the rose model in bulk. These analytical theories offer the advantage of being computationally less intensive than computer simulations by orders of magnitudes. Here we have applied the TPT to study the transfer of a nonpolar solute into rose water, the so-called hydrophobic effect. Similarly as in our previous work for bulk water, we have found that the theory reproduces the computer simulation results quite well at higher temperatures, while the theories predict the qualitative trends at low temperatures.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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3
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Ogrin P, Urbic T. Angle-dependent integral equation theory improves results of thermodynamics and structure of rose water model. J Chem Phys 2023; 159:114505. [PMID: 37732557 PMCID: PMC10908565 DOI: 10.1063/5.0159438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 08/18/2023] [Indexed: 09/22/2023] Open
Abstract
Orientation-dependent integral equation theory (ODIET) was applied to the rose water model. Structural and thermodynamic properties of water modeled with the rose model were calculated using ODIET and compared to results from orientation-averaged integral equation theory (IET) and Monte Carlo simulations. Rose water model is a simple two-dimensional water model where molecules of water are represented as Lennard-Jones disks with explicit hydrogen bonding potential in form of rose functions. Orientational dependency significantly improves IET, as the thermodynamic results obtained using ODIET are significantly more in agreement with results calculated using MC than in the case of the orientationally averaged version. At high temperatures, the agreement between the simulation and theory is quantitative; however, when temperatures lower, a slight deviation between results obtained with different methods appear. ODIET correctly predicts the radial distribution function; moreover, ODIet also enables the calculation of angular distributions. While the angular distributions obtained with ODIET are in qualitative agreement with distributions from MC simulations, the height of the peaks in angular distributions differs between methods. Using results from ODIET, the spatial distribution of water molecules was constructed, which aids in the interpretation of other structural properties. ODIET was also used to calculate fractions of molecules with different number of hydrogen bonds, which is in the agreement with the simulations. Overall, use of ODIET significantly improves the obtained results in comparison to standard IET.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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4
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Urbic T. Ben Naim's four-arm model with density anomaly: Theory and computer simulations. Phys Rev E 2023; 108:014136. [PMID: 37583205 DOI: 10.1103/physreve.108.014136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/01/2023] [Indexed: 08/17/2023]
Abstract
Molecular dynamics, Wertheim's integral equation theory (IET), and thermodynamics perturbation theory (TPT) were used to study the thermodynamics and structure of particles interacting through angle-dependent potential. The particles are modeled as two-dimensional Lennard-Jones disks with four hydrogen bonding arms arranged symmetrically. The model was introduced by Ben-Naim and we call it the BN4 model. The BN4 model exhibits density anomaly and other anomalous properties similar to those in water and in the Mercedes-Benz (MB) model. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation and correctly predicts the pair correlation function of the model at high temperatures. Both TPT and IET are in semiquantitative agreement with the simulation values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity.
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Affiliation(s)
- Tomaz Urbic
- University of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, SI-1000 Ljubljana, Slovenia
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5
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Ogrin P, Urbic T. Simple rose model of water in constant electric field. Phys Rev E 2023; 107:054801. [PMID: 37329104 DOI: 10.1103/physreve.107.054801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 04/12/2023] [Indexed: 06/18/2023]
Abstract
A simple two-dimensional statistical mechanical water model, called the rose model, was used in this work. We studied how a homogeneous constant electric field affects the properties of water. The rose model is a very simple model that helps explain the anomalous properties of water. Rose water molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. The original model is modified by addition of charges for interaction with the electric field. We studied what kind of influence the electric field strength has on the model's properties. To determine the structure and thermodynamics of the rose model under the influence of the electric field we used Monte Carlo simulations. Under the influence of a weak electric field the anomalous properties and phase transitions of the water do not change. On the other hand, the strong fields shift the phase transition points as well as the position of the density maximum.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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6
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Urbic T. The electric field changes the anomalous properties of the Mercedes Benz water model. Phys Chem Chem Phys 2023; 25:4987-4996. [PMID: 36722865 PMCID: PMC9906975 DOI: 10.1039/d2cp05670d] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The influence of a homogeneous constant electric field on water properties was assessed. We used a simple two-dimensional statistical mechanical model called the Mercedes-Benz (MB) model of water in the study. The MB water molecules are two-dimensional disks with Gaussian arms that mimic the formation of hydrogen bonds. The model is modified with added charges for interaction with the electric field. The influence of the strength of the electric field on the water's properties was studied using Monte Carlo simulations. The structure and thermodynamics of the water were determined as a function of the strength of the electric field. We observed that the properties and phase transitions of the water in the low strength electric field does not change. In contrast, the high strength electric field shifts boiling and melting points as well as the position of the density maxima. After further increasing the strength of the electric field the density anomaly disappears.
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Affiliation(s)
- Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, SI-1000, Slovenia.
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7
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Ogrin P, Urbic T. Rose water in random porous media: Associative replica Ornstein-Zernike theory study. J Mol Liq 2022; 368:120682. [PMID: 37731589 PMCID: PMC10508880 DOI: 10.1016/j.molliq.2022.120682] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
The properties of water are vastly affected by its local environment or in other words the system in which water is present. There are many systems in which water is confined in pores of different sizes and shapes. We studied the system in which porous media consisted of quenched Lennard-Jones disks and water modelled as rose water which was allowed to move inside pores. Associative replica Ornstein-Zernike theory was used to calculate the properties of the system. The accuracy of the theory under different conditions was tested against Monte Carlo simulations. The advantage of the theory is that it is magnitudes faster than computer simulations. From pair distribution functions calculated with the theory, the effects of different conditions on the structure of the system was investigated. We also studied how different conditions such as fluid temperature, fluid density, matrix density and matrix particle size affect a fraction of bonded molecules, excess internal energy and isothermal compressibility.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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8
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Pršlja P, Žibert T, Urbic T. Monte Carlo simulations of simple two dimensional water-alcohol mixtures. J Mol Liq 2022; 368:120692. [PMID: 37731590 PMCID: PMC10508878 DOI: 10.1016/j.molliq.2022.120692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Simple alcohols such as methanol and ethanol, are organic chemicals that can be used to store energy, which can be used as an alternative to fossil fuels. Each alcohol has at least one hydroxyl group attached to a carbon atom of an alkyl group. They can be considered as organic derivatives of water in which one of the hydrogen atoms is replaced by an alkyl group. In this work, we determined the thermodynamic and structural properties of two dimensional water-alcohol mixtures using the Monte Carlo method. We used two-dimensional Mercedes-Benz (MB) model for water and MB based models for lower alcohols. The structural and thermodynamic properties of the mixtures were studied by Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in the density maxima as in real water-alcohol mixtures. With increasing content of alcohols, the temperature of maxima increases and upon further increase starts to decrease and at high concentrations, the density maxima disappears.
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Affiliation(s)
- Paulina Pršlja
- Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, 02150 Espoo, Finland
| | - Taja Žibert
- Department of Physical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna pot 113, SI-1000, Slovenia
| | - Tomaz Urbic
- Department of Physical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna pot 113, SI-1000, Slovenia
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9
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Ogrin P, Urbic T. Liquid-vapour coexistence line and percolation line of rose water model. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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10
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Ogrin P, Urbic T, Fennell CJ. Statistical-mechanical liquid theories reproduce anomalous thermodynamic properties of explicit two-dimensional water models. Phys Rev E 2022; 106:034115. [PMID: 36266898 PMCID: PMC10061499 DOI: 10.1103/physreve.106.034115] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Accepted: 08/12/2022] [Indexed: 11/07/2022]
Abstract
We have developed an analytical theory for a simple model of liquid water. We apply Wertheim's thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the rose model, which is among the simplest models of water. The particles interact through rose potentials for orientation dependent pairwise interactions. Modifying both the shape and range of a three-petal rose function, we construct an efficient and dynamical mimic of the two-dimensional (2D) Mercedes-Benz (MB) water model. The particles in 2D MB are 2D Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz logo. Both models qualitatively predict both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. The IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation functions at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Christopher J. Fennell
- Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078, United States
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11
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Papez P, Urbic T. Simple two-dimensional models of alcohols. Phys Rev E 2022; 105:054608. [PMID: 35706252 PMCID: PMC10040488 DOI: 10.1103/physreve.105.054608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/11/2022] [Indexed: 05/03/2023]
Abstract
Alcohols are organic compounds characterized by one or more hydroxyl groups attached to a carbon atom of an alkyl group. They can be considered as organic derivatives of water in which one of the hydrogen atoms is replaced by an alkyl group. In this work, the Mercedes-Benz model of water is used to design simple two-dimensional (2D) models of lower alcohols. The structural and thermodynamic properties of the constructed simple models are studied by conducting Monte Carlo simulations in the isothermal-isobaric ensemble. We show that 2D models display similar trends in structuring and thermodynamics as in experiments. The present work on the smallest amphiphilc organic solutes provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.
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Affiliation(s)
- Petra Papez
- Laboratory for Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, SI-1001, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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12
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Ogrin P, Urbic T. Isothermal-isobaric algorithm to study the effects of rotational degrees of freedom-Benz water model. J Mol Liq 2022; 349:118152. [PMID: 37727581 PMCID: PMC10508877 DOI: 10.1016/j.molliq.2021.118152] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We have developed isothermal-isobaric algorithm for non-equilibrium Monte Carlo simulations. As first we have shown that the new method correctly predict density by comparing it to the density determined in canonical Monte Carlo simulations through the virial pressure. The new method was then used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes-Benz water model. By holding one of the temperatures constant and varying the other one, we investigated how the position of the density maxima changes. We have observed that upon increase of rotational temperature the fluid become more Lennard-Jones like and the density maxima disappears.
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Affiliation(s)
- Peter Ogrin
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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14
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Thermodynamic perturbation theory for rotational degrees of freedom. Application to the Mercedes–Benz water model. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115671] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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15
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Ogrin P, Urbic T. Integral equation study of the effects of rotational degrees of freedom on properties of the Mercedes–Benz water model. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2020.114880] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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16
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Nelson A, Kalyuzhnyi Y, Patsahan T, McCabe C. Liquid-vapor phase equilibrium of a simple liquid confined in a random porous media: Second-order Barker-Henderson perturbation theory and scaled particle theory. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112348] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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17
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Abstract
We investigate by Monte Carlo simulations density, diffusion, and structural anomalies of the simple two-dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also a variance of silica-like models. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy, and diffusivity anomalies for MB model. The orientational order parameters with three and six-fold symmetry were determined and maximum for each one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.
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Affiliation(s)
- Tomaz Urbic
- University of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, SI-1000 Ljubljana, Slovenia
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794-5252, USA
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Urbic T. Modelling water with simple Mercedes-Benz models. MOLECULAR SIMULATION 2018; 45:279-294. [PMID: 31156291 PMCID: PMC6542362 DOI: 10.1080/08927022.2018.1502430] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Accepted: 07/14/2018] [Indexed: 10/28/2022]
Abstract
The structures and properties of biomolecules like proteins, nucleic acids, and membranes depend on water. Water is also very important in industry. Overall, water is unusual substance with more than 70 anomalous properties. The understanding of water is advancing significantly due to theoretical and computational modeling. There are different kind of models, models with fine-scale properties and increasing structural detail with increasing computational expense and simple models which focus on global properties of water like thermodynamics, phase diagram and are less computational expensive. Simplified models give a better understanding of water in ways that complement more complex models. Here, we review a simple model, the two dimensional Mercedes-Benz (MB) model of water. We present results by Monte Carlo simulations for anomalies and phase diagram and application of various theoretical methods.
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Affiliation(s)
- Tomaz Urbic
- University of Ljubljana, Faculty of Chemistry and Chemical Technology,
Večna pot 113, SI-1000 Ljubljana, Slovenia
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19
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Abstract
Methanol is the simplest alcohol and possible energy carrier because it is easier to store than hydrogen and burns cleaner than fossil fuels. It is a colorless liquid, completely miscible with water and organic solvents and is very hygroscopic. Here, simple two-dimensional models of methanol, based on Mercedes-Benz (MB) model of water, are examined by Monte Carlo simulations. Methanol particles are modeled as dimers formed by an apolar Lennard-Jones disk, mimicking the methyl group, and a sphere with two hydrogen bonding arms for the hydroxyl group. The used models are the one proposed by Hribar-Lee and Dill (Acta Chimica Slovenica, 53:257, 2006.) with the overlapping discs and a new model with tangentially fused dimers. The comparison was done between the models, in connection to the MB water, as well as with experimental results and with new simulations done for 3D models of methanol. Both 2D models show similar trends in structuring and thermodynamics. The difference is the most pronounced at lower temperatures, where the smaller model exhibits spontaneous crystallization, while the larger model shows metastable states. The 2D structural organization represents well the clustering tendency observed in 3D models, as well as in experiments. The models qualitatively agree with the bulk methanol thermodynamic properties like density and isothermal compressibility, however, heat capacity at the constant pressure shows trend more similar to the water behavior. This work on the smallest amphiphilic organic solute provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.
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Affiliation(s)
- Tomislav Primorac
- Faculty of Science, University of Split, Rudjera Boškovića 33, 21000 Split, Croatia
- Fakultät für Maschinenbau, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
| | - Martina Požar
- Faculty of Science, University of Split, Rudjera Boškovića 33, 21000 Split, Croatia
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, F75252, Paris cedex 05, France
| | - Franjo Sokolić
- Faculty of Science, University of Split, Rudjera Boškovića 33, 21000 Split, Croatia
| | - Larisa Zoranić
- Faculty of Science, University of Split, Rudjera Boškovića 33, 21000 Split, Croatia
| | - Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, 1000 Ljubljana, Slovenia
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Urbic T. Liquid part of the phase diagram and percolation line for two-dimensional Mercedes-Benz water. Phys Rev E 2018; 96:032122. [PMID: 29346988 DOI: 10.1103/physreve.96.032122] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2017] [Indexed: 11/07/2022]
Abstract
Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional Mercedes-Benz (MB) model of water. The MB model of water is quite popular for explaining water properties, but the phase diagram has not been reported till now. In the MB model, water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids, which have been used before to predict the properties of the simple MB model. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.
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Affiliation(s)
- T Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, 1000 Ljubljana, Slovenia
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21
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Gladovic M, Bren U, Urbic T. Thermodynamic properties of water in confined environments: a Monte Carlo study. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1409911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Martin Gladovic
- Laboratory for Physical Chemistry and Chemical Thermodynamics, Faculty of Chemistry and Chemical Technology, University of Maribor, Maribor, Slovenia
- Chair of Physical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana, Slovenia
| | - Urban Bren
- Laboratory for Physical Chemistry and Chemical Thermodynamics, Faculty of Chemistry and Chemical Technology, University of Maribor, Maribor, Slovenia
- Laboratory of Molecular Modelling, National Institute of Chemistry, Ljubljana, Slovenia
| | - Tomaž Urbic
- Chair of Physical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana, Slovenia
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22
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Urbic T, Mohoric T. Effects of translational and rotational degrees of freedom on properties of the Mercedes–Benz water model. J Chem Phys 2017. [DOI: 10.1063/1.4977214] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- T. Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
| | - T. Mohoric
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna Pot 113, SI-1000 Ljubljana, Slovenia
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Urbic T. Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study. J Chem Phys 2016; 145:194503. [PMID: 27875894 PMCID: PMC5116027 DOI: 10.1063/1.4967807] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2016] [Accepted: 11/02/2016] [Indexed: 11/14/2022] Open
Abstract
Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures.
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Affiliation(s)
- Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Vecna pot 113, 1000 Lubljana, Slovenia
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Furlan AP, Fiore CE, Barbosa MC. Influence of disordered porous media on the anomalous properties of a simple water model. Phys Rev E 2015; 92:032404. [PMID: 26465479 DOI: 10.1103/physreve.92.032404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Indexed: 11/06/2022]
Abstract
The thermodynamic, dynamic, and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two-dimensional associating lattice gas model that exhibits density and diffusion anomalies, similar to the anomalies present in liquid water. The matrix is a triangular lattice in which fixed obstacles impose restrictions to the occupation of the particles. We show that obstacles shorten all lines, including the phase coexistence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppresses the anomalies but also the liquid-liquid critical point.
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Affiliation(s)
- A P Furlan
- Instituto de Física, Univeridade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-570, Porto Alegre, RS, Brazil
| | - Carlos E Fiore
- Instituto de Física, Universidade de São Paulo, Caixa Postal 19044, 81531 São Paulo, SP, Brazil
| | - M C Barbosa
- Instituto de Física, Univeridade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-570, Porto Alegre, RS, Brazil
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Banerjee S, Singh RS, Bagchi B. Orientational order as the origin of the long-range hydrophobic effect. J Chem Phys 2015; 142:134505. [PMID: 25854251 DOI: 10.1063/1.4916744] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The long range attractive force between two hydrophobic surfaces immersed in water is observed to decrease exponentially with their separation-this distance-dependence of effective force is known as the hydrophobic force law (HFL). We explore the microscopic origin of HFL by studying distance-dependent attraction between two parallel rods immersed in 2D Mercedes Benz model of water. This model is found to exhibit a well-defined HFL. Although the phenomenon is conventionally explained by density-dependent theories, we identify orientation, rather than density, as the relevant order parameter. The range of density variation is noticeably shorter than that of orientational heterogeneity. The latter is comparable to the observed distances of hydrophobic force. At large separation, attraction between the rods arises primarily from a destructive interference among the inwardly propagating oppositely oriented heterogeneity generated in water by the two rods. As the rods are brought closer, the interference increases leading to a decrease in heterogeneity and concomitant decrease in free energy of the system, giving rise to the effective attraction. We notice formation of hexagonal ice-like structures at the onset of attractive region which suggests that metastable free energy minimum may play a role in the origin of HFL.
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Affiliation(s)
- Saikat Banerjee
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Rakesh S Singh
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Biman Bagchi
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
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Kurtjak M, Urbic T. A simple water model in the presence of inert Lennard-Jones obstacles II: the hydrophobic effect. Mol Phys 2014. [DOI: 10.1080/00268976.2014.973919] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Lomba E, Bores C, Kahl G. Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation. J Chem Phys 2014; 141:164704. [DOI: 10.1063/1.4898713] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Cecilia Bores
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - Gerhard Kahl
- Institut für Theoretische Physik, Technische Universität Wien and Center for Computational Materials Science (CMS), Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
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Lukšič M, Urbic T, Hribar-Lee B, Dill KA. Simple model of hydrophobic hydration. J Phys Chem B 2012; 116:6177-86. [PMID: 22564051 DOI: 10.1021/jp300743a] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between water's hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure, and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.
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Affiliation(s)
- Miha Lukšič
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Slovenia
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Strekalova EG, Mazza MG, Stanley HE, Franzese G. Hydrophobic nanoconfinement suppresses fluctuations in supercooled water. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:064111. [PMID: 22277682 DOI: 10.1088/0953-8984/24/6/064111] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.
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Affiliation(s)
- E G Strekalova
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
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Strekalova EG, Corradini D, Mazza MG, Buldyrev SV, Gallo P, Franzese G, Stanley HE. Effect of hydrophobic environments on the hypothesized liquid-liquid critical point of water. J Biol Phys 2011; 38:97-111. [PMID: 23277673 DOI: 10.1007/s10867-011-9241-9] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2011] [Accepted: 09/27/2011] [Indexed: 11/26/2022] Open
Abstract
The complex behavior of liquid water, along with its anomalies and their crucial role in the existence of life, continue to attract the attention of researchers. The anomalous behavior of water is more pronounced at subfreezing temperatures and numerous theoretical and experimental studies are directed towards developing a coherent thermodynamic and dynamic framework for understanding supercooled water. The existence of a liquid-liquid critical point in the deep supercooled region has been related to the anomalous behavior of water. However, the experimental study of supercooled water at very low temperatures is hampered by the homogeneous nucleation of the crystal. Recently, water confined in nanoscopic structures or in solutions has attracted interest because nucleation can be delayed. These systems have a tremendous relevance also for current biological advances; e.g., supercooled water is often confined in cell membranes and acts as a solvent for biological molecules. In particular, considerable attention has been recently devoted to understanding hydrophobic interactions or the behavior of water in the presence of apolar interfaces due to their fundamental role in self-assembly of micelles, membrane formation and protein folding. This article reviews and compares two very recent computational works aimed at elucidating the changes in the thermodynamic behavior in the supercooled region and the liquid-liquid critical point phenomenon for water in contact with hydrophobic environments. The results are also compared to previous reports for water in hydrophobic environments.
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Affiliation(s)
- Elena G Strekalova
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215 USA
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Strekalova EG, Mazza MG, Stanley HE, Franzese G. Large decrease of fluctuations for supercooled water in hydrophobic nanoconfinement. PHYSICAL REVIEW LETTERS 2011; 106:145701. [PMID: 21561203 DOI: 10.1103/physrevlett.106.145701] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2010] [Revised: 01/31/2011] [Indexed: 05/30/2023]
Abstract
Using Monte Carlo simulations, we study a coarse-grained model of a water layer confined in a fixed disordered matrix of hydrophobic nanoparticles at different particle concentrations c. For c=0, we find a first-order liquid-liquid phase transition (LLPT) ending in one critical point at low pressure P. For c>0, our simulations are consistent with a LLPT line ending in two critical points at low and high P. For c=25%, at high P and low temperature, we find a dramatic decrease of compressibility, thermal expansion coefficient, and specific heat. Surprisingly, the effect is present also for c as low as 2.4%. We conclude that even a small presence of hydrophobic nanoparticles can drastically suppress thermodynamic fluctuations, making the detection of the LLPT more difficult.
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Affiliation(s)
- Elena G Strekalova
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Urbic T, Dill KA. A statistical mechanical theory for a two-dimensional model of water. J Chem Phys 2010; 132:224507. [PMID: 20550408 DOI: 10.1063/1.3454193] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a statistical mechanical model for the thermal and volumetric properties of waterlike fluids. Each water molecule is a two-dimensional disk with three hydrogen-bonding arms. Each water interacts with neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of the Truskett and Dill (TD) treatment of the "Mercedes-Benz" (MB) model. The present model gives better predictions than TD for hydrogen-bond populations in liquid water by distinguishing strong cooperative hydrogen bonds from weaker ones. We explore properties versus temperature T and pressure p. We find that the volumetric and thermal properties follow the same trends with T as real water and are in good general agreement with Monte Carlo simulations of MB water, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds for increasing temperature. The model reproduces that pressure squeezes out water's heat capacity and leads to a negative thermal expansion coefficient at low temperatures. In terms of water structuring, the variance in hydrogen-bonding angles increases with both T and p, while the variance in water density increases with T but decreases with p. Hydrogen bonding is an energy storage mechanism that leads to water's large heat capacity (for its size) and to the fragility in its cagelike structures, which are easily melted by temperature and pressure to a more van der Waals-like liquid state.
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Affiliation(s)
- Tomaz Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, 1000 Ljubljana, Slovenia.
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Bizjak A, Urbic T, Vlachy V, Dill KA. Theory for the three-dimensional Mercedes-Benz model of water. J Chem Phys 2010; 131:194504. [PMID: 19929057 DOI: 10.1063/1.3259970] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.
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Affiliation(s)
- Alan Bizjak
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, 1000 Ljubljana, Slovenia
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Urbic T, Vlachy V, Kalyuzhnyi YV, Dill KA. An improved thermodynamic perturbation theory for Mercedes-Benz water. J Chem Phys 2007; 127:174511. [DOI: 10.1063/1.2784124] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
We study water that is confined within small geometric spaces. We use the Mercedes-Benz (MB) model of water, in NVT and muVT Monte Carlo computer simulations. For MB water molecules between two planes separated by a distance d, we explore the structures, hydrogen bond networks, and thermodynamics as a function of d, temperature T, and water chemical potential mu. We find that squeezing the planes close enough together leads to a vaporization of waters out of the cavity. This vaporization transition has a corresponding peak in the heat capacity of the water. We also find that, in small pores, hydrogen bonding is not isotropic but, rather, it preferentially forms chains along the axis of the cavity. This may be relevant for fast proton transport in pores. Our simulations show oscillations in the forces between the inert plates, due to water structure, even for plate separations of 5-10 water diameters, consistent with experiments by Israelachvili et al. [Nature 1983, 306, 249]. Finally, we find that confinement affects water's heat capacity, consistent with recent experiments of Tombari et al. on Vycor nanopores [J. Chem. Phys. 2005, 122, 104712].
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Affiliation(s)
- T Urbic
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, SI-1000 Ljubljana, Slovenia
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