1
|
Filinov VS, Levashov PR, Larkin AS. Phase-space path-integral representation of the quantum density of states: Monte Carlo simulation of strongly correlated soft-sphere fermions. Phys Rev E 2024; 109:024137. [PMID: 38491615 DOI: 10.1103/physreve.109.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/30/2024] [Indexed: 03/18/2024]
Abstract
The Wigner formulation of quantum mechanics is used to derive a path-integral representation of the quantum density of states (DOS) of strongly correlated fermions in the canonical ensemble. A path-integral Monte Carlo approach for the simulation of DOS and other thermodynamic functions is suggested. The derived Wigner function in the phase space resembles the Maxwell-Boltzmann distribution but allows for quantum effects. We consider a three-dimensional quantum system of strongly correlated soft-sphere fermions at different densities and temperatures. The calculated properties include the DOS, momentum distribution functions, spin-resolved radial distribution functions, potentials of mean force, and related energy levels obtained from the Bohr-Sommerfeld condition. We observe sharp peaks on DOS and momentum distribution curves, which are explained by the appearance of fermionic bound states.
Collapse
Affiliation(s)
- V S Filinov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - A S Larkin
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
| |
Collapse
|
2
|
Filinov VS, Syrovatka RA, Levashov PR. Exchange-correlation bound states of the triplet soft-sphere fermions by path-integral Monte Carlo simulations. Phys Rev E 2023; 108:024136. [PMID: 37723742 DOI: 10.1103/physreve.108.024136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.
Collapse
Affiliation(s)
- V S Filinov
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
| | - R A Syrovatka
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
| |
Collapse
|
3
|
Antolović I, Staubach J, Stephan S, Vrabec J. Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature. Phys Chem Chem Phys 2023. [PMID: 37365979 DOI: 10.1039/d3cp01434g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.
Collapse
Affiliation(s)
- Ivan Antolović
- Thermodynamics, Technical University Berlin, 10587 Berlin, Germany.
| | - Jens Staubach
- Laboratory of Engineering Thermodynamics (LTD), RPTU Kaiserslautern, Kaiserslautern, Germany
| | - Simon Stephan
- Laboratory of Engineering Thermodynamics (LTD), RPTU Kaiserslautern, Kaiserslautern, Germany
| | - Jadran Vrabec
- Thermodynamics, Technical University Berlin, 10587 Berlin, Germany.
| |
Collapse
|
4
|
Staubach J, Stephan S. Interfacial properties of binary azeotropic mixtures of simple fluids: Molecular dynamics simulation and density gradient theory. J Chem Phys 2022; 157:124702. [PMID: 36182407 DOI: 10.1063/5.0100728] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Interfacial properties of binary azeotropic mixtures of Lennard-Jones truncated and shifted fluids were studied by molecular dynamics (MD) simulation and density gradient theory (DGT) in combination with an equation of state. Three binary mixtures were investigated, which differ in the energetic cross interaction parameter that yields different types of azeotropic behavior. This study covers a wide temperature and composition range. Mixture A exhibits a heteroazeotrope at low temperatures, which changes to a low-boiling azeotrope at high temperatures, mixture B exhibits a low-boiling azeotrope, and mixture C exhibits a high-boiling azeotrope. The phase behavior and fluid interfacial properties as well as their relation were studied. Vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria and interfaces were considered. Density profiles, the surface tension, the interfacial thickness, as well as the relative adsorption and enrichment of the components at the interface were studied. The results obtained from the two independent methods (MD and DGT) are overall in good agreement. The results provide insights into the relation of the phase behavior, particularly the azeotropic behavior, of simple fluid mixtures and the corresponding interfacial properties. Strong enrichment was found for the mixture with a heteroazeotrope in the vicinity of the three-phase equilibrium, which is related to a wetting transition.
Collapse
Affiliation(s)
- Jens Staubach
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Simon Stephan
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, 67663 Kaiserslautern, Germany
| |
Collapse
|
5
|
Transport Properties of Binary Lennard-Jones Mixtures: Insights from Entropy Scaling and Conformal Solution Theory. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
6
|
Filinov VS, Syrovatka RS, Levashov PR. Solution of the ‘sign problem’ in the path integral Monte Carlo simulations of strongly correlated Fermi systems: thermodynamic properties of helium-3. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2102549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- V. S. Filinov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
| | - R. S. Syrovatka
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
| | - P. R. Levashov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
| |
Collapse
|
7
|
Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations. UNIVERSE 2022. [DOI: 10.3390/universe8020079] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
The modified path integral representation of Wigner functions and the new Monte Carlo approach has been suggested to account for the impact of the interparticle interaction on the Pauli exclusion principle of fermions. This approach also allows to calculate the momentum distribution functions and to reduce the “sign problem” that is inaccessible to the standard path integral Monte Carlo methods. The obtained pair electron–electron distribution functions for the “uniform electron gas” demonstrate the short-range quantum ordering of electrons associated with exchange–correlation excitons. The exchange–correlation exciton is caused by the interaction of electrons with positively charged exchange holes and the excluded volume effect. The developed approach allows one to study the density–temperature range of the exciton arising, existence, and decay. Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels. The exchange–correlation excitons have not been observed earlier in the standard path integral Monte Carlo simulations.
Collapse
|
8
|
Stephan S, Deiters UK. Characteristic Curves of the Lennard-Jones Fluid. INTERNATIONAL JOURNAL OF THERMOPHYSICS 2020; 41:147. [PMID: 32863513 PMCID: PMC7441092 DOI: 10.1007/s10765-020-02721-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 07/25/2020] [Indexed: 05/25/2023]
Abstract
Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.
Collapse
Affiliation(s)
- Simon Stephan
- Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, Erwin-Schrödinger-Straße 44, 67663 Kaiserslautern, Germany
| | - Ulrich K. Deiters
- Institute of Physical Chemistry, University of Cologne, Greinstraße 4-6, 50939 Cologne, Germany
| |
Collapse
|
9
|
da Silva DJ, Longo RL. The activity coefficient within the solvation thermodynamics formalism: Fundamentals and applications to neutral solutes. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.03.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
10
|
Hvozd TV, Kalyuzhnyi YV, Cummings PT. Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory. J Phys Chem B 2018; 122:5458-5465. [PMID: 29656640 DOI: 10.1021/acs.jpcb.7b11741] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.
Collapse
Affiliation(s)
- Taras V Hvozd
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Yurij V Kalyuzhnyi
- Institute for Condensed Matter Physics , National Academy of Sciences of Ukraine , 1 Svientsitskii St. , Lviv 79011 , Ukraine
| | - Peter T Cummings
- Department of Chemical and Biochemical Engineering , Vanderbilt University , Nashville , Tennessee 37235-1604 , United States
| |
Collapse
|
11
|
Solana JR, Akhouri BP. The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1444802] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- J. R. Solana
- Departamento de Física Aplicada, Universidad de Cantabria, Santander, Spain
| | - B. P. Akhouri
- Department of Physics, Birsa College, Khunti, Jharkhand, India
| |
Collapse
|
12
|
Das M, Green JR. Self-Averaging Fluctuations in the Chaoticity of Simple Fluids. PHYSICAL REVIEW LETTERS 2017; 119:115502. [PMID: 28949206 DOI: 10.1103/physrevlett.119.115502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2017] [Indexed: 06/07/2023]
Abstract
Bulk properties of equilibrium liquids are a manifestation of intermolecular forces. Here, we show how these forces imprint on dynamical fluctuations in the Lyapunov exponents for simple fluids with and without attractive forces. While the bulk of the spectrum is strongly self-averaging, the first Lyapunov exponent self-averages only weakly and at a rate that depends on the length scale of the intermolecular forces; short-range repulsive forces quantitatively dominate longer-range attractive forces, which act as a weak perturbation that slows the convergence to the thermodynamic limit. Regardless of intermolecular forces, the fluctuations in the Kolmogorov-Sinai entropy rate diverge, as one expects for an extensive quantity, and the spontaneous fluctuations of these dynamical observables obey fluctuation-dissipation-like relationships. Together, these results are a representation of the van der Waals picture of fluids and another lens through which we can view the liquid state.
Collapse
Affiliation(s)
- Moupriya Das
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Center for Quantum and Nonequilibrium Systems, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| |
Collapse
|
13
|
Abstract
Using a chemical potential route, the square-well (SW) fluid model is solved in a quasichemical approximation (QCSW). At low temperatures, the liquid reaches a limiting density greater than the triple point density of a SW fluid but less than the equilibrium liquid-to-solid transition density for hard spheres. As this unique density is approached with decreasing temperature, the liquid entropy also approaches an asymptotic value, thus averting the "entropy catastrophe". Mean-field models in the van der Waals (VDW) genre fail to predict this type of behavior. In VDW models, attractive force contributions to the equation of state incorrectly diverge with decreasing temperature as 1/T, whereas those for the QCSW model asymptote to a fixed value. The QCSW model posits the intuitively pleasing idea that, at high densities, attractive contributions to the configurational energy begin to saturate well before zero temperature is reached. As a consequence, the force balance between repulsive and attractive forces stabilizes the liquid density, which thereafter becomes effectively independent of temperature. This fixed density in turn fixes all other density-dependent thermodynamic properties. These low-temperature, force-stabilized states are identified as glass states.
Collapse
Affiliation(s)
- Isaac C Sanchez
- McKetta Department of Chemical Engineering, The University of Texas , Austin, Texas 78712, United States
| | - Sean P O'Keefe
- McKetta Department of Chemical Engineering, The University of Texas , Austin, Texas 78712, United States
| |
Collapse
|
14
|
Sanchez IC, O'Keefe SP. A Theoretical Rational for a Thermodynamic Glass State. J Phys Chem A 2016. [DOI: 10.1021/acs.jpca.6b06653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
15
|
Gow AS, Kelly RB. Twenty-one new theoretically based cubic equations of state for athermal hard-sphere chain pure fluids and mixtures. AIChE J 2015. [DOI: 10.1002/aic.14757] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Arthur S. Gow
- Dept. of Chemistry and Chemical Engineering; University of New Haven; West Haven CT 06516
| | - Robert B. Kelly
- Dept. of Chemistry and Chemical Engineering; University of New Haven; West Haven CT 06516
| |
Collapse
|
16
|
Lim YR, Park SJ, Song S, Yang GS, Yoon YG, Kim JH, Sung J. Exchange symmetry, fluctuation-compressibility relation, and thermodynamic potentials of quantum liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062131. [PMID: 25019748 DOI: 10.1103/physreve.89.062131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
Liquid helium does not obey the Gibbs fluctuation-compressibility relation, which was noted more than six decades ago. However, still missing is a clear explanation of the reason for the deviation or the correct fluctuation-compressibility relation for the quantum liquid. Here we present the fluctuation-compressibility relation valid for any grand canonical system. Our result shows that the deviation from the Gibbs formula arises from a nonextensive part of thermodynamic potentials. The particle-exchange symmetry of many-body wave function of a strongly degenerate quantum gas is related to the thermodynamic extensivity of the system; a Bose gas does not always obey the Gibbs formula, while a Fermi gas does. Our fluctuation-compressibility relation works for classical systems as well as quantum systems. This work demonstrates that the application range of the Gibbs-Boltzmann statistical thermodynamics can be extended to encompass nonextensive open systems without introducing any postulate other than the principle of equal a priori probability.
Collapse
Affiliation(s)
- Yu Rim Lim
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Seong Jun Park
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Sanggeun Song
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Gil-Suk Yang
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Young-Gui Yoon
- Department of Physics, Chung-Ang University, Seoul 156-756, Korea
| | - Ji-Hyun Kim
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Jaeyoung Sung
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| |
Collapse
|
17
|
Zhou S, Solana JR. Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models. J Chem Phys 2013; 138:244115. [DOI: 10.1063/1.4811285] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
18
|
Nikoofard H, Esmaili BA. Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state. Mol Phys 2013. [DOI: 10.1080/00268976.2012.760056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
19
|
KOVALENKO ANDRIY, HIRATA FUMIO. TOWARDS A MOLECULAR THEORY FOR THE VAN DER WAALS–MAXWELL DESCRIPTION OF FLUID PHASE TRANSITIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000282] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to first-principles microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals–Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids.
Collapse
Affiliation(s)
- ANDRIY KOVALENKO
- Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
| | - FUMIO HIRATA
- Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
| |
Collapse
|
20
|
Pavlyukhin YT. Probability of fluctuations in the number of the nearest neighbours in a hard-sphere liquid: Probabilities of large deviations. J STRUCT CHEM+ 2010. [DOI: 10.1007/s10947-010-0041-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
21
|
|
22
|
Zhou S, Solana JR. Progress in the Perturbation Approach in Fluid and Fluid-Related Theories. Chem Rev 2009; 109:2829-58. [DOI: 10.1021/cr900094p] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China, and School of Physics Science and Technology, Central South University, Changsha, Hunan 410083, China
| | - J. R. Solana
- Applied Physics Department, University of Cantabria, 39005 Santander, Spain
| |
Collapse
|
23
|
Hoover WG, Hoover CG, Petravic J. Simulation of two- and three-dimensional dense-fluid shear flows via nonequilibrium molecular dynamics: comparison of time-and-space-averaged stresses from homogeneous Doll's and Sllod shear algorithms with those from boundary-driven shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:046701. [PMID: 18999555 DOI: 10.1103/physreve.78.046701] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2008] [Indexed: 05/27/2023]
Abstract
Homogeneous shear flows (with constant strainrate dv(x)/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear normal-stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, Pxx-Pyy, depend on both the thermostat type and the chosen shearflow algorithm. The Doll's and Sllod algorithms predict opposite signs for this normal-stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures: Txx > Tzz > Tyy.
Collapse
Affiliation(s)
- Wm G Hoover
- Ruby Valley Research Institute, Highway Contract 60, Box 598, Ruby Valley, Nevada 89833, USA
| | | | | |
Collapse
|
24
|
Yin X, Sundaresan S. Drag Law for Bidisperse Gas−Solid Suspensions Containing Equally Sized Spheres. Ind Eng Chem Res 2008. [DOI: 10.1021/ie800171p] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaolong Yin
- Chemical Engineering Department, Princeton University, Princeton, New Jersey 08543
| | - Sankaran Sundaresan
- Chemical Engineering Department, Princeton University, Princeton, New Jersey 08543
| |
Collapse
|
25
|
Affiliation(s)
- William G. Madden
- a Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania , 19174 , U.S.A
| | - Donald D. Fitts
- a Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania , 19174 , U.S.A
| |
Collapse
|
26
|
Díez A, Largo J, Solana JR. Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory. J Phys Chem B 2007; 111:10194-201. [PMID: 17683133 DOI: 10.1021/jp072059z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.
Collapse
Affiliation(s)
- A Díez
- Departamento de Física Aplicada, Universidad de Cantabria, E-39005 Santander, Spain
| | | | | |
Collapse
|
27
|
Schweizer KS, Curro JG. Integral Equation Theories of the Structure, Thermodynamics, and Phase Transitions of Polymer Fluids. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141571.ch1] [Citation(s) in RCA: 195] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
|
28
|
Andersen HC, Chandler D, Weeks JD. Roles of Repulsive and Attractive Forces in Liquids : The Equilibrium Theory of Classical Fluids. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142530.ch2] [Citation(s) in RCA: 212] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
|
29
|
Mccully MA, Mullins JC, Thies MC, Hartley IJ. Dehydration of Acetic Acid-Water Mixtures with Near Critical and Supercritical Fluid Solvents. SEP SCI TECHNOL 2006. [DOI: 10.1080/01496398808075683] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. A. Mccully
- a Dept. of Chemical Engineering , Clemson University , Clemson , South Carolina , 29634
- b Sirrine Environmental Consultants Corp. , Greenville , SC , 29606
| | - J. C. Mullins
- a Dept. of Chemical Engineering , Clemson University , Clemson , South Carolina , 29634
| | - M. C. Thies
- a Dept. of Chemical Engineering , Clemson University , Clemson , South Carolina , 29634
| | - I. J. Hartley
- a Dept. of Chemical Engineering , Clemson University , Clemson , South Carolina , 29634
- c Union Carbide Corp. , North Seadrift , TX , 77983
| |
Collapse
|
30
|
|
31
|
Parsafar GA, Shokouhi M. Modification of a new potential model used for calculation of the second virial coefficient and zero density transport properties. Mol Phys 2006. [DOI: 10.1080/00268970601082887] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
32
|
Zhou S. Improvement on macroscopic compressibility approximation and beyond. J Chem Phys 2006; 125:144518. [PMID: 17042620 DOI: 10.1063/1.2353834] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.
Collapse
Affiliation(s)
- Shiqi Zhou
- Institute of Modern Statistical Mechanics, Hunan University of Technology, Wenhua Road, Zhuzhou 412008, People's Republic of China.
| |
Collapse
|
33
|
Zhou S. Thermodynamic perturbation theory in fluid statistical mechanics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031119. [PMID: 17025606 DOI: 10.1103/physreve.74.031119] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2006] [Revised: 07/13/2006] [Indexed: 05/12/2023]
Abstract
A methodology is proposed that pushes the thermodynamic perturbation theory (TPT) from first order to higher order. The second-order correction is superior to a macroscopic compressibility (MC) approximation of Barker and Henderson. The present third-order TPT performs far better than the original first-order TPT and second-order TPT based on the MC approximation for many subfields in fluid statistical mechanics, such as predicting excess Helmholtz free energy, excess chemical potential, bulk pressure, gas-liquid coexistence, and solid-liquid equilibrium of very short-range potential fluids. A nonuniform version of the TPT is proposed; it is also shown that the nonuniform third-order TPT performs far better than the nonuniform first-order TPT in predicting density profile of fluids in critical region. The present report indicates that the TPT still can be a "universal" and accurate theoretical tool that has general applicability in fluid statistical mechanics, especially in soft-matter physics.
Collapse
Affiliation(s)
- Shiqi Zhou
- Institute of Modern Statistical Mechanics, Hunan University of Technology, Wenhua Road, Zhuzhou City, 412008, P.R. China.
| |
Collapse
|
34
|
Gibson W. Quantum corrections to the properties of a dense fluid with non-analytic intermolecular potential function. Mol Phys 2006. [DOI: 10.1080/00268977500101721] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- W.G. Gibson
- a Department of Applied Mathematics , University of Sydney , New South Wales , 2006 , Australia
| |
Collapse
|
35
|
Affiliation(s)
- Stanislav Labík
- a Department of Physical Chemistry , Institute of Chemical Technology , 166 28 , Prague , Czechoslovakia
| | - Anatol Malijevský
- a Department of Physical Chemistry , Institute of Chemical Technology , 166 28 , Prague , Czechoslovakia
| |
Collapse
|
36
|
Gibson W. Quantum corrections to the properties of a dense fluid with non-analytic intermolecular potential function. Mol Phys 2006. [DOI: 10.1080/00268977500101711] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- W.G. Gibson
- a Department of Applied Mathematics , University of Sydney , New South Wales , 2006 , Australia
| |
Collapse
|
37
|
Konior J, Jedrzejek C. Analytic formulation of the WCA type perturbation theory for a hard-core with one-Yukawa tail fluid. Mol Phys 2006. [DOI: 10.1080/00268978500101261] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
38
|
Heyes D. Cluster analysis and continuum percolation of 3D square-well phases MC and PY solutions. Mol Phys 2006. [DOI: 10.1080/00268979000100401] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- D.M. Heyes
- a Department of Chemistry , Royal Holloway and Bedford New College, University of London , Egham , Surrey , TW20 0EX , England
| |
Collapse
|
39
|
Labik S, Malijevsky A. Monte Carlo simulations of the radial distribution function of fluid hard spheres. Mol Phys 2006. [DOI: 10.1080/00268978100100581] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Stanislav Labik
- a Department of Physical Chemistry , Institute of Chemical Technology , Prague , Czechoslovakia
| | - Anatol Malijevsky
- a Department of Physical Chemistry , Institute of Chemical Technology , Prague , Czechoslovakia
| |
Collapse
|
40
|
Affiliation(s)
- Tomáˇs Boublík
- a Institute of Chemical Process Fundamentals, Czechoslovak Academy of Sciences , 165 02 , Prague , Czechoslovakia
| |
Collapse
|
41
|
Paricaud P. A general perturbation approach for equation of state development: Applications to simple fluids, ab initio potentials, and fullerenes. J Chem Phys 2006; 124:154505. [PMID: 16674240 DOI: 10.1063/1.2181979] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new perturbation scheme based on the Barker-Henderson perturbation theory [J. Chem. Phys. 47, 4714 (1967)] is proposed to predict the thermodynamic properties of spherical molecules. Accurate predictions of second virial coefficients and vapor-liquid coexistence properties are obtained for a large variety of potential functions (square well, Yukawa, Sutherland, Lennard-Jones, Buckingham, Girifalco). New Gibbs ensemble Monte Carlo simulations of the generalized exp-m Buckingham potential are reported. An extension of the perturbation approach to mixtures is proposed, and excellent predictions of vapor-liquid equilibria are obtained for Lennard-Jones mixtures. The perturbation scheme can be applied to complex potential functions fitted to ab initio data to predict the properties of real molecules such as neon. The new approach can also be used as an auxiliary tool in molecular simulation studies, to efficiently optimize an intermolecular potential on macroscopic properties or match force fields based on different potential functions.
Collapse
Affiliation(s)
- Patrice Paricaud
- Laboratoire Chimie et Procédé, UCP-ENSTA, 32 Boulevard Victor, 75739 Paris, France.
| |
Collapse
|
42
|
|
43
|
Štěpánek M, Matějíček P, Humpolíčková J, Havránková J, Podhájecká K, Špírková M, Tuzar Z, Tsitsilianis C, Procházka K. New insights on the solution behavior and self-assembly of polystyrene/poly(2-vinylpyridine) ‘hairy’ heteroarm star copolymers with highly asymmetric arms in polar organic and aqueous media. POLYMER 2005. [DOI: 10.1016/j.polymer.2005.08.031] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
44
|
Neimark AV, Vishnyakov A. Vapor-to-droplet transition in a Lennard-Jones fluid: simulation study of nucleation barriers using the ghost field method. J Phys Chem B 2005; 109:5962-76. [PMID: 16851651 DOI: 10.1021/jp0464066] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report a comprehensive Monte Carlo (MC) simulation study of the vapor-to-droplet transition in Lennard-Jones fluid confined to a spherical container with repulsive walls, which is a case study system to investigate homogeneous nucleation. The focus is made on the application of a modified version of the ghost field method (Vishnyakov, A.; Neimark, A. V. J. Chem. Phys. 2003, 119, 9755) to calculate the nucleation barrier. This method allows one to build up a continuous trajectory of equilibrium states stabilized by the ghost field potential, which connects a reference droplet with a reference vapor state. Two computation schemes are employed for free energy calculations, direct thermodynamic integration along the constructed trajectory and umbrella sampling. The nucleation barriers and the size dependence of the surface tension are reported for droplets containing from 260 to 2000 molecules. The MC simulation study is complemented by a review of the simulation methods applied to computing the nucleation barriers and a detailed analysis of the vapor-to-droplet transition by means of the classical nucleation theory.
Collapse
Affiliation(s)
- Alexander V Neimark
- Center for Modeling and Characterization of Nanoporous Materials, TRI/Princeton, 601 Prospect Avenue, Princeton, NJ 08542, USA.
| | | |
Collapse
|
45
|
Largo J, Solana JR. First-Order Perturbative Contribution to the Compressibility Factor of Square-Well Fluids from Monte Carlo and Integral Equation Theory. J Phys Chem B 2004. [DOI: 10.1021/jp048909h] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Julio Largo
- Departamento de Føsica Aplicada, Universidad de Cantabria, 39005 Santander, Spain
| | - José R. Solana
- Departamento de Føsica Aplicada, Universidad de Cantabria, 39005 Santander, Spain
| |
Collapse
|
46
|
Ben-Amotz D, Stell G. Analytical implementation and critical tests of fluid thermodynamic perturbation theory. J Chem Phys 2003. [DOI: 10.1063/1.1620995] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
47
|
Vega C, Abascal JLF, McBride C, Bresme F. The fluid–solid equilibrium for a charged hard sphere model revisited. J Chem Phys 2003. [DOI: 10.1063/1.1576374] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
48
|
Henchman RH. Partition function for a simple liquid using cell theory parametrized by computer simulation. J Chem Phys 2003. [DOI: 10.1063/1.1578622] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
49
|
Ben-Amotz D, Omelyan IP. The influence of molecular shape on chemical reaction thermodynamics. J Chem Phys 2001. [DOI: 10.1063/1.1410376] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
50
|
Bratkovsky AM, Vaks VG, Trefilov AV. On the accuracy of the liquid theory approximate methods for the description of liquid metal thermodynamics. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4608/13/12/010] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|