THERMAL SCIENCE

International Scientific Journal

Jiamei Zhao

,

Siwei Chen

,

Lijuan HeORCID

,

Wenxi You

ADVANCES IN MOLECULAR DYNAMICS SIMULATION OF PHASE EQUILIBRIUM

ABSTRACT
The molecular dynamics simulation method has developed into a more mature simulation tool for calculating the phase equilibria of pure substances and mixtures. This paper offers a detailed account of the fundamentals of the molecular dynamics method and an overview of its development, with an emphasis on the force fields that are closely related to the method. Based on this, the state of development regarding the application of molecular dynamics simulations for the calculation of phase equilibrium data for pure substances and mixtures of matter systems both domestically and internationally is reviewed in a classified manner. In addition, the combination of molecular dynamics simulation with machine learning for phase equilibrium calculations is presented. The limitations inherent in molecular dynamics simulation are objectively highlighted, potential future developments in this field are also envisioned.
KEYWORDS
Molecular dynamics simulations, phase equilibrium, thermodynamic properties, machine learning
PAPER SUBMITTED: 2025-11-25
PAPER REVISED: 2025-12-29
PAPER ACCEPTED: 2026-01-03
PUBLISHED ONLINE: 2026-03-07
DOI REFERENCE: https://doi.org/10.2298/TSCI251125025Z
REFERENCES
[1] Liu Zhiping, Huang Shiping, Wang Wenchuan. Molecular computational science--a new growth point for chemical engineering[J]. Journal of Chemical Engineering, 2003, (04):464-476
[2] Wang Hui, Yan Zhiguo, Zheng Ming, et al. Application of molecular simulation methods in non-homogeneous catalysis[J]. Petrochemicals, 2008, (05):522-527
[3] Smith F, Wang Wenchuan, et al. Molecular simulation-from algorithms to applications [M]. Beijing:Chemical Industry Press, 2002
[4] Panagiotopoulos A Z, Quirke N, et al. Phase equilibria by simulation in the Gibbs ensemble: Alternative derivation, generalization and application to mixture and membrane equilibria[J]. Molecular Physics, 1988, 63(4), 527-545
[5] Chen Zhenglong. Theory and practice of molecular simulation [M]. Beijing:Chemical Industry Press, 2007
[6] Hui Feng, Zhang Minhua, Ma Jing. Progress in simulating phase equilibrium by Monte Carlo method in Gibbs system[J]. Advances in Chemical Engineering, 2012, 31(08):1677-1684
[7] Alder B J, Wainwright T E. Phase Transition for a Hard Sphere System[J]. Journal of Chemical Physics, 1957, 27:1208-1209
[8] Rahman A. Correlations in the Motion of Atoms in Liquid Argon[J]. Physical Review, 1964, 136(2A):A405-A411
[9] Rahman A, Stillinger F H. Molecular Dynamics Study of Liquid Water[J]. The Journal of Chemical Physics, 1971, 55(7):3336-
[10] Anderson H C. Molecular Dynamics Simulations at Constant Pressure and/or Temperature[J]. The Journal of Chemical Physics, 1980, 72(4), 2384-2393
[11] Parrinello M, Rahman A. Crystal Structure and Pair Potentials: A Molecular-Dynamics Study[J]. Physical Review Letters, 1980, 45(14), 1196-1199
[12] Hu Kaixin, Du Kang, Chen Qisheng. Nonlinear waves in a sheared liquid film on a horizontal plane at small Reynolds numbers[J]. Journal of Fluid Mechanics, 2024, 999:A14
[13] Nose S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods[J]. The Journal of Chemical Physics, 1984, 81(1), 511-0
[14] Car R, Parrinello M. Unified Approach for Molecular Dynamics and Density-Functional Theory[J]. Physical Review Letters, 1985, 55(22), 2471-2474
[15] Cagin T, Pettit B M. Grand Canonical Monte Carlo and Molecular Dynamics Simulations of Fluid Adsorption in Micropores[J]. The Journal of Chemical Physics, 1991, 94(10), 6659-6666
[16] Chandler D, Wolynes P G. Exploring the Folding Free Energy Landscape of Proteins[J]. Science, 1993, 260(5108), 1310-1315
[17] Yao Ling. Gibbs system integrated Monte Carlo method for vapour-liquid phase equilibrium study of ethylene-vinyl acetate[D]. Tianjin University, 2013
[18] Allinger N L. Conformational Analysis 130 MM2 A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms[J]. Journal of the American Chemical Society, 1977, 99, 8127-8134
[19] Lii J H, Allinger N L. The MM3 Force Field for Amides, Polypeptides, and Proteins[J]. Journal of Computational Chemistry, 1991, 12(2), 186-195
[20] Allinger N L, Chen K H, Lii J H. An Improved Force Field (MM4) for Saturated Hydrocarbons[J]. Journal of Computational Chemistry, 1996, 17(5), 642-668
[21] Weiner S J, Kollman P A, et al. A New Force Field for Molecular Mechanical Simulation of Nucleic Acids and Proteins[J]. Journal of the American Chemical Society, 1984, 106, 765-784
[22] Brooks B R, Bruccoleri R E, et al. CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations[J]. Journal of Computational Chemistry, 1983, 4(2), 187-217
[23] Dauber-Osguthorpe P, Roberts V A, et al. Structure and Energetics of Ligand Binding to Proteins: Escherichia coli Dihydrofolate Reductase-Trimetrexate, a Test Case[J]. Proteins: Structure, Function, and Genetics, 1988, 4(1), 31-47
[24] Sun, H. COMPASS: An ab Initio Force Field Optimized for Condensed-Phase Applications Overview with Details on Alkane and Benzene Compounds[J]. Journal of Physical Chemistry B, 1998, 102(38), 7338-7364
[25] van Duin A C T, Dasgupta, S et al. ReaxFF: A Reactive Force Field for Hydrocarbons[J]. Journal of Physical Chemistry A, 2001, 105(41), 9396-9409
[26] Rahman A. Correlations in the motion of atoms in liquid argon[J]. Physical Review, 1964, 136(2A), A405-A411
[27] Abascal J L F, Vega C. A general purpose model for the condensed phases of water: TIP4P/2005[J]. The Journal of Chemical Physics, 2005, 123(23), 234505
[28] Rahman A. Correlations in the motion of atoms in liquid argon[J]. Physical Review, 1964, 136(2A), A405-A411
[29] Hong Lee, Hyung Suk Pak, Song Hi Lee. Molecular Dynamics Simulation of Liquid Alkanes 2. Thermodynamic, Structural, and Dynamic Properties of Branched-Chain Alkanes[J]. Bulletin of the Korean Chemical Society, 1997, 18(5): 478-484
[30] J L Qu. Molecular dynamics simulation and experimental study of the initial stage of the self-stabilised precipitation polymerisation reaction of C5 olefins with maleic anhydride [D]. Beijing University of Chemical Technology, 2022
[31] Yinhe Shen, Bo Qi, Yuandi Lin, et al. Molecular dynamics simulation of free radical generation during X-wax generation[J]. Power Engineering Technology, 2021, 40(01): 142-146
[32] Harris J G, Yung K H. Carbon dioxide's liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model[J]. The Journal of Physical Chemistry, 1995, 99(49), 16450-16455
[33] Borodin Oleg, Smith Grant D. Molecular Dynamics Simulations of Poly(ethylene oxide)/LiI Melts. 2. Dynamic Properties. Macromolecules, 2000, 33(6), 2273-2283
[34] Berendsen H J C, Postma J P M, van Gunsteren W F, et al. Interaction Models for Water in Relation to Protein Hydration[M]. Intermolecular Forces, ed. Dodrecht: Reidel, 1981: 331-354
[35] WANG Baohe, WANG Yunbo, LI Qun, et al. Equilibrium molecular dynamics simulation of water-vapour-liquid interfacial properties[J]. Henan Chemical Industry, 2012, 29(21): 31-35
[36] Izvekov, Sergei; Voth, Gregory A. Multiscale coarse graining of liquid-state systems. The Journal of Chemical Physics, 123(13), 134105
[37] Zakharov V V, Brodskaya E N, Laaksonen A. Surface tension of water droplets: A molecular dynamics study of model and size dependencies[J]. Journal of Chemical Physics, 107(24):10675-10683, 10.1063/1.474184
[38] Berendsen H J C, Grigera J R, Straatsma T P. The missing term in effective pair potentials. 91(24), 6269-6271
[39] Alejandre J, Tildesley D J, Chapela A. Molecular dynamics simulation of the orthobaric densities and surface tension of water[J]. The Journal of Chemical Physics, 102(11), 4574-4583
[40] Boulougouris G C, Economou I G, Theodorou D N. Engineering a Molecular Model for Water Phase Equilibrium over a Wide Temperature Range[J]. J. Phys. Chem. B, 1998, 102(6):1029-1035
[41] Liu Z P, Huang S P, Wang W Ch. Molecular computational science-a new growth point for chemical engineering[J]. Journal of Chemical Engineering, 2003, (04):464-476
[42] Bauer B A, Patel S. Properties of water along the liquid-vapor coexistence curve via molecular dynamics simulations using the polarizable TIP4P-QDP-LJ water model[J]. The Journal of Chemical Physics, 2009, 131: 084709
[43] Martin M G, Siepmann J I. Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes[J]. The Journal of Physical Chemistry B, 1998, 102(14), 2569-2577
[44] Gupta S, Choppin G R. Molecular dynamics simulations of water-octane mixtures[J]. Journal of Molecular Liquids, 2000, 88(1), 1-11
[45] Harris J G, Yung K H. Carbon dioxide's liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model[J]. The Journal of Physical Chemistry, 1995, 99(49), 16450-16455
[46] Di Xia. Molecular dynamics simulation of vapour-liquid phase equilibrium properties of HFO-1234yf workmass and its mixtures [D]. Chongqing University, 2016
[47] Wen Chengze, Dai Yuande. Molecular dynamics simulation study of gas-liquid phase equilibrium of R1234ze(E)[J]. Low Temperature and Superconductivity, 2023, 51(11): 61-67
[48] Zhi Yang, Maoqiong Gong, et al. Jianfeng Wu, Molecular modeling and simulation of vapor-liquid equilibrium of the refrigerant R152a and its mixture R152a+R32[J]. Fluid Phase Equilibria, 2015, 394: 93-100
[49] Raabe G. Molecular simulation studies in hydrofluoroolefine (HFO) working fluids and their blends[J]. Science and Technology for the Built Environment, 2016, 22(8), 1077-1089
[50] Md Sarwar Alam, Ji Hwan Jeong, Comparative molecular dynamics simulations of homogeneous condensation of refrigerants[J]. International Journal of Thermal Sciences, 2019, 141: 187-198
[51] Md Sarwar Alam, Ji Hwan Jeong, Thermodynamic properties and critical parameters of HFO-1123 and its binary blends with HFC-32 and HFC-134a using molecular simulations[J]. International Journal of Refrigeration, 2019, 104:311-320
[52] Alam MS, Jeong J H. Calculation of the thermodynamic properties of HFO/HFC-448A and HFO/HFC-449A in a saturation temperature range of 233.15 K to 343.15 K using molecular dynamics simulations[J]. International Communications in Heat and Mass Transfer, 116, 104717
[53] Shouyin Cai, Qibin Li, et al. Evaporation of R32/R152a mixtures on the Pt surface: A molecular dynamics study[J]. International Journal of Refrigeration, 2020, 113: 156-163
[54] Alam M S, Jeong J H. MD simulation estimation of saturation pressure and vapor-liquid equilibrium for binary blends of HFO-1234yf and HFO-1123[J]. Int. J. Air-Cond. Ref, 2022, 30: 9
[55] Chengze Wen. Molecular dynamics simulation of gas-liquid phase equilibrium properties of R1234ze(E) and its mixtures[D]. Nanchang University, 2024
[56] Borodin, Oleg A et al. Molecular Dynamics Study of the Influence of Solid Interfaces on Poly(ethylene oxide) Structure and Dynamics[J]. Macromolecules, 2003, 36: 7873-7883
[57] Xu R, Zhou Z, et al. First-Principles Molecular Dynamics Simulations on Water-Solid Interface Behavior of H2O-Based Atomic Layer Deposition of Zirconium Dioxide[J]. Nanomaterials, 2022, 12: 4362
[58] Yang M, Liu Y, Mo, Y. Lithium crystallization at solid interfaces[J]. Nat Commun, 2023, 14: 2986
[59] LI Zongyang, BI Lin, CHEN Qiangqiang. Study on the transformation mechanism between momentum and energy components of gas-solid interface interaction based on molecular dynamics simulation[C]//Chinese Society of Mechanics. Proceedings of the Chinese Mechanics Conference-2021+1 (Volume III). State Key Laboratory of Aerodynamics, China Aerodynamic Research and Development Centre, 2022: 1., 10.26914/c.cnkihy.2022.074269
[60] Xingfan Zhang, Peiru Zheng, et al. Atomic-scale understanding of oxidation mechanisms of materials by computational approaches: A review[J]. Materials & Design, 2022, 217:110605
[61] Zhang Ye. Molecular dynamics simulation and study of gas-solid interfacial interaction [D]. National University of Defence Technology, 2019
[62] Thompson A P, Swiler L P, et al. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials[J]. Journal of Computational Physics, 2015, 285: 316-330
[63] Huan T D, Batra, R, et al. A universal strategy for the creation of machine learning-based atomistic force fields[J]. NPJ Computational Materials, 2017, 3(1), 37
[64] Behler J, Parrinello M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces[J]. Physical Review Letters, 2007, 98(14): 146401
[65] Fabian L. Thiemann, et al. Introduction to machine learning potentials for atomistic simulations[J]. Chemical Physics, 2024
[66] Morawietz T, Singraber A, et al. How van der Waals interactions determine the unique properties of water[J]. Proceedings of the National Academy of Science, 2016, 113(30):8368-8373
[67] Behler J, Parrinello M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces[J]. Physical Review Letters, 2007, 98(14): 146401
[68] Behler J. Four Generations of High-Dimensional Neural Network Potentials[J]. Chemical Reviews, 2021, 121(16): 10037-10072
[69] Han Wang, Linfeng Zhang, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics[J]. Computer Physics Communications, 2018, 228: 178-184
[70] Himanen L, Marc O J, et al. DScribe: Library of descriptors for machine learning in materials science[J]. Computer Physics Communications, 2020, 247:106949
[71] LIU Dongfei, ZHANG Fan, et al. A review of machine learning potentials and their applications in molecular simulation[J]. Journal of Chemical Engineering, 2024, 75(04): 1241-1255
[72] Wang H, Zhang L F, Han J Q, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics[J]. Computer Physics Communications, 2018, 228: 178-184
[73] Castro E Z G, Binar, R M B, et al. Modeling the Vapor-Liquid Equilibrium of CO2-H2O-[CNC1Im][NTf2] Blends Using Machine Learning Techniques to Determine Feasible Solvent Conditions for CO2 Absorption in a Gas-Sweetening Unit[J]. Proceedings of the 7th International Conference on Materials Engineering and Nanotechnology 2023 (ICMEN 2023); 04-05 Nov, Kuala Lumpur, Malaysia. ICMEN 2023. Springer Proceedings in Physics, vol 411. Springer, Singapore
[74] Anirban Mondal, Dina Kussainova, Shuwen Yue, et al. Modeling Chemical Reactions in Alkali Carbonate-Hydroxide Electrolytes with Deep Learning Potentials[J]. Journal of Chemical Theory and Computation, 2022, 19(14):4584-4595
PDF VERSION [DOWNLOAD]
Advances in molecular dynamics simulation of phase equilibrium

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence