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Mirzaeinia A, Feyzi F. A perturbed-chain equation of state based on Wertheim TPT for the fully flexible LJ chains in the fluid and solid phases. J Chem Phys 2020; 152:134502. [PMID: 32268737 DOI: 10.1063/1.5134511] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
In the framework of thermodynamic perturbation theory (TPT), a new perturbed-chain equation of state (EOS) is presented for a fully flexible Lennard-Jones (LJ) chain system. The EOS is the sum of repulsive and perturbation contributions. The reference term of the EOS is derived based on first- and second-order TPT of Wertheim for the chains interacting with each other through the Weeks-Chandler-Anderson potential model. In order to derive the perturbation term, we have used the radial distribution function of the hard-chain system with a chain range of m = 2-10 and packing fraction range of η = 0.10-0.72, which cover the entire density range from vapor to solid phases. The performance of the EOS is tested against simulation data of the compressibility factor, residual internal energy, and phase equilibrium. A close agreement was observed across all cases. The EOS has three pure component parameters and is able to describe the global vapor-liquid-solid phase diagram of the LJ chain.
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Affiliation(s)
- Ali Mirzaeinia
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Farzaneh Feyzi
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
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2
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Abolala M, Peyvandi K, Varaminian F, Hashemianzadeh SM. Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2019.1582813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Mostafa Abolala
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Kiana Peyvandi
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Farshad Varaminian
- Gas Hydrate Research Laboratory, Faculty of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
| | - Seyed Majid Hashemianzadeh
- Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran, Iran
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Trombach L, Hoy RS, Wales DJ, Schwerdtfeger P. From sticky-hard-sphere to Lennard-Jones-type clusters. Phys Rev E 2018; 97:043309. [PMID: 29758765 DOI: 10.1103/physreve.97.043309] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Indexed: 06/08/2023]
Abstract
A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.
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Affiliation(s)
- Lukas Trombach
- Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0632 Auckland, New Zealand
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - David J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0632 Auckland, New Zealand
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Drammensveien 78, NO-0271 Oslo, Norway
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Mirzaeinia A, Feyzi F, Hashemianzadeh SM. Equations of state for the fully flexible WCA chains in the fluid and solid phases based on Wertheims-TPT2. J Chem Phys 2018; 148:104502. [PMID: 29544293 DOI: 10.1063/1.5018789] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
Based on Wertheim's second order thermodynamic perturbation theory (TPT2), equations of state (EOSs) are presented for the fluid and solid phases of tangent, freely jointed spheres. It is considered that the spheres interact with each other through the Weeks-Chandler-Anderson (WCA) potential. The developed TPT2 EOS is the sum of a monomeric reference term and a perturbation contribution due to bonding. MC NVT simulations are performed to determine the structural properties of the reference system in the reduced temperature range of 0.6 ≤ T* ≤ 4.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. Mathematical functions are fitted to the simulation results of the reference system and employed in the framework of Wertheim's theory to develop TPT2 EOSs for the fluid and solid phases. The extended EOSs are compared to the MC NPT simulation results of the compressibility factor and internal energy of the fully flexible chain systems. Simulations are performed for the WCA chain system for chain lengths of up to 15 at T* = 1.0, 1.5, 2.0, 3.0. Across all the reduced temperatures, the agreement between the results of the TPT2 EOS and MC simulations is remarkable. Overall Average Absolute Relative Percent Deviation at T* = 1.0 for the compressibility factor in the entire chain lengths we covered is 0.51 and 0.77 for the solid and fluid phases, respectively. Similar features are observed in the case of residual internal energy.
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Affiliation(s)
- Ali Mirzaeinia
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Farzaneh Feyzi
- Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
| | - Seyed Majid Hashemianzadeh
- Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran 16846-13114, Iran
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van Westen T, Vlugt TJH, Gross J. On the vapor-liquid equilibrium of attractive chain fluids with variable degree of molecular flexibility. J Chem Phys 2015; 142:224504. [DOI: 10.1063/1.4922264] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thijs van Westen
- Process and Energy Laboratory, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Thijs J. H. Vlugt
- Process and Energy Laboratory, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Joachim Gross
- Institut für Thermodynamik und Thermische Verfahrenstechnik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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Alavi F, Feyzi F. A new perturbed-chain equation of state for square-well chains in fluid and solid phases. J Chem Phys 2013; 139:074104. [DOI: 10.1063/1.4818420] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Alavi F, Feyzi F. The equation of state of flexible chains of tangent hard spheres at high-density region from simulation and thermodynamic perturbation theory. J Chem Phys 2013; 138:024903. [DOI: 10.1063/1.4774025] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hoy RS, Harwayne-Gidansky J, O'Hern CS. Structure of finite sphere packings via exact enumeration: implications for colloidal crystal nucleation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051403. [PMID: 23004757 DOI: 10.1103/physreve.85.051403] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2012] [Revised: 04/28/2012] [Indexed: 06/01/2023]
Abstract
We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres N, and their diversity of structure and symmetry increases with increasing N and decreases with increasing hyperstaticity H≡N_{c}-N_{ISO}, where N_{c} is the number of pair contacts and N_{ISO}=3N-6. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction f of nuclei with order compatible with the bulk (rhcp) crystal decreases sharply with increasing N due to a high propensity for stacking faults, five- and near-fivefold symmetric structures, and other motifs that preclude rhcp order. While f increases with increasing H, a significant fraction of hyperstatic nuclei for N as small as 11 retain non-rhcp structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of N≲10 particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.
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Affiliation(s)
- Robert S Hoy
- Department of Mechanical Engineering & Materials Science and Department of Physics, Yale University, New Haven, Connecticut, USA
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Lee JH, Shin MS, Yoo KP. Development of Single Insertion Probability for Equation of State Applicable to Three Phases of Matter. Ind Eng Chem Res 2011. [DOI: 10.1021/ie101853s] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Ju Ho Lee
- Department of Chemical and Biomolecular Engineering, Sogang University, Sinsu-Dong, Mapo-Gu, Seoul 121−742, Korea
| | - Moon Sam Shin
- Department of Dermatological Health Management, Eulji University, 212 Yangji-dong, Sujeong-gu, Seongnam-si, Gyeonggi-do, 461−713, Republic of Korea
| | - Ki-Pung Yoo
- Department of Chemical and Biomolecular Engineering, Sogang University, Sinsu-Dong, Mapo-Gu, Seoul 121−742, Korea
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Tan SP, Adidharma H, Radosz M. Recent Advances and Applications of Statistical Associating Fluid Theory. Ind Eng Chem Res 2008. [DOI: 10.1021/ie8008764] [Citation(s) in RCA: 241] [Impact Index Per Article: 15.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Sugata P. Tan
- Soft Material Laboratory, Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071
| | - Hertanto Adidharma
- Soft Material Laboratory, Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071
| | - Maciej Radosz
- Soft Material Laboratory, Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071
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