Lattice fluid with attractive interaction between nearest neighbors and repulsive interaction between next-next-nearest neighbors on simple cubic lattice

  • Yaroslav G. Groda Belarusian State Technological University, 13a Sviardlova Street, Minsk 220006, Belarus
  • Vyacheslav S. Vikhrenko Belarusian State Technological University, 13a Sviardlova Street, Minsk 220006, Belarus
  • Dung di Caprio National Graduate School of Chemistry, 11 Pierre and Marie Curie Street, Paris 75005, France https://orcid.org/0000-0001-6239-7427
DOI: https://doi.org/10.33581/2520-2243-2019-2-84-95

Abstract

The lattice system with competing interactions (attractive between nearest neighbors and repulsive between next-next-nearest neighbors) on a simple cubic lattice is studied. It is shown that the competing interactions lead to the order-disorder phase transitions. The geometric order parameter for localizing the second-order phase transition points is introduced. With its help the critical value of the interaction parameter was established, and the phase diagram of the system was constructed. An analytical quasi-chemical (QChA) approximation for evaluation of the equilibrium parameters of the system is proposed. The chemical potential, the thermodynamic factor, and the correlation functions are determined both within the framework of the developed approximate approach and as a result of the Monte Carlo simulation of the lattice system. The obtained dependence of the thermodynamic factor of the system on concentration indicates a strong suppression of fluctuations, characteristic for an ordered state. In turn, the complex nature of the concentration dependence of the correlation functions reflecting the structural features of the system demonstrates the important contribution of competing interactions. The proposed analytical approach allows one to correctly describe the qualitative features of the structural properties of systems with competing interactions and can be used to quantify the thermodynamic characteristics of these systems.

Author Biographies

Yaroslav G. Groda, Belarusian State Technological University, 13a Sviardlova Street, Minsk 220006, Belarus

PhD (physics and mathematics), docent; associate professor at the department of mechanics and engineering, faculty of chemical technology and engineering

Vyacheslav S. Vikhrenko, Belarusian State Technological University, 13a Sviardlova Street, Minsk 220006, Belarus

doctor of science (physics and mathematics), full professor; professor at the department of mechanics and engineering, faculty of chemical technology and engineering

Dung di Caprio, National Graduate School of Chemistry, 11 Pierre and Marie Curie Street, Paris 75005, France

PhD (physics); researcher

References

  1. Stradner A, Sedgwick H, Cardinaux F, Poon WCK, Egelhaaf SU, Schurtenberger P. Equilibrium cluster formation in concentrated protein solutions and colloids. Nature. 2004;432:492– 495. DOI: 10.1038/Nature03109.
  2. Khaldoun A, Moller P, Fall A, Wegdam G, De Leeuw B, Méheust Y, et al. Quick clay and landslides of clayey soils. Physical Review Letters. 2009;103(18):188301. DOI: 10.1103/PhysRevLett.103.188301.
  3. Meyra AG, Zarragoicoechea GJ, Kuz VA. Self-organization of plants in a dryland ecosystem: Symme-try breaking and critical cluster size. Physical Review E. 2015;91(5):052810. DOI: 10.1103/PhysRevE.91.052810.
  4. Archer AJ, Pini D, Evans R, Reatto L. Model colloidal fluid with competing interactions: Bulk and interfacial properties. Journal of Chemical Physics. 2007;126(1):014104. DOI: 10.1063/1.2405355.
  5. Pini D, Jialin G, Parola A, Reatto L. Enhanced density fluctuations in fluid systems with competing interactions. Chemical Physics Letters. 2000;327(3):209–215. DOI: 10.1016/S0009-2614(00)00763-6.
  6. Pekalski J, Ciach A, Almarza NG. Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases. Journal of Chemical Physics. 2014;140:114701. DOI: 10.1063/1.4868001.
  7. Almarza NG, Pekalski J, Ciach A. Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation. Journal of Chemical Physics. 2014;140:164708. DOI: 10.1063/1.4871901.
  8. Groda YaG, Bildanau EE, Gapanjuk DV. Critical parameter of the lattice fluid with SALR-potential on the simple square lattice. Trudy BGTU. Seriya 3. Fiziko-matematicheskie nauki i informatika [Internet]. 2018 [cited 2019 January 27];1(206):24 –28. Available from: elib.belstu.by/handle/123456789/25356. Russian.
  9. Groda YaG, Vikhrenko VS, di Caprio D. Equilibrium properties of the lattice system with SALR interaction potential on a square lattice: quasi-chemical approximation versus Monte Carlo simulation. Condensed Matter Physics. 2018;21(4):43002. DOI: 10.5488/CMP.21.43002.
  10. Uebing C, Gomer RA. Monte Carlo study of surface diffusion coefficients in the presence of adsorbate-adsorbate interactions. III. Repulsive nearest‐neighbor and attractive next‐nearest‐neighbor interactions. Journal of Chemical Physics. 1991;95(10):7626 –7652. DOI: 10.1063/1.461817.
  11. Binder K, Landau DP. Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions. Physical Review B. 1980;21(5):1941–1963. DOI: 10.1103/PhysRevB.21.1941.
  12. Groda YaG, Argyrakis P, Bokun GS, Vikhrenko VS. SCDA for 3D lattice gases with repulsive interaction. The European Physical Journal B. 2003;32(4):527–535. DOI: 10.1140/epjb/e2003-00118-3.
  13. Vikhrenko VS, Groda YaG, Bokun GS. Ravnovesnye i diffuzionnye kharakteristiki interkalyatsionnykh sistem na osnove reshetochnykh modelei [Internet]. Minsk: Belarusian State Technological University; 2008 [cited 2018 September 14]. 326 p. Available from: elib.belstu.by/handle/123456789/2716. Russian.
  14. Groda YaG, Lasovsky RN, Vikhrenko VS. Equilibrium and diffusional properties of two-level lattice systems: quasichemical and diagram approximation versus Monte Carlo simulation results. Solid State Ionics. 2005;176(19–22):1675–1680. DOI: 10.1016/j.ssi.2005.04.016.
  15. Bokun GS, Groda YaG, Belov VV, Uebing C, Vikhrenko VS. The self-consistent diagram approximation for lattice systems. European Physical Journal B. 2000;15(2):297–304. DOI: 10.1007/s100510051128.
  16. Bokun GS, Groda YaG, Uebing C, Vikhrenko VS. Statistical-mechanical description of diffusion in interacting lattice gases. Physica A: Statistical Mechanics and its Applications. 2001;296(1–2):83–105. DOI: 10.1016/S0378-4371(01)00163-7.
Published
2019-05-20
Keywords: lattice fluid, simple cubic lattice, competing interaction, SALR-potential, order parameter, Monte Carlo simulation, critical parameter, phase diagram, quasi-chemical approximation
Supporting Agencies The project has received funding from European Union’s Horizon-2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 734276, Institute for Nuclear Problems of Belarusian State University (agreement No. 209/103) and the Ministry of Education of the Republic of Belarus.
How to Cite
Groda, Y. G., Vikhrenko, V. S., & di Caprio, D. (2019). Lattice fluid with attractive interaction between nearest neighbors and repulsive interaction between next-next-nearest neighbors on simple cubic lattice. Journal of the Belarusian State University. Physics, 2, 84-95. https://doi.org/10.33581/2520-2243-2019-2-84-95
Issue
No 2 (2019): Journal of the Belarusian State University. Physics
Section
Condensed State Physics

Copyright (c) 2019 Journal of the Belarusian State University. Physics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The authors who are published in this journal agree to the following:

  1. The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
  2. The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
  3. The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)