1
|
Pasinetti PM, Ramirez-Pastor AJ, Vogel EE. Entropy-driven phases at high coverage adsorption of straight rigid rods on three-dimensional cubic lattices. Phys Rev E 2023; 107:064126. [PMID: 37464669 DOI: 10.1103/physreve.107.064126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
Combining Monte Carlo simulations and thermodynamic integration method, we study the configurational entropy per site of straight rigid rods of length k (k-mers) adsorbed on three-dimensional (3D) simple cubic lattices. The process is monitored by following the dependence of the lattice coverage θ on the chemical potential μ (adsorption isotherm). Then, we perform the integration of μ(θ) over θ to calculate the configurational entropy per site of the adsorbed phase s(k,θ) as a function of the coverage. Based on the behavior of the function s(k,θ), different phase diagrams are obtained according to the k values: k≤4, disordered phase; k=5,6, disordered and layered-disordered phases; and k≥7, disordered, nematic and layered-disordered phases. In the limit of θ→1 (full coverage), the configurational entropy per site is determined for values of k ranging between 2 and 8. For k≥6, MC data coincide (within the statistical uncertainty) with recent analytical predictions [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)2470-004510.1103/PhysRevE.103.042130] for very large rods. This finding represents the first numerical validation of the expression obtained by Dhar and Rajesh for d-dimensional lattices with d>2. In addition, for k≥5, the values of s(k,θ→1) for simple cubic lattices are coincident with those values reported in [P. M. Pasinetti et al., Phys. Rev. E 104, 054136 (2021)2470-004510.1103/PhysRevE.104.054136] for two-dimensional (2D) square lattices. This is consistent with the picture that at high densities and k≥5, the layered-disordered phase is formed on the lattice. Under these conditions, the system breaks to 2D layers, and the adsorbed phase becomes essentially 2D. The 2D behavior of the fully covered lattice reinforces the conjecture that the large-k behavior of entropy per site is superuniversal, and holds on d-dimensional hypercubical lattices for all d≥2.
Collapse
Affiliation(s)
- P M Pasinetti
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis - CONICET, Ejército de Los Andes 950, D5700HHW San Luis, Argentina
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis - CONICET, Ejército de Los Andes 950, D5700HHW San Luis, Argentina
| | - E E Vogel
- Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco 481180, Chile
- Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 9170124 Santiago, Chile
| |
Collapse
|
2
|
Dos Santos G, Cisternas E, Vogel EE, Ramirez-Pastor AJ. Orientational phase transition in monolayers of multipolar straight rigid rods: The case of 2-thiophene molecule adsorption on the Au(111) surface. Phys Rev E 2023; 107:014133. [PMID: 36797890 DOI: 10.1103/physreve.107.014133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Monte Carlo simulations and finite-size scaling theory have been carried out to study the critical behavior and universality for the isotropic-nematic (IN) phase transition in a system of straight rigid pentamers adsorbed on a triangular lattice with polarized nonhomogeneous intermolecular interactions. The model was inspired by the deposition of 2-thiophene molecules over the Au(111) surface, which was previously characterized by experimental techniques and density functional theory. A nematic phase, observed experimentally by the formation of a self-assembled monolayer of parallel molecules, is separated from the isotropic state by a continuous transition occurring at a finite density. The precise determination of the critical exponents indicates that the transition belongs to the three-state Potts universality class. The finite-size scaling analysis includes the study of mutability and diversity. These two quantities are derived from information theory and they have not previously been considered as part of the conventional treatment of critical phenomena for the determination of critical exponents. The results obtained here contribute to the understanding of formation processes of self-assembled monolayers, phase transitions, and critical phenomena from novel compression algorithms for studying mutual information in sequences of data.
Collapse
Affiliation(s)
- G Dos Santos
- Facultad de Ingeniería, Universidad de Mendoza, CONICET Mendoza, Argentina and Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, D5700HHW San Luis, Argentina
| | - E Cisternas
- Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile
| | - E E Vogel
- Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile and Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 9170124 Santiago, Chile
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, D5700HHW San Luis, Argentina
| |
Collapse
|
3
|
Akimenko SS, Myshlyavtsev AV, Myshlyavtseva MD, Gorbunov VA, Podgornyi SO, Solovyeva OS. Triangles on a triangular lattice: Insights into self-assembly in two dimensions driven by shape complementarity. Phys Rev E 2022; 105:044104. [PMID: 35590604 DOI: 10.1103/physreve.105.044104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 03/07/2022] [Indexed: 06/15/2023]
Abstract
A series of models for reversible filling of a triangular lattice with equilateral triangles has been developed and investigated. There are eight distinct models that vary in the set of prohibitions. In zeroth approximation, these models allow one to estimate the influence of the particles' shape and complementarity of their pair configurations on the self-assembly of dense monolayers formed by reversible filling. The most symmetrical models were found to be equivalent to hard-disk models on the hexagonal lattice. When any contact of hard triangles by vertices is prohibited, the dense monolayers are disordered, and their entropy tends to the constant. If only one pair configuration is prohibited, the close-packed layer appears through the continuous phase transition. In other cases, the weak first-order transition resulting in the self-assembly of close-packed layers is observed.
Collapse
Affiliation(s)
- S S Akimenko
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| | - A V Myshlyavtsev
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| | - M D Myshlyavtseva
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| | - V A Gorbunov
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| | - S O Podgornyi
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| | - O S Solovyeva
- Department of Chemistry and Chemical Engineering, Omsk State Technical University, Mira Avenue 11, Omsk 644050, Russian Federation
| |
Collapse
|
4
|
Shah A, Dhar D, Rajesh R. Phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice. Phys Rev E 2022; 105:034103. [PMID: 35428120 DOI: 10.1103/physreve.105.034103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 02/21/2022] [Indexed: 06/14/2023]
Abstract
A system of hard rigid rods of length k on hypercubic lattices is known to undergo two phase transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to a high-density phase with no orientational order. In this paper, we argue that, for large k, the second phase transition is a first-order transition with a discontinuity in density in all dimensions greater than 1. We show that the chemical potential at the transition is ≈kln[k/lnk] for large k, and that the density of uncovered sites drops from a value ≈(lnk)/k^{2} to a value of order exp(-ak), where a is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions d≥2. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length 9 on the square lattice.
Collapse
Affiliation(s)
- Aagam Shah
- Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Deepak Dhar
- Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| |
Collapse
|
5
|
Pasinetti PM, Ramirez-Pastor AJ, Vogel EE, Saravia G. Entropy-driven phases at high coverage adsorption of straight rigid rods on two-dimensional square lattices. Phys Rev E 2021; 104:054136. [PMID: 34942833 DOI: 10.1103/physreve.104.054136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 11/12/2021] [Indexed: 11/07/2022]
Abstract
Polymers are frequently deposited on different surfaces, which has attracted the attention of scientists from different viewpoints. In the present approach polymers are represented by rigid rods of length k (k-mers), and the substrate takes the form of an L×L square lattice whose lattice constant matches exactly the interspacing between consecutive elements of the k-mer chain. We briefly review the classical description of the nematic transition presented by this system for k≥7 observing that the high-coverage (θ) transition deserves a more careful analysis from the entropy point of view. We present a possible viewpoint for this analysis that justifies the phase transitions. Moreover, we perform Monte Carlo (MC) simulations in the grand canonical ensemble, supplemented by thermodynamic integration, to first calculate the configurational entropy of the adsorbed phase as a function of the coverage, and then to explore the different phases (and orientational transitions) that appear on the surface with increasing the density of adsorbed k-mers. In the limit of θ→1 (full coverage) the configurational entropy is obtained for values of k ranging between 2 and 10. MC data are discussed in comparison with recent analytical results [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)2470-004510.1103/PhysRevE.103.042130]. The comparative study allows us to establish the applicability range of the theoretical predictions. Finally, the structure of the high-coverage phase is characterized in terms of the statistics of k×l domains (domains of l parallel k-mers adsorbed on the surface). A distribution of finite values of l (l≪L) is found with a predominance of k×1 (single k-mers) and k×k domains. The distribution is the same in each lattice direction, confirming that at high density the adsorbed phase goes to a state with mixed orientations and no orientational preference. An order parameter measuring the number of k×k domains in the adsorbed layer is introduced.
Collapse
Affiliation(s)
- P M Pasinetti
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - E E Vogel
- Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco 481180, Chile and Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 9170124 Santiago, Chile
| | - G Saravia
- Los Eucaliptus 1189, Temuco 4812537, Chile
| |
Collapse
|
6
|
Negrete OA, Vargas P, Peña FJ, Saravia G, Vogel EE. Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model. ENTROPY 2021; 23:e23081019. [PMID: 34441159 PMCID: PMC8391205 DOI: 10.3390/e23081019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Revised: 08/05/2021] [Accepted: 08/05/2021] [Indexed: 11/16/2022]
Abstract
Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.
Collapse
Affiliation(s)
- Oscar A. Negrete
- Department of Physics, Universidad Técnica Federico Santa María, Vaparaíso 2390123, Chile; (O.A.N.); (F.J.P.)
- Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile;
| | - Patricio Vargas
- Department of Physics, Universidad Técnica Federico Santa María, Vaparaíso 2390123, Chile; (O.A.N.); (F.J.P.)
- Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile;
- Correspondence:
| | - Francisco J. Peña
- Department of Physics, Universidad Técnica Federico Santa María, Vaparaíso 2390123, Chile; (O.A.N.); (F.J.P.)
| | - Gonzalo Saravia
- Department of Physics, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile;
| | - Eugenio E. Vogel
- Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile;
- Department of Physics, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile;
| |
Collapse
|
7
|
Dhar D, Rajesh R. Entropy of fully packed hard rigid rods on d-dimensional hypercubic lattices. Phys Rev E 2021; 103:042130. [PMID: 34005993 DOI: 10.1103/physreve.103.042130] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2020] [Accepted: 03/22/2021] [Indexed: 11/07/2022]
Abstract
We determine the asymptotic behavior of the entropy of full coverings of a L×M square lattice by rods of size k×1 and 1×k, in the limit of large k. We show that full coverage is possible only if at least one of L and M is a multiple of k, and that all allowed configurations can be reached from a standard configuration of all rods being parallel, using only basic flip moves that replace a k×k square of parallel horizontal rods by vertical rods, and vice versa. In the limit of large k, we show that the entropy per site S_{2}(k) tends to Ak^{-2}lnk, with A=1. We conjecture, based on a perturbative series expansion, that this large-k behavior of entropy per site is superuniversal and continues to hold on all d-dimensional hypercubic lattices, with d≥2.
Collapse
Affiliation(s)
- Deepak Dhar
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| |
Collapse
|