1
|
Eustaquio-Armenta MDR, Méndez-Maldonado GA, González-Melchor M. The line tension of two-dimensional ionic fluids. J Chem Phys 2016; 144:134705. [PMID: 27059583 DOI: 10.1063/1.4944731] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Pressure tensor components are very useful in the calculation of the tension associated with a liquid-vapor interface. In this work, we present expressions for the pressure tensor components of two-dimensional ionic fluids, modeled at the level of the primitive model. As an application, we carried out molecular dynamics simulations of liquid-vapor interfaces to calculate the line tension of the 1:1 two-dimensional ionic fluid, whose liquid-vapor coexistence curve had already been obtained in a previous work. The pressure tensor components were validated by simulating states of one phase and reproducing the scalar pressure, previously obtained from bulk simulations and reported in the literature. The effects on the line tension and the coexisting densities, originated by the choice of the Ewald parameters, the cutoff radius, and the interfacial length were also evaluated.
Collapse
Affiliation(s)
| | | | - Minerva González-Melchor
- Instituto de Física "Luis Rivera Terrazas," Benemérita Universidad Autónoma de Puebla, Apdo. Postal J-48, 72570 Puebla, Mexico
| |
Collapse
|
2
|
|
3
|
Méndez-Maldonado GA, González-Melchor M, Alejandre J. Liquid-vapor phase diagram and cluster formation of two-dimensional ionic fluids. J Chem Phys 2012; 137:054711. [DOI: 10.1063/1.4738981] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
4
|
Affiliation(s)
- Alberto Striolo
- School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, OK 73019, U.S.A
| |
Collapse
|
5
|
DI CAPRIO D, STAFIEJ J, BADIALI JP. Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem, Gibbs adsorption and surface tension. Mol Phys 2009. [DOI: 10.1080/0026897031000154293] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- D. DI CAPRIO
- a Laboratoire d'Électrochimie et Chimie Analytique , UMR 7575, Université P. et M. Curie, Paris VI, Bât. , F74, BP 39, 4, Place Jussieu , 75230 , Paris Cedex 05 , France
| | - J. STAFIEJ
- b Department of Electrode Processes , Institute of Physical Chemistry of the Polish Academy of Sciences , ul. Kasprzaka 44/52, 01-224 , Warsaw , Poland
| | - J. P. BADIALI
- a Laboratoire d'Électrochimie et Chimie Analytique , UMR 7575, Université P. et M. Curie, Paris VI, Bât. , F74, BP 39, 4, Place Jussieu , 75230 , Paris Cedex 05 , France
| |
Collapse
|
6
|
Ciach A. Universal sequence of ordered structures obtained from mesoscopic description of self-assembly. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061505. [PMID: 19256844 DOI: 10.1103/physreve.78.061505] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2008] [Indexed: 05/27/2023]
Abstract
Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived by a systematic coarse-graining procedure. For particles interacting with spherically symmetric potentials of arbitrary form, the grand-thermodynamic potential consists of two terms. The first term is associated with microscopic length-scale fluctuations, and has the form of the standard density functional. The second term is associated with mesoscopic length-scale fluctuations, and has the form known from the statistical field theory. For the correlation function between density fluctuations in mesoscopic regions, a pair of equations similar to the Ornstein-Zernicke equation with a new closure is obtained. In the special case of weak ordering on the mesoscopic length scale, the theory takes a form similar to either the Landau-Ginzburg-Wilson (LGW) or the Landau-Brazovskii (LB) field theory, depending on the form of the interaction potential. Microscopic expressions for the phenomenological parameters that appear in the Landau-type theories are obtained. Within the framework of this theory, we obtain a universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. The sequence of phases agrees with experimental observations and with simulations of many self-assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential, we find the bicontinuous gyroid phase ( Ia3d symmetry) that may be related to a network-forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| |
Collapse
|
7
|
Ciach A, Góźdź WT, Stell G. Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051505. [PMID: 17677071 DOI: 10.1103/physreve.75.051505] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2006] [Indexed: 05/16/2023]
Abstract
The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa, Poland
| | | | | |
Collapse
|
8
|
Gutkowski KI, Bianchi HL, Japas ML. Nonasymptotic Critical Behavior of a Ternary Ionic System. J Phys Chem B 2007; 111:2554-64. [PMID: 17302450 DOI: 10.1021/jp067069z] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.
Collapse
Affiliation(s)
- Karin I Gutkowski
- Unidad de Actividad Química, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
| | | | | |
Collapse
|
9
|
Ren R, O'Keeffe CJ, Orkoulas G. Simulation of symmetric tricritical behavior in electrolytes. J Chem Phys 2006; 125:124504. [PMID: 17014188 DOI: 10.1063/1.2354148] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Despite extensive experimental, theoretical, and simulation efforts, a unified description of ionic phase transitions and criticality has not yet emerged. In this work, we investigate the phase behavior of the restricted primitive model of electrolyte solutions on the simple cubic lattice using grand canonical Monte Carlo simulations and finite-size scaling techniques. The phase diagram of the system is distinctly different from its continuum-space analog. We find order-disorder transitions for reduced temperatures T* < or approximately 0.51, where the ordered structures resemble those of the NaCl crystal. The order-disorder transition is continuous for 0.15 < or approximately T* < or approximately 0.51 and becomes first order at lower temperatures. The line of first-order transitions is a line of three-phase coexistence between a disordered and two ordered phases. The line of continuous, second-order transitions meets this line of triple points at a tricritical point at T* approximately equal to 0.1475. We locate the line of continuous transitions, and the line of triple points using finite-size scaling techniques. The tricritical temperature is estimated by extrapolation of the size-dependent tricritical temperatures obtained from a sixth-order Landau expansion of the free energy. Our calculated phase diagram is in qualitative agreement with mean-field theories.
Collapse
Affiliation(s)
- Ruichao Ren
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095, USA
| | | | | |
Collapse
|
10
|
Ciach A, Patsahan O. Field-theoretic description of ionic crystallization in the restricted primitive model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021508. [PMID: 17025438 DOI: 10.1103/physreve.74.021508] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2006] [Indexed: 05/12/2023]
Abstract
Effects of charge-density fluctuations on a phase behavior of the restricted primitive model are studied within a field-theoretic formalism. We focus on a lambda line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field theories, but is absent in simulation results. In our study the RPM is reduced to a phi(6) theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the lambda -line disappears. Instead, a fluctuation-induced first-order transition to a charge-ordered phase appears in the same region of a phase diagram, where the liquid-ionic-crystal transition is obtained in simulations. Our results indicate that the charge-ordered phase should be identified with an ionic crystal.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| | | |
Collapse
|
11
|
Ciach A. Universality class of the critical point in the restricted primitive model of ionic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066110. [PMID: 16906917 DOI: 10.1103/physreve.73.066110] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2006] [Indexed: 05/11/2023]
Abstract
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated into disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| |
Collapse
|
12
|
Diehl A, Panagiotopoulos AZ. Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion. J Chem Phys 2006; 124:194509. [PMID: 16729827 DOI: 10.1063/1.2192498] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.
Collapse
Affiliation(s)
- Alexandre Diehl
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760, Fortaleza, CE, Brazil
| | | |
Collapse
|
13
|
|
14
|
Diehl A, Panagiotopoulos AZ. Phase diagrams in the lattice restricted primitive model: from order-disorder to gas-liquid phase transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:046118. [PMID: 15903737 DOI: 10.1103/physreve.71.046118] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2004] [Indexed: 05/02/2023]
Abstract
The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (NN) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich phase behavior as the NN strength is varied. In particular, the phase diagram is very similar to that of the continuum RPM for high NN strength. Specifically, we have found both gas-liquid phase separation, with associated Ising critical point, and a first-order liquid-solid transition. We discuss how the line of continuous order-disorder transitions present for the low NN strength changes into continuum-space behavior as one increases the NN strength and compare our findings with recent theoretical results by Ciach and Stell [Phys. Rev. Lett. 91, 060601 (2003)].
Collapse
Affiliation(s)
- Alexandre Diehl
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760, Fortaleza, Ceará, Brazil.
| | | |
Collapse
|
15
|
Ciach A, Stell G. Criticality, tricriticality, and crystallization in discretized models of electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016114. [PMID: 15324136 DOI: 10.1103/physreve.70.016114] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2004] [Indexed: 05/24/2023]
Abstract
The Restricted Primitive Model of ionic systems is studied within a field-theoretic approach in order to provide a theoretic basis for the qualitative difference in the phase diagrams obtained in simulations for sigma/a=1,sigma/a=2, and sigma/a>/=3 ( a is the lattice constant and sigma is the ion diameter). The evolution of the phase diagrams from the case sigma/a=1 to the case sigma/a=square root[2] [nearest-neighbor ( NN ) occupancy excluded] is studied in the model with NN repulsion, 0</=J</= infinity, supplementing Coulomb forces. The boundary of stability of the charge-disordered phase with respect to short-wavelength charge fluctuations and the tricritical point are found in a mean-field ( MF ) approximation. Next, the effect of fluctuations is studied and we find that for J exceeding a particular value J0 a fluctuation-induced first-order phase transition should be expected instead of the continuous transition found in MF. At J= J0 the line of continuous transitions splits into two lines enclosing the two-phase region, whose thickness increases from zero when J>/= J0 increases. We argue that this transition corresponds to formation of a bcc ionic crystal. For high densities the ions form an fcc crystal, for which we find a fluctuation-induced first-order charge-ordered-charge-disordered transition, in agreement with recent simulation studies. Our results also shed light on the simulation results obtained for an off-lattice ionic system, for which a schematic phase diagram is constructed.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences 01-224 Warszawa, Poland
| | | |
Collapse
|
16
|
Kobelev V, Kolomeisky AB, Panagiotopoulos AZ. Thermodynamics of electrolytes on anisotropic lattices. ACTA ACUST UNITED AC 2003; 68:066110. [PMID: 14754272 DOI: 10.1103/physreve.68.066110] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2003] [Indexed: 11/07/2022]
Abstract
The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space 1/r electrostatic interactions have been investigated. At all degrees of anisotropy, only coexistence between a disordered low-density phase and an ordered high-density phase with the structure similar to ionic crystal was found, in contrast to recent theoretical predictions. Tricritical parameters were determined to be increasing functions of anisotropy parameters which is consistent with theoretical calculations based on the Debye-Hückel approach. At large anisotropies a two-dimensional-like behavior is observed, from which we estimated the dimensionless tricritical temperature and density for the two-dimensional square lattice electrolyte to be T*(tri)=0.14 and rho*(tri)=0.70.
Collapse
Affiliation(s)
- Vladimir Kobelev
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | | | | |
Collapse
|
17
|
Ciach A, Stell G. Effect of space discretization on phase diagrams in ionic systems: a field-theoretic approach. PHYSICAL REVIEW LETTERS 2003; 91:060601. [PMID: 12935060 DOI: 10.1103/physrevlett.91.060601] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2003] [Indexed: 05/24/2023]
Abstract
Using Landau-Ginzburg-Wilson field-theoretic methods we determine for what kind of space discretization the transition between charge-disordered and charge-ordered phases in the restricted primitive model is fluctuation-induced first order. We identify this transition with ionic-crystal formation. We predict four types of generic phase diagrams in ionic systems for various kinds of space discretization for low and intermediate densities of ions. Our results also shed light on the simulation results obtained for an off-lattice ionic system over a wide range of densities, including the fcc crystal.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences 01-224 Warszawa, Poland
| | | |
Collapse
|
18
|
Diehl A, Panagiotopoulos AZ. Phase transitions and tricriticality in the lattice restricted primitive model supplemented by short-range interactions. J Chem Phys 2003. [DOI: 10.1063/1.1545095] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
19
|
Ciach A, Góźdź WT, Evans R. Effect of a nearby charge-ordered phase on correlation functions in ionic systems. J Chem Phys 2003. [DOI: 10.1063/1.1539046] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
20
|
Gutkowski KI, Bianchi HL, Japas ML. Critical behavior of a ternary ionic system: A controversy. J Chem Phys 2003. [DOI: 10.1063/1.1536611] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
21
|
Brognara A, Parola A, Reatto L. Hierarchical reference theory study of the lattice restricted primitive model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066113. [PMID: 12188789 DOI: 10.1103/physreve.65.066113] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2001] [Indexed: 05/23/2023]
Abstract
A three dimensional model of point charges, named lattice restricted primitive model (LRPM), is investigated by using the hierachical reference theory of fluids. This approach, which generalizes the momentum renormalization group technique, is shown to capture the physics of the model and provides a quantitative description of the phase diagram. The comparison with recent numerical simulations and with other theoretical approaches is discussed both for the LRPM and for the Blume-Capel model, which can be seen as a screened version of LRPM. The nonuniversal crossover region close to the tricritical point is also discussed.
Collapse
Affiliation(s)
- A Brognara
- Dipartimento di Fisica, Università di Milano and Instituto Nazionale per la Fisica della Materia, Via Celoria 16, 20133 Milan, Italy
| | | | | |
Collapse
|
22
|
Almarza NG, Enciso E. Critical behavior of ionic solids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:042501. [PMID: 11690066 DOI: 10.1103/physreve.64.042501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2001] [Indexed: 05/23/2023]
Abstract
Phase transitions of lattice models of ionic crystals are studied by computer simulation. The nature of order-disorder transitions on different crystal structures is established and compared with the behavior of related Ising models. It is found that for both, continuous and first order transitions the basic features seem to be similar to those of Ising systems.
Collapse
Affiliation(s)
- N G Almarza
- Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense, E-28040 Madrid, Spain
| | | |
Collapse
|
23
|
Ciach A, Stell G. Effect of competition between Coulomb and dispersion forces on phase transitions in ionic systems. J Chem Phys 2001. [DOI: 10.1063/1.1342814] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|