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Ciach A, Góźdź WT. Self-consistent theory for systems with mesoscopic fluctuations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414010. [PMID: 27545343 DOI: 10.1088/0953-8984/28/41/414010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We have developed a theory for inhomogeneous systems that allows for the incorporation of the effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess [Formula: see text] of the volume fraction of particles ζ has been obtained, and an approximation leading to a closed set of equations for the two-point functions has been introduced for the disordered inhomogeneous phase. We have numerically solved the self-consistent equations for one-dimensional (1D) and three-dimensional (3D) models with short-range attraction and long-range repulsion. Predictions for all of the qualitative properties of the 1D model agree with the exact results, but only semi-quantitative agreement is obtained in the simplest version of the theory. The effects of fluctuations in the two 3D models considered are significantly different, despite the very similar properties of these models in the mean-field approximation. In both cases we obtain the sequence of large-small-large compressibility for increasing ζ. The very small compressibility is accompanied by the oscillatory decay of correlations with correlation lengths that are orders of magnitude larger than the size of particles. In one of the two models considered, the small compressibility becomes very small and the large compressibility becomes very large with decreasing temperature, and eventually van der Waals loops appear. Further studies are necessary in order to determine the nature of the strongly inhomogeneous phase present for intermediate volume fractions in 3D.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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Ciach A, Hall CK, Kahl G, Lomba E. Fifty years of liquid state physics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:410301. [PMID: 27545863 DOI: 10.1088/0953-8984/28/41/410301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
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Lindenberg EK, Patey GN. Melting point trends and solid phase behaviors of model salts with ion size asymmetry and distributed cation charge. J Chem Phys 2015; 143:024508. [DOI: 10.1063/1.4923344] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- E. K. Lindenberg
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - G. N. Patey
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
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Pȩkalski 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. J Chem Phys 2014; 140:114701. [DOI: 10.1063/1.4868001] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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Borzi RA, Slobinsky D, Grigera SA. Charge ordering in a pure spin model: dipolar spin ice. PHYSICAL REVIEW LETTERS 2013; 111:147204. [PMID: 24138269 DOI: 10.1103/physrevlett.111.147204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2013] [Indexed: 06/02/2023]
Abstract
We study the dipolar spin-ice model at fixed density of single excitations, ρ, using a Monte Carlo algorithm where processes of creation and annihilation of such excitations are banned. In the limit of ρ going to zero, this model coincides with the usual dipolar spin-ice model at low temperatures, with the additional advantage that a negligible number of monopoles allows for equilibration even at the lowest temperatures. Thus, the transition to the ordered fundamental state found by Melko, den Hertog, and Gingras in 2001 is reached using simple local spin flip dynamics. As the density is increased, the monopolar nature of the excitations becomes apparent: the system shows a rich ρ vs T phase diagram with "charge" ordering transitions analogous to that observed for Coulomb charges in lattices. A further layer of complexity is revealed by the existence of order both within the charges and their associated vacuum, which can only be described in terms of spins--the true microscopic degrees of freedom of the system.
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Affiliation(s)
- R A Borzi
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas UNLP-CONICET and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Argentina
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Siderius DW, Gelb LD. Thermodynamic and structural properties of finely discretized on-lattice hard-sphere fluids: Virial coefficients, free energies, and direct correlation functions. J Chem Phys 2009; 131:084503. [DOI: 10.1063/1.3207883] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ciach A, Perera A. A simple lattice model for the microstructure of neat alcohols: Application to liquid methanol. J Chem Phys 2009; 131:044505. [DOI: 10.1063/1.3184851] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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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.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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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.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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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.
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Affiliation(s)
- Alexandre Diehl
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760, Fortaleza, CE, Brazil
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Artyomov MN, Kolomeisky * AB. Thermodynamics and phase transitions of electrolytes on lattices with different discretization parameters. Mol Phys 2005. [DOI: 10.1080/00268970500142683] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Panagiotopoulos AZ. Thermodynamic properties of lattice hard-sphere models. J Chem Phys 2005; 123:104504. [PMID: 16178607 DOI: 10.1063/1.2008253] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.
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Affiliation(s)
- A Z Panagiotopoulos
- Department of Chemical Engineering, Princeton University, New Jersey 08540, USA.
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Patsahan O. First principle study of the phase behavior of ionic fluids. J Mol Liq 2005. [DOI: 10.1016/j.molliq.2004.07.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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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)].
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Affiliation(s)
- Alexandre Diehl
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760, Fortaleza, Ceará, Brazil.
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Ciach A. Effect of charge-density fluctuations on the order-disorder transition in the lattice restricted primitive models of electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046103. [PMID: 15600456 DOI: 10.1103/physreve.70.046103] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2004] [Revised: 06/23/2004] [Indexed: 05/24/2023]
Abstract
Lattice restricted primitive models, where equally charged ions of a diameter sigma are located at sites of a simple cubic lattice with a lattice constant a , are studied within the field-theoretic approach. We focus on the transition between charge-disordered and charge-ordered phases for sigma/a=1 and sigma/a=2 . By using renormalization-group methods we show that at high concentrations of ions the transition is continuous for sigma/a=1 , while for sigma/a=2 it is only first order, as found previously in simulations. For sigma/a=1 the effect of charge-density fluctuations on the positions of the continuous transition and the tricritical point (TCP) is determined within a formalism developed in this work. The temperature and the concentration of ions at the TCP agree very well with simulation results.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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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.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences 01-224 Warszawa, Poland
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