1
|
Costa D, Munaò G, Bomont JM, Malescio G, Palatella A, Prestipino S. Microphase versus macrophase separation in the square-well-linear fluid: A theoretical and computational study. Phys Rev E 2023; 108:034602. [PMID: 37849187 DOI: 10.1103/physreve.108.034602] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 08/10/2023] [Indexed: 10/19/2023]
Abstract
Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equation and the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.
Collapse
Affiliation(s)
- Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Gianpietro Malescio
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Amedeo Palatella
- Liceo Classico, Scientifico e delle Scienze Umane "Bonaventura Cavalieri", Via Madonna di Campagna 18, 28922 Verbania, Italy
| | - Santi Prestipino
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| |
Collapse
|
2
|
Maggs AC, Krauth W. Large-scale dynamics of event-chain Monte Carlo. Phys Rev E 2022; 105:015309. [PMID: 35193224 DOI: 10.1103/physreve.105.015309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulations. Rather than imposing detailed balance on the transition probabilities, the method enforces a weaker global-balance condition in order to guarantee convergence to equilibrium. In this paper, we generalize the factor-field variant of ECMC to higher space dimensions. In the two-dimensional fluid phase, factor-field ECMC saturates the lower bound z=0 for the dynamical scaling exponent for local dynamics, whereas molecular dynamics is characterized by z=1 and local Metropolis Monte Carlo by z=2. In the presence of hexatic order, factor fields are not found to speed up the convergence. We note that generalizations of factor fields could couple to orientational order.
Collapse
Affiliation(s)
- A C Maggs
- CNRS UMR7083, ESPCI Paris, Université PSL, 10 rue Vauquelin, 75005 Paris, France
| | - Werner Krauth
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75005 Paris, France
| |
Collapse
|
3
|
Charbonneau P, Tarzia M. Solution of disordered microphases in the Bethe approximation. J Chem Phys 2021; 155:024501. [PMID: 34266261 DOI: 10.1063/5.0052111] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.
Collapse
Affiliation(s)
| | - Marco Tarzia
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
| |
Collapse
|
4
|
Zheng M, Charbonneau P. Characterization and efficient Monte Carlo sampling of disordered microphases. J Chem Phys 2021; 154:244506. [DOI: 10.1063/5.0052114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Mingyuan Zheng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| |
Collapse
|
5
|
Bildanau E, Vikhrenko V. Adsorption time scales of cluster-forming systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:51. [PMID: 33844108 DOI: 10.1140/epje/s10189-021-00059-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle concentration and interaction energy during the adsorption of particles on a plane triangular lattice is investigated. The simulation results show a diverse behavior of the system time evolution depending on the temperature and chemical potential and finally on the formation of clusters in the system. The characteristic relaxation times of adsorption vary in several orders of magnitude depending on the thermodynamic parameters of the final equilibrium state of the adsorbate. A very fast adsorption of particles is observed for highly ordered adsorbate equilibrium states.
Collapse
Affiliation(s)
- Eldar Bildanau
- Belarusian State Technological University, 220006, Minsk, Belarus.
| | | |
Collapse
|
6
|
Bomont JM, Costa D, Bretonnet JL. Local order and cluster formation in model fluids with competing interactions: a simulation and theoretical study. Phys Chem Chem Phys 2020; 22:5355-5365. [DOI: 10.1039/c9cp06710h] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
In SALR fluids, theory and simulation predict tiny morphological changes in the density profile occurring at the onset of clustering.
Collapse
Affiliation(s)
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche
- Scienze Fisiche e Scienze della Terra
- Università degli Studi di Messina
- 98158 Messina
- Italy
| | | |
Collapse
|
7
|
Ciach A. Mesoscopic theory for systems with competing interactions near a confining wall. Phys Rev E 2019; 100:062607. [PMID: 31962426 DOI: 10.1103/physreve.100.062607] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Indexed: 06/10/2023]
Abstract
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler-Lagrange equations and the boundary conditions (BCs) for the local volume fraction and the correlation function are derived from the density functional theory expression for the grand thermodynamic potential. Various levels of approximation can be considered for the obtained equations. The lowest-order nontrivial approximation [generic model (GM)] resembles the Landau-Brazovskii-type theory for a semi-infinite system. Unlike in the original phenomenological theory, however, all coefficients in our equations and BCs are expressed in terms of the interaction potential and the thermodynamic state. Analytical solutions of the linearized equations in the GM are presented and discussed on a general level and for a particular example of the double-Yukawa potential. We show exponentially damped oscillations of the volume fraction and the correlation function in the direction perpendicular to the confining surface. The correlations show oscillatory decay in directions parallel to this surface too, with the decay length increasing significantly when the system boundary is approached. The framework of our theory allows for a systematic improvement of the accuracy of the results.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| |
Collapse
|
8
|
Abstract
Adsorption at an attractive surface in a system with particles self-assembling into small clusters is studied by molecular dynamics simulation. We assume Lennard-Jones plus repulsive Yukawa tail interactions and focus on small densities. The relative increase in the temperature at the critical cluster concentration near the attractive surface (CCCS) shows a power-law dependence on the strength of the wall-particle attraction. At temperatures below the CCCS, the adsorbed layer consists of undeformed clusters if the wall-particle attraction is not too strong. Above the CCCS or for strong attraction leading to flattening of the adsorbed aggregates, we obtain a monolayer that for strong or very strong attraction consists of flattened clusters or stripes, respectively. The accumulated repulsion from the particles adsorbed at the wall leads to a repulsive barrier that slows down the adsorption process, and the accession time grows rapidly with the strength of the wall-particle attraction. Beyond the adsorbed layer of particles, a depletion region of a thickness comparable with the range of the repulsive tail of interactions occurs, and the density in this region decreases with increasing strength of the wall-particle attraction. At larger separations, the exponentially damped oscillations of density agree with theoretical predictions for self-assembling systems. Structural and thermal properties of the bulk are also determined. In particular, a new structural crossover associated with the maximum of the specific heat and a double-peaked histogram of the cluster size distribution are observed.
Collapse
Affiliation(s)
- M Litniewski
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| |
Collapse
|
9
|
Lei Z, Krauth W, Maggs AC. Event-chain Monte Carlo with factor fields. Phys Rev E 2019; 99:043301. [PMID: 31108644 DOI: 10.1103/physreve.99.043301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2018] [Indexed: 11/07/2022]
Abstract
We study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular dynamics. We show, using simulations, that the autocorrelation time grows only with the square root of the system size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.
Collapse
Affiliation(s)
- Ze Lei
- Laboratoire de Physique Statistique, Ecole Normale Supérieure/PSL Research University, UPMC, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Werner Krauth
- Laboratoire de Physique Statistique, Ecole Normale Supérieure/PSL Research University, UPMC, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - A C Maggs
- CNRS UMR7083, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| |
Collapse
|
10
|
Bretonnet JL, Bomont JM, Costa D. A semianalytical “reverse” approach to link structure and microscopic interactions in two-Yukawa competing fluids. J Chem Phys 2018; 149:234907. [DOI: 10.1063/1.5047448] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jean-Louis Bretonnet
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
| |
Collapse
|
11
|
Hu Y, Fu L, Charbonneau P. Correlation lengths in quasi-one-dimensional systems via transfer matrices. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1479543] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Yi Hu
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Lin Fu
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| |
Collapse
|