1
|
De Virgiliis A, Meyra A, Ciach A. Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions. Molecules 2024; 29:1512. [PMID: 38611792 PMCID: PMC11013164 DOI: 10.3390/molecules29071512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Revised: 03/22/2024] [Accepted: 03/25/2024] [Indexed: 04/14/2024] Open
Abstract
A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.
Collapse
Affiliation(s)
- Andres De Virgiliis
- Instituto de Física de Líquidos y Sistemas Biológicos, Facultad de Ciencias Exactas-UNLP-CONICET, La Plata 1900, Argentina; (A.D.V.); (A.M.)
- Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata, La Plata 1900, Argentina
| | - Ariel Meyra
- Instituto de Física de Líquidos y Sistemas Biológicos, Facultad de Ciencias Exactas-UNLP-CONICET, La Plata 1900, Argentina; (A.D.V.); (A.M.)
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, La Plata 1900, Argentina
| | - Alina Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| |
Collapse
|
2
|
Patsahan O, Meyra A, Ciach A. Spontaneous pattern formation in monolayers of binary mixtures with competing interactions. SOFT MATTER 2024; 20:1410-1424. [PMID: 38224133 DOI: 10.1039/d3sm01537h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied using a mesoscopic theory and MC simulations. We assume hard-cores of the same size a for both components. For r > a, like particles attract and repel each other at short and large distances, respectively, with the same potential u(r) for both species, and the cross-interaction is -u(r). The model is inspired by oppositely charged particles or macromolecules with preferential solubility in different components of a solvent that is close to a miscibility critical point, in particular by inclusions in biological membranes. We obtain the phase diagram in the chemical potentials and temperature variables as well as in the concentration, density and temperature variables, using the mean-field one-shell approximation. We find that the presence of the second component significantly extends the temperature range of stability of the ordered phases. We obtain three stable phases with periodic concentration: the lamellar L phase with alternating stripes of the two components for similar chemical potentials, and a hexagonal arrangement of the clusters of the minority component in the liquid of the majority component. The latter two phases, however, are stable only at relatively high temperatures. At lower temperatures, the L phase coexists with a disordered one-component fluid or with very dilute gas with mixed components. At still lower temperatures, the one-component phase coexisting with the L phase can be disordered or ordered, depending on the chemical potentials. The theoretical results are confirmed by MC simulations for selected thermodynamic states.
Collapse
Affiliation(s)
- O Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine
| | - A Meyra
- Instituto de Física de Líquidos y Sistemas Bilógicos, UNLP-CONICET, 59-789, 1900 La Plata, Argentina
- Depto. Ing. Mecánica 60 124, UTN-FRLP, 1900 La Plata, Argentina
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.
| |
Collapse
|
3
|
Munaò G, Costa D, Malescio G, Bomont JM, Prestipino S. Like aggregation from unlike attraction: stripes in symmetric mixtures of cross-attracting hard spheres. Phys Chem Chem Phys 2023. [PMID: 37194397 DOI: 10.1039/d3cp01026k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Self-assembly of colloidal particles into striped phases is at once a process of relevant technological interest-just think about the possibility to realise photonic crystals with a dielectric structure modulated along a specific direction-and a challenging task, since striped patterns emerge in a variety of conditions, suggesting that the connection between the onset of stripes and the shape of the intermolecular potential is yet to be fully unravelled. Hereby, we devise an elementary mechanism for the formation of stripes in a basic model consisting of a symmetric binary mixture of hard spheres that interact via a square-well cross attraction. Such a model would mimic a colloid in which the interspecies affinity is of longer range and significantly stronger than the intraspecies interaction. For attraction ranges shorter enough than the particle size the mixture behaves like a compositionally-disordered simple fluid. Instead, for wider square-wells, we document by numerical simulations the existence of striped patterns in the solid phase, where layers of particles of one species are interspersed with layers of the other species; increasing the attraction range stabilises the stripes further, in that they also appear in the bulk liquid and become thicker in the crystal. Our results lead to the counterintuitive conclusion that a flat and sufficiently long-ranged unlike attraction promotes the aggregation of like particles into stripes. This finding opens a novel way for the synthesis of colloidal particles with interactions tailored at the development of stripe-modulated structures.
Collapse
Affiliation(s)
- 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.
| | - 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.
| | - 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.
| | | | - 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
|
4
|
Pattern Formation in Two-Component Monolayers of Particles with Competing Interactions. Molecules 2023; 28:molecules28031366. [PMID: 36771033 PMCID: PMC9920350 DOI: 10.3390/molecules28031366] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Revised: 01/18/2023] [Accepted: 01/19/2023] [Indexed: 02/04/2023] Open
Abstract
Competing interactions between charged inclusions in membranes of living organisms or charged nanoparticles in near-critical mixtures can lead to self-assembly into various patterns. Motivated by these systems, we developed a simple triangular lattice model for binary mixtures of oppositely charged particles with additional short-range attraction or repulsion between like or different particles, respectively. We determined the ground state for the system in contact with a reservoir of the particles for the whole chemical potentials plane, and the structure of self-assembled conglomerates for fixed numbers of particles. Stability of the low-temperature ordered patterns was verified by Monte Carlo simulations. In addition, we performed molecular dynamics simulations for a continuous model with interactions having similar features, but a larger range and lower strength than in the lattice model. Interactions with and without symmetry between different components were assumed. We investigated both the conglomerate formed in the center of a thin slit with repulsive walls, and the structure of a monolayer adsorbed at an attractive substrate. Both models give the same patterns for large chemical potentials or densities. For low densities, more patterns occur in the lattice model. Different phases coexist with dilute gas on the lattice and in the continuum, leading to different patterns in self-assembled conglomerates ('rafts').
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
|
Vasilyev OA, Marino E, Kluft BB, Schall P, Kondrat S. Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate. NANOSCALE 2021; 13:6475-6488. [PMID: 33885527 DOI: 10.1039/d0nr09076j] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few kBT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.
Collapse
Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany.
| | | | | | | | | |
Collapse
|
7
|
Bildanau E, Pękalski J, Vikhrenko V, Ciach A. Adsorption anomalies in a two-dimensional model of cluster-forming systems. Phys Rev E 2020; 101:012801. [PMID: 32069566 DOI: 10.1103/physreve.101.012801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Indexed: 06/10/2023]
Abstract
Adsorption on a boundary line confining a monolayer of particles self-assembling into clusters is studied by Monte Carlo simulations. We focus on a system of particles interacting via competing interaction potential in which effectively short-range attraction is followed by long-range repulsion. For the chemical potential values below the order-disorder phase transition the adsorption isotherms were shown to undergo nonstandard behavior, i.e., the adsorption exhibits a maximum on structural transition between structureless and disordered cluster fluid. In particular, we have found that the adsorption decreases for increasing chemical potential when (i) clusters dominate over monomers in the bulk, (ii) the density profile in the direction perpendicular to the confining line exhibits an oscillatory decay, and (iii) the correlation function in the layer near the adsorption wall exhibits an oscillatory decay in the direction parallel to this wall. Our report indicates striking differences between simple and complex fluid adsorption processes.
Collapse
Affiliation(s)
- E Bildanau
- Belarusian State Technological University, 220006 Minsk, Belarus
| | - J Pękalski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland and Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - V Vikhrenko
- Belarusian State Technological University, 220006 Minsk, Belarus
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| |
Collapse
|
8
|
Pkalski J, Bildanau E, Ciach A. Self-assembly of spiral patterns in confined systems with competing interactions. SOFT MATTER 2019; 15:7715-7721. [PMID: 31509146 DOI: 10.1039/c9sm01179j] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Colloidal particles in polymer solutions and functionalized nanoparticles often exhibit short-range attraction coupled with long-range repulsion (SALR) leading to the spontaneous formation of symmetric patterns. Chiral nanostructures formed by thin films of SALR particles have not been reported yet. In this study, we observe striking topological transitions from a symmetric pattern of concentric rings to a chiral structure of a spiral shape, when the system is in hexagonal confinement. We find that the spiral formation can be induced either by breaking the system symmetry with a wedge, or by melting of the rings. In the former case, the chirality of the spiral is determined by the orientation of the wedge and thus can be controlled. In the latter, the spiral arises due to thermally induced defects and is absent in the average particle distribution, which forms highly regular hexagonal patterns in the central part of the system. These hexagonal patterns can be explained by interference of planar density waves. Thermodynamic considerations indicate that equilibrium spirals can appear spontaneously in any stripe-forming system confined in a hexagon with a small wedge, provided that certain conditions are satisfied by a set of phenomenological parameters.
Collapse
Affiliation(s)
- J Pkalski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland. and Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - E Bildanau
- Belarusian State Technological University, 13a Sverdlov Str., 220006 Minsk, Belarus
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
| |
Collapse
|
9
|
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
|
10
|
Otero-Mato JM, Montes-Campos H, Cabeza O, Diddens D, Ciach A, Gallego LJ, Varela LM. 3D structure of the electric double layer of ionic liquid-alcohol mixtures at the electrochemical interface. Phys Chem Chem Phys 2018; 20:30412-30427. [PMID: 30500015 DOI: 10.1039/c8cp05632c] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Mixtures of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate with amphiphilic cosolvents, such as methanol and ethanol, nanoconfined between graphene walls are studied by means of molecular dynamics simulations and the results are compared with those of the pure ionic liquid and its mixtures with water confined in the same conditions. We investigate the adsorption of cosolvent molecules at the graphene walls as well as their distribution across the system. The results show that, due to a higher affinity of the polar groups to be close to the anions in combination with the electrostatic and excluded volume interactions, there exists a high tendency of the OH groups to lie close to the anode, inducing small changes in the first cation layer. The orientation of cosolvent molecules is found to be closely related to the alignment of the molecular dipole moment. We also investigate the lateral ionic distribution in the layers close to the electrodes, which shows a structural transition from liquid-like lamellar ordering to solid-like hexagonal patterns as the size of the cosolvent molecules increases leading to smaller position fluctuations of the ions. The dependence of the specific patterns on the nature of the electrodes is also studied. This study strongly suggests that the ionic patterns formed in the first ionic layers next to the charged interfaces are universal since their existence does not crucially depend on the atomic composition of the interfacial material, but only on the net charge density of the considered ionic layer, which significantly changes the ionic mobility in this region.
Collapse
Affiliation(s)
- José M Otero-Mato
- Grupo de Nanomateriais, Fotónica e Materia Branda, Departamento de Física de Partículas, Universidade de Santiago de Compostela, Campus Vida s/n E-15782, Santiago de Compostela, Spain.
| | | | | | | | | | | | | |
Collapse
|
11
|
Ciach A. Combined density functional and Brazovskii theories for systems with spontaneous inhomogeneities. SOFT MATTER 2018; 14:5497-5508. [PMID: 29923576 DOI: 10.1039/c8sm00602d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The low-T part of the phase diagram in self-assembling systems is correctly predicted by known versions of density functional theory (DFT). The high-T part obtained in DFT, however, does not agree with simulations even on the qualitative level. In this work, a new version of DFT for systems with spontaneous inhomogeneities on a mesoscopic length scale is developed. The contribution to the grand thermodynamic potential associated with mesoscopic fluctuations is explicitly taken into account. The expression for this contribution is obtained by methods known from the Brazovskii field theory. Apart from developing the approximate expression for the grand thermodynamic potential that contains the fluctuation contribution and is ready for numerical minimization, we develop a simplified version of the theory valid for weakly ordered phases, i.e. for the high-T part of the phase diagram. The simplified theory is verified by comparison with the results of simulations for a particular version of the short-range attraction long-range repulsion (SALR) interaction potential. Except for the fact that in our theory the ordered phases are stable at lower T than in simulations, a good agreement for the high-T part of the phase diagram is obtained for the range of density that was considered in simulations. In addition, the equation of state and compressibility isotherms are presented. Finally, the physical interpretation of the fluctuation-contribution to the grand potential is discussed in detail.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.
| |
Collapse
|
12
|
Pȩkalski J, Ciach A. Orientational ordering of lamellar structures on closed surfaces. J Chem Phys 2018; 148:174902. [PMID: 29739225 DOI: 10.1063/1.5026112] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Self-assembly of particles with short-range attraction and long-range repulsion interactions on a flat and on a spherical surface is compared. Molecular dynamics simulations are performed for the two systems having the same area and the density optimal for formation of stripes of particles. Structural characteristics, e.g., a cluster size distribution, a number of defects, and an orientational order parameter (OP), as well as the specific heat, are obtained for a range of temperatures. In both cases, the cluster size distribution becomes bimodal and elongated clusters appear at the temperature corresponding to the maximum of the specific heat. When the temperature decreases, orientational ordering of the stripes takes place and the number of particles per cluster or stripe increases in both cases. However, only on the flat surface, the specific heat has another maximum at the temperature corresponding to a rapid change of the OP. On the sphere, the crossover between the isotropic and anisotropic structures occur in a much broader temperature interval; the orientational order is weaker and occurs at significantly lower temperature. At low temperature, the stripes on the sphere form spirals and the defects resemble defects in the nematic phase of rods adsorbed at a sphere.
Collapse
Affiliation(s)
- J Pȩkalski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland
| |
Collapse
|
13
|
Montes-Campos H, Otero-Mato JM, Méndez-Morales T, Cabeza O, Gallego LJ, Ciach A, Varela LM. Two-dimensional pattern formation in ionic liquids confined between graphene walls. Phys Chem Chem Phys 2018; 19:24505-24512. [PMID: 28890961 DOI: 10.1039/c7cp04649a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
We perform molecular dynamics simulations of ionic liquids confined between graphene walls under a large variety of conditions (pure ionic liquids, mixtures with water and alcohols, mixtures with lithium salts and defective graphene walls). Our results show that the formation of striped and hexagonal patterns in the Stern layer can be considered as a general feature of ionic liquids at electrochemical interfaces, the transition between patterns being controlled by the net balance of charge in the innermost layer of adsorbed molecules. This explains previously reported experimental and computational results and, for the first time, why these pattern changes are triggered by any perturbation of the charge density at the innermost layer of the electric double layer (voltage and composition changes, and vacancies at the electrode walls, among others), which may help tuning electrode-ionic liquid interfaces. Using Monte Carlo simulations we show that such structures can be reproduced by a simple two-dimensional lattice model with only nearest-neighbour interactions, governed by highly screened ionic interactions and short-range and excluded volume interactions. We also show that the results of our simulations are consistent with those inferred from the Landau-Brazovskii theory of pattern formation in self-assembling systems. The presence of these patterns at the ionic liquid graphene-electrode interfaces may have a strong impact on the process of ionic transfer from the bulk mixtures to the electrodes, on the differential capacitance of the electrode-electrolyte double layer or on the rates of redox reactions at the electrodes, among other physicochemical properties, and is therefore an effect of great technological interest.
Collapse
Affiliation(s)
- Hadrián Montes-Campos
- Grupo de Nanomateriales, Fotónica y Materia Blanda, Departamentos de Física de Partículas y Física Aplicada, Facultade de Física, Universidade de Santiago de Compostela, Campus Vida s/n, E-15782 Santiago de Compostela, Spain.
| | | | | | | | | | | | | |
Collapse
|
14
|
Santos AP, Pȩkalski J, Panagiotopoulos AZ. Thermodynamic signatures and cluster properties of self-assembly in systems with competing interactions. SOFT MATTER 2017; 13:8055-8063. [PMID: 29052681 DOI: 10.1039/c7sm01721a] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Colloidal particles, amphiphiles and functionalized nanoparticles are examples of systems that frequently exhibit short-range attraction coupled with long-range repulsion. We vary the ratio of attraction and repulsion in a simple isotropic model with competing interactions, using molecular simulations, and observe significant differences in the properties of the self-assembled clusters that form. We report conditions that lead to the self-assembly of clusters of a preferred size, accompanied by a change in the slope of the pressure with respect to density, similar to micelles formed by amphiphilic molecules. We also report conditions where repulsion dominates, clusters of a preferred size form and the pressure vs. density slope is unaffected by self-assembly. We investigate cluster structure by calculating the size distributions, free colloid density, cluster shape and density profiles. The system dynamics are characterized by cluster life-times. We do not find qualitative differences in structure or dynamics of the clusters, regardless the pressure behavior. Therefore, thermodynamic and structural quantities are required to classify the different clustering characteristics that are observable in systems with competing interactions. Our results have implications in terms of development of design principles for stable cluster self-assembly.
Collapse
Affiliation(s)
- Andrew P Santos
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
| | | | | |
Collapse
|
15
|
Jadrich RB, Lindquist BA, Truskett TM. Probabilistic inverse design for self-assembling materials. J Chem Phys 2017. [DOI: 10.1063/1.4981796] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- R. B. Jadrich
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - B. A. Lindquist
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - T. M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| |
Collapse
|
16
|
Ciach A, Pękalski J. Exactly solvable model for self-assembly of hard core-soft shell particles at interfaces. SOFT MATTER 2017; 13:2603-2608. [PMID: 28327760 DOI: 10.1039/c7sm00191f] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
A generic model for self-assembly of a monolayer of hybrid core-shell particles at an interface is developed. We assume that for distances larger than the size of the incompressible core a soft repulsion appears, and the repulsion is followed by an attraction at larger separations. The model is solved exactly in a one-dimensional lattice version. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of nearly vertical segments at densities optimal for the periodic structures that are connected by segments with a small slope. The range of order depends very strongly on the strength of attraction and on the density. Our results agree with experimental observations.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
| | - J Pękalski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
| |
Collapse
|
17
|
Lindquist BA, Dutta S, Jadrich RB, Milliron DJ, Truskett TM. Interactions and design rules for assembly of porous colloidal mesophases. SOFT MATTER 2017; 13:1335-1343. [PMID: 28133680 DOI: 10.1039/c6sm02718k] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Porous mesophases, where well-defined particle-depleted 'void' spaces are present within a particle-rich background fluid, can be self-assembled from colloidal particles interacting via isotropic pair interactions with competing attractions and repulsions. While such structures could be of wide interest for technological applications (e.g., filtration, catalysis, absorption, etc.), relatively few studies have investigated the interactions that lead to these morphologies and how they compare to those that produce other micro-phase-separated structures, such as clusters. In this work, we use inverse methods of statistical mechanics to design model isotropic pair potentials that form porous mesophases. We characterize the resulting porous structures, correlating features of the pair potential with the targeted pore size and the particle packing fraction. The former is primarily encoded by the amplitude and range of the repulsive barrier of the designed pair potential and the latter by the attractive well depth. We observe a trade-off with respect to the packing fraction of the targeted morphology: greater values support more spherical and monodisperse pores that themselves organize into periodic structures, while lower values yield more mobile pores that do not assemble into ordered structures but remain stable over a larger range of packing fraction. We conclude by commenting on the limitations of targeting a specific pore diameter within the present inverse design approach as well as by describing future directions to overcome these limitations.
Collapse
Affiliation(s)
- Beth A Lindquist
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - Sayantan Dutta
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - Ryan B Jadrich
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - Delia J Milliron
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - Thomas M Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| |
Collapse
|
18
|
Almarza NG, Pȩkalski J, Ciach A. Effects of confinement on pattern formation in two dimensional systems with competing interactions. SOFT MATTER 2016; 12:7551-7563. [PMID: 27507622 DOI: 10.1039/c6sm01400c] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L2 between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L2. This structural order is lost at T = TK(L2) depending on L2 according to a Kelvin-like equation. Above the Kelvin temperature TK(L2) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L2 optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = TK(L2).
Collapse
Affiliation(s)
- N G Almarza
- Instituto de Químca Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain.
| | | | | |
Collapse
|
19
|
Zhuang Y, Charbonneau P. Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers. J Phys Chem B 2016; 120:7775-82. [DOI: 10.1021/acs.jpcb.6b05471] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuan Zhuang
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Patrick Charbonneau
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department
of Physics, Duke University, Durham, North Carolina 27708, United States
| |
Collapse
|
20
|
Packwood DM, Han P, Hitosugi T. State-space reduction and equivalence class sampling for a molecular self-assembly model. ROYAL SOCIETY OPEN SCIENCE 2016; 3:150681. [PMID: 27493765 PMCID: PMC4968457 DOI: 10.1098/rsos.150681] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/10/2015] [Accepted: 06/14/2016] [Indexed: 06/06/2023]
Abstract
Direct simulation of a model with a large state space will generate enormous volumes of data, much of which is not relevant to the questions under study. In this paper, we consider a molecular self-assembly model as a typical example of a large state-space model, and present a method for selectively retrieving 'target information' from this model. This method partitions the state space into equivalence classes, as identified by an appropriate equivalence relation. The set of equivalence classes H, which serves as a reduced state space, contains none of the superfluous information of the original model. After construction and characterization of a Markov chain with state space H, the target information is efficiently retrieved via Markov chain Monte Carlo sampling. This approach represents a new breed of simulation techniques which are highly optimized for studying molecular self-assembly and, moreover, serves as a valuable guideline for analysis of other large state-space models.
Collapse
Affiliation(s)
- Daniel M. Packwood
- Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan
- Japan Science and Technology Agency (PRESTO), Kawaguchi, Saitama 332-0012, Japan
| | - Patrick Han
- Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan
- California Nanosystems Institute, University of California, Los Angeles, CA 90095, USA
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095, USA
- Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095, USA
| | - Taro Hitosugi
- Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan
- Department of Applied Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8352, Japan
| |
Collapse
|
21
|
Ciach A, Gozdz WT. Density functional theory for systems with mesoscopic inhomogeneities. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244004. [PMID: 27116121 DOI: 10.1088/0953-8984/28/24/244004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study the effects of fluctuations on the mesoscopic length scale on systems with mesoscopic inhomogeneities. Equations for the correlation function and for the average volume fraction are derived in the self-consistent Gaussian approximation. The equations are further simplified by postulating the expression for the structure factor consistent with scattering experiments for self-assembling systems. Predictions of the approximate theory are verified by a comparison with the exact results obtained earlier for the one-dimensional lattice model with first-neighbor attraction and third-neighbor repulsion. We find qualitative agreement for the correlation function, the equation of state and the dependence of the chemical potential μ on the volume fraction ζ. Our results confirm also that strong inhomogeneities in the disordered phase are found only in the case of strong repulsion. The inhomogeneities are reflected in an oscillatory decay of the correlation function with a very large correlation length, three inflection points in the [Formula: see text] curve and a compressibility that for increasing ζ takes very large, very small and again very large values.
Collapse
Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| | | |
Collapse
|
22
|
Chacko B, Chalmers C, Archer AJ. Two-dimensional colloidal fluids exhibiting pattern formation. J Chem Phys 2015; 143:244904. [DOI: 10.1063/1.4937941] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Blesson Chacko
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
| | - Christopher Chalmers
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
| | - Andrew J. Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
| |
Collapse
|
23
|
Pȩkalski J, Almarza NG, Ciach A. Effects of rigid or adaptive confinement on colloidal self-assembly. Fixed vs. fluctuating number of confined particles. J Chem Phys 2015; 142:204904. [PMID: 26026462 DOI: 10.1063/1.4921787] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the grand canonical ensemble (GCE) in Pȩkalski et al. [J. Chem. Phys. 142, 014903 (2015)]. The model considers a pair interaction defined by a short-range attraction plus a longer-range repulsion. We consider thermodynamic states corresponding to self-assembly into clusters. Both fixed and adaptive boundaries are studied. For fixed boundaries, there are particular states in which, for equal average densities, the number of clusters in the GCE is larger than in the canonical ensemble. The dependence of pressure on density has a different form when the system size changes with fixed number of particles and when the number of particles changes with fixed size of the system. In the former case, the pressure has a nonmonotonic dependence on the system size. The anomalous increase of pressure for expanding system is accompanied by formation of a larger number of smaller clusters. In the case of elastic confining surfaces, we observe a bistability, i.e., two significantly different system sizes occur with almost the same probability. The mechanism of the bistability in the closed system is different to that of the case of permeable walls, where the two equilibrium system sizes correspond to a different number of particles.
Collapse
Affiliation(s)
- J Pȩkalski
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| | - N G Almarza
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| | - A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| |
Collapse
|
24
|
Guerrero AI, Stariolo DA, Almarza NG. Nematic phase in the J(1)-J(2) square-lattice Ising model in an external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052123. [PMID: 26066135 DOI: 10.1103/physreve.91.052123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2015] [Indexed: 06/04/2023]
Abstract
The J(1)-J(2) Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J(2)/|J(1)| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.
Collapse
Affiliation(s)
- Alejandra I Guerrero
- Departamento de Física, Universidade Federal do Rio Grande do Sul CP 15051, 91501-970 Porto Alegre, RS, Brazil
| | - Daniel A Stariolo
- Departamento de Física, Universidade Federal do Rio Grande do Sul and National Institute of Science and Technology for Complex Systems, CP 15051, 91501-970 Porto Alegre, RS, Brazil
| | - Noé G Almarza
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| |
Collapse
|
25
|
Szymańska P, Kochańczyk M, Miękisz J, Lipniacki T. Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022702. [PMID: 25768526 DOI: 10.1103/physreve.91.022702] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Indexed: 06/04/2023]
Abstract
We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.
Collapse
Affiliation(s)
- Paulina Szymańska
- College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, 02-089 Warsaw, Poland
| | - Marek Kochańczyk
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland
| | - Jacek Miękisz
- Institute of Applied Mathematics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland
| | - Tomasz Lipniacki
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland and Department of Statistics, Rice University, Houston, Texas 77005, USA
| |
Collapse
|
26
|
Pȩkalski J, Ciach A, Almarza NG. Bistability in a self-assembling system confined by elastic walls: exact results in a one-dimensional lattice model. J Chem Phys 2015; 142:014903. [PMID: 25573579 DOI: 10.1063/1.4905142] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pȩkalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.
Collapse
Affiliation(s)
- J Pȩkalski
- 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
| | - N G Almarza
- Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain
| |
Collapse
|
27
|
Pękalski J, Rogowski P, Ciach A. Self-assembly of lipids in water. Exact results from a one-dimensional lattice model. Mol Phys 2014. [DOI: 10.1080/00268976.2014.975765] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
28
|
Almarza NG, Pȩkalski J, Ciach A. Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation. J Chem Phys 2014; 140:164708. [DOI: 10.1063/1.4871901] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
|