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Hooshanginejad A, Barotta JW, Spradlin V, Pucci G, Hunt R, Harris DM. Interactions and pattern formation in a macroscopic magnetocapillary SALR system of mermaid cereal. Nat Commun 2024; 15:5466. [PMID: 38937449 PMCID: PMC11211465 DOI: 10.1038/s41467-024-49754-4] [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: 04/05/2024] [Accepted: 06/18/2024] [Indexed: 06/29/2024] Open
Abstract
When particles are deposited at a fluid interface they tend to aggregate by capillary attraction to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect and study their pattern formation in equilibrium. The pairwise energy landscape of two disks is described by a short-range attraction and long-range repulsion (SALR) interaction potential, previously documented in a number of microscopic condensed matter systems. Such competing interactions enable a variety of pairwise equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing. Two-dimensional (2D) experiments and simulations in confined geometries demonstrate that as the areal packing fraction is increased, the dilute repulsion-dominated lattice state becomes unstable to the spontaneous formation of localized clusters, which eventually merge into a system-spanning striped pattern. Finally, we demonstrate that the equilibrium pattern can be externally manipulated by the application of a supplemental vertical magnetic force that remotely enhances the effective capillary attraction.
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Affiliation(s)
- Alireza Hooshanginejad
- Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, USA
| | - Jack-William Barotta
- Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, USA
| | - Victoria Spradlin
- Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, USA
- The Wheeler School, Providence, RI, USA
| | - Giuseppe Pucci
- Consiglio Nazionale delle Ricerche - Istituto di Nanotecnologia (CNR-NANOTEC), Via P. Bucci 33C, 87036, Rende, Italy
- Université Rennes, CNRS, IPR (Institut de Physique de Rennes) UMR 6251, FR35000, Rennes, France
| | - Robert Hunt
- Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, USA
| | - Daniel M Harris
- Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI, USA.
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2
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Ackroyd AJ, De Paolis A, Xu YT, Momeni A, Hamad WY, MacLachlan MJ. Self-assembly of cellulose nanocrystals confined to square capillaries. NANOSCALE 2023; 15:14388-14398. [PMID: 37609826 DOI: 10.1039/d3nr02650g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/24/2023]
Abstract
Biological systems exploit restricted degrees of freedom to drive self-assembly of nano- and microarchitectures. Simplified systems, such as colloidal nanoparticles that behave as lyotropic liquid crystalline mesophases in confined geometric spaces, may be used to mimic biological structures. Cellulose nanocrystals (CNCs) are colloidally stable nanoparticles that self-assemble into chiral nematic (ChN) liquid crystalline mesophases. To date, the self-assembly of ChN mesophases of CNCs has been studied under confinement conditions within curved surfaces or under drying conditions that impose curvatures that can be exploited to control ChN ordering; however, their self-assembly has not been investigated in geometries with square cross-sections under static conditions. Here, we show that because of surface anchoring on perpendicular surfaces, the ChN CNC phase is unable to bend with the 90° angle of the square capillary under increasing confinement. Instead, the ChN phase forms radial layers in the shape of concentric squircle shells. With increasing layer distance from the capillary wall, the squircles transition into concentric cylinder shells. In larger capillaries, the radial shell layers appear as a continuous spiral pattern that engulfs fragmented ChN pseudolayers, a defect to accommodate the cylindrical confinement of the mesophase. These results are useful for understanding the fundamentals of self-assembling systems and development of new technologies.
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Affiliation(s)
- Amanda J Ackroyd
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada.
| | - Adam De Paolis
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada.
| | - Yi-Tao Xu
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada.
| | - Arash Momeni
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada.
| | - Wadood Y Hamad
- Transformation and Interfaces Group, Bioproducts Innovation Centre of Excellence, FPInnovations, 2665 East Mall, Vancouver, British Columbia V6T 1Z4, Canada
| | - Mark J MacLachlan
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1Z1, Canada.
- Stewart Blusson Quantum Matter Institute, 2355 East Mall, Vancouver, British Columbia V6T 1Z4, Canada
- WPI Nano Life Science Institute, Kanazawa University, Kanazawa, 920-1192, Japan
- UBC BioProducts Institute, 2385 East Mall, Vancouver, British Columbia V6T 1Z4, Canada
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3
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Effect of a confining surface on a mixture with spontaneous inhomogeneities. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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4
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Xu X, Tang T, Gu M. Structural transitions in two-dimensional modulated systems under triangular confinement. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:72. [PMID: 36070024 DOI: 10.1140/epje/s10189-022-00229-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 08/24/2022] [Indexed: 06/15/2023]
Abstract
We study numerically the structural transitions of two-dimensional systems of classic particles with competing interactions under a triangular confinement with two different types of soft-wall potentials. We observe a variety of novel confinement-induced equilibrium configurations as a function of particle density and confinement steepness for each considered confinement potential. The specific role played by the confining potentials on the ordering of the particle clusters is revealed. These findings allow us to control the self-organization of modulated systems through using external confinements.
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Affiliation(s)
- Xibin Xu
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China.
| | - Tao Tang
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China
| | - Min Gu
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China
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5
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Serna H, Meyra AG, Noya EG, Góźdź WT. Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells. J Phys Chem B 2022; 126:7059-7065. [PMID: 36047942 PMCID: PMC9483920 DOI: 10.1021/acs.jpcb.2c04850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.
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Affiliation(s)
- Horacio Serna
- Institute of Physical Chemistry Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Ariel G Meyra
- IFLYSIB (UNLP,CONICET), 59 No. 789, B1900BTE La Plata, Argentina.,Departamento de Ingeniería Mecánica, UTN-FRLP, Av. 60 esq. 124, 1900 La Plata, Argentina
| | - Eva G Noya
- Instituto de Química Física Rocasolano, CSIC, C/Serrano 119, 28006 Madrid, Spain
| | - Wojciech T Góźdź
- Institute of Physical Chemistry Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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6
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Soft core fluid with competing interactions at a hard wall. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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7
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Franzini S, Reatto L, Pini D. Phase diagram of SALR fluids on spherical surfaces. SOFT MATTER 2021; 18:186-197. [PMID: 34859802 DOI: 10.1039/d1sm01257f] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous work in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find several inhomogeneous patterns that can be separated into three broad classes: cluster crystals, stripes, and bubble crystals, each containing topological defects. Interestingly, while the periodicity of inhomogeneous phases at large densities is mainly determined by the position of the negative minimum of the potential expansion, the finite size of the system induces a richer behavior at smaller densities.
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Affiliation(s)
- Stefano Franzini
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
| | - Luciano Reatto
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
| | - Davide Pini
- Dipartimento di Fisica "A. Pontremoli", Università di Milano, Via Celoria 16, 20133 Milano, Italy.
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8
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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.
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Affiliation(s)
| | - Marco Tarzia
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
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9
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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
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10
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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.
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Affiliation(s)
- Eldar Bildanau
- Belarusian State Technological University, 220006, Minsk, Belarus.
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11
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Xu XB, Tang T, Wang ZH, Xu XN, Fang GY, Gu M. Nonequilibrium pattern formation in circularly confined two-dimensional systems with competing interactions. Phys Rev E 2021; 103:012604. [PMID: 33601588 DOI: 10.1103/physreve.103.012604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 12/19/2020] [Indexed: 11/07/2022]
Abstract
We numerically investigate the nonequilibrium behaviors of classic particles with competing interactions confined in a two-dimensional logarithmic trap. We reveal a quench-induced surprising dynamics exhibiting rich dynamic patterns depending upon confinement strength and trap size, which is attributed to the time-dependent competition between interparticle repulsions and attractions under a circular confinement. Moreover, in the collectively diffusive motions of the particles, we find that the emergence of dynamic structure transformation coincides with a diffusive mode transition from superdiffusion to subdiffusion. These findings are likely useful in understanding the pattern selection and evolution in various chemical and biological systems in addition to modulated systems, and add a new route to tailoring the morphology of pattern-forming systems.
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Affiliation(s)
- X B Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - T Tang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - Z H Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - X N Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - G Y Fang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - M Gu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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12
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Marolt K, Roth R. Statics and dynamics of a finite two-dimensional colloidal system with competing attractive critical Casimir and repulsive magnetic dipole interactions. Phys Rev E 2020; 102:042608. [PMID: 33212601 DOI: 10.1103/physreve.102.042608] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 09/22/2020] [Indexed: 11/07/2022]
Abstract
We continue our theoretical study of a recently proposed two-dimensional colloidal system with attractive critical Casimir and repulsive magnetic dipole forces that can be tuned easily and independently from each other via the temperature and the strength of an external magnetic field, respectively [K. Marolt, M. Zimmermann, and R. Roth, Phys. Rev. E 100, 052602 (2019)2470-004510.1103/PhysRevE.100.052602]. Using this freedom, it is possible to construct a competing interaction potential that causes microphase separation featuring spatially inhomogeneous cluster, stripe, and bubble phases in the bulk, i.e., in an infinite system without an external potential. In the present work, we demonstrate by means of density functional theory that microphase separation can also occur in finite geometries. In a square cell with a side length of 20 or 30 colloid diameters, we observe the emergence of highly structured cluster and ring phases at intermediate bulk densities in addition to almost uniform fluid phases for lower and higher bulk densities. We then employ dynamic density functional theory to determine how the system reacts when the temperature and the magnetic field are altered over time, and we show how to induce a transition from the liquid to the cluster/ring phase and also from the cluster directly to the ring phase. We find that often a slowly varying and nontrivial path in parameter space is required to reach a stable state, whereas abrupt changes are prone to lead to metastable configurations.
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Affiliation(s)
- Kevin Marolt
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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13
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Pȩkalski J, Rządkowski W, Panagiotopoulos AZ. Shear-induced ordering in systems with competing interactions: A machine learning study. J Chem Phys 2020; 152:204905. [DOI: 10.1063/5.0005194] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- J. Pȩkalski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - W. Rządkowski
- Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
| | - A. Z. Panagiotopoulos
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
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14
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Xu XB, Wang ZH, Xu XN, Fang GY, Gu M. Structural transitions for 2D systems with competing interactions in logarithmic traps. J Chem Phys 2020; 152:054906. [DOI: 10.1063/1.5140816] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- X. B. Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - Z. H. Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - X. N. Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - G. Y. Fang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - M. Gu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
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15
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Serna H, Noya EG, Góźdź WT. The influence of confinement on the structure of colloidal systems with competing interactions. SOFT MATTER 2020; 16:718-727. [PMID: 31821400 DOI: 10.1039/c9sm02002k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Colloidal systems with competing interactions have a complex phase diagram with several periodic microphases, in which particles are arranged in lamellae, cylinders or clusters. Using grand canonical Monte Carlo simulations, we investigate how the structure of the colloidal fluid can be modified by confinement in channels with different cross-section geometries and sizes. We pay particular attention to the hexagonal cylindrical phase since it is the most susceptible to form new structures from. In particular, we considered pores with elliptical, triangular, squared, hexagonal, and wedged-cylindrical cross-sections. Our results show that the structure of the confined fluid depends on the commensurability of the bulk periodic structure with the confining cross-section of the channel. We also find that the structure of the confined fluid can be modified by inserting wedges of appropriate geometry and size. These geometrical modifications of the confining pores can be exploited for the controlled assembly of colloidal structures.
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Affiliation(s)
- Horacio Serna
- Institute of Physical Chemistry Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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16
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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.
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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
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17
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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.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
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