1
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Kelley MM, Quinton J, Fazel K, Karimitari N, Sutton C, Sundararaman R. Bridging electronic and classical density-functional theory using universal machine-learned functional approximations. J Chem Phys 2024; 161:144101. [PMID: 39377323 DOI: 10.1063/5.0223792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2024] [Accepted: 09/15/2024] [Indexed: 10/09/2024] Open
Abstract
The accuracy of density-functional theory (DFT) calculations is ultimately determined by the quality of the underlying approximate functionals, namely the exchange-correlation functional in electronic DFT and the excess functional in the classical DFT formalism of fluids. For both electrons and fluids, the exact functional is highly nonlocal, yet most calculations employ approximate functionals that are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations show promise in advancing applications of both electronic and classical DFTs, but so far these two distinct research areas have implemented disparate approaches with limited generality. Here, we formulate a universal ML framework and training protocol to learn nonlocal functionals that combine features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this new approach for several 1D and quasi-1D problems and demonstrate that functionals with exactly the same hyperparameters achieve excellent accuracy for a diverse set of systems, including the hard-rod fluid, the inhomogeneous Ising model, the exact exchange energy of electrons, the electron kinetic energy for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to approximate exact 3D functionals spanning electronic and classical DFTs.
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Affiliation(s)
- Michelle M Kelley
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Joshua Quinton
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Kamron Fazel
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - Nima Karimitari
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Christopher Sutton
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Ravishankar Sundararaman
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
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2
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Wassermair M, Kahl G, Roth R, Archer AJ. Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system. J Chem Phys 2024; 161:124503. [PMID: 39344889 DOI: 10.1063/5.0226954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2024] [Accepted: 09/09/2024] [Indexed: 10/01/2024] Open
Abstract
We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.
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Affiliation(s)
- Michael Wassermair
- Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| | - Gerhard Kahl
- Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, D-72076 Tübingen, Germany
| | - Andrew J Archer
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom
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3
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Frink LJD, van Swol F, Malanoski AP, Petsev DN. Film swelling and contaminant adsorption at polymer coated surfaces: Insights from density functional theory. J Chem Phys 2024; 161:114710. [PMID: 39301856 DOI: 10.1063/5.0225085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2024] [Accepted: 09/04/2024] [Indexed: 09/22/2024] Open
Abstract
Designing coatings and films that can protect surfaces is important in a wide variety of applications from corrosion prevention to anti-fouling. These systems are challenging from a modeling perspective because they are invariably multicomponent, which quickly leads to an expansive design space. At a minimum, the system has a substrate, a film (often composed of a polymeric material), a ubiquitous carrier solvent, which may be either a vapor or liquid phase, and one or more contaminants. Each component has an impact on the effectiveness of coating. This paper focuses on films that are used as a barrier to surface contamination, but the results also extend to surface coatings that are designed to extract a low density species from the fluid phase as in liquid chromatography. A coarse-grained model is developed using Yukawa potentials that encompasses both repulsive and attractive interactions among the species. Classical density functional theory calculations are presented to show how contaminant adsorption is controlled by the molecular forces in the system. Two specific vectors through the parameter space are considered to address likely experimental manipulations that change either the solvent or the polymer in a system. We find that all the adsorption results can be unified by considering an appropriate combination of molecular parameters. As a result, these calculations provide a link between molecular interactions and film performance and may serve to guide the rational design of films.
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Affiliation(s)
- Laura J Douglas Frink
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Frank van Swol
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Anthony P Malanoski
- United States Naval Research Laboratory, Center for Biomolecular Science and Engineering, Washington, D.C. 20375, USA
| | - Dimiter N Petsev
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
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4
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Bernet T, Ravipati S, Cárdenas H, Müller EA, Jackson G. Beyond the mean-field approximation for pair correlations in classical density functional theory: Reference inhomogeneous non-associating monomeric fluids for use with SAFT-VR Mie DFT. J Chem Phys 2024; 161:094115. [PMID: 39234971 DOI: 10.1063/5.0219968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2024] [Accepted: 08/14/2024] [Indexed: 09/06/2024] Open
Abstract
A free-energy functional is presented to explicitly take into account pair correlations between molecules in inhomogeneous fluids. The framework of classical density functional theory (DFT) is used to describe the variation in the density of molecules interacting through a Mie (generalized Lennard-Jones) potential. Grand Canonical Monte Carlo simulations are performed for the systems to validate the new functional. The statistical associating fluid theory developed for Mie fluids (SAFT-VR Mie) is selected as a reference for the homogeneous bulk limit of the DFT and is applied here to systems of spherical non-associating particles. The importance of a correct description of the pair correlations for a reliable representation of the free energy in the development of the equation of state is duly noted. Following the Barker-Henderson high-temperature expansion, an analogous formulation is proposed from the general DFT formalism to develop an inhomogeneous equivalent of the SAFT-VR Mie free energy as a functional of the one-body density. In order to make use of this new functional in adsorption studies, a non-local version of the DFT is considered, with specific weighted densities describing the effects of neighboring molecules. The computation of these quantities is possible in three-dimensional space for any pore geometry with repulsive or attractive walls. We showcase examples to validate the new functional, revealing a very good agreement with molecular simulation. The new SAFT-DFT approach is well-adapted to describe realistic complex fluids.
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Affiliation(s)
- Thomas Bernet
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, Total, LFCR, Anglet, France
| | - Srikanth Ravipati
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Harry Cárdenas
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Erich A Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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5
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Petersen T. Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory. J Phys Chem B 2024; 128:3981-3996. [PMID: 38626457 PMCID: PMC11056995 DOI: 10.1021/acs.jpcb.3c08045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 04/02/2024] [Accepted: 04/03/2024] [Indexed: 04/18/2024]
Abstract
The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.
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Affiliation(s)
- Thomas Petersen
- Sonny Astani Department of
Civil and Environmental Engineering, University
of Southern California, Los Angeles, California 90089, United States
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6
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Sammüller F, Hermann S, Schmidt M. Why neural functionals suit statistical mechanics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:243002. [PMID: 38467072 DOI: 10.1088/1361-648x/ad326f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Accepted: 03/11/2024] [Indexed: 03/13/2024]
Abstract
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammülleret al(2023Proc. Natl Acad. Sci.120e2312484120) gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online athttps://github.com/sfalmo/NeuralDFT-Tutorial.
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Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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7
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Shchekin AK, Gosteva LA, Lebedeva TS, Tatyanenko DV. Confinement Effects in Droplet Formation on a Solid Particle. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:5174-5182. [PMID: 38415650 DOI: 10.1021/acs.langmuir.3c03342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/29/2024]
Abstract
Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement. The analysis is conducted first on a macroscopic thermodynamic level of description, and then the results are supported by studies within two versions of classical density functional theory: the square-gradient approximation with the Carnahan-Starling equation of state for hard spheres on a completely wettable particle and the random-phase approximation with the fundamental measure theory on a poorly wettable particle. In the latter case, a solution breaking the spherical symmetry is observed at a small total number of molecules.
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Affiliation(s)
- Alexander K Shchekin
- Department of Statistical Physics, Saint Petersburg State University, Faculty of Physics, 7-9 Universitetskaya nab., St. Petersburg, 199034, Russia
| | - Liubov A Gosteva
- Department of Statistical Physics, Saint Petersburg State University, Faculty of Physics, 7-9 Universitetskaya nab., St. Petersburg, 199034, Russia
| | - Tatiana S Lebedeva
- Department of Statistical Physics, Saint Petersburg State University, Faculty of Physics, 7-9 Universitetskaya nab., St. Petersburg, 199034, Russia
| | - Dmitry V Tatyanenko
- Department of Statistical Physics, Saint Petersburg State University, Faculty of Physics, 7-9 Universitetskaya nab., St. Petersburg, 199034, Russia
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8
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Barthes A, Bernet T, Grégoire D, Miqueu C. A molecular density functional theory for associating fluids in 3D geometries. J Chem Phys 2024; 160:054704. [PMID: 38341691 DOI: 10.1063/5.0180795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 01/03/2024] [Indexed: 02/13/2024] Open
Abstract
A new free-energy functional is proposed for inhomogeneous associating fluids. The general formulation of Wertheim's thermodynamic perturbation theory is considered as the starting point of the derivation. We apply the hypotheses of the statistical associating fluid theory in the classical density functional theory (DFT) framework to obtain a tractable expression of the free-energy functional for inhomogeneous associating fluids. Specific weighted functions are introduced in our framework to describe association interactions for a fluid under confinement. These weighted functions have a mathematical structure similar to the weighted densities of the fundamental-measure theory (i.e., they can be expressed as convolution products) such that they can be efficiently evaluated with Fourier transforms in a 3D space. The resulting free-energy functional can be employed to determine the microscopic structure of inhomogeneous associating fluids of arbitrary 3D geometry. The new model is first compared with Monte Carlo simulations and previous versions of DFT for a planar hard wall system in order to check its consistency in a 1D case. As an example of application in a 3D configuration, we then investigate the extreme confinement of an associating hard-sphere fluid inside an anisotropic open cavity with a shape that mimics a simplified model of zeolite. Both the density distribution and the corresponding molecular bonding profile are given, revealing complementary information to understand the structure of the associating fluid inside the cavity network. The impact of the degree of association on the preferential positions of the molecules inside the cavity is investigated as well as the competition between association and steric effect on adsorption.
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Affiliation(s)
- Antoine Barthes
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, Anglet, France
| | - Thomas Bernet
- Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, Institute for Molecular Science and Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - David Grégoire
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, Anglet, France
- Institut Universitaire de France, Paris, France
| | - Christelle Miqueu
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, Anglet, France
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9
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Hermann S, Schmidt M. Active crystallization from power functional theory. Phys Rev E 2024; 109:L022601. [PMID: 38491681 DOI: 10.1103/physreve.109.l022601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2023] [Accepted: 02/06/2024] [Indexed: 03/18/2024]
Abstract
We address the gas, liquid, and crystal phase behaviors of active Brownian particles in three dimensions. The nonequilibrium force balance at coexistence leads to equality of state functions for which we use power functional approximations. Motility-induced phase separation starts at a critical point and quickly becomes metastable against active freezing for Péclet numbers above a nonequilibrium triple point. The mean swim speed acts as a state variable, similar to the density of depletion agents in colloidal demixing. We obtain agreement with recent simulation results and correctly predict the strength of particle number fluctuations in active fluids.
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Affiliation(s)
- Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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10
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Simon A, Weimar J, Martius G, Oettel M. Machine Learning of a Density Functional for Anisotropic Patchy Particles. J Chem Theory Comput 2024. [PMID: 38231855 DOI: 10.1021/acs.jctc.3c01238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here, we formulate an approach to the Kern-Frenkel model via the classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning (ML) techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries are formulated. The mean-field kernel is constructed via ML on the basis of hard wall simulation data. The results are compared to the well-known random-phase approximation, which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full-density functional via ML.
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Affiliation(s)
- Alessandro Simon
- Institute for Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
- Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany
| | - Jens Weimar
- Institute for Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Georg Martius
- Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany
| | - Martin Oettel
- Institute for Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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11
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Yetkin M, Wani YM, Kritika K, Howard MP, Kappl M, Butt HJ, Nikoubashman A. Structure Formation in Supraparticles Composed of Spherical and Elongated Particles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:1096-1108. [PMID: 38153401 DOI: 10.1021/acs.langmuir.3c03410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2023]
Abstract
We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.
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Affiliation(s)
- Melis Yetkin
- Department of Physics at Interfaces, Max-Planck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany
| | - Yashraj M Wani
- Institute of Physics, Johannes Gutenberg University of Mainz, Staudingerweg 7, Mainz 55128, Germany
| | - Kritika Kritika
- Institute of Physics, Johannes Gutenberg University of Mainz, Staudingerweg 7, Mainz 55128, Germany
- Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Straße 6, Dresden 01069, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden 01069, Germany
| | - Michael P Howard
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Michael Kappl
- Department of Physics at Interfaces, Max-Planck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany
| | - Hans-Jürgen Butt
- Department of Physics at Interfaces, Max-Planck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University of Mainz, Staudingerweg 7, Mainz 55128, Germany
- Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Straße 6, Dresden 01069, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden 01069, Germany
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12
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Sammüller F, Hermann S, de las Heras D, Schmidt M. Neural functional theory for inhomogeneous fluids: Fundamentals and applications. Proc Natl Acad Sci U S A 2023; 120:e2312484120. [PMID: 38060556 PMCID: PMC10723051 DOI: 10.1073/pnas.2312484120] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 10/07/2023] [Indexed: 12/17/2023] Open
Abstract
We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the one-body direct correlation function is represented locally by a deep neural network. We substantiate the general framework for the hard sphere fluid and use grand canonical Monte Carlo simulation data of systems in randomized external environments during training and as reference. Functional calculus is implemented on the basis of the neural network to access higher-order correlation functions via automatic differentiation and the free energy via functional line integration. Thermal Noether sum rules are validated explicitly. We demonstrate the use of the neural functional in the self-consistent calculation of density profiles. The results outperform those from state-of-the-art fundamental measure density functional theory. The low cost of solving an associated Euler-Lagrange equation allows to bridge the gap from the system size of the original training data to macroscopic predictions upon maintaining near-simulation microscopic precision. These results establish the machine learning of functionals as an effective tool in the multiscale description of soft matter.
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Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, BayreuthD-95447, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, BayreuthD-95447, Germany
| | - Daniel de las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, BayreuthD-95447, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, BayreuthD-95447, Germany
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13
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Wu J, Gu M. Perfecting Liquid-State Theories with Machine Intelligence. J Phys Chem Lett 2023; 14:10545-10552. [PMID: 37975624 DOI: 10.1021/acs.jpclett.3c02804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2023]
Abstract
Recent years have seen a significant increase in the use of machine intelligence for predicting the electronic structure, molecular force fields, and physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging recent advancements in functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction, and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability, and computational efficiency, enabling their broader applications across diverse materials and chemical systems.
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Affiliation(s)
- Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Mengyang Gu
- Department of Statistics and Applied Probability, University of California, Santa Barbara, California 93106, United States
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14
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Archer AJ, Goddard BD, Roth R. Stability of nanoparticle laden aerosol liquid droplets. J Chem Phys 2023; 159:194503. [PMID: 37982479 DOI: 10.1063/5.0172137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 10/26/2023] [Indexed: 11/21/2023] Open
Abstract
We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid, such as water, surrounded by gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapor phase is in the thermodynamic equilibrium state, then, of course, droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e., on the nature of the particle interactions with the liquid and, of course, also on the vapor temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapor, thereby demonstrating droplet stability.
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Affiliation(s)
- A J Archer
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - B D Goddard
- School of Mathematics and the Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - R Roth
- Institute for Theoretical Physics, University of Tübingen, 72076 Tübingen, Germany
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15
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Cats P, Härtel A. In-plane structure of the electric double layer in the primitive model using classical density functional theory. J Chem Phys 2023; 159:184707. [PMID: 37955323 DOI: 10.1063/5.0176309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 10/24/2023] [Indexed: 11/14/2023] Open
Abstract
The electric double layer (EDL) has a pivotal role in screening charges on surfaces as in supercapacitor electrodes or colloidal and polymer solutions. Its structure is determined by correlations between the finite-sized ionic charge carriers of the underlying electrolyte, and, this way, these correlations affect the properties of the EDL and of applications utilizing EDLs. We study the structure of EDLs within classical density functional theory (DFT) in order to uncover whether a structural transition in the first layer of the EDL that is driven by changes in the surface potential depends on specific particle interactions or has a general footing. This transition has been found in full-atom simulations. Thus far, investigating the in-plane structure of the EDL for the primitive model (PM) using DFT has proved a challenge. We show here that the use of an appropriate functional predicts the in-plane structure of EDLs in excellent agreement with molecular dynamics simulations. This provides the playground to investigate how the structure factor within a layer parallel to a charged surface changes as a function of both the applied surface potential and its separation from the surface. We discuss pitfalls in properly defining an in-plane structure factor and fully map out the structure of the EDL within the PM for a wide range of electrostatic electrode potentials. However, we do not find any signature of a structural crossover and conclude that the previously reported effect is not fundamental but rather occurs due to the specific force field of ions used in the simulations.
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Affiliation(s)
- Peter Cats
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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16
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Roden JC, Goddard BD, Pearson JW. Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems. J Chem Phys 2023; 159:154102. [PMID: 37846952 DOI: 10.1063/5.0166458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 09/22/2023] [Indexed: 10/18/2023] Open
Abstract
Modelling of many real-world processes, such as drug delivery, wastewater treatment, and pharmaceutical production, requires accurate descriptions of the dynamics of hard particles confined in complicated domains. In particular, when modelling sedimentation processes or systems with driven flows, it is important to accurately capture volume exclusion effects. This work applies Dynamic Density Functional Theory to the evolution of a particle density under diffusion, external forces, particle-particle interaction, and volume exclusion. Using a spectral element framework, for the first time it is possible to include all of these effects in dynamic simulations on complex domains. Moreover, this allows one to apply complicated no-flux, and other non-local, non-linear, boundary conditions. The methodology is also extended to control problems, addressing questions of how to enhance production set-up in industrially-motivated processes. In this work the relevant models are introduced, numerical methods are discussed, and several example problems are solved to demonstrate the methods' versatility. It is shown that incorporating volume exclusion is crucial for simulation accuracy and we illustrate that the choice of boundary conditions significantly impacts the dynamics.
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Affiliation(s)
- Jonna C Roden
- School of Mathematics and Maxwell Institute for Mathematical Sciences, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Benjamin D Goddard
- School of Mathematics and Maxwell Institute for Mathematical Sciences, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - John W Pearson
- School of Mathematics and Maxwell Institute for Mathematical Sciences, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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17
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Borgis D, Laage D, Belloni L, Jeanmairet G. Dielectric response of confined water films from a classical density functional theory perspective. Chem Sci 2023; 14:11141-11150. [PMID: 37860645 PMCID: PMC10583706 DOI: 10.1039/d3sc01267k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 08/21/2023] [Indexed: 10/21/2023] Open
Abstract
We re-examine the problem of the dielectric response of highly polar liquids such as water in confinement between two walls using simple two-variable density functional theory involving number and polarisation densities. In the longitudinal polarisation case where a perturbing field is applied perpendicularly to the walls, we show that the notion of the local dielectric constant, although ill-defined at a microscopic level, makes sense when coarse-graining over the typical size of a particle is introduced. The approach makes it possible to study the effective dielectric response of thin liquid films of various thicknesses in connection with the recent experiments of Fumagalli et al., [Science, 2018, 360, 1339-1342], and to discuss the notion of the interfacial dielectric constant. We argue that the observed properties as a function of slab dimensions, in particular the very low dielectric constants of the order of 2-3 measured for thin slabs of ∼1 nm thickness do not highlight any special properties of water but can be recovered for a generic polar solvent having similar particle size and the same high dielectric constant. Regarding the transverse polarisation case where the perturbing field is parallel to the walls, the associated effective dielectric constant as a function of slab dimensions reaches bulk-like values at much shorter widths than in the longitudinal case. In both cases, we find an oscillatory behaviour for slab thicknesses in the one nanometer range due to packing effects.
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Affiliation(s)
- Daniel Borgis
- Maison de la Simulation, CNRS-CEA-Université Paris-Saclay UAR 3441 91191 Gif-sur-Yvette France
- PASTEUR, Département de chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS 75005 Paris France
| | - Damien Laage
- PASTEUR, Département de chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS 75005 Paris France
| | - Luc Belloni
- Université Paris-Saclay, CEA, CNRS, NIMBE 91191 Gif-sur-Yvette France
| | - Guillaume Jeanmairet
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX F-75005 Paris France
- Réseau sur le Stockage Électrochimique de l'Énergie (RS2E), FR CNRS 3459 80039 Amiens Cedex France
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18
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van Swol F, Douglas Frink LJ, Malanoski AP, Petsev DN. Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings. J Chem Phys 2023; 159:084705. [PMID: 37622595 DOI: 10.1063/5.0164257] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 08/07/2023] [Indexed: 08/26/2023] Open
Abstract
We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.
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Affiliation(s)
- Frank van Swol
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Laura J Douglas Frink
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Anthony P Malanoski
- United States Naval Research Laboratory, Center for Biomolecular Science and Engineering, Washington, DC 20375, USA
| | - Dimiter N Petsev
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
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19
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Wittmann R, Monderkamp PA, Löwen H. Statistics of carrier-cargo complexes. Phys Rev E 2023; 107:064602. [PMID: 37464670 DOI: 10.1103/physreve.107.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 05/17/2023] [Indexed: 07/20/2023]
Abstract
We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.
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Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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20
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Kondrat S, Feng G, Bresme F, Urbakh M, Kornyshev AA. Theory and Simulations of Ionic Liquids in Nanoconfinement. Chem Rev 2023; 123:6668-6715. [PMID: 37163447 PMCID: PMC10214387 DOI: 10.1021/acs.chemrev.2c00728] [Citation(s) in RCA: 23] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Indexed: 05/12/2023]
Abstract
Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.
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Affiliation(s)
- Svyatoslav Kondrat
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
- Institute
for Computational Physics, University of
Stuttgart, Stuttgart 70569, Germany
| | - Guang Feng
- State
Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology (HUST), Wuhan 430074, China
- Nano
Interface Centre for Energy, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fernando Bresme
- Department
of Chemistry, Molecular Sciences Research
Hub, White City Campus, London W12 0BZ,United Kingdom
- Thomas Young
Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- London
Centre for Nanotechnology, Imperial College
London, London SW7 2AZ, United Kingdom
| | - Michael Urbakh
- School
of Chemistry and the Sackler Center for Computational Molecular and
Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Alexei A. Kornyshev
- Department
of Chemistry, Molecular Sciences Research
Hub, White City Campus, London W12 0BZ,United Kingdom
- Thomas Young
Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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21
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Bera A, Binder K, Egorov SA, Das SK. Phase behavior and dynamics in a colloid-polymer mixture under spherical confinement. SOFT MATTER 2023; 19:3386-3397. [PMID: 37128824 DOI: 10.1039/d3sm00362k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.
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Affiliation(s)
- Arabinda Bera
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Staudinger Weg 7, Germany
| | - Sergei A Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, USA
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
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22
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Jung G, Franosch T. Computer simulations and mode-coupling theory of glass-forming confined hard-sphere fluids. Phys Rev E 2023; 107:054101. [PMID: 37328986 DOI: 10.1103/physreve.107.054101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 04/17/2023] [Indexed: 06/18/2023]
Abstract
We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated using the full system of matrix-valued integro-differential equations. We investigate several dynamical properties of supercooled liquids including scattering functions, frequency-dependent susceptibilities, and mean-square displacements. Close to the glass transition, we find quantitative agreement between the coherent scattering function predicted from theory and that evaluated from simulations, which enables us to make quantitative statements on caging and relaxation dynamics of the confined hard-sphere fluid.
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Affiliation(s)
- Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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23
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de Las Heras D, Zimmermann T, Sammüller F, Hermann S, Schmidt M. Perspective: How to overcome dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:271501. [PMID: 37023762 DOI: 10.1088/1361-648x/accb33] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Accepted: 04/06/2023] [Indexed: 06/19/2023]
Abstract
We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.
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Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Toni Zimmermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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24
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Härtel A, Bültmann M, Coupette F. Anomalous Underscreening in the Restricted Primitive Model. PHYSICAL REVIEW LETTERS 2023; 130:108202. [PMID: 36962045 DOI: 10.1103/physrevlett.130.108202] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 12/19/2022] [Accepted: 02/08/2023] [Indexed: 06/18/2023]
Abstract
Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.
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Affiliation(s)
- Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Moritz Bültmann
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Fabian Coupette
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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25
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Sammüller F, Hermann S, Schmidt M. Comparative study of force-based classical density functional theory. Phys Rev E 2023; 107:034109. [PMID: 37072997 DOI: 10.1103/physreve.107.034109] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.
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Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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26
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Goh S, Menzel AM, Wittmann R, Löwen H. Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels. J Chem Phys 2023; 158:054909. [PMID: 36754783 DOI: 10.1063/5.0133207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.
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Affiliation(s)
- Segun Goh
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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27
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Coe MK, Evans R, Wilding NB. Understanding the physics of hydrophobic solvation. J Chem Phys 2023; 158:034508. [PMID: 36681639 DOI: 10.1063/5.0134060] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius Rs → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with Rs, the strength of solute-water attraction ɛsf, and the deviation from liquid-vapor coexistence of the chemical potential, δμ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation.
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Affiliation(s)
- Mary K Coe
- H. H. Wills Physics Laboratory, Royal Fort, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Robert Evans
- H. H. Wills Physics Laboratory, Royal Fort, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Nigel B Wilding
- H. H. Wills Physics Laboratory, Royal Fort, University of Bristol, Bristol BS8 1TL, United Kingdom
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28
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Mantha S, Chao H, Ylitalo AS, Fitzgibbons TC, Zhou W, Ginzburg VV, Wang ZG. Surfactant in a Polyol-CO 2 Mixture: Insights from a Classical Density Functional Theory Study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:16172-16182. [PMID: 36524704 PMCID: PMC9798868 DOI: 10.1021/acs.langmuir.2c02913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 11/26/2022] [Indexed: 06/17/2023]
Abstract
Silicone-polyether (SPE) surfactants, made of a polydimethyl-siloxane (PDMS) backbone and polyether branches, are commonly used as additives in the production of polymeric foams with improved properties. A key step in the production of polymeric foams is the nucleation of gas bubbles in the polymer matrix upon supersaturation of dissolved gas. However, the role of SPE surfactants in the nucleation of gas bubbles is not well understood. In this study, we use classical density functional theory to investigate the effect of an SPE surfactant on the nucleation of CO2 bubbles in a polyol foam formulation. We find that the addition of an SPE surfactant leads to a ∼3-fold decrease in the polyol-CO2 interfacial tension at the surfactant's critical micelle concentration. Additionally, the surfactant is found to reduce the free energy barrier and affect the minimum free energy pathway (MFEP) associated with CO2 bubble nucleation. In the absence of a surfactant, a CO2-rich bubble nucleates from a homogeneous CO2-supersaturated polyol solution by following an MFEP characterized by a single nucleation barrier. Adding a surfactant results in a two-step nucleation process with reduced free energy barriers. The first barrier corresponds to the formation of a spherical aggregate with a liquid-like CO2 core. This spherical aggregate then grows into a CO2-rich bubble (spherical aggregate with a vapor-like CO2 core) of a critical size representing the second barrier. We hypothesize that the stronger affinity of CO2 for PDMS (than polyether) stabilizes the spherical aggregate with the liquid-like CO2 core, leading to a lower free energy barrier for CO2 bubble nucleation. Stabilization of such an aggregate during the early stages of the nucleation may lead to foams with more, smaller bubbles, which can improve their microstrustural features and insulating abilities.
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Affiliation(s)
- Sriteja Mantha
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Huikuan Chao
- Dow,
Inc., Midland, Michigan 48667, United States
| | - Andrew S. Ylitalo
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | | | - Weijun Zhou
- Dow,
Inc., Lake Jackson, Texas 77566, United States
| | - Valeriy V. Ginzburg
- Dow,
Inc., Midland, Michigan 48667, United States
- Michigan
State University, East Lansing, Michigan 48910, United States
| | - Zhen-Gang Wang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
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29
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Tschopp SM, Brader JM. First-principles superadiabatic theory for the dynamics of inhomogeneous fluids. J Chem Phys 2022; 157:234108. [PMID: 36550050 DOI: 10.1063/5.0131441] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
For classical many-body systems subject to Brownian dynamics, we develop a superadiabatic dynamical density functional theory (DDFT) for the description of inhomogeneous fluids out-of-equilibrium. By explicitly incorporating the dynamics of the inhomogeneous two-body correlation functions, we obtain superadiabatic forces directly from the microscopic interparticle interactions. We demonstrate the importance of these nonequilibrium forces for an accurate description of the one-body density by numerical implementation of our theory for three-dimensional hard-spheres in a time-dependent planar potential. The relaxation of the one-body density in superadiabatic-DDFT is found to be slower than that predicted by standard adiabatic DDFT and significantly improves the agreement with Brownian dynamics simulation data. We attribute this improved performance to the correct treatment of structural relaxation within the superadiabatic-DDFT. Our approach provides fundamental insight into the underlying structure of dynamical density functional theories and makes possible the study of situations for which standard approaches fail.
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Affiliation(s)
- S M Tschopp
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - J M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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30
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Yang Y, Che Ruslan MFA, Narayanan Nair AK, Qiao R, Sun S. Interfacial properties of the hexane + carbon dioxide + water system in the presence of hydrophilic silica. J Chem Phys 2022; 157:234704. [PMID: 36550045 DOI: 10.1063/5.0130986] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
Molecular dynamics simulations were conducted to study the interfacial behavior of the CO2 + H2O and hexane + CO2 + H2O systems in the presence of hydrophilic silica at geological conditions. Simulation results for the CO2 + H2O and hexane + CO2 + H2O systems are in reasonable agreement with the theoretical predictions based on the density functional theory. In general, the interfacial tension (IFT) of the CO2 + H2O system exponentially (linearly) decreased with increasing pressure (temperature). The IFTs of the hexane + CO2 + H2O (two-phase) system decreased with the increasing mole fraction of CO2 in the hexane/CO2-rich phase xCO2 . Here, the negative surface excesses of hexane lead to a general increase in the IFTs with increasing pressure. The effect of pressure on these IFTs decreased with increasing xCO2 due to the positive surface excesses of carbon dioxide. The simulated water contact angles of the CO2 + H2O + silica system fall in the range from 43.8° to 76.0°, which is in reasonable agreement with the experimental results. These contact angles increased with pressure and decreased with temperature. Here, the adhesion tensions are influenced by the variations in fluid-fluid IFT and contact angle. The simulated water contact angles of the hexane + H2O + silica system fall in the range from 58.0° to 77.0° and are not much affected by the addition of CO2. These contact angles increased with pressure, and the pressure effect was less pronounced at lower temperatures. Here, the adhesion tensions are mostly influenced by variations in the fluid-fluid IFTs. In all studied cases, CO2 molecules could penetrate into the interfacial region between the water droplet and the silica surface.
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Affiliation(s)
- Yafan Yang
- State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
| | - Mohd Fuad Anwari Che Ruslan
- Physical Science and Engineering Division (PSE), Computational Transport Phenomena Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
| | - Arun Kumar Narayanan Nair
- Physical Science and Engineering Division (PSE), Computational Transport Phenomena Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
| | - Rui Qiao
- Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Shuyu Sun
- Physical Science and Engineering Division (PSE), Computational Transport Phenomena Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
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31
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Te Vrugt M, Wittkowski R. Perspective: New directions in dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:041501. [PMID: 35917827 DOI: 10.1088/1361-648x/ac8633] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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32
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Egorov SA. Depletion Interactions between Nanoparticles: The Effect of the Polymeric Depletant Stiffness. Polymers (Basel) 2022; 14:polym14245398. [PMID: 36559764 PMCID: PMC9780964 DOI: 10.3390/polym14245398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2022] [Revised: 12/06/2022] [Accepted: 12/06/2022] [Indexed: 12/13/2022] Open
Abstract
A Density Functional Theory is employed to study depletion interactions between nanoparticles mediated by semiflexible polymers. The four key parameters are the chain contour length and the persistence length of the polymeric depletant, its radius of gyration, and the nanoparticle radius. In the Density Functional Theory calculation of the depletion interaction between the nanoparticles mediated by semiflexible polymers, the polymer gyration radius is kept constant by varying the contour length and the persistence length simultaneously. This makes it possible to study the effect of the chain stiffness on the depletion potential of mean force between the nanoparticles for a given depletant size. It is found that the depletion attraction becomes stronger for stiffer polymer chains and larger colloids. The depletion potential of mean force is used as input to compute the phase diagram for an effective one-component colloidal system.
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Affiliation(s)
- Sergei A Egorov
- Department of Chemistry, University of Virginia, Charlottesville, VA 22901, USA
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33
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Finster KL, Krebs EJ, May CJ, Kreitzberg PA, Roundy D. Soft fundamental measure theory functional for the Weeks-Chandler-Andersen repulsive potential. Phys Rev E 2022; 106:064134. [PMID: 36671089 DOI: 10.1103/physreve.106.064134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/02/2022] [Indexed: 12/28/2022]
Abstract
We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid. We find that this approach is comparable in accuracy to the Barker-Henderson approach combined with the White Bear density functional for the hard-sphere fluid.
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Affiliation(s)
- K L Finster
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | - Eric J Krebs
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | - Christopher J May
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
| | | | - David Roundy
- Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
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34
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Schoonen C, Lutsko JF. Using classical density functional theory to determine crystal-fluid surface tensions. Phys Rev E 2022; 106:064110. [PMID: 36671108 DOI: 10.1103/physreve.106.064110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 11/16/2022] [Indexed: 06/17/2023]
Abstract
Classical density functional theory is used to determine the fluid-solid surface tensions for low-index faces of crystals of hard spheres and Lennard-Jones particles. The calculations make use of the recently introduced explicitly stable fundamental measure theory model for hard spheres, and we show that this gives state-of-the-art accuracy compared to simulation. For the Lennard-Jones system, results are presented for both solid-liquid and solid-vapor interfaces, and in both cases the FCC results compare favorably with existing results from the literature. We find that the BCC crystal has significantly lower solid-liquid surface tension than the FCC structure. For the solid-vapor interface, our results indicate that the BCC phase is unstable with respect to transition to the HCP structure, in agreement with various zero-temperature results in the literature.
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Affiliation(s)
- Cédric Schoonen
- Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, Blvd. du Triomphe, 1050 Brussels, Belgium
| | - James F Lutsko
- Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, Blvd. du Triomphe, 1050 Brussels, Belgium
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35
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Kundu M, Howard MP. Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals. J Chem Phys 2022; 157:184904. [DOI: 10.1063/5.0118695] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions, including local-density approximations based on the ideal-gas, virial, and Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes, such as solvent drying, solvent freezing, and sedimentation.
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Affiliation(s)
- Mayukh Kundu
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, USA
| | - Michael P. Howard
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, USA
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36
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Archer AJ, Dotera T, Rucklidge AM. Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry. Phys Rev E 2022; 106:044602. [PMID: 36397536 DOI: 10.1103/physreve.106.044602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 08/03/2022] [Indexed: 06/16/2023]
Abstract
Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal type. Here we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length scales that form aperiodic stable states with two different examples of rectangle-triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.
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Affiliation(s)
- Andrew J Archer
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Tomonari Dotera
- Department of Physics, Kindai University, 3-4-1 Kowakae Higashi, Osaka 577-8502, Japan
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37
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Alston H, Parry AO, Voituriez R, Bertrand T. Intermittent attractive interactions lead to microphase separation in nonmotile active matter. Phys Rev E 2022; 106:034603. [PMID: 36266896 DOI: 10.1103/physreve.106.034603] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 07/26/2022] [Indexed: 06/16/2023]
Abstract
Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.
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Affiliation(s)
- Henry Alston
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
- Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
| | - Thibault Bertrand
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
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38
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Alkhadra M, Su X, Suss ME, Tian H, Guyes EN, Shocron AN, Conforti KM, de Souza JP, Kim N, Tedesco M, Khoiruddin K, Wenten IG, Santiago JG, Hatton TA, Bazant MZ. Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion. Chem Rev 2022; 122:13547-13635. [PMID: 35904408 PMCID: PMC9413246 DOI: 10.1021/acs.chemrev.1c00396] [Citation(s) in RCA: 60] [Impact Index Per Article: 30.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Indexed: 02/05/2023]
Abstract
Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.
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Affiliation(s)
- Mohammad
A. Alkhadra
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Xiao Su
- Department
of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Matthew E. Suss
- Faculty
of Mechanical Engineering, Technion—Israel
Institute of Technology, Haifa 3200003, Israel
- Wolfson
Department of Chemical Engineering, Technion—Israel
Institute of Technology, Haifa 3200003, Israel
- Nancy
and Stephen Grand Technion Energy Program, Technion—Israel Institute of Technology, Haifa 3200003, Israel
| | - Huanhuan Tian
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Eric N. Guyes
- Faculty
of Mechanical Engineering, Technion—Israel
Institute of Technology, Haifa 3200003, Israel
| | - Amit N. Shocron
- Faculty
of Mechanical Engineering, Technion—Israel
Institute of Technology, Haifa 3200003, Israel
| | - Kameron M. Conforti
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - J. Pedro de Souza
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Nayeong Kim
- Department
of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Michele Tedesco
- European
Centre of Excellence for Sustainable Water Technology, Wetsus, Oostergoweg 9, 8911 MA Leeuwarden, The Netherlands
| | - Khoiruddin Khoiruddin
- Department
of Chemical Engineering, Institut Teknologi
Bandung, Jl. Ganesha no. 10, Bandung, 40132, Indonesia
- Research
Center for Nanosciences and Nanotechnology, Institut Teknologi Bandung, Jl. Ganesha no. 10, Bandung 40132, Indonesia
| | - I Gede Wenten
- Department
of Chemical Engineering, Institut Teknologi
Bandung, Jl. Ganesha no. 10, Bandung, 40132, Indonesia
- Research
Center for Nanosciences and Nanotechnology, Institut Teknologi Bandung, Jl. Ganesha no. 10, Bandung 40132, Indonesia
| | - Juan G. Santiago
- Department
of Mechanical Engineering, Stanford University, Stanford, California 94305, United States
| | - T. Alan Hatton
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Martin Z. Bazant
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Mathematics, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
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39
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Martin SC, Hansen-Goos H, Roth R, Laird BB. Inside and out: surface thermodynamics from positive to negative curvature. J Chem Phys 2022; 157:054702. [DOI: 10.1063/5.0099295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To explore the curvature dependence of solid-fluid interfacial thermodynamics, we calculate, using Grand Canonical Monte Carlo simulation, the surface free energy γ for a 2-d hard-disk fluid confined in a circular hard container of radius R as a function of the bulk packing fraction η and wall curvature C = −1/ R. (The curvature is negative because the surface is concave) Combining this with our previous data [J. Phys. Chem. B, 124, 7938 (2020)] for the positive curvature case (a hard-disk fluid at a circular wall, C = +1/ R), we obtain a full picture of surface thermodynamics in this system over the full range of positive and negative wall curvatures. Our results show that γ is linear in C with a slope that is the same for both positive and negative wall curvatures, with deviations seen only at high negative curvatures (strong confinement) and high density. This observation indicates that the surface thermodynamics of this system is consistent with the predictions of so-called Morphometric Thermodynamics at both positive and negative curvatures. In addition, we show that classical Density Functional Theory and a generalized scaled particle theory can be constructed that give excellent agreement with the simulation data over most of the range of curvatures and densities. For extremely high curvatures, where only one or two disks can occupy the container at maximum packing, it is possible to calculate γ exactly. In this limit the simulations and DFT calculations are in remarkable agreement with the exact results.
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Affiliation(s)
| | | | - Roland Roth
- University of Tübingen Department of Physics, Germany
| | - Brian B. Laird
- Chemistry, University of Kansas, United States of America
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40
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Tschopp SM, Sammüller F, Hermann S, Schmidt M, Brader JM. Force density functional theory in- and out-of-equilibrium. Phys Rev E 2022; 106:014115. [PMID: 35974621 DOI: 10.1103/physreve.106.014115] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 06/06/2022] [Indexed: 06/15/2023]
Abstract
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.
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Affiliation(s)
- Salomée M Tschopp
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Joseph M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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41
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Jung G, Franosch T. Structural properties of liquids in extreme confinement. Phys Rev E 2022; 106:014614. [PMID: 35974617 DOI: 10.1103/physreve.106.014614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 07/10/2022] [Indexed: 06/15/2023]
Abstract
We simulate a hard-sphere liquid in confined geometry where the separation of the two parallel, hard walls is smaller than two particle diameters. By systematically reducing the wall separation we analyze the behavior of structural and thermodynamic properties, such as inhomogeneous density profiles, structure factors, and compressibilities when approaching the two-dimensional limit. In agreement with asymptotic predictions, we find for quasi-two-dimensional fluids that the density profile becomes parabolic and the structure factor converges toward its two-dimensional counterpart. To extract the compressibility in polydisperse samples a perturbative expression is used which qualitatively influences the observed nonmonotonic dependence of the compressibility with wall separation. We also present theoretical calculations based on fundamental-measure theory and integral-equation theory, which are in very good agreement with the simulation results.
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Affiliation(s)
- Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria
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42
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Villada-Balbuena A, Jung G, Zuccolotto-Bernez AB, Franosch T, Egelhaaf SU. Layering and packing in confined colloidal suspensions. SOFT MATTER 2022; 18:4699-4714. [PMID: 35702953 PMCID: PMC9241587 DOI: 10.1039/d2sm00412g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
Confinement modifies the properties of a fluid. The particle density is no longer uniform but depends on the distance from the walls; parallel to the walls, layers with different particle densities form. This affects the particle packing in the layers. We investigated colloidal fluids with volume fractions between 0.19 and 0.32 confined between rough walls. The particle-particle interactions were dominated by hard-sphere interactions but also contained some electrostatic interactions. The particle locations were determined using confocal microscopy and served to calculate the density profile, radial distribution function, anisotropic and generalized structure factors but also to characterize the arrangement of the wall particles leading to the roughness of the walls. The experiments are complemented by molecular dynamics simulations and fundamental-measure theory. While the particle arrangements are mainly controlled by hard-core interactions, electrostatic interactions become more important as the volume fraction decreases. Furthermore, the structure of the rough walls was varied and found to have a significant effect on the fluid structure. An appropriate representation of the rough walls in the simulations is thus crucial to successfully mimic the experiments.
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Affiliation(s)
- Alejandro Villada-Balbuena
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany.
| | - Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, 6020 Innsbruck, Austria
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Angel B Zuccolotto-Bernez
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany.
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, 6020 Innsbruck, Austria
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany.
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43
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de Souza JP, Kornyshev AA, Bazant MZ. Polar liquids at charged interfaces: A dipolar shell theory. J Chem Phys 2022; 156:244705. [PMID: 35778078 DOI: 10.1063/5.0096439] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.
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Affiliation(s)
- J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
| | - Alexei A Kornyshev
- Department of Chemistry and Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Molecular Sciences Research Hub, White City Campus, London W12 0BZ, United Kingdom
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
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44
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Kanygin Y, Nesterova I, Lomovitskiy P, Khlyupin A. Variation-Free Approach for Density Functional Theory: Data-Driven Stochastic Optimization. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c00547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuriy Kanygin
- Moscow Institute of Physics and Technology, Dolgoprudny, Russia, 141700
| | - Irina Nesterova
- Moscow Institute of Physics and Technology, Dolgoprudny, Russia, 141700
| | - Pavel Lomovitskiy
- Moscow Institute of Physics and Technology, Dolgoprudny, Russia, 141700
| | - Aleksey Khlyupin
- Moscow Institute of Physics and Technology, Dolgoprudny, Russia, 141700
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45
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Egorov SA. Bulk and interfacial properties of semiflexible polymers: A density functional theory study. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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46
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Wu J. Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics. Chem Rev 2022; 122:10821-10859. [PMID: 35594506 DOI: 10.1021/acs.chemrev.2c00097] [Citation(s) in RCA: 128] [Impact Index Per Article: 64.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.
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Affiliation(s)
- Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
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47
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Riva S, Banetta L, Zaccone A. Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate Péclet numbers. Phys Rev E 2022; 105:054606. [PMID: 35706254 DOI: 10.1103/physreve.105.054606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors k and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower k in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high k is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.
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Affiliation(s)
- Simone Riva
- Department of Physics, A. Pontremoli, University of Milan, Via Celoria 16, 20133 Milan, Italy
| | - Luca Banetta
- Department of Applied Science and Technology (DISAT), Politecnico of Turin, Italy
| | - Alessio Zaccone
- Department of Physics, A. Pontremoli, University of Milan, Via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
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48
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Hermann S, Schmidt M. Why Noether's theorem applies to statistical mechanics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:213001. [PMID: 35255482 DOI: 10.1088/1361-648x/ac5b47] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
Noether's theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of classical mechanics or on the basis of field theory. We have recently shown (2021Commun. Phys.4176) that Noether's reasoning also applies to thermal systems, where fluctuations are paramount and one aims for a statistical mechanical description. Here we give a pedagogical introduction based on the canonical ensemble and apply it explicitly to ideal sedimentation. The relevant mathematical objects, such as the free energy, are viewed as functionals. This vantage point allows for systematic functional differentiation and the resulting identities express properties of both macroscopic average forces and molecularly resolved correlations in many-body systems, both in and out-of-equilibrium, and for active Brownian particles. To provide further background, we briefly describe the variational principles of classical density functional theory, of power functional theory, and of classical mechanics.
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Affiliation(s)
- Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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49
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Bültmann M, Härtel A. The primitive model in classical density functional theory: beyond the standard mean-field approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:235101. [PMID: 35294927 DOI: 10.1088/1361-648x/ac5e7a] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 03/16/2022] [Indexed: 06/14/2023]
Abstract
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory (DFT) the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation of the pair potential for an uncharged reference system of hard spheres. This mean-field electrostatic term particularly contributes at particle separations that are forbidden due to hard-core overlap. In this work we modify the mean-field contribution such that the pair potential is constant for distances smaller than the contact distance of the ions. We motivate our modification by the underlying splitting of the potential, which is similar to the splitting of the Weeks-Chandler-Andersen potential and leads to higher-order terms in the respective expansion of the functional around the reference system. The resulting formalism involves weighted densities similar to the ones found in fundamental measure theory. To test our modifications, we analyze and compare density profiles, direct and total correlation functions, and the thermodynamic consistency of the functional via a widely established sum rule and the virial pressure formula for our modified functional, for established functionals, and for data from computer simulations. We found that our modifications clearly show improvements compared to the standard mean-field functional, especially when predicting layering effects and direct correlation functions in high concentration scenarios; for the latter we also find improved consistency when calculated via different thermodynamic routes. In conclusion, we demonstrate how modifications toward higher order corrections beyond mean-field functionals can be made and how they perform, by this providing a basis for systematic future improvements in classical DFT for the description of electrostatic interactions.
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Affiliation(s)
- Moritz Bültmann
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
| | - Andreas Härtel
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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50
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Singh SL, Schimmele L, Dietrich S. Intrusion of liquids into liquid-infused surfaces with nanoscale roughness. Phys Rev E 2022; 105:044803. [PMID: 35590586 DOI: 10.1103/physreve.105.044803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 03/28/2022] [Indexed: 06/15/2023]
Abstract
We present a theoretical study of the intrusion of an ambient liquid into the pores of a nanocorrugated wall w. The pores are prefilled with a liquid lubricant that adheres to the walls of the pores more strongly than the ambient liquid does. The two liquids are modeled as a binary liquid mixture of two species of particles, A and B. The mixture can decompose into a liquid rich in A particles, representing the ambient liquid, and another one rich in B particles, representing the liquid lubricant. The wall is taken to attract the B particles more strongly than the A particles. The ratio w-A/w-B of these interaction strengths is changed in order to tune the contact angle θ_{AB} formed by the A-rich/B-rich liquid interface between the two fluids and a planar wall, composed of the same material as the one forming the pores. We use classical density functional theory in order to capture the effects of microscopic details on the intrusion transition, which occurs as the concentration of the minority component or the pressure in the bulk of the ambient liquid is varied, moving away from bulk liquid-liquid coexistence within the single-phase domain of the A-rich bulk ambient liquid. These liquid structures have been studied as a function of the contact angle θ_{AB} and for various widths and depths of the pores. We also studied the reverse process in which a pore initially filled with the ambient liquid is refilled with the liquid lubricant. The location of the intrusion transition, with respect to its dependence on the contact angle θ_{AB} and the width of the pore, qualitatively follows the corresponding shift of the capillary-coexistence line away from the bulk liquid-liquid coexistence line, as predicted by a macroscopic capillarity model. Quantitatively, the transition found in the microscopic approach occurs somewhat closer to the bulk liquid-liquid coexistence line than predicted by the macroscopic capillarity model. The quantitative discrepancies become larger for narrower cavities. In cases in which the wall is completely wetted by the lubricant (θ_{AB}=0) and for small contact angles, the reverse transition follows the same path as for intrusion; there is no hysteresis. For larger contact angles, hysteresis is observed. The width of the hysteresis increases with increasing contact angle. A reverse transition is not found inside the domain within which the ambient liquid forms a single phase in the bulk once θ_{AB} exceeds a geometry-dependent threshold value. According to the macroscopic capillarity theory, for the considered geometry, this is the case for θ_{AB}>54.7^{∘}. Our computations show, however, that nanoscale effects shift this threshold value to much higher values. This shift increases strongly if the widths of the pores become smaller (below about ten times the diameter of the A and B particles).
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Affiliation(s)
- Swarn Lata Singh
- Max-Planck-Institut für Intelligente Systeme, D-70569 Stuttgart, Heisenbergstrasse 3, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
- Department of Physics, Mahila Mahavidyalaya (MMV), Banaras Hindu University, Varanasi, UP, 221005, India
| | - Lothar Schimmele
- Max-Planck-Institut für Intelligente Systeme, D-70569 Stuttgart, Heisenbergstrasse 3, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, D-70569 Stuttgart, Heisenbergstrasse 3, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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