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Beneduce C, Sciortino F, Šulc P, Russo J. Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures. ACS NANO 2023; 17:24841-24853. [PMID: 38048489 PMCID: PMC10753881 DOI: 10.1021/acsnano.3c05569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Revised: 11/08/2023] [Accepted: 11/09/2023] [Indexed: 12/06/2023]
Abstract
The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.
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Affiliation(s)
- Camilla Beneduce
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Francesco Sciortino
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Petr Šulc
- School
of Molecular Sciences and Center for Molecular Design and Biomimetics,
The Biodesign Institute, Arizona State University, 1001 South McAllister Avenue, Tempe, Arizona 85281, United States
- School
of Natural Sciences, Department of Bioscience, TU Munich, Am Coulombwall
4a, 85748, Garching, Germany
| | - John Russo
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
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2
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Opdam J, Peters VFD, Wensink HH, Tuinier R. Multiphase Coexistence in Binary Hard Colloidal Mixtures: Predictions from a Simple Algebraic Theory. J Phys Chem Lett 2023; 14:199-206. [PMID: 36580685 PMCID: PMC9841575 DOI: 10.1021/acs.jpclett.2c03138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
A general theoretical framework is proposed to quantify the thermodynamic properties of multicomponent hard colloidal mixtures. This framework is used to predict the phase behavior of mixtures of rods with spheres and rods with plates taking into account (liquid) crystal phases of both components. We demonstrate a rich and complex range of phase behaviors featuring a large variety of different multiphase coexistence regions, including two five-phase coexistence regions for hard rod/sphere mixtures, and even a six-phase equilibrium for hard rod/plate dispersions. The various multiphase coexistences featured in a particular mixture are in line with a recently proposed generalized phase rule and can be tuned through subtle variations of the particle shape and size ratio. Our approach qualitatively accounts for certain multiphase equilibria observed in rod/plate mixtures of clay colloids and will be a useful guide in tuning the phase behavior of shape-disperse mixtures in general.
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Affiliation(s)
- J. Opdam
- Laboratory
of Physical Chemistry, Department of Chemical Engineering and Chemistry,
and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MBEindhoven, The Netherlands
| | - V. F. D. Peters
- Laboratory
of Physical Chemistry, Department of Chemical Engineering and Chemistry,
and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MBEindhoven, The Netherlands
- Department
of Earth Sciences, Utrecht University, Princetonlaan 8a, 3584CBUtrecht, The Netherlands
| | - H. H. Wensink
- Laboratoire
de Physique des Solides, Université Paris-Saclay and CNRS, 91405Orsay, France
| | - R. Tuinier
- Laboratory
of Physical Chemistry, Department of Chemical Engineering and Chemistry,
and Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MBEindhoven, The Netherlands
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3
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Fijan D, Wilson M. Thermodynamic anomalies in silicon and the relationship to the phase diagram. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:425404. [PMID: 34293720 DOI: 10.1088/1361-648x/ac16f5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Accepted: 07/22/2021] [Indexed: 06/13/2023]
Abstract
The evolution of thermodynamic anomalies are investigated in the pressure-temperature (pT) plane for silicon using the well-established Stillinger-Weber potential. Anomalies are observed in the density, compressibility and heat capacity. The relationships between them and with the liquid stability limit are investigated and related to the known thermodynamic constraints. The investigations are extended into the deeply supercooled regime using replica exchange techniques. Thermodynamic arguments are presented to justify the extension to low temperature, although a region of phase space is found to remain inaccessible due to unsuppressible crystallisation. The locus corresponding to the temperature of minimum compressibility is shown to display a characteristic 'S'-shape in thepTprojection which appears correlated with the underlying crystalline phase diagram. The progression of the anomalies is compared to the known underlying phase diagrams for both the crystal/liquid and amorphous/liquid states. The locations of the anomalies are also compared to those obtained from previous simulation work and (limited) experimental observations.
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Affiliation(s)
- Domagoj Fijan
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Mark Wilson
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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Li M, Yue Z, Chen Y, Tong H, Tanaka H, Tan P. Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition. Nat Commun 2021; 12:4042. [PMID: 34193874 PMCID: PMC8245452 DOI: 10.1038/s41467-021-24256-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 06/08/2021] [Indexed: 11/22/2022] Open
Abstract
Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase's softness and defect landscape.
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Affiliation(s)
- Minhuan Li
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China
| | - Zhengyuan Yue
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China
| | - Yanshuang Chen
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China
| | - Hua Tong
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Department of Physics, University of Science and Technology of China, Hefei, China
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, Tokyo, Japan
| | - Hajime Tanaka
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, Tokyo, Japan.
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan.
| | - Peng Tan
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China.
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Peters VFD, Vis M, García ÁG, Wensink HH, Tuinier R. Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures. PHYSICAL REVIEW LETTERS 2020; 125:127803. [PMID: 33016722 DOI: 10.1103/physrevlett.125.127803] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 07/10/2020] [Indexed: 05/24/2023]
Abstract
Using a minimal algebraic model for the thermodynamics of binary rod-polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our model is based on equations of state for the relevant liquid crystal phases that are in quantitative agreement with computer simulations. We argue that the appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic and smectic liquid crystal, and two solid phases, can be reconciled with a generalized Gibbs phase rule in which the two intrinsic length scales of the athermal colloid-polymer mixture act as additional field variables.
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Affiliation(s)
- V F D Peters
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - M Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
- Laboratoire de Chimie, École Normale Supérieure de Lyon, 69364 Lyon CEDEX 07, France
| | - Á González García
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH Utrecht, Netherlands
| | - H H Wensink
- Laboratoire de Physique des Solides-UMR 8502, CNRS & Université Paris-Saclay, 91405 Orsay, France
| | - R Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH Utrecht, Netherlands
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Fijan D, Wilson M. Liquid state anomalies and the relationship to the crystalline phase diagram. Phys Rev E 2019; 99:010103. [PMID: 30780346 DOI: 10.1103/physreve.99.010103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Indexed: 06/09/2023]
Abstract
A relationship between the observation of a density anomaly and the underlying crystalline phase diagram is demonstrated. The crystal phase diagram and temperature of maximum density (TMD) lines are calculated over a range of parameter space using a Stillinger-Weber potential. Relationships between the loci of density maxima in the PT plane for the liquid state and the underlying crystalline phase diagram are investigated. Two key potential parameters are systematically varied in order to control the balance between the model two- and three-body interaction terms, and the relative effects of varying the potential parameters analyzed. The respective TMD lines diverge at extreme values with one set of lines showing a reentrant behavior. For each parameter set the TMD lines are extrapolated to T=0K. The corresponding pressures are related to the crystalline phase diagram and are found to lie on or near specific crystal-crystal coexistence lines for a wide range of potential parameters. The density anomaly is observed to vanish corresponding to regions in the crystal phase diagram which lack crystal-crystal coexistence lines potentially offering a new interpretation for the emergence of anomalous behavior.
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Affiliation(s)
- Domagoj Fijan
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Mark Wilson
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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García ÁG, Tuinier R, Maring JV, Opdam J, Wensink HH, Lekkerkerker HNW. Depletion-driven four-phase coexistences in discotic systems. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1463471] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Álvaro González García
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, & Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology , Eindhoven, The Netherlands
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University , Utrecht, The Netherlands
| | - Remco Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, & Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology , Eindhoven, The Netherlands
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University , Utrecht, The Netherlands
| | - Jasper V. Maring
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, & Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology , Eindhoven, The Netherlands
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University , Utrecht, The Netherlands
| | - Joeri Opdam
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, & Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology , Eindhoven, The Netherlands
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University , Utrecht, The Netherlands
| | - Henricus H. Wensink
- Laboratoire de Physique des Solides - UMR 8502, Université Paris-Sud, Université Paris-Saclay and CNRS , Orsay, France
| | - Henk N. W. Lekkerkerker
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University , Utrecht, The Netherlands
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Abstract
Water is the most common and yet least understood material on Earth. Despite its simplicity, water tends to form tetrahedral order locally by directional hydrogen bonding. This structuring is known to be responsible for a vast array of unusual properties, e.g., the density maximum at 4 °C, which play a fundamental role in countless natural and technological processes, with the Earth’s climate being one of the most important examples. By systematically tuning the degree of tetrahedrality, we succeed in continuously interpolating between water-like behavior and simple liquid-like behavior. Our approach reveals what physical factors make water so anomalous and special even compared with other tetrahedral liquids. Tetrahedral interactions describe the behavior of the most abundant and technologically important materials on Earth, such as water, silicon, carbon, germanium, and countless others. Despite their differences, these materials share unique common physical behaviors, such as liquid anomalies, open crystalline structures, and extremely poor glass-forming ability at ambient pressure. To reveal the physical origin of these anomalies and their link to the shape of the phase diagram, we systematically study the properties of the Stillinger–Weber potential as a function of the strength of the tetrahedral interaction λ. We uncover a unique transition to a reentrant spinodal line at low values of λ, accompanied with a change in the dynamical behavior, from non-Arrhenius to Arrhenius. We then show that a two-state model can provide a comprehensive understanding on how the thermodynamic and dynamic anomalies of this important class of materials depend on the strength of the tetrahedral interaction. Our work establishes a deep link between the shape of the phase diagram and the thermodynamic and dynamic properties through local structural ordering in liquids and hints at why water is so special among all substances.
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Fijan D, Wilson M. The characterisation of the “X” crystal structure in the Stillinger-Weber potential. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.07.083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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