1
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Bickmann J, Bröker S, Te Vrugt M, Wittkowski R. Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns. Phys Rev E 2023; 108:044601. [PMID: 37978644 DOI: 10.1103/physreve.108.044601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 08/24/2023] [Indexed: 11/19/2023]
Abstract
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.
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Affiliation(s)
- Jens Bickmann
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Stephan Bröker
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - 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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2
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Eckert T, Schmidt M, de Las Heras D. Effect of sample height and particle elongation in the sedimentation of colloidal rods. SOFT MATTER 2023; 19:2214-2223. [PMID: 36883340 DOI: 10.1039/d3sm00191a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We study theoretically the effect of a gravitational field on the equilibrium behaviour of a colloidal suspension of rods with different length-to-width aspect ratios. The bulk phases of the system are described with analytical equations of state. The gravitational field is then incorporated via sedimentation path theory, which assumes a local equilibrium condition at each altitude of the sample. The bulk phenomenology is significantly enriched by the presence of the gravitational field. In a suspension of elongated rods with five stable phases in bulk, the gravitational field stabilizes up to fifteen different stacking sequences. The sample height has a non-trivial effect on the stable stacking sequence. New layers of distinct bulk phases appear either at the top, at the bottom, or simultaneously at the top and the bottom when increasing the sample height at constant colloidal concentration. We also study sedimentation in a mass-polydisperse suspension in which all rods have the same shape but different buoyant masses.
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Affiliation(s)
- Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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3
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Eckert T, Schmidt M, de Las Heras D. Sedimentation path theory for mass-polydisperse colloidal systems. J Chem Phys 2022; 157:234901. [PMID: 36550036 DOI: 10.1063/5.0129916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.
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Affiliation(s)
- Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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4
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Stemplinger S, Prévost S, Zemb T, Horinek D, Dufrêche JF. Theory of Ternary Fluids under Centrifugal Fields. J Phys Chem B 2021; 125:12054-12062. [PMID: 34694817 DOI: 10.1021/acs.jpcb.1c05875] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
In this work, we developed a general theoretical description of ternary solutions of small molecules under a centrifugal field, from which we obtained the centrifugation map (CMap) as a general tool to understand observations or to predict composition profiles in centrifugal fields of arbitrary strength. The theoretical formalism is based on the classical density functional theory with established models for liquid mixtures. Thermodynamics also yields a general criterion for apparent aggregation. The strength of the CMap approach is illustrated for a ternary model system where ethanol is a co-solvent.
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Affiliation(s)
- Simon Stemplinger
- Institut für Physikalische und Theoretische Chemie, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany.,Institut de Chimie Séparative de Marcoule (ICSM) UMR 5257 CEA/CNRS/UM/ENSCM, Site de Marcoule, 30207 Bagnols sur Cèze, France
| | - Sylvain Prévost
- Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble, France
| | - Thomas Zemb
- Institut de Chimie Séparative de Marcoule (ICSM) UMR 5257 CEA/CNRS/UM/ENSCM, Site de Marcoule, 30207 Bagnols sur Cèze, France
| | - Dominik Horinek
- Institut für Physikalische und Theoretische Chemie, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany
| | - Jean-François Dufrêche
- Institut de Chimie Séparative de Marcoule (ICSM) UMR 5257 CEA/CNRS/UM/ENSCM, Site de Marcoule, 30207 Bagnols sur Cèze, France
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5
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Braz Teixeira R, de Las Heras D, Tavares JM, Telo da Gama MM. Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravity. J Chem Phys 2021; 155:044903. [PMID: 34340383 DOI: 10.1063/5.0056652] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim's perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory-Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.
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Affiliation(s)
- Rodrigo Braz Teixeira
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - José Maria Tavares
- Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
| | - Margarida M Telo da Gama
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
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6
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González-Martínez AD, Chávez-Rojo MA, Sambriski EJ, Moreno-Razo JA. Defect-mediated colloidal interactions in a nematic-phase discotic solvent. RSC Adv 2019; 9:33413-33427. [PMID: 35529161 PMCID: PMC9073280 DOI: 10.1039/c9ra05377h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2019] [Accepted: 09/04/2019] [Indexed: 01/30/2023] Open
Abstract
Interactions between colloidal inclusions dispersed in a nematic discotic liquid-crystalline solvent were investigated for different solute-solvent coupling conditions. The solvent was treated at the level of Gay-Berne discogens. Colloidal inclusions were coupled to the solvent with a generalized sphere-ellipsoid interaction potential. Energy strengths were varied to promote either homeotropic or planar mesogenic anchoring. Colloid-colloid interactions were modeled using a soft, excluded-volume contribution. Single-colloid and colloid-pair samples were evolved with Molecular Dynamics simulations. Equilibrium trajectories were used to characterize structural and dynamical properties of topological defects arising in the mesomorphic phase due to colloidal inclusions. Boojums were observed with planar anchoring, whereas Saturn rings were obtained with homeotropic anchoring. The manner in which these topological defects drive colloidal interactions was assessed through a free energy analysis, taking into account the relative orientation between a colloidal dyad and the nematic-field director. The dynamical behavior of defects was qualitatively surveyed from equilibrium trajectories borne from computer simulations.
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Affiliation(s)
- Aurora D González-Martínez
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa Avenida San Rafael Atlixco No. 186, Colonia Vicentina, Delegación Iztapalapa Mexico City 09340 Mexico
| | - Marco A Chávez-Rojo
- Facultad de Ciencias Químicas, Universidad Autónoma de Chihuahua Circuito Universitario #1 s/n, Nuevo Campus Universitario Chihuahua Chihuahua 31000 Mexico
| | - Edward J Sambriski
- Department of Chemistry, Delaware Valley University Doylestown Pennsylvania 18901 USA
| | - José A Moreno-Razo
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa Avenida San Rafael Atlixco No. 186, Colonia Vicentina, Delegación Iztapalapa Mexico City 09340 Mexico
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7
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Sui J. Stratification in the dynamics of sedimenting colloidal platelet-sphere mixtures. SOFT MATTER 2019; 15:4714-4722. [PMID: 31139810 DOI: 10.1039/c9sm00485h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The dynamics of sedimentation in a binary mixture of colloidal platelets-spheres is studied theoretically using the minimal energy model. Revisiting a sedimenting mixture of platelets, we find that nematic phase behaviors are formed, coupled with certain stratification structures in the mixed sediments, which has never been discussed before. Non-equilibrium sedimentation-diffusion equations involving excluded volume interactions between the colloids have been developed to show the occurrence of the stratified structures in the mixed platelet-sphere sediments. The model shows clearly how the nematic configuration occurs corresponding to the stratifications (the peak-like concentration profiles) over time. Both initial sphere concentration and size ratio are found to have great effects on these two coupled structural configurations, which has been illustrated in two state diagrams in detail. It is found that the stratification structure of sphere-on-top corresponds to the nematic bottom phase configuration for a small size ratio; meanwhile, the platelet-on-top structure occurs corresponding to the floating nematic phase configuration for a large size ratio. Interestingly, we can specify a moderate range of size ratio in which the mixture displays only the nematic phase configuration (either the nematic bottom phase or the floating nematic phase depending on the sphere loadings), while the mixed sediments are unstratified as a bulk.
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Affiliation(s)
- Jize Sui
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
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8
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Sui J, Doi M, Ding Y. Dynamics of the floating nematic phase formation in platelet suspension with thickness polydispersity by sedimentation. SOFT MATTER 2018; 14:8956-8961. [PMID: 30364923 DOI: 10.1039/c8sm01177j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
An inverted phase coexistence, where an ordered phase appears on top of a disordered phase, has been observed in polydisperse colloidal suspensions. Herein, we studied the dynamics of this phenomenon in a suspension of a mixture of two types of platelets, namely, thick and thin. We show that the thick platelets preferentially sediment first excluding the thin platelets, and create a region enriched with thin platelets at some place above the bottom, which eventually gives the inverted configuration. We show that such interplay between the sedimentation and the isotropic-nematic phase transition can cause a rich and complex sedimentation dynamic. Depending on the initial concentration and the gravity strength, the interface between the isotropic phase and the nematic phase can move up or down during the sedimentation, and a variety of final equilibrium structures can appear.
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Affiliation(s)
- Jize Sui
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China.
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9
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Stuhlmüller NCX, Eckert T, de Las Heras D, Schmidt M. Structural Nonequilibrium Forces in Driven Colloidal Systems. PHYSICAL REVIEW LETTERS 2018; 121:098002. [PMID: 30230856 DOI: 10.1103/physrevlett.121.098002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 07/13/2018] [Indexed: 06/08/2023]
Abstract
We identify a structural one-body force field that sustains spatial inhomogeneities in nonequilibrium overdamped Brownian many-body systems. The structural force is perpendicular to the local flow direction, it is free of viscous dissipation, it is microscopically resolved in both space and time, and it can stabilize density gradients. From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations, and a novel power functional approximation, we obtain a quantitative understanding of viscous and structural forces, including memory and shear migration.
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Affiliation(s)
- Nico C X Stuhlmüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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10
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Zhang I, Pinchaipat R, Wilding NB, Faers MA, Bartlett P, Evans R, Royall CP. Composition inversion in mixtures of binary colloids and polymer. J Chem Phys 2018; 148:184902. [PMID: 29764136 DOI: 10.1063/1.5023393] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple." Here, we consider a very simple mixture of two colloidal and one non-adsorbing polymer species, which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixtures) or whether, additionally, liquid-liquid demixing of two colloidal phases can occur. Particle-resolved experiments show demixing-like behaviour, but when combined with bespoke Monte Carlo simulations, this proves illusory, and we reveal that only a single liquid-vapor transition occurs. Progressive migration of the small particles to the liquid phase as the polymer concentration increases gives rise to composition inversion-a maximum in the large particle concentration in the liquid phase. Close to criticality, the density fluctuations are found to be dominated by the larger colloids.
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Affiliation(s)
- Isla Zhang
- School of Chemistry, Cantock's Close, University of Bristol, Bristol BS8 1TS, United Kingdom
| | | | - Nigel B Wilding
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | | | - Paul Bartlett
- School of Chemistry, Cantock's Close, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Robert Evans
- HH Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - C Patrick Royall
- School of Chemistry, Cantock's Close, University of Bristol, Bristol BS8 1TS, United Kingdom
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11
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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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12
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Dasgupta T, Dijkstra M. Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation. SOFT MATTER 2018; 14:2465-2475. [PMID: 29561059 DOI: 10.1039/c8sm00237a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Colloidal photonic crystals, which show a complete band gap in the visible region, have numerous applications in fibre optics, energy storage and conversion, and optical wave guides. Intriguingly, two of the best examples of photonic crystals, the diamond and pyrochlore structure, can be self-assembled into the colloidal MgCu2 Laves phase crystal from a simple binary hard-sphere mixture. For these colloidal length scales thermal and gravitational energies are often comparable and therefore it is worthwhile to study the sedimentation phase behavior of these systems. For a multicomponent system this is possible through a theoretical construct known as a stacking diagram, which constitutes a set of all possible stacking sequences of phases in a sedimentation column, and uses as input the bulk phase diagram of the system in the chemical potential plane. We determine the stable phases for binary hard-sphere systems with varying diameter ratios using Monte Carlo simulations and analytical equations of state available in literature and calculate the corresponding stacking diagrams. We also discuss observations from event-driven Brownian dynamics simulations in relation to our theoretical stacking diagrams.
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Affiliation(s)
- Tonnishtha Dasgupta
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
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13
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Yamaguchi N, Anraku S, Paineau E, Safinya CR, Davidson P, Michot LJ, Miyamoto N. Swelling Inhibition of Liquid Crystalline Colloidal Montmorillonite and Beidellite Clays by DNA. Sci Rep 2018. [PMID: 29531235 PMCID: PMC5847546 DOI: 10.1038/s41598-018-22386-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
Exploring the interaction of nucleic acids with clay minerals is important to understand such issues as the persistence in soils of biomolecules and the appearance of genetic polymers in prebiotic environments. Colloidal dispersions of double stranded DNA and clay nanosheets may also provide interesting model systems to study the statistical physics of mixtures of semi-flexible rods and plates. Here, we show that adding very small amounts of DNA to liquid-crystalline montmorillonite and beidellite smectite clay suspensions strongly widens the isotropic/nematic phase coexistence region. Moreover, a spectroscopic study shows that, upon DNA addition, the first DNA molecules adsorb onto the clay particles. Remarkably, synchrotron small-angle X-ray scattering experiments reveal that the average distance between the clay sheets, in the nematic phase at coexistence, decreases with increasing DNA concentration and that the inhibition of swelling by DNA becomes almost independent of clay concentration. We interpret this DNA-mediated attraction between clay nanosheets by bridging conformations of DNA strands (plates on a string structure). In addition to bridging, DNA chains can form “loops” between sections adsorbed on the same particle, giving rise to sheet repulsions due to protruding loops. This interpretation agrees with the observed inter-clay spacings being dependent only on the DNA concentration.
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Affiliation(s)
- Naoya Yamaguchi
- Fukuoka Institute of Technology, Department of Life, Environment and Materials Science, 3-30-1 Wajirohigashi, Higashiku, Fukuoka, 811-0295, Japan
| | - Shinya Anraku
- Fukuoka Institute of Technology, Department of Life, Environment and Materials Science, 3-30-1 Wajirohigashi, Higashiku, Fukuoka, 811-0295, Japan
| | - Erwan Paineau
- Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay Cedex, France
| | - Cyrus R Safinya
- Physics Department, Materials Department, and Molecular, Cellular and Developmental Biology Department, University of California, Santa Barbara, California, 93106, United States
| | - Patrick Davidson
- Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay Cedex, France.
| | - Laurent J Michot
- Laboratoire Phenix, CNRS-Sorbonne Université-UPMC, UMR 8234, 4, Place Jussieu, 75252, Paris Cedex 5, France
| | - Nobuyoshi Miyamoto
- Fukuoka Institute of Technology, Department of Life, Environment and Materials Science, 3-30-1 Wajirohigashi, Higashiku, Fukuoka, 811-0295, Japan.
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14
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Hermann S, Schmidt M. Active ideal sedimentation: exact two-dimensional steady states. SOFT MATTER 2018; 14:1614-1621. [PMID: 29411843 DOI: 10.1039/c7sm02515g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.
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Affiliation(s)
- Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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15
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Härtel A. Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:423002. [PMID: 28898203 DOI: 10.1088/1361-648x/aa8342] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.
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Affiliation(s)
- Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
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16
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Avvisati G, Dasgupta T, Dijkstra M. Fabrication of Colloidal Laves Phases via Hard Tetramers and Hard Spheres: Bulk Phase Diagram and Sedimentation Behavior. ACS NANO 2017; 11:7702-7709. [PMID: 28787126 PMCID: PMC5571468 DOI: 10.1021/acsnano.7b00505] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Colloidal photonic crystals display peculiar optical properties that make them particularly suitable for application in different fields. However, the low packing fraction of the targeted structures usually poses a real challenge in the fabrication stage. Here, we propose a route to colloidal photonic crystals via a binary mixture of hard tetramers and hard spheres. By combining theory and computer simulations, we calculate the phase diagram as well as the stacking diagram of the mixture and show that a colloidal analogue of the MgCu2 Laves phase-which can serve as a precursor of a photonic band-gap structure-is a thermodynamically stable phase in a large region of the phase diagram. Our findings show a relatively large coexistence region between the fluid and the Laves phase, which is potentially accessible by experiments. Furthermore, we determine the sedimentation behavior of the suggested mixture, by identifying several stacking sequences in the sediment. Our work uncovers a self-assembly path toward a photonic structure with a band gap in the visible region.
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17
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Chen M, He M, Lin P, Chen Y, Cheng Z. Staged phase separation in the I-I-N tri-phase region of platelet-sphere mixtures. SOFT MATTER 2017; 13:4457-4463. [PMID: 28580472 DOI: 10.1039/c7sm00478h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Mixtures of colloids with different sizes or shapes are ubiquitous in nature and extensively applied in industries. Phase transition pathways and kinetics in this model system should be investigated because of the difficulty in observing tri-phase coexistence in colloidal platelet-sphere mixtures. Similar to the polymer-sphere mixtures, the phase transition pathway has three main categories. Analytical results show a staged phase transition process in which the mixture first separates into one or two metastable phases, then further separates, and subsequently reaches tri-phase equilibrium. Unique to our system, and different from the gas-liquid-crystal coexistence in colloid-polymer mixtures, the platelet-sphere mixture reached a gas-liquid-liquid crystal (nematic) coexistence. Thus, the different phases are easy to distinguish using the birefringence of the liquid crystals. In addition, the volume fraction of the liquid crystal formation in the ZrP platelet suspensions is much lower than for the crystal formation in hard spheres.
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Affiliation(s)
- Mingfeng Chen
- Soft Matter Center, Guangdong Provincial Key Laboratory on Functional Soft Condensed Matter, School of Materials and Energy, Guangdong University of Technology, Guangzhou, 510006, China
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Geigenfeind T, de Las Heras D. The role of sample height in the stacking diagram of colloidal mixtures under gravity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:064006. [PMID: 28002052 DOI: 10.1088/1361-648x/aa4e04] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Bulk phase separation is responsible for the occurrence of stacks of different layers in sedimentation of colloidal mixtures. A recently proposed theory (de las Heras and Schmidt 2013 Soft Matter 9 8636) establishes a unique connection between the bulk phase behaviour and sedimentation-diffusion-equilibrium. The theory constructs a stacking diagram of all possible sequences of stacks under gravity in the limit of very high (infinite) sample heights. Here, we study the stacking diagrams of colloidal mixtures at finite sample height, h. We demonstrate that h plays a vital role in sedimentation-diffusion-equilibrium of colloidal mixtures. The region of the stacking diagram occupied by a given sequence of stacks depends on h. Hence, two samples with different heights but identical colloidal concentrations can develop different stacking sequences. In addition, the stacking diagrams for different heights can be qualitatively different since some stacking sequences occur only in a given interval of sample heights. We use the theory to investigate the stacking diagrams of both model bulk systems and mixtures of patchy particles that differ either by the number or by the types of patches.
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Affiliation(s)
- Thomas Geigenfeind
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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19
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Drwenski T, Hooijer P, van Roij R. Sedimentation stacking diagrams of binary mixtures of thick and thin hard rods. SOFT MATTER 2016; 12:5684-5692. [PMID: 27279434 DOI: 10.1039/c6sm00736h] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use Onsager theory and the local density approximation to study sedimentation-diffusion equilibrium density profiles of binary mixtures of thick and thin hard rods. We construct stacking diagrams for three diameter ratios, and find that even a simple spindle-shaped phase diagram with only isotropic-nematic demixing can lead to counter-intuitive stacking sequences such as an isotropic phase sandwiched between two nematic phases. For the most complex phase diagram considered here, we find sixteen distinct stacking sequences, including several with five sedimented layers. By adding sedimentation paths to composition-pressure and density-density phase diagrams and calculating density and composition profiles, we show that conclusions about bulk phase diagrams of binary mixtures on the basis of sedimentation-diffusion equilibria should be drawn warily.
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Affiliation(s)
- Tara Drwenski
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
| | - Patrick Hooijer
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
| | - René van Roij
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
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20
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de las Heras D, Treffenstädt LL, Schmidt M. Reentrant network formation in patchy colloidal mixtures under gravity. Phys Rev E 2016; 93:030601. [PMID: 27078278 DOI: 10.1103/physreve.93.030601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 06/05/2023]
Abstract
We study a two-dimensional binary mixture of patchy colloids in sedimentation-diffusion equilibrium using Monte Carlo simulation and Wertheim's theory. By tuning the buoyant masses of the colloids we can control the gravity-induced sequence of fluid stacks of differing density and percolation properties. We find complex stacking sequences with up to four layers and reentrant network formation, consistently in simulations and theoretically using only the bulk phase diagram as input. Our theory applies to general patchy colloidal mixtures and is relevant to understanding experiments under gravity.
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Affiliation(s)
- Daniel de las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Lucas L Treffenstädt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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Aliabadi R, Moradi M, Varga S. Tracking three-phase coexistences in binary mixtures of hard plates and spheres. J Chem Phys 2016; 144:074902. [DOI: 10.1063/1.4941981] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Rubio-Martinez M, Leong T, Juliano P, Hadley TD, Batten MP, Polyzos A, Lim KS, Hill MR. Scalable simultaneous activation and separation of metal–organic frameworks. RSC Adv 2016. [DOI: 10.1039/c5ra24994e] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Despite the many promising applications of Metal–Organic Frameworks (MOFs) the key advances to boost production to industrial scale still remain elusive.
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Affiliation(s)
| | - Thomas Leong
- CSIRO Food and Nutrition
- Werribee
- Australia
- Department of Mechanical and Product Design Engineering
- Faculty of Science
| | | | - Trevor D. Hadley
- CSIRO Mineral Resources, Manufacturing and Energy
- Clayton South MDC
- Australia
| | - Michael P. Batten
- CSIRO Mineral Resources, Manufacturing and Energy
- Clayton South MDC
- Australia
| | - Anastasios Polyzos
- CSIRO Mineral Resources, Manufacturing and Energy
- Clayton South MDC
- Australia
| | - Kok-Seng Lim
- CSIRO Mineral Resources, Manufacturing and Energy
- Clayton South MDC
- Australia
| | - Matthew R. Hill
- CSIRO Mineral Resources, Manufacturing and Energy
- Clayton South MDC
- Australia
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Woolston P, van Duijneveldt JS. Three-Phase Coexistence in Colloidal Rod-Plate Mixtures. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:9290-9295. [PMID: 26262770 DOI: 10.1021/acs.langmuir.5b02224] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Aqueous suspensions of clay particles, such as montmorillonite (MMT) platelets and sepiolite (Sep) rods, tend to form gels at concentrations around 1 vol %. For Sep rods, adsorbing sodium polyacrylate to the surface allows for an isotropic-nematic phase separation to be seen instead. Here, MMT is added to such Sep suspensions, resulting in a complex phase behavior. Across a range of clay concentrations, separation into three phases is observed: a lower, nematic phase dominated by Sep rods, a MMT-rich middle layer, which is weakly birefringent and probably a gel, and a dilute top phase. Analysis of phase volumes suggests that the middle layer may contain as much as 6 vol % MMT.
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Affiliation(s)
- Phillip Woolston
- School of Chemistry, University of Bristol , Cantock's Close, Bristol BS8 1TS, United Kingdom
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Chen M, Li H, Chen Y, Mejia AF, Wang X, Cheng Z. Observation of isotropic-isotropic demixing in colloidal platelet-sphere mixtures. SOFT MATTER 2015; 11:5775-5779. [PMID: 26095942 DOI: 10.1039/c5sm00615e] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Mixtures of colloids with different sizes and shapes are ubiquitous in nature and industry. The possible existence of isotropic-isotropic (I1-I2) demixing of platelets and spheres remains an open question. Here we present direct experimental evidence of I1-I2 demixing using platelets with a very small thickness-to-diameter ratio mixed with silica spheres at the size ratio q = R(sphere)/R(disk) = 0.0901 ± 0.0004. The platelets cause the isotropic-to-nematic phase transition at a very low volume fraction because of their highly anisometric shape. The presence of silica spheres in the suspension accelerates the phase transition and packs the nematic phase more densely via depletion interaction. Increasing the sphere volume fraction to 0.0014, a tri-phase region emerges. This direct observation of I1-I2 demixing seems to validate the free-volume scaled particle theory and indicates the need for refinement of the fundamental measure density functional theory.
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Affiliation(s)
- Mingfeng Chen
- Soft Matter Center, Guangdong Provincial Key Laboratory on Functional Soft Condensed Matter, School of Materials and Energy, Guangdong University of Technology, Guangzhou, 510006, China.
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Lekkerkerker H, Tuinier R, Wensink H. Multiphase coexistence in mixed suspensions of large and small hard platelets. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1048319] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- H.N.W. Lekkerkerker
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University , Utrecht, the Netherlands
| | - R. Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry and Institute for Complex Molecular Systems, Eindhoven University of Technology , Eindhoven, the Netherlands
| | - H.H. Wensink
- Laboratoire de Physique des Solides, Université Paris-Sud and CNRS , Orsay Cedex, France
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de las Heras D, Schmidt M. Sedimentation stacking diagram of binary colloidal mixtures and bulk phases in the plane of chemical potentials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194115. [PMID: 25923506 DOI: 10.1088/0953-8984/27/19/194115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We give a full account of a recently proposed theory that explicitly relates the bulk phase diagram of a binary colloidal mixture to its phase stacking phenomenology under gravity (de las Heras and Schmidt 2013 Soft Matter 9 8636). As we demonstrate, the full set of possible phase stacking sequences in sedimentation-diffusion equilibrium originates from straight lines (sedimentation paths) in the chemical potential representation of the bulk phase diagram. From the analysis of various standard topologies of bulk phase diagrams, we conclude that the corresponding sedimentation stacking diagrams can be very rich, even more so when finite sample height is taken into account. We apply the theory to obtain the stacking diagram of a mixture of nonadsorbing polymers and colloids. We also present a catalog of generic phase diagrams in the plane of chemical potentials in order to facilitate the practical application of our concept, which also generalizes to multi-component mixtures.
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Affiliation(s)
- Daniel de las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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27
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Abrahamsson C, Nordstierna L, Bergenholtz J, Altskär A, Nydén M. Magnetically induced structural anisotropy in binary colloidal gels and its effect on diffusion and pressure driven permeability. SOFT MATTER 2014; 10:4403-4412. [PMID: 24803339 DOI: 10.1039/c4sm00315b] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We report on the synthesis, microstructure and mass transport properties of a colloidal hydrogel self-assembled from a mixture of colloidal silica and nontronite clay plates at different particle concentrations. The gel-structure had uniaxial long-range anisotropy caused by alignment of the clay particles in a strong external magnetic field. After gelation the colloidal silica covered the clay particle network, fixing the orientation of the clay plates. Comparing gels with a clay concentration between 0 and 0.7 vol%, the magnetically oriented gels had a maximum water permeability and self-diffusion coefficient at 0.3 and 0.7 vol% clay, respectively. Hence the specific clay concentration resulting in the highest liquid flux was pressure dependent. This study gives new insight into the effect of anisotropy, particle concentration and bound water on mass transport properties in nano/microporous materials. Such findings merit consideration when designing porous composite materials for use in for example fuel cell, chromatography and membrane technology.
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Affiliation(s)
- Christoffer Abrahamsson
- Department of Chemical and Biological Engineering, Chalmers University of Technology, Kemivägen 10, 412 96, Gothenburg, Sweden.
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Piazza R. Settled and unsettled issues in particle settling. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:056602. [PMID: 24801715 DOI: 10.1088/0034-4885/77/5/056602] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.
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Affiliation(s)
- Roberto Piazza
- Department of Chemistry, Material Science, and Chemical Engineering Politecnico di Milano, via Ponzio 34/3, 20133 Milano, Italy
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Piazza R, Buzzaccaro S, Secchi E, Parola A. On the general concept of buoyancy in sedimentation and ultracentrifugation. Phys Biol 2013; 10:045005. [DOI: 10.1088/1478-3975/10/4/045005] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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30
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de las Heras D, Schmidt M. Bulk fluid phase behaviour of colloidal platelet-sphere and platelet-polymer mixtures. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120259. [PMID: 23459962 DOI: 10.1098/rsta.2012.0259] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation, with strong broadening of the biphasic region, upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameters, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that, for low platelet-polymer size ratio, in addition to isotropic-nematic and nematic-nematic phase coexistence, platelet-polymer mixtures also display isotropic-isotropic demixing. By contrast, we do not find isotropic-isotropic demixing in hard-core platelet-sphere mixtures for the size ratios considered.
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Affiliation(s)
- Daniel de las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany.
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Parola A, Buzzaccaro S, Secchi E, Piazza R. Sedimentation equilibrium and the generalized Archimedes' principle. J Chem Phys 2013; 138:114907. [DOI: 10.1063/1.4795427] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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