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Miyazaki K, Schweizer KS, Thirumalai D, Tuinier R, Zaccarelli E. The Asakura–Oosawa theory: Entropic forces in physics, biology, and soft matter. J Chem Phys 2022; 156:080401. [DOI: 10.1063/5.0085965] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- K. Miyazaki
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan
| | - K. S. Schweizer
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
| | - D. Thirumalai
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - R. Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - E. Zaccarelli
- CNR-ISC (National Research Council–Institute for Complex Systems) and Department of Physics, Sapienza University of Rome, Rome, Italy
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2
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Peters VFD, Tuinier R, Vis M. Effects of polymer nonideality on depletion-induced phase behaviour of colloidal disks and rods. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:144008. [PMID: 35038683 DOI: 10.1088/1361-648x/ac4c11] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2021] [Accepted: 01/17/2022] [Indexed: 06/14/2023]
Abstract
Colloidal dispersions composed of either platelets or rods exhibit liquid crystalline phase behaviour that is strongly influenced by the addition of nonadsorbing polymers. In this work we examined how polymer segment-segment interactions affect this phase behaviour as compared to using either penetrable hard spheres (PHS) or ideal ('ghost') chains as depletants. We find that the simplified polymer description predicts the same phase diagram topologies as the more involved polymer descriptions. Therefore the PHS description is still adequate for qualitative predictions. For sufficiently large polymer sizes we find however that the precise polymer description significantly alters the locations of the phase coexistence regions. Especially the stability region of isotropic-isotropic coexistence is affected by the polymer interactions. To illustrate the quantitative effects some examples are presented.
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Affiliation(s)
- Vincent F D Peters
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Remco Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Mark Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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3
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Peters VD, González García Á, Wensink HH, Vis M, Tuinier R. Multiphase Coexistences in Rod-Polymer Mixtures. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:11582-11591. [PMID: 34553593 PMCID: PMC8495896 DOI: 10.1021/acs.langmuir.1c01896] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Revised: 09/09/2021] [Indexed: 06/13/2023]
Abstract
Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod-polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer-rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod-polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. ( J. Chem. Phys. 107, 1997 1551).
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Affiliation(s)
- Vincent
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, The Netherlands
| | - Álvaro González García
- Sustainable
Polymer Chemistry Group, Department of Molecules & Materials, MESA + Institute for Nanotechnology, University of
Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Henricus H. Wensink
- Laboratoire
de Physique des Solides − UMR 8502, CNRS & Université
Paris-Saclay, 91400 Orsay, France
| | - Mark 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, The Netherlands
| | - Remco 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, The Netherlands
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4
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Opdam J, Schelling MPM, Tuinier R. Phase behavior of binary hard-sphere mixtures: Free volume theory including reservoir hard-core interactions. J Chem Phys 2021; 154:074902. [DOI: 10.1063/5.0037963] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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 MB Eindhoven, The Netherlands
| | - M. P. M. Schelling
- 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 MB Eindhoven, The Netherlands
| | - 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 MB Eindhoven, The Netherlands
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5
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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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6
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González García Á, Tuinier R, de With G, Cuetos A. Directional-dependent pockets drive columnar-columnar coexistence. SOFT MATTER 2020; 16:6720-6724. [PMID: 32578661 DOI: 10.1039/d0sm00802h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The rational design of materials requires a fundamental understanding of the mechanisms driving their self-assembly. This may be particularly challenging in highly dense and shape-asymmetric systems. Here we show how the addition of tiny non-adsorbing spheres (depletants) to a dense system of hard disc-like particles (discotics) leads to coexistence between two distinct, highly dense (liquid)-crystalline columnar phases. This coexistence emerges due to the directional-dependent free-volume pockets for depletants. Theoretical results are confirmed by simulations explicitly accounting for the binary mixture of interest. We define the stability limits of this columnar-columnar coexistence and quantify the directional-dependent depletant partitioning.
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Affiliation(s)
- Álvaro González García
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, The Netherlands. and Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University, The Netherlands.
| | - Remco Tuinier
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University, The Netherlands.
| | - Gijsbertus de With
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University, The Netherlands.
| | - Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Universidad Pablo Olavide, 41013 Sevilla, Spain
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7
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Schönhöfer PWA, Marechal M, Cleaver DJ, Schröder-Turk GE. Self-assembly and entropic effects in pear-shaped colloid systems. II. Depletion attraction of pear-shaped particles in a hard-sphere solvent. J Chem Phys 2020; 153:034904. [PMID: 32716194 DOI: 10.1063/5.0007287] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent for two different model realizations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the previous studies. This is done by determining their differing depletion attractions via Monte Carlo simulations of PHGO and HPR particles in a pool of hard spheres and comparing them with excluded volume calculations of numerically obtained ideal configurations on the microscopic level. While the HPR model behaves as predicted by the analysis of excluded volumes, the PHGO model showcases a preference for splay between neighboring particles, which can be attributed to the special non-additive characteristics of the PHGO contact function. Lastly, we propose a potentially experimentally realizable pear-shaped particle model, the non-additive hard pear of revolution model, which is based on the HPR model but also features non-additive traits similar to those of PHGO particles to mimic their depletion behavior.
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Affiliation(s)
- Philipp W A Schönhöfer
- College of Science, Health, Engineering and Education, Mathematics and Statistics, Murdoch University, 90 South Street, Murdoch WA 6150, Australia
| | - Matthieu Marechal
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Douglas J Cleaver
- Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, United Kingdom
| | - Gerd E Schröder-Turk
- College of Science, Health, Engineering and Education, Mathematics and Statistics, Murdoch University, 90 South Street, Murdoch WA 6150, Australia
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8
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Schönhöfer PWA, Marechal M, Cleaver DJ, Schröder-Turk GE. Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems. J Chem Phys 2020; 153:034903. [PMID: 32716179 DOI: 10.1063/5.0007286] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.
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Affiliation(s)
- Philipp W A Schönhöfer
- College of Science, Health, Engineering and Education, Mathematics and Statistics, Murdoch University, 90 South Street, 6150 Murdoch, WA, Australia
| | - Matthieu Marechal
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Douglas J Cleaver
- Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, United Kingdom
| | - Gerd E Schröder-Turk
- College of Science, Health, Engineering and Education, Mathematics and Statistics, Murdoch University, 90 South Street, 6150 Murdoch, WA, Australia
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9
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Dekker F, González García Á, Philipse AP, Tuinier R. Phase stability of dispersions of hollow silica nanocubes mediated by non-adsorbing polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:38. [PMID: 32556853 DOI: 10.1140/epje/i2020-11962-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 05/28/2020] [Indexed: 06/11/2023]
Abstract
Although there are theoretical predictions (Eur. Phys. J. E 41, 110 (2018)) for the rich-phase behaviour of colloidal cubes mixed with non-adsorbing polymers, a thorough verification of this phase behaviour is still underway; experimental studies on mixtures of cubes and non-adsorbing polymers in bulk are scarce. In this paper, mixtures of hollow silica nanocubes and linear polystyrene in N,-N-dimethylformamide are used to measure the structure factor of the colloidal cubes as a function of non-adsorbing polymer concentration. Together with visual observations these structure factors enabled us to assess the depletion-mediated phase stability of cube-polymer mixtures. The theoretical and experimental phase boundaries for cube-depletant mixtures are in remarkable agreement, despite the simplifications underlying the theory employed.
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Affiliation(s)
- F Dekker
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padulaan 8, 3584 CH, Utrecht, The Netherlands
| | - Á González García
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padulaan 8, 3584 CH, Utrecht, The Netherlands
- 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, The Netherlands
| | - A P Philipse
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padulaan 8, 3584 CH, Utrecht, The Netherlands
| | - 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, The Netherlands.
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10
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Peters VFD, Vis M, Wensink HH, Tuinier R. Algebraic equations of state for the liquid crystalline phase behavior of hard rods. Phys Rev E 2020; 101:062707. [PMID: 32688562 DOI: 10.1103/physreve.101.062707] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 06/01/2020] [Indexed: 05/24/2023]
Abstract
Based on simplifications of previous numerical calculations [H. Graf and H. Löwen, Phys. Rev. E 59, 1932 (1999)1063-651X10.1103/PhysRevE.59.1932], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.
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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, The 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, The Netherlands
- Laboratoire de Chimie, École Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France
| | - H H Wensink
- Laboratoire de Physique des Solides - UMR 8502, CNRS & Université Paris-Saclay, 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, The Netherlands
- Van t Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute for Nanomaterials Science, Utrecht University, 3584 CH Utrecht, The Netherlands
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11
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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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12
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González García Á, Opdam J, Tuinier R. Phase behaviour of colloidal superballs mixed with non-adsorbing polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:110. [PMID: 30229326 DOI: 10.1140/epje/i2018-11719-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Accepted: 08/24/2018] [Indexed: 06/08/2023]
Abstract
Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F1-F2 coexistence, but also SC1-SC2 coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F1-F2-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.
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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, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry, & Debye Institute, Utrecht University, Padualaan 8, 3584 CH, 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, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry, & Debye Institute, Utrecht University, Padualaan 8, 3584 CH, 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, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands.
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry, & Debye Institute, Utrecht University, Padualaan 8, 3584 CH, Utrecht, The Netherlands.
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