1
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Tonti L, García Daza FA, Romero-Enrique JM, Patti A. Structural and dynamical equilibrium properties of hard board-like particles in parallel confinement. J Chem Phys 2024; 160:124903. [PMID: 38533886 DOI: 10.1063/5.0193126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Accepted: 03/10/2024] [Indexed: 03/28/2024] Open
Abstract
We performed Monte Carlo and dynamic Monte Carlo simulations to model the diffusion of monodispersed suspensions composed of impenetrable cuboidal particles, specifically hard board-like particles (HBPs), in the presence of parallel hard walls. The impact of the walls was investigated by adjusting the size of the simulation box while maintaining constant packing fractions, fixed at η = 0.150, for systems consisting of HBPs with prolate, dual-shaped, and oblate geometries. We observed that increasing the distance between the walls led to the recovery of an isotropic bulk phase, while local particle organization near the walls remained stable. Due to their shape, oblate HBPs exhibit more efficient anchoring at wall surfaces compared to prolate shapes. The formation of nematic-like particle assemblies near the walls, confirmed by theoretical calculations based on density functional theory, significantly influenced local particle dynamics. This effect was particularly pronounced to the extent that a modest portion of cuboids near the walls tended to diffuse exclusively in planes parallel to the confinement, even more efficiently than observed in the bulk regions.
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Affiliation(s)
- Luca Tonti
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Fabián A García Daza
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
| | - José Manuel Romero-Enrique
- Departamento de Física Atómica, Molecular y Nuclear, Área de Física Teórica, Universidad de Sevilla, Avenida de Reina Mercedes s/n, 41012 Sevilla, Spain
- Carlos I Institute of Theoretical and Computational Physics, Fuente Nueva s/n, 18071 Granada, Spain
| | - Alessandro Patti
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
- Carlos I Institute of Theoretical and Computational Physics, Fuente Nueva s/n, 18071 Granada, Spain
- Department of Applied Physics, University of Granada, Fuente Nueva s/n, 18071 Granada, Spain
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2
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Sharma AK, Escobedo FA. Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles. J Chem Phys 2023; 158:044502. [PMID: 36725523 DOI: 10.1063/5.0135461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.
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Affiliation(s)
- Abhishek K Sharma
- R. F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Fernando A Escobedo
- R. F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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3
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Rodríguez-Rivas Á, Patti A, Cuetos A. Dynamics in field-induced biaxial nematic liquid crystals of board-like particles. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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4
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Rafael EM, Tonti L, Daza FAG, Patti A. Active microrheology of colloidal suspensions of hard cuboids. Phys Rev E 2022; 106:034612. [PMID: 36266794 DOI: 10.1103/physreve.106.034612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 08/31/2022] [Indexed: 06/16/2023]
Abstract
By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.
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Affiliation(s)
- Effran Mirzad Rafael
- Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Luca Tonti
- Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Fabián A García Daza
- Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Alessandro Patti
- Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom
- Department of Applied Physics, University of Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
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5
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Jaleel AAA, Mandal D, Rajesh R. Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: One or two phase transitions? J Chem Phys 2021; 155:224101. [PMID: 34911313 DOI: 10.1063/5.0066098] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [Darjani et al., J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Although a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show that there is only a single phase transition in the system between a low-density fluid phase and a high density ordered sublattice phase and that a hexatic phase is absent. The transition is shown to be first order in nature, and the critical parameters are determined accurately.
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Affiliation(s)
- Asweel Ahmed A Jaleel
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
| | - Dipanjan Mandal
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
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6
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Jaleel AAA, Thomas JE, Mandal D, Sumedha, Rajesh R. Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases. Phys Rev E 2021; 104:045310. [PMID: 34781550 DOI: 10.1103/physreve.104.045310] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Accepted: 10/06/2021] [Indexed: 11/07/2022]
Abstract
We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k=1,2,3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.
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Affiliation(s)
- Asweel Ahmed A Jaleel
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Jetin E Thomas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Dipanjan Mandal
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Sumedha
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India.,School of Physical Sciences, National Institute of Science Education and Research, Bhubaneswar, P.O. Jatni, Khurda, Odisha 752050, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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7
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Morillo N, Martínez-Haya B, Cuetos A. Tailoring the phase diagram of discotic mesogens. SOFT MATTER 2021; 17:8693-8704. [PMID: 34519327 DOI: 10.1039/d1sm00624j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The computational modelling of discotic molecules is a central topic in colloid science that is key for the smart design of a broad range of modern functional materials. This work lays out a versatile interaction model capable of exposing the rich mesogenic behaviour of discotics. A single coarse-grained spheroplatelet core framework is employed to generate a variety of pair interaction anisotropy classes, favouring specific relative orientations of the particles (stacked, side-side, crossed, T-shaped). This paves the way for the systematic tailoring of the discotic liquid phase diagram. Monte Carlo simulations are performed for an ensemble of case studies to illustrate the correlation between the topology of the interaction and the formation of stable nematic, smectic and columnar phases, as well as of less common cubatic, uniaxial and biaxial columnar domains.
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Affiliation(s)
- Neftalí Morillo
- Department of Theoretical Physics, Universidad Complutense de Madrid, Avda. de la Complutense S/N, 28040 Madrid, Spain.
| | - Bruno Martínez-Haya
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
| | - Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
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8
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Tonti L, García Daza FA, Patti A. Diffusion of globular macromolecules in liquid crystals of colloidal cuboids. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.116640] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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9
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Dos Santos CTG, Vieira AP, Salinas SR, Andrade RFS. Real-space renormalization-group treatment of the Maier-Saupe-Zwanzig model for biaxial nematic structures. Phys Rev E 2021; 103:032111. [PMID: 33862734 DOI: 10.1103/physreve.103.032111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 02/11/2021] [Indexed: 11/07/2022]
Abstract
The Maier-Saupe-Zwanzig model for the nematic phase transitions in liquid crystals is investigated in a diamond hierarchical lattice. The model takes into account a parameter to describe the biaxiality of the microscopic units. Also, a suitably chosen external field is added to the Hamiltonian to allow the determination of critical parameters associated with the nematic phase transitions. Using the transfer-matrix technique, the free energy and its derivatives are obtained in terms of recursion relations between successive generations of the hierarchical lattice. In addition, a real-space renormalization-group approach is developed to obtain the critical parameters of the same model system. Results of both methods are in excellent agreement. There are indications of two continuous phase transitions. One of them corresponds to a uniaxial-isotropic transition, in the class of universality of the three-state Potts model on the diamond hierarchical lattice. The transition between the biaxial and the uniaxial phases is in the universality class of the Ising model on the same lattice.
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Affiliation(s)
- Cícero T G Dos Santos
- Instituto de Física, Universidade Federal da Bahia, 40170-115 Salvador, Brazil.,Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, 56302-100 Petrolina, Brazil
| | - André P Vieira
- Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao, 1371, 05508-090 Sao Paulo, SP, Brazil
| | - Silvio R Salinas
- Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao, 1371, 05508-090 Sao Paulo, SP, Brazil
| | - Roberto F S Andrade
- Instituto de Física, Universidade Federal da Bahia, 40170-115 Salvador, Brazil.,Centre for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, 41745-715 Salvador, Brazil
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10
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Martínez-Ratón Y, Velasco E. Orientational ordering in a fluid of hard kites: A density-functional-theory study. Phys Rev E 2020; 102:052128. [PMID: 33327136 DOI: 10.1103/physreve.102.052128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 11/09/2020] [Indexed: 11/07/2022]
Abstract
Using density-functional theory we theoretically study the orientational properties of uniform phases of hard kites-two isosceles triangles joined by their common base. Two approximations are used: scaled particle theory and a new approach that better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters, kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus, a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic, and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to 90^{∘}, 60^{∘}, and 75^{∘}. Kites with one of their unequal angles fixed to 72^{∘}, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to 60^{∘} stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to 75^{∘} have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally, the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to 72^{∘}. These particles also present a phase diagram with stable tetratic and triatic phases.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés, Madrid, Spain
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC) and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049, Madrid, Spain
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11
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Mirzad Rafael E, Corbett D, Cuetos A, Patti A. Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase. SOFT MATTER 2020; 16:5565-5570. [PMID: 32539067 DOI: 10.1039/d0sm00484g] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.
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Affiliation(s)
- Effran Mirzad Rafael
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
| | - Daniel Corbett
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
| | - Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
| | - Alessandro Patti
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK.
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12
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Cuetos A, Patti A. Dynamics of hard colloidal cuboids in nematic liquid crystals. Phys Rev E 2020; 101:052702. [PMID: 32575326 DOI: 10.1103/physreve.101.052702] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.
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Affiliation(s)
- Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
| | - Alessandro Patti
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL, United Kingdom
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13
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Skutnik RA, Geier IS, Schoen M. A biaxial nematic liquid crystal composed of matchbox-symmetric molecules. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1726520] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Robert A. Skutnik
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Berlin, Germany
| | - Immanuel S. Geier
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Berlin, Germany
| | - Martin Schoen
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Berlin, Germany
- Department of Chemical Engineering, Imperial College London, London, UK
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14
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D'Urso C, Celebre G, Cinacchi G. Phase behavior of hard C_{2h}-symmetric particle systems. Phys Rev E 2019; 100:012709. [PMID: 31499787 DOI: 10.1103/physreve.100.012709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Indexed: 06/10/2023]
Abstract
Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.
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Affiliation(s)
- Christian D'Urso
- Dipartimento di Chimica e Tecnologie Chimiche, Università della Calabria, via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
| | - Giorgio Celebre
- Dipartimento di Chimica e Tecnologie Chimiche, Università della Calabria, via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
| | - Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales "Nicolás Cabrera," Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain
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15
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Affiliation(s)
- Michael P. Allen
- Department of Physics, University of Warwick, Coventry, UK
- H. H. Wills Physics Laboratory, Royal Fort, Bristol, UK
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16
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Villada-Gil S, Palacio-Betancur V, Armas-Pérez JC, de Pablo JJ, Hernández-Ortiz JP. Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:175101. [PMID: 30703761 DOI: 10.1088/1361-648x/ab0394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.
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Affiliation(s)
- Stiven Villada-Gil
- Departamento de Materiales y Nanotecnología, Universidad Nacional de Colombia, Sede Medellín, Calle 75 # 79A-51, Bloque M17, Medellín, 050034, Colombia. Facultad de Ciencias Básicas, Sociales y Humanas, Politécnico Colombiano Jaime Isaza Cadavid, Medellín, Colombia
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17
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Cuetos A, Mirzad Rafael E, Corbett D, Patti A. Biaxial nematics of hard cuboids in an external field. SOFT MATTER 2019; 15:1922-1926. [PMID: 30756112 DOI: 10.1039/c8sm02283f] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
By computer simulation, we model the phase behaviour of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (NB) liquid crystal phase. The external field promotes the rearrangement of the initial isotropic (I) or uniaxial nematic (NU) phase and the formation of the NB phase. In particular, very weak field strengths are sufficient to spark a direct I-NB or NU-NB phase transition at the self-dual shape, where prolate and oblate particle geometries fuse into one. By contrast, forming the NB phase at any other geometry requires stronger fields and thus reduces the energy efficiency of the phase transformation. Our simulation results show that self-dual shaped board-like particles with moderate anisotropy are able to form NB liquid crystals under the effect of a surprisingly weak external stimulus and suggest a path to exploit low-energy uniaxial-to-biaxial order switching.
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Affiliation(s)
- Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Sevilla, Spain
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18
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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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19
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Tortora MMC, Doye JPK. Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics. J Chem Phys 2018; 147:224504. [PMID: 29246043 DOI: 10.1063/1.5002666] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally relevant particle models. We illustrate the method through the determination of the cholesteric behavior of hard, structurally resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of 45°. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold.
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Affiliation(s)
- Maxime M C Tortora
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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20
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Dussi S, Chiappini M, Dijkstra M. On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1471231] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Simone Dussi
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
| | - Massimiliano Chiappini
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
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21
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Dussi S, Tasios N, Drwenski T, van Roij R, Dijkstra M. Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths. PHYSICAL REVIEW LETTERS 2018; 120:177801. [PMID: 29756829 DOI: 10.1103/physrevlett.120.177801] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Indexed: 06/08/2023]
Abstract
We use computer simulations to study the existence and stability of a biaxial nematic N_{b} phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long (L), medium (M), and short (S) particle axis. For all three shape families, we find stable N_{b} states provided the shape is not only close to the so-called dual shape with M=sqrt[LS] but also sufficiently anisotropic with L/S>9,11,14,23 for rhombi, (two types of) triangular prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-N_{b} transition does not occur in these systems due to a destabilization of N_{b} by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small L/S or by an intervening uniaxial nematic phase at large L/S. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.
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Affiliation(s)
- Simone Dussi
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Nikos Tasios
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Tara Drwenski
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
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22
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González García Á, Wensink HH, Lekkerkerker HNW, Tuinier R. Entropic patchiness drives multi-phase coexistence in discotic colloid-depletant mixtures. Sci Rep 2017; 7:17058. [PMID: 29213049 PMCID: PMC5719020 DOI: 10.1038/s41598-017-16415-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Accepted: 11/07/2017] [Indexed: 11/09/2022] Open
Abstract
Entropy-driven equilibrium phase behaviour of hard particle dispersions can be understood from excluded volume arguments only. While monodisperse hard spheres only exhibit a fluid-solid phase transition, anisotropic hard particles such as rods, discs, cuboids or boards exhibit various multi-phase equilibria. Ordering of such anisotropic particles increases the free volume entropy by reducing the excluded volume between them. The addition of depletants gives rise to an entropic patchiness represented by orientation-dependent attractions resulting in non-trivial phase behaviour. We show that free volume theory is a simple, generic and tractable framework that enables to incorporate these effects and rationalise various experimental findings. Plate-shaped particles constitute the main building blocks of clays, asphaltenes and chromonic liquid crystals that find widespread use in the food, cosmetics and oil industry. We demonstrate that mixtures of platelets and ideal depletants exhibit a strikingly rich phase behaviour containing several types of three-phase coexistence areas and even a quadruple region with four coexisting phases.
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Affiliation(s)
- Á 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, The Netherlands
| | - H H Wensink
- Laboratoire de Physique des Solides-UMR 8502, Université Paris Sud, Université Paris-Saclay and CNRS, 91405, Orsay Cedex, France
| | - H N W Lekkerkerker
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute, Utrecht University, Padualaan 8, 3584 CH, The Netherlands
| | - R 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, The Netherlands.
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23
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Patti A, Cuetos A. Monte Carlo simulation of binary mixtures of hard colloidal cuboids. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1402307] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- A. Patti
- School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, UK
| | - A. Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University,
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