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Martínez-Rivera J, Villada-Balbuena A, Sandoval-Puentes MA, Egelhaaf SU, Méndez-Alcaraz JM, Castañeda-Priego R, Escobedo-Sánchez MA. Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials. J Chem Phys 2023; 159:194110. [PMID: 37982478 DOI: 10.1063/5.0168098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 10/25/2023] [Indexed: 11/21/2023] Open
Abstract
A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.
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Affiliation(s)
- Jaime Martínez-Rivera
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanjuato, Mexico
| | | | - Miguel A Sandoval-Puentes
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanjuato, Mexico
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, 40225 Düsseldorf, Germany
| | - José M Méndez-Alcaraz
- Departamento de Física, Cinvestav, Avenida Instituto Politécnico Nacional 2508, Colonia San Pedro Zacatenco, 07360 Ciudad de México, Mexico
| | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
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2
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Li YW, Yao Y, Ciamarra MP. Two-Dimensional Melting of Two- and Three-Component Mixtures. PHYSICAL REVIEW LETTERS 2023; 130:258202. [PMID: 37418714 DOI: 10.1103/physrevlett.130.258202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Revised: 05/16/2023] [Accepted: 06/01/2023] [Indexed: 07/09/2023]
Abstract
We elucidate the interplay between diverse two-dimensional melting pathways and establish solid-hexatic and hexatic-liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects, respectively, overcomes ρ_{d,s}≃0.046 and ρ_{d,h}≃0.123.
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Affiliation(s)
- Yan-Wei Li
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Yugui Yao
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore; CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy; and CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore 138602, Singapore
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3
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de los Santos Lopez NM, Pérez Ángel G, Castañeda-Priego R, Méndez Alcaraz JM. Determining depletion interactions by contracting forces. J Chem Phys 2022; 157:074903. [DOI: 10.1063/5.0099919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Depletion forces are fundamental for determining the phase behavior of a vast number of materials and colloidal dispersions, and have been used for the manipulation of in- and out-of-equilibrium thermodynamic states. The entropic nature of depletion forces is well understood; however, most theoretical approaches, and also molecular simulations, work quantitatively at moderate size ratios in very diluted systems, since large size asymmetries and high particle concentrations are difficult to deal with. The existing approaches for integrating out the degrees of freedom of the depletant species may fail under these extreme physical conditions. Thus, the main goal of this contribution is to introduce a general physical formulation for obtaining the depletion forces even in those cases where the concentration of all species is relevant. We show that the contraction of the bare forces uniquely determines depletion interactions. Our formulation is tested by studying depletion forces in binary and ternary colloidal mixtures. We report here results for dense systems, with total packing fractions of 45\% and 55\%. Our results open up the possibility of finding an efficient route to determine effective interactions at finite concentration, even at non-equilibrium thermodynamic conditions.
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Sandoval-Puentes MA, Torres-Carbajal A, Zavala-Martínez AB, Castañeda-Priego R, Méndez-Alcaraz JM. Soft representation of the square-well and square-shoulder potentials to be used in Brownian and molecular dynamics simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:164001. [PMID: 35108690 DOI: 10.1088/1361-648x/ac5139] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
The discrete hard-sphere (HS), square-well (SW), and square-shoulder (SS) potentials have become the battle horse of molecular and complex fluids because they contain the basic elements to describe the thermodynamic, structural, and transport properties of both types of fluids. The mathematical simplicity of these discrete potentials allows us to obtain some analytical results despite the nature and complexity of the modeled systems. However, the divergent forces arising at the potential discontinuities may lead to severe issues when discrete potentials are used in computer simulations with uniform time steps. One of the few routes to avoid these technical problems is to replace the discrete potentials with continuous and differentiable forms built under strict physical criteria to capture the correct phenomenology. The match of the second virial coefficient between the discrete and the soft potentials has recently been successfully used to construct a continuous representation that mimics some physical properties of HSs (Báezet al2018J. Chem. Phys.149164907). In this paper, we report an extension of this idea to construct soft representations of the discrete SW and SS potentials. We assess the accuracy of the resulting soft potential by studying structural and thermodynamic properties of the modeled systems by using extensive Brownian and molecular dynamics computer simulations. Besides, Monte Carlo results for the original discrete potentials are used as benchmark. We have also implemented the discrete interaction models and their soft counterparts within the integral equations theory of liquids, finding that the most widely used approximations predict almost identical results for both potentials.
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Affiliation(s)
- Miguel A Sandoval-Puentes
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 Gustavo A. Madero, CDMX, Mexico
| | - Alexis Torres-Carbajal
- Instituto de Física 'Manuel Sandoval Vallarta', Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, Mexico
| | - Arantza B Zavala-Martínez
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 Gustavo A. Madero, CDMX, Mexico
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
| | - José M Méndez-Alcaraz
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 Gustavo A. Madero, CDMX, Mexico
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5
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Perdomo-Pérez R, Martínez-Rivera J, Palmero-Cruz NC, Sandoval-Puentes MA, Gallegos JAS, Lázaro-Lázaro E, Valadez-Pérez NE, Torres-Carbajal A, Castañeda-Priego R. Thermodynamics, static properties and transport behaviour of fluids with competing interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:144005. [PMID: 35026739 DOI: 10.1088/1361-648x/ac4b29] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well (SW), an intermediate-ranged square-shoulder and a long-ranged SW. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.
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Affiliation(s)
- Román Perdomo-Pérez
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Jaime Martínez-Rivera
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Norma C Palmero-Cruz
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Miguel A Sandoval-Puentes
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Javier A S Gallegos
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Edilio Lázaro-Lázaro
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Néstor E Valadez-Pérez
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata km 8, 29050 Tuxtla Gutiérrez, Mexico
| | - Alexis Torres-Carbajal
- Unidad Profesional Interdisciplinaria de Ingeniería, Campus Tlaxcala, Instituto Politécnico Nacional. Plaza Bicentenario, Guillermo Valle 11, Centro, 9000 Tlaxcala de Xicohténcatl, Tlaxcala, México
| | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
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6
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Mei B, Schweizer KS. Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses. J Chem Phys 2021; 155:054505. [PMID: 34364324 DOI: 10.1063/5.0056920] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.
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Affiliation(s)
- Baicheng Mei
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
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7
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de Los Santos-López NM, Pérez-Ángel G, Méndez-Alcaraz JM, Castañeda-Priego R. Competing interactions in the depletion forces of ternary colloidal mixtures. J Chem Phys 2021; 155:024901. [PMID: 34266249 DOI: 10.1063/5.0052369] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Depletion interactions between colloidal particles surrounded by smaller depletants are typically characterized by a strong attraction at contact and a moderately repulsive barrier in front of it that extends at distances similar to the size of the depletants; the appearance and height of the barrier basically depend on the concentration and, therefore, the correlation between depletants. From a thermodynamic point of view, the former can drive the system to phase separation or toward non-equilibrium states, such as gel-like states, but its effects on both local and global properties may be controlled by the latter, which acts as a kind of entropic gate. However, the latter has not been entirely analyzed and understood within the context of colloidal mixtures mainly driven by entropy. In this contribution, we present a systematic study of depletion forces in ternary mixtures of hard spherical particles with two species of depletants, in two and three dimensions. We focus the discussion on how the composition of the depletants becomes the main physical parameter that drives the competition between the attractive well and the repulsive barrier. Our results are obtained by means of the integral equation theory of depletion forces and techniques of contraction of the description adapted to molecular dynamics computer simulations.
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Affiliation(s)
| | - Gabriel Pérez-Ángel
- Departamento de Física Aplicada, Cinvestav-Mérida, AP 73 "Cordemex," 97310 Mérida, Yucatán, Mexico
| | - José M Méndez-Alcaraz
- Departamento de Física, Cinvestav, Av. IPN 2508, Col. San Pedro Zacatenco, Gustavo A. Madero, 07360 Ciudad de México, Mexico
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Guanajuato, Mexico
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8
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Mei B, Schweizer KS. Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility. SOFT MATTER 2021; 17:2624-2639. [PMID: 33528485 DOI: 10.1039/d0sm02215b] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant-matrix pair correlation function and the penetrant-matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.
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Affiliation(s)
- Baicheng Mei
- Department of Materials Science, University of Illinois, Urbana, IL 61801, USA. and Materials Research Laboratory, University of Illinois, Urbana, IL 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, IL 61801, USA. and Materials Research Laboratory, University of Illinois, Urbana, IL 61801, USA and Department of Chemistry, University of Illinois, Urbana, IL 61801, USA and Department of Chemical & Biomolecular Engineering, University of Illinois, Urbana, IL 61801, USA
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9
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Pattern detection in colloidal assembly: A mosaic of analysis techniques. Adv Colloid Interface Sci 2020; 284:102252. [PMID: 32971396 DOI: 10.1016/j.cis.2020.102252] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Revised: 08/27/2020] [Accepted: 08/28/2020] [Indexed: 01/19/2023]
Abstract
Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.
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10
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Gao Y, Kim PY, Hoagland DA, Russell TP. Bidisperse Nanospheres Jammed on a Liquid Surface. ACS NANO 2020; 14:10589-10599. [PMID: 32806023 DOI: 10.1021/acsnano.0c04682] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Jammed packings of bidisperse nanospheres were assembled on a nonvolatile liquid surface and visualized to the single-particle scale by using an in situ scanning electron microscopy method. The PEGylated silica nanospheres, mixed at different number fractions and size ratios, had large enough in-plane mobilities prior to jamming to form uniform monolayers reproducibly. From the collected nanometer-resolution images, local order and degree of mixing were assessed by standard metrics. For equimolar mixtures, a large-to-small size ratio of about 1.5 minimized correlated metrics for local orientational and positional order, as previously predicted in simulations of bidisperse disk jamming. Despite monolayer uniformity, structural and depletion interactions caused spheres of a similar size to cluster, a feature evident at size ratios above 2. Uniform nanoparticle monolayers of high packing disorder are sought in many liquid interface technologies, and these experiments outlined key design principles, buttressing extensive theory/simulation literature on the topic.
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Affiliation(s)
- Yige Gao
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, United States
| | - Paul Y Kim
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David A Hoagland
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, United States
| | - Thomas P Russell
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China
- Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan
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11
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Zhou Y, Mei B, Schweizer KS. Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids. Phys Rev E 2020; 101:042121. [PMID: 32422713 DOI: 10.1103/physreve.101.042121] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2020] [Accepted: 03/24/2020] [Indexed: 06/11/2023]
Abstract
We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.
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Affiliation(s)
- Yuxing Zhou
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Baicheng Mei
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Chemistry and Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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12
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Zhou Y, Schweizer KS. Local structure, thermodynamics, and phase behavior of asymmetric particle mixtures: Comparison between integral equation theories and simulation. J Chem Phys 2019; 150:214902. [PMID: 31176349 DOI: 10.1063/1.5099369] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Yuxing Zhou
- Department of Materials Science, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
- Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
| | - Kenneth S. Schweizer
- Department of Materials Science, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
- Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
- Department of Chemical and Biomolecular Engineering, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
- Department of Chemistry, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
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13
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Hansen-Goos H. Scaling with a fractional power: Overcoming the shortage of scaled-particle variables for the hard-disk fluid. J Chem Phys 2019; 150:011101. [DOI: 10.1063/1.5084328] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hendrik Hansen-Goos
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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14
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Báez CA, Torres-Carbajal A, Castañeda-Priego R, Villada-Balbuena A, Méndez-Alcaraz JM, Herrera-Velarde S. Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential. J Chem Phys 2018; 149:164907. [DOI: 10.1063/1.5049568] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- César Alejandro Báez
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
| | - Alexis Torres-Carbajal
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
| | - Alejandro Villada-Balbuena
- Departamento de Física, Cinvestav, Avenida Instituto Politécnico Nacional 2508, Colonia San Pedro Zacatenco, 07360 Ciudad de México, Mexico
| | - José Miguel Méndez-Alcaraz
- Departamento de Física, Cinvestav, Avenida Instituto Politécnico Nacional 2508, Colonia San Pedro Zacatenco, 07360 Ciudad de México, Mexico
| | - Salvador Herrera-Velarde
- Subdirección de Postgrado e Investigación, Instituto Tecnológico Superior de Xalapa, Sección 5A Reserva Territorial s/n, 91096 Xalapa, Veracruz, Mexico
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Lavergne FA, Diana S, Aarts DGAL, Dullens RPA. Equilibrium Grain Boundary Segregation and Clustering of Impurities in Colloidal Polycrystalline Monolayers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:12716-12724. [PMID: 27934528 DOI: 10.1021/acs.langmuir.6b02683] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We investigate the segregation of impurities to grain boundaries in colloidal polycrystalline monolayers using video microscopy. A model colloidal alloy is prepared by embedding large spherical impurities in a polycrystalline monolayer of small host colloidal hard spheres, which stops grain growth at a finite grain size. The size ratio between the impurities and the host particles determines whether they behave as interstitial or substitutional impurities in the bulk crystal, akin to those in real alloys. We find that the partitioning of impurities between the grains and the grain boundaries is in very good agreement with the Langmuir-McLean adsorption model for equilibrium grain boundary segregation. This enables the direct measurement of the free energy of adsorption for the two types of impurities. Near saturation, we characterize the spatial distribution of the adsorbed impurities and find that it strongly depends on their interstitial or substitutional nature. This is because the relative importance of clustering and mixing due to nonadditivity is determined by geometrical constraints imposed by the crystalline host lattice.
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Affiliation(s)
- François A Lavergne
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford , South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Samuel Diana
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford , South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford , South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford , South Parks Road, Oxford OX1 3QZ, United Kingdom
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