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Cao Y, Scholte A, Prehm M, Anders C, Chen C, Song J, Zhang L, He G, Tschierske C, Liu F. Understanding the Role of Trapezoids in Honeycomb Self-Assembly-Pathways between a Columnar Liquid Quasicrystal and its Liquid-Crystalline Approximants. Angew Chem Int Ed Engl 2024; 63:e202314454. [PMID: 38009676 DOI: 10.1002/anie.202314454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Revised: 11/21/2023] [Accepted: 11/23/2023] [Indexed: 11/29/2023]
Abstract
Quasiperiodic patterns and crystals-having long range order without translational symmetry-have fascinated researchers since their discovery. In this study, we report on new p-terphenyl-based T-shaped facial polyphiles with two alkyl end chains and a glycerol-based hydrogen-bonded side group that self-assemble into an aperiodic columnar liquid quasicrystal with 12-fold symmetry and its periodic liquid-crystalline approximants with complex superstructures. All represent honeycombs formed by the self-assembly of the p-terphenyls, dividing space into prismatic cells with polygonal cross-sections. In the perspective of tiling patterns, the presence of unique trapezoidal tiles, consisting of three rigid sides formed by the p-terphenyls and one shorter, incommensurate, and adjustable side by the alkyl end chains, plays a crucial role for these phases. A delicate temperature-dependent balance between conformational, entropic and space-filling effects determines the role of the alkyl chains, either as network nodes or trapezoid walls, thus resulting in the order-disorder transitions associated with emergence of quasiperiodicity. In-depth analysis suggests a change from a quasiperiodic tiling involving trapezoids to a modified one with a contribution of trapezoid pair fusion. This work paves the way for understanding quasiperiodicity emergence and develops fundamental concepts for its generation by chemical design of non-spherical molecules, aggregates, and frameworks based on dynamic reticular chemistry.
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Affiliation(s)
- Yu Cao
- Shaanxi International Research Center for Soft Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
| | - Alexander Scholte
- Institute of Chemistry, Martin Luther University Halle-Wittenberg, Kurt Mothes Str. 2, 06120, Halle/Saale, Germany
| | - Marko Prehm
- Institute of Chemistry, Martin Luther University Halle-Wittenberg, Kurt Mothes Str. 2, 06120, Halle/Saale, Germany
| | - Christian Anders
- Institute of Chemistry, Martin Luther University Halle-Wittenberg, Kurt Mothes Str. 2, 06120, Halle/Saale, Germany
| | - Changlong Chen
- Shaanxi International Research Center for Soft Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
| | - Jiangxuan Song
- Shaanxi International Research Center for Soft Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
| | - Lei Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
| | - Gang He
- Frontier Institute for Science and Technology, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
| | - Carsten Tschierske
- Institute of Chemistry, Martin Luther University Halle-Wittenberg, Kurt Mothes Str. 2, 06120, Halle/Saale, Germany
| | - Feng Liu
- Shaanxi International Research Center for Soft Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, P. R. China
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Kalyuzhnyi Y, Jamnik A, Cummings P. Integral equation theory for a valence-limited model of colloidal systems. J Mol Liq 2023. [DOI: 10.1016/j.molliq.2022.121073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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3
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Zhang DM, Sun DY, Gong XG. Angell plot from the potential energy landscape perspective. Phys Rev E 2022; 106:064129. [PMID: 36671189 DOI: 10.1103/physreve.106.064129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 11/22/2022] [Indexed: 12/24/2022]
Abstract
Within the scenario of the potential energy landscape (PEL), a thermodynamic model has been developed to uncover the physics behind the Angell plot. In our model, by separating the barrier distribution in PELs into a Gaussian-like and a power-law form, we obtain a general relationship between the relaxation time and the temperature. The wide range of the experimental data in the Angell plot, as well as the molecular-dynamics data, can be excellently fitted by two characteristic parameters, the effective barrier (ω) and the effective width (σ) of a Gaussian-like distribution. More importantly, the fitted ω and σ^{2} for all glasses are found to have a simple linear relationship within a very narrow band, and fragile and strong glasses are well separated in the ω-σ^{2} plot, which indicates that glassy states appear only in a specific region of the PEL.
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Affiliation(s)
- D M Zhang
- Key Laboratory for Computational Physical Sciences (MOE), Institute of Computational Physics, Fudan University, Shanghai 200433, China
| | - D Y Sun
- Engineering Research Center for Nanophotonics & Advanced Instrument (MOE), School of Physics and Electronic Science, East China Normal University, 200241 Shanghai, China.,Shanghai Qi Zhi Institution, Shanghai 200030, China
| | - X G Gong
- Key Laboratory for Computational Physical Sciences (MOE), Institute of Computational Physics, Fudan University, Shanghai 200433, China.,Shanghai Qi Zhi Institution, Shanghai 200030, China
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Stepanenko OO, Jamnik A, Reščič J, Kalyuzhnyi YV. Thermodynamic perturbation theory for a valence-limited model of colloidal systems. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1662124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
| | - A. Jamnik
- Faculty of Chemistry and Chemical Technology, University of Lubljana, Lubljana, Slovenia
| | - J. Reščič
- Faculty of Chemistry and Chemical Technology, University of Lubljana, Lubljana, Slovenia
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Saito S, Bagchi B, Ohmine I. Crucial role of fragmented and isolated defects in persistent relaxation of deeply supercooled water. J Chem Phys 2018; 149:124504. [DOI: 10.1063/1.5044458] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Biman Bagchi
- Indian Institute of Science, Bangalore 560012, India
| | - Iwao Ohmine
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
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Coslovich D, Ozawa M, Kob W. Dynamic and thermodynamic crossover scenarios in the Kob-Andersen mixture: Insights from multi-CPU and multi-GPU simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:62. [PMID: 29774433 DOI: 10.1140/epje/i2018-11671-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 04/25/2018] [Indexed: 05/23/2023]
Abstract
The physical behavior of glass-forming liquids presents complex features of both dynamic and thermodynamic nature. Some studies indicate the presence of thermodynamic anomalies and of crossovers in the dynamic properties, but their origin and degree of universality is difficult to assess. Moreover, conventional simulations are barely able to cover the range of temperatures at which these crossovers usually occur. To address these issues, we simulate the Kob-Andersen Lennard-Jones mixture using efficient protocols based on multi-CPU and multi-GPU parallel tempering. Our setup enables us to probe the thermodynamics and dynamics of the liquid at equilibrium well below the critical temperature of the mode-coupling theory, [Formula: see text]. We find that below [Formula: see text] the analysis is hampered by partial crystallization of the metastable liquid, which nucleates extended regions populated by large particles arranged in an fcc structure. By filtering out crystalline samples, we reveal that the specific heat grows in a regular manner down to [Formula: see text] . Possible thermodynamic anomalies suggested by previous studies can thus occur only in a region of the phase diagram where the system is highly metastable. Using the equilibrium configurations obtained from the parallel tempering simulations, we perform molecular dynamics and Monte Carlo simulations to probe the equilibrium dynamics down to [Formula: see text]. A temperature-derivative analysis of the relaxation time and diffusion data allows us to assess different dynamic scenarios around [Formula: see text]. Hints of a dynamic crossover come from analysis of the four-point dynamic susceptibility. Finally, we discuss possible future numerical strategies to clarify the nature of crossover phenomena in glass-forming liquids.
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Affiliation(s)
- Daniele Coslovich
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France.
| | - Misaki Ozawa
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France
| | - Walter Kob
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France
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7
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Parmar ADS, Sastry S. Kinetic and Thermodynamic Fragilities of Square Well Fluids with Tunable Barriers to Bond Breaking. J Phys Chem B 2015; 119:11243-52. [DOI: 10.1021/acs.jpcb.5b03122] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Anshul D. S. Parmar
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560 064, India
- TIFR Centre for Interdisciplinary Sciences, Hyderabad 500 075, India
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560 064, India
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Jadrich RB, Schweizer KS. Directing colloidal assembly and a metal-insulator transition using a quench-disordered porous rod template. PHYSICAL REVIEW LETTERS 2014; 113:208302. [PMID: 25432057 DOI: 10.1103/physrevlett.113.208302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/04/2023]
Abstract
Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.
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Affiliation(s)
- Ryan B Jadrich
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA and Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
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Computer Simulations of Liquid Silica: Water-Like Thermodynamic and Dynamic Anomalies, and the Evidence for Polyamorphism. ACTA ACUST UNITED AC 2013. [DOI: 10.1002/9781118540350.ch14] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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10
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Romano F, Sanz E, Tartaglia P, Sciortino F. Phase diagram of trivalent and pentavalent patchy particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:064113. [PMID: 22277769 DOI: 10.1088/0953-8984/24/6/064113] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We compute the equilibrium phase diagram of two simple models for patchy particles with three and five patches in a very broad range of pressure and temperature. The phase diagram presents low-density crystal structures which compete with the fluid phase. The phase diagram of the five-patch model shows re-entrant melting, in analogy with the previously studied four-patch case, a metastable gas-liquid critical point and a stable, high-density liquid. The three-patch model shows a stable gas-liquid critical point and, in the region of temperatures where equilibration is numerically feasible, a stable liquid phase, suggesting the possibility that in this small valence model the liquid retains its thermodynamic stability down to the vanishing range limit.
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Affiliation(s)
- Flavio Romano
- Dipartimento di Fisica, Sapienza-Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
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11
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Saika-Voivod I, King HM, Tartaglia P, Sciortino F, Zaccarelli E. Silica through the eyes of colloidal models--when glass is a gel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:285101. [PMID: 21659694 DOI: 10.1088/0953-8984/23/28/285101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We perform molecular dynamics simulations of 'floating bond' (FB) models of network-forming liquids and compare the structure and dynamics against the BKS model of silica (van Beest et al 1990 Phys. Rev. Lett. 64 1955), with the aim of gaining a better understanding of glassy silica in terms of the variety of non-ergodic states seen in colloids. At low densities, all the models form tetrahedral networks. At higher densities, tailoring the FB model to allow a higher number of bonds does not capture the structure seen in BKS. Upon rescaling the time and length in order to compare mean squared displacements between models, we find that there are significant differences in the temperature dependence of the diffusion coefficient at high density. Additionally, the FB models show a greater range in variability in the behavior of the non-ergodicity parameter and caging length, quantities used to distinguish colloidal gels and glasses. Hence, we find that the glassy behavior of BKS silica can be interpreted as a 'gel' at low densities, with only a marginal gel-to-glass crossover at higher densities.
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Affiliation(s)
- Ivan Saika-Voivod
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St John's, NL, Canada
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12
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Xu WS, Sun ZY, An LJ. Dense packing in the monodisperse hard-sphere system: a numerical study. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 31:377-382. [PMID: 20405156 DOI: 10.1140/epje/i2010-10583-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2009] [Revised: 12/07/2009] [Accepted: 03/15/2010] [Indexed: 05/29/2023]
Abstract
We report a numerical study of the close packing of monodisperse hard spheres. The close packings of hard spheres are produced by the Lubachesky-Stillinger (LS) compression algorithm and span the range from the disordered states to the ordered states. We provide quantitative evidence for the claim that the density and structural order of the arrested close packing can be determined by the compression rate, i.e., with slower rates producing denser and more ordered structures. Through deeply analyzing the structure of the resulting arrested close packings, a transition region has been identified in the plane of density and reciprocal compression rate, in between what have been historically thought of as amorphous and crystalline packings. We also find clear system size dependences in studying the structural properties of the packings from the disordered ones to the ordered ones. These detailed investigations, on the structure of the arrested close packings, may provide a link between the glassy states and the crystalline states in the hard spheres.
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Affiliation(s)
- W-S Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022, Changchun, PRC
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13
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Abstract
In this article I will review some recent studies of the phase behavior and of the self-assembly of patchy colloidal particles. These studies have been based on simple primitive models for colloid–colloid interactions, effectively extending to soft matter the seminal work of I. Nezbeda on associated fluids. I will discuss the possibilities offered by the study of the self-assembly of particles with limited valence in deepening our understanding of the onset of the liquid state, of the differences between gels and glasses and of the possible connection between physical and chemical gels. A review with 55 references.
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Mayer C, Sciortino F, Tartaglia P, Zaccarelli E. A spherical model with directional interactions: II. Dynamics and landscape properties. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104110. [PMID: 21389444 DOI: 10.1088/0953-8984/22/10/104110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.
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Affiliation(s)
- Christian Mayer
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Rome, Italy
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Heuer A. Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:373101. [PMID: 21694408 DOI: 10.1088/0953-8984/20/37/373101] [Citation(s) in RCA: 199] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.
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Affiliation(s)
- Andreas Heuer
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Corrensstraße 30, Germany
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Ghosh J, Faller R. Comparing the density of states of binary Lennard-Jones glasses in bulk and film. J Chem Phys 2008; 128:124509. [DOI: 10.1063/1.2883697] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Zaccarelli E, Sciortino F, Tartaglia P. A spherical model with directional interactions. I. Static properties. J Chem Phys 2007; 127:174501. [DOI: 10.1063/1.2799522] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Salmon PS, Barnes AC, Martin RA, Cuello GJ. Structure of glassy GeO 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2007; 19:415110. [PMID: 28192322 DOI: 10.1088/0953-8984/19/41/415110] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The full set of partial structure factors for glassy germania, or GeO2, were accurately measured by using the method of isotopic substitution in neutron diffraction in order to elucidate the nature of the pair correlations for this archetypal strong glass former. The results show that the basic tetrahedral Ge(O1/2)4 building blocks share corners with a mean inter-tetrahedral Ge-Ô-Ge bond angle of 132(2)°. The topological and chemical ordering in the resultant network displays two characteristic length scales at distances greater than the nearest neighbour. One of these describes the intermediate range order, and manifests itself by the appearance of a first sharp diffraction peak in the measured diffraction patterns at a scattering vector kFSDP≈1.53 Å-1, while the other describes so-called extended range order, and is associated with the principal peak at kPP = 2.66(1) Å-1. We find that there is an interplay between the relative importance of the ordering on these length scales for tetrahedral network forming glasses that is dominated by the extended range ordering with increasing glass fragility. The measured partial structure factors for glassy GeO2 are used to reproduce the total structure factor measured by using high energy x-ray diffraction and the experimental results are also compared to those obtained by using classical and first principles molecular dynamics simulations.
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Puertas AM, De Michele C, Sciortino F, Tartaglia P, Zaccarelli E. Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses. J Chem Phys 2007; 127:144906. [DOI: 10.1063/1.2772628] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sciortino F, Bianchi E, Douglas JF, Tartaglia P. Self-assembly of patchy particles into polymer chains: A parameter-free comparison between Wertheim theory and Monte Carlo simulation. J Chem Phys 2007; 126:194903. [PMID: 17523836 DOI: 10.1063/1.2730797] [Citation(s) in RCA: 163] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.
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Affiliation(s)
- Francesco Sciortino
- Dipartimento di Fisica and INFM-CNR-SOFT, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
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De Michele C, Tartaglia P, Sciortino F. Slow dynamics in a primitive tetrahedral network model. J Chem Phys 2006; 125:204710. [PMID: 17144726 DOI: 10.1063/1.2393239] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report extensive Monte Carlo and event-driven molecular dynamics simulations of the fluid and liquid phase of a primitive model for silica recently introduced by Ford et al. [J. Chem. Phys. 121, 8415 (2004)]. We evaluate the isodiffusivity lines in the temperature-density plane to provide an indication of the shape of the glass transition line. Except for large densities, arrest is driven by the onset of the tetrahedral bonding pattern and the resulting dynamics is strong in Angell's classification scheme [J. Non-Cryst. Solids 131-133, 13 (1991)]. We compare structural and dynamic properties with corresponding results of two recently studied primitive models of network forming liquids-a primitive model for water and an angular-constraint-free model of four-coordinated particles-to pin down the role of the geometric constraints associated with bonding. Eventually we discuss the similarities between "glass" formation in network forming liquids and "gel" formation in colloidal dispersions of patchy particles.
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Affiliation(s)
- Cristiano De Michele
- Dipartimento di Fisica and INFM-CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Rome, Italy.
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Foffi G, Sciortino F. Extended law of corresponding states in short-range square wells: a potential energy landscape study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:050401. [PMID: 17279866 DOI: 10.1103/physreve.74.050401] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2006] [Revised: 09/25/2006] [Indexed: 05/13/2023]
Abstract
We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth -u0) as a function of the range of attraction Delta to provide thermodynamic insights of the Noro and Frenkel [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a vibrational (Delta dependent) and a floppy (Delta independent) component. We also show that the partition function is a function of Deltaebetauo, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).
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Affiliation(s)
- Giuseppe Foffi
- Institut Romand de Recherche Numérique en Physique des Matériaux IRRMA, PPH-Ecublens, CH-105 Lausanne, Switzerland.
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La Nave E, Sastry S, Sciortino F. Relation between local diffusivity and local inherent structures in the Kob-Andersen Lennard-Jones model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:050501. [PMID: 17279867 DOI: 10.1103/physreve.74.050501] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2006] [Revised: 09/14/2006] [Indexed: 05/13/2023]
Abstract
We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard-Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient D can be estimated as a sum over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed nonlinearity in the relation between local diffusion and basin depth is responsible for the peculiar dynamic behavior observed in supercooled states and provide an interpretation for the presence of dynamic heterogeneities.
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Affiliation(s)
- Emilia La Nave
- Dipartimento di Fisica and CNR-INFM Udr and CRS-SOFT: Complex Dynamics in Structured Systems, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy
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Saksaengwijit A, Heuer A. Dynamics of liquid silica as explained by properties of the potential energy landscape. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061503. [PMID: 16906832 DOI: 10.1103/physreve.73.061503] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2006] [Revised: 04/27/2006] [Indexed: 05/11/2023]
Abstract
The dynamics of silica displays an Arrhenius temperature dependence, classifying silica as a strong glass-former. Using recently developed concepts to analyze the potential energy landscape, one can get a far-reaching understanding of the long-range transport of silica. It can be expressed in terms of properties of the thermodynamics as well as local relaxation processes, thereby extending the phenomenological standard picture of a strong glass-former. The local relaxation processes are characterized by complex correlated sequences of bond breaking and reformation processes.
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Affiliation(s)
- A Saksaengwijit
- Westfälische Wilhelms-Universität Münster, Institut für Physikalische Chemie, Corrensstrasse 30, 48149 Münster, Germany
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Moreno AJ, Saika-Voivod I, Zaccarelli E, La Nave E, Buldyrev SV, Tartaglia P, Sciortino F. Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy. J Chem Phys 2006; 124:204509. [PMID: 16774355 DOI: 10.1063/1.2196879] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.
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Affiliation(s)
- A J Moreno
- Dipartimento di Fisica, Università degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy.
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De Michele C, Gabrielli S, Tartaglia P, Sciortino F. Dynamics in the Presence of Attractive Patchy Interactions. J Phys Chem B 2006; 110:8064-79. [PMID: 16610908 DOI: 10.1021/jp056380y] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.
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Affiliation(s)
- Cristiano De Michele
- Dipartimento di Fisica and INFM-CRS-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Rome, Italy
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Zaccarelli E, Saika-Voivod I, Buldyrev SV, Moreno AJ, Tartaglia P, Sciortino F. Gel to glass transition in simulation of a valence-limited colloidal system. J Chem Phys 2006; 124:124908. [PMID: 16599726 DOI: 10.1063/1.2177241] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.
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Affiliation(s)
- E Zaccarelli
- Dipartimento di Fisica and CNR-INFM-SOFT, Universitá di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185, Roma, Italy.
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