We provide an overview of the different types of computational techniques developed over the years to study supercooled liquids, glassy materials and the physics of the glass transition. We organise these numerical strategies into four broad families. For each of them, we describe the general ideas without discussing any technical details. We summarise the type of questions which can be addressed by any given approach and outline the main results which have been obtained. Finally we describe two important directions for future computational studies of glassy systems.
Nous présentons une vue d’ensemble des différents types de techniques de calcul développées au fil des ans pour étudier les liquides surfondus, les matériaux vitreux et la physique de la transition vitreuse. Nous organisons ces stratégies numériques en quatre grandes familles. Pour chacune d’entre elles, nous décrivons les idées générales sans discuter des détails techniques. Nous résumons le type de questions qui peuvent être abordées par une approche donnée et décrivons les principaux résultats qui ont été obtenus. Enfin, nous décrivons deux directions importantes pour les futures études informatiques des systèmes vitreux.
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Mots-clés : transition vitreuse, simulation informatique, solides amorphes, liquides surfondus, méthodes de Monte Carlo
Jean-Louis Barrat 1; Ludovic Berthier 2, 3
CC-BY 4.0
@article{CRPHYS_2023__24_S1_57_0,
author = {Jean-Louis Barrat and Ludovic Berthier},
title = {Computer simulations of the glass transition and glassy materials},
journal = {Comptes Rendus. Physique},
pages = {57--72},
publisher = {Acad\'emie des sciences, Paris},
volume = {24},
number = {S1},
year = {2023},
doi = {10.5802/crphys.129},
language = {en},
}
Jean-Louis Barrat; Ludovic Berthier. Computer simulations of the glass transition and glassy materials. Comptes Rendus. Physique, From everyday glass to disordered solids, Volume 24 (2023) no. S1, pp. 57-72. doi : 10.5802/crphys.129. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.129/
[1] Simulation of liquids and solids, North-Holland, 1987
[2] Correlations in the motion of atoms in liquid argon, Phys. Rev., Volume 136 (1964) no. 2A, p. A405-A411 | DOI
[3] Phase transitions of the Lennard-Jones system, Phys. Rev., Volume 184 (1969) no. 1, p. 151 | DOI
[4] Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys., Volume 83 (2011) no. 2, pp. 587-645 | DOI
[5] Packing of spheres: co-ordination of randomly packed spheres, Nature, Volume 188 (1960) no. 4754, pp. 910-911 | DOI
[6] The Bakerian lecture, 1962. The structure of liquids, Proc. R. Soc. Lond., Ser. A, Volume 280 (1964) no. 1382, pp. 299-322
[7] Properties of vitreous silica: Analysis of random network models, Nature, Volume 212 (1966) no. 5068, pp. 1354-1356 | DOI
[8] Structural model for amorphous silicon and germanium, J. Non Cryst. Solids, Volume 5 (1971) no. 5, pp. 365-376 | DOI
[9] Relaxation of the Bernal model, Nature, Volume 257 (1975) no. 5522, pp. 120-122 | DOI
[10] Viscous liquids and the glass transition: a potential energy barrier picture, J. Chem. Phys., Volume 51 (1969) no. 9, pp. 3728-3739 | DOI
[12] Energy landscapes, inherent structures, and condensed-matter phenomena, Princeton University Press, 2015 | DOI
[13] Eighty years of random networks, Phys. Status Solidi B Basic Res., Volume 250 (2013) no. 5, pp. 931-936 | DOI
[14] The atomic arrangement in glass, J. Am. Chem. Soc., Volume 54 (1932) no. 10, pp. 3841-3851 | DOI
[15] Computer generation of structural models of amorphous Si and Ge, Phys. Rev. Lett., Volume 54 (1985) no. 13, pp. 1392-1395 | DOI
[16] High-quality continuous random networks, Phys. Rev. B, Volume 62 (2000) no. 8, pp. 4985-4990 | DOI
[17] Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure, Phys. Rev., Volume 145 (1966) no. 2, pp. 637-645 | DOI
[18] Computer simulation of local order in condensed phases of silicon, Phys. Rev. B, Volume 31 (1985) no. 8, pp. 5262-5271 | DOI
[19] Jamming is not just cool any more, Nature, Volume 396 (1998) no. 6706, pp. 21-22 | DOI
[20] Jamming and rheology: constrained dynamics on microscopic and macroscopic scales, CRC Press, 2001 | DOI
[21] Random packings of frictionless particles, Phys. Rev. Lett., Volume 88 (2002) no. 7, 075507 | DOI
[22] The jamming transition and the marginally jammed solid, Ann. Rev. Cond. Matter Phys., Volume 1 (2010) no. 1, pp. 347-369 | DOI
[23] Theory of simple glasses: exact solutions in infinite dimensions, Cambridge University Press, 2020 | DOI
[24] Foam mechanics at the bubble scale, Phys. Rev. Lett., Volume 75 (1995) no. 26, pp. 4780-4783 | DOI
[25] Glass transition of dense fluids of hard and compressible spheres, Phys. Rev. E, Volume 80 (2009) no. 2, 021502 | DOI
[26] Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E, Volume 68 (2003) no. 1, 011306 | DOI
[27] Effects of compression on the vibrational modes of marginally jammed solids, Phys. Rev. E, Volume 72 (2005) no. 5, 051306 | DOI
[28] Critical scaling of shear viscosity at the jamming transition, Phys. Rev. Lett., Volume 99 (2007) no. 17, 178001 | DOI
[29] Unified study of glass and jamming rheology in soft particle systems, Phys. Rev. Lett., Volume 109 (2012) no. 1, 018301 | DOI
[30] Relaxation in viscous liquids and glasses, American Ceramic Society, 1985
[31] Relaxation processes in supercooled liquids, Rep. Prog. Phys., Volume 55 (1992) no. 3, pp. 241-376 | DOI
[32] Molecular dynamics simulations of a supercooled monatomic liquid and glass, J. Phys. Chem., Volume 88 (1984) no. 18, pp. 4019-4027 | DOI
[33] Dynamical Transition in a Dense Fluid Approaching Structural Arrest, Phys. Rev. Lett., Volume 54 (1985) no. 14, pp. 1509-1512 | DOI
[34] Molecular-dynamics study of glassy and supercooled states of a binary mixture of soft spheres, Phys. Rev. A, Volume 36 (1987) no. 7, pp. 3300-3311 | DOI
[35] Soft-sphere model for the glass transition in binary alloys: Pair structure and self-diffusion, Phys. Rev. A, Volume 36 (1987), pp. 4891-4903 | DOI
[36] Dynamical diagnostics for the glass transition in soft-sphere alloys, J. Phys.: Condens. Matter, Volume 1 (1989) no. 39, pp. 7171-7186 | DOI
[37] Diffusion, viscosity and structural slowing down in soft sphere alloys near the kinetic glass transition, Chem. Phys., Volume 149 (1990) no. 1-2, pp. 197-208 | DOI
[38] Molecular dynamics simulations of supercooled liquids near the glass transition, Annu. Rev. Phys. Chem., Volume 42 (1991) no. 1, pp. 23-53 | DOI
[39] Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function, Phys. Rev. E, Volume 51 (1995) no. 5, pp. 4626-4641 | DOI
[40] Testing mode-coupling theory for a supercooled binary Lennard–Jones mixture. II. Intermediate scattering function and dynamic susceptibility, Phys. Rev. E, Volume 52 (1995) no. 4, pp. 4134-4153 | DOI
[41] Supercooled liquids for pedestrians, Phys. Rep., Volume 476 (2009) no. 4-6, pp. 51-124 | DOI
[42] Physical aging in amorphous polymers and other materials, Ph. D. Thesis (1977)
[43] Aging as dynamics in configuration space, Eur. Phys. Lett., Volume 49 (2000) no. 5, pp. 590-596 | DOI
[44] -spin-interaction spin-glass models: Connections with the structural glass problem, Phys. Rev. B, Volume 36 (1987) no. 10, p. 5388 | DOI
[45] Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model, Phys. Rev. Lett., Volume 71 (1993) no. 1, pp. 173-176 | DOI
[46] Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics, Phys. Rev. E, Volume 55 (1997) no. 4, pp. 3898-3914 | DOI
[47] A two-time-scale, two-temperature scenario for nonlinear rheology, Phys. Rev. E, Volume 61 (2000) no. 5, pp. 5464-5472 | DOI
[48] Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals, Phys. Rev. Lett., Volume 89 (2002) no. 9, 095702 | DOI
[49] Effective Temperatures of a Driven System Near Jamming, Phys. Rev. Lett., Volume 89 (2002) no. 9, 095703 | DOI
[50] Unifying fluctuation-dissipation temperatures of slow-evolving nonequilibrium systems from the perspective of inherent structures, Sci. adv., Volume 7 (2021) no. 31, eabg6766 | DOI
[51] Spatially heterogeneous dynamics in supercooled liquids, Annu. Rev. Phys. Chem., Volume 51 (2000) no. 1, pp. 99-128 | DOI
[52] Dynamical susceptibility of glass formers: Contrasting the predictions of theoretical scenarios, Phys. Rev. E, Volume 71 (2005) no. 4, 041505 | DOI
[53] Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, International Series of Monographs on Physics, 150, Oxford University Press, 2011 | DOI
[54] An overview of the theories of the glass transition, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media (International Series of Monographs on Physics), Volume 150, Oxford University Press, 2011, pp. 39-62 | DOI
[55] Kinetic structure of a two-dimensional liquid, Phys. Rev. E, Volume 52 (1995) no. 2, pp. 1694-1698 | DOI
[56] Dynamical Heterogeneities in a Supercooled Lennard–Jones Liquid, Phys. Rev. Lett., Volume 79 (1997) no. 15, pp. 2827-2830 | DOI
[57] Stringlike Cooperative Motion in a Supercooled Liquid, Phys. Rev. Lett., Volume 80 (1998) no. 11, pp. 2338-2341 | DOI
[58] Relaxation of spatially heterogeneous dynamic domains in supercooled ortho-terphenyl, J. Chem. Phys., Volume 103 (1995) no. 13, pp. 5684-5692 | DOI
[59] Dynamic heterogeneity in supercooled ortho-terphenyl studied by multidimensional deuteron NMR, Eur. Phys. Lett., Volume 36 (1996) no. 1, pp. 55-60 | DOI
[60] Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function, J. Chem. Phys., Volume 119 (2003) no. 14, pp. 7372-7387 | DOI
[61] Direct Experimental Evidence of a Growing Length Scale Accompanying he Glass Transition, Science, Volume 310 (2005) no. 5755, pp. 1797-1800 | DOI
[62] Local versus Global Stretched Mechanical Response in a Supercooled Liquid near the Glass Transition, Phys. Rev. Lett., Volume 122 (2019) no. 10, 105501 | DOI
[63] Self-Induced Heterogeneity in Deeply Supercooled Liquids, Phys. Rev. Lett., Volume 127 (2021) no. 8, 088002 | DOI
[64] Dynamic Order-Disorder in Atomistic Models of Structural Glass Formers, Science, Volume 323 (2009) no. 5919, pp. 1309-1313 | DOI
[65] Constrained dynamics of localized excitations causes a non-equilibrium phase transition in an atomistic model of glass formers, J. Chem. Phys., Volume 136 (2012) no. 18, 184509 | DOI
[66] Dynamical first-order phase transition in kinetically constrained models of glasses, Phys. Rev. Lett., Volume 98 (2007) no. 19, 195702 | DOI
[67] Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode Coupling Temperature, Phys. Rev. Lett., Volume 127 (2021) no. 4, 048002 | DOI
[68] Microscopic origin of excess wings in relaxation spectra of supercooled liquids, Nat. Phys., Volume 18 (2022), pp. 468-472 | DOI
[69] A new algorithm for Monte Carlo simulation of Ising spin systems, J. Comput. Phys., Volume 17 (1975) no. 1, pp. 10-18 | DOI
[70] An overview of spatial microscopic and accelerated kinetic Monte Carlo methods, J. Computer-Aided Mater. Des., Volume 14 (2007) no. 2, pp. 253-308 | DOI
[71] Potential energy landscape of simple structural glasses, J. Phys. IV France, Volume 8 (1998) no. PR6, p. Pr6-63–Pr6-67 | DOI
[72] Exponential multiplicity of inherent structures, Phys. Rev. E, Volume 59 (1999) no. 1, pp. 48-51 | DOI
[73] Event-Based Relaxation of Continuous Disordered Systems, Phys. Rev. Lett., Volume 77 (1996) no. 21, pp. 4358-4361 | DOI
[74] Algorithmic developments of the kinetic activation-relaxation technique: Accessing long-time kinetics of larger and more complex systems, J. Chem. Phys., Volume 147 (2017) no. 15, 152712 | DOI
[75] Exploring canyons in glassy energy landscapes using metadynamics (2022) (https://arxiv.org/abs/2204.00587) | DOI
[76] Computing the viscosity of supercooled liquids, J. Chem. Phys., Volume 130 (2009) no. 22, 224504 | DOI
[77] Simulated tempering: a new Monte Carlo scheme, Eur. Phys. Lett., Volume 19 (1992) no. 6, p. 451 | DOI
[78] Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Japan, Volume 65 (1996) no. 6, pp. 1604-1608 | DOI
[79] Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys., Volume 7 (2005) no. 23, pp. 3910-3916 | DOI
[80] Replica-exchange molecular dynamics simulation for supercooled liquids, Phys. Rev. E, Volume 61 (2000) no. 5, pp. 5473-5476 | DOI
[81] Hybrid Monte Carlo simulation of a glass-forming binary mixture, Phys. Rev. E, Volume 73 (2006) no. 6, 061505 | DOI
[82] Equilibrium ultrastable glasses produced by random pinning, J. Chem. Phys., Volume 141 (2014) no. 22, 224503 | DOI
[83] Probing a liquid to glass transition in equilibrium, Phys. Rev. Lett., Volume 110 (2013) no. 24, 245702 | DOI
[84] Ideal glass transitions by random pinning, Proc. Natl. Acad. Sci. USA, Volume 109 (2012) no. 23, pp. 8850-8855 | DOI
[85] Static point-to-set correlations in glass-forming liquids, Phys. Rev. E, Volume 85 (2012) no. 1, 011102 | DOI
[86] Growing length scales in a supercooled liquid close to an interface, Philos. Mag., B, Volume 82 (2002) no. 3, pp. 283-290 | DOI
[87] Non-monotonic temperature evolution of dynamic correlations in glass-forming liquids, Nat. Phys., Volume 8 (2012) no. 2, pp. 164-167 | DOI
[88] Mosaic multistate scenario versus one-state description of supercooled liquids, Phys. Rev. Lett., Volume 98 (2007) no. 18, 187801 | DOI
[89] Thermodynamic signature of growing amorphous order in glass-forming liquids, Nat. Phys., Volume 4 (2008) no. 10, pp. 771-775 | DOI
[90] Rigorous inequalities between length and time scales in glassy systems, J. Stat. Phys., Volume 125 (2006) no. 1, pp. 23-54 | DOI | MR | Zbl
[91] On the Adam–Gibbs–Kirkpatrick–Thirumalai–Wolynes scenario for the viscosity increase in glasses, J. Chem. Phys., Volume 121 (2004) no. 15, pp. 7347-7354 | DOI
[92] Efficient measurement of point-to-set correlations and overlap fluctuations in glass-forming liquids, J. Chem. Phys., Volume 144 (2016) no. 2, 024501 | DOI
[93] Point-to-set lengths, local structure, and glassiness, Phys. Rev. E, Volume 94 (2016) no. 3, 032605 | DOI
[94] Ideal glass states are not purely vibrational: Insight from randomly pinned glasses, Phys. Rev. Lett., Volume 121 (2018) no. 20, 205501 | DOI
[95] Equation of state calculations by fast computing machines, J. Chem. Phys., Volume 21 (1953) no. 6, pp. 1087-1092 | DOI | Zbl
[96] The Monte Carlo dynamics of a binary Lennard-Jones glass-forming mixture, J. Phys.: Condens. Matter, Volume 19 (2007) no. 20, 205130 | DOI
[97] Efficient measurement of linear susceptibilities in molecular simulations: Application to aging supercooled liquids, Phys. Rev. Lett., Volume 98 (2007) no. 22, 220601 | DOI
[98] Revisiting the slow dynamics of a silica melt using Monte Carlo simulations, Phys. Rev. E, Volume 76 (2007) no. 1, 011507 | DOI
[99] Collective Monte Carlo updating for spin systems, Phys. Rev. Lett., Volume 62 (1989) no. 4, pp. 361-364 | DOI
[100] Applicability of dynamic facilitation theory to binary hard disk systems, Phys. Rev. Lett., Volume 117 (2016) no. 14, 145701 | DOI
[101] Absence of thermodynamic phase transition in a model glass former, Nature, Volume 405 (2000) no. 6786, pp. 550-551 | DOI
[102] Fast Monte Carlo algorithm for supercooled soft spheres, Phys. Rev. E, Volume 63 (2001) no. 4, 045102 | DOI
[103] Critical behavior of the specific heat in glass formers, Phys. Rev. E, Volume 73 (2006) no. 2, 020501 | DOI
[104] Numerical investigation of the entropy crisis in model glass formers, J. Phys. Chem. B, Volume 108 (2004) no. 21, pp. 6832-6837 | DOI
[105] Equilibrium sampling of hard spheres up to the jamming density and beyond, Phys. Rev. Lett., Volume 116 (2016) no. 23, 238002 | DOI | MR
[106] Models and algorithms for the next generation of glass transition studies, Phys. Rev. X, Volume 7 (2017) no. 2, 021039 | DOI
[107] Organic glasses with exceptional thermodynamic and kinetic stability, Science, Volume 315 (2007) no. 5810, pp. 353-356 | DOI
[108] Perspective: Highly stable vapor-deposited glasses, J. Chem. Phys., Volume 147 (2017) no. 21, 210901 | DOI
[109] Low-frequency vibrational modes of stable glasses, Nat. Commun., Volume 10 (2019) no. 1, 26 | DOI
[110] Local order and crystallization of dense polydisperse hard spheres, J. Phys.: Condens. Matter, Volume 30 (2018) no. 14, 144004 | DOI
[111] A localization transition underlies the mode-coupling crossover of glasses, SciPost Phys., Volume 7 (2019) no. 6, 077 | DOI | MR
[112] Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling, Proc. Natl. Acad. Sci. USA, Volume 114 (2017) no. 43, pp. 11356-11361 | DOI
[113] Zero-temperature glass transition in two dimensions, Nat. Commun., Volume 10 (2019) no. 1, 1508, p. 7 | DOI
[114] Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 26, pp. 6656-6661 | DOI
[115] Glass stability changes the nature of yielding under oscillatory shear, Phys. Rev. Lett., Volume 124 (2020) no. 22, 225502 | DOI
[116] Sound attenuation in stable glasses, Soft Matter, Volume 15 (2019) no. 35, pp. 7018-7025 | DOI
[117] Does the Adam–Gibbs relation hold in simulated supercooled liquids?, J. Chem. Phys., Volume 151 (2019) no. 8, 084504 | DOI
[118] Random-field Ising model criticality in a glass-forming liquid, Phys. Rev. E, Volume 102 (2020) no. 4, 042129 | DOI | MR
[119] Statistical mechanics of coupled supercooled liquids in finite dimensions, SciPost Phys., Volume 12 (2022) no. 3, 091 | DOI | MR
[120] Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope, J. Chem. Phys., Volume 156 (2022) no. 19, 194503 | DOI
[121] Growing timescales and lengthscales characterizing vibrations of amorphous solids, Proc. Natl. Acad. Sci. USA, Volume 113 (2016) no. 30, pp. 8397-8401 | DOI
[122] Nature of excitations and defects in structural glasses, Nat. Commun., Volume 10 (2019) no. 1, 5102 | DOI
[123] Absence of marginal stability in a structural glass, Phys. Rev. Lett., Volume 119 (2017) no. 20, 205501 | DOI
[124] Depletion of two-level systems in ultrastable computer-generated glasses, Phys. Rev. Lett., Volume 124 (2020) no. 22, 225901 | DOI
[125] Relaxation dynamics in the energy landscape of glass-forming liquids, Phys. Rev. X, Volume 12 (2022) no. 2, 021001 | DOI
[126] Fast generation of ultrastable computer glasses by minimization of an augmented potential energy, Phys. Rev. E, Volume 99 (2019) no. 1, 012106 | DOI
[127] Transient learning degrees of freedom for introducing function in materials, Proc. Natl. Acad. Sci. USA, Volume 119 (2022) no. 19, e2117622119 | DOI | MR
[128] Origin of ultrastability in vapor-deposited glasses, Phys. Rev. Lett., Volume 119 (2017) no. 18, 188002 | DOI
[129] Front-Mediated Melting of Isotropic Ultrastable Glasses, Phys. Rev. Lett., Volume 123 (2019) no. 17, 175501 | DOI
[130] How to “measure” a structural relaxation time that is too long to be measured?, J. Chem. Phys., Volume 153 (2020) no. 4, 044501 | DOI
[131] et al. Reproducibility in density functional theory calculations of solids, Science, Volume 351 (2016) no. 6280, aad3000 | DOI
[132] The nature of glass remains anything but clear, New York Times (2008) (https://www.nytimes.com/2008/07/29/science/29glass.html)
[133] et al. RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles, SciPost Phys., Volume 3 (2017) no. 6, 038 | DOI
[134] Dynamic and thermodynamic crossover scenarios in the Kob-Andersen mixture: Insights from multi-CPU and multi-GPU simulations, Eur. Phys. J. E, Volume 41 (2018) no. 5, 62 | DOI
[135] A structural approach to relaxation in glassy liquids, Nat. Phys., Volume 12 (2016) no. 5, pp. 469-471 | DOI
[136] et al. Unveiling the predictive power of static structure in glassy systems, Nat. Phys., Volume 16 (2020) no. 4, pp. 448-454 | DOI
[137] Comparing machine learning techniques for predicting glassy dynamics, J. Chem. Phys., Volume 156 (2022) no. 20, 204503 | DOI
[138] Challenges and opportunities in atomistic simulations of glasses: a review, Comptes Rendus. Géoscience, Volume 354 (2022) no. S1, pp. 35-77 | DOI
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