Random First Order Transition from a Supercooled Liquid to an Ideal Glass (Review)

Abstract

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated in a way that allows a description of the transition from the initial equilibrium state to the final metastable state without considering any kinetic processes. The RFOT and its applications for real molecular systems (multicomponent liquids with various intermolecular potentials, gel systems, etc.) are widely represented in English-language sources. However, these studies are practically not described in any Russian sources. This paper presents an overview of the studies carried out in this field.

REFERENCES

1. Sanditov D. S., Ojovan M. I. Relaxation aspects
of the liquid—glass transition. Uspekhi Fizicheskih
Nauk. 2019;189(2): 113–133. DOI: https://doi.org/10.3367/ufnr.2018.04.038319
2. Tsydypov Sh. B., Parfenov A. N., Sanditov D. S.,
Agrafonov Yu. V., Nesterov A. S. Application of the
molecular dynamics method and the excited state
model to the investigation of the glass transition in
argon. Available at: http://www.isc.nw.ru/Rus/GPCJ/Content/2006/tsydypov_32_1.pdf (In Russ.). Glass
Physics and Chemistry. 2006;32(1): 83–88. DOI: https://doi.org/10.1134/S1087659606010111
3. Berthier L., Witten T. A. Glass transition of dense
fluids of hard and compressible spheres. Physical
Review E. 2009;80(2): 021502. DOI: https://doi.org/10.1103/PhysRevE.80.021502
4. Sarkisov G. N. Molecular distribution functions
of stable, metastable and amorphous classical models.
Uspekhi Fizicheskih Nauk. 2002;172(6): 647–669. DOI:
https://doi.org/10.3367/ufnr.0172.200206b.0647
5. Hoover W. G., Ross M., Johnson K. W., Henderson
D., Barker J. A., Brown, B. C. Soft-sphere equation
of state. The Journal of Chemical Physics, 1970;52(10):
4931–4941. DOI: https://doi.org/10.1063/1.1672728
6. Cape J. N., Woodcock L. V. Glass transition in a
soft-sphere model. The Journal of Chemical Physics,
1980;72(2): 976–985. DOI: https://doi.org/10.1063/1.439217
7. Franz S., Mezard M., Parisi G., Peliti L. The
response of glassy systems to random perturbations:
A bridge between equilibrium and off-equilibrium.
Journal of Statistical Physics. 1999;97(3–4): 459–488.
DOI: https://doi.org/10.1023/A:1004602906332
8. Marc Mezard and Giorgio Parisi. Thermodynamics
of glasses: a first principles computation. J. of Phys.:
Condens. Matter. 1999;11: A157–A165.
9. Berthier L., Jacquin H., Zamponi F. Microscopic
theory of the jamming transition of harmonic spheres.
Physical Review E, 2011;84(5): 051103. DOI: https://doi.org/10.1103/PhysRevE.84.051103
10. Berthier L., Biroli, G., Charbonneau P.,
Corwin E. I., Franz S., Zamponi F. Gardner physics in
amorphous solids and beyond. The Journal of Chemical
Physics. 2019;151(1): 010901. DOI: https://doi.org/10.1063/1.5097175
11. Berthier L., Ozawa M., Scalliet C. Configurational
entropy of glass-forming liquids. The Journal of
Chemical Physics. 2019;150(16): 160902. DOI: https://doi.org/10.1063/1.5091961
12. Bomont J. M., Pastore G. An alternative scheme
to find glass state solutions using integral equation
theory for the pair structure. Molecular Physics.
2015;113(17–18): 2770–2775. DOI: https://doi.org/10.1080/00268976.2015.1038325
13. Bomont J. M., Hansen J. P., Pastore G.
Hypernetted-chain investigation of the random firstorder
transition of a Lennard-Jones liquid to an ideal
glass. Physical Review E. 2015;92(4): 042316. DOI:
https://doi.org/10.1103/PhysRevE.92.042316
14. Bomont J. M., Pastore G., Hansen J. P.
Coexistence of low and high overlap phases in a
supercooled liquid: An integral equation investigation.
The Journal of Chemical Physics. 2017;146(11): 114504.
DOI: https://doi.org/10.1063/1.4978499
15. Bomont J. M., Hansen J. P., Pastore G. Revisiting
the replica theory of the liquid to ideal glass transition.
The Journal of Chemical Physics. 2019;150(15): 154504.
DOI: https://doi.org/10.1063/1.5088811
16. Cammarota C., Seoane B. First-principles
computation of random-pinning glass transition, glass
cooperative length scales, and numerical comparisons.
Physical Review B. 2016;94(18): 180201. DOI: https://doi.org/10.1103/PhysRevB.94.180201
17. Charbonneau P., Ikeda A., Parisi G., Zamponi F.
Glass transition and random close packing above three
dimensions. Physical Review Letters. 2011;107(18):
185702. DOI: https://doi.org/10.1103/PhysRevLett.107.185702
18. Ikeda A., Miyazaki K. Mode-coupling theory as
a mean-field description of the glass transition.
Physical Review Letters. 2010;104(25): 255704. DOI:
https://doi.org/10.1103/PhysRevLett.104.255704
19. McCowan D. Numerical study of long-time
dynamics and ergodic-nonergodic transitions in dense
simple fluids. Physical Review E. 2015;92(2): 022107.
DOI: https://doi.org/10.1103/PhysRevE.92.022107
20. Ohtsu H., Bennett T. D., Kojima T., Keen D. A.,
Niwa Y., Kawano M. Amorphous–amorphous transition
in a porous coordination polymer. Chemical
Communications. 2017;53(52): 7060–7063. DOI:
https://doi.org/10.1039/C7CC03333H
21. Schmid B., Schilling R. Glass transition of hard
spheres in high dimensions. Physical Review E.
2010;81(4): 041502. DOI: https://doi.org/10.1103/PhysRevE.81.041502
22. Parisi G., Slanina, F. Toy model for the meanfield
theory of hard-sphere liquids. Physical Review E.
2000;62(5): 6554. DOI: https://doi.org/10.1103/Phys-RevE.62.6554
23. Parisi G., Zamponi F. The ideal glass transition
of hard spheres. The Journal of Chemical Physics.
2005;123(14): 144501. DOI: https://doi.org/10.1063/1.2041507
24. Parisi G., Zamponi F. Amorphous packings of
hard spheres for large space dimension. Journal of
Statistical Mechanics: Theory and Experiment. 2006;03:
P03017. DOI: https://doi.org/10.1088/1742-5468/2006/03/P03017
25. Parisi G., Procaccia I., Shor C., Zylberg J. Effective
forces in thermal amorphous solids with generic
interactions. Physical Review E. 2019;99(1): 011001. DOI:
https://doi.org/10.1103/PhysRevE.99.011001
26. Stevenson J. D., Wolynes P. G. Thermodynamic −
kinetic correlations in supercooled liquids: a critical
survey of experimental data and predictions of the
random first-order transition theory of glasses. The
Journal of Physical Chemistry B. 2005;109(31): 15093–
15097. DOI: https://doi.org/10.1021/jp052279h
27. Xia X., Wolynes P. G. Fragilities of liquids
predicted from the random first order transition theory
of glasses. Proceedings of the National Academy of
Sciences. 2000;97(7): 2990–2994. DOI: https://doi.org/10.1073/pnas.97.7.2990
28. Kobryn A. E., Gusarov S., Kovalenko A. A closure
relation to molecular theory of solvation for
macromolecules. Journal of Physics: Condensed Matter.
2016; 28 (40): 404003. DOI: https://doi.org/10.1088/0953-8984/28/40/404003
29. Coluzzi B. , Parisi G. , Verrocchio P.
Thermodynamical liquid-glass transition in a Lennard-
Jones binary mixture. Physical Review Letters.
2000;84(2): 306. DOI: https://doi.org/10.1103/PhysRevLett.84.306
30. Sciortino F., Tartaglia P. Extension of the
fluctuation-dissipation theorem to the physical aging
of a model glass-forming liquid. Physical Review Letters.
2001;86(1): 107. DOI: https://doi.org/10.1103/Phys-RevLett.86.107
31. Sciortino, F. One liquid, two glasses. Nature
Materials. 2002;1(3): 145–146. DOI: https://doi.org/10.1038/nmat752
32. Farr R. S., Groot R. D. Close packing density of
polydisperse hard spheres. The Journal of Chemical
Physics. 2009;131(24): 244104. DOI: https://doi.org/10.1063/1.3276799
33. Barrat J. L., Biben T., Bocquet, L. From Paris to
Lyon, and from simple to complex liquids: a view on
Jean-Pierre Hansen’s contribution. Molecular Physics.
2015;113(17-18): 2378–2382. DOI: https://doi.org/10.1080/00268976.2015.1031843
34. Gaspard J. P. Structure of Melt and Liquid Alloys.
In Handbook of Crystal Growth. Elsevier; 2015. 580 p.
DOI: https://doi.org/10.1016/B978-0-444-56369-9.00009-5
35. Heyes D. M., Sigurgeirsson H. The Newtonian
viscosity of concentrated stabilized dispersions:
comparisons with the hard sphere fluid. Journal of
Rheology. 2004;48(1): 223–248. DOI: https://doi.org/10.1122/1.1634986
36. Ninarello A., Berthier L., Coslovich D. Structure
and dynamics of coupled viscous liquids. MolecularPhysics. 2015;113(17-18): 2707–2715. DOI: https://doi.org/10.1080/00268976.2015.1039089
37. Russel W. B., Wagner N. J., Mewis J. Divergence
in the low shear viscosity for Brownian hard-sphere
dispersions: at random close packing or the glass
transition? Journal of Rheology. 2013;57(6): 1555–1567.
DOI: https://doi.org/10.1122/1.4820515
38. Schaefer T. Fluid dynamics and viscosity in
strongly correlated fluids. Annual Review of Nuclear
and Particle Science. 2014;64: 125–148. DOI: https://doi.org/10.1146/annurev-nucl-102313-025439
39. Matsuoka H. A macroscopic model that
connects the molar excess entropy of a supercooled
liquid near its glass transition temperature to its
viscosity. The Journal of Chemical Physics. 2012;137(20):
204506. DOI: https://doi.org/10.1063/1.4767348
40. de Melo Marques F. A., Angelini R., Zaccarelli E.,
Farago B., Ruta B., Ruocco, G., Ruzicka B. Structural
and microscopic relaxations in a colloidal glass. Soft
Matter. 2015;11(3): 466–471. DOI: https://doi.org/10.1039/C4SM02010C
41. Deutschländer S., Dillmann P., Maret G., Keim
P. Kibble–Zurek mechanism in colloidal monolayers.
Proceedings of the National Academy of Sciences.
2015;112(22): 6925–6930. DOI: https://doi.org/10.1073/pnas.1500763112
42. Chang J., Lenhoff A. M., Sandler S. I.
Determination of fluid–solid transitions in model
protein solutions using the histogram reweighting
method and expanded ensemble simulations. The
Journal of Chemical Physics. 2004;120(6): 3003–3014.
DOI: https://doi.org/10.1063/1.1638377
43. Gurikov P., Smirnova I. Amorphization of drugs
by adsorptive precipitation from supercritical
solutions: a review. The Journal of Supercritical Fluids.
2018;132: 105–125. DOI: https://doi.org/10.1016/j.supflu.2017.03.005
44. Baghel S., Cathcart H., O’Reilly N. J. Polymeric
amorphoussolid dispersions: areviewof
amorphization, crystallization, stabilization, solidstate
characterization, and aqueous solubilization of
biopharmaceutical classification system class II drugs.
Journal of Pharmaceutical Sciences. 2016;105(9):
2527–2544. DOI: https://doi.org/10.1016/j.xphs.2015.10.008
45. Kalyuzhnyi Y. V., Hlushak S. P. Phase coexistence
in polydisperse multi-Yukawa hard-sphere fluid: high
temperature approximation. The Journal of Chemical
Physics. 2006;125(3): 034501. DOI: https://doi.org/10.1063/1.2212419
46. Mondal C., Sengupta S. Polymorphism,
thermodynamic anomalies, and network formation in
an atomistic model with two internal states. Physical
Review E. 2011;84(5): 051503. DOI: https://doi.org/10.1103/PhysRevE.84.051503
47. Bonn D., Denn M. M., Berthier L., Divoux T.,
Manneville S. Yield stress materials in soft condensed
matter. Reviews of Modern Physics. 2017;89(3): 035005.
DOI: https://doi.org/10.1103/RevModPhys.89.035005
48. Tanaka H. Two-order-parameter model of the
liquid–glass transition. I. Relation between glass
transition and crystallization. Journal of Non-
Crystalline Solids. 2005;351(43-45): 3371–3384. DOI:
https://doi.org/10.1016/j.jnoncrysol.2005.09.008
49. Balesku R. Ravnovesnaya i neravnovesnaya
statisticheskaya mekhanika [Equilibrium and nonequilibrium
statistical mechanics]. Moscow: Mir Publ.;
1978. vol. 1. 404 c. (In Russ.)
50. Chari S., Inguva R., Murthy K. P. N. A new
truncation scheme for BBGKY hierarchy: conservation
of energy and time reversibility. arXiv preprint
arXiv: 1608. 02338. DOI: https://arxiv.org/abs/1608.02338
51. Gallagher I., Saint-Raymond L., Texier B. From
Newton to Boltzmann: hard spheres and short-range
potentials. European Mathematical Society.
arXiv:1208.5753. DOI: https://arxiv.org/abs/1208.5753
52. Rudzinski J. F., Noid W. G. A generalized-Yvon-
Born-Green method for coarse-grained modeling. The
European Physical Journal Special Topics. 224(12),
2193–2216. DOI: https://doi.org/10.1140/epjst/e2015-02408-9
53. Franz B., Taylor-King J. P., Yates C., Erban R.
Hard-sphere interactions in velocity-jump models.
Physical Review E. 2016;94(1): 012129. DOI: https://doi.org/10.1103/PhysRevE.94.012129
54. Gerasimenko V., Gapyak I. Low-Density
asymptotic behavior of observables of hard sphere
fluids. Advances in Mathematical Physics. 2018:
6252919. DOI: https://doi.org/10.1155/2018/6252919
55. Lue L. Collision statistics, thermodynamics,
and transport coefficients of hard hyperspheres in
three, four, and five dimensions. The Journal of
Chemical Physics. 2005;122(4): 044513. DOI: https://doi.org/10.1063/1.1834498
56. Cigala G., Costa D., Bomont J. M., Caccamo C.
Aggregate formation in a model fluid with microscopic
piecewise-continuous competing interactions.
Molecular Physics. 2015;113(17–18): 2583–2592.
DOI: https://doi.org/10.1080/00268976.2015.1078006
57. Jadrich R., Schweizer K. S. Equilibrium theory
of the hard sphere fluid and glasses in the metastable
regime up to jamming. I. Thermodynamics. The Journal
of Chemical Physics. 2013;139(5): 054501. DOI: https://doi.org/10.1063/1.4816275
58. Mondal A., Premkumar L., Das S. P. Dependence
of the configurational entropy on amorphous
structures of a hard-sphere fluid. Physical Review E.
2017;96(1): 012124. DOI: https://doi.org/10.1103/PhysRevE.96.012124
59. Sasai M. Energy landscape picture of
supercooled liquids: application of a generalized
random energy model. The Journal of Chemical Physics.2003;118(23): 10651–10662. DOI: https://doi.org/10.1063/1.1574781
60. Sastry S. Liquid limits: Glass transition and
liquid-gas spinodal boundaries of metastable liquids.
Physical Review Letters. 2000;85(3): 590. DOI: https://doi.org/10.1103/PhysRevLett.85.590
61. Uche O. U., Stillinger F. H., Torquato S. On the
realizability of pair correlation functions. Physica A:
Statistical Mechanics and its Applications. 2006;360(1):
21–36. DOI: https://doi.org/10.1016/j.physa.2005.03.058
62. Bi D., Henkes S., Daniels K. E., Chakraborty B.
The statistical physics of athermal materials. Annu.
Rev. Condens. Matter Phys. 2015;6(1): 63–83. DOI:
https://doi.org/10.1146/annurev-conmatphys-031214-014336
63. Bishop M., Masters A., Vlasov A. Y. Higher virial
coefficients of four and five dimensional hard
hyperspheres. The Journal of Chemical Physics.
2004;121(14): 6884–6886. DOI: https://doi.org/10.1063/1.1777574
64. Sliusarenko O. Y., Chechkin A. V., Slyusarenko
Y. V. The Bogolyubov-Born-Green-Kirkwood-
Yvon hierarchy and Fokker-Planck equation for manybody
dissipative randomly driven systems. Journal of
Mathematical Physics. 2015;56(4): 043302. DOI:
https://doi.org/10.1063/1.4918612
65. Tang Y. A new grand canonical ensemble
method to calculate first-order phase transitions. The
Journal of chemical physics. 2011;134(22): 224508. DOI:
https://doi.org/10.1063/1.3599048
66. Tsednee T., Luchko T. Closure for the Ornstein-
Zernike equation with pressure and free energy
consistency. Physical Review E. 2019;99(3): 032130.
DOI: https://doi.org/10.1103/PhysRevE.99.032130
67. Maimbourg T., Kurchan J., Zamponi, F. Solution
of the dynamics of liquids in the large-dimensional
limit. Physical review letters. 2016;116(1): 015902. DOI:
https://doi.org/10.1103/PhysRevLett.116.015902
68. Mari, R., & Kurchan, J. Dynamical transition of
glasses: from exact to approximate. The Journal of
Chemical Physics. 2011;135(12): 124504. DOI: https://doi.org/10.1063/1.3626802
69. Frisch H. L., Percus J. K. High dimensionality
as an organizing device for classical fluids. Physical
Review E. 1999;60(3): 2942. DOI: https://doi.org/10.1103/PhysRevE.60.2942
70. Finken R., Schmidt M., Löwen H. Freezing
transition of hard hyperspheres. Physical Review E.
2001;65(1): 016108. DOI: https://doi.org/10.1103/PhysRevE.65.016108
71. Torquato S., Uche O. U., Stillinger F. H. Random
sequential addition of hard spheres in high Euclidean
dimensions. Physical Review E. 2006;74(6): 061308.
DOI: https://doi.org/10.1103/PhysRevE.74.061308
72. Martynov G. A. Fundamental theory of liquids;
method of distribution functions. Bristol: Adam Hilger;
1992, 470 p.
73. Vompe A. G., Martynov G. A. The self-consistent
statistical theory of condensation. The Journal of
Chemical Physics. 1997;106(14): 6095–6101. DOI:
https://doi.org/10.1063/1.473272
74. Krokston K. Fizika zhidkogo sostoyaniya.
Statisticheskoe vvedenie [Physics of the liquid state.
Statistical introduction]. Moscow: Mir Publ.; 1978.
400 p. (In Russ.)
75. Rogers F. J., Young D. A. New, thermodynamically
consistent, integral equation for simple fluids. Physical
Review A. 1984;30(2): 999. DOI: https://doi.org/10.1103/PhysRevA.30.999
76. Wertheim M. S. Exact solution of the Percus–
Yevick integral equation for hard spheres Phys. Rev.
Letters. 1963;10(8): 321–323. DOI: https://doi.org/10.1103/PhysRevLett.10.321
77. Tikhonov D. A., Kiselyov O. E., Martynov G. A.,
Sarkisov G. N. Singlet integral equation in the
statistical theory of surface phenomena in liquids. J.
of Mol. Liquids. 1999;82(1–2): 3– 17. DOI: https://doi.org/10.1016/S0167-7322(99)00037-9
78. Agrafonov Yu., Petrushin I. Two-particle
distribution function of a non-ideal molecular system
near a hard surface. Physics Procedia. 2015;71. 364–
368. DOI: https://doi.org/10.1016/j.phpro.2015.08.353
79. Agrafonov Yu., Petrushin I. Close order in the
molecular system near hard surface. Journal of Physics:
Conference Series. 2016;747: 012024. DOI: https://doi.org/10.1088/1742-6596/747/1/012024
80. He Y., Rice S. A., Xu X. Analytic solution of the
Ornstein-Zernike relation for inhomogeneous liquids.
The Journal of Chemical Physics. 2016;145(23): 234508.
DOI: https://doi.org/10.1063/1.4972020
81. Agrafonov Y. V., Petrushin I. S. Using
molecular distribution functions to calculate the
structural properties of amorphous solids. Bulletin
of the Russian Academy of Sciences: Physics. 2020;84:
783–787. DOI: https://doi.org/10.3103/S1062873820070035
82. Bertheir L., Ediger M. D. How to “measure” a
structural relaxation time that is too long to be
measured? arXiv:2005.06520v1. DOI: https://arxiv.org/abs/2005.06520
83. Karmakar S., Dasgupta C., Sastry S. Length
scales in glass-forming liquids and related systems: a
review. Reports on Progress in Physics. 2015;79(1):
016601. DOI: https://doi.org/10.1088/0034-4885/79/1/016601
84. De Michele C., Sciortino F., Coniglio A. Scaling
in soft spheres: fragility invariance on the repulsive
potential softness. Journal of Physics: Condensed
Matter. 2004;16(45): L489. DOI: https://doi.org/10.1088/0953-8984/16/45/L01
85. Niblett S. P., de Souza V. K., Jack R. L., Wales D. J.
Effects of random pinning on the potential energy
landscape of a supercooled liquid. The Journal of
Chemical Physics. 2018;149(11): 114503. DOI: https://doi.org/10.1063/1.5042140
86. Wolynes P. G., Lubchenko V. Structural glasses
and supercooled liquids: Theory, experiment, and
applications. New York: John Wiley & Sons; 2012. 404
p. DOI: https://doi.org/10.1002/9781118202470
87. Jack R. L., Garrahan J. P. Phase transition for
quenched coupled replicas in a plaquette spin model
of glasses. Physical Review Letters. 2016;116(5): 055702.
DOI: https://doi.org/10.1103/PhysRevLett.116.055702
88. Habasaki J., Ueda A. Molecular dynamics study
of one-component soft-core system: thermodynamic
properties in the supercooled liquid and glassy states.
The Journal of Chemical Physics. 2013;138(14): 144503.
DOI: https://doi.org/10.1063/1.4799880
89. Bomont J. M., Hansen J. P., Pastore G. An
investigation of the liquid to glass transition using
integral equations for the pair structure of coupled
replicae. J. Chem. Phys. 2014;141(17): 174505. DOI:
https://doi.org/10.1063/1.4900774
90. Parisi G., Urbani P., Zamponi F. Theory of Simple
Glasses: Exact Solutions in Infinite Dimensions.
Cambridge: Cambridge University Press; 2020. 324 p.
DOI: https://doi.org/10.1017/9781108120494
91. Robles M., López de Haro M., Santos A., Bravo
Yuste S. Is there a glass transition for dense hardsphere
systems? The Journal of Chemical Physics.
1998;108(3): 1290–1291. DOI: https://doi.org/10.1063/1.475499
92. Grigera T. S., Martín-Mayor V., Parisi G.,
Verrocchio P. Asymptotic aging in structural glasses.
Physical Review B, 2004;70(1): 014202. DOI: https://doi.org/10.1103/PhysRevB.70.014202
93. Vega C., Abascal J. L., McBride C., Bresme F.
The fluid–solid equilibrium for a charged hard sphere
model revisited. The Journal of Chemical Physics.
2003; 119 (2): 964–971. DOI: https://doi.org/10.1063/1.1576374
94. Kaneyoshi T. Surface amorphization in a
transverse Ising nanowire; effects of a transverse field.
Physica B: Condensed Matter. 2017;513: 87–94. DOI:
https://doi.org/10.1016/j.physb.2017.03.015
95. Paganini I. E., Davidchack R. L., Laird B. B.,
Urrutia I. Properties of the hard-sphere fluid at a planar
wall using virial series and molecular-dynamics
simulation. The Journal of Chemical Physics. 2018;149(1):
014704. DOI: https://doi.org/10.1063/1.5025332
96. Properzi L., Santoro M., Minicucci M., Iesari F.,
Ciambezi M., Nataf L., Di Cicco A. Structural evolution
mechanisms of amorphous and liquid As2 Se3 at high
pressures. Physical Review B. 2016;93(21): 214205. DOI:
https://doi.org/10.1103/PhysRevB.93.214205
97. Sesé L. M. Computational study of the meltingfreezing
transition in the quantum hard-sphere system
for intermediate densities. I. Thermodynamic results.
The Journal of Chemical Physics. 2007;126(16): 164508.
DOI: https://doi.org/10.1063/1.2718523
98. Shetty R., Escobedo F. A. On the application of
virtual Gibbs ensembles to the direct simulation of
fluid–fluid and solid–fluid phase coexistence. The
Journal of Chemical Physics. 2002;116(18): 7957–7966.
DOI: https://doi.org/10.1063/1.1467899