1
|
Vasin MG. Glass transition as a topological phase transition. Phys Rev E 2022; 106:044124. [PMID: 36397462 DOI: 10.1103/physreve.106.044124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 09/21/2022] [Indexed: 06/16/2023]
Abstract
The glass transition is described as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered in both static and dynamic cases. It is shown that the proposed model reproduces most of the characteristic thermodynamic and kinetic properties of glass transition: the Vogel-Fulcher-Tammann law, the behavior of susceptibility and nonlinear susceptibilities, and heat capacity behavior as well as the appearance of a boson peak in the frequency dependence of the dynamic structure factor near the glass transition temperature.
Collapse
Affiliation(s)
- M G Vasin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, 108840 Moscow, Russia
| |
Collapse
|
2
|
Baggioli M, Landry M, Zaccone A. Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory. Phys Rev E 2022; 105:024602. [PMID: 35291146 DOI: 10.1103/physreve.105.024602] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).
Collapse
Affiliation(s)
- Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Michael Landry
- Department of Physics, Center for Theoretical Physics, Columbia University, 538 West 120th Street, New York, New York 10027, USA
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, CB30HE Cambridge, United Kingdom
| |
Collapse
|
3
|
|
4
|
Thermodynamics at Solid-Liquid Interfaces. ENTROPY 2018; 20:e20050362. [PMID: 33265452 PMCID: PMC7512882 DOI: 10.3390/e20050362] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Revised: 04/26/2018] [Accepted: 05/09/2018] [Indexed: 11/17/2022]
Abstract
The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid-liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid-liquid interaction, affect the thermal conductivity of the liquid at the interface. The molecular model consists of liquid argon confined by two parallel, smooth, solid walls, separated by a distance of 6.58 σ. We find that the component of the thermal conductivity parallel to the surface increases with the affinity of the solid and liquid.
Collapse
|
5
|
Fomin YD, Ryzhov VN, Tsiok EN, Proctor JE, Prescher C, Prakapenka VB, Trachenko K, Brazhkin VV. Dynamics, thermodynamics and structure of liquids and supercritical fluids: crossover at the Frenkel line. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:134003. [PMID: 29443011 DOI: 10.1088/1361-648x/aaaf39] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We review recent work aimed at understanding dynamical and thermodynamic properties of liquids and supercritical fluids. The focus of our discussion is on solid-like transverse collective modes, whose evolution in the supercritical fluids enables one to discuss the main properties of the Frenkel line separating rigid liquid-like and non-rigid gas-like supercritical states. We subsequently present recent experimental evidence of the Frenkel line showing that structural and dynamical crossovers are seen at a pressure and temperature corresponding to the line as predicted by theory and modelling. Finally, we link dynamical and thermodynamic properties of liquids and supercritical fluids by the new calculation of liquid energy governed by the evolution of solid-like transverse modes. The disappearance of those modes at high temperature results in the observed decrease of heat capacity.
Collapse
Affiliation(s)
- Yu D Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia
| | | | | | | | | | | | | | | |
Collapse
|
6
|
Trachenko K. Lagrangian formulation and symmetrical description of liquid dynamics. Phys Rev E 2017; 96:062134. [PMID: 29347330 DOI: 10.1103/physreve.96.062134] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Indexed: 06/07/2023]
Abstract
Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.
Collapse
Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| |
Collapse
|
7
|
Yang C, Dove MT, Brazhkin VV, Trachenko K. Emergence and Evolution of the k Gap in Spectra of Liquid and Supercritical States. PHYSICAL REVIEW LETTERS 2017; 118:215502. [PMID: 28598668 DOI: 10.1103/physrevlett.118.215502] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Indexed: 06/07/2023]
Abstract
Fundamental understanding of strongly interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in a solidlike transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.
Collapse
Affiliation(s)
- C Yang
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - M T Dove
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - V V Brazhkin
- Institute for High Pressure Physics, RAS, 108840 Troitsk, Moscow, Russia
| | - K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| |
Collapse
|
8
|
Wang L, Yang C, Dove MT, Fomin YD, Brazhkin VV, Trachenko K. Direct links between dynamical, thermodynamic, and structural properties of liquids: Modeling results. Phys Rev E 2017; 95:032116. [PMID: 28415224 DOI: 10.1103/physreve.95.032116] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Indexed: 06/07/2023]
Abstract
We develop an approach to liquid thermodynamics based on collective modes. We perform extensive molecular-dynamics simulations of noble, molecular, and metallic liquids, and we provide direct evidence that liquid energy and specific heat are well-described by the temperature dependence of the Frenkel (hopping) frequency. The agreement between predicted and calculated thermodynamic properties is seen in the notably wide range of temperature spanning tens of thousands of Kelvin. The range includes both subcritical liquids and supercritical fluids. We discuss the structural crossover and interrelationships between the structure, dynamics, and thermodynamics of liquids and supercritical fluids.
Collapse
Affiliation(s)
- L Wang
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - C Yang
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - M T Dove
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - Yu D Fomin
- Institute for High Pressure Physics, RAS, 142190 Moscow, Russia
| | - V V Brazhkin
- Institute for High Pressure Physics, RAS, 142190 Moscow, Russia
| | - K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| |
Collapse
|
9
|
Trachenko K, Brazhkin VV. Anomalous vacuum energy and stability of a quantum liquid. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:12LT01. [PMID: 26909505 DOI: 10.1088/0953-8984/28/12/12lt01] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives a negative contribution to a system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.
Collapse
Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, UK
| | | |
Collapse
|
10
|
Trachenko K, Brazhkin VV. Collective modes and thermodynamics of the liquid state. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:016502. [PMID: 26696098 DOI: 10.1088/0034-4885/79/1/016502] [Citation(s) in RCA: 97] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.
Collapse
Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, UK
| | | |
Collapse
|
11
|
Brazhkin VV, Lyapin AG, Ryzhov VN, Trachenko K, Fomin YD, Tsiok EN. The Frenkel line and supercritical technologies. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2015. [DOI: 10.1134/s199079311408003x] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
12
|
Brazhkin VV, Trachenko K. Collective Excitations and Thermodynamics of Disordered State: New Insights into an Old Problem. J Phys Chem B 2014; 118:11417-27. [DOI: 10.1021/jp503647s] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. V. Brazhkin
- Institute
for High Pressure Physics, RAS, 142190, Moscow, Russia
| | - K. Trachenko
- School
of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, U.K
| |
Collapse
|
13
|
Rabochiy P, Wolynes PG, Lubchenko V. Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: the comparative role of configurational entropy and elasticity. J Phys Chem B 2013; 117:15204-19. [PMID: 24195747 DOI: 10.1021/jp409502k] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
We compute the temperature-dependent barrier for α-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition (RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes (Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 2990), which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko (J. Chem. Phys. 2013, 138, 12A534), which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance--a kinetic quantity--from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. (Science 2005, 310, 1797) procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.
Collapse
Affiliation(s)
- Pyotr Rabochiy
- Department of Chemistry, University of Houston , Houston, Texas 77204-5003, United States
| | | | | |
Collapse
|
14
|
Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN, Tsiok EN, Trachenko K. "Liquid-gas" transition in the supercritical region: fundamental changes in the particle dynamics. PHYSICAL REVIEW LETTERS 2013; 111:145901. [PMID: 24138256 DOI: 10.1103/physrevlett.111.145901] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Indexed: 06/02/2023]
Abstract
Recently, we have proposed a new dynamic line on the phase diagram in the supercritical region, the Frenkel line. Crossing the line corresponds to the radical changes of system properties. Here, we focus on the dynamics of model Lennard-Jones and soft-sphere fluids. We show that the location of the line can be rigorously and quantitatively established on the basis of the velocity autocorrelation function (VAF) and mean-square displacements. VAF is oscillatory below the line at low temperature, and is monotonically decreasing above the line at high temperature. Using this criterion, we show that the crossover of particle dynamics and key liquid properties occur on the same line. We also show that positive sound dispersion disappears in the vicinity of the line in both systems. We further demonstrate that the dynamic line bears no relationship to the existence of the critical point. Finally, we find that the region of existence of liquidlike dynamics narrows with the increase of the exponent of the repulsive part of interatomic potential.
Collapse
Affiliation(s)
- V V Brazhkin
- Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow, Russia
| | | | | | | | | | | |
Collapse
|
15
|
Symmetry breaking gives rise to energy spectra of three states of matter. Sci Rep 2013; 3:2794. [PMID: 24077388 PMCID: PMC3786290 DOI: 10.1038/srep02794] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2013] [Accepted: 08/22/2013] [Indexed: 01/08/2023] Open
Abstract
A fundamental task of statistical physics is to start with a microscopic Hamiltonian, predict the system's statistical properties and compare them with observable data. A notable current fundamental challenge is to tell whether and how an interacting Hamiltonian predicts different energy spectra, including solid, liquid and gas phases. Here, we propose a new idea that enables a unified description of all three states of matter. We introduce a generic form of an interacting phonon Hamiltonian with ground state configurations minimising the potential. Symmetry breaking SO(3) to SO(2), from the group of rotations in reciprocal space to its subgroup, leads to emergence of energy gaps of shear excitations as a consequence of the Goldstone theorem, and readily results in the emergence of energy spectra of solid, liquid and gas phases.
Collapse
|
16
|
Rabochiy P, Lubchenko V. Microscopic calculation of the free energy cost for activated transport in glass-forming liquids. J Chem Phys 2013; 138:12A534. [PMID: 23556785 DOI: 10.1063/1.4790399] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Activated transport in liquids--supercooled liquids in particular--occurs via mutual nucleation of alternative, aperiodic minima of the free energy. Xia and Wolynes [Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000)] have made a general argument that at temperatures near the ideal glass transition, the surface penalty for this kind of nucleation is largely determined by the temperature and the logarithm of the size of the vibrational fluctuation of rigid molecular units about the local minimum. Here, we independently show how to estimate this surface tension and, hence, the activation barrier for the activated transport for several actual liquids, using their structure factors and knowledge of the finite-frequency elastic constants. In this estimate, the activation free energy, while depending on the configurational entropy, also depends on the elastic modulus as in the "shoving" models. The resulting estimates are however consistent with the estimate provided by Xia and Wolynes' argument near the glass transition and, in addition, reflect the barrier softening effects predicted earlier for fragile substances.
Collapse
Affiliation(s)
- Pyotr Rabochiy
- Department of Chemistry, University of Houston, Houston, Texas 77204-5003, USA
| | | |
Collapse
|
17
|
Levashov VA, Morris JR, Egami T. The origin of viscosity as seen through atomic level stress correlation function. J Chem Phys 2013; 138:044507. [DOI: 10.1063/1.4789306] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
18
|
Abstract
Liquids flow, and in this sense are close to gases. At the same time, interactions in liquids are strong as in solids. The combination of these two properties is believed to be the ultimate obstacle to constructing a general theory of liquids. Here, we adopt a new approach: instead of focusing on the problem of strong interactions, we zero in on the relative contributions of vibrational and diffusional motion. We show that liquid energy and specific heat are given, to a very good approximation, by their vibrational contributions as in solids over almost entire range of relaxation time in which liquids exist as such, and demonstrate that this result is consistent with liquid entropy exceeding solid entropy. Our analysis therefore reveals an interesting duality of liquids not hitherto known: they are close to solids from the thermodynamic perspective and to flowing gases. We discuss several implications of this result.
Collapse
Affiliation(s)
- K Trachenko
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, UK.
| | | |
Collapse
|
19
|
Benassi P, Nardone M, Giugni A. Ultraviolet and visible Brillouin scattering study of viscous relaxation in 3-methylpentane down to the glass transition. J Chem Phys 2012; 137:094504. [PMID: 22957578 DOI: 10.1063/1.4748354] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Brillouin light scattering spectra from transverse and longitudinal acoustic waves in liquid and supercooled 3-methylpentane have been collected from room temperature down to 80 K, just above the glass transition. Spectra at different wave vectors have been obtained using 532 nm and 266 nm excitation. We found evidence of a shear relaxation with a characteristic time of 100 s at the glass transition which only partly accounts for the relaxation observed in the propagation and attenuation of the longitudinal modes. The inclusion of a relaxing bulk viscosity contribution with a relaxation time of the order of 10(2) ns at the glass transition is found to adequately reproduce the experimental data including transient grating data at a much lower frequency. A consistent picture of relaxed shear and bulk moduli as a function of temperature is derived. These two quantities are found to be related by a linear relation suggesting that a Cauchy-like relation holds also above the glass transition.
Collapse
Affiliation(s)
- P Benassi
- Dipartimento di Fisica and CNISM-CNR, Università de L'Aquila, via Vetoio, 67100 Coppito, Italy
| | | | | |
Collapse
|
20
|
Bolmatov D, Brazhkin VV, Trachenko K. The phonon theory of liquid thermodynamics. Sci Rep 2012; 2:421. [PMID: 22639729 PMCID: PMC3359528 DOI: 10.1038/srep00421] [Citation(s) in RCA: 85] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2012] [Accepted: 05/11/2012] [Indexed: 11/27/2022] Open
Abstract
Heat capacity of matter is considered to be its most important property because it holds information about system's degrees of freedom as well as the regime in which the system operates, classical or quantum. Heat capacity is well understood in gases and solids but not in the third main state of matter, liquids, and is not discussed in physics textbooks as a result. The perceived difficulty is that interactions in a liquid are both strong and system-specific, implying that the energy strongly depends on the liquid type and that, therefore, liquid energy can not be calculated in general form. Here, we develop a phonon theory of liquids where this problem is avoided. The theory covers both classical and quantum regimes. We demonstrate good agreement of calculated and experimental heat capacity of 21 liquids, including noble, metallic, molecular and hydrogen-bonded network liquids in a wide range of temperature and pressure.
Collapse
Affiliation(s)
- D Bolmatov
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK.
| | | | | |
Collapse
|
21
|
Rabochiy P, Lubchenko V. Liquid State Elasticity and the Onset of Activated Transport in Glass Formers. J Phys Chem B 2012; 116:5729-37. [DOI: 10.1021/jp300681y] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Pyotr Rabochiy
- Departments of †Chemistry and ‡Physics, University of Houston, Houston, Texas 77204-5003, United
States
| | - Vassiliy Lubchenko
- Departments of †Chemistry and ‡Physics, University of Houston, Houston, Texas 77204-5003, United
States
| |
Collapse
|
22
|
Brazhkin VV, Fomin YD, Lyapin AG, Ryzhov VN, Trachenko K. Two liquid states of matter: a dynamic line on a phase diagram. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031203. [PMID: 22587085 DOI: 10.1103/physreve.85.031203] [Citation(s) in RCA: 77] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2011] [Indexed: 05/31/2023]
Abstract
It is generally agreed that the supercritical region of a liquid consists of one single state (supercritical fluid). On the other hand, we show here that liquids in this region exist in two qualitatively different states: "rigid" and "nonrigid" liquids. Rigid to nonrigid transition corresponds to the condition τ≈τ(0), where τ is the liquid relaxation time and τ(0) is the minimal period of transverse quasiharmonic waves. This condition defines a new dynamic crossover line on the phase diagram and corresponds to the loss of shear stiffness of a liquid at all available frequencies and, consequently, to the qualitative change in many important liquid properties. We analyze this line theoretically as well as in real and model fluids and show that the transition corresponds to the disappearance of high-frequency sound, to the disappearance of roton minima, qualitative changes in the temperature dependencies of sound velocity, diffusion, viscous flow, and thermal conductivity, an increase in particle thermal speed to half the speed of sound, and a reduction in the constant volume specific heat to 2k(B) per particle. In contrast to the Widom line that exists near the critical point only, the new dynamic line is universal: It separates two liquid states at arbitrarily high pressure and temperature and exists in systems where liquid-gas transition and the critical point are absent altogether. We propose to call the new dynamic line on the phase diagram "Frenkel line".
Collapse
Affiliation(s)
- V V Brazhkin
- Institute for High Pressure Physics RAS, 142190 Troitsk Moscow Region, Russia.
| | | | | | | | | |
Collapse
|
23
|
Abstract
AbstractIn the light of the strong and fragile classification of simple liquids we review some of the relaxation data for some well-known polymers to see the extent to which a similar pattern may be manifested. Relaxation time data rather than viscosity data are used in the polymer case to avoid complications from long chain effects on the Vogel-Fulcher equation pre exponent. A combination of light scattering and 13C NMR data seem to provide the most reliable guide to the microviscosity of interest to the classification. A pattern similar to that for viscous liquids is recovered with polyisobutylene, the “strongest” chain polymer and bisphenol polycarbonate, the most fragile. The extent to which correlations of other properties with fragility, found in the non-polymeric liquids cases, will carry over to the polymer case is still being evaluated, though the work of Hodge on the analysis of the more complicated problem of non-linear thermal relaxation, suggests the carry over may be extensive.
Collapse
|
24
|
Hong L, Gujrati PD, Novikov VN, Sokolov AP. Molecular cooperativity in the dynamics of glass-forming systems: A new insight. J Chem Phys 2009; 131:194511. [DOI: 10.1063/1.3266508] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
25
|
Msall ME, Wright OB, Matsuda O. Seeking shear waves in liquids with picosecond ultrasonics. ACTA ACUST UNITED AC 2007. [DOI: 10.1088/1742-6596/92/1/012026] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
26
|
Stevens LL, Orler EB, Dattelbaum DM, Ahart M, Hemley RJ. Brillouin-scattering determination of the acoustic properties and their pressure dependence for three polymeric elastomers. J Chem Phys 2007; 127:104906. [PMID: 17867779 DOI: 10.1063/1.2757173] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The acoustic properties of three polymer elastomers, a cross-linked poly(dimethylsiloxane) (Sylgard 184), a cross-linked terpolymer poly(ethylene-vinyl acetate-vinyl alcohol), and a segmented thermoplastic poly(ester urethane) copolymer (Estane 5703), have been measured from ambient pressure to approximately 12 GPa by using Brillouin scattering in high-pressure diamond anvil cells. The Brillouin-scattering technique is a powerful tool for aiding in the determination of equations of state for a variety of materials, but to date has not been applied to polymers at pressures exceeding a few kilobars. For the three elastomers, both transverse and longitudinal acoustic modes were observed, though the transverse modes were observed only at elevated pressures (>0.7 GPa) in all cases. From the Brillouin frequency shifts, longitudinal and transverse sound speeds were calculated, as were the C(11) and C(12) elastic constants, bulk, shear, and Young's moduli, and Poisson's ratios, and their respective pressure dependencies. P-V isotherms were then constructed, and fit to several empirical/semiempirical equations of state to extract the isothermal bulk modulus and its pressure derivative for each material. Finally, the lack of shear waves observed for any polymer at ambient pressure, and the pressure dependency of their appearance is discussed with regard to instrumental and material considerations.
Collapse
Affiliation(s)
- Lewis L Stevens
- Dynamic and Energetic Materials Division, MS P952, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | |
Collapse
|
27
|
Torell LM, Börjesson L, Sokoiov AP. The liquid-glass transition in a strong glassformer. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/00411459508203946] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- L. M. Torell
- a Department of Physics , Chalmers University of Technology , S-412 96 , Göteborg , Sweden
| | - L. Börjesson
- b Department of Physics , Royal Institute of Technology , S-100 44 , Stockholm , Sweden
| | - A. P. Sokoiov
- c Max-Planck-Institut für Polymerforschung , D-6500 , Mainz , Germany
| |
Collapse
|
28
|
Kozhevnikov VF, Payne WB, Olson JK, McDonald CL, Inglefield CE. Physical properties of sulfur near the polymerization transition. J Chem Phys 2006; 121:7379-86. [PMID: 15473808 DOI: 10.1063/1.1794031] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Acoustical measurements, electron spin resonance, and Raman spectroscopy have been employed to probe sulfur over the temperature range 80-180 degrees C, which includes the polymerization transition and the supercooled liquid state. Acoustical properties (sound velocity, absorption, and impedance) have been studied with both longitudinal and transverse waves at frequencies between 500 kHz and 22 MHz. The results confirm that polymeric sulfur is a solution of long chain molecules in monomeric solvent, and that the polymerization transition is not a second-order phase transition, as was proposed theoretically. Sulfur is a viscous liquid, but not viscoelastic, both below and above the polymerization transition temperature. It is shown that the classical Navier-Stokes theory is not applicable to the sound absorption in liquid sulfur in the highly viscous state.
Collapse
Affiliation(s)
- V F Kozhevnikov
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
| | | | | | | | | |
Collapse
|
29
|
Dreyfus C, Lebon MJ, Vivicorsi F, Aouadi A, Pick RM, Cummins HZ. Brillouin scattering study of molten zinc chloride. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:041509. [PMID: 11308850 DOI: 10.1103/physreve.63.041509] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2000] [Indexed: 05/23/2023]
Abstract
Polarized and depolarized Brillouin scattering experiments on molten ZnCl2 were performed between 300 and 600 degrees C in different geometries. VV spectra measured in backscattering and small angle scattering were analyzed with conventional viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We also analyzed in the same way the temperature dependence of the transverse Brillouin lines detected in a 90 degrees VH geometry. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars, and are about 2.5 times smaller than the alpha relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.
Collapse
Affiliation(s)
- C Dreyfus
- LMDH, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | | | | | | | | | | |
Collapse
|
30
|
Ribeiro MCC, Almeida LCJ. Validating a polarizable model for the glass-forming liquid Ca0.4K0.6(NO3)1.4 by ab initio calculations. J Chem Phys 2000. [DOI: 10.1063/1.1289147] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
31
|
Das SP. Elastic behavior in a supercooled liquid: analysis of viscoelasticity using an extended mode coupling model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:1670-1673. [PMID: 11088627 DOI: 10.1103/physreve.62.1670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/1999] [Revised: 03/28/2000] [Indexed: 05/23/2023]
Abstract
The transverse current correlations are analyzed using the formalism of extended mode coupling theory. The undercooled liquid can sustain shear waves up to a minimum wave number. With the increase of density this wave number decreases, indicating a growing length scale that is related to the dynamics. The speed of the propagating shear waves goes to zero approaching a critical wave number. The maximum wavelength shows an initial enhancement approaching the mode coupling transition and finally grows at a slower rate as the sharp transition is cut off.
Collapse
Affiliation(s)
- SP Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| |
Collapse
|
32
|
Pimenov A, Lunkenheimer P, Rall H, Kohlhaas R, Loidl A, Böhmer R. Ion transport in the fragile glass former 3KNO3-2Ca(NO3)2. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:676-684. [PMID: 9965115 DOI: 10.1103/physreve.54.676] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
33
|
Fernández-Perea R, Bermejo FJ, Enciso E. Molecular dynamics on a realistic model for a strong glass. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:6215-6224. [PMID: 9982021 DOI: 10.1103/physrevb.53.6215] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
34
|
Dyre JC, Olsen NB, Christensen T. Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:2171-2174. [PMID: 9983702 DOI: 10.1103/physrevb.53.2171] [Citation(s) in RCA: 143] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
35
|
Ram S. Infrared study of the dynamics of boroxol rings in the crystallization of BaFe12O19 microcrystals in borate glasses. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:6280-6286. [PMID: 9977166 DOI: 10.1103/physrevb.51.6280] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
36
|
Ricci M, Foggi P, Righini R, Torre R. Orientational dynamics on glassformer 2 [Ca(NO3)2]⋅3[KNO3]: A study by transient optical Kerr effect. J Chem Phys 1993. [DOI: 10.1063/1.464944] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
37
|
Börjesson L, Hassan AK, Swenson J, Torell LM, Fontana A. Is there a correlation between the first sharp diffraction peak and the low frequency vibrational behavior of glasses? PHYSICAL REVIEW LETTERS 1993; 70:1275-1278. [PMID: 10054335 DOI: 10.1103/physrevlett.70.1275] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
38
|
Kim B. Stretching, mode coupling, and the glass transition. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:1992-2003. [PMID: 9908334 DOI: 10.1103/physreva.46.1992] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
39
|
Hassan AK, Torell LM, Börjesson L, Doweidar H. Structural changes of B2O3 through the liquid-glass transition range: A Raman-scattering study. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:12797-12805. [PMID: 10001339 DOI: 10.1103/physrevb.45.12797] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
40
|
Tao NJ, Li G, Cummins HZ. Brillouin-scattering study of the liquid-glass transition in CaKNO3: Mode-coupling analysis. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:686-696. [PMID: 10001108 DOI: 10.1103/physrevb.45.686] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
41
|
Tao NJ, Li G, Cummins HZ. Self-similar light-scattering spectra of beta relaxation near the liquid-glass transition. PHYSICAL REVIEW LETTERS 1991; 66:1334-1337. [PMID: 10043179 DOI: 10.1103/physrevlett.66.1334] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
42
|
Tao NJ, Li G, Cummins HZ. Brillouin-scattering study of the liquid-glass transition in supercooled aqueous lithium chloride solutions: Generalized hydrodynamics and mode-coupling analyses. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:5815-5830. [PMID: 9997984 DOI: 10.1103/physrevb.43.5815] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
43
|
Neutron and light scattering study of relaxation dynamics in a glass-forming fragile molecular liquid. Chem Phys 1990. [DOI: 10.1016/0301-0104(90)80140-s] [Citation(s) in RCA: 71] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
44
|
Silence SM, Goates SR, Nelson KA. Impulsive stimulated scattering study of normal and supercooled liquid triphenylphosphite. Chem Phys 1990. [DOI: 10.1016/0301-0104(90)80142-k] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
45
|
Signorini GF, Barrat J, Klein ML. Structural relaxation and dynamical correlations in a molten state near the liquid–glass transition: A molecular dynamics study. J Chem Phys 1990. [DOI: 10.1063/1.458139] [Citation(s) in RCA: 152] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|