Mechanical relaxation and the notion of time-dependent extent of ergodicity during the glass transition

Johari, G. P.

doi:10.1103/physreve.84.021501

Cited by 11 publications

(6 citation statements)

References 60 publications

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“…In an alternative form concentrating on its consequences, Gyan P. Johari discussed this problem. He noted in [ 105 ], “ A postulate that ergodicity and entropy continuously decrease to zero on cooling a liquid to a glassy state was used to support the view that glass has no residual entropy, and the features of mechanical relaxation spectra were cited as proof for the decrease. We investigate whether such spectra and the relaxation isochrones can serve as the proof.…”

Section: Residual Entropy Of Glassesmentioning

confidence: 99%

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Schmelzer¹,

Тропин

2018

Entropy

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A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play-beyond the topics widely discussed and reviewed here-a major role.

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Section: Residual Entropy Of Glassesmentioning

confidence: 99%

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Schmelzer¹,

Тропин

2018

Entropy

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“…In this view, a glass is structurally heterogeneous containing ergodic regions, i.e., the overall state of a glass is not entirely nonergodic, a subject discussed before. 130 The viewpoint that all molecules participate in the density, structure, and polarization fluctuations by small-angle orientational and/or the usual translational motions in a homogeneous, out-of-equilibrium structure of a glass is in conflict with (i) our understanding that fluctuations are an equilibrium-state property and (ii) the findings of the JG-process in metallic glasses and decrease in its relaxation strength generally on cooling and isothermal aging as the vibrational contributions to a thermodynamic property decrease. 131 If cooperative motions of all molecules were invoked also for the JG-process, it would require sufficiently large regions for such motions to occur.…”

Section: Discussionmentioning

confidence: 99%

“…An analysis of the contribution to entropy from JG-process in a glass shows that a relatively small population of molecules participates in this process, and they are likely to occur in loosely packed regions of internal equilibrium in a glass structure. In this view, a glass is structurally heterogeneous containing ergodic regions, i.e., the overall state of a glass is not entirely nonergodic, a subject discussed before …”

Section: Discussionmentioning

confidence: 99%

Source of JG-Relaxation in the Entropy of Glass

Johari

2019

J. Phys. Chem. B

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Intrinsic mobility of the glassy state is known as Johari−Goldstein (JG)relaxation. Its source is either rotational and translational motions of a small number of molecules or small-angle orientational motion of all molecules, which may include restricted translational motion of part of their flexible segments. We examine the merits of the two views by using the excess entropy, S exc , the difference between the entropy of a glass and its crystal state. Its value at the glass-forming temperature, S exc (T g ), is the sum of (1) S exc from phonons and anharmonic forces and (2) the configurational entropy from (a) the JG-process and, (b) the unfrozen modes of the α-process. If all molecules participated in the JG-process, the minimum configurational entropy from this process would be R ln(2) [= 5.76 J/(mol K)], and [S exc (T g ) − S exc (0 K)] cannot be less than that. Analysis of data for 33 liquid and 3 liquid crystal glasses and 7 orientational glasses shows that its value is less than or comparable to R ln(2) for 10 liquids and 2 orientational glasses. If contributions from ( 1) and (2b) were known and subtracted from S exc (T g ), the [S exc (T g ) − S exc (0 K)] value would be less than R ln(2) for more glasses. Cooperative motions to explain our finding and heterogeneous dynamics to explain the broad JG-relaxation spectra would require sufficiently large local mobility regions. We also argue that all molecules cannot participate in small-angle orientational fluctuations, cite evidence against such fluctuations for the JG-process, and note that nucleation and crystallization in a glass structure indicate such regions. After discussing the consequences for the entropy theory, the available NMR studies, the Eshelby inclusions, the potential energy landscape, and the Gardner transition, we conclude that JG-process likely occurs in local regions in internal equilibrium in a glass structure.

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“…To critically examine whether or not an unstable, time-dependent state of LDA can be ergodic, we recall the concept of ergodenhypothese , which is attributed to Boltzmann, who described it in his papers on the kinetic theory of gases. (For citations and description of ergodenhypothese, see ref .) Boltzmann postulated that all microstates in phase space corresponding to the surface of constant energy can be, and are, accessed over a sufficiently long period of time.…”

Section: Ambiguous Nature and Instability Of Hdasmentioning

confidence: 99%

“…No time scale was specified nor was any intermediate system state defined. In thermodynamic terms, a system is ergodic if its structure fluctuates, with equal probability, through all possible microstates consistent with a macrostate . However, when there is a broad distribution of relaxation times, not all modes of motion in an “ergodic” liquid come to equilibrium in a finite time.…”

Section: Ambiguous Nature and Instability Of Hdasmentioning

confidence: 99%

Thermodynamic Analysis of the Two-Liquid Model for Anomalies of Water, HDL–LDL Fluctuations, and Liquid–Liquid Transition

Johari

Teixeira

2015

J. Phys. Chem. B

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After reviewing the protocol-dependent properties of HDA, which thermally anneals to LDA, and the data gap over an unusually large T-range between HDA, LDA, and water, we investigate whether or not, despite HDA's ill-defined state and distinction from a glass, the HDL-LDL fluctuations view of the two-liquid model can explain water's anomalous behavior. An analysis of the density, ρ, compressibility, β, heat capacity, Cp, and thermal conductivity, κ, of water over a monotonic (continuous) path bridging this data gap shows the following: (i) Such a path between ρwater at 320 K and ρHDA yields an untenable thermal expansion coefficient of water. (ii) There is neither a continuous path between βwater at 353 K and βHDA, nor between Cp,water at 363 K and Cp,HDA. (iii) The same value of ρwater, of βwater, or of Cp,water at two temperatures separated by a maxima or a minima is incompatible with the HDL-LDL fluctuations view. (iv) κLDA at ∼140 K is about twice that of κ water at 253 K. (v) κHDA at 120 K is incompatible with κwater at T > 320 K. Thus, there is an internal inconsistency between the thermodynamics of HDA seen as a glass and that of water seen as an HDL-LDL mixture, which is incompatible with both the HDL-LDL fluctuations view and the liquid-liquid transition.

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Mechanical relaxation and the notion of time-dependent extent of ergodicity during the glass transition

Cited by 11 publications

References 60 publications

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

Source of JG-Relaxation in the Entropy of Glass

Thermodynamic Analysis of the Two-Liquid Model for Anomalies of Water, HDL–LDL Fluctuations, and Liquid–Liquid Transition

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