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Adaptive Elastic Networks as models of supercooled liquids  [PDF]
Le Yan,Matthieu Wyart
Physics , 2015, DOI: 10.1103/PhysRevE.92.022310
Abstract: The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.
The kinetic fragility of liquids as manifestation of the elastic softening  [PDF]
F. Puosi,D. Leporini
Physics , 2011, DOI: 10.1140/epje/i2015-15087-2
Abstract: We show that the fragility $m$, the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities ($33 \le m \le 115$), leading to a fragility-independent elastic master curve extending over eighteen decades in viscosity and relaxation time. The master curve is accounted for by a cavity model pointing out the roles of both the available free volume and the cage softness. A major implication of our findings is that ultraslow relaxations, hardly characterised experimentally, become predictable by linear elasticity. As an example, the viscosity of supercooled silica is derived over about fifteen decades with no adjustable parameters.
Fragility and elasticity - a new perspective  [PDF]
U. Buchenau
Physics , 2009, DOI: 10.1103/PhysRevB.80.172201
Abstract: The fragility (the abnormally strong temperature dependence of the viscosity) of highly viscous liquids is shown to have two sources. The first is the temperature dependence of the barriers between inherent states considered earlier. The second is the recently discovered asymmetry between the actual inherent state and its neighbors. One needs both terms for a quantitative description.
Correlations between vibrational entropy and dynamics in super-cooled liquids  [PDF]
Matthieu Wyart
Physics , 2009, DOI: 10.1103/PhysRevLett.104.095901
Abstract: A relation between vibrational entropy and particles mean square displacement is derived in super-cooled liquids, assuming that the main effect of temperature changes is to rescale the vibrational spectrum. Deviations from this relation, in particular due to the presence of a Boson Peak whose shape and frequency changes with temperature, are estimated. Using observations of the short-time dynamics in liquids of various fragility, it is argued that (i) if the crystal entropy is significantly smaller than the liquid entropy at $T_g$, the extrapolation of the vibrational entropy leads to the correlation $T_K\approx T_0$, where $T_K$ is the Kauzmann temperature and $T_0$ is the temperature extracted from the Vogel-Fulcher fit of the viscosity. (ii) The jump in specific heat associated with vibrational entropy is very small for strong liquids, and increases with fragility. The analysis suggests that these correlations stem from the stiffening of the Boson Peak under cooling, underlying the importance of this phenomenon on the dynamical arrest.
Vibrational entropy, configurational entropy, and the fragility of glassforming liquids  [PDF]
L. -M. Martinez,C. A. Angell
Physics , 2000,
Abstract: A thermodynamic measure of the fragility of liquids has recently (Ito et al ref.1) been defined in terms of the temperature dependence of the excess entropy of liquid over crystal, scaled by the excess entropy at the glass transition temperature, and it has been correlated with kinetic fragility. The correlation has been vigorously contested [2] using dielectric relaxation data on some molecular liquids. We put this conflict in perspective using an extensive data set covering all classes of liquids while retaining the cases of ref 2. The excess entropy of the liquid, used in the thermodynamic quantity being correlated, has both configurational and vibrational components. This is the source of a second conflict which concerns the relative importance of these two components. Experimental tests supporting the Adam-Gibbs "entropy" theory of the temperature dependence of transport in viscous liquids have mostly been made using the excess entropy, but recent simulation studies on the hard sphere fluid [3] SPC-E water [4] and mixed LJ [5,6] have shown, as in the A-G theory, a correlation with the configurational component. We show why, in laboratory studies, the correlation should be with both, inextricably. In the course of this demonstration we identify a key role for excess vibrational entropy in causing fragile behavior in ambient pressure liquids.
On the correlation between fragility and stretching in glassforming liquids  [PDF]
Kristine Niss,Cecile Dalle-Ferrier,Gilles Tarjus,Christiane Alba-Simionesco
Physics , 2006, DOI: 10.1088/0953-8984/19/7/076102
Abstract: We study the pressure and temperature dependences of the dielectric relaxation of two molecular glassforming liquids, dibutyl phtalate and m-toluidine. We focus on two characteristics of the slowing down of relaxation, the fragility associated with the temperature dependence and the stretching characterizing the relaxation function. We combine our data with data from the literature to revisit the proposed correlation between these two quantities. We do this in light of constraints that we suggest to put on the search for empirical correlations among properties of glassformers. In particular, argue that a meaningful correlation is to be looked for between stretching and isochoric fragility, as both seem to be constant under isochronic conditions and thereby reflect the intrinsic effect of temperature.
Importance of glassy fragility for energy applications of ionic liquids  [PDF]
P. Sippel,P. Lunkenheimer,S. Krohns,E. Thoms,A. Loidl
Physics , 2015, DOI: 10.1038/srep13922
Abstract: Ionic liquids (ILs) are salts that are liquid close to room temperature. Their possible applications are numerous, e.g., as solvents for green chemistry in various electrochemical devices, and even for such "exotic" purposes as spinning-liquid mirrors for lunar telescopes. Here we concentrate on their use for new advancements in energy-storage and -conversion devices: Batteries, supercapacitors or fuel cells using ILs as electrolytes could be important building blocks for the sustainable energy supply of tomorrow. Interestingly, ILs show glassy freezing and the universal, but until now only poorly understood dynamic properties of glassy matter, dominate many of their physical properties. We show that the conductivity of ILs, an essential figure of merit for any electrochemical application, depends in a systematic way not only on their glass temperature but also on the so-called fragility, characterizing the non-canonical super-Arrhenius temperature dependence of their ionic mobility.
Thermodynamics, kinetics and fragility of bulk metallic glass forming liquids  [PDF]
Ralf Busch,Zach Evenson,Isabella Gallino,Shuai Wei
Physics , 2014,
Abstract: This review deals with the kinetic and thermodynamic fragility of bulk metallic glass forming liquids. The experimental methods to determine the kinetic fragility, relaxation behavior and thermodynamic functions of undercooled metallic liquids are introduced. Existing data are assessed and discussed using the Vogel-Fulcher-Tammann equation and in the frameworks of the Adam-Gibbs as well as the Cohen-Turnbull free volume approach. In contrast to pure metals and most non glass forming alloys, bulk glass formers are moderately strong liquids. In general the fragility parameter $D^{*} $ increases with the complexity of the alloy with differences between the alloy families, e.g. noble-metal based alloys being more fragile than Zr-based alloys. At least some bulk metallic glass forming liquids, such as Vitreloy 1, undergo transitions from a fragile state at high temperatures to a strong state at low temperatures with indications that in Zr-based alloys this behavior is a common phenomenon.
The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids  [PDF]
Srikanth Sastry
Physics , 2000, DOI: 10.1038/35051524
Abstract: Glass is a microscopically disordered, solid form of matter that results when a fluid is cooled or compressed in such a fashion that it does not crystallise. Almost all types of materials are capable of glass formation -- polymers, metal alloys, and molten salts, to name a few. Given such diversity, organising principles which systematise data concerning glass formation are invaluable. One such principle is the classification of glass formers according to their fragility\cite{fragility}. Fragility measures the rapidity with which a liquid's properties such as viscosity change as the glassy state is approached. Although the relationship between features of the energy landscape of a glass former, its configurational entropy and fragility have been analysed previously (e. g.,\cite{speedyfr}), an understanding of the origins of fragility in these features is far from being well established. Results for a model liquid, whose fragility depends on its bulk density, are presented in this letter. Analysis of the relationship between fragility and quantitative measures of the energy landscape (the complicated dependence of energy on configuration) reveal that the fragility depends on changes in the vibrational properties of individual energy basins, in addition to the total number of such basins present, and their spread in energy. A thermodynamic expression for fragility is derived, which is in quantitative agreement with {\it kinetic} fragilities obtained from the liquid's diffusivity.
Slow dynamics, dynamic heterogeneities, and fragility of supercooled liquids confined in random media  [PDF]
Kang Kim,Kunimasa Miyazaki,Shinji Saito
Physics , 2010, DOI: 10.1088/0953-8984/23/23/23412
Abstract: Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-Gaussian parameter, and the fragility. Cooperative and spatially heterogeneous dynamics are suppressed as the obstacle density increases, which lead to the more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are qualitatively consistent with the results of recent experimental and numerical studies for various classes of spatially heterogeneous systems. We also investigate the dependence of the dynamics of mobile particles on the protocol to generate the random matrix. A reentrant transition from the arrested phase to the liquid phase as the mobile particle density {\it increases} is observed for a class of protocols. This reentrance is explained in terms of the distribution of the volume of the voids that are available to the mobile particles.
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