Thermodynamics of binary mixture glasses

Coluzzi, Barbara; Mézard, Marc; Parisi, G.; Verrocchio, P.

doi:10.1063/1.480246

Cited by 121 publications

(214 citation statements)

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“…This is the spirit of different recent theories 4,9,[12][13][14] , but seems at odds with others 5,15 , at least at first sight. In particular, the crucial physical mechanism at the root of random first-order theory 4 (RFOT) is the emergence of long-range amorphous order, the precise definition and quantitative characterization of which is however far from obvious.…”

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confidence: 91%

Thermodynamic signature of growing amorphous order in glass-forming liquids

Biroli

Bouchaud

Cavagna³

et al. 2008

Nature Phys

343

468

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Supercooled liquids exhibit a pronounced slowdown of their dynamics on cooling 1 without showing any obvious structural or thermodynamic changes 2 . Several theories relate this slowdown to increasing spatial correlations 3-6 . However, no sign of this is seen in standard static correlation functions, despite indirect evidence from considering specific heat 7 and linear dielectric susceptibility 8 . Whereas the dynamic correlation function progressively becomes more non-exponential as the temperature is reduced, so far no similar signature has been found in static correlations that can distinguish qualitatively between a high-temperature and a deeply supercooled glass-forming liquid in equilibrium. Here, we show evidence of a qualitative thermodynamic signature that differentiates between the two. We show by numerical simulations with fixed boundary conditions that the influence of the boundary propagates into the bulk over increasing length scales on cooling. With the increase of this static correlation length, the influence of the boundary decays non-exponentially. Such long-range susceptibility to boundary conditions is expected within the random first-order theory 4,9,10 (RFOT) of the glass transition. However, a quantitative account of our numerical results requires a generalization of RFOT, taking into account surface tension fluctuations between states.Inspired by critical phenomena, it is natural to expect that the slowing down of the dynamics is related to the vicinity of a thermodynamic phase transition, where some kind of long-range order would set in 11 . This is the spirit of different recent theories 4,9,[12][13][14] , but seems at odds with others 5,15 , at least at first sight. In particular, the crucial physical mechanism at the root of random first-order theory 4 (RFOT) is the emergence of long-range amorphous order, the precise definition and quantitative characterization of which is however far from obvious. Dynamic heterogeneities 16 do show a growing dynamic correlation length accompanying the glass transition, both experimentally 17 and numerically 18 . This is certainly a first important step, but not sufficient to prune down-even at a qualitative level-different theories of the glass transition. In particular, it is not clear whether this phenomenon is due to an underlying static or purely dynamic phase transition.The approach followed here is based on the very definition of a thermodynamic phase transition, where the effect of boundary conditions becomes long-ranged. The problem is that for glasses there are no natural boundary conditions, because these should be as 'random' as the bulk amorphous states that they favour. A possible solution is to use equilibrium liquid configurations to define the boundary 19 . In the context of RFOT, this was suggested in ref. 9 (and further discussed in ref. 11), but the scope and some conclusions of this Gedankenexperiment are more general [19][20][21] . Starting from a given equilibrium configuration, we freeze the motion of all particles outside a ...

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confidence: 91%

Thermodynamic signature of growing amorphous order in glass-forming liquids

Biroli

Bouchaud

Cavagna³

et al. 2008

Nature Phys

343

468

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“…As discussed in [28], we assume that in the replicated liquid molecules are built of particles of the same type. This amounts to assume that in a glassy state particles of different type cannot easily exchange.…”

Section: Replica Theory For Multicomponent Mixturesmentioning

confidence: 99%

“…According to [28], to each molecule of the replicated liquid we can attach a label µ = 1, · · · , n according to the type of particles that build the molecule. We denote coordinates in a molecule byx = (x 1 , · · · , x m ).…”

Section: Replica Theory For Multicomponent Mixturesmentioning

confidence: 99%

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Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

et al. 2009

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We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.Amorphous packings of hard spheres are ubiquitous in physics: they have been used as models for liquids, glasses, colloidal systems, granular systems, and powders. They are also related to important problems in mathematics and information theory, such as digitalization of signals, error correcting codes, and optimization problems. Moreover, the structure and density (or porosity) of amorphous multicomponent packings is important in many branches of science and technology, ranging from oil extraction to storage of grains in silos.Despite being empirically studied since at least sixty years, amorphous packings still lack a precise mathematical definition, due to the intrinsic difficulty of quantifying "randomness" [1]. Indeed, even if a sphere packing is a purely geometrical object, in practice dense amorphous packings always result from rather complicated dynamical protocols: for instance, spheres can be thrown at random in a box that is subsequently shaken to achieve compactification [2], or they can be deposited onto a random seed cluster [3]. In numerical simulations, one starts from a random distribution of small spheres and inflates them until a jammed state is reached [4,5]; alternatively, one starts from large overlapping spheres and reduces the diameter in order to eliminate the overlaps [6][7][8][9]. In principle, each of these dynamical prescriptions produces an ensemble of final packings that depends on the details of the procedure used. Still, very remarkably, if the presence of crystalline regions is avoided, the structural properties of amorphous packings turn out to be very similar. This observation led to the proposal that "typical" amorphous packings should have common structure and density; the latter has been denoted Random Close Packing (RCP) density. The definition of RCP has been intensively debated in the last few years, in connection with the progresses of numerical simulations [1,10].Nevertheless, the empirical evidence, that amorphous packings produced according to very different protocols have common structural properties, is striking and call for an explanation. This is all the more true for binary or multicomponent mixtures, where in addition to the usual structural observables, such as the structure factor, one can investigate other quantities such as the coordination between spheres of different type, and study their variation with the composition of the mixture.In earlier attempts to build statistical models of ...

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“…A way to increase the entropy contribution of mobility defects and find a relationship between dynamics and thermodynamics seems to be through extended defects. This is the path followed (using different arguments) in [14,15,16,27,28,29] (see also [30,31] for quantitative computation of the excess configurational entropy in model systems). In all these scenarii, the presence of mobility regions, that are typically interfaces (e.g.…”

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confidence: 99%

Are defect models consistent with the entropy and specific heat of glass formers?

Biroli

Bouchaud

Tarjus

2005

The Journal of Chemical Physics

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We show that point-like defect model of glasses cannot explain thermodynamic properties of glassformers, as for example the excess specific heat close to the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler [Proc. Natl. Acad. Sci. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.Kinetically constrained models (kcm) display trivial thermodynamics but non trivial dynamics [1,2,3]. They encapsulate in a specific way the 'free volume' idea according to which the slow dynamics of glasses is due to rare, localized mobility defects [4,5]. For most kcms, slow dynamics is indeed due to defect motions [3]. A remarkable aspect of these models is that although the dynamical rules are very simple and local, the emergent defect dynamics lead to highly non trivial physical behaviour. As a consequence kcms provide a theoretical framework for understanding many of the remarkable dynamical properties of fragile glass-formers, such as superArrhenius relaxation time [3,6,7], dynamical heterogeneities [8,9,10,11] and viscosity/diffusion decoupling [12]. That these models may in fact describe quantitatively the physical properties of glasses has been strongly advocated in a series of papers by J.P. Garrahan and D. Chandler (gc) [9,10], and investigated further in [13].One of the major tenet of kcms is the complete decoupling between dynamics and thermodynamics, at variance with the traditional view of Adam and Gibbs [14], and others [15,16], in which the decrease of configurational entropy with temperature is the fundamental underlying mechanism for the viscous slowing down. It is therefore a priori surprising that kcms could have anything sensible to say about the entropy and specific heat of real materials -even if these turn out to be acceptable models of their dynamics. Nevertheless, the claim made in [10] is that these models are also in quantitative agreement with the specific heat of these materials. More precisely, assuming a perfect gas of free defects, gc give a formula for the specific heat at fixed pressure per particle of the liquid (in excess of that of the solid), which we reproduce from ref.[10] to be:where N is the number of physical molecules contributing to enthalpy fluctuations in a coarse-graining cell, J is the enthalpy cost, in kelvins, for creating a mobile cell (remember that liquids are considered here at constant pressure, hence the importance of distinguishing between enthalpy and energy). The concentration of mobile cells c is assumed to be given by c(T )/(1 − c(T )) = A exp(−J/T ), where the numerical prefactor A is argued by gc to be rather large: ln A is akin to an entropy gain ∆s 0 /k B associated with the creation of a mobile cell. Note that there is a small difference between the specific heat in excess to that of the glass (considered in [10]) and that in excess of the crystal; this difference is however irrelevant for the present discussion.In the following we first adress the results of [10] showing that even if the value o...

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Thermodynamics of binary mixture glasses

Cited by 121 publications

References 36 publications

Thermodynamic signature of growing amorphous order in glass-forming liquids

Thermodynamic signature of growing amorphous order in glass-forming liquids

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

Are defect models consistent with the entropy and specific heat of glass formers?

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