Frequency dependence and equilibration of the specific heat of glass-forming liquids

Yu, Clare C.; Carruzzo, Hervé M.

doi:10.1103/physreve.69.051201

Cited by 28 publications

(34 citation statements)

References 42 publications

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“…1 we observe that the kinetic glass transition is at ÿ c ' 1:45 for 0:24. This value coincides with the one found for the soft-spheres binary mixtures [i.e., a bimodal P ] with 0:09 [34] and 0:16 [35]. This suggests that ÿ c is independent on .…”

Section: Prl 98 085702 (2007) P H Y S I C a L R E V I E W L E T T E supporting

confidence: 76%

Phase Diagram of a Polydisperse Soft-Spheres Model for Liquids and Colloids

2007

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The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon. DOI: 10.1103/PhysRevLett.98.085702 PACS numbers: 64.70.Dv, 64.70.Pf The equilibrium phase diagram of dense classical fluids is far from being fully understood, especially in regards to the influence of the freezing transition of some disorder in the parameters of the interaction. While fluids made of identical atoms crystallize easily upon lowering the temperature or increasing the density, the fate of polydisperse systems (colloids, for instance), where the particle size is sampled from a probability distribution, P , is still a matter of debate.On the theoretical side, the effect of size dispersion, measured by the quantity [the ratio among the standard deviation and the mean of P ] over the phase diagram, has been addressed mostly in the case of the hard-spheres model, which is meant to describe colloidal systems [1]. At least for small polydispersity, seems to be the only feature of P that controls the physical results. Different theories predict conflicting scenarios in the region of large . The moment free-energy method [2] suggests phase separation between many different crystal phases, each one with a much narrower size dispersion than (a phenomenon termed fractionation). However, a density functional analysis [3] predicts the existence of a terminal polydispersity t beyond which the formation of the crystal is thermodynamically suppressed. Numeric simulations of the hard sphere model find some agreement with both the fractionation [4,5] and the terminal polydispersity [6] scenarios. As regards models with a soft potential (e.g., Lennard-Jones), which are more appropriate to describe liquids, no extensive study on the effects of polydispersity has been performed so far.On the experimental side, crystallization of very viscous colloidal samples with > t 0:12 does not occur, even after months spent from the preparation [7]. Further evidence supporting the terminal polydispersity scenario comes from the finding of reentrant melting (crystal to fluid transition when increasing the density) on polydisperse colloids in confined geometry [8].Yet, these experimental results do not necessarily reveal features of the phase diagram. Indeed, the processes needed to keep the system in thermodynamic equilibrium often become exceedingly slow. Such processes are the nucleation of the solid within the fluid and the relaxation in the supercooled fluid [9].Here we obtain the equilibrium phase diagram of ...

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Section: Prl 98 085702 (2007) P H Y S I C a L R E V I E W L E T T E supporting

confidence: 76%

Phase Diagram of a Polydisperse Soft-Spheres Model for Liquids and Colloids

2007

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“…[10] (Fig.3). Furthermore, for both the σ A /σ B = 1.2 and the σ A /σ B = 1.4 models, local swap finds a crystallization phase transition, to highly disordered crystals on the bcc family, not reported on previous studies [11,10] [10] (error estimates were not provided in Ref. [10]).…”

Section: The Local Swap Monte Carlo Algorithmmentioning

confidence: 94%

“…[11,10]. Since the potential energy per particle, e shows the slowest excitations [5,11], we shall focus here only in this observable, the internal energy being 3 2 k B T + e (for other quantities, see Ref.…”

Section: Models and Observablesmentioning

confidence: 99%

“…Constants C αβ are chosen to ensure continuity at r c . The simulations are at constant volume, with particle density fixed to σ In the second model [11,10] the choice σ B = 1.4σ A is made. Naming x = r/(σ α + σ β ), the pair potential in units ǫ = 1 is V (x) = x −12 +x−13/12 12/13 if x < 12 1/13 and zero otherwise (thus, the cut-off distance depends on the type of interacting species).…”

Section: Models and Observablesmentioning

confidence: 99%

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Optimized Monte Carlo method for glasses

Fernández

Martı́n-Mayor

Verrocchio

2007

Philosophical Magazine

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A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm is shown to thermalize well below the Mode Coupling temperature and to outperform other optimized Monte Carlo methods. Using the algorithm, we obtain finite size effects in the specific heat. This effect points to the existence of a large correlation length measurable in equal time correlation functions.

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“…23). Equilibration time is considerably shortened, so we can perform equilibrium simulations of large systems well below T MC =0.226 [20,24]. This is important, since in the standard MS T MC acts like a spinodal temperature [15], above which there are not many states and the surface tension is zero [31].…”

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confidence: 99%

Mosaic Multistate Scenario Versus One-State Description of Supercooled Liquids

2007

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According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.It is common opinion that in finite dimension a divergence of a relaxation time τ at nonzero temperature is associated to a diverging characteristic length ξ. The idea is that when this length increases, relaxation proceeds through the rearrangement of ever larger regions, taking a longer and longer time. The relation between τ and ξ depends on the physical mechanism of relaxation. Two main mechanisms are activated relaxation of a ψ-dimensional droplet of size ξ, giving τ ∼ exp(Aξ ψ /T ), and critical slowing down, whereGlass-forming liquids are tricky: relaxation times grow spectacularly (more than ten decades) upon lowering the temperature, without clear evidence of a growing static cooperative lenght. In particular, density fluctuations are thought to remain correlated over short distances close to the glass transition (although there are some indication that energy fluctuations might develop larger correlations [2,3]). Thus the concept of dynamic heterogeneities is central to several theories of the glass transition [4,5,6,7], where the role of order parameter is played by dynamic quantities such as local time correlators, which become correlated over the growing dynamic lenght scale ξ dyn . No thermodynamic singularity is present in these theories. Dynamic singularities are also typically absent at finite temperatures, with the notable exception of mode coupling theory (MCT) [8], recently recast in terms of dynamic heterogeneities [9]. Note, however, that the experimental values of ξ dyn [10,11,12,13] are barely in the nm range, the same as density correlations [14].The mosaic scenario (MS) [15,16,17], working within the conceptual framework of nucleation theory, identifies on the other hand a static correlation length. Deeply rooted in the physics of mean-field spin glasses, the MS crucially assumes the existence of exponentially many inequivalent states exp(N Σ), below the mode coupling temperature T MC (Σ is called complexity or configurational entropy, and N is the size of the system). Suppose the system is in a state α and ask: what is the free energy cost for a region of linear size R to rearrange...

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Frequency dependence and equilibration of the specific heat of glass-forming liquids

Cited by 28 publications

References 42 publications

Phase Diagram of a Polydisperse Soft-Spheres Model for Liquids and Colloids

Phase Diagram of a Polydisperse Soft-Spheres Model for Liquids and Colloids

Optimized Monte Carlo method for glasses

Mosaic Multistate Scenario Versus One-State Description of Supercooled Liquids

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