Mosaic Multistate Scenario Versus One-State Description of Supercooled Liquids

Abstract

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...

Thermodynamic signature of growing amorphous order in glass-forming liquids

“…Figure 3 shows that the generalized RFOT encoded in (8) and the one-state prediction given by the formula (6) of ref. 23 fit the total overlap data at T = 0.203 at a comparable level of accuracy. Following Occam's razor principle ('entia non sunt multiplicanda praeter necessitatem'), the one-state theory should be chosen, which is the one with the smallest number of parameters.…”

“…23 the influence of the boundary conditions on the total overlap within the sphere was studied. It was observed that the decay of q tot (R) is described sufficiently well within the single-state framework and the standard RFOT scenario was ruled out.…”

“…Interestingly, the value of the length scale ξ found here is significantly larger than those in ref. 23. This is partly due to the fact that ζ > 1 at low temperatures (see Supplementary Information for further discussion).…”

Phase-Separation Perspective on Dynamic Heterogeneities in Glass-Forming Liquids

“…Arguably, the first breakthrough has been the discovery of dynamic heterogeneities [1], and the detection of a growing dynamical correlation length, ξ d [2,3]. If we take two snapshots of the system separated by a time lag comparable to the α relaxation time, τ α , the particle displacements vary enormously across the system, and the typical size ξ d of the mobility-correlated regions increases on lowering the temperature.More recently, by studying the thermodynamics of systems subject to amorphous boundary conditions [4,5], an entirely different, fully static, correlation length ξ s has been discovered [6,7]. ξ s also grows upon cooling, even though its surge occurs at lower temperatures than ξ d .…”

Free energy cost of forming an interface between a crystal and its frozen version

“…An analogous situation corresponding to a supercooled liquid in contact with a wall consisting of particles frozen into the same amorphous structure as the liquid has been widely studied in recent years in order to investigate the relaxation dynamics of glass-forming systems [12][13][14][15][16][17][18][19]. Recently, an experimental investigation of such a system was carried out using colloidal particles [20].…”