Equilibrium phase diagram of a randomly pinned glass-former

Abstract

We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature T K (c) at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., T K (c) is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally, we determine the geometrical properties of the potential energy landscape, notably the T-and c dependence of the saddle index, and use these properties to obtain the dynamic transition temperature T d (c). The two temperatures T K (c) and T d (c) cross at a finite value of c and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first-order transition theory.ideal glass transition | computer simulations | random first-order transition theory | Kauzmann temperature | configurational entropy U pon cooling, glass-forming liquids show a dramatic increase of their viscosities and relaxation times before they eventually fall out of equilibrium at low temperatures (1, 2). This laboratory glass transition is a purely kinetic effect because it occurs at the temperature at which the relaxation time of the system crosses the time scale imposed by the experiment, e.g., via the cooling rate. Despite the intensive theoretical, numerical, and experimental studies of the last five decades, the mechanism responsible for the slowing down and thus for the (kinetic) glass transition is still under debate and hence a topic of intense research. From a fundamental point of view the ultimate goal of these studies is to find an answer to the big question in the field: Does a finite temperature exist at which the dynamics truly freezes and, if so, is this ideal glass transition associated with a thermodynamic singularity or is it of kinetic origin (3-6)?Support for the existence of a kinetic transition comes from certain lattice gas models with a "facilitated dynamics" (6). In these models, the dynamics is due to the presence of "defects" and hence for such systems the freezing is not related to any thermodynamic singularity. However, the first evidence that there does indeed exist a thermodynamic singularity goes back to Kauzmann, who found that the residual entropy (the difference of the entropy of the liquid state from that of the crystalline state) vanishes at a finite temperature T K if it is extrapolated to temperatures below the laboratory glass transition (7). Subsequently many theoretical scenarios that invoke the presence of a thermodynamic transition have been proposed (8-10). One of these is the so-called ...

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

“…It is argued [18] that the temperature T K at which the configurational entropy goes to zero in such a system increases as the concentration of pinned particles is increased, thereby making it possible to equilibrate the liquid near the higher transition temperature. Results of numerical studies [19,20,22] of equilibrium properties of such randomly pinned systems are consistent with the predictions of Ref. [18].…”

“…[21,23] that the α relaxation time defined there remains finite at temperatures close to the values at which the equilibrium calculation of Ref. [22] predicts a vanishing of the configurational entropy. These results raise important questions about the validity of the relation between the configurational entropy and the α relaxation time predicted in RFOT theory.…”

“…[24] that the relaxation time extracted from the full density autocorrelation function should be considered in a check of whether the relaxation time diverges at the points at which the configurational entropy vanishes according to the numerical results of Ref. [22]. We have calculated the autocorrelation function of the full density in one of the three-dimensional models (the Kob-Andersen model [26] which was also considered in Ref.…”

Structures and Dynamics of Glass-Forming Colloidal Liquids under Spherical Confinement

“…First, we confirm the numerical and theoretical predictions on the 1/3 scaling of the pinning length [33,34] and illustrate a divergent static length scale in the colloidal glass transition when φ → φ c . Moreover, we show that glass-forming liquids with randomly pinned particles show quantitatively similar dynamics as colloidal liquids under spherical confinement [10,13,27,33]. Thus, the RFOT can be applied for understanding confined colloidal liquids-an extensively studied subject in colloidal science [15][16][17][18][19][20][21][22].…”

“…We find that q c reaches the plateau when F s decays to 0 (Fig. 2c) [10,27]. Accordingly, we measure the equilibrium overlap, q ∞ = q c (R, t = t * ) at a time t * when F s = 0.…”