Glass transition in fullerenes: Mode-coupling theory predictions

Abstract

We report idealized mode-coupling theory results for the glass transition of ensembles of model fullerenes interacting via phenomenological two-body potentials. Transition lines are found for C60, C70 and C96 in the temperature-density plane. We argue that the observed glass-transition behavior is indicative of kinetic arrest that is strongly driven by the inter-particle attraction in addition to excluded-volume repulsion. In this respect, these systems differ from most standard glass-forming liquids. They feature arrest that occurs at lower densities and that is stronger than would be expected for repulsion-dominated hard-sphere-like or Lennard-Jones-like systems. The influence of attraction increases with increasing the number of carbon atoms per molecule. However, unrealistically large fullerenes would be needed to yield behavior reminiscent of recently investigated model colloids with strong short-ranged attraction (glass-glass transitions and logarithmic decay of time-correlation functions).

Glass Transition Line in C60: A Mode-Coupling/Molecular-Dynamics Study

“…By contrast, the non-ergodicity factors, also shown in the same figure, are hardly affected by the density variation, and infact run almost superimposed on top of each other, thus predicting a glassy phase all along the isotherm T = 1200 K. These evidences support the theoretical observation that MCT predictions for glasses characterized by short-range attractions, are barely sensitive to the low-k behavior of the structure factor [21]. The non-zero ergodicity factors displayed in Figure 2 would allow us to shift to lower densities the T = 1200 K MCT vitrification threshold, causing a net bending of the glass transition line, even more pronounced than that predicted in ref [19]. Although this feature would indicate an enhancement of the attraction-driven properties of the glass phase, the tendency to phase separate of our sample detected during MD simulations prompts us to some caution as far as any definite conclusion about this point is concerned.…”

“…On the whole, we judge the agreement between theory and simulations quite satisfactory, especially if we take into account that all data recorded in Figure 7 have been obtained by pushing the integral equation scheme toward "extreme conditions", as far as the regime in which such tools are known to give the best performances is concerned. Figures 5 and 7 document the good agreement between present simulation results, our thoretical predictions, and those obtained by Greenall and Voigtmann [19], equally from the point of view of MCT transition threshold, and at the level of input structure factor calculations. Our evidences indirectly support the conclusions drawn in ref [19] that, in the framework provided by the modecoupling theory, and in the thermodynamic region T 3000 K, the attractive part of the Girifalco potential is short-range enough to begin to influence the approach to the structural arrest of the system.…”

“…As a consequence, we have deduced in refs [2,3] that the hard-sphere behavior plays the main role in determining the structure of the C 60 glass, which hence results essentially repulsion-driven in nature. In order to reconcile the attractive nature of the MCT glass discussed in ref [19] with the results of refs [2,3] it is worth observing in Figure 5 that in the low temperatures regime the bending of the MD curve is milder, with respect to the MCT predictions. In this case, it could be possible that, on lowering the temperature further, also the glass observed in our previous studies would display a more pronounced attraction-driven effects.…”

“…On the other hand, the arguments put forward in ref [19] hinge on two approximate liquid state approaches, like the HNC and the PY theories, and on a previous analysis carried out by the same authors [21], about the (weak) sensitivity of MCT predictions to the S(k) behaviour in the lowk region, below the first diffraction peak. This scenario motivates in our opinion an investigation of MCT predictions implemented through the use of accurate structure factors.…”

“…Besides our simulations investigations [2,3], the study of the glass transition line in the Girifalco model has been recently addressed by Greenall and Voigtmann [19]. In ref [19] these authors carry out ideal MCT calculations, using as input data for the theory the static structure factors S(k) obtained from the Hypernetted Chain (HNC) and Percus-Yevick (PY) liquid state theories [20].…”