The PLUMED consortium (2019). Promoting transparency and reproducibility in enhanced molecular simulations. Nature Methods, 16(8), 670-673. https://doi.

If liquids, polymers, bio-materials, metals and molten salts can avoid crystallization during cooling or compression, they freeze into a microscopically disordered solid-like state, a glass 1,2 . On approaching the glass transition, particles become trapped in transient cages-in which they rattle on picosecond timescales-formed by their nearest neighbours; the particles spend increasing amounts of time in their cages as the average escape time, or structural relaxation time τ α , increases from a few picoseconds to thousands of seconds through the transition. Owing to the huge difference between relaxation and vibrational timescales, theoretical 3-9 studies addressing the underlying rattling process have challenged our understanding of the structural relaxation. Numerical 10-13 and experimental studies on liquids 14 In the solid state atoms oscillate with mean square amplitude u 2 around their equilibrium positions (henceforth to be referred to as the Debye-Waller (DW) factor). With increasing temperature, solids meet different fates depending on the structural degree of order. In the crystalline state the ordered structure melts at T m , whereas in the amorphous state the disordered structure softens at the glass transition temperature T g , above which flow occurs with viscosity η. The empirical law T g 2/3T m (refs 1,2,7) suggests that the two phenomena have a common basis. In fact, this viewpoint motivated extensions to glasses 24 of the Lindemann melting criterion for crystalline solids 22 and pictures the glass transition as a freezing in an aperiodic crystal structure (ACS) 5 .According to the ACS model, the viscous flow is due to activated jumps over energy barriers E ∝ k B T a 2 / u 2 , where a is the displacement to overcome the barrier, k B is the Boltzmann constant and T the temperature. The usual rate theory leads to the Hall-Wolynes (HW) equation 5,21 τ α , η ∝ exp(a 2 /2 u 2 ). u 2 is the DW factor of the liquid, that is, it is the amplitude of the rattling motion within the cage of the surrounding atoms. This vibrational regime is assumed to occur on short timescales largely separated by those of the brownian diffusion. The ACS model is expected to fail when τ α becomes comparable to the typical rattling times corresponding to picosecond timescales, a condition that is met at high temperatures (for example, in selenium it occurs at T m + 104 K (ref. 14)).

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbors, whereas its average escape time, the structural relaxation time tau(alpha), increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between tau(alpha) and the rattling amplitude, expressed by the Debye-Waller factor, was carried out. Molecular-dynamics simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density rho, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The present simulations, together with MD studies on other glassformers, evidence the scaling between the structural relaxation and the caged dynamics. An analytic model of the master curve is developed in terms of two characteristic length scales a(2) (1/2) and sigma(a(2) ) (1/2), pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply tau(alpha) divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. In particular, the density scaling of the length scales a(2) (1/2), sigma(a(2) ) (1/2) proportional to rho(-1/3) is shown to be not supported by the present simulations. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.

We numerically study the dependence of the dynamics on the range of interaction Delta for the short-range square well potential. We find that, for small Delta, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive-glass line and the liquid-gas line does not depend on Delta. This proves that, in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.