The T-shaped anisotropic molecule model: a unique perspective of the glass transition and gelation in low valence, directional, network forming liquids

Abstract

Glass and gel formers exhibit unusual mechanical characteristics and amorphous phases which are highly dependent on their thermal history. We introduce a lattice model with T-shaped molecules that exhibits glassy and gel-like states without introducing artificial frustration. This system has a large number of degenerate energy minima separated by small barriers leading to a broad, kinetically-explored landscape. It particularly replicates valence-limited materials, which can form self-assembled materials with highly controlled physical properties. Despite its remarkable simplicity, this model reveals some of the fundamental kinetic and thermodynamic properties of the glass transition and of gel formation. A dearth of low temperature experimental and simulation measurements has inhibited investigation in this field. We overcome this difficulty by using a modified Metropolis Monte Carlo method to quickly provide equilibrium samples. Then kinetic Monte Carlo techniques are used to explore the properties of the equilibrium system, providing a touchstone for the non-equilibrium glassy states. Fully-dense simulation samples reveal a fragile-to-strong crossover (FSC) near the mean-field (MF) spinodal. At the FSC, the relaxation time returns to Arrhenius behavior with cooling. There is an inflection point in the configurational entropy. This behavior resolves the Kauzmann Paradox which is a result of extrapolation from above the inflection point. In contrast, we find that the configurational entropy remains finite as the temperature goes to zero. We also observe different kinetics as the system is quenched below the FSC, resulting in non-equilibrium, amorphous states with high potential energy persisting for long periods of time. Simulation samples remain at non-equilibrium conditions for observation times exceeding those permitting complete equilibration slightly above the FSC. This suggests the FSC would often be identified as the glass transition without indication that there is true arrest or a diverging length scale. Indeed, our simulations show these samples do equilibrate if sufficient time is allowed. To elucidate the complex, interdependent relation time and length scales at the FSC will require careful consideration of the spatial-dynamic heterogeneity. Dynamic mean-field simulations at high density and in the solvated regime reveal a rich range of morphological features. They are consistent with simulated and experimental results in colloidal systems. Stability limits of decreasing length scales beneath the phase separation bimodal coincide into a single curve, which terminates at the fully-dense MF spinodal, suggesting that gelation and vitrification are the same phenomena. Our work indicates that gelation is, therefore, a result of phase separation arrested by a glass transition.