Statistical Mechanics of the Glass Transition in One-Component Liquids with an Anisotropic Potential

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with an anisotropic potential. This system is interesting per se and as a model of liquids such as glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.

Figure 1

Potential curves for particle pairs with two spins, one spin, or no spin in the favored position (continuous blue line, dashed green line, or dotted red line, respectively). Inset: The measured energies of particle pairs, falling in three distinct ranges with gaps between them, allowing us to define the quasiparticles. The peak in each colored curve corresponds to the minimum in the main figure.

Figure 2

An example of an $n$ star with $n=5$, $i=2$, $j=2$, and $k=1$. The central particle has a spin with the favored orientation with respect to edges 1 and 2. Thus, these edges can be either blue or green, and this central spin cannot be favored with respect to any other edge. In the interesting range of temperatures, we observe 36 $n$ stars with $4\le i+j+k\le 6$.

Figure 3

Direct numerical simulation of the constraint (6).

Figure 4

Comparison of the direct numerical simulations to the theoretical prediction. Shown are the mol fractions $c_k$, with $k=0$ (dashed-dotted red line), $k=1$ (dashed green line), and $k=2$ (continuous blue line). One sees the point of departure of the direct numerical simulations from equilibrium (the point of jamming) which is estimated to be about $T=0.17$. Inset: The same concentrations on a logarithmic scale.

Figure 5

Comparison of the measured spin rotational relaxation times ${\tau }_{\alpha }$ (points) with the relaxation time predicted by Eq. (10) (continuous line).