A Theory of High-Temperature Arrhenius Relaxation in Two-Dimensional Glass-forming Liquids

The relaxation time of dense liquids is Arrhenius at a wide range of temperatures, including glass-forming liquids above the onset temperature $T_o$ for glassy dynamics. Below $T_o$, one may invoke dynamical facilitation theory to understand dynamics via spatially localized excitations, which drive relaxation through the facilitation of nearby excitations. In this talk, we discuss a theory for Arrhenius relaxation above $T_o$, where excitations emerge without facilitation as localized pure-shear events [1]. The theory builds upon recent work [2] that describes the onset of glassy dynamics as a melting transition, where supercooled liquids lose their inherent rigidity due to excitation softening. In two dimensions (2D), this scenario is similar to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario for melting in 2D solids [3]. The KTHNY scenario implies critical fluctuations near $T_o$ that renormalize the shear modulus, which affects the excitation activation energy $E_a$. We model how excitations emerge without facilitation via a Poisson point process, allowing us to connect $E_a$ to the Arrhenius relaxation time and derive the logarithmic finite-size scaling in diffusivity. The predicted activation energies agree with those obtained from simulations of 2D model glass formers. These results provide a basis for localized excitations appearing above but close to $T_o$ and strengthen the role of such excitations for broadly understanding dynamics in glass-forming liquids.

[1] Hasyim, M. R., and Mandadapu, K. K., J. Chem. Phys. 155 (4), 44504, (2021)

[2] Fraggedakis, D., Hasyim, M. R., and Mandadapu, K. K., arXiv:2204.07528, (2022)

[3] Nelson, D.R., and Halperin, B.I., Phys. Rev. B 19, 2457, (1979)