Vanishing of configurational entropy may not imply an ideal glass transition in randomly pinned liquids

Ozawa et. al [1] presented numerical results for the configurational entropy density, $s_c$, of a model glass-forming liquid in the presence of random pinning. The location of a"phase boundary"in the pin density ($c$) - temperature ($T$) plane, that separates an"ideal glass"phase from the supercooled liquid phase, is obtained by finding the points at which $s_c(T,c) \to 0$. According to the theoretical arguments by Cammarota et. al. [2], an ideal glass transition at which the $\alpha$-relaxation time $\tau_\alpha$ diverges takes place when $s_c$ goes to zero. We have studied the dynamics of the same system using molecular dynamics simulations. We have calculated the time-dependence of the self intermediate scattering function, $F_s(k,t)$ at three state points in the $(c-T)$ plane where $s_c(T,c) \simeq 0$ according to Ref. [1]. It is clear from the plots that the relaxation time is finite [$\tau_\alpha \sim \mathcal{O}(10^6)]$ at these state points. Similar conclusions have been obtained in Ref.[3] where an overlap function was used to calculate $\tau_\alpha$ at these state points.

Vanishing of configurational entropy may not imply an ideal glass transition in randomly pinned liquids.Saurish Chakrabarty * ,Smarajit Karmakar † , and Chandan Dasgupta * ‡ * Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, 560012, India, † TIFR Center for Interdisciplinary Science, Narsingi, Hyderabad 500075, India, and ‡ Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India.
Submitted to Proceedings of the National Academy of Sciences of the United States of America Ref. [1] presents numerical results for the configurational entropy density, sc, of a model glass-forming liquid in the presence of random pinning.The location of a "phase boundary" in the pin density (c) -temperature (T ) plane, that separates an "ideal glass" phase from the supercooled liquid phase, is obtained by finding the points at which sc(T, c) → 0. According to the theoretical arguments in Ref. [2], an ideal glass transition at which the α-relaxation time τα diverges takes place when sc goes to zero.
We have studied the dynamics of the same system using molecular dynamics simulations.In Fig. 1 (left panel), we show the time-dependence of the self intermediate scattering function, Fs(k, t), calculated at three state points in the (c − T ) plane where sc(T, c) ≃ 0 according to Ref. [1].It is clear from the plots that the relaxation time is finite [τα ∼ O(10 6 )] at these state points.Similar conclusions have been obtained in Ref. [3] where an overlap function was used to calculate τα at these state points.
If the numerical results for sc(T, c) reported in Ref. [1] are correct, then our explicit demonstration of the fact that τα does not diverge at state points where sc = 0 according to Ref. [1] would have fundamental implications for theories of the glass transition.The well-known Random First Order Transition (RFOT) description of the glass transition is based on the premise that the vanishing of sc causes a divergence of τα.The prediction [2] of the existence of a line of ideal glass transitions in the (c − T ) plane for randomly pinned liquids was based on the RFOT description.Our results for τα would imply that the RFOT description is not valid for pinned liquids.Since a divergence of τα is the defining feature of the glass transition, the entropy-vanishing "transition" found in Ref. [1] at which τα does not diverge should not be called a glass transition.
where k is the wavenumber at the first peak of the static structure factor, . . .implies an average over thermal history, [. ..] represents an average over different realization of the pinned particles, and Nm is the number of unpinned mobile particles.Results are shown for three state points at which sc(T, c) ≃ 0 according to Ref. [1].The α-relaxation time τα is calculated using a fit to the form Fs(k, t) If, on the other hand, we disregard the results for sc(T, c) reported in Ref. [1], then all available data for the dynamics of this system [3,4] can be understood from a description that is consistent with RFOT and the requirement that the presence of pinning must decrease sc.This description [3] is based on the assumption that sc(T, c) = B(c)sc(T, 0) for small values of c, where B(c) is a smooth function that decreases with increasing c, with B(0) = 1.This assumption, when com-bined with the Adam-Gibbs relation, predicts that the logarithm of τα(T, c) should be a linear function of 1/[T sc(T, 0)] with a coefficient that increases with c.The data for τα(T, c) in Ref. [3] are consistent with this prediction (see Fig. 1, right panel).We have verified that the data for τα(T, c) and sc(T, 0) in Ref. [1] are also consistent with this prediction (see Fig. 1, middle panel).This observation provides a way of reconciling the behavior of τα(T, c) with RFOT, but it also implies that the data for sc(T, c) reported in Ref. [1] are not quantitatively accurate.