Comment on “Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems” [J. Chem. Phys. 133, 164503 (2010)]

Abstract

A critical examination shows that the specific heat and shear modulus relaxation spectra do not support the notions of continuously broken ergodicity and loss of configurational contribution on isothermal glass transition, nor does the long-known result that Cp → 0 as T → 0 K prove that Sconf → 0. Spectra show variation of the real and imaginary components due to phase lag and not due to loss of configurational degrees of freedom. The high-frequency shear modulus, G∞, of glass increases with time as its fictive temperature decreases and dG∞/dT decreases when a glass forms.

Specific heat relaxation-based critique of isothermal glass transition, zero residual entropy and time-average formalism for ergodicity loss

“…Numerous comparisons of the specific heat, dielectric and ultrasonic relaxation spectroscopy results by others [36,37] have confirmed their conclusions [28,29]. But, Mauro et al [26,27] interpreted Birge and Nagel's study as an experiment for observing structural freezing and unfreezing, and disregarded the significance of C p and the loss tangent, tan ı (= C p /C p ) while asserting that (i) the C p spectra shows a continuous loss of C p and S conf with decreasing t obs , (ii) the C p spectra is a feature of isothermally occurring glass transition, and (iii) the decrease in C p , the loss of ergodic behavior and of S conf , the liquid-glass transition and attainment of an apparently non-equilibrium state by cooling and/or reducing t obs are manifestations of the same occurrence. Those who are aware of Birge and Nagel and others [30][31][32][33][34][36][37][38][39][40][41][42] analyses of the C p and C p spectra for obtaining ˇ and , and comparison of the results obtained against other spectroscopy results would be surprised by the assertion [26]: "Thus, application of ergodic statistical mechanics cannot account for the dependence of heat capacity on observation time, an experimentally proven effect determined by Birge and Nagel."…”

“…Unfortunately, Mauro et al [26,27] treated the characteristic time scales of (small) external perturbations as if they are temperature oscillations corresponding to the cooling/heating rates that cause kinetic freezing/unfreezing, and they compared them both with the internal time scale of the system while it is obvious that these two have to be distinguished and compared separately. Moreover, one is led to untenable situations when different definitions of the external time scale are used.…”

“…Third: Bearing in mind that there is no experimental proof for partial ergodicity and time-dependent decrease in ergodicity and entropy -and there have been numerous objections [10][11][12][13][14][15][16][18][19][20][21][22]59,60] to these notions -it is worth inquiring what really led to these notions [26,27]: We find that the loss of ergodic behavior, the loss of S conf and decrease in C p , failure of a system to reach equilibrium, and the respective time and temperaturedependences of all were seen, first, as manifestations of the phenomena of liquid-glass transition [26,27]. Thereafter, all the preceding five manifestations were linked, (i) to the hypothesis that the state of a system is trapped in a specific description of configurational minimum in the potential energy landscape by using a set of conditional probabilities, (ii) to an interpretation of ergodicity out of several disputed ones (some arguing that liquid-glass transition is not an ergodic to non-ergodic transition) and, (iii) to the view that the ratio D is equal to /t obs with t obs = 1/ω, which is not the original definition of D, and ignoring the C p peak.…”

“…It does not mean that Brownian motion of some of the molecules has become kinetically frozen. It is strange that unlike the original authors [28,29], Mauro et al [26,27] treated external perturbations like temperature oscillations equivalent to the cooling rates during kinetic freezing, and compared them both with the internal time scale of Brownian diffusion in the system. One cannot escape the conclusion that decreases in C p as "proof" [26] for loss of configurational C p , S conf and ergodicity on the time scale of was based on misinterpretation of the spectra.…”

“…Therefore, it does not seem meaningful to describe glass formation as a process of continuously broken ergodicity with loss of entropy. A critique of their interpretation of C p relaxation spectra was given in a Comment, and they provided a reply [27]. Both may be consulted.…”