Nonlinear energy response of glass forming materials

Abstract

A theory for the nonlinear energy response of a system subjected to a heat bath is developed when the temperature of the heat bath is modulated sinusoidally. The theory is applied to a model glass forming system, where the landscape is assumed to have 20 basins and transition rates between basins obey a power law distribution. It is shown that the statistics of eigenvalues of the transition rate matrix, the glass transition temperature T g , the Vogel-Fulcher temperature T 0 and the crossover temperature T x can be determined from the 1st-and 2nd-order ac specific heats, which are defined as coefficients of the 1st-and 2nd-order energy responses. The imaginary part of the 1st-order ac specific heat has a broad peak corresponding to the distribution of the eigenvalues.When the temperature is decreased below T g , the frequency of the peak decreases and the width increases. Furthermore, the statistics of eigenvalues can be obtained from the frequency dependence of the 1st-order ac specific heat. The 2nd-order ac specific heat shows extrema as a function of the frequency. The extrema diverge at the Vogel-Fulcher temperature T 0 . The temperature dependence of the extrema changes significantly near T g and some extrema vanish near T x .

Free energy landscape theory of glass transition and entropy

“…They showed that the anomalous behavior of the specific heat can be understood as a transition from the annealed average at high temperatures to the quenched average at low temperatures [13,14] and that the cooling rate dependence of the glass transition temperature can be accounted by the FEL frame work [15]. Recently, non-linear energy response of glass forming materials has been analyzed on the basis of the FEL picture and it is shown that the second order ac specific heat will exhibit characteristic behaviors related to the glass transition temperature and the Vogel-Fulcher temperature [16].…”

Thermodynamic Study of Simple Molecular Glasses: Universal Features in Their Heat Capacity and the Size of the Cooperatively Rearranging Regions

“…Therefore, the glass transition is usually recognized as a ''dynamic phase transition'' and T 0 is sometimes called an ''ideal glass transition temperature.'' There are many models to explain the divergence of the viscosity at T 0 , e.g., the entropy theories [1][2][3][4], free volume theories [5,6], free energy landscape scenarios [7][8][9][10][11], mode-coupling theories [12,13], and replica theory [14], etc. It is, of course, impossible to reach T 0 experimentally because the experimantal time scale is 10 6 s at longest.…”

Dynamic heat capacity in spatially restricted systems with phase transition

“…Notably that the linearization of the free energy (2) above T ∞ c leads to the harmonic (therefore, symmetric) potential with the second and the fourth eigenvalue given in equation ( 21). For the harmonic potential only the second eigenvalue contributes to the dynamic heat capacity, i.e., above T ∞ c in the bulk limit a = 0 and b = 0 in equation (17). However, the linearization below T ∞ c leads to the shifted harmonic (asymmetric) potential with the first eigenvalue 2α(T ∞ c − T ).…”

“…The static heat capacity (7) may be written in terms of a and b as C 0 = V 2 T 2 (a + b). The frequency-dependent heat capacity (17) indicates that generally for the symmetric (even) potential the timescales of the energy relaxation are defined by the even eigenvalues of the Fokker-Planck operator. For the harmonic potential only the second eigenvalue of the appropriate Fokker-Planck operator contributes to the relaxation process [14].…”

“…Several theoretical approaches for the formulation of the dynamic specific heat were suggested, e.g., generalized hydrodynamics [13], the fluctuation-dissipation theorem [14], projection operator formalism [15], the generalized constitutive equation [16], the framework of the free energy landscape [17], or non-equilibrium considerations [18]. Simulations have been able to reproduce various qualitative features [15,19].…”