Brillouin scattering from bulk polybutadiene: distribution of relaxation times versus single relaxation time approach

Why the Brillouin Light Scattering Relaxation Times of Molten Zinc Chloride Are Shorter and Weaker in Temperature Dependence than the Structural Relaxation Times from Depolarized Light and Neutron Spin Echo Spectroscopy

A longstanding problem in the Brillouin light scattering (BLS) study of polymers is the relaxation times τ_BLS(T) being more than an order of magnitude shorter than the α-relaxation times τ_α(T) determined by dielectric, depolarized light scattering (DLS), and molecular dynamics simulations. In tackling the problem, τ_BLS(T) was identified with the relaxation time τ₀(T) of the primitive relaxation in the coupling model, which can be calculated from τ_α(T) and the stretch exponent β_K of the Kohlrausch correlation function for the α-relaxation.. The problem was solved by finding that indeed τ₀(T) is in good agreement with τ_BLS(T). A recent work performed the neutron spin echo study of the structural α-relaxation of the network ionic liquid ZnCl₂ and found the same anomaly as polymers. The α-relaxation time τ_NSE(T) from neutron spin echo (NSE) as well as the α-relaxation time τ_DLS(T) from DLS of ZnCl₂ are much longer than τ_BLS(T) from BLS obtained before by several research groups. The finding of the same anomaly in ZnCl₂ and polymers with very different chemical and physical structures offers an opportunity to critically test the explanation given before. The test was carried out by calculating the primitive relaxation times τ_0,DLS(T) and τ_0,NSE(T) from τ_DLS(T) and τ_NSE(T), respectively, in zinc chloride. Good agreements of τ_BLS(T) from BLS with τ_0,DLS(T) and τ_0,NSE(T) were found and thus the explanation given for polymers remains valid for ZnCl₂. The test was extended to glycerol by comparing τ_BLS(T) with τ_0,ICNS(T) and τ_0,CNS(T) calculated from the α-relaxation time τ_ICNS(T) and τ_CNS(T) from incoherent and coherent neutron scattering, respectively. There is good agreement between τ_BLS(T) and τ_0,ICNS(T) in glycerol. There is also semiquantitative agreement of τ_BLS(T) with τ_0,DS(T) from dielectric spectroscopy as well as τ_0,CNS(T). Thus, the explanation for polymers is verified in the two very different glass formers, ZnCl₂ and glycerol, and it is an advancement in the application of BLS to study the dynamics of glass formers.

Mechanical relaxation and the notion of time-dependent extent of ergodicity during the glass transition

A postulate that ergodicity and entropy continuously decrease to zero on cooling a liquid to a glassy state was used to support the view that glass has no residual entropy, and the features of mechanical relaxation spectra were cited as proof for the decrease. We investigate whether such spectra and the relaxation isochrones can serve as the proof. We find that an increase in the real component of elastic moduli with an increase in spectral frequency does not indicate continuous loss of ergodicity and entropy, and the spectra do not confirm isothermal glass transition or loss of entropy. Variation in ergodicity and entropy with the spectral frequency has untenable consequences for both thermodynamics and molecular dynamics and implies that, despite a broad distribution of its relaxation times, an equilibrium liquid can be considered as always ergodic. Perturbation from equilibrium used to obtain a spectrum does not have the effect of dynamic freezing and unfreezing, and Maxwell-Voigt models for the mechanical response function have neither the characteristic irreversibility of liquid-glass transition nor are commutable to ergodicity or entropy.