Shear and Structural Relaxation in Molten Zinc Chloride

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.

Neutron Spin-Echo Studies of the Structural Relaxation of Network Liquid ZnCl2 at the Structure Factor Primary Peak and Prepeak

Using neutron spin-echo spectroscopy, we studied the microscopic structural relaxation of a prototypical network ionic liquid ZnCl₂ at the structure factor primary peak and prepeak. The results show that the relaxation at the primary peak is faster than the prepeak and that the activation energy is ∼33% higher. A stretched exponential relaxation is observed even at temperatures well-above the melting point T_m. Surprisingly, the stretching exponent shows a rapid increase upon cooling, especially at the primary peak, where it changes from a stretched exponential to a simple exponential on approaching the T_m. These results suggest that the appearance of glassy dynamics typical of the supercooled state even in the equilibrium liquid state of ZnCl₂ as well as the difference of activation energy at the two investigated length scales are related to the formation of a network structure on cooling.

Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: the comparative role of configurational entropy and elasticity

We compute the temperature-dependent barrier for α-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition (RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes (Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 2990), which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko (J. Chem. Phys. 2013, 138, 12A534), which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance--a kinetic quantity--from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. (Science 2005, 310, 1797) procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.

Microscopic calculation of the free energy cost for activated transport in glass-forming liquids

Activated transport in liquids--supercooled liquids in particular--occurs via mutual nucleation of alternative, aperiodic minima of the free energy. Xia and Wolynes [Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000)] have made a general argument that at temperatures near the ideal glass transition, the surface penalty for this kind of nucleation is largely determined by the temperature and the logarithm of the size of the vibrational fluctuation of rigid molecular units about the local minimum. Here, we independently show how to estimate this surface tension and, hence, the activation barrier for the activated transport for several actual liquids, using their structure factors and knowledge of the finite-frequency elastic constants. In this estimate, the activation free energy, while depending on the configurational entropy, also depends on the elastic modulus as in the "shoving" models. The resulting estimates are however consistent with the estimate provided by Xia and Wolynes' argument near the glass transition and, in addition, reflect the barrier softening effects predicted earlier for fragile substances.

Glass Transition and Ultrasonic Relaxation in Polystyrene

We present measurements of the glass transition and the ultrasonic relaxation modulus in a series of monodisperse polystyrenes. The temperature dependence of the modulus was analyzed using Havriliak-Negami relaxation model (HN) and Vogel-Tammann-Fulcher equation (VTF) for the relaxation time. The results allowed us to determine the fragility index, m, which decreases with increasing molecular weight, Mn. Furthermore, the relaxation time was found to saturate at high molecular weights and varies as Mnp, in the low molecular weight region. The exponent is p≈2 at high temperatures and p ≈ 7 at low temperatures close to Tg.

Brillouin scattering study of molten zinc chloride

Polarized and depolarized Brillouin scattering experiments on molten ZnCl2 were performed between 300 and 600 degrees C in different geometries. VV spectra measured in backscattering and small angle scattering were analyzed with conventional viscoelastic theory using either a Debye or a Cole-Davidson model for the memory function. We also analyzed in the same way the temperature dependence of the transverse Brillouin lines detected in a 90 degrees VH geometry. We show that the Cole-Davidson memory function yields a consistent interpretation of all the spectra. The resulting shear and longitudinal relaxation times are equal within their error bars, and are about 2.5 times smaller than the alpha relaxation time previously determined. The static shear viscosity values deduced from the analysis of the propagating transverse waves agree, at all temperatures, with the measured viscosity values.