Similarity of relaxation in supercooled liquids and interacting arrays of oscillators

Abstract

Dielectric relaxation and dynamic light scattering of small molecule glass-forming liquids invariably show that the fractional exponent beta(alpha) of the Kohlrausch-Williams-Watts correlation function, exp[-(t/tau(alpha))(beta(alpha))], used to fit the alpha-relaxation data is temperature dependent, increasing towards the value of unity as temperature is raised and the relaxation time tau decreased. Comparing different glass formers, another property is the existence of a correlation between the value of (1-beta(alpha)) at the glass temperature, T(g), and the T(g)-scaled temperature dependence of tau(alpha). We analyze a system of interacting arrays of globally coupled nonlinear oscillators. Each array has its oscillators coupled among themselves with a coupling strength K. The coupling between arrays is characterized by the interarray coupling strength K'. The decay of the phase coherence r for each array is slowed down by the interarray coupling and its time dependence is well approximated at sufficiently long times by exp[-(t/tau)(beta)]. For a fixed K', on increasing K the results exhibit a decrease of tau and a concomitant increase of beta, similar to the properties of dielectric relaxation and dynamic light scattering of glass-forming liquids on increasing temperature. For each K' we define K(g) to be the value of K at which tau is equal to an arbitrarily chosen long time. We find that beta(K(g)) is correlated with the K(g)-scaled K dependence of tau. The results obtained in this manner at various fixed values of K' reproduce the relaxation properties and temperature dependencies of strong, intermediate, and fragile glass-forming liquids.

Temperature and Density Effects on the Local Segmental and Global Chain Dynamics of Poly(oxybutylene)

“…While the shape of the normal mode peak reflects in part the sample's polydispersity (M w /M n = 1.10), the breadth of the segmental mode depends on the chemical structure of the repeat unit 71 . It is expected empirically 76 and on theoretical grounds 39,40 that the sensitivity of relaxation times to temperature will correlate with the breadth of the dispersion. Thus, the inference from Figure 5 is that the separation of the normal and segmental peaks should not vary strongly with T or P. To probe this in more detail, we analyze the temperature and pressure dependences of the two relaxation times.…”

Influence of thermally induced oxygen order on mobile ion dynamics inGd2(Ti0.65Zr0.35)2Moreno1, Fuentes2, Mączka3 et al. 2007Phys. Rev. B445190View full textAdd to dashboardCite

“…4 has been previously related to the existence of cooperative effects in the dynamics of hopping ions, with the fractional exponent n ͑0 ഛ n Ͻ 1͒ determined by the degree of ion-ion interactions existing in the ionic hopping process; i.e., in the absence of interactions among mobile ions ͑independent random ion hopping͒, the exponent n would be 0, while n would tend to 1 for a completely correlated ion motion. 23,24 An alternative representation of experimental conductivity data can be made by plotting the frequency dependence of the complex electric modulus, M * ͑ ͒, which is directly related to the complex conductivity as M * ͑ ͒ =1/ * ͑ ͒ = j 0 / * ͑ ͒, with 0 the permittivity of vacuum. The use of the electric modulus allows us to obtain the relaxation function ⌽͑t͒ in the time domain for the decay of the electric field inside the material under the constraint of a constant displacement vector.…”

“…7͒, as the sintering temperature is increased, can be rationalized in terms of the coupling model ͑CM͒. 24,29,30 The CM starts with the consideration of the independent hops of ions to vacant adjacent sites with exponential correlation function, ⌽͑t͒ = exp͑−t / 0 ͒, and relaxation time 0 . Such independent hops cannot occur for all ions at the same time because of ion-ion interactions and correlations.…”

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

“…Buchenau and Kahle 34 and Buchenau 35 have argued that the same result as obtained by the minimal model may be obtained by a model that attributes the damping to relaxing units distributed around the asymmetry zero with a probability proportional to their weighting factor. The Gilroy-Phillips model has also been reconsidered for the origin of the ␤-relaxation process by Coffey et al 36 Ngai and co-workers have suggested that the coupling model's [37][38][39] primitive relaxation 38 ͑the exponential relaxation of a single oscillator array, i.e., in the noninteracting case͒ is related to the JG relaxations in glasses. 27,40 The primitive relaxation rate may be calculated from the param-eters of the ␣-relaxation process, namely, the ␣-relaxation time and the Kohlrausch-Williams-Watts ͑KWW͒ stretched exponential parameter, and it has been found to be approximately the same as the JG relaxation rate.…”