Cornelius T. Moynihan

STRUCTURAL RELAXATION IN VITREOUS MATERIALS

When a liquid is subjected to a sudden change in temperature T or pressure P, its properties (volume V , enthalpy H , index of refraction n, shear viscosity v , etc.) exhibit an instantaneous, solidlike change. This is followed by a slower, liquidlike structural relaxation to new equilibrium values a t the new temperature or pressure. It is generally presumed that this structural relaxation involves some change of the average molecular configuration of the liquid. The time scale for the structural relaxation increases rapidly with decreasing temperature and increasing pressure and in the so-called glass transition region-which should be thought of as an area in the T-P plane-reaches magnitudes (seconds to days) readily perceptible to human investigators. Above the glass transition region, (i.e., a t temperatures above and pressures below) the structure rearranges promptly in response to changes in T o r P and measured properties ( H , V , n , etc.) are said to be those of the equilibrium liquid. Below the glass transition region (ix., a t temperatures below and pressures above), the structural rearrangement is kinetically arrested, measured changes in properties ( H , V , n, etc.) in response to changes in T and P d o not contain contributions from the structural rearrangement, and the material is referred to as a glass. As a consequence, there is in general a difference between the second derivatives of Gibbs free energy-namely, heat capacity Cp, the thermal expansion coefficient a, and isothermal compressibility, K-for equilibrium liquid and glass. In FIGURES 1 and 2 the time dependence of liquid properties due to the structural relaxation is shown schematically for the the isobaric response of enthalpy to temperature changes. In FIGURE 1 the system is initially a t equilibrium a t temperature To; the temperature is stepped at time t , by an amount A T . Immediately the system exhibits the solidlike enthalpy change AH, from the initial equilibrium value He, at To; this is followed by a further change with time by an amount A H , due to the structural relaxation to the equilibrium value H e , at the new temperature. The equilibrium liquid and glass heat capacities, C,, and Cpg, are then defined in terms of this experiment by

Thermodynamic determination of fragility in liquids and a fragile-to- strong liquid transition in water

If crystallization can be avoided when a liquid is cooled, it will typically form a glass. Near the glass transition temperature the viscosity increases continuously but rapidly with cooling. As the glass forms, the molecular relaxation time increases with an Arrhenius-like (simple activated) form in some liquids, but shows highly non-Arrhenius behaviour in others. The former are said to be ‘strong’ liquids, and the latter ‘fragile’,. Here we show that the fragility of a liquid can be determined from purely thermodynamic data (as opposed to measurements of kinetics) near and below the melting point. We find that for most liquids the fragilities estimated this way are consistent with those obtained by previous methods and by a new method (ref. 3 and K.I., C.A.A. and C.T.M., unpublished data) at temperatures near the glass transition. But water is an exception. The thermodynamic method indicates that near its melting point it is the most fragile of all liquids studied, whereas the kinetic approach indicates that near the glass transition it is the least fragile. We propose that this discrepancy can be explained by a fragile-to-strong transition in supercooled water near 228 K, corresponding to a change in the liquids structure at this point.

Non-exponential structural relaxation, anomalous light scattering and nanoscale inhomogeneities in glass-forming liquids

Abstract Light scattering from glass-forming liquids exhibits an anomalous time dependence in the glass transition region, e.g. maxima in the scattering intensity versus temperature curves during heating. It is shown that this behavior is consistent with the presence of nanoscale inhomogeneities (density fluctuations) which relax at different rates. It is suggested that this could be the source of non-exponential structural relaxation kinetics. An expression relating the size of these regions to structural relaxation kinetic parameters has been developed and predicts sizes in excellent agreement with those determined by other methods.

Prigogine–Defay ratio for systems with more than one order parameter

The Prigogine–Defay ratio, Π≡ΔCp Δκ/TV (Δα)2, has been derived for systems whose states need to be specified in terms of a number of order parameters z by considering the conditions of tangency of the equilibrium free energy surface and the free energy surface for constant values of the order parameters. It is shown that Π?1. The equality applies for the case of a single order parameter or for the case of more than one order parameter which satisfies the constraint (∂V/∂zi)/ (∂S/∂zi) = (∂V/∂zk)/(∂S/∂zk). The inequality applies for the case of more than one order parameter which does not satisfy this constraint. The relevance of the Prigogine–Defay ratio to the kinetics of the structural relaxation in glass is discussed.

Comparison of Shear and Conductivity Relaxation Times for Concentrated Lithium Chloride Solutions

Shear viscosity measurements over the temperature interval 23 –− 124 °C (5×10−2– 108 P) and shear impedance measurements at 88 MHz over the interval −75–−130°C have been performed for concentrated aqueous lithium chloride solutions in the concentration range R=4.49 – 5.77 where R is the mole ratio of water to salt. Average shear relaxation times, 〈 τs 〉, have been calculated from these results and compared with average conductivity relaxation times, 〈 τσ 〉, reported previously by Moynihan, Bressel, and Angell. 〈 τs 〉 and 〈 τσ 〉 are within 30% of one another at the low viscosity end ( ∼104 P) of the range of comparison, but at higher viscosities the 〈τs 〉/〈τσ 〉 ratio becomes significantly larger than unity (2–3 at the highest viscosities for which data are available). Estimated 〈τs 〉/〈τσ 〉 ratios for other ionic liquids suggest that the occurrence of 〈τs 〉/〈τσ 〉 ratios greater than unity at high visosities may be a common phenomenon. Description of the shear relaxation process for concentrated LiCl—H2O sol...

Intrinsic and impurity infrared absorption in As2Se3 glass

Abstract A quantitative study of infrared absorption in the 250–4000 cm −1 region of As 2 Se 3 glasses doped with small amounts of As 2 O 3 or purified by various procedures has been carried out with particular attention to absorption in the wavelength regions of the CO 2 and CO lasers. The dependence of the relative intensities of the oxide impurity bands in the 650–1340 cm −1 region on the total amount of As 2 O 3 added to the glass indicates the existence of three distinct oxide-impurity species. A number of higher-frequency impurity bands which are due to the presence of hydrogen in the glass and whose intensities are highly dependent on the glass-melting conditions have been observed and classified. Intrinsic multiphonon absorption in the 400–1100 cm −1 region has been interpreted in terms of combination and overtone bands of the two highest-frequency fundamental vibrational modes. Absorption coefficients of As 2 Se 3 glass in the 920–1090 cm −1 CO 2 laser region are limited by intrinsic multiphonon absorption to values of around 10 −2 cm −1 . The lowest absorption coefficients measured in the 1700–2000 cm −1 CO laser region were around 2 × 10 −3 cm −1 and may contain contributions from hydrogen-impurity bands.

Description and analysis of electrical relaxation data for ionically conducting glasses and melts

In recent years there has arisen considerable controversy and some confusion with regard to analysis and interpretation of electrical relaxation data for ionically conducting glasses and melts. For example, there are questions as to whether the data are better described using the electric modulus formalism with a KWW distribution of relaxation times or by using a Jonscher power law fit to the frequency dependent electrical conductivity. This topic is reviewed and discussed, with some emphasis placed on the degree to which information on the electrical relaxation mechanisms and the microscopic sources of nonexponential relaxation can be extracted from data presentation and analysis using the electric modulus formalism with a well behaved electric field relaxation function.

Effect of thermal history on conductivity and electrical relaxation in alkali silicate glasses

Electrical conductivity σ0 and electric field relaxation measurements have been carried out as a function of thermal history for two alkali silicate glasses, Na2O3SiO2 and K2O3SiO2. Specimens of each glass with three different thermal histories, two of the anneal-and-quench type and one of the rate-cool type, were studied. The average structural or fictive temperature Tf of each of the specimens was characterized by measuring their indices of refraction. Effects of thermal history on σ0 and its activation enthalpy Hσ∗ were in accord with results of previous investigators. That is, for a given type of thermal history σ0 was lower and Hσ∗ higher the lower Tf. In addition it was found that for two specimens with the same Tf or index of refraction but different thermal histories the rate-cooled specimen exhibited a lower conductivity than the annealed-and-quenched specimen, in accord with the results of Ritland. The distribution of relaxation times τσ for decay of the electric field due to ionic migration was found to be due primarily to a distribution in the pre-exponential term ln τσ∗ in the equation ln τσ = ln τσ∗ + H∗/RT; the distribution in H∗ was extremely narrow. Differences in thermal history caused small differences in the distribution of τσ, but no difference in the average activation enthalpy 〈H∗〉 for τσ. From this result it appeared that the dependence of the conductivity activation enthalpy Hσ∗ on thermal history was due to the effect of thermal history on the temperature dependence of the distribution in τσ.

Analysis of electrical relaxation in glasses and melts with large concentrations of mobile ions

Abstract Various analyses of or fits to electrical relaxation data for a model Li 2 OAl 2 O 3 2SiO 2 glass s were tried. These included three-parameter fits using Kohlrausch-Williams-Watts (KWW) and Cole-Davidson (CD) distributions of electric field relaxation times, along with a four-parameter σ ′ ( ω n ) fit using the distribution implicitin the Jonscher expression for the frequency dependence of the real part of the complex conductivity, σ ′ = σ + Aω n . In the frequency range 10 −2 ≤ ω τ > ≤10 2 , where is the mean electric field relaxation time, the KWW firt was best, the σ ′ ( ω n ) fit second best and the CD fit the worst. Because the σ ′ ( ω n ) fit predicts qualitattively incorrect relaxation behavior at low frequencies, it is suggested that this method of data analysis not be used. It was noted that the dependence of σ ′ on ω 1 observed for ionically conducting solids at very high frequencies or very low temperatures make a nearly negligible contribution to the relaxation of the electric field.

Linear and non-linear structural relaxation

Abstract The widely applied Tool-Narayanaswamy (TN) model for structural relaxation associated with the glass transition is discussed and critiqued. The TN model accounts for the non-exponential character of the structural relaxation by effectively invoking a distribution of relaxation times and for the non-linear character by allowing the relaxation times to depend both on temperature and structure. The model successfully explains qualitatively all of the at first glance unusual features of experimental structural relaxation results and usually also gives a good quantitative fit to such data, provided that the system is not extremely far out of equilibrium. Analysis of some rate cooling/rate heating enthalpy structural relaxation experiments, however, reveals some deficiencies in the TN model. In particular, the model appears to fail a critical test in which the TN analysis of non-linear relaxation experiments on glycerol cannot be reconciled with the results of linear ac calorimetry relaxation experiments on the same material.