Deviations from thermally activated and from exponential response are typical features of the vitrification phenomenon and previously have been studied using viscoelastic, dielectric, calorimetric, optical, and other techniques. Linear response data from literature on about 70 covalent glass formers, ionic melts, supercooled liquids, amorphous polymers, and glassy crystals are surveyed. Except for orientational glasses and monohydric aliphatic alcohols a distinct but broad correlation of non‐Debye behavior with non‐Arrhenius relaxations is found. Within the broad trend several groups of materials, distinguished by their respective molecular complexity, can be identified and are shown to exhibit narrow correlations. At a given degree of deviation from Arrhenius behavior externally imposed stresses are relaxed with a departure from exponential behavior which is stronger the more the molecular or atomic subunits of the glassforming material are interconnected with each other.

Nonexponential relaxations in strong and fragile glass formers

An overview of relaxational phenomenology is given in a manner intended to highlight a number of the important problems which, notwithstanding much recent sophisticated investigation, continue to confront the field. The rapidly lengthening timescale for diffusional and/or reorientational motion, which provokes the glass transition, is examined within the framework of the ‘strong’ and ‘fragile’ classification of both liquids and plastic crystals. The behavior patterns observed are related to the topological features of the potential energy hypersurfaces which may characterize each extreme. In view of the implication that the observed glass transition is the kinetically obscured reflection of an underlying higher order thermodynamic transition which could be associated with a diverging length scale (at least for fragile systems), the problem of the basic diffusional length scale at the glass transition, using a probe molecule approach, is considered. Then, details of the kinetics of relaxation under isothermal conditions are reviewed to decide on the range of deviations from Debye behavior which may be encountered. A correlation with fragility is strongly indicated. The phenomena of serial decoupling of relaxational modes from the main structural relaxation as T g is approached is outlined and, finally, the additional phenomena that may be encountered in experiments that explore the state-dependence (or non-linearity) of relaxation are briefly examined.

Relaxation in liquids, polymers and plastic crystals — strong/fragile patterns and problems☆

The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, τ, consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log10 units of time above τ. In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; τS = ηS/G∞ (where τS is the shear relaxation time, G∞ is the shear modulus at infinite frequency and ηS is the zero frequency shear viscosity). The value of G∞ known for SiO2 and several other silicate glasses. The shear modulus, G∞, and the bulk modulus, K∞, are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to ηS, G∞ may be considered a constant (independent of composition and temperature) and the value of ηS, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.

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Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes

A compilation of data for small molecule organic, polymeric, and inorganic glass-forming liquids shows that the original expectation, that there be a positive correlation between the thermodynamic measure of fragility Cpl/Cpg (or Cpl/Cpc) and the dynamic fragility index m, is not generally true. The results are consistent with three classes of behavior: (1) a decrease in m with increasing Cpl/Cpg for the polymeric glass formers; (2) a nearly constant value of m independent of Cpl/Cpc for small molecule organics and hydrogen bonding small molecules; (3) an increasing value of m with increasing Cpl/Cpc for inorganic glass formers as originally considered by Angell.

New insights into the fragility dilemma in liquids

Why C1 = 16-17 in the WLF equation is physical - And the fragility of polymers

The compressive stress relaxation modulus of a container glass composition was investigated over a wide range of strain, time, modulus, and temperature. It is shown that the glass behaves in a linear viscoelastic manner up to a 2% strain level, and that the relaxation modulus is a smooth function of time, with no pseudo-rubbery plateau apparent down to a modulus of 108 dyn/cm2. The data cover roughly five decades of modulus, five decades of time, and a temperature range of 150° C above the glass transition, Tg = 536°C. Within experimental error, the effect of temperature on the stress relaxation behavior is to simply shift the modulus-time curves along the time axis with no change in shape. Temperature dependent shift factor data are expressed in terms of the WLF relation, and are shown to be in good agreement with data found in the literature for other silicate compositions. Viscosity data derived from the generated stress relaxation data agree well with data obtained by more direct methods.

J.J. Mills

Papers

Stress relaxation behavior of soda-lime glass between the transformation and softening temperatures