Universal relation between viscous flow and fast dynamics in glass-forming materials

Abstract

The connection between viscous flow and vibrational properties in glass-forming materials is scrutinized examining the fragility of a wide set of liquids and the nonergodicity factor of the corresponding glasses. Building on the same line of reasoning which allows us to extend the connection between viscosity and thermodynamics in complex systems, we show here how the two quantities are strongly correlated once the effect of those secondary relaxation processes due to internal degrees of freedom is correctly accounted for. This result provides a missing thermodynamic rationale for the recently debated universality of the correlation between fast and slow degrees of freedom. Glass-forming liquids can cross the melting line avoiding crystallization, and upon cooling below the melting temperature, their viscosity increases by several orders of magnitude, eventually leading to the glass transition. This is a kinetic transition usually defined by the condition in which the structural relaxation time ͑the ␣ process͒ equals a given value, arbitrarily fixed to 100 s. At the glass transition temperature, T g , the shear viscosity of most systems is in the range of 10 11 Ͻ Ͻ 10 13 poise, values high enough to consider the system as "solid" from the mechanical point of view.The rapidity of the increase in the viscosity when approaching T g from the liquid side led in the scientific community to the classification of glasses into long and short, 1 a concept widespread by Angell introducing the kinetic "fragility" 2 m = limSince Ϸ 10 −4 poise is the "infinite" temperature limit in basically any material and ͑T͒ is always found to be a concave function of T −1 , the lowest fragility value is around m = 17, and the systems in the low m side are named "strong" liquids and show an Arrhenius behavior. Conversely, it is empirically found that for the most "fragile" systems, where a high ͑and T-dependent͒ apparent activation energy is found, m Ͼ 150. Despite decisive theoretical steps forward in the comprehension of the glass transition, 3 the phenomenological relations associating the fragility to other physical properties still play a central role in this field, allowing to shed light on possible deep links among apparently uncorrelated quantities. Among them, ͑i͒ the thermodynamic approach to the fragility 4,5 also in the light of the Adam-Gibbs ͑AG͒ theory 6-8 and the random first-order transition; 9 ͑ii͒ the ratio between the maximum and the minimum of the boson peak, i.e., of the bump observed at the Thz frequencies in the Raman-and neutron-scattering spectra of glass-forming materials; 10 ͑iii͒ the degree of stretching in the nonexponential decay of the correlation functions in the liquid close to T g ͑Ref. 11͒; ͑iv͒ the statistics of the minima in a potential energy landscape-based description of the diffusion process in supercooled liquids; 12,13 ͑v͒ the temperature behavior of the high frequency shear elastic modulus in the supercooled liquid; 14 ͑vi͒ the Poisson ratio; 15-18 ͑vii͒ the mean squared displacement in a glass...

Poisson's ratio and modern materials

“…7a) reveals how Poisson's ratio ν increases across many glasses, as the melts from which they are quenched increase in fragility m (refs [100][101][102]. Although objections to this relationship were originally voiced 104,110 , many of these have been overcome as more glasses have been added 79,101,102,106,111,112 and the central proposition that "the fragility of a liquid (might be) embedded in the properties of its glass" 105 has generally been strengthened. Although it is true that the point scatter in the m versus B/G plots is considerable, it is also clear that groups of glasses can be differentiated 79,111 , forming an approximately radial arrangement from modified oxide glasses through single glass formers to the dense metallic glasses.…”

“…In particular, f 0 = (1 -αT/T g ) -1 , where α is a constant 105,106 . The factor f 0 is a measure of the magnitude of density fluctuations present at a given temperature and to a first approximation 100 f 0 ≈ (V t /V l ) 2 = 3G/(4G + 3B).…”

“…Poisson's ratio and non-ergodicity Covering a broad range of single-phase glasses, two interesting empirical relationships have emerged linking melt fragility with the elastic properties of the glass [100][101][102]105,106 : m versus B/G and m versus α. The ratio B/G relates directly to Poisson's ratio ν and α to the non-ergodicity factor f 0 (ref.…”

“…7a). Together with the degree of non-ergodicity f 0 frozen into the glass 79,105,106 , the melt fragility m is measured at the glass transition T g (Box 2) where the viscous relaxation time reaches ~100 s and the liquid is considered solid 26,79,[107][108][109] . Its elastic properties, however, clearly differ from those measured under ambient conditions (Fig.…”

Combining Flash DSC, DSC and broadband dielectric spectroscopy to determine fragility

“…The reliability of these investigations is demonstrated by comparing results obtained from two polymeric systems selected for their amorphous structure: polystyrene (PS), considered as a reference material because extensively studied by F-DSC, and poly(ethylene terephthalate)-glycol (PETg) which is much rarely studied by F-DSC techniques. In a second time, the temperature dependence of the cooling rate obtained by F-DSC and DSC combination has been compared to the temperature dependence of the relaxation times classically obtained from broadband dielectric spectroscopy, experiment considered as the reference concerning the fragility measurements [22][23][24][25][26][27][28][29][30].…”