A kinetic model for liquids: Relaxation in liquids, origin of the Vogel–Tammann–Fulcher equation, and the essence of fragility

Abstract

On the basis of the kinetic model for liquids, which gave a quantitative description of liquid substructures, atomic relaxations in a model liquid were calculated. A crossover temperature Tcoop was recognized: relaxations were noncooperative at temperatures above Tcoop while cooperative below Tcoop. The cooperation in relaxation was responsible for the very slow dynamics near glass transition, departing significantly from the Arrhenius relation. This found supports in a large variety of glass forming liquids. The degree of cooperation in relaxation was straightforwardly determined by the number of atoms, N, in the liquid substructure and was responsible for the fragility of liquids: the larger the N was, the more fragile a liquid was.

Bond Strength—Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids

“…Similarly, Rault has indicated that the connection between cooperative motion of α- relaxation and β KWW leads to the VFT law [ 53 ]. This picture of the cooperativity gained through the quantity N B is also in harmony with the concepts proposed by others such as the “cooperativity of atomic migrations” given by Wang and Fecht [ 54 ], and the “supercooled liquid as an elastic medium” given by Trachenko [ 55 , 56 ], etc . Our view of the cooperativity gives the same result and provides an alternative view to understand the structural relaxation, that is, in terms of the structural units which is determined by the bonding nature.…”

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids

“…Recently, two of these authors proposed a new model for the consideration of atomic cooperativity in liquids in which the very slow dynamics near T g was directly related to atomic cooperativity [14]. However, in [14], the gradual changes in the temperature dependence of relaxation time at temperatures near T g were missed.…”

“…Recently, two of these authors proposed a new model for the consideration of atomic cooperativity in liquids in which the very slow dynamics near T g was directly related to atomic cooperativity [14]. However, in [14], the gradual changes in the temperature dependence of relaxation time at temperatures near T g were missed. In this work the theory in [14] will be further developed by distinguishing thermodynamic and kinetic cooperativities in glass-forming liquids so that the gradual changes in liquid dynamics are reproduced.…”

Extracting energy and structure properties of glass-forming liquids from structural relaxation time

“…A significant feature to be stressed here is that in both the high and low temperature ranges the temperature dependence of structural relaxation times tends to an Arrhenius law. This phenomenon, obvious for B 2 O 3 [42], 2Ca(NO 3 ) 2 -3KNO 3 (CKN) [18,19], and simple organic liquids [31,38], seemed a general liquid feature [65][66][67][68] and was captured in the kinetic liquid model used here [35,62]. With this fact made clear, both experimentally and theoretically, it may be helpful in evaluating the measured structural relaxation times at the high and low temperature extremes.…”

“…(Anyway, the VFT equation may still serve as a convenient and good approximation for the structural relaxation times, especially those measured in a limited temperature range. In such situations, the VFT temperature may be taken as a rough estimate of the degree in cooperativity, see figure 4 of [62]. )…”