On the glass transition and correlation functions
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ORIGINAL CONTRIBUTION
On the glass transition and correlation functions Henrich Frielinghaus1 Received: 24 March 2020 / Revised: 5 May 2020 / Accepted: 11 May 2020 © The Author(s) 2020
Abstract Correlation functions are the basis for the understanding of many thermodynamic systems that can be directly observed by scattering experiments. In this manuscript, the correlation functions include the steric repulsion of atoms that also leads to distinct shells of neighbors. A free energy is derived on the basis of these assumptions, and in the following the temperature dependence of the density (or specific volume), the typical time scale of the α-relaxation, and the heat capacity. From this, I argue that the glass transition is dominated by the vicinity of a first-order phase transition. While the correlation length stays rather constant in the vicinity of the glass transition, the intensity of the fluctuations is considerably increasing. The scattering amplitude is connected to the cluster size, also introduced in the cooperativity argument. Additionally, correlations of loops are discussed. The additional correlations describe rather small structures. Applying this to scattering intensities, a correlation peak was described that may be connected to the “Boson Peak” or a “cooperativity length.” The new concept of correlation functions on sterically repulsive atoms may find more attention in the wider field of physics. Keywords Glass transition · Scattering functions · Free energy · Heat capacity
Introduction The glass transition has been investigated and discussed over many decades with the result of clear experimental temperature dependencies of the specific volume, the typical time scale of the α-relaxation, and the heat capacity [1, 2] to show either steeper steps, divergencies, or peaks at the glass transition temperature. However, the exact physical meaning of all these observations was left partially unclear such that different authors even contradict each other [3]. Classically, the time scale t of the α-relaxation measured by dielectric spectroscopy or as a viscosity η ∼ t was empirically described by the Vogel-Fulcher equation [4, 5] as given by: DT0 (1) t = t∞ exp T − T0 The high temperature limit of the time scale is t∞ , D is a constant, and T0 is the Vogel-Fulcher temperature that Henrich Frielinghaus
[email protected] 1
Forschungszentrum J¨ulich GmbH, J¨ulich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, Lichtenbergstr. 1, 85747, Garching, Germany
points towards the glass transition temperature. D is also called the “fragility” parameter [6] that is connected to the degree of deviation from the pure Arrhenius behavior: EA (2) t = t∞ exp kB T with EA being the activation energy and kB being the Boltzmann constant. Usually, the Vogel-Fulcher temperature T0 is found approx. 40K below the glass transition temperature Tg . It should be stressed that the glass transition is a thermo-kinetic phenomenon, which means that around Tg and below most observations are dominated b
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