Abstract
The glass transition is described as a time- and history-independent singular event, which takes place in an interval dependent on the distribution width of molecular vibration amplitudes. The intrinsic glass transition is not seen as a relaxation phenomenon, but is characterized by a fixed volumetric state at the glass temperature Tg0. The relaxation behavior of the transport properties depends on the distance to Tg0. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into condensed matter and the resulting combined interactions between the vibration elements. This creates vacancies between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such apertures depend on the size and axis orientation and do not require further energetic activation. After a displacement, additional volume is created by delays in occupying abandoned positions and restoring the energetic equilibrium. The different possibilities of axis orientation in space result in the different diffusive behavior of simple molecules and chain molecules, silicate network formers, and associated liquids. Glass transformation takes place at a critical volume Vg0 when the cross-section of apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg0 is assigned to Vg0 and is therefore independent of molecular relaxation processes. Tg0 is well above the Kauzmann and Vogel temperatures, usually just a few degrees below the conventionally measured glass temperature Tg(qT). The specific volume at the two temperatures mentioned above cannot be achieved by a glass with an unordered structure but only with aligned molecular axes, i.e. in a crystalline state. Simple liquids consisting of non-spherical molecules additionally alter their behavior above Vg0 at Vgl where the biggest gaps are as small as the largest molecular diameter. Tgl is located in the region of the crystalline melting point Tm. Both regions, above and below Tm, belong to different physical states and have to be treated separately. In the region close to Vg0 respectively Tg0, the distribution of vibration amplitudes has to be taken into account. The limiting volume Vg0 and the formation of apertures larger than the cross-section of the vibrating elements or parts thereof, in conjunction with the distribution width of molecular vibrations as Vg0 is approached, and the spatial orientation of the molecular axes is key to understanding the glass transition.
Highlights
Since the constan required shearagainst forcesthe increase, as adjacent a directelements consequence of the time field forces depend on the distance between the cavity boundaries and the center of mass τ for the adjustment of the internal structural equilibrium and that of the coefficients fo of a passing element, it follows that the smaller the difference between the cross-sections, self‐diffusion, viscosity, and other transport variables increases
Both o-terphenyl and the salt blend potassium nitrate/calcium nitrate 60/40 showed a distinct kink at a certain temperature, which was interpreted as a change in packing density in connection with pre-crystallization appearing in the vicinity of the melting point
Since the molecular spacing is closer to energetic equilibrium when the molecular axes are oriented uniformly than when the axes point in all spatial directions, the system prefers the crystalline state and attempts to achieve it by partial rotations
Summary
Based on the theoretically established and experimentally confirmed equivalence between diffusion and viscosity dependence in the liquid range above Tgl and due to the rich data material, the subsequent verification of the new model concept was mainly performed using viscosity data This does not mean that the equalization is completely beyond doubt, because the process of self-diffusion is a microscopic one, whereas viscosity has some macroscopic aspects. The results of the dielectric measurements, which are said to be more accurate than viscosity measurements but decouple slightly from the latter when approaching Tg0 [2,24], are not included in the study It is, according to the author’s understanding, imperative and of fundamental importance for the precise prediction of liquid characteristics to involve the glass transition into the theory of the liquid state. Pioneer studies and comprehensive surveys on the subject are presented, for example Kauzmann, 1946 [25], Tool, 1947 [26], Fox and Flory, 1950/1954 [27,28], Ritland, 1953 [29], Rost 1955 [30], Williams et al, 1955 [31], Cohen and Turnbull, 1961 [32], Kovacs, 1963 [33], Barlow et al, 1965 [34], Koppelmann, 1965 [35], Rötger, 1968 [36], Plazek et al., 1966/1968/1994/1999 [37,38,39,40], Davis and Matheson, 1966 [41], Breuer and Rehage, 1967 [42], Kanig, 1969 [43], Goldstein, 1969 [9], Donth, 1981 [44], McKenna and Angell, 1991 [45], Brüning and Samwer, 1992 [46], Böhmer et al, 1993 [47], Angell, 1995 [48], Ediger et al., 1996 [49], Colucci et al, 1997 [50], Rössler et al, 1998 [51], Ngai, 2000 [52], Tarjus and Kivelson, 2000 [53], Berthier and Garrahan, 2003 [54], Yue et al, 2004 [55], Tanaka, 2005 [56], Dyre, 2006 [13], Ojovan, 2008 [57], Hutchinson, 2009 [58], Liu and Nagel, 2010 [15], Tarjus, 2010 [59], Berthier and Piroli, 2011 [60], Chen et al, 2012 [2], Stillinger and Debenedetti, 2013 [61], Biroli and Garrahan, 2013 [62], Langer, 2013 [63], Miracle and Senkov, 2016 [64], Schmelzer and Tropin, 2018 [65], and Zheng et al, 2019 [66]
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