Theory of the highly viscous flow

Abstract

In an undercooled liquid close to the glass transition [1][2][3], the flow begins by many thermally activated back-and-forth jumps, structural Eshelby [4] rearrangements of strained regions. Together, they lead at short times t to the Kohlrausch t β shear relaxation, with β around 1/2, before the jumps become irreversible and the viscous flow begins. The Kohlrausch behavior is not yet well understood. Here, a theoretical explanation is given, starting from an exact result for the irreversible jumps [5], the lifetime distribution of the critical Eshelby region. A new close-packing picture is proposed for the numerically found [6] string motion in soft vibrations and low-barrier relaxations in glasses. It enables a quantitative understanding of the Kohlrausch behavior. A continuity relation between the irreversible and the reversible Kohlrausch relaxation time distribution is derived. The full spectrum can be used in many ways, not only to describe shear relaxation data, but also to relate shear relaxation data to dielectric and bulk relaxation spectra, and to predict aging from shear relaxation data, as demonstrated for a very recent aging experiment [7].

Strain field of soft modes in glasses

“…In this context, it should be mentioned that the string motion was not only found in the soft modes and low temperature relaxations [3], but also in the relaxational motion at the glass transition [35] (without mentioning the earlier glass work). The finding supports the recent explanation of the highly viscous flow [33] in terms of the creation and annihilation of soft modes.…”

“…The accurate determination of the two minimal energies in both directions requires the subtraction of the linear potential term. The average creation energy is 1.25 E 0 (2.5 k B T g ) for both the normal modes and the quartic modes, in reasonable agreement with the recent theoretical estimate 3.22 k B T g on the basis of an atomic model of the motion [33]. It explains the strong reduction in the number of soft modes in glasses [14] cooled to low glass temperatures with the swap mechanism [34].…”

A note on Kauzmann's paradox

“…1 shows the calculated liquid heat capacity for a cutoff energy E s = 3.6k B T g . According to a recent theory of the highly viscous flow [34], the Kohlrausch exponent β describing the stretching of the shear relaxation should be 0.3 for this soft mode creation energy, in reasonable agreement with the measured values 0.31 [35] and 0.42 [36].…”

“…The more or less universal density of tunneling states found at low temperatures [15,47] indicates more or less equal values of E s /k B T g for the creation energy E s of the soft modes in all glass formers. According to a recent theory of the highly viscous flow [34], E s /k B T g ≈ 2.5 determines the Kohlrausch β close to 1/2 found in all glass formers. Fig.…”

Hydrogen bond dynamics at the glass transition

“…A theoretical analysis of the reversible and irreversible shear transformation processes in the five-dimensional shear space [24][25][26] in terms of asymmetric double-well potentials, with the asymmetry determined exclusively by the different shear misfit of the inner Eshelby domain [27] or shear transformation zone [28,29] in its two structural alternatives, leads to the relaxation time distribution in the barrier variable v = ln(τ /τ c )…”