Origin of the Kohlrausch exponent

According to a recent numerical finding, the dynamics of a glass former is exclusively due to the forces within the first coordination shell. This implies that the Kohlrausch beta should be understandable in terms of the effective nearest-neighbor potential. The present paper proposes a relation for the Kohlrausch beta based on the Adam-Gibbs conjecture of a flow barrier proportional to the number of atoms or molecules in a cooperatively rearranging region. The conjecture implies that beta is given by the ratio of the structural entropy increase per particle to the barrier increase per particle. Making use of a recent numerical determination of the structural entropy per particle in Lennard-Jones-like potentials, one can show that the relation leads to values between 0.3 and 0.6.Comment: Third completely changed versio

Irreversible Eshelby description of aging in glasses

The recent description of the cooling through the glass transition in terms of irreversible structural Eshelby rearrangements with a single average fictive temperature is extended to a distribution of fictive temperatures around the average one. The extension has only little influence on the cooling scans, but turns out to be necessary to understand the heating back to equilibrium.Comment: 3 pages, 3 figure

Modeling the nonlinear dielectric response of glass formers

The recently developed pragmatical model of asymmetric double-well potentials with a finite lifetime is applied to nonlinear dielectric data in polar undercooled liquids. The viscous effects from the finite lifetime provide a crossover from the cooperative jumps of many molecules at short times to the motion of statistically independent molecules at long times. The model allows to determine the size of cooperatively rearranging regions from nonlinear {\omega}-data and throws a new light on a known inconsistency between nonlinear {\omega} and 3{\omega}-signals for glycerol and propylene carbonate.Comment: Version 4 after hot discussions with Referee

Eshelby description of highly viscous flow -- half model, half theory

A recent description of the highly viscous flow ascribes it to irreversible thermally activated Eshelby transitions, which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. The description is extended to include reversible Eshelby transitions, with the Kohlrausch exponent $\beta$ as a free parameter. The model answers several open questions in the field.Comment: 11 pages, 9 figures, corrected following referee advic

Thermodynamics and dynamics of the inherent states at the glass transition

It has been recently shown that one can understand the Prigogine-Defay ratio at the glass transition in terms of freezing into one of the many inherent states of the undercooled liquid. In the present paper, the treatment is extended to the dynamics at the glass transition to show the connection to isomorphism and density scaling. In addition, the energy limits for stable inherent states are discussed.Comment: paper accepted for Proceedings IDMRCS 2013 in Barcelona, special issue of Journal of Non-Crystalline Solid

Retardation and flow at the glass transition

The crossover from back-and-forth jumps between structural minima to the no-return jumps of the viscous flow is modeled in terms of an ensemble of double-well potentials with a finite decay probability. The ensemble is characterized by the Kohlrausch-exponent $\beta$ of the time dependence $t^\beta$ of the response at short times. The model is applied to shear and dielectric data from the literature.Comment: Second version changed according to advice of Referees: Rewritten to Regular Article. New data included, in particular monoalcohol data, which argue for a common crossover to viscous processes in dielectrics and shea

Structural relaxation and highly viscous flow

The highly viscous flow is due to thermally activated Eshelby transitions which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. A self-consistent determination of the viscosity in this picture explains why the average structural relaxation time is a factor of eight longer than the Maxwell time. The physical reason for the short Maxwell time is the very large contribution of strongly strained inherent states to the fluidity (the inverse viscosity). At the Maxwell time, the viscous no-return processes coexist with the back-and-forth jumping retardation processes.Comment: 6 pages, 3 figures, version published in Journal of Chemical Physic

Supplemental Material: Eshelby ensemble of highly viscous flow out of equilibrium

Supplemental Material to ArXiv:1902.0274

Eshelby description of highly viscous flow III

The recent Eshelby description of the highly viscous flow leads to the prediction of a factor of two different viscosities in stationary and alternating flow, in agreement with experimental evidence. The Kohlrausch barrier density increase with increasing barrier height finds a physical justification in the Adam-Gibbs increase of the number of structural alternatives of the Eshelby region with its increasing size. The new Ansatz allows to determine the number of atoms or molecules in the rearranging Eshelby domains from a combination of dynamic shear relaxation and calorimetric data.Comment: 9 pages, four figures, continuation of two preceding paper

Gr\"uneisen model for melts

The Gr\"uneisen relation is shown to be important for the thermodynamics of dense liquids