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The shear misfit model for the highly viscous flow is based upon a theoretical prediction for its terminal stage in terms of irreversible Eshelby relaxations in the five-dimensional shear space. The model is shown to predict a small delta-function (Debye peak) in the dielectric spectrum, in agreement with experimental evidence. It is extended from shear fluctuations to density fluctuations, a new relation between adiabatic and isothermal compressibility jumps at the glass transition is derived, and the model is brought into a form which requires only three temperature-dependent parameters for the fit of shear relaxation data of a glass former with a secondary relaxation peak. The model is applied to high precision measurements of the shear, dielectric and bulk relaxation data in two vacuum pump oils and in squalane, a short chain polymer with a strong secondary relaxation peak. In all three substances, the adiabatic compressibility equilibrates much earlier than the isothermal one. The terminal stage of aging data in squalane demonstrate that one sees also the adiabatic density fluctuations in the thermal expansion, explaining why it seems to equilibrate a bit faster than the dynamic heat capacity., Comment: 9 pages, 6 figures

The glass transition in hydrogen-bonded glass formers differs from the glass transition in other glass formers. The Eshelby rearrangements of the highly viscous flow are superimposed by strongly asymmetric hydrogen bond rupture processes, responsible for the excess wing. Their influence on the shear relaxation spectrum is strong in glycerol and close to zero in PPE, reflecting the strength of the hydrogen bond contribution to the high frequency shear modulus. A recent theory of the highly viscous flow enables a quantitative common description of the relaxation spectra in shear, linear and non-linear dielectrics, and heat capacity., Comment: 4 pages, 3 figures; Supplement 5 pages, 6 figures

The rapid structural and vibrational entropy decrease with decreasing temperature in undercooled liquids is explained in terms of the disappearance of local structural instabilities, which freeze in at the glass temperature as boson peak modes and low temperature tunneling states. At the Kauzmann temperature, their density extrapolates to zero, as evidenced by neutron and heat capacity data in liquid selenium., Comment: 5 pages, 4 figures

The paper presents a description of the sound wave absorption in glasses, from the lowest temperatures up to the glass transition, in terms of three compatible phenomenological models. Resonant tunneling, the rise of the relaxational tunneling to the tunneling plateau and the crossover to classical relaxation are universal features of glasses and are well described by the tunneling model and its extension to include soft vibrations and low barrier relaxations, the soft potential model. Its further extension to non-universal features at higher temperatures is the very flexible Gilroy-Phillips model, which allows to determine the barrier density of the energy landscape of the specific glass from the frequency and temperature dependence of the sound wave absorption in the classical relaxation domain. To apply it properly at elevated temperatures, one needs its formulation in terms of the shear compliance. As one approaches the glass transition, universality sets in again with an exponential rise of the barrier density reflecting the frozen fast Kohlrausch t^beta-tail (in time t, with beta close to 1/2) of the viscous flow at the glass temperature. The validity of the scheme is checked for literature data of several glasses and polymers with and without secondary relaxation peaks. The frozen Kohlrausch tail of the mechanical relaxation shows no indication of the strongly temperature-dependent barrier density observed in dielectric data of molecular glasses with hydrogen bonds. Instead, the mechanical relaxation data indicate an energy landscape describable with a frozen temperature-independent barrier density for any glass., Comment: Review on sound absorption in glasses, 23 pages, 17 figures

The strain field surrounding the center of low frequency vibrational modes is analyzed for numerically created binary glasses with a 1/r^10 repulsive interatomic potential. Outside the unstable inner core of five to twenty atoms, one finds a mixture of a motion similar to the string motion in the core with the strain field of three oscillating elastic dipoles in the center. The additional outside string motion contributes more to the stabilization of the core than the strain field, but the strain field dominates at long distances, in agreement with recent numerical findings. The small restoring force of the outside string motion places its average frequency close to the boson peak. The average creation energy of a soft mode in this binary glass is about 2.5 times the thermal energy at the freezing temperature. Scaling the soft potential parameters of the numerical modes to metallic glasses, one finds quantitative agreement with measurements of the sound absorption by tunneling states at low temperatures and by the excess modes at the boson peak., Comment: 8 pages, 5 figures

The recent theoretical treatment of irreversible jumps between inherent states with a constant density in shear space is extended to a full theory, attributing the shear relaxation to structural Eshelby rearrangements involving the creation and annihilation of soft modes. The scheme explains the Kohlrausch exponent close to 1/2 and the connection to the low temperature glass anomalies. 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., Comment: 7 pages, 5 figures, last attempt to publish in a journal

Inelastic neutron scattering is not only capable of determining a generalized vibrational density of states around the boson peak of a glass, but can also be used to get information on the eigenvectors. The eigenvectors determine the dynamic structure factor, which is $Q^2S(Q)$ ($Q$ wavevector) for long wavelength sound waves. This enables the determination of the sound wave fraction below and at the boson peak, done for SiO$_2$, B$_2$O$_3$, polybutadiene and amorphous germanium. The temperature dependence of the boson peak in silica and glycerol is shown. X-ray Brillouin scattering data show that the damping of the longitudinal sound waves in silica and glycerol follows the soft potential model $\omega^4$ prediction in the limit of low frequency., Comment: 6 pages, 4 figures, 1 table

The anharmonic soft modes studied in recent numerical work in the glass phase of simple liquids have an unstable core, stabilized by the positive restoring forces of the surrounding elastic medium. The present paper formulates an unstable core version of the phenomenological soft potential model for the low temperature anomalies of glasses, relates a new numerical finding on low-barrier relaxations to old soft potential model results, and discusses experimental evidence for an unstable core of the boson peak modes., Comment: Again corrected version

Supplemental Material to ArXiv:1902.02746

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 figures

The recent description of the highly viscous flow in terms of irreversible structural Eshelby rearrangements is extended to calculate the heat capacity of a glass former at a constant cooling rate through the glass transition. The result is compared to measured data from the literature, showing that the explanation works both for polymers and other glass formers., Comment: 4 pages, second submitted version

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 papers

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 advice

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 Physics

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

The paper derives a relation for the viscosity of undercooled liquids on the basis of the pragmatical model concept of Eshelby relaxations with a finite lifetime. From accurate shear relaxation data in the literature, one finds that slightly less than half of the internal stresses relax directly via single Eshelby relaxations; the larger part dissolves at the terminal lifetime, which is a combined effect of many Eshelby relaxations., Comment: 4 pages

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 version

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 Referees

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 shear

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 Solids

Making use of the classical second moment sum rule, it is possible to convert a series of constant-Q x-ray Brillouin scattering scans (Q momentum transfer) into a series of constant frequency scans over the measured $Q$ range. The method is applied to literature results for the phonon dispersion in liquid vitreous silica and in glassy polybutadiene. It turns out that the constant frequency scans are again well fitted by the damped harmonic oscillator function, but now in terms of a Q-independent phonon damping depending exclusively on the frequency. At low frequency, the sound velocity and the damping of both evaluations agree, but at higher frequencies one gets significant differences. The results in silica suggest a new interpretation of x-ray Brillouin data in terms of a strong mixing of longitudinal and transverse phonons toward higher frequencies. The results in polybutadiene enlighten the crossover from Brillouin to Umklapp scattering., Comment: submitted to PRE as a Rapid Communication

The Lindemann criterion is reformulated in terms of the average shear modulus $G_c$ of the melting crystal, indicating a critical melting shear strain which is necessary to form the many different inherent states of the liquid. In glass formers with covalent bonds, one has to distinguish between soft and hard degrees of freedom to reach agreement. The temperature dependence of the picosecond mean square displacements of liquid and crystal shows that there are two separate contributions to the divergence of the viscosity with decreasing temperature: the anharmonic increase of the shear modulus and a diverging correlation length ., Comment: 4 pages, 3 figures

In undercooled liquids, the anharmonicity of the interatomic potentials causes a volume increase of the inherent structures with increasing energy content. In most glass formers, this increase is stronger than the vibrational Gr\"uneisen volume expansion and dominates the thermal expansion of the liquid phase. For a gaussian distribution of inherent states in energy, the generic case, this implies a 1/T-squared temperature dependence of the additional thermal expansion and the additional heat capacity at zero pressure. The corresponding compressibility contribution has the Prigogine-Defay ratio one. In experiment, one finds a higher Prigogine-Defay ratio, explainable in terms of structural volume changes without any energy change. These should always exist, though their influence becomes weak in close-packing systems, at the crossover to soft matter., Comment: 4 pages, 2 figures, 29 references; presented at XIII Workshop on Complex Systems, Andalo, March 2012; derivation of Ehrenfest relation for glass transition included in eq. (13) of third version

The ratio between the couplings of a relaxational process to compression and shear, respectively, is calculated in the Eshelby picture of structural rearrangements within a surrounding elastic matrix, assuming a constant density of stable structures in distortion space. The result is compared to experimental data for the low-temperature tunneling states in glasses and to Prigogine-Defay data at the glass transition from the literature., Comment: 6 pages, 2 figures, 53 references; version after understanding the Prigogine-Defay ratio at the glass transition in the accompanying paper arXiv:1203.3555 [cond-mat.dis-nn]

The asymmetry model for the highly viscous flow postulates thermally activated jumps from a practically undistorted ground state to strongly distorted, but stable structures, with a pronounced Eshelby backstress from the distorted surroundings. The viscosity is ascribed to those stable distorted structures which do not jump back, but relax by the relaxation of the surrounding viscoelastic matrix. It is shown that this mechanism implies a description in terms of the shear compliance, with a viscosity which can be calculated from the cutoff of the retardation spectrum. Consistency requires that this cutoff lies close to the Maxwell time. The improved asymmetry model compares well with experiment., Comment: 8 pages, 3 figures, 49 references; revised version accepted in Journal of Chemical Physics

A relation between shear and dielectric spectra is derived for highly viscous liquids with a small rotational contribution $\Delta\epsilon$ to the dielectric constant. It is valid if the shear fluctuations and the electric dipole fluctuations have the same spectrum. The comparison to literature data, taken under carefully controlled conditions to ensure samples from the same charge and the same temperature control in both measurements, indicates that the relation may be fulfilled or not depending on the substance. The connection to recent work on strong correlations is discussed., Comment: 4 pages, 4 figures, 13 references

The position and strength of the boson peak in silica glass vary considerably with temperature $T$. Such variations cannot be explained solely with changes in the Debye energy. New Brillouin scattering measurements are presented which allow determining the $T$-dependence of unrelaxed acoustic velocities. Using a velocity based on the bulk modulus, scaling exponents are found which agree with the soft-potential model. The unrelaxed bulk modulus thus appears to be a good measure for the structural evolution of silica with $T$ and to set the energy scale for the soft potentials., Comment: Accepted for publication in Physical Review Letters

The fragility (the abnormally strong temperature dependence of the viscosity) of highly viscous liquids is shown to have two sources. The first is the temperature dependence of the barriers between inherent states considered earlier. The second is the recently discovered asymmetry between the actual inherent state and its neighbors. One needs both terms for a quantitative description., Comment: 3 pages, 1 figure

The shear flow is modeled in terms of local structural rearrangements. Most of these rearrangements are strongly asymmetric, because the embedding matrix tends to be elastically adapted to the initial state and to have a marked elastic misfit with regard to the final state. As one approaches the Maxwell time, the asymmetry becomes time-dependent, thus enabling the system to leave the initial state. The model explains the Kohlrausch behavior at the main peak in terms of the interaction between different local structural rearrangements., Comment: third version, improved beyond recognition by qualified referees, 6 pages, 2 figures

The boson peak in metallic glasses is modeled in terms of local structural shear rearrangements. Using Eshelby's solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate the saddle point energy of such a structural rearrangement. The neighbourhood of the saddle point gives rise to soft resonant vibrational modes. One can calculate their density, their kinetic energy, their fourth order potential term and their coupling to longitudinal and transverse sound waves., Comment: 9 pages, 7 figures, 31 references, contribution to 11th International Workshop on Complex Systems, Andalo (Italy), March 2008

The shear flow and the dielectric alpha-process in molecular glass formers is modeled in terms of local structural rearrangements which reverse a strong local shear. Using Eshelby's solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate the recoverable compliance and estimate the lifetime of the symmetric double-well potential characterizing such a structural rearrangement. A full modeling of the shear relaxation spectra requires an additional parametrization of the barrier density of these structural rearrangements. The dielectric relaxation spectrum can be described as a folding of these relaxations with the Debye process., Comment: 6 pages, five figures, ESF conference "Glassy liquids under pressure" in Ustron, Poland, 10-14 October 2007, to be published J. Phys. C: Condens. Matter

Published dielectric and shear data of six molecular glass formers and one polymer are evaluated in terms of a spectrum of thermally activated processes, with the same barrier density for the retardation spectrum of shear and dielectrics. The viscosity, an independent parameter of the fit, seems to be related to the high-barrier cutoff time of the dielectric signal, in accordance with the idea of a renewal of the relaxing entities after this critical time. In the five cases where one can fit accurately, the temperature dependence of the high-barrier cutoff follows the shoving model. The Johari-Goldstein peaks, seen in four of our seven cases, are describable in terms of gaussians in the barrier density, superimposed on the high-frequency tail of the $\alpha$-process. Dielectric and shear measurements of the same substance find the same peak positions and widths of these gaussians, but in general a different weight., Comment: Contribution to the Ngai Fest issue of J. Non-Cryst. Solids; 8 pages, 8 figures, 30 references

We derive an energy landscape interpretation of dielectric relaxation times in undercooled liquids, comparing it to the traditional Debye and Gemant-DiMarzio-Bishop pictures. The interaction between different local structural rearrangements in the energy landscape explains qualitatively the recently observed splitting of the flow process into an initial and a final stage. The initial mechanical relaxation stage is attributed to hopping processes, the final thermal or structural relaxation stage to the decay of the local double-well potentials. The energy landscape concept provides an explanation for the equality of thermal and dielectric relaxation times. The equality itself is once more demonstrated on the basis of literature data for salol., Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems, Molveno 2006, submitted to Philosophical Magazine

Literature dielectric data of glycerol, propylene carbonate and ortho-terphenyl (OTP) show that the measured dielectric relaxation is a decade faster than the Debye expectation, but still a decade slower than the breakdown of the shear modulus. From a comparison of time scales, the dielectric relaxation seems to be due to a process which relaxes not only the molecular orientation, but the entropy, the short-range order and the density as well. On the basis of this finding, we propose an alternative to the Gemant-DiMarzio-Bishop extension of the Debye picture., Comment: 7 pages, 4 figures, 68 references; 3. version extended following referee advice

The incoherent approximation for the determination of the vibrational density of states of glasses from inelastic neutron or x-ray scattering data is extended to treat the coherent scattering. The method is applied to new room temperature measurements of vitreous silica and germania on the thermal time-of-flight spectrometer IN4 at the High Flux Reactor in Grenoble. The inelastic dynamic structure factor at the boson peak turns out to be reasonably well described in terms of a mixture of rotation and translation of practically undistorted SiO4 or GeO4 tetrahedra. The translational component exceeds the expectation of the Debye model by a factor of two. A possible relation of this excess to the phonon shift and broadening observed in x-ray Brillouin scattering experiments is discussed., Comment: 13 pages, 13 figures, 39 references

A recent hypothesis claims that the glass transition itself, though it is a very pronounced relaxation peak, is no separate relaxation process at all, but is just the breakdown of the shear modulus due to the weak elastic dipole interaction between all the quasi-independent relaxation centers of the glass. Two derivations are considered, one of them in terms of a breakdown of the shear modulus and the second in terms of a divergence of the shear compliance. Mechanical relaxation data from the literature for vitreous silica, glycerol, polymethylmethacrylate and polystyrene are found to be consistent with the first hypothesis., Comment: 9 pages, 2 figures, 20 references. Accepted in Journal of Low Temperature Physics in a volume dedicated to Sigi Hunklinger's 65th birthday 2004

A close inspection of neutron spectra of glass formers in the frequency region above the boson peak does not show the constant eigenvalue density expected for a random dynamical matrix, but a slow decrease towards higher eigenvalues. In 1,4-polybutadiene and selenium, the slope becomes steeper with increasing temperature in the undercooled liquid, suggesting an influence of the vibrational entropy. One can describe the behaviour quantitatively in terms of a balance between level repulsion (from the randomness of the dynamical matrix) and vibrational entropy. On the basis of this evidence, the boson peak must be a crossover from such a balance at higher frequencies to a mixture of sound waves and additional excitations at low frequency., Comment: Letter, 4 pages, 4 figures, 24 references

Isothermal compressibilities and Brillouin sound velocities from the literature allow to separate the compressibility at the glass transition into a high-frequency vibrational and a low-frequency relaxational part. Their ratio shows the linear fragility relation discovered by x-ray Brillouin scattering [1], though the data bend away from the line at higher fragilities. Using the concept of constrained degrees of freedom, one can show that the vibrational part follows the fragility-independent Lindemann criterion; the fragility dependence seems to stem from the relaxational part. The physical meaning of this finding is discussed. [1] T. Scopigno, G. Ruocco, F. Sette and G. Monaco, Science 302, 849 (2003), Comment: 4 pages, 2 figures, 2 tables, 33 references. Slightly changed after refereeing

This is a comment on the beautiful results of Jeppe Dyre and Niels Boie Olsen, published as a recent Physical Review Letter., Comment: Comment to PRL; 1 page, 1 figure, 2 references

There is a growing belief that the mode coupling theory is the proper microscopic theory for the dynamics of the undercooled liquid above a critical temperature T_c. In addition, there is some evidence that the system leaves the saddlepoints of the energy landscape to settle in the valleys at this critical temperature. Finally, there is a microscopic theory for the entropy at the calorimetric glass transition T_g by Mezard and Parisi, which allows to calculate the Kauzmann temperature from the atomic pair potentials. The dynamics of the frozen glass phase is at present limited to phenomenological models. In the spirit of the energy landscape concept, one considers an ensemble of independent asymmetric double-well potentials with a wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips model). The model gives an excellent description of the relaxation of glasses up to about T_g/4. Above this temperature, the interaction between different relaxation centers begins to play a role. One can show that the interaction reduces the number of relaxation centers needed to bring the shear modulus down to zero by a factor of three., Comment: Contribution to the III Workshop on Nonequilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials, 22-27 September 2002, Pisa; 14 pages, 3 figures; Version 3 takes criticque at Pisa into account; final version 4 will be published in J.Phys.: Condens.Matter

The glass transition is described in terms of thermally activated local structural rearrangements, the secondary relaxations of the glass phase. The interaction between these secondary relaxations leads to a much faster and much more dramatic breakdown of the shear modulus than without interaction, thus creating the impression of a separate primary process which in reality does not exist. The model gives a new view on the fragility and the stretching, two puzzling features of the glass transition., Comment: 4 pages, 5 figures, 13 references; version 2 changed in title, reduced claims and modified arguments according to referee criticque from PRL. One equation was omitted; otherwise equations are unchanged Paper rejected by PRL; Version 3 accepted as part of the proceedings Workshop Disordered Solids in Andalo 2003 to appear in Phil. Mag. B

The Gilroy-Phillips model of relaxational jumps in asymmetric double-well potentials, developed for the Arrhenius-type secondary relaxations of the glass phase, is extended to a formal description of the breakdown of the shear modulus at the glass transition, the flow process., Comment: 13 pages, 11 figures, 49 refs

New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient $C(\omega)$ and, in particular, its low frequency limit. This study indicates that in the $\omega \to 0$ limit $C(\omega)$ extrapolates to a non vanishing value, giving important indications on the characteristics of the vibrational modes in disordered materials; in particular our results indicate that even in the limit of very long wavelength the local disorder implies non-regular local atomic displacements., Comment: Revtex, 4 ps figures