arXiv subjects
Publications and source records attributed to U. Buchenau.
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 $β$ of the time dependence $t^β$ of the response at short times. The model is applied to shear and dielectric data from the literature.
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.
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.
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 .
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 Grüneisen 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.
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.
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.
A relation between shear and dielectric spectra is derived for highly viscous liquids with a small rotational contribution $Δε$ 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.
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.
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.
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.
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.
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.
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 $α$-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.
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.
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.
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.
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.