Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyl trimethyl trisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus ($10^{5} -10^{10}$ Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyl trimethyl trisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical $\beta$ process is found. Although the the high-frequency power law behavior $\omega^{-\alpha}$ of the shear-loss may approach a limiting value of $\alpha=0.5$ when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyl trimethyl trisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the the relaxation-time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.Comment: 7 pages, 6 figure

Solidity of viscous liquids. IV. Density fluctuations

This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k-space of the form $\Gamma_0+Dk^2$ with $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultra local. As an illustration of the theory the case with the simplest non-trivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an $\omega^{-1/2}$ decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed

The instantaneous shear modulus in the shoving model

We point out that the instantaneous shear modulus of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a minor role

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

Impact of Daily Arctic Sea Ice Variability in CAM3.0 during Fall and Winter

Climate projections suggest that an ice-free summer Arctic Ocean is possible within several decades and with this comes the prospect of increased ship traffic and safety concerns. The daily sea ice concentration tendency in five Coupled Model Intercomparison Project phase 5 (CMIP5) simulations is compared with observations to reveal that many models underestimate this quantity that describes high-frequency ice movements, particularly in the marginal ice zone. To investigate whether high-frequency ice variability impacts the atmosphere, the Community Atmosphere Model, version 3.0 (CAM3.0), is forced by sea ice with and without daily fluctuations. Two 100-member ensemble experiments with daily varying (DAILY) and smoothly varying (SMTH) sea ice are conducted, along with a climatological control, for an anoma- lously low ice period (August 2006–November 2007). Results are presented for three periods: September 2006, October 2006, and December–February (DJF) 2006/07. The atmospheric response differs between DAILY and SMTH. In September, sea ice differences lead to an anomalous high and weaker storm activity over northern Europe. During October, the ice expands equatorward faster in DAILY than SMTH in the Siberian seas and leads to a local response of near-surface cooling. In DJF, there is a 1.5-hPa positive sea level pressure anomaly over North America, leading to anomalous northerly flow and anomalously cool continental U.S. temperatures. While the atmospheric responses are modest, the differences arising from high temporal frequency ice variability cannot be ignored. Increasing the accuracy of coupled model sea ice variations on short time scales is needed to improve short-term coupled model forecasts

A repulsive reference potential reproducing the dynamics of a liquid with attractions

A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by repulsive forces. The WCA potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this reference gives quite wrong results for the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. We show that repulsive inverse-power law potentials provide a useful reference for this liquid by reproducing its structure, dynamics, and isochoric heat capacity

Anisotropic thermally activated diffusion in percolation systems

We present a study of static and frequency-dependent diffusion with anisotropic thermally activated transition rates in a two-dimensional bond percolation system. The approach accounts for temperature effects on diffusion coefficients in disordered anisotropic systems. Static diffusion shows an Arrhenius behavior for low temperatures with an activation energy given by the highest energy barrier of the system. From the frequency-dependent diffusion coefficients we calculate a characteristic frequency $\omega_{c}\sim 1/t_{c}$, related to the time $t_c$ needed to overcome a characteristic barrier. We find that $\omega_c$ follows an Arrhenius behavior with different activation energies in each direction.Comment: 5 pages, 4 figure

Landscape equivalent of the shoving model

It is shown that the shoving model expression for the average relaxation time of viscous liquids follows largely from a classical "landscape" estimation of barrier heights from curvature at energy minima. The activation energy involves both instantaneous bulk and shear moduli, but the bulk modulus contributes less than 8% to the temperature dependence of the activation energy. This reflects the fact that the physics of the two models are closely related.Comment: 4 page

Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics

This paper is the fifth in a series exploring the physical consequences of the solidity of glass-forming liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the nonconserved type with rates in $k$ space of the form $\Gamma_0+Dk^2$. The model assumes that $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance; this inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) to a good approximation may be taken to be ultralocal. In the present paper we argue that this is the simplest model consistent with the following three experimental facts: 1) Viscous liquids approaching the glass transition do not develop long-range order; 2) The glass has lower compressibility than the liquid; 3) The alpha process involves several decades of relaxation times shorter than the mean relaxation time. The paper proceeds to list six further experimental facts characterizing equilibrium viscous liquid dynamics and shows that these are readily understood in terms of the model; some are direct consequences, others are quite natural when viewed in light of the model

Effective one-dimensionality of AC hopping conduction in the extreme disorder limit

It is argued that in the limit of extreme disorder AC hopping is dominated by "percolation paths". Modelling a percolation path as a one-dimensional path with a sharp jump rate cut-off leads to an expression for the universal AC conductivity, that fits computer simulations in two and three dimensions better than the effective medium approximation.Comment: 6 postscript figure