Shear Viscosity and Diffusion in Supercooled Liquids

A theory is developed for diffusion in supercooled liquids. The viewpoint taken is that the dynamics of system, represented by a point in configuration space, consists of long sojourns in the vicinity of the local minima of the total potential, interrupted by relatively infrequent barrier crossings to adjacent minima. An equation due to Zwanzig, plus a new relation for the hopping rate among the local minima, are combined in a theory for the self-diffusion constant D. All the quantities entering the two equations are shown to be derivable from the configuration-averaged densities of vibrational states, 〈ρ(ω)〉, introduced by us previously; the contribution of unstable modes plays a crucial role. Solution of the coupled equations reveals the existence of a critical temperature below which D vanishes. The theory is in excellent agreement with molecular dynamics values for D, over a wide temperature range in which D displays activated behavior, in Lennard-Jones argon at a reduced density of unity.

The instantaneous normal mode (INM) approach to liquid state dynamics is presented. INM is put in historical context, and the underlying physical ideas, including the importance of the potential energy landscape, are explained. It is shown that INM can be the basis of a general starting point for dynamical calculations in liquids, and the theoretical developments necessary for future development are indicated. New results are given for the general INM formalism, as well as for depolarized light scattering, the “Boson peak” in supercooled liquids, friction on a vibrating bond, nonadiabatic solvent induced transitions of a quantum system coupled to a liquid, and diffusion in supercooled liquids.

Unveiling relaxation and crystal nucleation interplay in supercooled germanium liquid

On the interpretation of shear viscosity ultrasonic measurements

The nature of the simplest transport processes in water, namely, self-diffusion and shear viscosity, is analyzed on the basis of a version of the microinhomogeneous structure model. The study predicts the existence of locally ordered groups of molecules, taking into account considerations of acoustic properties, light scattering, and computer simulation findings. In particular, it is shown that the anomalous properties of water in supercooled states are mainly connected with the existence of quasiordered regions, which we call clusters. Furthermore, the spatial sizes and evolution times of the crystal-like clusters, as well as the temperature dependence of their fraction volume, are established. Special invariants of the characteristic parameters of molecular motion are pointed out. Finally, it is shown that the self-diffusion in supercooled water is caused by the processes of formation and destruction of crystal-like clusters, while the processes of internal partial reconstruction give the main contribution to the shear viscosity coefficient.

We measured the thermal diffusivity of amorphous solid and supercooled liquid in a Zr41Ti14Cu12Ni10Be23 bulk metallic glass (BMG) and its crystalline counterpart alloy at temperatures ranging from room temperature to 700 K, using a laser flash method. The thermal diffusivity and conductivity of the amorphous solid were weakly temperature dependent and increased with increasing temperature up to the glass transition temperature. The thermal diffusivity of the supercooled liquid was approximately 3.5×10−6 m2 s−1 and quite constant with temperature. The amorphous solid and supercooled liquid of Zr41Ti14Cu12Ni10Be23 BMG showed lower thermal diffusivity and conductivity than the crystalline counterpart in the range from room temperature to crystallization temperature.

Molecular dynamics simulations employing a many-body embedding potential model have been conducted to calculate both bulk and shear viscosity of pure liquid iron at the Earth's outer core conditions. Liquid iron shear viscosity thus obtained is in the order of 10−2 Pa · s and is in close agreement with previous estimates. In contrast, liquid iron bulk viscosity is in the order of 10−3 to 10−4 Pa · s and is much smaller than previous estimates. Consequently, the ratio of bulk to shear viscosity is close to 0.1. This value disagrees with both the common speculation that bulk and shear viscosities are equal at ambient pressure, and the previous inference that bulk viscosity of liquid iron is much larger than shear viscosity at outer core conditions. Potential implications of present data are also briefly given for the dynamic state of the outer core.

Here we study the relation between the mobility and the translational diffusion in supercooled two-dimensional polydisperse colloidal liquids, using numerical simulations. We find an apparent violation of the Einstein-Smoluchowski (ES) relation D=kB T micro (D: diffusion constant; mu: mobility; kB; Boltzmann's constant; T: temperature). The violation is a direct consequence of the fact that it is difficult for a driven particle to enter a jammed region with high order due to its yield stress. The degree of this apparent ES violation is controlled solely by the characteristic size of slow jammed regions, xi. Our finding implies that the characteristic time of this problem is not the structural relaxation time tau alpha but the lifetime of dynamic heterogeneity, tau xi. A supercooled liquid can be regarded to be ergodic only over tau xi, which may be the slowest intrinsic time scale of the system.

Granular matter submitted to external perturbations exhibits various behaviors depending on the vibration intensity: when strongly vibrated, the system has a aspect, whereas under low intensity perturbations, it is in a quasi-solid phase. In this work, we clarify these analogies: we discuss to what extent a granular fluid is close to a standard liquid and, on the other hand, investigate the similarities between weakly perturbed materials and supercooled liquids undergoing a glass transition. We first consider the case where a medium undergoes vibrations of high intensity (with accelerations of about 1 to 10 times that of gravity). This vibrated system is investigated using an immersed torsion oscillator which is sensitive to the agitation and which, as a result, exhibits irregular angular deflections that can be analyzed to give information on the grains' motion. This oscillator can also be used in forced mode: applying a torque allows measures of the mechanical susceptibility, which displays a resonance peak similar to that of a damped oscillator. It is thus possible to introduce a viscosity parameter for the system, which is found to be inversely proportional to the vibration acceleration imposed to the container. Moreover, by considering both the fluctuations (given by the diffusive noise, with the oscillator in free mode) and the susceptibility (forced mode), the validity of the fluctuation-dissipation theorem can be tested. Surprisingly, it turns out that very complicated system, even though far from equilibrium, satisfies this basic law of equilibrium statistical mechanics in first approximation, and therefore behaves very much like a plain liquid. The immersed oscillator can thus be compared to a pollen particle exhibiting motion due to the continuous molecular – here, the – agitation. We can thus also introduce an effective parameter for vibration-fluidized matter and discuss its properties. In particular, we observe that the temperature defined is inhomogeneous and anisotropic, contrary to usual liquids. An interesting issue is also studied carefully: when the damping becomes large (for when the imposed vibrations are lower, or when the oscillator is deeply immersed), a stiffening phenomenon is observed, in which the apparent elastic constant increases linearly with the friction. An elementary rheological model suggests that this may be caused by the appearance of a force chains fretwork resisting the probe rotation. Various materials are analyzed with this met hod. The grain mass seems to be an important parameter, as well as the grain surface state. Experiments in which the grains are etched with acid in order to modify the surface roughness are also discussed. While we know what happens to a liquid when its temperature is decreased one can wonder what happens to a system when the perturbations become critically low. By using vibrations of weak intensity (with accelerations below that of gravity), we study how the system reaches a frozen static configuration when the perturbation intensity is decreased. The observed diffusive noise appears to approach the final jammed state according to the Vogel-Fulcher-Tammann law, that also describes the temperature dependence of viscosity or diffusivity in supercooled liquids, thus showing strong analogies with the vitrification process. Here, the parameter playing the role of temperature in the equations is found to depend only on the vibration amplitude. Finally, we briefly discuss how a small modification of the experimental setup may allow to create a Brownian motor generating useful work out of the random agitation of the grains.

SuperArrhenius character of supercooled glass-forming liquids

Equilibrium molecular dynamics methods were used in conjunction with linear response theory and a recently published potential-energy surface [J. Phys. Chem. B 103, 3570 (1999)] to compute the liquid shear viscosity and self-diffusion coefficient of the high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) over the temperature domain 550–800 K. Predicted values of the shear viscosity range from 0.0055 Pa *s at the highest temperature studied up to 0.45 Pa *s for temperatures near the melting point. The results, which represent the first publication of the shear viscosity of HMX, are found to be described by an Arrhenius rate law over the entire temperature domain studied. The apparent activation energy for the shear viscosity is found to scale with the heat of vaporization in a fashion consistent with those for a wide variety of simple nonmetallic liquids. The self-diffusion coefficient, which requires significantly shorter trajectories than the shear viscosity for accurate calculation, also exhibits an Arrhenius temperature dependence over the simulated temperature domain. This has potentially important implications for predictions of the shear viscosity at temperatures near the melting point.

The shear viscosity of a finite two-dimensional (2D) Yukawa liquid is calculated using non-equilibrium Langevin simulations. Two counter-propagating shear forces are used to push the particles and cause shear-induced melting of the cluster. The melting temperature of the 2D cluster system is used to derive the effective coupling parameter Γ * of this finite system and allows us to investigate the relationship between shear viscosity and system properties Γ * and κ. The simulation data shows that the value of the shear viscosity rises for coupling parameters Γ * > 20 and follows a simple universal scaling for appropriate normalization. It is further found that the Green–Kubo relation is applicable to determine viscosity in finite non-equilibrium systems with Γ * < 80.

We analyze the behavior of supercooled fluids under shear both theoretically and numerically. Theoretically, we generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the set of generalized fluctuating hydrodynamic equations with a convection term. A nonlinear integrodifferential equation for the intermediate scattering function is constructed. This theory is applied to a two-dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and the shear viscosity is analyzed. We have also performed extensive numerical simulations of a two-dimensional binary liquid with soft-core interactions near, but above, the glass transition temperature. Both theoretical and numerical results show the following. (i) A drastic reduction of the structural relaxation time and the shear viscosity due to shear. Both the structural relaxation time and the viscosity decrease as gamma(-nu) with an exponent nu< or =1, where gamma; is the shear rate. (ii) Almost isotropic dynamics regardless of the strength of the anisotropic shear flow.

Discusses critically the existing mean-field theories of the metastable supercooled state of a classical liquid. The authors' criticism is based on a wealth of experimental and computer simulation data which seem to be in disagreement with the mean-field theories. They propose an essentially non-mean-field model, which links the properties of the supercooled liquid to those of Ds is also discussed in view of its relation to the shear viscosity and the rate of nucleation of the new crystalline phase. In all the considerations the static characteristics of the liquid-for example, the radial correlation function-are perfectly regular and do not exhibit any singularity near the limit of stability.

Solid plasticity and supercooled-liquid thermoplasticity of Zr–Cu-enriched hypoeutectic Zr–Cu–Ni–Al cast glassy alloys