The Potential Energy Landscape and Mechanisms of Diffusion in Liquids

The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics. Molecular dynamics simulations with a time dependent mapping to the associated local mininum or inherent structure (IS) are performed on unit-density Lennard-Jones (LJ). New dynamical quantities introduced include r2_{is}(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g_{loc}(t) the mean waiting time in a cooperative region. At intermediate T, r2_{is}(t) posesses an interval of linear t-dependence allowing calculation of an intrabasin diffusion constant D_{is}. Near T_{c} diffusion is intrabasin dominated with D = D_{is}. Below T_{c} the local waiting time tau_{loc} exceeds the time, tau_{pl}, needed for the system to explore the basin, indicating the action of barriers. The distinction between motion among the IS below T_{c} and saddle, or border dynamics above T_{c} is discussed.Comment: submitted to pr

Potential energy landscape-based extended van der Waals equation

The inherent structures ({\it IS}) are the local minima of the potential energy surface or landscape, $U({\bf r})$, of an {\it N} atom system. Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$ coefficients, holds on the high-temperature plateau of the averaged {\it IS} energy. However, an additional ``landscape'' contribution to the pressure is found at lower $T$. The resulting extended {\it vdW} equation, unlike the original, is capable of yielding a water-like density anomaly, flat isotherms in the coexistence region {\it vs} {\it vdW} loops, and several other desirable features. The plateau energy, the width of the distribution of {\it IS}, and the ``top of the landscape'' temperature are simulated over a broad reduced density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be useful at high density; it nevertheless reproduces the known values of $a$ and $b$ at the critical point

Inherent-Structure Dynamics and Diffusion in Liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima of the potential (inherent structure, IS) and their correlations. The formulae are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST are associated with a hopping mechanism, the condition D ~ D_{0} provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST.Comment: submitted to PR

Anharmonic Potentials in Supercooled Liquids: The Soft-Potential Model

Instantaneous normal modes (INM) are the harmonic approximation to liquid dynamics. This is an extension of the phonon description of lattice dynamics, in which case Bloch\u27s theorem shows that all modes are extended. Long-range order is destroyed in liquids and glasses, and the INM spectrum has contributions from both extended and localized modes. We use the soft-potential mode to describe localized modes. This model is a high-temperature extension of the standard two-level-system model for glasses. The equilibrium position of any atom in the liquid has only temporary character, and relaxation processes in the liquid are associated with particles hopping over potential energy barriers. Barrier tops have negative curvature so that an INM spectrum has an imaginary frequency (unstable) lobe in addition to the conventional stable mode contributions; conversely the unstable modes carry information about diffusion. We derive analytic expressions for the frequency and temperature dependence of the unstable lobe that are in agreement with results from computer simulations. Self-diffusion of particles in the liquid is governed by the fraction of unstable modes originating from double-well potentials. For the diffusion constant, we find a crossover behavior from Arrhenius temperature dependence to Zwanzig-Bässler dependence. We find an explicit expression for the distribution of barrier heights. In agreement with Stillinger\u27s inherent structure approach to glass-forming liquids, this distribution is uniform, or Gaussian, for high and low temperatures, respectively

Comment on “Direct Observation of Stretched-Exponential Relaxation in Low-Temperature Lennard-Jones Systems Using the Cage Correlation Function”

A Comment on the Letter by Eran Rabani, J. Daniel Gezelter, and D. J. Berne, Phys. Rev. Lett. 82, 3649 (1999). The authors of the Letter offer a Reply

Comment on “Direct Observation of Stretched-Exponential Relaxation in Low-Temperature Lennard-Jones Systems Using the Cage Correlation Function”

A Comment on the Letter by Eran Rabani, J. Daniel Gezelter, and D. J. Berne, Phys. Rev. Lett. 82, 3649 (1999). The authors of the Letter offer a Reply

Anharmonic Potentials in Supercooled Liquids: The Soft-Potential Model

Instantaneous normal modes (INM) are the harmonic approximation to liquid dynamics. This is an extension of the phonon description of lattice dynamics, in which case Bloch\u27s theorem shows that all modes are extended. Long-range order is destroyed in liquids and glasses, and the INM spectrum has contributions from both extended and localized modes. We use the soft-potential mode to describe localized modes. This model is a high-temperature extension of the standard two-level-system model for glasses. The equilibrium position of any atom in the liquid has only temporary character, and relaxation processes in the liquid are associated with particles hopping over potential energy barriers. Barrier tops have negative curvature so that an INM spectrum has an imaginary frequency (unstable) lobe in addition to the conventional stable mode contributions; conversely the unstable modes carry information about diffusion. We derive analytic expressions for the frequency and temperature dependence of the unstable lobe that are in agreement with results from computer simulations. Self-diffusion of particles in the liquid is governed by the fraction of unstable modes originating from double-well potentials. For the diffusion constant, we find a crossover behavior from Arrhenius temperature dependence to Zwanzig-Bässler dependence. We find an explicit expression for the distribution of barrier heights. In agreement with Stillinger\u27s inherent structure approach to glass-forming liquids, this distribution is uniform, or Gaussian, for high and low temperatures, respectively

Configurational Entropy and Collective Modes in Normal and Supercooled Liquids

Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 K. The soft-potential model consists of a collection of double-well potentials that are distorted by a linear term representing local stress in the liquid. Double-well modes contribute to the configurational entropy of the system. Based on the Adam-Gibbs theory of entropically driven relaxation in liquids, we show that the presence of stress drives the transition from Arrhenius to Zwanzig-Bässler temperature dependence of relaxation times. At some temperature below the glass transition, the energy scale is dominated by local stress, and soft modes are described by single wells only. It follows that the configurational entropy vanishes, in agreement with the “Kauzmann paradox.” We discuss a possible connection between soft vibrational modes and ultrafast processes that dominate liquid dynamics near the glass transition

Configurational Entropy and Collective Modes in Normal and Supercooled Liquids

Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 K. The soft-potential model consists of a collection of double-well potentials that are distorted by a linear term representing local stress in the liquid. Double-well modes contribute to the configurational entropy of the system. Based on the Adam-Gibbs theory of entropically driven relaxation in liquids, we show that the presence of stress drives the transition from Arrhenius to Zwanzig-Bässler temperature dependence of relaxation times. At some temperature below the glass transition, the energy scale is dominated by local stress, and soft modes are described by single wells only. It follows that the configurational entropy vanishes, in agreement with the “Kauzmann paradox.” We discuss a possible connection between soft vibrational modes and ultrafast processes that dominate liquid dynamics near the glass transition

Noise reduction in a Mach 5 wind tunnel with a rectangular rod-wall sound shield

A rod wall sound shield was tested over a range of Reynolds numbers of 0.5 x 10 to the 7th power to 8.0 x 10 to the 7th power per meter. The model consisted of a rectangular array of longitudinal rods with boundary-layer suction through gaps between the rods. Suitable measurement techniques were used to determine properties of the flow and acoustic disturbance in the shield and transition in the rod boundary layers. Measurements indicated that for a Reynolds number of 1.5 x 10 to the 9th power the noise in the shielded region was significantly reduced, but only when the flow is mostly laminar on the rods. Actual nozzle input noise measured on the nozzle centerline before reflection at the shield walls was attenuated only slightly even when the rod boundary layer were laminar. At a lower Reynolds number, nozzle input noise at noise levels in the shield were still too high for application to a quiet tunnel. At Reynolds numbers above 2.0 x 10 the the 7th power per meter, measured noise levels were generally higher than nozzle input levels, probably due to transition in the rod boundary layers. The small attenuation of nozzle input noise at intermediate Reynolds numbers for laminar rod layers at the acoustic origins is apparently due to high frequencies of noise