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 over the range T(A) > or =T > or =T(c). Molecular dynamics simulations with a time dependent mapping to the associated local minimum or inherent structure (IS) are performed on unit-density Lennard-Jones. 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(t), the distribution of IS waiting times. The configuration space is treated as a composite of the contributions of cooperative local regions, and a method is given to obtain the physically meaningful g(loc)(t) and mean waiting time tau(loc) from g(t). An understanding of the crossover is obtained in terms of r2(is)(t) and tau(loc). At intermediate T, r2(is)(t) possesses an interval of linear t dependence allowing calculation of an intrabasin diffusion constant D(is). Near T(c), where intrabasin diffusion is well established for t<tau(loc), diffusion is intrabasin dominated with D=D(is); D may be calculated within a basin. Below T(c), tau(loc) exceeds the time tau(pl) needed for the system to explore the basin, indicating the action of barriers at the border; tau(loc)=tau(pl) is a criterion for transition to activated hopping. Intrabasin diffusion provides a means of confinement not involving barriers and plays a key role in the dynamics above T(c). The distinction is discussed between motion among the IS (IS dynamics) below T(c) and saddle or border dynamics above T(c), where the system is always close to one of the saddle barriers connecting the basins and IS boundaries are closely spaced and easily crossed. A border index is introduced based upon the relation of R2(t) to the conventional MSD, and shown to vanish at T approximately T(c). It is proposed that intrabasin diffusion is a manifestation of saddle dynamics.

Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids

Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.

Inherent-structure dynamics and diffusion in liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima (inherent structures, IS) of the N-body potential-energy surface or landscape, and their correlations. The formulas are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors D0, greatly exceeds D for the highest T, but merges with simulation at reduced T approximately 0.50, close to the estimated mode-coupling temperature T(c). Since uncorrelated IST's are associated with a hopping mechanism, the condition D approximately D0 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's.

Entropy, dynamics, and instantaneous normal modes in a random energy model

It is shown that the fraction f(u) of imaginary-frequency instantaneous normal modes (INM) may be defined and calculated in a random energy model (REM) of liquids. The configurational entropy S(c) and the averaged hopping rate among the states, R, are also obtained and related to f(u) with the results R approximately f(u) and S(c)=a+b ln(f(u)). The proportionality between R and f(u) is the basis of existing INM theories of diffusion, so the REM further confirms their validity. A link to S(c) opens new avenues for introducing INM into dynamical theories. Liquid states are usually defined by assigning a configuration to the minimum to which it will drain, but the REM naturally treats saddle barriers on the same footing as minima, which may be a better mapping of the continuum of configurations to discrete states. Requirements for a detailed REM description of liquids are discussed.

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.