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Register a new userThe Potential Energy Landscape and Mechanisms of Diffusion in Liquids
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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.
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We numerically study the relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmonic value at low temperatures. We demonstrate that this apparent evolution is controlled by a temperature-dependent population of localised excitations. Our work unifies several recent lines of studies aiming at a detailed characterization of the complex potential energy landscape of glass-formers.
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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.
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.
Configurational states that are to be associated, according to Goldstein, with the basins in the potential energy landscape cannot be characterized by any particular basin identifier such as the basin minima, the lowest barrier, the most probable energy barrier, etc. since the basin free energy turns out to be independent of the energies of these identifiers. Thus, our analysis utilizes basin free energies to characterize configurational states. When the basin identifier energies are monotonic, we can express the equilibrium basin free energy as a function of an equilibrium basin identifier energy, as we explain, but it is not necessarily unique.
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