59 research outputs found
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
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 of a detailed REM description of liquids are
discussed
Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
Molecular dynamics simulations are used to generate an ensemble of saddles of
the potential energy of a Lennard-Jones liquid. Classifying all extrema by
their potential energy u and number of unstable directions k, a well defined
relation k(u) is revealed. The degree of instability of typical stationary
points vanishes at a threshold potential energy, which lies above the energy of
the lowest glassy minima of the system. The energies of the inherent states, as
obtained by the Stillinger-Weber method, approach the threshold energy at a
temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio
Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids
We present a model for the motion of an average atom in a liquid or
supercooled liquid state and apply it to calculations of the velocity
autocorrelation function and diffusion coefficient . The model
trajectory consists of oscillations at a distribution of frequencies
characteristic of the normal modes of a single potential valley, interspersed
with position- and velocity-conserving transits to similar adjacent valleys.
The resulting predictions for and agree remarkably well with MD
simulations of Na at up to almost three times its melting temperature. Two
independent processes in the model relax velocity autocorrelations: (a)
dephasing due to the presence of many frequency components, which operates at
all temperatures but which produces no diffusion, and (b) the transit process,
which increases with increasing temperature and which produces diffusion.
Because the model provides a single-atom trajectory in real space and time,
including transits, it may be used to calculate all single-atom correlation
functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and
cond-mat/0002058 combined Minor changes made to coincide with published
versio
Saddles in the energy landscape probed by supercooled liquids
We numerically investigate the supercooled dynamics of two simple model
liquids exploiting the partition of the multi-dimension configuration space in
basins of attraction of the stationary points (inherent saddles) of the
potential energy surface. We find that the inherent saddles order and potential
energy are well defined functions of the temperature T. Moreover, decreasing T,
the saddle order vanishes at the same temperature (T_MCT) where the inverse
diffusivity appears to diverge as a power law. This allows a topological
interpretation of T_MCT: it marks the transition from a dynamics between basins
of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).Comment: 4 pages, 3 figures, to be published on PR
Instantaneous Normal Mode Analysis of Supercooled Water
We use the instantaneous normal mode approach to provide a description of the
local curvature of the potential energy surface of a model for water. We focus
on the region of the phase diagram in which the dynamics may be described by
the mode-coupling theory. We find, surprisingly, that the diffusion constant
depends mainly on the fraction of directions in configuration space connecting
different local minima, supporting the conjecture that the dynamics are
controlled by the geometric properties of configuration space. Furthermore, we
find an unexpected relation between the number of basins accessed in
equilibrium and the connectivity between them.Comment: 5 pages, 4 figure
A single saddle model for the beta-relaxation in supercooled liquids
We study the Langevin equation for a single harmonic saddle as an elementary
model for the beta-relaxation in supercooled liquids close to Tc. The input of
the theory is the spectrum of the eigenvalues of the dominant stationary points
at a given temperature. We prove in general the existence of a time-scale
t_eps, which is uniquely determined by the spectrum, but is not simply related
to the fraction of negative eigenvalues. The mean square displacement develops
a plateau of length t_eps, such that a two-step relaxation is obtained if t_eps
diverges at Tc. We analyze the specific case of a spectrum with bounded left
tail, and show that in this case the mean square displacement has a scaling
dependence on time identical to the beta-relaxation regime of Mode Coupling
Theory, with power law approach to the plateau and power law divergence of
t_eps at Tc.Comment: Revised versio
Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism
We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch of 85 drug-like molecules. Simulations of model enantiomers in a range of fluids such as - and -Ru(bpy)_3]Cl_2 in water and (R,R)- and (S,S)-atorvastatin in methanol support predictions made using molecular pitch values.A competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally-achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a non-zero molecular pitch
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