Role of unstable directions in the equilibrium and aging dynamics of supercooled liquids

Physical Review Letters

Volumn 85, Issue 7, 2000, Pages 1464-1467

  Donati, Claudio ^a   Sciortino, Francesco ^a   Tartaglia, Piero ^a  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY MIXTURES; COMPUTATIONAL METHODS; LIQUIDS; PHASE EQUILIBRIA; POTENTIAL ENERGY; SUPERCOOLING; SURFACES; THERMAL EFFECTS;

AGING DYNAMICS; LENNARD JONES ATOM; POTENTIAL ENERGY SURFACE; THERMAL EQUILIBRIUM;

MOLECULAR DYNAMICS;

EID: 0034248192     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.1464     Document Type: Article

References (38)

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34. Motion along a straight direction in configuration space will always be associated with a fast rise of the energy profile, since every direction will always describe pairs of atoms moving close enough to probe the repulsive part of the pair potentials [11]. In systems with steep repulsive potentials, such an unphysical rise of the potential energy profile along the straight eigenmode direction sets in very early. In other words, the eigenvector direction changes very rapidly as the system moves in configuration space and very soon the energy profile differs from the profile evaluated along the straight eigenvector approximation. The major effects of such an artificial rise in energy are [11] (i) the transformation of dw direction in sh directions and (ii) the arbitrary location of the two minima along the dw direction and the extremely low value of the one-dimensional barriers along the dw. In particular, effect (i) sets in when, in the studied direction, the system is located far from the saddle and effect (ii) sets in when the system is located close to the saddle point [T. Keyes and W.-X. Li, J. Chem. Phys. 111, 5503 (1999)]. Notwithstanding these potential pitfalls in the classification procedure, the classification helps in understanding the dynamical changes taking place in the liquid as a function of T and ρ. Indeed the only saddles which are relevant for the dynamical behavior of the system are the ones which are explored by the system, i.e., the ones located in a potential energy range V ± ΔV - where V is the average potential energy of the system and ΔV is a measure of the potential energy fluctuations. The accessed saddles are included in the type (ii) classification in the above list. As a result, the classification performed along straight directions retains its validity, even if no physical meaning can be attributed to the calculated one-dimensional energy profile. Of course, it would be more appropriate to recalculate the eigenvectors at each step and follow the curved one-dimensional energy profile. Such a procedure could still suffer from the frequent mode-crossing events which are known to characterize the liquid dynamics [M. Buchener and T. Dorfmüller, J. Mol. Liq. 65/66, 157 (1995)].
35. Motion along a straight direction in configuration space will always be associated with a fast rise of the energy profile, since every direction will always describe pairs of atoms moving close enough to probe the repulsive part of the pair potentials [11]. In systems with steep repulsive potentials, such an unphysical rise of the potential energy profile along the straight eigenmode direction sets in very early. In other words, the eigenvector direction changes very rapidly as the system moves in configuration space and very soon the energy profile differs from the profile evaluated along the straight eigenvector approximation. The major effects of such an artificial rise in energy are [11] (i) the transformation of dw direction in sh directions and (ii) the arbitrary location of the two minima along the dw direction and the extremely low value of the one-dimensional barriers along the dw. In particular, effect (i) sets in when, in the studied direction, the system is located far from the saddle and effect (ii) sets in when the system is located close to the saddle point [T. Keyes and W.-X. Li, J. Chem. Phys. 111, 5503 (1999)]. Notwithstanding these potential pitfalls in the classification procedure, the classification helps in understanding the dynamical changes taking place in the liquid as a function of T and ρ. Indeed the only saddles which are relevant for the dynamical behavior of the system are the ones which are explored by the system, i.e., the ones located in a potential energy range V ± ΔV - where V is the average potential energy of the system and ΔV is a measure of the potential energy fluctuations. The accessed saddles are included in the type (ii) classification in the above list. As a result, the classification performed along straight directions retains its validity, even if no physical meaning can be attributed to the calculated one-dimensional energy profile. Of course, it would be more appropriate to recalculate the eigenvectors at each step and follow the curved one-dimensional energy profile. Such a procedure could still suffer from the frequent mode-crossing events which are known to characterize the liquid dynamics [M. Buchener and T. Dorfmüller, J. Mol. Liq. 65/66, 157 (1995)].
36. Such an estimate of the free exploration to activated dynamics crossover temperature could be biased by the arbitrary choice of the IS configuration (the T = 0.446 configurations).
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