126 research outputs found
Bulk and shear relaxation in glasses and highly viscous liquids
The ratio between the couplings of a relaxational process to compression and
shear, respectively, is calculated in the Eshelby picture of structural
rearrangements within a surrounding elastic matrix, assuming a constant density
of stable structures in distortion space. The result is compared to
experimental data for the low-temperature tunneling states in glasses and to
Prigogine-Defay data at the glass transition from the literature.Comment: 6 pages, 2 figures, 53 references; version after understanding the
Prigogine-Defay ratio at the glass transition in the accompanying paper
arXiv:1203.3555 [cond-mat.dis-nn
General features of the energy landscape in Lennard-Jones like model liquids
Features of the energy landscape sampled by supercooled liquids are
numerically analyzed for several Lennard-Jones like model systems. The
properties of quasisaddles (minima of the square gradient of potential energy
W=|grad V|^2), are shown to have a direct relationship with the dynamical
behavior, confirming that the quasisaddle order extrapolates to zero at the
mode-coupling temperature T_MCT. The same result is obtained either analyzing
all the minima of W or the saddles (absolute minima of W), supporting the
conjectured similarity between quasisaddles and saddles, as far as the
temperature dependence of the properties influencing the slow dynamics is
concerned. We find evidence of universality in the shape of the landscape:
plots for different systems superimpose into master curves, once energies and
temperatures are scaled by T_MCT. This allows to establish a quantitative
relationship between T_MCT and potential energy barriers for LJ-like systems,
and suggests a possible generalization to different model liquids.Comment: 8 pages, 5 figure
Non-equilibrium thermodynamics. IV: Generalization of Maxwell, Claussius-Clapeyron and Response Functions Relations, and the Prigogine-Defay Ratio for Systems in Internal Equilibrium
We follow the consequences of internal equilibrium in non-equilibrium systems
that has been introduced recently [Phys. Rev. E 81, 051130 (2010)] to obtain
the generalization of Maxwell's relation and the Clausius-Clapeyron relation
that are normally given for equilibrium systems. The use of Jacobians allow for
a more compact way to address the generalized Maxwell relations; the latter are
available for any number of internal variables. The Clausius-Clapeyron relation
in the subspace of observables show not only the non-equilibrium modification
but also the modification due to internal variables that play a dominant role
in glasses. Real systems do not directly turn into glasses (GL) that are frozen
structures from the supercooled liquid state L; there is an intermediate state
(gL) where the internal variables are not frozen. Thus, there is no single
glass transition. A system possess several kinds of glass transitions, some
conventional (L \rightarrow gL; gL\rightarrow GL) in which the state change
continuously and the transition mimics a continuous or second order transition,
and some apparent (L\rightarrow gL; L\rightarrow GL) in which the free energies
are discontinuous so that the transition appears as a zeroth order transition,
as discussed in the text. We evaluate the Prigogine-Defay ratio {\Pi} in the
subspace of the observables at these transitions. We find that it is normally
different from 1, except at the conventional transition L\rightarrow gL, where
{\Pi}=1 regardless of the number of internal variables.Comment: 42 pages, 3 figures, citations correcte
Weak links between fast mobility and local structure in molecular and atomic liquids
We investigate by molecular-dynamics simulations, the fast mobility-the rattling amplitude of the particles temporarily trapped by the cage of the neighbors-in mildly supercooled states of dense molecular (linear trimers) and atomic (binary mixtures) liquids. The mixture particles interact by the Lennard-Jones potential. The non-bonded particles of the molecular system are coupled by the more general Mie potential with variable repulsive and attractive exponents in a range which is a characteristic of small n-alkanes and n-alcohols. Possible links between the fast mobility and the geometry of the cage (size and shape) are searched. The correlations on a per-particle basis are rather weak. Instead, if one groups either the particles in fast-mobility subsets or the cages in geometric subsets, the increase of the fast mobility with both the size and the asphericity of the cage is revealed. The observed correlations are weak and differ in states with equal relaxation time. Local forces between a tagged particle and the first-neighbour shell do not correlate with the fast mobility in the molecular liquid. It is concluded that the cage geometry alone is unable to provide a microscopic interpretation of the known, universal link between the fast mobility and the slow structural relaxation. We suggest that the particle fast dynamics is affected by regions beyond the first neighbours, thus supporting the presence of collective, extended fast modes
Cage effect in supercooled molecular liquids: Local anisotropies and collective solid-like response
Both local geometry and collective extended excitations drive the moves of a particle in the cage of its neighbours in dense liquids. The strength of their influence is investigated by the molecular dynamics simulations of a supercooled liquid of fully flexible trimers with semirigid or rigid bonds. The rattling in the cage is investigated on different length scales. First, the rattling anisotropy due to local order is characterized by two order parameters sensing the monomers succeeding or failing to escape from the cage. Then the collective response of the surroundings excited by the monomer-monomer collisions is considered. The collective response is initially restricted to the nearest neighbours of the colliding particle by a Voronoi analysis revealing elastic contributions. Then the long-range excitation of the farthest neighbours is scrutinised by searching spatially extended correlations between the simultaneously fast displacements of the caged particle and the surroundings. It is found that the longitudinal component has stronger spatial modulation than the transverse one with a wavelength of about one particle diameter, in close resemblance with experimental findings on colloids. It is concluded that the cage rattling is largely affected by solid-like extended modes
Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses
Starting from the second law of thermodynamics applied to an isolated system
consisting of the system surrounded by an extremely large medium, we formulate
a general non-equilibrium thermodynamic description of the system when it is
out of equilibrium. We then apply it to study the structural relaxation in
glasses and establish the phenomenology behind the concept of the fictive
temperature and of the empirical Tool-Narayanaswamy equation on firmer
theoretical foundation.Comment: 20 pages, 1 figur
Feasibility of single-order parameter description of equilibrium viscous liquid dynamics
Molecular dynamics results for the dynamic Prigogine-Defay ratio are
presented for two glass-forming liquids, thus evaluating the experimentally
relevant quantity for testing whether metastable-equilibrium liquid dynamics to
a good approximation are described by a single parameter. For the Kob-Andersen
binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid
a single-parameter description works quite well. This is confirmed by
time-domain results where it is found that energy and pressure fluctuations are
strongly correlated on the alpha-time scale in the NVT ensemble; in the NpT
ensemble energy and volume fluctuations similarly correlate strongly.Comment: Phys. Rev. E, in pres
Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems
On approaching the glass transition, the microscopic kinetic unit spends
increasing time rattling in the cage of the first neighbours whereas its
average escape time, the structural relaxation time , increases
from a few picoseconds up to thousands of seconds. A thorough study of the
correlation between and the rattling amplitude, expressed by the
Debye-Waller factor (DW), was carried out. Molecular-dynamics (MD) simulations
of both a model polymer system and a binary mixture were performed by varying
the temperature, the density , the potential and the polymer length to
consider the structural relaxation as well as both the rotational and the
translation diffusion. The simulations evidence the scaling between the
and the Debye-Waller factor. An analytic model of the master
curve is developed in terms of two characteristic length scales pertaining to
the distance to be covered by the kinetic unit to reach a transition state. The
model does not imply divergences. The comparison with the
experiments supports the numerical evidence over a range of relaxation times as
wide as about eighteen orders of magnitude. A comparison with other scaling and
correlation procedures is presented. The study suggests that the equilibrium
and the moderately supercooled states of the glassformers possess key
information on the huge slowing-down of their relaxation close to the glass
transition. The latter, according to the present simulations, exhibits features
consistent with the Lindemann melting criterion and the free-volume model.Comment: 8 pages, 11 figure
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