1,595 research outputs found
Complex free energy landscapes in biaxial nematics and role of repulsive interactions : A Wang - Landau study
General quadratic Hamiltonian models, describing interaction between crystal
molecules (typically with symmetry) take into account couplings
between their uniaxial and biaxial tensors. While the attractive contributions
arising from interactions between similar tensors of the participating
molecules provide for eventual condensation of the respective orders at
suitably low temperatures, the role of cross-coupling between unlike tensors is
not fully appreciated. Our recent study with an advanced Monte Carlo technique
(entropic sampling) showed clearly the increasing relevance of this cross term
in determining the phase diagram, contravening in some regions of model
parameter space, the predictions of mean field theory and standard Monte Carlo
simulation results. In this context, we investigated the phase diagrams and the
nature of the phases therein, on two trajectories in the parameter space: one
is a line in the interior region of biaxial stability believed to be
representative of the real systems, and the second is the extensively
investigated parabolic path resulting from the London dispersion approximation.
In both the cases, we find the destabilizing effect of increased cross-coupling
interactions, which invariably result in the formation of local biaxial
organizations inhomogeneously distributed. This manifests as a small, but
unmistakable, contribution of biaxial order in the uniaxial phase.The free
energy profiles computed in the present study as a function of the two dominant
order parameters indicate complex landscapes, reflecting the difficulties in
the ready realization of the biaxial phase in the laboratory.Comment: 23 pages, 12 figure
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
The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
Glass is a microscopically disordered, solid form of matter that results when
a fluid is cooled or compressed in such a fashion that it does not crystallise.
Almost all types of materials are capable of glass formation -- polymers, metal
alloys, and molten salts, to name a few. Given such diversity, organising
principles which systematise data concerning glass formation are invaluable.
One such principle is the classification of glass formers according to their
fragility\cite{fragility}. Fragility measures the rapidity with which a
liquid's properties such as viscosity change as the glassy state is approached.
Although the relationship between features of the energy landscape of a glass
former, its configurational entropy and fragility have been analysed previously
(e. g.,\cite{speedyfr}), an understanding of the origins of fragility in these
features is far from being well established. Results for a model liquid, whose
fragility depends on its bulk density, are presented in this letter. Analysis
of the relationship between fragility and quantitative measures of the energy
landscape (the complicated dependence of energy on configuration) reveal that
the fragility depends on changes in the vibrational properties of individual
energy basins, in addition to the total number of such basins present, and
their spread in energy. A thermodynamic expression for fragility is derived,
which is in quantitative agreement with {\it kinetic} fragilities obtained from
the liquid's diffusivity.Comment: 8 pages, 3 figure
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