Incollection,
Locally preferred structure in model liquids
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
An apparent paradox stands at the heart of the glass transition
of liquids and polymers: on cooling the system in a narrow
temperature range, the dramatic increase of relaxation times
and viscosity has no counterpart in a significant variation of
static two-body correlation functions. This is at odds with
general arguments which predict an increasing length scale
associated with an increasing time scale. Recent computer
simulations and experiments have focused on dynamic
heterogeneities: the dynamics of particles are spatially
correlated and it is possible to identify a dynamic
length scale associated with such a correlation
L. Berthier et al., Science 310, 1797 (2005).
It is now time to ask if the above dynamic length scale is
associated with an underlying increasing static length scale.
This task obviously calls for a more in-depth comprehension of
structural correlations in supercooled liquids and glasses.
A large body of experimental and numerical work on bulk systems
demonstrates the tendency to form local icosahedral order on
lowering temperature. Two facts are of great interest in this
context. On one hand, the competition between extension of a
local order and global constraints---associated with periodic
tiling of the space---gives rise to geometrical frustration,
which can be connected to the dynamic slowing down in the
supercooled liquid state. On the other hand, the nature of local
icosahedral order in bulk liquids, well understood in the case of
isolated clusters of particles
F.~C. Frank, Proc. Roy. Soc. A 215, 43 (1952),
is still unclear.
Here we describe a general method to predict the locally
preferred structure in bulk model atomic liquids S. Mossa and
G. Tarjus, Journal of Non-Crystalline Solids 352, 4847 (2006).
The latter is determined numerically as the ground state of the
effective energy surface of small clusters of particles embedded
in a liquid-like mean field environment. The structure of the
outside liquid is therefore only characterized by the bulk pair
distribution function (known from computer simulations). With this
approach we minimize the surface effects present in isolated
clusters but avoid introducing full blown geometrical frustration,
by neglecting the detailed many body structure of the environment.
We also describe how to deal with molecular systems.
