|
Résumé |
We are initially interested in the phase transitions that take place in
liquid crystals (LC), from a theoretical and numerical point of view.
Indeed, the results presented here are derived from Monte Carlo (MC)
simulations and analytical developments based on statistical physics and
condensed matter models. A strong analogy exists between spin systems
and LC. For example, the latter have phases where the molecules are all
aligned in the same direction (orientational order) comparable to spins
in ferromagnetic materials. Other phases, called cholesteric, are
characterized by a molecular arrangement similar to the helimagnetic
structures. But liquid crystals being an intermediate state of matter,
between the solid and the liquid phase, it is necessary to take into
account the motions of the molecules in the models and to adapt
accordingly the MC algorithm.
It led us to study the dynamics leading to the formation of the nematic
and smectic phases using a mobile Potts model.
We have also studied the formation of specific topological structure
like skyrmions that are structures observed (theorically) in LC. We use
a Dzyaloshinski-Moria (DM) interaction of strength D in addition to an
exchange interaction J to study properties of thin films.
|
