Simulation of liquid crystals
Computer simulation has become a well-used method for the study of liquid crystalline systems. Current state-of-the-art includes work right across the time and length scales encompassing lattice models, anisotropic single site potentials (both hard and soft), multi-site coarse-grained models and atomistic modelling. In each area, the first generation of challenges has been met; and it is now possible to
see many simple liquid crystal phase (nematics, smectics) in the computer (i.e. produce effective models that capture the essential interactions),
make predictions for key materials properties such as order parameters, nematic elastic constants and rotational viscosities,
calculate complete phase diagrams for simple models.
However, recently a new set of challenges have arisen, which demand new models, and new simulation techniques. These include the following areas
simulation of novel phases (cubatics, bicontinuous cubic, banana phases, blue phases) and the simulation of unusual molecular architectures e.g. (bowlic, multipedal mesogens)
the study of chiral interactions and the formation of chiral structures and phases from achiral molecules;
simulation of biaxial nematics - the role played by dipole and quadrupole interactions in the stabilization of bent core mesogens, including the importance (or lack of) of ferroelectric cybotactic domain formation in bent core species
simulation of chromonics liquid crystals (the role of enthalpic vs. entropic driving forces in aggregation)
interaction of mesogens with surfaces and formation of defects
simulation of macromolecular liquid crystal species
developments in atomistic simulations - use of polarizable potentials
simulation of liquid crystals across the length and time scales (coarse-graining)
extraction of direct correlation functions in calamitic nematic, discotic nematic, smectic-A and columnar phases for comparison with theory
-linking of coarse-grained simulation to continuum models and theory.
These simulation challenges can be summarized as involving three key tasks, (i) the simulation of new phases through the development of new models, (ii) the development/application of new simulation methods to liquid crystalline systems, (iii) dramatically improving the link between simulation and theory (see below).
The equilibrium theory of isotropic fluids is fairly mature. One can use virial expansions, integral equation theory and perturbation methods to provide good predictions of the structure and thermodynamic properties of homogeneous systems, whilst the advent of good density functional theories, such as provided by fundamental measure theory, has allowed an excellent understanding of inhomogeneous situations.
On the dynamical front, Enskog theory has proved successful in predicting transport properties of gases up to moderate densities and mode-coupling approaches have now allowed one to study dense fluids and made striking predictions about the glass transition.
The theory of liquid crystals is much less advanced. To date, most equilibrium theory is based on a scaled second virial approach, which is very unsophisticated compared to the methods commonly applied to isotropic systems. Very few systems are amenable to fundamental measure theory (infinitely thin hard plates being a rare example) so little is known at a molecular scale about inhomogeneous systems.
As for dynamics, Enskog theory has been applied to nematics but, to our knowledge, no high density techniques, such as mode-coupling theory, have been applied. For more ordered liquid crystalline phases, such as smectics or columnar phases, there is virtually no molecular-based theoretical accounts.
It is possible to outline a series of outstanding problems:
Is it possible to apply liquid state integral equation theory and/or high level virial expansions to liquid crystalline phases?
What are the prospects of extending methodologies, such as SAFT, to provide high quality predictions of the behaviour of real liquid crystalline systems?
What are the prospects for developing fundamental measure theories applicable to inhomogeneous liquid crystals?
How can one apply Enskog/mode-coupling theory to liquid crystalline phases?
How might computer simulation best be used to advance this field?
In brief, the theory challenges can be summarized as involving two key tasks, (i) the development of higher levels theories for liquid crystalline systems, and (ii) and dramatically improving the link between simulation and theory.