Isotropic-nematic phase transition computer simulations

The Onsager theory, or second virial expansion, is very successful in predicting the qualitative behavior of the isotropic-nematic phase transition of hard rods. H owever, it is an exact theory in the limit ofI/D—>oo. Straley has estimated that, for L/D < 20, the contribution of the third virial coefficient to the free energy in the nematic phase should be at least comparable to that of the second virial coefficient [22]. For more concentrated solutions, an alternative approach such as the Flory lattice model [3, 5] is required. The full phase diagram of rod-like colloidal systems has been obtained in computer simulations [23, 24]. The effects of polydispersity of rods [19, 25] and charged rods [10] are also important in the phase transitions. The comparison between Onsager theory and experimental results has been summarized by Vroege and Lekkerkerker [26]. 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

A third motivation is that with present day computers even for medium chain length N of the polymers it is very difficult to study collective long-wavelength phenomena (associated with phase transitions, phase eoexis-tence, etc.), since huge linear dimensions L of the simulation box and a huge number Nm of (effective) monomers in the simulation are required. For example, for a finite size scaling [11] study of the nematic isotropic phase transition in a model for a melt of semiflexible polymers a lattiee with L = 130 was used, and with the bond fluctuation model [12,13] at volume fraction of about occupied sites this choice allowed for 6865 chains... 

To avoid phase separation between the two moieties, a vast effort was devoted towards the synthesis of chemically linked disc-rod molecules [25-27], Beyond that, mixtures of prolate and oblate mesogens have stimulated theorists to perform intensive computer simulations. Simulations and molecular field theories predict the biaxial nematic phase to occur around the minimum of the transition temperature T from the nematic to the isotropic phase [22]. Furthermore, a strong decrease of the transition enthalpy is expected upon approaching the tricritical point. 

---