Statistical thermodynamics of thermotropic biaxial nematic liquid crystals: An effective, molecular-field based theoretical description by means of a closed approximate form of the orientational partition function

In this work, we show that the use of a molecular-field approach and of a closed, effective (even though approximate) form of the orientational partition function, leads to trustworthy predictions of order parameters and other important thermodynamic functions (as heat capacity, orientational internal energy and entropy) of real and/or virtual biaxial nematic mesophases. As a matter of fact, when the partition function Z is explicitly known, all about the thermodynamics of the studied systems becomes in principle accessible, since the thermodynamic functions can be directly calculated through the usual formulas provided by the statistical mechanics. We were successful in obtaining such an approximate expression for Z that works well and allows for almost instantaneous, reliable simulations (it is worthwhile to emphasize that, being available in the present case an analytical expression of Z, the derivatives occurring in the statistical mechanics formulas can be calculated analytically and instantaneously). Several examples of the performances of our approach are presented where, besides the second-rank order parameters, also heat capacities and changes in entropy and internal energy are quantitatively assessed, often for the first time, for the treated cases; moreover, an evaluation of some of the most important fourth-rank order parameters for the treated phases has been carried out. The results are good and our treatment proves to be suitable and promising also for future studies.