A recently proposed molecular-field approach, based on the formulation of an approximate, analytical orientational partition function to describe the thermodynamic properties of D2h thermotropic biaxial nematics governed by fully attractive orientational interactions (G. Celebre, J. Mol. Liq. 209 (2015) 104–114), has now been extended to treat also the partially repulsive regime of orientational interactions. This has been made by the implementation of a Minimax algorithm to locate the stationary, stable points of the Helmholtz Free Energy for the studied systems. The developed tool paved the way to new interesting (and intriguing) scenarios, allowing us to virtually explore a wide range of cases, where the features determining the existence of possible stable biaxial nematic mesophaseswere basically dictated by the geometric parameters characterizing the single D2h mesogenic particles. Many cases have been revisited to validate the method (starting from the pioneering work of Straley), and also new simulated and experimental (goethite) cases have been addressed. Particular attention has been paid to the physical meaning of the two biaxiality parameters (called γ and λ), weighting the biaxial extra-terms in the molecular-field expression of the mean-torque potential. Moreover, an explicit mathematical relation has been found between the parameter λ, ruling the dominant biaxial interaction, and the ratio of the biaxial-to-uniaxial and uniaxial-to-isotropic transition temperatures, whereas a substantial uncorrelation amongst the transition temperatures TNB-NU and the other biaxiality parameter, γ, has been verified.
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